ASCEND - User contributions [en]

User:Karthik0112358

2011-08-26T03:32:26Z

Karthik0112358:

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on adding the Mass Matrix functionality in Radau5 Solver for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## <strike style="color:green">Identifying all derivatives in an equation.</strike>
### <strike style="color:green">Finding the real values of derivative variables.</strike>
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## <strike style="color:green">Checking if the equation is linear with respect to the derivatives.</strike>
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### <strike style="color:green">If the derivative is inside a function.</strike>
### <strike style="color:green">If the coefficient of derivative contains a function.</strike>
### <strike style="color:green">Display corresponding error messages.</strike>
## <strike style="color:green">Evaluating the coefficient.</strike>
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
## Test with CUnit.
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''August 24'''

Example of mass matrix for DAE.

[[File:Demonstration of Mass Matrix for DAE.png]]

'''August 22'''

Added some screen shots:

[[File:Computing Coefficient.png]]

[[File:Derivative in index.png]]

[[File:Derivative raised to power.png]]

[[File:Non-Constant_coefficients.png]]

[[File:Check_in_Denominator.png]]

'''August 19'''

Wrote [http://ascend4.org/User:Karthik0112358/test_radau5 test_radau5.c]. Working on some issues.

'''August 15'''

* CUnit up and running.
* Code completed for writing mass matrix, adding comments and checking if I missed any cases. Only integrating to Radau5 left.

'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]
[[Category:ASCEND Contributors]]

== Mathematical note on my project ==

* RADAU5 is used to find numerical solutions for a stiff (or differential algebraic) system of first order ordinary differential equations.
* Problems must be of the form <math>\mathrm{M} \mathbf{y^{'}} = \mathbf{f} \left(\mathbf{t},\mathbf{y} \right)</math> with possibly singular matrix <math>\mathrm{M}</math>. Any solution to this equation is a function <math>\mathbf{u} \left(\mathbf{t} \right)</math> satisfying <math>\mathrm{M} \mathbf{u^{'}\left(\mathbf{t} \right)} = \mathbf{f} \left(\mathbf{t},\mathbf{u\left(\mathbf{t} \right)} \right)</math>.
* An implicit Runge-Kutta method of order 5 (Radau IIA) is implemented to solve problems.
* We refer to <math>\mathrm{M}</math> in <math>\mathrm{M} \mathbf{y^{'}} = \mathbf{f} \left(\mathbf{t},\mathbf{y} \right)</math>, as the Mass Matrix for the set of equations.
* If the dimension of the Mass Matrix, <math>\mathrm{M}</math> is ''a''x''b'' (i.e. ''a'' rows and ''b'' columns) then ''a'' is equal to the number of equations and ''b'' is equal to the dimension of vector space in which ''y(t)'' lies.
* Let ''m''ij be the element at the ''m''th row and ''n''th column of Mass Matrix <math>\mathrm{M}</math>. So ''m''ij are the coefficients of the derivative operators in the set of Differential Algebraic equations. Note that every ''m''ij has to be a constant.
* Initial data and the set of equations are accepted through ascend model files and the mass matrix is calculated (ONCE).
* The solutions are determined in a neighborhood of the initial input time by RADAU5 solver.

User:Karthik0112358

2011-08-25T15:40:48Z

Karthik0112358: /* Mathematical note on my project */

== Progress reports ==
'''August 24'''

Example of mass matrix for DAE.

[[File:Demonstration of Mass Matrix for DAE.png]]

'''August 22'''

Added some screen shots:

[[File:Computing Coefficient.png]]

[[File:Derivative in index.png]]

[[File:Derivative raised to power.png]]

[[File:Non-Constant_coefficients.png]]

[[File:Check_in_Denominator.png]]

'''August 19'''

Wrote [http://ascend4.org/User:Karthik0112358/test_radau5 test_radau5.c]. Working on some issues.

'''August 15'''

* CUnit up and running.
* Code completed for writing mass matrix, adding comments and checking if I missed any cases. Only integrating to Radau5 left.

'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]
[[Category:ASCEND Contributors]]

== Mathematical note on my project ==

* RADAU5 is used to find numerical solutions for a stiff (or differential algebraic) system of first order ordinary differential equations.
* Problems must be of the form <math>\mathrm{M} \mathbf{y^{'}} = \mathbf{f} \left(\mathbf{t},\mathbf{y} \right)</math> with possibly singular matrix <math>\mathrm{M}</math>. Any solution to this equation is a function <math>\mathbf{u} \left(\mathbf{t} \right)</math> satisfying <math>\mathrm{M} \mathbf{u^{'}\left(\mathbf{t} \right)} = \mathbf{f} \left(\mathbf{t},\mathbf{u\left(\mathbf{t} \right)} \right)</math>.
* An implicit Runge-Kutta method of order 5 (Radau IIA) is implemented to solve problems.
* We refer to <math>\mathrm{M}</math> in <math>\mathrm{M} \mathbf{y^{'}} = \mathbf{f} \left(\mathbf{t},\mathbf{y} \right)</math>, as the Mass Matrix for the set of equations.
* If the dimension of the Mass Matrix, <math>\mathrm{M}</math> is ''a''x''b'' (i.e. ''a'' rows and ''b'' columns) then ''a'' is equal to the number of equations and ''b'' is equal to the dimension of vector space in which ''y(t)'' lies.
* Let ''m''ij be the element at the ''m''th row and ''n''th column of Mass Matrix <math>\mathrm{M}</math>. So ''m''ij are the coefficients of the derivative operators in the set of Differential Algebraic equations. Note that every ''m''ij has to be a constant.
* Initial data and the set of equations are accepted through ascend model files and the mass matrix is calculated (ONCE).
* The solutions are determined in a neighborhood of the initial input time by RADAU5 solver.

User:Karthik0112358

2011-08-25T15:39:29Z

Karthik0112358: /* Progress reports */

== Progress reports ==
'''August 24'''

Example of mass matrix for DAE.

[[File:Demonstration of Mass Matrix for DAE.png]]

'''August 22'''

Added some screen shots:

[[File:Computing Coefficient.png]]

[[File:Derivative in index.png]]

[[File:Derivative raised to power.png]]

[[File:Non-Constant_coefficients.png]]

[[File:Check_in_Denominator.png]]

'''August 19'''

Wrote [http://ascend4.org/User:Karthik0112358/test_radau5 test_radau5.c]. Working on some issues.

'''August 15'''

* CUnit up and running.
* Code completed for writing mass matrix, adding comments and checking if I missed any cases. Only integrating to Radau5 left.

'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]
[[Category:ASCEND Contributors]]

== Mathematical note on my project ==

* RADAU5 is used to find numerical solutions for a stiff (or differential algebraic) system of first order ordinary differential equations.
* Problems must be of the form <math>\mathrm{M} \mathbf{y^{'}} = \mathbf{f} \left(\mathbf{t},\mathbf{y} \right)</math> with possibly singular matrix <math>\mathrm{M}</math>. Any solution to this equation is a function <math>\mathbf{u} \left(\mathbf{t} \right)</math> satisfying <math>\mathrm{M} \mathbf{u^{'}\left(\mathbf{t} \right)} = \mathbf{f} \left(\mathbf{t},\mathbf{u\left(\mathbf{t} \right)} \right)</math>.
* An implicit Runge-Kutta method of order 5 (Radau IIA) is implemented to solve problems.
* We refer to <math>\mathrm{M}</math> in <math>\mathrm{M} \mathbf{y^{'}} = \mathbf{f} \left(\mathbf{t},\mathbf{y} \right)</math>, as the Mass Matrix for the set of equations.
* If the dimension of the Mass Matrix, <math>\mathrm{M}</math> is ''a''x''b'' (i.e. ''a'' rows and ''b'' columns) then ''a'' is equal to the number of equations and ''b'' is equal to the dimension of vector space in which ''y(t)'' lies.
* Let ''m''ij be the element at the ''m''th row and ''n''th column of Mass Matrix <math>\mathrm{M}</math>. So ''m''ij are the coefficients of the derivative operators in the set of Differential Algebraic equations. Note that every ''m''ij has to be a constant.
* Initial data and the set of equations are accepted through ascend model files and the mass matrix is calculated.
* The solutions are determined in a neighborhood of the initial input time by RADAU5 solver.

File:Demonstration of Mass Matrix for DAE.png

2011-08-24T22:36:00Z

Karthik0112358:

User:Karthik0112358

2011-08-24T22:35:23Z

Karthik0112358: /* Progress reports */

File:Check in Denominator.png

2011-08-22T23:35:18Z

Karthik0112358: uploaded a new version of "File:Check in Denominator.png"

User:Karthik0112358

2011-08-22T23:23:17Z

Karthik0112358:

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on adding the Mass Matrix functionality in Radau5 Solver for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## <strike style="color:green">Identifying all derivatives in an equation.</strike>
### <strike style="color:green">Finding the real values of derivative variables.</strike>
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## <strike style="color:green">Checking if the equation is linear with respect to the derivatives.</strike>
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### <strike style="color:green">If the derivative is inside a function.</strike>
### <strike style="color:green">If the coefficient of derivative contains a function.</strike>
### <strike style="color:green">Display corresponding error messages.</strike>
## <strike style="color:green">Evaluating the coefficient.</strike>
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
## Test with CUnit.
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''August 22'''

Added some screen shots:

[[File:Computing Coefficient.png]]

[[File:Derivative in index.png]]

[[File:Derivative raised to power.png]]

[[File:Non-Constant_coefficients.png]]

[[File:Check_in_Denominator.png]]

'''August 19'''

Wrote [http://ascend4.org/User:Karthik0112358/test_radau5 test_radau5.c]. Working on some issues.

'''August 15'''

* CUnit up and running.
* Code completed for writing mass matrix, adding comments and checking if I missed any cases. Only integrating to Radau5 left.

'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]
[[Category:ASCEND Contributors]]

File:Check in Denominator.png

2011-08-22T23:22:57Z

Karthik0112358:

File:Non-Constant coefficients.png

2011-08-22T23:22:27Z

Karthik0112358:

File:Derivative raised to power.png

2011-08-22T23:21:42Z

Karthik0112358:

File:Derivative in index.png

2011-08-22T23:19:58Z

Karthik0112358: Detects if derivative is present in index.

Detects if derivative is present in index.

User:Karthik0112358

2011-08-22T23:16:24Z

Karthik0112358:

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on adding the Mass Matrix functionality in Radau5 Solver for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## <strike style="color:green">Identifying all derivatives in an equation.</strike>
### <strike style="color:green">Finding the real values of derivative variables.</strike>
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## <strike style="color:green">Checking if the equation is linear with respect to the derivatives.</strike>
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### <strike style="color:green">If the derivative is inside a function.</strike>
### <strike style="color:green">If the coefficient of derivative contains a function.</strike>
### <strike style="color:green">Display corresponding error messages.</strike>
## <strike style="color:green">Evaluating the coefficient.</strike>
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
## Test with CUnit.
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''August 22'''

Added some screen shots:

[[File:Computing Coefficient.png]]

'''August 19'''

Wrote [http://ascend4.org/User:Karthik0112358/test_radau5 test_radau5.c]. Working on some issues.

'''August 15'''

* CUnit up and running.
* Code completed for writing mass matrix, adding comments and checking if I missed any cases. Only integrating to Radau5 left.

'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]
[[Category:ASCEND Contributors]]

User:Karthik0112358

2011-08-22T23:15:36Z

Karthik0112358:

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on adding the Mass Matrix functionality in Radau5 Solver for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## <strike style="color:green">Identifying all derivatives in an equation.</strike>
### <strike style="color:green">Finding the real values of derivative variables.</strike>
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## <strike style="color:green">Checking if the equation is linear with respect to the derivatives.</strike>
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### <strike style="color:green">If the derivative is inside a function.</strike>
### <strike style="color:green">If the coefficient of derivative contains a function.</strike>
### <strike style="color:green">Display corresponding error messages.</strike>
## <strike style="color:green">Evaluating the coefficient.</strike>
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
## Test with CUnit.
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''August 22'''

Added some screen shots:

[[File:Demonstration of Computation of Mass Matrix - Computing Coefficient.png]]

'''August 19'''

Wrote [http://ascend4.org/User:Karthik0112358/test_radau5 test_radau5.c]. Working on some issues.

'''August 15'''

* CUnit up and running.
* Code completed for writing mass matrix, adding comments and checking if I missed any cases. Only integrating to Radau5 left.

'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]
[[Category:ASCEND Contributors]]

File:Computing Coefficient.png

2011-08-22T23:14:18Z

Karthik0112358: This computes the Mass matrix, provided linearity in derivatives across all equations.

This computes the Mass matrix, provided linearity in derivatives across all equations.

