octave /tags/R2009-06-07/main/odepkg/inst/ode23d.m

Language MATLAB Lines 717
MD5 Hash 8874bc7f2038f77a9d575c07c4af8399
Repository https://octave.svn.sourceforge.net/svnroot/octave View Raw File
  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
%# Copyright (C) 2008, 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}.
%#
%# 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, solve 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
%# @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

  %# 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 %# 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 for MvPattern option is missing
%! %# test for InitialSlope option is missing
%! %# test for MaxOrder option is missing
%! %# test for BDF option is missing
%!
%!  warning ('on', 'OdePkg:InvalidOption');

%# Local Variables: ***
%# mode: octave ***
%# End: ***
Back to Top