xref: /petsc/src/ts/interface/ts.c (revision 5e4ed32f0140df3e357a2244cf5f0301f2d2ad78)
1 
2 #include <petsc/private/tsimpl.h>        /*I "petscts.h"  I*/
3 #include <petscdmshell.h>
4 #include <petscdmda.h>
5 #include <petscviewer.h>
6 #include <petscdraw.h>
7 
8 /* Logging support */
9 PetscClassId  TS_CLASSID, DMTS_CLASSID;
10 PetscLogEvent TS_AdjointStep, TS_Step, TS_PseudoComputeTimeStep, TS_FunctionEval, TS_JacobianEval;
11 
12 const char *const TSExactFinalTimeOptions[] = {"UNSPECIFIED","STEPOVER","INTERPOLATE","MATCHSTEP","TSExactFinalTimeOption","TS_EXACTFINALTIME_",0};
13 
14 struct _n_TSMonitorDrawCtx {
15   PetscViewer   viewer;
16   Vec           initialsolution;
17   PetscBool     showinitial;
18   PetscInt      howoften;  /* when > 0 uses step % howoften, when negative only final solution plotted */
19   PetscBool     showtimestepandtime;
20 };
21 
22 #undef __FUNCT__
23 #define __FUNCT__ "TSMonitorSetFromOptions"
24 /*@C
25    TSMonitorSetFromOptions - Sets a monitor function and viewer appropriate for the type indicated by the user
26 
27    Collective on TS
28 
29    Input Parameters:
30 +  ts - TS object you wish to monitor
31 .  name - the monitor type one is seeking
32 .  help - message indicating what monitoring is done
33 .  manual - manual page for the monitor
34 .  monitor - the monitor function
35 -  monitorsetup - a function that is called once ONLY if the user selected this monitor that may set additional features of the TS or PetscViewer objects
36 
37    Level: developer
38 
39 .seealso: PetscOptionsGetViewer(), PetscOptionsGetReal(), PetscOptionsHasName(), PetscOptionsGetString(),
40           PetscOptionsGetIntArray(), PetscOptionsGetRealArray(), PetscOptionsBool()
41           PetscOptionsInt(), PetscOptionsString(), PetscOptionsReal(), PetscOptionsBool(),
42           PetscOptionsName(), PetscOptionsBegin(), PetscOptionsEnd(), PetscOptionsHead(),
43           PetscOptionsStringArray(),PetscOptionsRealArray(), PetscOptionsScalar(),
44           PetscOptionsBoolGroupBegin(), PetscOptionsBoolGroup(), PetscOptionsBoolGroupEnd(),
45           PetscOptionsFList(), PetscOptionsEList()
46 @*/
47 PetscErrorCode  TSMonitorSetFromOptions(TS ts,const char name[],const char help[], const char manual[],PetscErrorCode (*monitor)(TS,PetscInt,PetscReal,Vec,PetscViewerAndFormat*),PetscErrorCode (*monitorsetup)(TS,PetscViewerAndFormat*))
48 {
49   PetscErrorCode    ierr;
50   PetscViewer       viewer;
51   PetscViewerFormat format;
52   PetscBool         flg;
53 
54   PetscFunctionBegin;
55   ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject)ts),((PetscObject)ts)->prefix,name,&viewer,&format,&flg);CHKERRQ(ierr);
56   if (flg) {
57     PetscViewerAndFormat *vf;
58     ierr = PetscViewerAndFormatCreate(viewer,format,&vf);CHKERRQ(ierr);
59     ierr = PetscObjectDereference((PetscObject)viewer);CHKERRQ(ierr);
60     if (monitorsetup) {
61       ierr = (*monitorsetup)(ts,vf);CHKERRQ(ierr);
62     }
63     ierr = TSMonitorSet(ts,(PetscErrorCode (*)(TS,PetscInt,PetscReal,Vec,void*))monitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);CHKERRQ(ierr);
64   }
65   PetscFunctionReturn(0);
66 }
67 
68 #undef __FUNCT__
69 #define __FUNCT__ "TSAdjointMonitorSetFromOptions"
70 /*@C
71    TSAdjointMonitorSetFromOptions - Sets a monitor function and viewer appropriate for the type indicated by the user
72 
73    Collective on TS
74 
75    Input Parameters:
76 +  ts - TS object you wish to monitor
77 .  name - the monitor type one is seeking
78 .  help - message indicating what monitoring is done
79 .  manual - manual page for the monitor
80 .  monitor - the monitor function
81 -  monitorsetup - a function that is called once ONLY if the user selected this monitor that may set additional features of the TS or PetscViewer objects
82 
83    Level: developer
84 
85 .seealso: PetscOptionsGetViewer(), PetscOptionsGetReal(), PetscOptionsHasName(), PetscOptionsGetString(),
