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view main/odepkg/inst/ode23d.m @ 9386:982dcd268ac4 octave-forge
Somebody crahes odepkg/inst - old files have been checked in. I reverted the files of this directory to my local copy: revision 8337.
author | treichl |
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date | Sun, 29 Jan 2012 11:42:54 +0000 |
parents | 55c73f24f0ee |
children | 31a8ff1c879c |
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%# Copyright (C) 2008-2011, Thomas Treichl <treichl@users.sourceforge.net> %# OdePkg - A package for solving ordinary differential equations and more %# %# 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 of the License, 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, see <http://www.gnu.org/licenses/>. %# -*- texinfo -*- %# @deftypefn {Function File} {[@var{}] =} ode23d (@var{@@fun}, @var{slot}, @var{init}, @var{lags}, @var{hist}, [@var{opt}], [@var{par1}, @var{par2}, @dots{}]) %# @deftypefnx {Command} {[@var{sol}] =} ode23d (@var{@@fun}, @var{slot}, @var{init}, @var{lags}, @var{hist}, [@var{opt}], [@var{par1}, @var{par2}, @dots{}]) %# @deftypefnx {Command} {[@var{t}, @var{y}, [@var{xe}, @var{ye}, @var{ie}]] =} ode23d (@var{@@fun}, @var{slot}, @var{init}, @var{lags}, @var{hist}, [@var{opt}], [@var{par1}, @var{par2}, @dots{}]) %# %# This function file can be used to solve a set of non--stiff delay differential equations (non--stiff DDEs) with a modified version of the well known explicit Runge--Kutta method of order (2,3). %# %# If this function is called with no return argument then plot the solution over time in a figure window while solving the set of DDEs that are defined in a function and specified by the function handle @var{@@fun}. The second input argument @var{slot} is a double vector that defines the time slot, @var{init} is a double vector that defines the initial values of the states, @var{lags} is a double vector that describes the lags of time, @var{hist} is a double matrix and describes the history of the DDEs, @var{opt} can optionally be a structure array that keeps the options created with the command @command{odeset} and @var{par1}, @var{par2}, @dots{} can optionally be other input arguments of any type that have to be passed to the function defined by @var{@@fun}. %# %# In other words, this function will solve a problem of the form %# @example %# dy/dt = fun (t, y(t), y(t-lags(1), y(t-lags(2), @dots{}))) %# y(slot(1)) = init %# y(slot(1)-lags(1)) = hist(1), y(slot(1)-lags(2)) = hist(2), @dots{} %# @end example %# %# If this function is called with one return argument then return the solution @var{sol} of type structure array after solving the set of DDEs. The solution @var{sol} has the fields @var{x} of type double column vector for the steps chosen by the solver, @var{y} of type double column vector for the solutions at each time step of @var{x}, @var{solver} of type string for the solver name and optionally the extended time stamp information @var{xe}, the extended solution information @var{ye} and the extended index information @var{ie} all of type double column vector that keep the informations of the event function if an event function handle is set in the option argument @var{opt}. %# %# If this function is called with more than one return argument then return the time stamps @var{t}, the solution values @var{y} and optionally the extended time stamp information @var{xe}, the extended solution information @var{ye} and the extended index information @var{ie} all of type double column vector. %# %# For example: %# @itemize @minus %# @item %# the following code solves an anonymous implementation of a chaotic behavior %# %# @example %# fcao = @@(vt, vy, vz) [2 * vz / (1 + vz^9.65) - vy]; %# %# vopt = odeset ("NormControl", "on", "RelTol", 1e-3); %# vsol = ode23d (fcao, [0, 100], 0.5, 2, 0.5, vopt); %# %# vlag = interp1 (vsol.x, vsol.y, vsol.x - 2); %# plot (vsol.y, vlag); legend ("fcao (t,y,z)"); %# @end example %# %# @item %# to solve the following problem with two delayed state variables %# %# @example %# d y1(t)/dt = -y1(t) %# d y2(t)/dt = -y2(t) + y1(t-5) %# d y3(t)/dt = -y3(t) + y2(t-10)*y1(t-10) %# @end example %# %# one might do the following %# %# @example %# function f = fun (t, y, yd) %# f(1) = -y(1); %% y1' = -y1(t) %# f(2) = -y(2) + yd(1,1); %% y2' = -y2(t) + y1(t-lags(1)) %# f(3) = -y(3) + yd(2,2)*yd(1,2); %% y3' = -y3(t) + y2(t-lags(2))*y1(t-lags(2)) %# endfunction %# T = [0,20] %# res = ode23d (@@fun, T, [1;1;1], [5, 10], ones (3,2)); %# @end example %# %# @end itemize %# @end deftypefn %# %# @seealso{odepkg} function [varargout] = ode23d (vfun, vslot, vinit, vlags, vhist, varargin) if (nargin == 0) %# Check number and types of all input arguments help ('ode23d'); error ('OdePkg:InvalidArgument', ... 'Number of input arguments must be greater than zero'); elseif (nargin < 5) print_usage; elseif (~isa (vfun, 'function_handle')) error ('OdePkg:InvalidArgument', ... 'First input argument must be a valid function handle'); elseif (~isvector (vslot) || length (vslot) < 2) error ('OdePkg:InvalidArgument', ... 'Second input argument must be a valid vector'); elseif (~isvector (vinit) || ~isnumeric (vinit)) error ('OdePkg:InvalidArgument', ... 'Third input argument must be a valid numerical value'); elseif (~isvector (vlags) || ~isnumeric (vlags)) error ('OdePkg:InvalidArgument', ... 'Fourth input argument must be a valid numerical value'); elseif ~(isnumeric (vhist) || isa (vhist, 'function_handle')) error ('OdePkg:InvalidArgument', ... 'Fifth input argument must either be numeric or a function handle'); elseif (nargin >= 6) if (~isstruct (varargin{1})) %# varargin{1:len} are parameters for vfun vodeoptions = odeset; vfunarguments = varargin; elseif (length (varargin) > 1) %# varargin{1} is an OdePkg options structure vopt vodeoptions = odepkg_structure_check (varargin{1}, 'ode23d'); vfunarguments = {varargin{2:length(varargin)}}; else %# if (isstruct (varargin{1})) vodeoptions = odepkg_structure_check (varargin{1}, 'ode23d'); vfunarguments = {}; end else %# if (nargin == 5) vodeoptions = odeset; vfunarguments = {}; end %# Start preprocessing, have a look which options have been set in %# vodeoptions. Check if an invalid or unused option has been set and %# print warnings. vslot = vslot(:)'; %# Create a row vector vinit = vinit(:)'; %# Create a row vector vlags = vlags(:)'; %# Create a row vector %# Check if the user has given fixed points of time if (length (vslot) > 2), vstepsizegiven = true; %# Step size checking else vstepsizegiven = false; end %# Get the default options that can be set with 'odeset' temporarily vodetemp = odeset; %# Implementation of the option RelTol has been finished. This option %# can be set by the user to another value than default value. if (isempty (vodeoptions.RelTol) && ~vstepsizegiven) vodeoptions.RelTol = 1e-6; warning ('OdePkg:InvalidOption', ... 'Option "RelTol" not set, new value %f is used', vodeoptions.RelTol); elseif (~isempty (vodeoptions.RelTol) && vstepsizegiven) warning ('OdePkg:InvalidOption', ... 'Option "RelTol" will be ignored if fixed time stamps are given'); %# This implementation has been added to odepkg_structure_check.m %# elseif (~isscalar (vodeoptions.RelTol) && ~vstepsizegiven) %# error ('OdePkg:InvalidOption', ... %# 'Option "RelTol" must be set to a scalar value for this solver'); end %# Implementation of the option AbsTol has been finished. This option %# can be set by the user to another value than default value. if (isempty (vodeoptions.AbsTol) && ~vstepsizegiven) vodeoptions.AbsTol = 1e-6; warning ('OdePkg:InvalidOption', ... 'Option "AbsTol" not set, new value %f is used', vodeoptions.AbsTol); elseif (~isempty (vodeoptions.AbsTol) && vstepsizegiven) warning ('OdePkg:InvalidOption', ... 