User:Karthik0112358

2011-08-22T23:05:22Z

Karthik0112358:

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on adding the Mass Matrix functionality in Radau5 Solver for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## <strike style="color:green">Identifying all derivatives in an equation.</strike>
### <strike style="color:green">Finding the real values of derivative variables.</strike>
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## <strike style="color:green">Checking if the equation is linear with respect to the derivatives.</strike>
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### <strike style="color:green">If the derivative is inside a function.</strike>
### <strike style="color:green">If the coefficient of derivative contains a function.</strike>
### <strike style="color:green">Display corresponding error messages.</strike>
## <strike style="color:green">Evaluating the coefficient.</strike>
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
## Test with CUnit.
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''August 22'''

Added some screen shots:
[[File:PyGTK Study - 15.png]]

'''August 19'''

Wrote [http://ascend4.org/User:Karthik0112358/test_radau5 test_radau5.c]. Working on some issues.

'''August 15'''

* CUnit up and running.
* Code completed for writing mass matrix, adding comments and checking if I missed any cases. Only integrating to Radau5 left.

'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]
[[Category:ASCEND Contributors]]

User:Karthik0112358/test radau5

2011-08-19T23:22:58Z

Karthik0112358:

<source lang="c">
#include <string.h>
#include <stdlib.h>
#include <stdio.h>

#include <ascend/general/env.h>
#include <ascend/general/ospath.h>
#include <ascend/general/list.h>
#include <ascend/general/ltmatrix.h>

#include <ascend/general/platform.h>
#include <ascend/utilities/ascEnvVar.h>
#include <ascend/utilities/error.h>

#include <ascend/compiler/ascCompiler.h>
#include <ascend/compiler/module.h>
#include <ascend/compiler/parser.h>
#include <ascend/compiler/library.h>
#include <ascend/compiler/symtab.h>
#include <ascend/compiler/simlist.h>
#include <ascend/compiler/instquery.h>
#include <ascend/compiler/parentchild.h>
#include <ascend/compiler/atomvalue.h>
#include <ascend/compiler/relation_io.h>
#include <ascend/compiler/reverse_ad.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/mathinst.h>
#include <ascend/compiler/watchpt.h>
#include <ascend/compiler/initialize.h>
#include <ascend/compiler/name.h>
#include <ascend/compiler/visitinst.h>
#include <ascend/compiler/functype.h>
#include <ascend/compiler/safe.h>
#include <ascend/compiler/qlfdid.h>
#include <ascend/compiler/instance_io.h>

#include <ascend/compiler/slvreq.h>

#include <ascend/system/system.h>
#include <ascend/system/slv_client.h>
#include <ascend/solver/solver.h>
#include <ascend/system/slv_server.h>
#include <ascend/system/slv_param.h>
#include <ascend/integrator/integrator.h>

#include <test/common.h>
/* Help taken from Shrikanth */
/* a simple integrator reporter for testing */
int test_radau5_reporter_init(struct IntegratorSystemStruct *integ){
return 0;
}

int test_radau5_reporter_write(struct IntegratorSystemStruct *integ){
return 0; /* no interrupt */
}

int test_radau5_reporter_writeobs(struct IntegratorSystemStruct *integ){
CONSOLE_DEBUG("x = %f", var_value(integ->x));
return 0;
}

int test_radau5_reporter_close(struct IntegratorSystemStruct *integ){
return 0;
}

IntegratorReporter test_radau5_reporter = {
test_radau5_reporter_init
,test_radau5_reporter_write
,test_radau5_reporter_writeobs
,test_radau5_reporter_close
};

/*
Test solving a simple IPOPT model
*/
static void test_boundary(){

struct module_t *m;

Asc_CompilerInit(1);
Asc_PutEnv(ASC_ENV_LIBRARY "=models:solvers/conopt:solvers/qrslv:solvers/cmslv:solvers/ida:solvers/lsode:solvers/ipopt");

/* load the file */
char path[PATH_MAX];
strcpy((char *)path,"test/radau5/");
#define FILESTEM "boundaries"
strncat(path, FILESTEM, PATH_MAX - strlen(path));
strncat(path, ".a4c", PATH_MAX - strlen(path));
{
int status;
m = Asc_OpenModule(path,&status);
CU_ASSERT_FATAL(status == 0);
}

/* parse it */
CU_ASSERT(0 == zz_parse());

/* find the model */
CU_ASSERT(FindType(AddSymbol(FILESTEM))!=NULL);

/* instantiate it */
struct Instance *siminst = SimsCreateInstance(AddSymbol(FILESTEM), AddSymbol("sim1"), e_normal, NULL);
CU_ASSERT_FATAL(siminst!=NULL);

CONSOLE_DEBUG("RUNNING ON_LOAD");

/** Call on_load */
struct Name *name = CreateIdName(AddSymbol("on_load"));
enum Proc_enum pe = Initialize(GetSimulationRoot(siminst),name,"sim1", ASCERR, WP_STOPONERR, NULL, NULL);
CU_ASSERT(pe==Proc_all_ok);

/* create the integrator */

slv_system_t sys = system_build(GetSimulationRoot(siminst));
CU_ASSERT_FATAL(sys != NULL);

IntegratorSystem *integ = integrator_new(sys,siminst);

CU_ASSERT_FATAL(0 == integrator_set_engine(integ,"RADAU5"));
CONSOLE_DEBUG("Assigned integrator '%s'...",integ->internals->name);

slv_parameters_t p;
CU_ASSERT(0 == integrator_params_get(integ,&p));
/* TODO set some parameters? */

/* perform problem analysis */
CU_ASSERT_FATAL(0 == integrator_analyse(integ));

/* TODO assign an integrator reporter */
integrator_set_reporter(integ, &test_radau5_reporter);

integrator_set_minstep(integ,0);
integrator_set_maxstep(integ,0);
integrator_set_stepzero(integ,0);
integrator_set_maxsubsteps(integ,0);

/* set a linearly-distributed samplelist */
double start = 0, end = 2.0;
int num = 500;
dim_type d;
SetDimFraction(d,D_TIME,CreateFraction(1,1));
SampleList *samplelist = samplelist_new(num+1, &d);
double val = start;
double inc = (end-start)/(num);
unsigned long i;
for(i=0; i<=num; ++i){
samplelist_set(samplelist,i,val);
val += inc;
}
integrator_set_samples(integ,samplelist);

CU_ASSERT_FATAL(0 == integrator_solve(integ, 0, samplelist_length(samplelist)-1));

integrator_free(integ);
samplelist_free(samplelist);

CU_ASSERT_FATAL(NULL != sys);
system_destroy(sys);
system_free_reused_mem();

/* destroy all that stuff */
CONSOLE_DEBUG("Destroying instance tree");
CU_ASSERT(siminst != NULL);

solver_destroy_engines();
sim_destroy(siminst);
Asc_CompilerDestroy();
}

/*===========================================================================*/
/* Registration information */

#define TESTS(T) \
T(boundary)

REGISTER_TESTS_SIMPLE(solver_radau5, TESTS)
</source>

User:Karthik0112358

2011-08-19T22:48:05Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## <strike style="color:green">Identifying all derivatives in an equation.</strike>
### <strike style="color:green">Finding the real values of derivative variables.</strike>
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## <strike style="color:green">Checking if the equation is linear with respect to the derivatives.</strike>
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### <strike style="color:green">If the derivative is inside a function.</strike>
### <strike style="color:green">If the coefficient of derivative contains a function.</strike>
### <strike style="color:green">Display corresponding error messages.</strike>
## <strike style="color:green">Evaluating the coefficient.</strike>
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
## Test with CUnit.
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''August 19'''

Wrote [http://ascend4.org/User:Karthik0112358/test_radau5 test_radau5.c]. Working on some issues.

'''August 15'''

* CUnit up and running.
* Code completed for writing mass matrix, adding comments and checking if I missed any cases. Only integrating to Radau5 left.

'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]
[[Category:ASCEND Contributors]]

User:Karthik0112358/test radau5

2011-08-19T22:47:33Z

Karthik0112358: Created page with '<source lang="c"> #include <string.h> #include <stdlib.h> #include <stdio.h> #include <ascend/general/env.h> #include <ascend/general/ospath.h> #include <ascend/general/list.h> …'

<source lang="c">
#include <string.h>
#include <stdlib.h>
#include <stdio.h>

#include <ascend/general/env.h>
#include <ascend/general/ospath.h>
#include <ascend/general/list.h>
#include <ascend/general/ltmatrix.h>

#include <ascend/general/platform.h>
#include <ascend/utilities/ascEnvVar.h>
#include <ascend/utilities/error.h>

#include <ascend/compiler/ascCompiler.h>
#include <ascend/compiler/module.h>
#include <ascend/compiler/parser.h>
#include <ascend/compiler/library.h>
#include <ascend/compiler/symtab.h>
#include <ascend/compiler/simlist.h>
#include <ascend/compiler/instquery.h>
#include <ascend/compiler/parentchild.h>
#include <ascend/compiler/atomvalue.h>
#include <ascend/compiler/relation_io.h>
#include <ascend/compiler/reverse_ad.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/mathinst.h>
#include <ascend/compiler/watchpt.h>
#include <ascend/compiler/initialize.h>
#include <ascend/compiler/name.h>
#include <ascend/compiler/visitinst.h>
#include <ascend/compiler/functype.h>
#include <ascend/compiler/safe.h>
#include <ascend/compiler/qlfdid.h>
#include <ascend/compiler/instance_io.h>

#include <ascend/compiler/slvreq.h>

#include <ascend/system/system.h>
#include <ascend/system/slv_client.h>
#include <ascend/solver/solver.h>
#include <ascend/system/slv_server.h>
#include <ascend/system/slv_param.h>
#include <ascend/integrator/integrator.h>

#include <test/common.h>

/* a simple integrator reporter for testing */
int test_radau5_reporter_init(struct IntegratorSystemStruct *integ){
return 0;
}

int test_radau5_reporter_write(struct IntegratorSystemStruct *integ){
return 0; /* no interrupt */
}

int test_radau5_reporter_writeobs(struct IntegratorSystemStruct *integ){
CONSOLE_DEBUG("x = %f", var_value(integ->x));
return 0;
}

int test_radau5_reporter_close(struct IntegratorSystemStruct *integ){
return 0;
}

IntegratorReporter test_radau5_reporter = {
test_radau5_reporter_init
,test_radau5_reporter_write
,test_radau5_reporter_writeobs
,test_radau5_reporter_close
};

/*
Test solving a simple IPOPT model
*/
static void test_boundary(){

struct module_t *m;

Asc_CompilerInit(1);
Asc_PutEnv(ASC_ENV_LIBRARY "=models:solvers/conopt:solvers/qrslv:solvers/cmslv:solvers/ida:solvers/lsode:solvers/ipopt");

/* load the file */
char path[PATH_MAX];
strcpy((char *)path,"test/radau5/");
#define FILESTEM "boundaries"
strncat(path, FILESTEM, PATH_MAX - strlen(path));
strncat(path, ".a4c", PATH_MAX - strlen(path));
{
int status;
m = Asc_OpenModule(path,&status);
CU_ASSERT_FATAL(status == 0);
}

/* parse it */
CU_ASSERT(0 == zz_parse());

/* find the model */
CU_ASSERT(FindType(AddSymbol(FILESTEM))!=NULL);

/* instantiate it */
struct Instance *siminst = SimsCreateInstance(AddSymbol(FILESTEM), AddSymbol("sim1"), e_normal, NULL);
CU_ASSERT_FATAL(siminst!=NULL);

CONSOLE_DEBUG("RUNNING ON_LOAD");

/** Call on_load */
struct Name *name = CreateIdName(AddSymbol("on_load"));
enum Proc_enum pe = Initialize(GetSimulationRoot(siminst),name,"sim1", ASCERR, WP_STOPONERR, NULL, NULL);
CU_ASSERT(pe==Proc_all_ok);

/* create the integrator */

slv_system_t sys = system_build(GetSimulationRoot(siminst));
CU_ASSERT_FATAL(sys != NULL);

IntegratorSystem *integ = integrator_new(sys,siminst);

CU_ASSERT_FATAL(0 == integrator_set_engine(integ,"RADAU5"));
CONSOLE_DEBUG("Assigned integrator '%s'...",integ->internals->name);

slv_parameters_t p;
CU_ASSERT(0 == integrator_params_get(integ,&p));
/* TODO set some parameters? */

/* perform problem analysis */
CU_ASSERT_FATAL(0 == integrator_analyse(integ));

/* TODO assign an integrator reporter */
integrator_set_reporter(integ, &test_radau5_reporter);

integrator_set_minstep(integ,0);
integrator_set_maxstep(integ,0);
integrator_set_stepzero(integ,0);
integrator_set_maxsubsteps(integ,0);

/* set a linearly-distributed samplelist */
double start = 0, end = 2.0;
int num = 500;
dim_type d;
SetDimFraction(d,D_TIME,CreateFraction(1,1));
SampleList *samplelist = samplelist_new(num+1, &d);
double val = start;
double inc = (end-start)/(num);
unsigned long i;
for(i=0; i<=num; ++i){
samplelist_set(samplelist,i,val);
val += inc;
}
integrator_set_samples(integ,samplelist);

CU_ASSERT_FATAL(0 == integrator_solve(integ, 0, samplelist_length(samplelist)-1));

integrator_free(integ);
samplelist_free(samplelist);

CU_ASSERT_FATAL(NULL != sys);
system_destroy(sys);
system_free_reused_mem();

/* destroy all that stuff */
CONSOLE_DEBUG("Destroying instance tree");
CU_ASSERT(siminst != NULL);

solver_destroy_engines();
sim_destroy(siminst);
Asc_CompilerDestroy();
}

/*===========================================================================*/
/* Registration information */

#define TESTS(T) \
T(boundary)

REGISTER_TESTS_SIMPLE(solver_radau5, TESTS)
</source>

User:Karthik0112358

2011-08-15T11:16:29Z

Karthik0112358: /* Goals */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## <strike style="color:green">Identifying all derivatives in an equation.</strike>
### <strike style="color:green">Finding the real values of derivative variables.</strike>
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## <strike style="color:green">Checking if the equation is linear with respect to the derivatives.</strike>
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### <strike style="color:green">If the derivative is inside a function.</strike>
### <strike style="color:green">If the coefficient of derivative contains a function.</strike>
### <strike style="color:green">Display corresponding error messages.</strike>
## <strike style="color:green">Evaluating the coefficient.</strike>
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
## Test with CUnit.
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''August 15'''

* CUnit up and running.
* Code completed for writing mass matrix, adding comments and checking if I missed any cases. Only integrating to Radau5 left.

