DOPRI5 - Revision history

Jpye at 10:25, 19 May 2010

2010-05-19T10:25:13Z

← Older revision		Revision as of 10:25, 19 May 2010
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	'''DOPRI5''' is an explicit one-step integration code that we are currently working on connecting with ASCEND. It was [http://www.unige.ch/~hairer/software.html originally written] in Fortran by [http://www.unige.ch/~hairer Ernst Hairer] & [http://www.unige.ch/~wanner/ Gerhard Wanner] at the Université de Genève, later translated to C by J Colinge. The [http://www.unige.ch/~hairer/prog/nonstiff/cprog.tar C code version] describes itself as follows:		'''DOPRI5''' is an explicit one-step integration code that we are currently working on connecting with ASCEND. It was [http://www.unige.ch/~hairer/software.html originally written] in Fortran by [http://www.unige.ch/~hairer Ernst Hairer] & [http://www.unige.ch/~wanner/ Gerhard Wanner] at the Université de Genève, later translated to C by J Colinge. The [http://www.unige.ch/~hairer/prog/nonstiff/cprog.tar C code version] describes itself as follows:


	<blockquote>This code computes the numerical solution of a system of first order ordinary		<blockquote>This code computes the numerical solution of a system of first order ordinary
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	We are implementing a wrapper for the essentially unmodified '''DOPRI5''' code as an additional choice for integration algorithms for a couple of reasons:		We are implementing a wrapper for the essentially unmodified '''DOPRI5''' code as an additional choice for integration algorithms for a couple of reasons:


	* a one-step explicit integrator is the simplest kind and in many ways should be the starting point for solving ODE problems; if difficulties are detected, then using a one-step explicit integrator might help to indicate the nature of those difficulties.		* a one-step explicit integrator is the simplest kind and in many ways should be the starting point for solving ODE problems; if difficulties are detected, then using a one-step explicit integrator might help to indicate the nature of those difficulties.
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	The '''DOPRI5''' code is recommended by [http://www.cs.ubc.ca/~ascher/ Uri Ascher] and [http://www.me.ucsb.edu/dept_site/people/new_faculty_pages/petzold_page.html Linda Petzold] in their book ''Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations'', SIAM press, 1998.		The '''DOPRI5''' code is recommended by [http://www.cs.ubc.ca/~ascher/ Uri Ascher] and [http://www.me.ucsb.edu/dept_site/people/new_faculty_pages/petzold_page.html Linda Petzold] in their book ''Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations'', SIAM press, 1998.


	Changes made to the '''DOPRI5''' code were simply those required to allow a 'user pointer' to be passed through '''DOPRI5''' to the FcnEqnDiff and SolTrait hook functions, allowing '''DOPRI5''' to interface with ASCEND without the need for global variables. These changes can be browsed online at {{srcdir\|solvers/dopri5}}.		Changes made to the '''DOPRI5''' code were simply those required to allow a 'user pointer' to be passed through '''DOPRI5''' to the FcnEqnDiff and SolTrait hook functions, allowing '''DOPRI5''' to interface with ASCEND without the need for global variables. These changes can be browsed online at {{srcdir\|solvers/dopri5}}.


	== Trying it ==		== Trying it ==
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	'''DOPRI5''' will be available in standard ASCEND distributions but will need to be <tt>IMPORT</tt>ed before it wil be accessible. In other words, if writing an ODE model, add the following at the start:		'''DOPRI5''' will be available in standard ASCEND distributions but will need to be <tt>IMPORT</tt>ed before it wil be accessible. In other words, if writing an ODE model, add the following at the start:

	<source lang="a4c">IMPORT ~~"johnpye/~~dopri5~~/dopri5";~~</source>		<source lang="a4c">IMPORT "dopri5"</source>

	The option ''''DOPRI5'''' should then appear in the Integrator dialog, at least in the PyGTK GUI.		The option ''''DOPRI5'''' should then appear in the Integrator dialog, at least in the PyGTK GUI.
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	The sample Arenstorf Orbit problem is available in the Model Library as {{src\|models/test/dopri5/aren.a4c}}. The expected solution of this model is that at x=xend, the values of y[0] and y[1] are equal to their starting values. The FORTRAN implementation gives this result accurate to 1e-5 absolute.		The sample Arenstorf Orbit problem is available in the Model Library as {{src\|models/test/dopri5/aren.a4c}}. The expected solution of this model is that at x=xend, the values of y[0] and y[1] are equal to their starting values. The FORTRAN implementation gives this result accurate to 1e-5 absolute.

	~~<div class="thumb tnone"><div class="thumbinner" style="width:402px;">~~[[Image:Diverging.png]] ~~<div class="thumbcaption"><div class="magnify">[[File:Diverging.png\|<img src="/skins/common/images/magnify-clip.png" width="15" height="11" alt="" />]]</div>~~Arenstorf orbit integrated with the experimental '''DOPRI5''' integrator. We're still working on why this solution is diverging as currently shown.~~</div></div></div>~~		[[Image:Diverging.png]]
			Arenstorf orbit integrated with the experimental '''DOPRI5''' integrator. We're still working on why this solution is diverging as currently shown.

	== Parameters ==		== Parameters ==
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	Parameters can be set using the Integrator window, or using Python scripts.		Parameters can be set using the Integrator window, or using Python scripts.