'Option "AbsTol" will be ignored if fixed time stamps are given'); else %# create column vector vodeoptions.AbsTol = vodeoptions.AbsTol(:); end %# Implementation of the option NormControl has been finished. This %# option can be set by the user to another value than default value. if (strcmp (vodeoptions.NormControl, 'on')), vnormcontrol = true; else vnormcontrol = false; end %# Implementation of the option NonNegative has been finished. This %# option can be set by the user to another value than default value. if (~isempty (vodeoptions.NonNegative)) if (isempty (vodeoptions.Mass)), vhavenonnegative = true; else vhavenonnegative = false; warning ('OdePkg:InvalidOption', ... 'Option "NonNegative" will be ignored if mass matrix is set'); end else vhavenonnegative = false; end %# Implementation of the option OutputFcn has been finished. This %# option can be set by the user to another value than default value. if (isempty (vodeoptions.OutputFcn) && nargout == 0) vodeoptions.OutputFcn = @odeplot; vhaveoutputfunction = true; elseif (isempty (vodeoptions.OutputFcn)), vhaveoutputfunction = false; else vhaveoutputfunction = true; end %# Implementation of the option OutputSel has been finished. This %# option can be set by the user to another value than default value. if (~isempty (vodeoptions.OutputSel)), vhaveoutputselection = true; else vhaveoutputselection = false; end %# Implementation of the option Refine has been finished. This option %# can be set by the user to another value than default value. if (isequal (vodeoptions.Refine, vodetemp.Refine)), vhaverefine = true; else vhaverefine = false; end %# Implementation of the option Stats has been finished. This option %# can be set by the user to another value than default value. %# Implementation of the option InitialStep has been finished. This %# option can be set by the user to another value than default value. if (isempty (vodeoptions.InitialStep) && ~vstepsizegiven) vodeoptions.InitialStep = abs (vslot(1,1) - vslot(1,2)) / 10; vodeoptions.InitialStep = vodeoptions.InitialStep / 10^vodeoptions.Refine; warning ('OdePkg:InvalidOption', ... 'Option "InitialStep" not set, new value %f is used', vodeoptions.InitialStep); end %# Implementation of the option MaxStep has been finished. This option %# can be set by the user to another value than default value. if (isempty (vodeoptions.MaxStep) && ~vstepsizegiven) vodeoptions.MaxStep = abs (vslot(1,1) - vslot(1,length (vslot))) / 10; %# vodeoptions.MaxStep = vodeoptions.MaxStep / 10^vodeoptions.Refine; warning ('OdePkg:InvalidOption', ... 'Option "MaxStep" not set, new value %f is used', vodeoptions.MaxStep); end %# Implementation of the option Events has been finished. This option %# can be set by the user to another value than default value. if (~isempty (vodeoptions.Events)), vhaveeventfunction = true; else vhaveeventfunction = false; end %# The options 'Jacobian', 'JPattern' and 'Vectorized' will be ignored %# by this solver because this solver uses an explicit Runge-Kutta %# method and therefore no Jacobian calculation is necessary if (~isequal (vodeoptions.Jacobian, vodetemp.Jacobian)) warning ('OdePkg:InvalidOption', ... 'Option "Jacobian" will be ignored by this solver'); end if (~isequal (vodeoptions.JPattern, vodetemp.JPattern)) warning ('OdePkg:InvalidOption', ... 'Option "JPattern" will be ignored by this solver'); end if (~isequal (vodeoptions.Vectorized, vodetemp.Vectorized)) warning ('OdePkg:InvalidOption', ... 'Option "Vectorized" will be ignored by this solver'); end if (~isequal (vodeoptions.NewtonTol, vodetemp.NewtonTol)) warning ('OdePkg:InvalidArgument', ... 'Option "NewtonTol" will be ignored by this solver'); end if (~isequal (vodeoptions.MaxNewtonIterations,... vodetemp.MaxNewtonIterations)) warning ('OdePkg:InvalidArgument', ... 