'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]
[[Category:ASCEND Contributors]]

User:Karthik0112358

2011-08-15T11:13:56Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## <strike style="color:green">Evaluating the coefficient.</strike>
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''August 15'''

* CUnit up and running.
* Code completed for writing mass matrix, adding comments and checking if I missed any cases. Only integrating to Radau5 left.

'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]
[[Category:ASCEND Contributors]]

User:Karthik0112358/Coefficient Calculator

2011-08-04T23:01:13Z

Karthik0112358:

<source lang="c">
/* ASCEND modelling environment
Copyright (C) 1997, 2006 Carnegie Mellon University
Copyright (C) 1993, 1994 Joseph James Zaher, Benjamin Andrew Allan
Copyright (C) 1993 Joseph James Zaher
Copyright (C) 1990 Thomas Guthrie Epperly, Karl Michael Westerberg

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA.
*/
/*
KARTHIK C S, June 2011
*/
#include <math.h>
#include "relation_util.h"
#include <ascend/general/ascMalloc.h>
#include <ascend/general/panic.h>
#include "relation_type.h"
#include "expr_types.h"
#include "instance_enum.h"
#include "functype.h"
#include "mathinst.c"
/*------------------------------------------------------------------------------
FINDING COEFFICIENTS OF THE DERIVATIVE TERMS IN A RELATION
*/

/**
Compute the coefficients of the derivative terms in the relation (compiler-side routine)

@param i Instance pointer through which the coefficients of the derivative terms of the relation are found
@param coefficient pointer to a double in which the coefficients shall be stored (must have already been allocated)
@param Info of structure Info_abt_deriv which contains the real value of all the derivative variables

@return 0 on success, and otherwise on failure

Here we compute the coefficients of the derivative terms by first extracting each term.
We then check if its a derivative variable and if so we compute its coefficient by considering the terms previous to it and after it.
In this process we also check if the equation is linear wrt its derivatives. Suitable error messages are displayed if its not.
*/
/* Started reorganizing the entire Inspect_Equation(). Providing modularity for efficiency and flexibility.*/
/*
static int Inspect_Equation(struct Info_abt_deriv Info,int *order,double *var,double *func,int *ope,unsigned long length_rel){
int i,j,k;
int varc=-1,opec=-1,funcc=-1,numc=-1;
int flag,count,c,denom_flag,point;
unsigned long bin_num,pass,new_bin_num;
for (i=0;i<Info.no_of_deriv;i++){
flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
//Write Error catching analysis code here
if(Info.deriv_values[i]==var[varc]) {
if(order[j-1]==2) {
count=1;
c=1;
k=0;
while(count!=0&&(j+c)<=length_rel) {
count=(order[c+j]==3)?--count:++count;
k=(order[c+j]==3)?++k:k;
++c;
}
--c;
if(ope[opec+k]!=1||ope[opec+k]!=2){
CONSOLE_DEBUG("The coefficient of the derivative term contains a non constant term");
}
}else if(order[j+1]==2) {
count=1;
c=2;
k=0;
while(count!=0&&(j+c)<=length_rel){
count=(order[c+j]==3)?--count:++count;
k=(order[c+j]==3)?++k:k;
++c;
}
--c;
if(ope[opec+k]!=1||ope[opec+k]!=2){
CONSOLE_DEBUG("The coefficient of the derivative term contains a non constant term");
}
}
c=1;
count=0;
denom_flag=0;
while(order[j+c]!=4&&(j+c)<=length_rel) {
if(order[c+j]==3) {
++count;
if(ope[opec+count]==4) {
if(count>c-count) {
denom_flag=(denom_flag==0)?1:0;
}
}
}
++c;
}
if(denom_flag==1){
CONSOLE_DEBUG("The derivative is in denominator");
}
c=1;
count=0;
while(order[j+c]!=4&&(j+c)<=length_rel) {
if(order[c+j]==3) {
++count;
if(ope[opec+count]==6) {
if(count>c-count) {
CONSOLE_DEBUG("The derivative is in index");
}
}
}
++c;
}
/* We implement here an algorithm which finds the span of an operator. The span of an operator
is defined as the number of terms the operator links in an expression. We see if the derivative
is in the upper span (the set of terms to the left of an operator in infix form) of the operator,
by using a variable to point at the location of the derivative in a binary representation of the
relation where 0 means a number or variable and 1 means an operator. Then we display an error is
the derivative is raised to a higher/lower power.* /
c=0;
count=-1;
bin_num=0;
pass=0;
/* Need to write code here to check if the derivative is being raised to power 1.
The idea is to locate every ^ operator and see if the item immediately following
it in the infix notation is 1 which does not have any prior connection with any other
operator. * /
/* As a second thought, I think I will segregate each Error case as a function, considering the recursive algorithms used in some of the cases. * /
if(flag==0){
while(order[c]!=4){
++c;
}
for(k=c-1;k>=0;k--) {
if(order[k]==3) {
bin_num+=pow(2,c-k-1);
}
}
point=j;
for(k=c-1;k>=0;k--) {
if(bin_num-pass>0) {
++count;
pass+=pow(2,k);
if(point+k==c-3) {
if(ope[count]==6) {
CONSOLE_DEBUG("The derivative is raised to a power other than one");
} else {

}
} else {

}
}
}
}else {
while(order[c]!=4){
++c;
}
++c;
while(c<=length_rel) {
++c;
}
}
}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message * /
break;
}
}
}
return 1;
}
*/

/* So here it begins */

char* find_left_bin_number(int *,unsigned long ,int *);
char* find_right_bin_number(int *,unsigned long ,int *);
int find_variable(struct Info_abt_deriv, double);
check_for_alg_coeff();

/* Functions need to write:
check_in denominator();
check_in_indices();
check_in_bases();
check_for_func_coeff();
check_inside_func();
shift_by_one();
shift_by_two();
*/

static int Inspect_Equation(struct Info_abt_deriv Info,int *order,double *var,double *func,int *ope,unsigned long length_rel){
int result;
int var_index;
char *left_bin_num,*right_bin_num;
int *len_left_bin_num,*len_right_bin_num; /* Pointers are used so that these can be passed by reference */
left_bin_num=ASC_NEW_ARRAY(char,length_rel);
right_bin_num=ASC_NEW_ARRAY(char,length_rel);
left_bin_num=find_left_bin_number(order,length_rel,len_left_bin_num);
right_bin_num=find_right_bin_number(order,length_rel,len_right_bin_num);
result=0;
/* We write here an inspection for special cases, like : 3=4+Q(x,y)/x, where is Q(x,y) is a linear function in x */

/* End of special cases */

/* We start inspecting general cases */

flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
/* Write Error catching analysis code here */
var_index=find_variable(Info,var[varc]);
if(var_index!=0){
result+=check_in denominator(left_bin_num,len_left_bin_num,right_bin_num,len_right_bin_num,var_index,flag);
result+=check_in_indices();
result+=check_in_bases();
result+=check_for_alg_coeff();
result+=check_for_func_coeff();
result+=check_inside_func();
}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message */
break;
}
}
return (result>0)?0:1;
}
char* find_left_bin_number(int *order,unsigned long length_rel,int *len_left_bin_num) {
int i;
char *bin_num;
bin_num=ASC_NEW_ARRAY(char,length_rel);
for(i=0;order[i]!=4;i++) {
bin_num[i](order[i]<=2)?'0':'1';
*len_left_bin_num=i+1;
}
return bin_num;
}
char* find_right_bin_number(int *order,unsigned long length_rel,int *len_right_bin_num) {
int i,j;
char *bin_num;
bin_num=ASC_NEW_ARRAY(char,length_rel);
for(i=0;order[i]!=4;i++);
for(j=i+1;j<=length_rel;j++) {
bin_num[j-i-1](order[j]<=2)?'0':'1';
*len_right_bin_num=j-i-1;
}
return bin_num;
}

int find_variable(struct Info_abt_deriv Info, double index) {
int i=0;
for(i=0;i<Info.no_of_deriv;i++) {
if(Info.deriv_values[i]==index) {
return 1;
}
}
return 0;
}

int check_for_alg_coeff() {
/* start code here */
}

void coefficient_match(double *coefficient,struct Info_abt_deriv Info,int *order,double *num,double *var,double *func,int *ope, unsigned long length_rel){
int i,j,k,p;
double value;
int flag;
int varc=-1,opec=-1,funcc=-1,numc=-1;
int c;
if(Inspect_Equation(Info,order,var,func,ope,length_rel)==1){
for (i=0;i<Info.no_of_deriv;i++){
value=1.0;
flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
/*if(Info.deriv_values[i]==var[varc]) {
if(order[j-1]==1&&order[j+1]==3) {
if(ope[opec+1]==3) {
value=num[numc];
}
}else if(order[j+1]==1&&order[j+2]==3) {
if(ope[opec+1]==3) {
value=num[numc+1];
}
}else {
while(order[c+j]!=4){
c=1;
while(order[c+j]==2||order[c+j]==1) {
c++;
}
}
}
}*/
/*
We write here a piece of code which sees the relation as follows:
(i) the variable whose coefficient we have to find is replaced by 1.
(ii) every other variable is replaced by 0.
(iii) we simplify the expression we have but with certain new rules:
(iii) (i) If + or - operator is encountered then we replace the number preceeding or succeeding it by 0.
(iii) (ii) If ^ is encountered we ignore it and the number following it(which has to be 1).
*/
for(p=0;order[p]!=4;p++) {
/* Implement above algorithm here*/
\ }
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message */
break;
}
}
}
}else {
CONSOLE_DEBUG("Equation cannot be accepted by solver");
}
}

static int coefficient_calculator(struct Instance *i,double *coefficient,struct Info_abt_deriv Info){
struct relation *r;
enum Expr_enum reltype;
unsigned long t; /* the current term in the relation r */
unsigned long num_var; /* the number of variables in the relation r */
unsigned long v; /* loop variable */
int lhs; /* looking at left(=1) or right(=0) hand side of r */
unsigned long length_lhs, length_rhs;
double *num; /* pointer for storing all constants in relation */
double *var; /* pointer for storing all real value of variables in relation */
int *ope; /* pointer for storing all operators in relation */
double *func; /* pointer for storing all functions in relation */
int *order; /* pointer for storing order of all constants, variables and operators in postfix form in relation */
int varc=0,numc=0,orderc=0,opec=0,funcc=0; /* counters for various arrays */
CONST struct relation_term *term;
CONST struct Func *fxnptr;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
CONSOLE_DEBUG("null relation\n");
return -1;
}
num_var = NumberVariables(r);
length_lhs = RelationLength(r, 1);
length_rhs = RelationLength(r, 0);
num=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
var=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
ope=ASC_NEW_ARRAY(int,length_lhs+length_rhs);
func=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
order = ASC_NEW_ARRAY(int,(length_lhs+length_rhs+1));
lhs = 1;
t = 0;

