Goal seeking solver - Revision history

Jpye at 08:09, 29 March 2011

2011-03-29T08:09:29Z

← Older revision		Revision as of 08:09, 29 March 2011
Line 1:		Line 1:
	{{experimental}}		{{experimental}}
	There is a single-variable goal-seeking solver -- similar to the 'goal seek' functionality in spreadsheets -- implemented as an [[EXTERNAL]] method call. The solver used is a Brent solver<~~sup id="_ref-0" class="reference"~~>~~<a href="#_note-0" title="">[1]<~~/~~a><~~/~~sup><sup id="_ref-0" class="reference"><a href="#_note-0" title="">[1]<~~/a></~~sup~~>, and it can easily wrap around any other solver that can be invoked from a METHOD declaration (currently this includes [[QRSlv]] only). Below is a working example from {{src\|models/test/brent.a4c}}, also reproduced below.		There is a single-variable goal-seeking solver -- similar to the 'goal seek' functionality in spreadsheets -- implemented as an [[EXTERNAL]] method call. The solver used is a Brent solver<ref>http://en.wikipedia.org/wiki/Brent%27s_method</ref>, and it can easily wrap around any other solver that can be invoked from a METHOD declaration (currently this includes [[QRSlv]] only). Below is a working example from {{src\|models/test/brent.a4c}}, also reproduced below.

	The line		The line

Jpye at 08:08, 29 March 2011

2011-03-29T08:08:47Z

← Older revision		Revision as of 08:08, 29 March 2011
Line 1:		Line 1:
	~~<div class="pageexperimental">''This page documents an '''~~experimental''' feature. You can help out by '''testing it''' and <span class="plainlinks">[http://ascendwiki.cheme.cmu.edu/index.php?title=Goal_seeking_solver&action=edit recording]</span> your experiences.''</div>		{{experimental}}
	There is a single-variable goal-seeking solver -- similar to the 'goal seek' functionality in spreadsheets -- implemented as an [[EXTERNAL]] method call. The solver used is a Brent solver<sup id="_ref-0" class="reference"><a href="#_note-0" title="">[1]</a></sup><sup id="_ref-0" class="reference"><a href="#_note-0" title="">[1]</a></sup>, and it can easily wrap around any other solver that can be invoked from a METHOD declaration (currently this includes [[QRSlv]] only). Below is a working example from {{src\|models/test/brent.a4c}}, also reproduced below.		There is a single-variable goal-seeking solver -- similar to the 'goal seek' functionality in spreadsheets -- implemented as an [[EXTERNAL]] method call. The solver used is a Brent solver<sup id="_ref-0" class="reference"><a href="#_note-0" title="">[1]</a></sup><sup id="_ref-0" class="reference"><a href="#_note-0" title="">[1]</a></sup>, and it can easily wrap around any other solver that can be invoked from a METHOD declaration (currently this includes [[QRSlv]] only). Below is a working example from {{src\|models/test/brent.a4c}}, also reproduced below.

Line 54:		Line 54:

	== References ==		== References ==
			<references/>



	~~[[Category:Experimental]]~~
	[[Category:Documentation]]		[[Category:Documentation]]

Jpye at 07:52, 26 May 2010

2010-05-26T07:52:28Z

← Older revision		Revision as of 07:52, 26 May 2010
Line 16:		Line 16:
	Note that one could in principle nest several of these brent routines, but only by using submodels, and by carefully choosing what to put in your <tt>solve</tt> method.		Note that one could in principle nest several of these brent routines, but only by using submodels, and by carefully choosing what to put in your <tt>solve</tt> method.

	<source lang="a4c">REQUIRE ~~"~~atoms.a4l~~&quot~~;;		<source lang="a4c">
			REQUIRE "atoms.a4l";
	IMPORT ~~"~~johnpye/brent/brent~~"~~;		IMPORT "johnpye/brent/brent";
			IMPORT "sensitivity/solve";
	IMPORT ~~"~~sensitivity/solve~~"~~;

	MODEL brent1;		MODEL brent1;

UploadBot: Restored page from Google Cache, uploaded by John Pye

2010-05-13T13:38:29Z

Restored page from Google Cache, uploaded by John Pye

New page

<div class="pageexperimental">''This page documents an '''experimental''' feature. You can help out by '''testing it''' and <span class="plainlinks">[http://ascendwiki.cheme.cmu.edu/index.php?title=Goal_seeking_solver&action=edit recording]</span> your experiences.''</div>
There is a single-variable goal-seeking solver -- similar to the 'goal seek' functionality in spreadsheets -- implemented as an [[EXTERNAL]] method call. The solver used is a Brent solver<sup id="_ref-0" class="reference"><a href="#_note-0" title="">[1]</a></sup><sup id="_ref-0" class="reference"><a href="#_note-0" title="">[1]</a></sup>, and it can easily wrap around any other solver that can be invoked from a METHOD declaration (currently this includes [[QRSlv]] only). Below is a working example from {{src|models/test/brent.a4c}}, also reproduced below.

The line

<source lang="a4c">EXTERNAL brent(SELF,err,x);</source>

can be interpreted as saying 'solve the variable <tt>err</tt> for a value of 0, by varying the value of <tt>x</tt> between <tt>x.lower_bound</tt> and <tt>x.upper_bound</tt>'. For <tt>brent</tt> to work, you must provide a method named <tt>solve</tt>; the recommended contents of that method is as shown below, using the <tt>senstivity/solve</tt> module. This method is called each <tt>err(x)</tt> needs to be evaluated.

The variable <tt>err</tt> will be considered 'solved' when the absolute value of <tt>err</tt> is less than 1.0e-7 times <tt>err.nominal</tt>. If you want to alter the solving tolerance, the only easy way to do so is to modify <tt>err.nominal</tt>: the value 1.0e-7 is hard-wired into the <tt>brent</tt> routine.

The most common problem when using this routine is that you won't have properly 'bracketed' your solution. At the bounds of <tt>x</tt>, the sign of the variable <tt>err</tt> must be opposite; ie the variable must certainly have a root, if the relationship <tt>err(x)</tt> is continuous.

Note that one could in principle nest several of these brent routines, but only by using submodels, and by carefully choosing what to put in your <tt>solve</tt> method.

<source lang="a4c">REQUIRE "atoms.a4l";

IMPORT "johnpye/brent/brent";

IMPORT "sensitivity/solve";

MODEL brent1;
x IS_A solver_var;

y IS_A solver_var;
z IS_A solver_var;
y = -x^2 - 4*x + 4;

z = sin(x);
err IS_A solver_var;
err = y - z;

METHODS
METHOD on_load;
FIX x;
x.lower_bound := 0;

x.upper_bound := 10;
err.nominal := 1;

RUN intersect;
END on_load;
METHOD solve;

EXTERNAL do_solve(SELF);
END solve;
METHOD intersect;

EXTERNAL brent(SELF,err,x);
END intersect;

END brent1;</source>

== References ==

[[Category:Experimental]]
[[Category:Documentation]]