'Option "MaxNewtonIterations" will be ignored by this solver'); end %# Implementation of the option Mass has been finished. This option %# can be set by the user to another value than default value. if (~isempty (vodeoptions.Mass) && ismatrix (vodeoptions.Mass)) vhavemasshandle = false; vmass = vodeoptions.Mass; %# constant mass elseif (isa (vodeoptions.Mass, 'function_handle')) vhavemasshandle = true; %# mass defined by a function handle else %# no mass matrix - creating a diag-matrix of ones for mass vhavemasshandle = false; %# vmass = diag (ones (length (vinit), 1), 0); end %# Implementation of the option MStateDependence has been finished. %# This option can be set by the user to another value than default %# value. if (strcmp (vodeoptions.MStateDependence, 'none')) vmassdependence = false; else vmassdependence = true; end %# Other options that are not used by this solver. Print a warning %# message to tell the user that the option(s) is/are ignored. if (~isequal (vodeoptions.MvPattern, vodetemp.MvPattern)) warning ('OdePkg:InvalidOption', ... 'Option "MvPattern" will be ignored by this solver'); end if (~isequal (vodeoptions.MassSingular, vodetemp.MassSingular)) warning ('OdePkg:InvalidOption', ... 'Option "MassSingular" will be ignored by this solver'); end if (~isequal (vodeoptions.InitialSlope, vodetemp.InitialSlope)) warning ('OdePkg:InvalidOption', ... 'Option "InitialSlope" will be ignored by this solver'); end if (~isequal (vodeoptions.MaxOrder, vodetemp.MaxOrder)) warning ('OdePkg:InvalidOption', ... 'Option "MaxOrder" will be ignored by this solver'); end if (~isequal (vodeoptions.BDF, vodetemp.BDF)) warning ('OdePkg:InvalidOption', ... 'Option "BDF" will be ignored by this solver'); end %# Starting the initialisation of the core solver ode23d vtimestamp = vslot(1,1); %# timestamp = start time vtimelength = length (vslot); %# length needed if fixed steps vtimestop = vslot(1,vtimelength); %# stop time = last value if (~vstepsizegiven) vstepsize = vodeoptions.InitialStep; vminstepsize = (vtimestop - vtimestamp) / (1/eps); else %# If step size is given then use the fixed time steps vstepsize = abs (vslot(1,1) - vslot(1,2)); vminstepsize = eps; %# vslot(1,2) - vslot(1,1) - eps; end vretvaltime = vtimestamp; %# first timestamp output if (vhaveoutputselection) %# first solution output vretvalresult = vinit(vodeoptions.OutputSel); else vretvalresult = vinit; end %# Initialize the OutputFcn if (vhaveoutputfunction) feval (vodeoptions.OutputFcn, vslot', ... vretvalresult', 'init', vfunarguments{:}); end %# Initialize the History if (isnumeric (vhist)) vhmat = vhist; vhavehistnumeric = true; else %# it must be a function handle for vcnt = 1:length (vlags); vhmat(:,vcnt) = feval (vhist, (vslot(1)-vlags(vcnt)), vfunarguments{:}); end vhavehistnumeric = false; end %# Initialize DDE variables for history calculation vsaveddetime = [vtimestamp - vlags, vtimestamp]'; vsaveddeinput = [vhmat, vinit']'; vsavedderesult = [vhmat, vinit']'; %# Initialize the EventFcn if (vhaveeventfunction) odepkg_event_handle (vodeoptions.Events, vtimestamp, ... {vretvalresult', vhmat}, 'init', vfunarguments{:}); end vpow = 1/3; %# 20071016, reported by Luis Randez va = [ 0, 0, 0; %# The Runge-Kutta-Fehlberg 2(3) coefficients 1/2, 0, 0; %# Coefficients proved on 20060827 -1, 2, 0]; %# See p.91 in Ascher & Petzold vb2 = [0; 1; 0]; %# 2nd and 3rd order vb3 = [1/6; 2/3; 1/6]; %# b-coefficients vc = sum (va, 2); %# The solver main loop - stop if the endpoint has been reached vcntloop = 2; vcntcycles = 1; vu = vinit; vk = vu' * zeros(1,3); vcntiter = 0; vunhandledtermination = true; while ((vtimestamp < vtimestop && vstepsize >= vminstepsize)) %# Hit the endpoint of the time slot exactely if ((vtimestamp + vstepsize) > vtimestop) vstepsize = vtimestop - vtimestamp; end %# Estimate the three results when using this solver for j = 1:3 vthetime = vtimestamp + vc(j,1) * vstepsize; vtheinput = vu' + vstepsize * vk(:,1:j-1) * va(j,1:j-1)'; %# Claculate