for (v=0; v<length_lhs+length_rhs; v++) {
/* Initializing all entries to 0 */
order[v]=0;
func[v]=0.0;
ope[v]=0;
num[v]=0.0;
var[v]=0.0;
}
order[length_lhs+length_rhs]=0;
while(1) {
if( lhs && (t >= length_lhs) ) {
/* need to switch to the right hand side--if it exists */
if( length_rhs ) {
lhs = t = 0;
order[orderc++]=4;
} else {
/*
We know that (length_lhs+length_rhs>0) and that (length_rhs==0),
the length_lhs must be > 0
*/
coefficient_match(coefficient,Info,order,num,var,func,ope,length_lhs+length_rhs+1);
return 0;
}
} else if( (!lhs) && (t >= length_rhs) ) {
/* we have processed both sides, quit */
coefficient_match(coefficient,Info,order,num,var,func,ope,length_lhs+length_rhs+1);
return 0;
}
term = NewRelationTerm(r, t++, lhs);
switch( RelationTermType(term) ) {
case e_zero:
num[numc++]=0.0;
order[orderc++]=1;
break;
case e_real:
num[numc++]=(double)TermReal(term);
order[orderc++]=1;
break;
case e_int:
num[numc++]=(double)TermInteger(term);
order[orderc++]=1;
break;
case e_var:
var[varc++]= TermVariable(r, term);
order[orderc++]=2;
break;
case e_plus:
ope[opec++]=1;
order[orderc++]=3;
break;
case e_minus:
ope[opec++]=2;
order[orderc++]=3;
break;
case e_times:
ope[opec++]=3;
order[orderc++]=3;
break;
case e_divide:
ope[opec++]=4;
order[orderc++]=3;
break;
case e_uminus:
ope[opec++]=5;
order[orderc++]=3;
break;
case e_power:
ope[opec++]=6;
order[orderc++]=3;
break;
case e_ipower:
ope[opec++]=7;
order[orderc++]=3;
break;
case e_func:
ope[opec++]=8;
order[orderc++]=3;
fxnptr = TermFunc(term);
func[funcc] = FuncEval( fxnptr, func[funcc] );
++funcc;
break;
default:
ASC_PANIC("Unknown relation term type");
break;
}

}
}
</source>

User:Karthik0112358

2011-08-04T22:16:14Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## <strike style="color:green">Evaluating the coefficient.</strike>
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''August 4'''

I have completed writing the function which evaluates the coefficient after confirming the equation is linear with respect to the derivatives. Code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. Hence Goal 1.4 complete.

'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-08-04T22:06:33Z

Karthik0112358: /* Goals */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## <strike style="color:green">Evaluating the coefficient.</strike>
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-08-04T22:05:51Z

Karthik0112358: /* Goals */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## Evaluating the coefficient.
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### <strike style="color:green">Compounding the base coefficient while processing terms in the equation.</strike>
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358/Coefficient Calculator

2011-07-31T22:39:00Z

Karthik0112358:

<source lang="c">
/* ASCEND modelling environment
Copyright (C) 1997, 2006 Carnegie Mellon University
Copyright (C) 1993, 1994 Joseph James Zaher, Benjamin Andrew Allan
Copyright (C) 1993 Joseph James Zaher
Copyright (C) 1990 Thomas Guthrie Epperly, Karl Michael Westerberg

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA.
*/
/*
KARTHIK C S, June 2011
*/
#include <math.h>
#include "relation_util.h"
#include <ascend/general/ascMalloc.h>
#include <ascend/general/panic.h>
#include "relation_type.h"
#include "expr_types.h"
#include "instance_enum.h"
#include "functype.h"
#include "mathinst.c"
/*------------------------------------------------------------------------------
FINDING COEFFICIENTS OF THE DERIVATIVE TERMS IN A RELATION
*/

/**
Compute the coefficients of the derivative terms in the relation (compiler-side routine)

@param i Instance pointer through which the coefficients of the derivative terms of the relation are found
@param coefficient pointer to a double in which the coefficients shall be stored (must have already been allocated)
@param Info of structure Info_abt_deriv which contains the real value of all the derivative variables

@return 0 on success, and otherwise on failure

Here we compute the coefficients of the derivative terms by first extracting each term.
We then check if its a derivative variable and if so we compute its coefficient by considering the terms previous to it and after it.
In this process we also check if the equation is linear wrt its derivatives. Suitable error messages are displayed if its not.
*/
/* Started reorganizing the entire Inspect_Equation(). Providing modularity for efficiency and flexibility.*/
/*
static int Inspect_Equation(struct Info_abt_deriv Info,int *order,double *var,double *func,int *ope,unsigned long length_rel){
int i,j,k;
int varc=-1,opec=-1,funcc=-1,numc=-1;
int flag,count,c,denom_flag,point;
unsigned long bin_num,pass,new_bin_num;
for (i=0;i<Info.no_of_deriv;i++){
flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
//Write Error catching analysis code here
if(Info.deriv_values[i]==var[varc]) {
if(order[j-1]==2) {
count=1;
c=1;
k=0;
while(count!=0&&(j+c)<=length_rel) {
count=(order[c+j]==3)?--count:++count;
k=(order[c+j]==3)?++k:k;
++c;
}
--c;
if(ope[opec+k]!=1||ope[opec+k]!=2){
CONSOLE_DEBUG("The coefficient of the derivative term contains a non constant term");
}
}else if(order[j+1]==2) {
count=1;
c=2;
k=0;
while(count!=0&&(j+c)<=length_rel){
count=(order[c+j]==3)?--count:++count;
k=(order[c+j]==3)?++k:k;
++c;
}
--c;
if(ope[opec+k]!=1||ope[opec+k]!=2){
CONSOLE_DEBUG("The coefficient of the derivative term contains a non constant term");
}
}
c=1;
count=0;
denom_flag=0;
while(order[j+c]!=4&&(j+c)<=length_rel) {
if(order[c+j]==3) {
++count;
if(ope[opec+count]==4) {
if(count>c-count) {
denom_flag=(denom_flag==0)?1:0;
}
}
}
++c;
}
if(denom_flag==1){
CONSOLE_DEBUG("The derivative is in denominator");
}
c=1;
count=0;
while(order[j+c]!=4&&(j+c)<=length_rel) {
if(order[c+j]==3) {
++count;
if(ope[opec+count]==6) {
if(count>c-count) {
CONSOLE_DEBUG("The derivative is in index");
}
}
}
++c;
}
/* We implement here an algorithm which finds the span of an operator. The span of an operator
is defined as the number of terms the operator links in an expression. We see if the derivative
is in the upper span (the set of terms to the left of an operator in infix form) of the operator,
by using a variable to point at the location of the derivative in a binary representation of the
relation where 0 means a number or variable and 1 means an operator. Then we display an error is
the derivative is raised to a higher/lower power.* /
c=0;
count=-1;
bin_num=0;
pass=0;
/* Need to write code here to check if the derivative is being raised to power 1.
The idea is to locate every ^ operator and see if the item immediately following
it in the infix notation is 1 which does not have any prior connection with any other
operator. * /
/* As a second thought, I think I will segregate each Error case as a function, considering the recursive algorithms used in some of the cases. * /
if(flag==0){
while(order[c]!=4){
++c;
}
for(k=c-1;k>=0;k--) {
if(order[k]==3) {
bin_num+=pow(2,c-k-1);
}
}
point=j;
for(k=c-1;k>=0;k--) {
if(bin_num-pass>0) {
++count;
pass+=pow(2,k);
if(point+k==c-3) {
if(ope[count]==6) {
CONSOLE_DEBUG("The derivative is raised to a power other than one");
} else {

}
} else {

}
}
}
}else {
while(order[c]!=4){
++c;
}
++c;
while(c<=length_rel) {
++c;
}
}
}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message * /
break;
}
}
}
return 1;
}
*/

/* So here it begins */

char* find_left_bin_number(int *,unsigned long ,int *);
char* find_right_bin_number(int *,unsigned long ,int *);
int find_variable(struct Info_abt_deriv, double);
check_for_alg_coeff();

/* Functions need to write:
check_in denominator();
check_in_indices();
check_in_bases();
check_for_func_coeff();
check_inside_func();
shift_by_one();
shift_by_two();
*/

static int Inspect_Equation(struct Info_abt_deriv Info,int *order,double *var,double *func,int *ope,unsigned long length_rel){
int result;
int var_index;
char *left_bin_num,*right_bin_num;
int *len_left_bin_num,*len_right_bin_num; /* Pointers are used so that these can be passed by reference */
left_bin_num=ASC_NEW_ARRAY(char,length_rel);
right_bin_num=ASC_NEW_ARRAY(char,length_rel);
left_bin_num=find_left_bin_number(order,length_rel,len_left_bin_num);
right_bin_num=find_right_bin_number(order,length_rel,len_right_bin_num);
result=0;
/* We write here an inspection for special cases, like : 3=4+Q(x,y)/x, where is Q(x,y) is a linear function in x */

/* End of special cases */

/* We start inspecting general cases */

flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
/* Write Error catching analysis code here */
var_index=find_variable(Info,var[varc]);
if(var_index!=0){
result+=check_in denominator(left_bin_num,len_left_bin_num,right_bin_num,len_right_bin_num,var_index,flag);
result+=check_in_indices();
result+=check_in_bases();
result+=check_for_alg_coeff();
result+=check_for_func_coeff();
result+=check_inside_func();
}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message */
break;
}
}
return (result>0)?0:1;
}
char* find_left_bin_number(int *order,unsigned long length_rel,int *len_left_bin_num) {
int i;
char *bin_num;
bin_num=ASC_NEW_ARRAY(char,length_rel);
for(i=0;order[i]!=4;i++) {
bin_num[i](order[i]<=2)?'0':'1';
*len_left_bin_num=i+1;
}
return bin_num;
}
char* find_right_bin_number(int *order,unsigned long length_rel,int *len_right_bin_num) {
int i,j;
char *bin_num;
bin_num=ASC_NEW_ARRAY(char,length_rel);
for(i=0;order[i]!=4;i++);
for(j=i+1;j<=length_rel;j++) {
bin_num[j-i-1](order[j]<=2)?'0':'1';
*len_right_bin_num=j-i-1;
}
return bin_num;
}

int find_variable(struct Info_abt_deriv Info, double index) {
int i=0;
for(i=0;i<Info.no_of_deriv;i++) {
if(Info.deriv_values[i]==index) {
return 1;
}
}
return 0;
}

int check_for_alg_coeff() {
/* start code here */
}

void coefficient_match(double *coefficient,struct Info_abt_deriv Info,int *order,double *num,double *var,double *func,int *ope, unsigned long length_rel){
int i,j,k;
double value;
int flag;
int varc=-1,opec=-1,funcc=-1,numc=-1;
int c;
if(Inspect_Equation(Info,order,var,func,ope,length_rel)==1){
for (i=0;i<Info.no_of_deriv;i++){
value=1.0;
flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
if(Info.deriv_values[i]==var[varc]) {
if(order[j-1]==1&&order[j+1]==3) {
if(ope[opec+1]==3) {
value=num[numc];
}
}else if(order[j+1]==1&&order[j+2]==3) {
if(ope[opec+1]==3) {
value=num[numc+1];
}
}else {
while(order[c+j]!=4){
c=1;
while(order[c+j]==2||order[c+j]==1) {
c++;
}
}
}
}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message */
break;
}
}
}
}else {
CONSOLE_DEBUG("Equation cannot be accepted by solver");
}
}

static int coefficient_calculator(struct Instance *i,double *coefficient,struct Info_abt_deriv Info){
struct relation *r;
enum Expr_enum reltype;
unsigned long t; /* the current term in the relation r */
unsigned long num_var; /* the number of variables in the relation r */
unsigned long v; /* loop variable */
int lhs; /* looking at left(=1) or right(=0) hand side of r */
unsigned long length_lhs, length_rhs;
double *num; /* pointer for storing all constants in relation */
double *var; /* pointer for storing all real value of variables in relation */
int *ope; /* pointer for storing all operators in relation */
double *func; /* pointer for storing all functions in relation */
int *order; /* pointer for storing order of all constants, variables and operators in postfix form in relation */
int varc=0,numc=0,orderc=0,opec=0,funcc=0; /* counters for various arrays */
CONST struct relation_term *term;
CONST struct Func *fxnptr;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
CONSOLE_DEBUG("null relation\n");
return -1;
}
num_var = NumberVariables(r);
length_lhs = RelationLength(r, 1);
length_rhs = RelationLength(r, 0);
num=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
var=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
ope=ASC_NEW_ARRAY(int,length_lhs+length_rhs);
func=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
order = ASC_NEW_ARRAY(int,(length_lhs+length_rhs+1));
lhs = 1;
t = 0;