	== TODO ==		== TODO ==

Jpye at 10:16, 19 May 2010

2010-05-19T10:16:59Z

← Older revision		Revision as of 10:16, 19 May 2010
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			'''DOPRI5''' is an explicit one-step integration code that we are currently working on connecting with ASCEND. It was [http://www.unige.ch/~hairer/software.html originally written] in Fortran by [http://www.unige.ch/~hairer Ernst Hairer] & [http://www.unige.ch/~wanner/ Gerhard Wanner] at the Université de Genève, later translated to C by J Colinge. The [http://www.unige.ch/~hairer/prog/nonstiff/cprog.tar C code version] describes itself as follows:


			<blockquote>This code computes the numerical solution of a system of first order ordinary
			differential equations y'=f(x,y). It uses an explicit Runge-Kutta method of
			order (4)5 due to Dormand & Prince with step size control and dense output.</blockquote>

			We are implementing a wrapper for the essentially unmodified '''DOPRI5''' code as an additional choice for integration algorithms for a couple of reasons:


			* a one-step explicit integrator is the simplest kind and in many ways should be the starting point for solving ODE problems; if difficulties are detected, then using a one-step explicit integrator might help to indicate the nature of those difficulties.
			* '''DOPRI5''' can detect likely stiff problems and alert the user in that case
			* it is stable and well-tested
			* it provides predictor-corrector adjustment of step length
			* it allows us to test the design of our Integrator API and identify shortcomings in it
			* the developer has a problem that he is concerned may not be as stiff as he thought it was; this will aid in understanding whether or not that is true.

			As part of this work, the ability to load [[external Integrators]] at runtime will be provided. At present, this facility has not yet been implemented [[External_Solvers\|for Solvers]], but that solver code is older and may require more re-working before that is possible. So this will provide some useful experience before that is attempted.

			The '''DOPRI5''' code is recommended by [http://www.cs.ubc.ca/~ascher/ Uri Ascher] and [http://www.me.ucsb.edu/dept_site/people/new_faculty_pages/petzold_page.html Linda Petzold] in their book ''Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations'', SIAM press, 1998.


			Changes made to the '''DOPRI5''' code were simply those required to allow a 'user pointer' to be passed through '''DOPRI5''' to the FcnEqnDiff and SolTrait hook functions, allowing '''DOPRI5''' to interface with ASCEND without the need for global variables. These changes can be browsed online at {{srcdir\|solvers/dopri5}}.


			== Trying it ==

			<font color="red">Implementation of '''DOPRI5''' is basically complete, but this integrator needs careful testing. Also there is some discrepancy between our integration results and the results of test problem that hasn't yet been resolved (see plot below).</font>
			'''DOPRI5''' will be available in standard ASCEND distributions but will need to be <tt>IMPORT</tt>ed before it wil be accessible. In other words, if writing an ODE model, add the following at the start:

			<source lang="a4c">IMPORT "johnpye/dopri5/dopri5";</source>

			The option ''''DOPRI5'''' should then appear in the Integrator dialog, at least in the PyGTK GUI.

			The sample Arenstorf Orbit problem is available in the Model Library as {{src\|models/test/dopri5/aren.a4c}}. The expected solution of this model is that at x=xend, the values of y[0] and y[1] are equal to their starting values. The FORTRAN implementation gives this result accurate to 1e-5 absolute.

			<div class="thumb tnone"><div class="thumbinner" style="width:402px;">[[Image:Diverging.png]] <div class="thumbcaption"><div class="magnify">[[File:Diverging.png\|<img src="/skins/common/images/magnify-clip.png" width="15" height="11" alt="" />]]</div>Arenstorf orbit integrated with the experimental '''DOPRI5''' integrator. We're still working on why this solution is diverging as currently shown.</div></div></div>

			== Parameters ==

			Parameters for the '''DOPRI5''' integrator will be documented here as they are implemented. The full set of '''possible''' parameters can be seen in the source code for {{src\|solvers/dopri5/dopri5.h}}

			* '''<tt>tolvect</tt>''': whether to use a single tolerance for all variables (0), or whether to use a per-variable tolerances (1). Default is 1.
			* '''<tt>rtol</tt>''': relative tolerance for all variables if <tt>tolvect</tt> is 0. Otherwise ignored.
			* '''<tt>atol</tt>''': absolute tolerance for all variables if <tt>tolvect</tt> is 0. Otherwise ignored.
			* '''<tt>nstiff</tt>''': number of steps considered stiff. If too many (><tt>nstiff</tt>) small steps are being required by the predictor-corrector pair, integration will be aborted with a warning about a likely stiff problem. Default is 1000.

			The initial and maximum step size can also be configured using the standard [[Integrator API]] functions.

			Parameters can be set using the Integrator window, or using Python scripts.


			== TODO ==

			Need to fix asc_dopri5.c to make use of the <tt>contd5</tt> function provided by '''DOPRI5''' for polynomial interpolation within timesteps. Currently that code is disabled.

			See also [[LSODE]] and [[IDA]].

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

WikiSysop at 03:45, 14 May 2010

2010-05-14T03:45:57Z

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WikiSysop: Created page with '{{missing}} Category:Development Cateogry:Documentation'

2010-05-14T03:45:46Z

Created page with '{{missing}} Category:Development Cateogry:Documentation'

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