the history values (or get them from an external %# function) that are needed for the next step of solving if (vhavehistnumeric) for vcnt = 1:length (vlags) %# Direct implementation of a 'quadrature cubic Hermite interpolation' %# found at the Faculty for Mathematics of the University of Stuttgart %# http://mo.mathematik.uni-stuttgart.de/inhalt/aussage/aussage1269 vnumb = find (vthetime - vlags(vcnt) >= vsaveddetime); velem = min (vnumb(end), length (vsaveddetime) - 1); vstep = vsaveddetime(velem+1) - vsaveddetime(velem); vdiff = (vthetime - vlags(vcnt) - vsaveddetime(velem)) / vstep; vsubs = 1 - vdiff; %# Calculation of the coefficients for the interpolation algorithm vua = (1 + 2 * vdiff) * vsubs^2; vub = (3 - 2 * vdiff) * vdiff^2; vva = vstep * vdiff * vsubs^2; vvb = -vstep * vsubs * vdiff^2; vhmat(:,vcnt) = vua * vsaveddeinput(velem,:)' + ... vub * vsaveddeinput(velem+1,:)' + ... vva * vsavedderesult(velem,:)' + ... vvb * vsavedderesult(velem+1,:)'; end else %# the history must be a function handle for vcnt = 1:length (vlags) vhmat(:,vcnt) = feval ... (vhist, vthetime - vlags(vcnt), vfunarguments{:}); end end if (vhavemasshandle) %# Handle only the dynamic mass matrix, if (vmassdependence) %# constant mass matrices have already vmass = feval ... %# been set before (if any) (vodeoptions.Mass, vthetime, vtheinput, vfunarguments{:}); else %# if (vmassdependence == false) vmass = feval ... %# then we only have the time argument (vodeoptions.Mass, vthetime, vfunarguments{:}); end vk(:,j) = vmass \ feval ... (vfun, vthetime, vtheinput, vhmat, vfunarguments{:}); else vk(:,j) = feval ... (vfun, vthetime, vtheinput, vhmat, vfunarguments{:}); end end %# Compute the 2nd and the 3rd order estimation y2 = vu' + vstepsize * (vk * vb2); y3 = vu' + vstepsize * (vk * vb3); if (vhavenonnegative) vu(vodeoptions.NonNegative) = abs (vu(vodeoptions.NonNegative)); y2(vodeoptions.NonNegative) = abs (y2(vodeoptions.NonNegative)); y3(vodeoptions.NonNegative) = abs (y3(vodeoptions.NonNegative)); end vSaveVUForRefine = vu; %# Calculate the absolute local truncation error and the acceptable error if (~vstepsizegiven) if (~vnormcontrol) vdelta = y3 - y2; vtau = max (vodeoptions.RelTol * vu', vodeoptions.AbsTol); else vdelta = norm (y3 - y2, Inf); vtau = max (vodeoptions.RelTol * max (norm (vu', Inf), 1.0), ... vodeoptions.AbsTol); end else %# if (vstepsizegiven == true) vdelta = 1; vtau = 2; end %# If the error is acceptable then update the vretval variables if (all (vdelta <= vtau)) vtimestamp = vtimestamp + vstepsize; vu = y3'; %# MC2001: the higher order estimation as "local extrapolation" vretvaltime(vcntloop,:) = vtimestamp; if (vhaveoutputselection) vretvalresult(vcntloop,:) = vu(vodeoptions.OutputSel); else vretvalresult(vcntloop,:) = vu; end vcntloop = vcntloop + 1; vcntiter = 0; %# Update DDE values for next history calculation vsaveddetime(end+1) = vtimestamp; vsaveddeinput(end+1,:) = vtheinput'; vsavedderesult(end+1,:) = vu; %# Call plot only if a valid result has been found, therefore this %# code fragment has moved here. Stop integration if plot function %# returns false if (vhaveoutputfunction) if (vhaverefine) %# Do interpolation for vcnt = 0:vodeoptions.Refine %# Approximation between told and t vapproxtime = (vcnt + 1) * vstepsize / (vodeoptions.Refine + 2); vapproxvals = vSaveVUForRefine' + vapproxtime * (vk * vb3); if (vhaveoutputselection) vapproxvals = vapproxvals(vodeoptions.OutputSel); end feval (vodeoptions.OutputFcn, (vtimestamp - vstepsize) + vapproxtime, ... vapproxvals, [], vfunarguments{:}); end end vpltret = feval (vodeoptions.OutputFcn, vtimestamp, ... vretvalresult(vcntloop-1,:)', [], vfunarguments{:}); if (vpltret), vunhandledtermination = false; break; end end %# Call event only if a valid result has been found, therefore this %# code fragment has moved here. Stop integration if veventbreak is %# true if (vhaveeventfunction) vevent = ... odepkg_event_handle (vodeoptions.Events, vtimestamp, ... {vu(:), vhmat}, [], vfunarguments{:}); if (~isempty (vevent{1}) && vevent{1} == 1) vretvaltime(vcntloop-1,:) = vevent{3}(end,:); vretvalresult(vcntloop-1,:) = vevent{4}(end,:); vunhandledtermination = false; break; end end end %# If the error is acceptable ... %# Update the step size for the next integration step if (~vstepsizegiven) %# vdelta may be 0 or even negative - could be an iteration problem vdelta = max (vdelta, eps); vstepsize = min (vodeoptions.MaxStep, ... min (0.8 * vstepsize * (vtau ./ vdelta) .^ vpow)); elseif (vstepsizegiven) if (vcntloop < vtimelength) vstepsize = vslot(1,vcntloop-1) - vslot(1,vcntloop-2); end end %# Update counters that count the number of iteration cycles vcntcycles = vcntcycles + 1; %# Needed for postprocessing vcntiter = vcntiter + 1; %# Needed to find iteration problems %# Stop solving because the last 1000 steps no successful valid %# value has been found if (vcntiter >= 5000) error (['Solving has not been successful. The iterative', ... ' integration loop exited at time t = %f before endpoint at', ... ' tend = %f was reached. This happened because the iterative', ... ' integration loop does not find a valid solution at this time', ... ' stamp. Try to reduce the value of "InitialStep" and/or', ... ' "MaxStep" with the command "odeset".\n'], vtimestamp, vtimestop); end end %# The main loop %# Check if integration of the ode has been successful if (vtimestamp < vtimestop) if (vunhandledtermination == true) error (['Solving has not been successful. The iterative', ... ' integration loop exited at time t = %f', ... ' before endpoint at tend = %f was reached. This may', ... ' happen if the stepsize grows smaller than defined in', ... ' vminstepsize. Try to reduce the value of "InitialStep" and/or', ... ' "MaxStep" with the command "odeset".\n'], vtimestamp, vtimestop); else warning ('OdePkg:HideWarning', ... ['Solver has been stopped by a call of "break" in', ... ' the main iteration loop at time t = %f before endpoint at', ... ' tend = %f was reached. This may happen because the @odeplot', ... ' function returned "true" or the @event function returned "true".'], ... vtimestamp, vtimestop); end end %# Postprocessing, do whatever when terminating integration algorithm if (vhaveoutputfunction) %# Cleanup plotter feval (vodeoptions.OutputFcn, vtimestamp, ... vretvalresult(vcntloop-1,:)', 'done', vfunarguments{:}); end if (vhaveeventfunction) %# Cleanup event function handling odepkg_event_handle (vodeoptions.Events, vtimestamp, ... {vretvalresult(vcntloop-1,:), vhmat}, 'done', vfunarguments{:}); end %# Print additional information if option Stats is set if (strcmp (vodeoptions.Stats, 'on')) vhavestats = true; vnsteps = vcntloop-2; %# vcntloop from 2..end vnfailed = (vcntcycles-1)-(vcntloop-2)+1; %# vcntcycl from 1..end vnfevals = 3*(vcntcycles-1); %# number of ode evaluations vndecomps = 0; %# number of LU decompositions vnpds = 0; %# number of partial derivatives vnlinsols = 0; %# no. of solutions of linear systems %# Print cost statistics if no output argument is given if (nargout == 0) vmsg = fprintf (1, 'Number of successful steps: %d', vnsteps); vmsg = fprintf (1, 'Number of failed attempts: %d', vnfailed); vmsg = fprintf (1, 'Number of function calls: %d', vnfevals); end else vhavestats = false; end if (nargout == 1) %# Sort output variables, depends on nargout varargout{1}.x = vretvaltime; %# Time stamps are saved in field x varargout{1}.y = vretvalresult; %# Results are saved in field y varargout{1}.solver = 'ode23d'; %# Solver name is saved in field solver if (vhaveeventfunction) varargout{1}.ie = vevent{2}; %# Index info which event occured varargout{1}.xe = vevent{3}; %# Time info when an event occured varargout{1}.ye = vevent{4}; %# Results when an event occured end if (vhavestats) varargout{1}.stats = struct; varargout{1}.stats.nsteps = vnsteps; varargout{1}.stats.nfailed = vnfailed; varargout{1}.stats.nfevals = vnfevals; varargout{1}.stats.npds = vnpds; varargout{1}.stats.ndecomps = vndecomps; varargout{1}.stats.nlinsols = vnlinsols; end elseif (nargout == 2) varargout{1} = vretvaltime; %# Time stamps are first output argument varargout{2} = vretvalresult; %# Results are second output argument elseif (nargout == 5) varargout{1} = vretvaltime; %# Same as (nargout == 2) varargout{2} = vretvalresult; %# Same as (nargout == 2) varargout{3} = []; %# LabMat doesn't accept lines like varargout{4} = []; %# varargout{3} = varargout{4} = []; varargout{5} = []; if (vhaveeventfunction) varargout{3} = vevent{3}; %# Time info when an event occured varargout{4} = vevent{4}; %# Results when an event occured varargout{5} = vevent{2}; %# Index info which event occured end %# else nothing will be returned, varargout{1} undefined end %! # We are using a "pseudo-DDE" implementation for all tests that %! # are done for this function. We also define an Events and a %! # pseudo-Mass implementation. For further tests we also define a %! # reference solution (computed at high accuracy) and an OutputFcn. %!function [vyd] = fexp (vt, vy, vz, varargin) %! vyd(1,1) = exp (- vt) - vz(1); %# The DDEs that are %! vyd(2,1) = vy(1) - vz(2); %# used for all examples %!function [vval, vtrm, vdir] = feve (vt, vy, vz, varargin) %! vval = fexp (vt, vy, vz); %# We use the derivatives %! vtrm = zeros (2,1); %# don't stop solving here %! vdir = ones (2,1); %# in positive direction %!function [vval, vtrm, vdir] = fevn (vt, vy, vz, varargin) %! vval = fexp (vt, vy, vz); %# We use the derivatives %! vtrm = ones (2,1); %# stop solving here %! vdir = ones (2,1); %# in positive direction %!function [vmas] = fmas (vt, vy, vz, varargin) %! vmas = [1, 0; 0, 1]; %# Dummy mass matrix for tests %!function [vmas] = fmsa (vt, vy, vz, varargin) %! vmas = sparse ([1, 0; 0, 1]); %# A dummy sparse matrix %!function [vref] = fref () %# The reference solution %! vref = [0.12194462133618, 0.01652432423938]; %!function [vout] = fout (vt, vy, vflag, varargin) %! if (regexp (char (vflag), 'init') == 1) %! if (any (size (vt) ~= [2, 1])) error ('"fout" step "init"'); end %! elseif (isempty (vflag)) %! if (any (size (vt) ~= [1, 1])) error ('"fout" step "calc"'); end %! vout = false; %! elseif (regexp (char (vflag), 'done') == 1) %! if (any (size (vt) ~= [1, 1])) error ('"fout" step "done"'); end %! else error ('"fout" invalid vflag'); %! end %! %! %# Turn off output of warning messages for all tests, turn them on %! %# again if the last test is called %!error %# input argument number one %! warning ('off', 'OdePkg:InvalidOption'); %! B = ode23d (1, [0 5], [1; 0], 1, [1; 0]); %!error %# input argument number two %! B = ode23d (@fexp, 1, [1; 0], 1, [1; 0]); %!error %# input argument number three %! B = ode23d (@fexp, [0 5], 1, 1, [1; 0]); %!error %# input argument number four %! B = ode23d (@fexp, [0 5], [1; 0], [1; 1], [1; 0]); %!error %# input argument number five %! B = ode23d (@fexp, [0 5], [1; 0], 1, 1); %!test %# one output argument %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0]); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %! assert (isfield (vsol, 'solver')); %! assert (vsol.solver, 'ode23d'); %!test %# two output arguments %! [vt, vy] = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0]); %! assert ([vt(end), vy(end,:)], [5, fref], 1e-1); %!test %# five output arguments and no Events %! [vt, vy, vxe, vye, vie] = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0]); %! assert ([vt(end), vy(end,:)], [5, fref], 1e-1); %! assert ([vie, vxe, vye], []); %!test %# anonymous function instead of real function %! faym = @(vt, vy, vz) [exp(-vt) - vz(1); vy(1) - vz(2)]; %! vsol = ode23d (faym, [0 5], [1; 0], 1, [1; 0]); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# extra