for (v=0; v<length_lhs+length_rhs; v++) {
/* Initializing all entries to 0 */
order[v]=0;
func[v]=0.0;
ope[v]=0;
num[v]=0.0;
var[v]=0.0;
}
order[length_lhs+length_rhs]=0;
while(1) {
if( lhs && (t >= length_lhs) ) {
/* need to switch to the right hand side--if it exists */
if( length_rhs ) {
lhs = t = 0;
order[orderc++]=4;
} else {
/*
We know that (length_lhs+length_rhs>0) and that (length_rhs==0),
the length_lhs must be > 0
*/
coefficient_match(coefficient,Info,order,num,var,func,ope,length_lhs+length_rhs+1);
return 0;
}
} else if( (!lhs) && (t >= length_rhs) ) {
/* we have processed both sides, quit */
coefficient_match(coefficient,Info,order,num,var,func,ope,length_lhs+length_rhs+1);
return 0;
}
term = NewRelationTerm(r, t++, lhs);
switch( RelationTermType(term) ) {
case e_zero:
num[numc++]=0.0;
order[orderc++]=1;
break;
case e_real:
num[numc++]=(double)TermReal(term);
order[orderc++]=1;
break;
case e_int:
num[numc++]=(double)TermInteger(term);
order[orderc++]=1;
break;
case e_var:
var[varc++]= TermVariable(r, term);
order[orderc++]=2;
break;
case e_plus:
ope[opec++]=1;
order[orderc++]=3;
break;
case e_minus:
ope[opec++]=2;
order[orderc++]=3;
break;
case e_times:
ope[opec++]=3;
order[orderc++]=3;
break;
case e_divide:
ope[opec++]=4;
order[orderc++]=3;
break;
case e_uminus:
ope[opec++]=5;
order[orderc++]=3;
break;
case e_power:
ope[opec++]=6;
order[orderc++]=3;
break;
case e_ipower:
ope[opec++]=7;
order[orderc++]=3;
break;
case e_func:
ope[opec++]=8;
order[orderc++]=3;
fxnptr = TermFunc(term);
func[funcc] = FuncEval( fxnptr, func[funcc] );
++funcc;
break;
default:
ASC_PANIC("Unknown relation term type");
break;
}

}
}
</source>

User:Karthik0112358

2011-07-31T22:38:07Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

Code branch: {{srcbranchdir|karthik|}}

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## Evaluating the coefficient.
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### Compounding the base coefficient while processing terms in the equation.
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''July 31'''

More added to [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358/Coefficient Calculator

2011-07-25T21:02:10Z

Karthik0112358:

<source lang="c">
/* ASCEND modelling environment
Copyright (C) 1997, 2006 Carnegie Mellon University
Copyright (C) 1993, 1994 Joseph James Zaher, Benjamin Andrew Allan
Copyright (C) 1993 Joseph James Zaher
Copyright (C) 1990 Thomas Guthrie Epperly, Karl Michael Westerberg

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA.
*/
/*
KARTHIK C S, June 2011
*/
#include <math.h>
#include "relation_util.h"
#include <ascend/general/ascMalloc.h>
#include <ascend/general/panic.h>
#include "relation_type.h"
#include "expr_types.h"
#include "instance_enum.h"
#include "functype.h"
#include "mathinst.c"
/*------------------------------------------------------------------------------
FINDING COEFFICIENTS OF THE DERIVATIVE TERMS IN A RELATION
*/

/**
Compute the coefficients of the derivative terms in the relation (compiler-side routine)

@param i Instance pointer through which the coefficients of the derivative terms of the relation are found
@param coefficient pointer to a double in which the coefficients shall be stored (must have already been allocated)
@param Info of structure Info_abt_deriv which contains the real value of all the derivative variables

@return 0 on success, and otherwise on failure

Here we compute the coefficients of the derivative terms by first extracting each term.
We then check if its a derivative variable and if so we compute its coefficient by considering the terms previous to it and after it.
In this process we also check if the equation is linear wrt its derivatives. Suitable error messages are displayed if its not.
*/
/* Started reorganizing the entire Inspect_Equation(). Providing modularity for efficiency and flexibility.*/
/*
static int Inspect_Equation(struct Info_abt_deriv Info,int *order,double *var,double *func,int *ope,unsigned long length_rel){
int i,j,k;
int varc=-1,opec=-1,funcc=-1,numc=-1;
int flag,count,c,denom_flag,point;
unsigned long bin_num,pass,new_bin_num;
for (i=0;i<Info.no_of_deriv;i++){
flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
//Write Error catching analysis code here
if(Info.deriv_values[i]==var[varc]) {
if(order[j-1]==2) {
count=1;
c=1;
k=0;
while(count!=0&&(j+c)<=length_rel) {
count=(order[c+j]==3)?--count:++count;
k=(order[c+j]==3)?++k:k;
++c;
}
--c;
if(ope[opec+k]!=1||ope[opec+k]!=2){
CONSOLE_DEBUG("The coefficient of the derivative term contains a non constant term");
}
}else if(order[j+1]==2) {
count=1;
c=2;
k=0;
while(count!=0&&(j+c)<=length_rel){
count=(order[c+j]==3)?--count:++count;
k=(order[c+j]==3)?++k:k;
++c;
}
--c;
if(ope[opec+k]!=1||ope[opec+k]!=2){
CONSOLE_DEBUG("The coefficient of the derivative term contains a non constant term");
}
}
c=1;
count=0;
denom_flag=0;
while(order[j+c]!=4&&(j+c)<=length_rel) {
if(order[c+j]==3) {
++count;
if(ope[opec+count]==4) {
if(count>c-count) {
denom_flag=(denom_flag==0)?1:0;
}
}
}
++c;
}
if(denom_flag==1){
CONSOLE_DEBUG("The derivative is in denominator");
}
c=1;
count=0;
while(order[j+c]!=4&&(j+c)<=length_rel) {
if(order[c+j]==3) {
++count;
if(ope[opec+count]==6) {
if(count>c-count) {
CONSOLE_DEBUG("The derivative is in index");
}
}
}
++c;
}
/* We implement here an algorithm which finds the span of an operator. The span of an operator
is defined as the number of terms the operator links in an expression. We see if the derivative
is in the upper span (the set of terms to the left of an operator in infix form) of the operator,
by using a variable to point at the location of the derivative in a binary representation of the
relation where 0 means a number or variable and 1 means an operator. Then we display an error is
the derivative is raised to a higher/lower power.* /
c=0;
count=-1;
bin_num=0;
pass=0;
/* Need to write code here to check if the derivative is being raised to power 1.
The idea is to locate every ^ operator and see if the item immediately following
it in the infix notation is 1 which does not have any prior connection with any other
operator. * /
/* As a second thought, I think I will segregate each Error case as a function, considering the recursive algorithms used in some of the cases. * /
if(flag==0){
while(order[c]!=4){
++c;
}
for(k=c-1;k>=0;k--) {
if(order[k]==3) {
bin_num+=pow(2,c-k-1);
}
}
point=j;
for(k=c-1;k>=0;k--) {
if(bin_num-pass>0) {
++count;
pass+=pow(2,k);
if(point+k==c-3) {
if(ope[count]==6) {
CONSOLE_DEBUG("The derivative is raised to a power other than one");
} else {

}
} else {

}
}
}
}else {
while(order[c]!=4){
++c;
}
++c;
while(c<=length_rel) {
++c;
}
}
}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message * /
break;
}
}
}
return 1;
}
*/

/* So here it begins */

static int Inspect_Equation(struct Info_abt_deriv Info,int *order,double *var,double *func,int *ope,unsigned long length_rel){
double var_index;
char *left_bin_num,*right_bin_num;
left_bin_num=find_left_bin_number(order,length_rel);
right_bin_num=find_right_bin_number(order,length_rel);
/* We write here an inspection for special cases, like : 3=4+Q(x,y)/x, where is Q(x,y) is a linear function in x */

/* End of special cases */

/* We start inspecting general cases */

flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
/* Write Error catching analysis code here */
var_index=find_variable(Info,var[varc]);
if(var_index!=0){

}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message */
break;
}
}
return 1;
}

void coefficient_match(double *coefficient,struct Info_abt_deriv Info,int *order,double *num,double *var,double *func,int *ope, unsigned long length_rel){
int i,j,k;
double value;
int flag;
int varc=-1,opec=-1,funcc=-1,numc=-1;
int c;
if(Inspect_Equation(Info,order,var,func,ope,length_rel)==1){
for (i=0;i<Info.no_of_deriv;i++){
value=1.0;
flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
if(Info.deriv_values[i]==var[varc]) {
if(order[j-1]==1&&order[j+1]==3) {
if(ope[opec+1]==3) {
value=num[numc];
}
}else if(order[j+1]==1&&order[j+2]==3) {
if(ope[opec+1]==3) {
value=num[numc+1];
}
}else {
while(order[c+j]!=4){
c=1;
while(order[c+j]==2||order[c+j]==1) {
c++;
}
}
}
}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message */
break;
}
}
}
}else {
CONSOLE_DEBUG("Equation cannot be accepted by solver");
}
}

static int coefficient_calculator(struct Instance *i,double *coefficient,struct Info_abt_deriv Info){
struct relation *r;
enum Expr_enum reltype;
unsigned long t; /* the current term in the relation r */
unsigned long num_var; /* the number of variables in the relation r */
unsigned long v; /* loop variable */
int lhs; /* looking at left(=1) or right(=0) hand side of r */
unsigned long length_lhs, length_rhs;
double *num; /* pointer for storing all constants in relation */
double *var; /* pointer for storing all real value of variables in relation */
int *ope; /* pointer for storing all operators in relation */
double *func; /* pointer for storing all functions in relation */
int *order; /* pointer for storing order of all constants, variables and operators in postfix form in relation */
int varc=0,numc=0,orderc=0,opec=0,funcc=0; /* counters for various arrays */
CONST struct relation_term *term;
CONST struct Func *fxnptr;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
CONSOLE_DEBUG("null relation\n");
return -1;
}
num_var = NumberVariables(r);
length_lhs = RelationLength(r, 1);
length_rhs = RelationLength(r, 0);
num=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
var=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
ope=ASC_NEW_ARRAY(int,length_lhs+length_rhs);
func=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
order = ASC_NEW_ARRAY(int,(length_lhs+length_rhs+1));
lhs = 1;
t = 0;

for (v=0; v<length_lhs+length_rhs; v++) {
/* Initializing all entries to 0 */
order[v]=0;
func[v]=0.0;
ope[v]=0;
num[v]=0.0;
var[v]=0.0;
}
order[length_lhs+length_rhs]=0;
while(1) {
if( lhs && (t >= length_lhs) ) {
/* need to switch to the right hand side--if it exists */
if( length_rhs ) {
lhs = t = 0;
order[orderc++]=4;
} else {
/*
We know that (length_lhs+length_rhs>0) and that (length_rhs==0),
the length_lhs must be > 0
*/
coefficient_match(coefficient,Info,order,num,var,func,ope,length_lhs+length_rhs+1);
return 0;
}
} else if( (!lhs) && (t >= length_rhs) ) {
/* we have processed both sides, quit */
coefficient_match(coefficient,Info,order,num,var,func,ope,length_lhs+length_rhs+1);
return 0;
}
term = NewRelationTerm(r, t++, lhs);
switch( RelationTermType(term) ) {
case e_zero:
num[numc++]=0.0;
order[orderc++]=1;
break;
case e_real:
num[numc++]=(double)TermReal(term);
order[orderc++]=1;
break;
case e_int:
num[numc++]=(double)TermInteger(term);
order[orderc++]=1;
break;
case e_var:
var[varc++]= TermVariable(r, term);
order[orderc++]=2;
break;
case e_plus:
ope[opec++]=1;
order[orderc++]=3;
break;
case e_minus:
ope[opec++]=2;
order[orderc++]=3;
break;
case e_times:
ope[opec++]=3;
order[orderc++]=3;
break;
case e_divide:
ope[opec++]=4;
order[orderc++]=3;
break;
case e_uminus:
ope[opec++]=5;
order[orderc++]=3;
break;
case e_power:
ope[opec++]=6;
order[orderc++]=3;
break;
case e_ipower:
ope[opec++]=7;
order[orderc++]=3;
break;
case e_func:
ope[opec++]=8;
order[orderc++]=3;
fxnptr = TermFunc(term);
func[funcc] = FuncEval( fxnptr, func[funcc] );
++funcc;
break;
default:
ASC_PANIC("Unknown relation term type");
break;
}

}
}
</source>

User:Karthik0112358/Coefficient Calculator

2011-07-25T20:59:48Z

Karthik0112358:

<source lang="c">
/* ASCEND modelling environment
Copyright (C) 1997, 2006 Carnegie Mellon University
Copyright (C) 1993, 1994 Joseph James Zaher, Benjamin Andrew Allan
Copyright (C) 1993 Joseph James Zaher
Copyright (C) 1990 Thomas Guthrie Epperly, Karl Michael Westerberg

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA.
*/
/*
KARTHIK C S, June 2011
*/
#include <math.h>
#include "relation_util.h"
#include <ascend/general/ascMalloc.h>
#include <ascend/general/panic.h>
#include "relation_type.h"
#include "expr_types.h"
#include "instance_enum.h"
#include "functype.h"
#include "mathinst.c"
/*------------------------------------------------------------------------------
FINDING COEFFICIENTS OF THE DERIVATIVE TERMS IN A RELATION
*/

/**
Compute the coefficients of the derivative terms in the relation (compiler-side routine)

@param i Instance pointer through which the coefficients of the derivative terms of the relation are found
@param coefficient pointer to a double in which the coefficients shall be stored (must have already been allocated)
@param Info of structure Info_abt_deriv which contains the real value of all the derivative variables

@return 0 on success, and otherwise on failure

Here we compute the coefficients of the derivative terms by first extracting each term.
We then check if its a derivative variable and if so we compute its coefficient by considering the terms previous to it and after it.
In this process we also check if the equation is linear wrt its derivatives. Suitable error messages are displayed if its not.
*/
/* Started reorganizing the entire Inspect_Equation(). Providing modularity for efficiency and flexibility.*/
/*
static int Inspect_Equation(struct Info_abt_deriv Info,int *order,double *var,double *func,int *ope,unsigned long length_rel){
int i,j,k;
int varc=-1,opec=-1,funcc=-1,numc=-1;
int flag,count,c,denom_flag,point;
unsigned long bin_num,pass,new_bin_num;
for (i=0;i<Info.no_of_deriv;i++){
flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
//Write Error catching analysis code here
if(Info.deriv_values[i]==var[varc]) {
if(order[j-1]==2) {
count=1;
c=1;
k=0;
while(count!=0&&(j+c)<=length_rel) {
count=(order[c+j]==3)?--count:++count;
k=(order[c+j]==3)?++k:k;
++c;
}
--c;
if(ope[opec+k]!=1||ope[opec+k]!=2){
CONSOLE_DEBUG("The coefficient of the derivative term contains a non constant term");
}
}else if(order[j+1]==2) {
count=1;
c=2;
k=0;
while(count!=0&&(j+c)<=length_rel){
count=(order[c+j]==3)?--count:++count;
k=(order[c+j]==3)?++k:k;
++c;
}
--c;
if(ope[opec+k]!=1||ope[opec+k]!=2){
CONSOLE_DEBUG("The coefficient of the derivative term contains a non constant term");
}
}
c=1;
count=0;
denom_flag=0;
while(order[j+c]!=4&&(j+c)<=length_rel) {
if(order[c+j]==3) {
++count;
if(ope[opec+count]==4) {
if(count>c-count) {
denom_flag=(denom_flag==0)?1:0;
}
}
}
++c;
}
if(denom_flag==1){
CONSOLE_DEBUG("The derivative is in denominator");
}
c=1;
count=0;
while(order[j+c]!=4&&(j+c)<=length_rel) {
if(order[c+j]==3) {
++count;
if(ope[opec+count]==6) {
if(count>c-count) {
CONSOLE_DEBUG("The derivative is in index");
}
}
}
++c;
}
/* We implement here an algorithm which finds the span of an operator. The span of an operator
is defined as the number of terms the operator links in an expression. We see if the derivative
is in the upper span (the set of terms to the left of an operator in infix form) of the operator,
by using a variable to point at the location of the derivative in a binary representation of the
relation where 0 means a number or variable and 1 means an operator. Then we display an error is
the derivative is raised to a higher/lower power.*/
c=0;
count=-1;
bin_num=0;
pass=0;
/* Need to write code here to check if the derivative is being raised to power 1.
The idea is to locate every ^ operator and see if the item immediately following
it in the infix notation is 1 which does not have any prior connection with any other
operator. */
/* As a second thought, I think I will segregate each Error case as a function, considering the recursive algorithms used in some of the cases. */
if(flag==0){
while(order[c]!=4){
++c;
}
for(k=c-1;k>=0;k--) {
if(order[k]==3) {
bin_num+=pow(2,c-k-1);
}
}
point=j;
for(k=c-1;k>=0;k--) {
if(bin_num-pass>0) {
++count;
pass+=pow(2,k);
if(point+k==c-3) {
if(ope[count]==6) {
CONSOLE_DEBUG("The derivative is raised to a power other than one");
} else {

}
} else {

}
}
}
}else {
while(order[c]!=4){
++c;
}
++c;
while(c<=length_rel) {
++c;
}
}
}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message */
break;
}
}
}
return 1;
}
*/

/* So here it begins */

static int Inspect_Equation(struct Info_abt_deriv Info,int *order,double *var,double *func,int *ope,unsigned long length_rel){
double var_index;
char *left_bin_num,*right_bin_num;
left_bin_num=find_left_bin_number(order,length_rel);
right_bin_num=find_right_bin_number(order,length_rel);
/* We write here an inspection for special cases, like : 3=4+Q(x,y)/x, where is Q(x,y) is a linear function in x */

/* End of special cases */

/* We start inspecting general cases */

flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
/* Write Error catching analysis code here */
var_index=find_variable(Info,var[varc]);
if(var_index!=0){

}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message */
break;
}
}
return 1;
}

void coefficient_match(double *coefficient,struct Info_abt_deriv Info,int *order,double *num,double *var,double *func,int *ope, unsigned long length_rel){
int i,j,k;
double value;
int flag;
int varc=-1,opec=-1,funcc=-1,numc=-1;
int c;
if(Inspect_Equation(Info,order,var,func,ope,length_rel)==1){
for (i=0;i<Info.no_of_deriv;i++){
value=1.0;
flag=0;
for(j=0;j<length_rel;j++){
switch(order[j]){
case 1:
++numc;
break;
case 2:
++varc;
if(Info.deriv_values[i]==var[varc]) {
if(order[j-1]==1&&order[j+1]==3) {
if(ope[opec+1]==3) {
value=num[numc];
}
}else if(order[j+1]==1&&order[j+2]==3) {
if(ope[opec+1]==3) {
value=num[numc+1];
}
}else {
while(order[c+j]!=4){
c=1;
while(order[c+j]==2||order[c+j]==1) {
c++;
}
}
}
}
break;
case 3:
++opec;
break;
case 4:
flag=1;
break;
default:
/* Give Error Message */
break;
}
}
}
}else {
CONSOLE_DEBUG("Equation cannot be accepted by solver");
}
}

static int coefficient_calculator(struct Instance *i,double *coefficient,struct Info_abt_deriv Info){
struct relation *r;
enum Expr_enum reltype;
unsigned long t; /* the current term in the relation r */
unsigned long num_var; /* the number of variables in the relation r */
unsigned long v; /* loop variable */
int lhs; /* looking at left(=1) or right(=0) hand side of r */
unsigned long length_lhs, length_rhs;
double *num; /* pointer for storing all constants in relation */
double *var; /* pointer for storing all real value of variables in relation */
int *ope; /* pointer for storing all operators in relation */
double *func; /* pointer for storing all functions in relation */
int *order; /* pointer for storing order of all constants, variables and operators in postfix form in relation */
int varc=0,numc=0,orderc=0,opec=0,funcc=0; /* counters for various arrays */
CONST struct relation_term *term;
CONST struct Func *fxnptr;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
CONSOLE_DEBUG("null relation\n");
return -1;
}
num_var = NumberVariables(r);
length_lhs = RelationLength(r, 1);
length_rhs = RelationLength(r, 0);
num=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
var=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
ope=ASC_NEW_ARRAY(int,length_lhs+length_rhs);
func=ASC_NEW_ARRAY(double,length_lhs+length_rhs);
order = ASC_NEW_ARRAY(int,(length_lhs+length_rhs+1));
lhs = 1;
t = 0;

for (v=0; v<length_lhs+length_rhs; v++) {
/* Initializing all entries to 0 */
order[v]=0;
func[v]=0.0;
ope[v]=0;
num[v]=0.0;
var[v]=0.0;
}
order[length_lhs+length_rhs]=0;
while(1) {
if( lhs && (t >= length_lhs) ) {
/* need to switch to the right hand side--if it exists */
if( length_rhs ) {
lhs = t = 0;
order[orderc++]=4;
} else {
/*
We know that (length_lhs+length_rhs>0) and that (length_rhs==0),
the length_lhs must be > 0
*/
coefficient_match(coefficient,Info,order,num,var,func,ope,length_lhs+length_rhs+1);
return 0;
}
} else if( (!lhs) && (t >= length_rhs) ) {
/* we have processed both sides, quit */
coefficient_match(coefficient,Info,order,num,var,func,ope,length_lhs+length_rhs+1);
return 0;
}
term = NewRelationTerm(r, t++, lhs);
switch( RelationTermType(term) ) {
case e_zero:
num[numc++]=0.0;
order[orderc++]=1;
break;
case e_real:
num[numc++]=(double)TermReal(term);
order[orderc++]=1;
break;
case e_int:
num[numc++]=(double)TermInteger(term);
order[orderc++]=1;
break;
case e_var:
var[varc++]= TermVariable(r, term);
order[orderc++]=2;
break;
case e_plus:
ope[opec++]=1;
order[orderc++]=3;
break;
case e_minus:
ope[opec++]=2;
order[orderc++]=3;
break;
case e_times:
ope[opec++]=3;
order[orderc++]=3;
break;
case e_divide:
ope[opec++]=4;
order[orderc++]=3;
break;
case e_uminus:
ope[opec++]=5;
order[orderc++]=3;
break;
case e_power:
ope[opec++]=6;
order[orderc++]=3;
break;
case e_ipower:
ope[opec++]=7;
order[orderc++]=3;
break;
case e_func:
ope[opec++]=8;
order[orderc++]=3;
fxnptr = TermFunc(term);
func[funcc] = FuncEval( fxnptr, func[funcc] );
++funcc;
break;
default:
ASC_PANIC("Unknown relation term type");
break;
}

}
}
</source>

User:Karthik0112358

2011-07-25T20:57:46Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## Evaluating the coefficient.
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### Compounding the base coefficient while processing terms in the equation.
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''July 25'''

Was not able to commit to svn due to current LAN problems at college. Will commit tomorrow. For now here is the code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-14T18:55:53Z

Karthik0112358: /* Goals */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## Evaluating the coefficient.
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### Compounding the base coefficient while processing terms in the equation.
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-14T18:55:13Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### If the derivative is raised to a power other than 1.
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## Evaluating the coefficient.
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### Compounding the base coefficient while processing terms in the equation.
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''July 14'''

Wrote code for catching errors in equation where the derivative is raised to a higher/lower power. This was part of Goal 1.3.2. Svn committed the code: http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c .

'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-13T21:57:35Z

Karthik0112358: /* Goals */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### If the derivative is raised to a power other than 1.
### <strike style="color:green">If the derivative is in the denominator.</strike>
### <strike style="color:green">If the derivative is present in the index of any term.</strike>
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## Evaluating the coefficient.
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### Compounding the base coefficient while processing terms in the equation.
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-13T19:33:50Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### If the derivative is present in the index of any term.
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## Evaluating the coefficient.
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### Compounding the base coefficient while processing terms in the equation.
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''July 13'''

I have come up with a simplified algorithm for Goal 1.4.2 after going through the code which simplifies equations. Will try to implement it.

'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-13T18:02:57Z

Karthik0112358: /* Goals */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## <strike style="color:green">Accepting all equations and creating a mass matrix of correct dimensions.</strike>
## Identifying all derivatives in an equation.
### Finding the real values of derivative variables.
### <strike style="color:green">Identifying the derivatives using these real values.</strike>
## Checking if the equation is linear with respect to the derivatives.
### <strike style="color:green">If the coefficient of the derivative contains another variable which is not fixed.</strike>
### <strike style="color:green">If the derivative is raised to a power other than 1.</strike>
### <strike style="color:green">If the derivative is in the denominator.</strike>
### If the derivative is present in the index of any term.
### If the derivative is inside a function.
### If the coefficient of derivative contains a function.
### Display corresponding error messages.
## Evaluating the coefficient.
### <strike style="color:green">Evaluating a base coefficient to the derivative.</strike>
### Compounding the base coefficient while processing terms in the equation.
### <strike style="color:green">Processing the coefficients and entering them to the mass matrix.</strike>
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-13T17:27:11Z

Karthik0112358: /* Goals */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during [[GSOC2011]].