input arguments passed trhough %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], 'KL'); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# empty OdePkg structure *but* extra input arguments %! vopt = odeset; %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt, 12, 13, 'KL'); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!error %# strange OdePkg structure %! vopt = struct ('foo', 1); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %!test %# AbsTol option %! vopt = odeset ('AbsTol', 1e-5); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# AbsTol and RelTol option %! vopt = odeset ('AbsTol', 1e-7, 'RelTol', 1e-7); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# RelTol and NormControl option %! vopt = odeset ('AbsTol', 1e-7, 'NormControl', 'on'); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], .5e-1); %!test %# NonNegative for second component %! vopt = odeset ('NonNegative', 1); %! vsol = ode23d (@fexp, [0 2.5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [2.5, 0.001, 0.237], 1e-1); %!test %# Details of OutputSel and Refine can't be tested %! vopt = odeset ('OutputFcn', @fout, 'OutputSel', 1, 'Refine', 5); %! vsol = ode23d (@fexp, [0 2.5], [1; 0], 1, [1; 0], vopt); %!test %# Stats must add further elements in vsol %! vopt = odeset ('Stats', 'on'); %! vsol = ode23d (@fexp, [0 2.5], [1; 0], 1, [1; 0], vopt); %! assert (isfield (vsol, 'stats')); %! assert (isfield (vsol.stats, 'nsteps')); %!test %# InitialStep option %! vopt = odeset ('InitialStep', 1e-8); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# MaxStep option %! vopt = odeset ('MaxStep', 1e-2); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# Events option add further elements in vsol %! vopt = odeset ('Events', @feve); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert (isfield (vsol, 'ie')); %! assert (vsol.ie, [1; 1]); %! assert (isfield (vsol, 'xe')); %! assert (isfield (vsol, 'ye')); %!test %# Events option, now stop integration %! warning ('off', 'OdePkg:HideWarning'); %! vopt = odeset ('Events', @fevn, 'NormControl', 'on'); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.ie, vsol.xe, vsol.ye], ... %! [1.0000, 2.9219, -0.2127, -0.2671], 1e-1); %!test %# Events option, five output arguments %! vopt = odeset ('Events', @fevn, 'NormControl', 'on'); %! [vt, vy, vxe, vye, vie] = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vie, vxe, vye], ... %! [1.0000, 2.9219, -0.2127, -0.2671], 1e-1); %! %! %# test for Jacobian option is missing %! %# test for Jacobian (being a sparse matrix) is missing %! %# test for JPattern option is missing %! %# test for Vectorized option is missing %! %# test for NewtonTol option is missing %! %# test for MaxNewtonIterations option is missing %! %!test %# Mass option as function %! vopt = odeset ('Mass', eye (2,2)); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# Mass option as matrix %! vopt = odeset ('Mass', eye (2,2)); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# Mass option as sparse matrix %! vopt = odeset ('Mass', sparse (eye (2,2))); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# Mass option as function and sparse matrix %! vopt = odeset ('Mass', @fmsa); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# Mass option as function and MStateDependence %! vopt = odeset ('Mass', @fmas, 'MStateDependence', 'strong'); %! vsol = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vsol.x(end), vsol.y(end,:)], [5, fref], 1e-1); %!test %# Set BDF option to something else than default %! vopt = odeset ('BDF', 'on'); %! [vt, vy] = ode23d (@fexp, [0 5], [1; 0], 1, [1; 0], vopt); %! assert ([vt(end), vy(end,:)], [5, fref], 0.5); %! %! %# test for MvPattern option is missing %! %# test for InitialSlope option is missing %! %# test for MaxOrder option is missing %! %! warning ('on', 'OdePkg:InvalidOption'); %# Local Variables: *** %# mode: octave *** %# End: ***