== Goals ==
# Evaluation of mass matrix for a wide range of systems of equations, in the form of a set of CUnit test cases:
## Identifying all derivatives in an equation.
## Checking if the equation is linear with respect to the derivatives.
## Evaluating the coefficient.
# Complete DAE solution of those solutions using RADAU5.

== Progress reports ==
'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-12T23:11:29Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during GSOC2011.

== Goals ==
# I would like to implement the option of generating mass matrix in RADAU5. There are 4 parts to this:
## Identify all terms in equation
## Checking each term for derivative variables
## For terms that have a derivative, checking if all factors are constant-valued
## Evaluating those constant-valued factors and multiplying them together
# The reduced space SQP (rSQP) algorithm has seen many applications in large-scale engineering models. I intend to accept an input and parse it such that the solver can act on it. Further I am going to take up various test cases and check for bugs/inconsistencies. And if time permits I would like to write an optimization algorithm/code which, based on the given input, decides which is the best solver to send the input to.

== Progress reports ==
'''July 12'''

I have decided to get the job done in two parts. First a function called Inspect_Equation, which determines if the equation can be solved by Radau5 and is linear. Once the given set of equations pass this function, the coefficients are evaluated in the coefficient_match function.

'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-07T04:25:35Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during GSOC2011.

== Goals ==
# I would like to implement the option of generating mass matrix in RADAU5. There are 4 parts to this:
## Identify all terms in equation
## Checking each term for derivative variables
## For terms that have a derivative, checking if all factors are constant-valued
## Evaluating those constant-valued factors and multiplying them together
# The reduced space SQP (rSQP) algorithm has seen many applications in large-scale engineering models. I intend to accept an input and parse it such that the solver can act on it. Further I am going to take up various test cases and check for bugs/inconsistencies. And if time permits I would like to write an optimization algorithm/code which, based on the given input, decides which is the best solver to send the input to.

== Progress reports ==
'''July 6'''

I have some svn commits:
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/compiler/coefficient_calculate.c
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.h
# http://code.ascend4.org/viewvc/code/branches/karthik/ascend/system/mass_matrix.c

One more function in progress. Will add that too ASAP.

'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-02T20:54:18Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during GSOC2011.

== Goals ==
# I would like to implement the option of generating mass matrix in RADAU5. There are 4 parts to this:
## Identify all terms in equation
## Checking each term for derivative variables
## For terms that have a derivative, checking if all factors are constant-valued
## Evaluating those constant-valued factors and multiplying them together
# The reduced space SQP (rSQP) algorithm has seen many applications in large-scale engineering models. I intend to accept an input and parse it such that the solver can act on it. Further I am going to take up various test cases and check for bugs/inconsistencies. And if time permits I would like to write an optimization algorithm/code which, based on the given input, decides which is the best solver to send the input to.

== Progress reports ==
'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

* John Pye suggested I concentrate only on linear equations in y'. This reduces my job to give errors in every other case. I am thinking of trying to read if the coefficients of derivatives are either algebraic variables or constants. Otherwise I will display an error message for now. John Pye asked me to display helpful messages along with errors. I will work on that right at the next stage.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-02T00:40:22Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during GSOC2011.

== Goals ==
# I would like to implement the option of generating mass matrix in RADAU5. There are 4 parts to this:
## Identify all terms in equation
## Checking each term for derivative variables
## For terms that have a derivative, checking if all factors are constant-valued
## Evaluating those constant-valued factors and multiplying them together
# The reduced space SQP (rSQP) algorithm has seen many applications in large-scale engineering models. I intend to accept an input and parse it such that the solver can act on it. Further I am going to take up various test cases and check for bugs/inconsistencies. And if time permits I would like to write an optimization algorithm/code which, based on the given input, decides which is the best solver to send the input to.

== Progress reports ==
'''July 1'''

* I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

* So currently I am looking at a way to implement this piece of code, I had written a few days back: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()]. I need to tweak it into [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] so that I can identify if a term has a derivative. They rest is already done.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-07-01T23:55:02Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during GSOC2011.

== Goals ==
# I would like to implement the option of generating mass matrix in RADAU5. There are 4 parts to this:
## Identify all terms in equation
## Checking each term for derivative variables
## For terms that have a derivative, checking if all factors are constant-valued
## Evaluating those constant-valued factors and multiplying them together
# The reduced space SQP (rSQP) algorithm has seen many applications in large-scale engineering models. I intend to accept an input and parse it such that the solver can act on it. Further I am going to take up various test cases and check for bugs/inconsistencies. And if time permits I would like to write an optimization algorithm/code which, based on the given input, decides which is the best solver to send the input to.

== Progress reports ==
'''July 1'''

I just found out that during execution, the relations are stored in a simplified manner. As in if we have an equation:

(20+9)*6*dx_dt[2]= ((3.0+1)*dx_dt[1]) + 4*x[1] + 7/x[2]

Then it gets reprocessed as:

174*dx_dt[2]= 4.0*dx_dt[1] + 4*x[1] + 7/x[2]

So, Evaluation of coefficient is solved pre-hand. I do not need to worry about this. The equations are simplified and stored in relation structure.

'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358/Coefficient Calculator

2011-06-30T10:58:26Z

Karthik0112358:

<source lang="c">
#define INTEG_OTHER_VAR -1L
#define INTEG_ALGEBRAIC_VAR 0L
#define INTEG_STATE_VAR 1L
int Coefficient_Calculator(struct Instance *i,double *coefficient){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
long index, type;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
// the current term in the relation r
unsigned long t;
// the number of variables in the relation r
unsigned long num_var;
// the index of the variable we are looking at
unsigned long v;
// looking at left(=1) or right(=0) hand side of r
int lhs;
// the memory for the stacks
double *stacks;
// height of each stack
unsigned long stack_height;
// the top position in the stacks
long s = -1;
unsigned long length_lhs, length_rhs;
CONST struct relation_term *term;
CONST struct Func *fxnptr;
num_var = NumberVariables(r);
length_lhs = RelationLength(r, 1);
length_rhs = RelationLength(r, 0);
if( (length_lhs + length_rhs) == 0 ) {
for( v = 0; v < num_var; v++ ) coefficient[v] = 0.0;
*residual = 0.0;
return 0;
}
else {
stack_height = 1 + MAX(length_lhs,length_rhs);
}
//creating stacks
stacks = tmpalloc_array(((num_var+1)*stack_height),double);
if( stacks == NULL ) return 1;
#define res_stack(s) stacks[(s)]
#define coeff_stack(v,s) stacks[((v)*stack_height)+(s)]
lhs = 1;
t = 0;
while(1) {
if( lhs && (t >= length_lhs) ) {
if( length_rhs ) {
lhs = t = 0;
}
else {
for( v = 1; v <= num_var; v++ ) coefficient[v-1] = coeff_stack(v,s);
return 0;
}
}
else if( (!lhs) && (t >= length_rhs) ) {
if( length_lhs ) {
for( v = 1; v <= num_var; v++ ) {
coefficient[v-1] = coeff_stack(v,s-1) - coeff_stack(v,s);
}
return 0;
}
else {
for( v = 1; v <= num_var; v++ ) {
coefficient[v-1] = -coeff_stack(v,s);
}
return 0;
}
}
term = NewRelationTerm(r, t++, lhs);
/*
// Here I need something to take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure.
// Let me assume its done. Let me call it info.
type = Classify_Var(info,&index);
if(type==INTEG_ALGEBRAIC_VAR){
// It is an algebraic variable (solver variable)
}else if(type==INTEG_OTHER_VAR){
// It is an independent variable
}else if(type>=INTEG_STATE_VAR){
if(type == 1){
// It is one of the states.One of y_i
}else if(type == 2){
// Detects it as first order derivative. Write suitable code for determining coefficient here.
}else{
// Error message for higher order derivatives.
}
}
*/
switch( RelationTermType(term) ) {
case e_zero:
case e_real:
case e_int:
break;
case e_var:
//write code here
break;
case e_plus:
case e_minus:
case e_times:
case e_divide:
case e_uminus:
case e_power:
case e_ipower:
break;
case e_func:
break;
}
}
#undef grad_stack
#undef res_stack
}
</source>

User:Karthik0112358/coefficient find

2011-06-30T08:16:22Z

Karthik0112358:

<source lang="c">
//This is just a function. I am not sure where to place it (either in a separate place or with in the previous skeletal code).
int coefficient_find(struct rel_relation *rel, const var_filter_t *filter,real64 *coefficients,int32 *variables,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
real64 *coefficient;
int status;
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);
vlist = rel_incidence_list(rel);
*count = 0;
coefficient = (real64 *)rel_tmpalloc(len*sizeof(real64));
assert(coefficient !=NULL);
status =(int32)Coefficient_Calculator(rel_instance(rel),coefficient);
for (c=0; c < len; c++) {
if (var_apply_filter(vlist[c],filter)) {
variables[*count] = var_sindex(vlist[c]);
coefficients[*count] = coefficient[c];
(*count)++;
}
}
}
</source>

User:Karthik0112358

2011-06-30T07:19:03Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during GSOC2011.

== Goals ==
# I would like to implement the option of generating mass matrix in RADAU5. There are 4 parts to this:
## Identify all terms in equation
## Checking each term for derivative variables
## For terms that have a derivative, checking if all factors are constant-valued
## Evaluating those constant-valued factors and multiplying them together
# The reduced space SQP (rSQP) algorithm has seen many applications in large-scale engineering models. I intend to accept an input and parse it such that the solver can act on it. Further I am going to take up various test cases and check for bugs/inconsistencies. And if time permits I would like to write an optimization algorithm/code which, based on the given input, decides which is the best solver to send the input to.

== Progress reports ==
'''June 30'''

Implementation of the pseudo-code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-06-29T03:28:19Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during GSOC2011.

== Goals ==
# I would like to implement the option of generating mass matrix in RADAU5. There are 4 parts to this:
## Identify all terms in equation
## Checking each term for derivative variables
## For terms that have a derivative, checking if all factors are constant-valued
## Evaluating those constant-valued factors and multiplying them together
# The reduced space SQP (rSQP) algorithm has seen many applications in large-scale engineering models. I intend to accept an input and parse it such that the solver can act on it. Further I am going to take up various test cases and check for bugs/inconsistencies. And if time permits I would like to write an optimization algorithm/code which, based on the given input, decides which is the best solver to send the input to.

== Progress reports ==
'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-06-29T03:26:07Z

Karthik0112358: /* Progress reports */

== Progress reports ==
'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested to consider more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-06-29T03:24:52Z

Karthik0112358: /* Progress reports */

== Progress reports ==
'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator
# After evaluating the entire relation, if a particular derivative was not found, then by default it will be assigned a coefficient of 0.

Again this was the basic outline. After discussing with John Pye, he suggested I considered more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-06-29T03:22:31Z

Karthik0112358: /* Progress reports */

== Progress reports ==
'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:
# So the code for reading each equation and extracting each term is written in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]. So I start here at the point where I have each term.
# I write a switch case which considers cases based on the type of the relation term. However each term processed is stored in an structure in a particular way. All numbers are stored in an floating point array, all variables in a character array, all operators in an enum and and array to maintain the order of entry of these terms.
## Its a real number
## If its a variable, then:
### If identified as a term containing a derivative, then I evaluate the coefficient the following way:
#### Since we have the relation evaluated in postfix manner, I run backwards in the array which contains the order, to find the last collection of terms which makes sense, as in numbers separated properly by operator, etc. I evaluate this to be the coefficient.
## Its an operator

Again this was the basic outline. After discussing with John Pye, he suggested I considered more cases and I will build on the above pseudo-code.

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-06-29T01:38:19Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during GSOC2011.

== Goals ==
# I would like to implement the option of generating mass matrix in RADAU5. There are 4 parts to this:
## Identify all terms in equation
## Checking each term for derivative variables
## For terms that have a derivative, checking if all factors are constant-valued
## Evaluating those constant-valued factors and multiplying them together
# The reduced space SQP (rSQP) algorithm has seen many applications in large-scale engineering models. I intend to accept an input and parse it such that the solver can act on it. Further I am going to take up various test cases and check for bugs/inconsistencies. And if time permits I would like to write an optimization algorithm/code which, based on the given input, decides which is the best solver to send the input to.

== Progress reports ==
'''June 29'''

So I am updating here some Pseudo-Code regarding the approach at the lowest level:

'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-06-29T00:45:54Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during GSOC2011.

== Goals ==
# I would like to implement the option of generating mass matrix in RADAU5. There are 4 parts to this:
## Identify all terms in equation
## Checking each term for derivative variables
## For terms that have a derivative, checking if all factors are constant-valued
## Evaluating those constant-valued factors and multiplying them together
# The reduced space SQP (rSQP) algorithm has seen many applications in large-scale engineering models. I intend to accept an input and parse it such that the solver can act on it. Further I am going to take up various test cases and check for bugs/inconsistencies. And if time permits I would like to write an optimization algorithm/code which, based on the given input, decides which is the best solver to send the input to.

== Progress reports ==
'''June 28'''

So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]

User:Karthik0112358

2011-06-29T00:45:23Z

Karthik0112358: /* Progress reports */

'''C S Karthik''' is an undergraduate at IIT-Bombay and is working on addition of an rSQP optimiser for ASCEND during GSOC2011.

== Goals ==
# I would like to implement the option of generating mass matrix in RADAU5. There are 4 parts to this:
## Identify all terms in equation
## Checking each term for derivative variables
## For terms that have a derivative, checking if all factors are constant-valued
## Evaluating those constant-valued factors and multiplying them together
# The reduced space SQP (rSQP) algorithm has seen many applications in large-scale engineering models. I intend to accept an input and parse it such that the solver can act on it. Further I am going to take up various test cases and check for bugs/inconsistencies. And if time permits I would like to write an optimization algorithm/code which, based on the given input, decides which is the best solver to send the input to.

== Progress reports ==
'''June 28'''
So what am I able to code uptill now? The following have been accomplished:
# I am able to read each equation independently.
# I am able to segregate each term. I am able to identify them as numbers, operators or variables.
# I am able to find an index for all variables. The algebraic come first followed by the differential.
What are the problems to be addressed?
# I am able to capture coefficients of all the terms. But how do I separate the differential terms from the algebraic ones? If only there was a way I knew to find the number of differential or algebraic variables involved (ascend/integrator has some code which addresses this. But it uses variable_var structure).

'''June 25'''

Some more doxy searches. I am assuming code written on June 24 to be correct and proceed with exploiting var_variable structure.

So here is an idea. To understand the working of relation_term structure, I add print statements in {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}} and try to see how the data members interact.

Apparently, Expr_enum is there for abstraction or atleast it seems so. I do not see any other way out other than the code I wrote yesterday. Need some suggestion here. As a last resort in case John Pye does not agree with my previous idea, I will have to brute force every equation into a particular way by moving terms across (which John Pye did not like).

'''June 24'''

I am writing skeletal code for Goal Part 1.1 and 1.2. Will remove it if John Pye tells me it is not apt.

So I have added some code here: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

Further I have written a function needed for above code here: [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()].

I went through a lot of doxy pages, but I was unable to find a way by which I could take data from relation_term structure's term and pass it to Classify_Var() which accepts var_variable structure. I need some assistance here. If I am able to find a way then Goals: 1.1 and 1.2 would be over.

PS: All function references used in [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()] and [http://ascend4.org/User:Karthik0112358/Classify_Var Classify_Var()] are either from ascend/compiler or ascend/system and none of ascend/integrator are used.

'''June 23'''

Today is more like a "No-Coding-day". I plan to spend the entire day studying all the references John Pye has given me over the last 2 days. Trying to understand expression evaluation data structures to greater depths. Will report more.

# [http://ascend4.org/images/7/77/Ascendimpl.pdf Implementation of an Ascend Interpreter]: Ascend is an object oriented language and hence the concept of dealing with instances. A tree data structure was chosen so that parent-child linkage could be exploited for effective storage and referencing. It is followed by explanation of various functionalities - same, alike, arrays in ASCEND. Base types, Relations are discussed. After Parsing, we finally come to the main topic- Instantiation. There is stress on the fact that ASCEND executes in a line by line fashion. The Multi-Pass Instantiator seems to have solved the problem of the interpreter's capability to allow multiple passes by storage of unexecuted instructions in instance data structure. The explanation provided through an algorithm is excellent demonstration. Final Note: Although gave me nice insight, not useful for resolving problem at hand.

'''June 21'''

Finally I have been able to reach the lowest level for coding this mass matrix. It involves rewriting {{doxy|dc/d30/a00508_source.html|RelationEvaluateResidualGradientSafe()}}. The code as stated below requires some understanding. John Pye had provided some references. Will see if they are related and may help me.

Hopefully the last of the skeletal code: [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()].

So here is some explanation of the intent of [http://ascend4.org/User:Karthik0112358/Coefficient_Calculator Coefficient_Calculator()]: I have assumed the equation looks like Q(x,y,y')=0. I have tried to find the length of the relation and get each term out. I have dealt with finishing cases also such as when both lhs and rhs are processed or when pointers are passed to top of stack. I would like to add a switch case for various terms which would be preceded by the following code segment:
<source lang="c">
term = NewRelationTerm(r, t++, lhs);
</source>

'''June 20'''

I have worked on a skeletal code (this is an addition to previous skeletal code- in other words providing some flesh to the skeleton) where I try to determine a row entry of the mass matrix: [http://ascend4.org/User:Karthik0112358/coefficient_find coefficient_find()].

Again here I have tried to get a required version of relman_diff2() of {{src|ascend/system/relman.c}}. So in crux the entire task boils down to rewriting RelationCalcResidGradSafe() of {{src|ascend/compiler/relation_util.c}} into a function which gets the coefficients of the derivative terms - Coefficient_Calculator(). I will get a code out for that.

As of now I have a partial code for Coefficient_Calculator():
<source lang="c">
int Coefficient_Calculator(struct Instance *i){
struct relation *r;
enum Expr_enum reltype;
int dummy_int;
r = (struct relation *)GetInstanceRelation(i, &reltype);
if( r == NULL ) {
ERROR_REPORTER_HERE(ASC_PROG_ERR,"null relation\n");
return -1;
}
//At this point of writing the code, I realize the significance of why John Pye had asked me to understand expression-evaluation data structures. I need to write cases for reltype. I need some thinking.
}
</source>

As part of understanding {{doxy|d8/d7f/a00787.html#ga87d7fb16138e4b6b8ae5a1372b18c81b|Expr_enum}} better, I would like to do a bit of "doxy search". Will get back with some update.

Simultaneously I will also write some test code file in compiler/test/ and try to see if I can get to know the contents of the structure. I will report worthy findings here.

'''June 19'''

So here is some skeletal-code: [http://ascend4.org/User:Karthik0112358/massmatrix massmatrix()]. This is code for one of the top layers.

I know I haven't followed the coding style of Ascend. I will modify code ASAP once other parts fall into place.

'''June 17'''

After giving it some thought, I think the structure of the mass matrix function should look more like system_jacobian() which is present in [http://www.ascend4.org/doxy/d1/d56/a00707_source.html#l00028 jacobian.c] in ascend/system. Will sketch a pseudo code out after better clarity.

I am trying to see how to utilize {{doxy|d5/d0f/a00308.html|System Structure}}, as I see potential information regarding extracting coefficients of ''y''''i''''' '' in equation. Since I am asked not to access the structure directly, I am looking through its implementation in slv_client.h.

After reading {{src|ascend/system/slv_client.h}} comments (which I might add are very descriptive and helpful), I realize the importance of the rel_relation structure as this contains the equation data. I have stopped trying to understand struct system and focus back on rel_relation.

So here is a plan. I replicate the entire set of codes required to find the Jacobian matrix. Now from what I know entries to the Jacobian are done row wise. Now Jacobian(''mXn'' matrix) is found out for functions ''F'' : '''R'''''n'' → '''R'''''m''. However with the mass matrix problem, I am dealing with equations. So, my idea is to manipulate these equations into functions and replace the content of the (''i'',''j'') entry (by replacing the code which writes the content) into Jacobian with a different set of code, so that we get desirable result. Will get back on this.

'''June 16'''
* Reading relman_diff2() and trying to understand what are the input variables, which header to include, etc. Got some nice help from http://www.ascend4.org/doxy/d0/d7e/a00770.html#ga9469a6f8ff5a7d0eec8a1cad74732fdf. Came up with a vague code structure:
<source lang="c">
#include <ascend/compiler/rel_blackbox.h>
#include <ascend/compiler/relation.h>
#include <ascend/compiler/relation_util.h>
#include <ascend/compiler/relation_io.h>
#include "mass_matrix.h"
#include "slv_server.h"
#define IPTR(i) ((struct Instance *)(i))
#define KILL 0 /* compile dead code if kill = 1 */
#define REIMPLEMENT 0 /* code that needs to be reimplemented */
#define rel_tmpalloc_array(nelts,type) \
((nelts) > 0 ? (type *)tmpalloc((nelts)*sizeof(type)) : NULL)
static double dsolve_scratch = 0.0; /* some workspace */
#define DSOLVE_TOLERANCE 1.0e-08 /* no longer needed */
#define BROKENKIRK 0
/* return 0 on success (derivatives, variables and count are output vars too) */
int massmatrix(struct rel_relation *rel, const var_filter_t *filter
,real64 *derivatives, int32 *variables
,int32 *count){
const struct var_variable **vlist=NULL;
int32 len,c;
int status;
//CONSOLE_DEBUG("In Function: relman_diff2");
assert(rel!=NULL && filter!=NULL);
len = rel_n_incidences(rel);//this gives me the length of incidence- which I think is the number of columns of mass matrix
vlist = rel_incidence_list(rel);//have to write rel_mass_matrix() which basically does the same thing
*count = 0;

for (c=0; c < len; c++) {
//write the stuff here

}
return status;
}
</source>

'''June 15'''
* Trying to understand about expression-evaluation data structures by reading the following c code: ascend/system/relman.c.
* Re-reading [http://ascend4.org/Developer%27s_Manual Developer's Manual] for better clarity.
* Checked out contents of [http://trilinos.sandia.gov/packages/moocho/ Moocho] and broadly read basic documentation.
* Installing MOOCHO: Downloaded [http://trilinos.sandia.gov/download/trilinos-10.6.html trilinos-10.6.4-Source.tar.gz]. As first step of the [http://trilinos.sandia.gov/Trilinos10CMakeQuickstart.txt installation], I downloaded [http://www.cmake.org/cmake/resources/software.html CMake]. In the last step of Installation of CMake, I got the following error:

CMake Error at cmake_install.cmake:36 (FILE):
file cannot create directory: /usr/local/doc/cmake-2.8. Maybe need
administrative privileges.

make: *** [install] Error 1

Further on trying to install Trilinos, with the following commands, I got the following error :

~/SOME_BUILD_DIR$ cmake \

> -D CMAKE_BUILD_TYPE:STRING=DEBUG \

> -D Trilinos ENABLE <moocho>:BOOL=ON \

> -D Trilinos_ENABLE_TESTS:BOOL=ON \

> -D DART_TESTING_TIMEOUT:STRING=600 \

> $EXTRA_ARGS \

> {TRILINOS_HOME}

bash: moocho: No such file or directory

I contacted Bartlett, Roscoe A (rabartl@sandia.gov) via email regarding this problem. Hoping for an early reply.

'''June 6 - June 12'''

Finding a temporary fix for the mass matrix problem. I have split the task as to finding solution to 2 problems:
* (i) Making sure algebraic equations are being sent to solver.
* (ii) Writing a feasible mass matrix function to generate the mass matrix. This depends on (i).

Regarding Solving Part (i), I made an outside link and was able to capture all the variables involved. Trying to use them to find total number of equations. In completing part (ii) I am facing "INSUFFICIENT MEMORY" problem. Trying to fix that too. I am at present able to count total number of variables, solver variables, independent variables and number of differential equations. I would like to figure out a way to count number of free variables.

I have been able to find a solution to part(i), but it has 2 constraints,
* If number of total variables>>total number of equations, then the max number of substeps has to be reduced.
* The solution involves providing data outside given data structures and thus cannot employed as it is to ascend.

As far as part (ii) goes, there seems to be a simple fix. I am trying to figure it out through Valgrind's Memory loss method.

'''May 30 - June 5'''
* Completed reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''May 23 - May 29'''
* Continue reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].

'''Prior to 23 May 2011:'''

Related to rSQP:
* Started reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO]. However was later redirected to chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms" from Winston, 1994, 3rd (or a later) Ed., Duxbury Press (Belmont, California) as a preliminary reading for mathematical background.
* Completed reading chapter 12 (Nonlinear programming) of "Operations Research: Applications and Algorithms".
* Re-reading [http://trilinos.sandia.gov/packages/docs/r10.6/packages/moocho/doc/html/MoochoOverview.pdf Mathematical and High-Level Overview of MOOCHO].
* Revisited theory behind the Simplex Algorithm from "Introduction to Algorithms", 3rd Edition, Page 864-879 authored by Cormen, Leisersin, Rivest, Stein.

Related to Radau5:
* Investigated code ascend/integrator/integrator.h and ascend/integrator/integrator.c to understand the data structures used.
* Devised and tried implementation of various for the mass matrix problem in solvers/radau5/asc_radau5.c.
* Settled on the idea of replacing neq with total number of equations as compared to the previous implementation of number of states.
[[Category:GSOC2011]]