86           PetscOptionsGetIntArray(), PetscOptionsGetRealArray(), PetscOptionsBool()
87           PetscOptionsInt(), PetscOptionsString(), PetscOptionsReal(), PetscOptionsBool(),
88           PetscOptionsName(), PetscOptionsBegin(), PetscOptionsEnd(), PetscOptionsHead(),
89           PetscOptionsStringArray(),PetscOptionsRealArray(), PetscOptionsScalar(),
90           PetscOptionsBoolGroupBegin(), PetscOptionsBoolGroup(), PetscOptionsBoolGroupEnd(),
91           PetscOptionsFList(), PetscOptionsEList()
92 @*/
93 PetscErrorCode  TSAdjointMonitorSetFromOptions(TS ts,const char name[],const char help[], const char manual[],PetscErrorCode (*monitor)(TS,PetscInt,PetscReal,Vec,PetscInt,Vec*,Vec*,PetscViewerAndFormat*),PetscErrorCode (*monitorsetup)(TS,PetscViewerAndFormat*))
94 {
95   PetscErrorCode    ierr;
96   PetscViewer       viewer;
97   PetscViewerFormat format;
98   PetscBool         flg;
99 
100   PetscFunctionBegin;
101   ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject)ts),((PetscObject)ts)->prefix,name,&viewer,&format,&flg);CHKERRQ(ierr);
102   if (flg) {
103     PetscViewerAndFormat *vf;
104     ierr = PetscViewerAndFormatCreate(viewer,format,&vf);CHKERRQ(ierr);
105     ierr = PetscObjectDereference((PetscObject)viewer);CHKERRQ(ierr);
106     if (monitorsetup) {
107       ierr = (*monitorsetup)(ts,vf);CHKERRQ(ierr);
108     }
109     ierr = TSAdjointMonitorSet(ts,(PetscErrorCode (*)(TS,PetscInt,PetscReal,Vec,PetscInt,Vec*,Vec*,void*))monitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);CHKERRQ(ierr);
110   }
111   PetscFunctionReturn(0);
112 }
113 
114 #undef __FUNCT__
115 #define __FUNCT__ "TSSetFromOptions"
116 /*@
117    TSSetFromOptions - Sets various TS parameters from user options.
118 
119    Collective on TS
120 
121    Input Parameter:
122 .  ts - the TS context obtained from TSCreate()
123 
124    Options Database Keys:
125 +  -ts_type <type> - TSEULER, TSBEULER, TSSUNDIALS, TSPSEUDO, TSCN, TSRK, TSTHETA, TSALPHA, TSGLLE, TSSSP, TSGLEE
126 .  -ts_save_trajectory - checkpoint the solution at each time-step
127 .  -ts_max_steps <maxsteps> - maximum number of time-steps to take
128 .  -ts_final_time <time> - maximum time to compute to
129 .  -ts_dt <dt> - initial time step
130 .  -ts_exact_final_time <stepover,interpolate,matchstep> whether to stop at the exact given final time and how to compute the solution at that ti,e
131 .  -ts_max_snes_failures <maxfailures> - Maximum number of nonlinear solve failures allowed
132 .  -ts_max_reject <maxrejects> - Maximum number of step rejections before step fails
133 .  -ts_error_if_step_fails <true,false> - Error if no step succeeds
134 .  -ts_rtol <rtol> - relative tolerance for local truncation error
135 .  -ts_atol <atol> Absolute tolerance for local truncation error
136 .  -ts_adjoint_solve <yes,no> After solving the ODE/DAE solve the adjoint problem (requires -ts_save_trajectory)
137 .  -ts_fd_color - Use finite differences with coloring to compute IJacobian
138 .  -ts_monitor - print information at each timestep
139 .  -ts_monitor_lg_solution - Monitor solution graphically
140 .  -ts_monitor_lg_error - Monitor error graphically
141 .  -ts_monitor_lg_timestep - Monitor timestep size graphically
142 .  -ts_monitor_lg_snes_iterations - Monitor number nonlinear iterations for each timestep graphically
143 .  -ts_monitor_lg_ksp_iterations - Monitor number nonlinear iterations for each timestep graphically
144 .  -ts_monitor_sp_eig - Monitor eigenvalues of linearized operator graphically
145 .  -ts_monitor_draw_solution - Monitor solution graphically
146 .  -ts_monitor_draw_solution_phase  <xleft,yleft,xright,yright> - Monitor solution graphically with phase diagram, requires problem with exactly 2 degrees of freedom
147 .  -ts_monitor_draw_error - Monitor error graphically, requires use to have provided TSSetSolutionFunction()
148 .  -ts_monitor_solution [ascii binary draw][:filename][:viewerformat] - monitors the solution at each timestep
149 .  -ts_monitor_solution_vtk <filename.vts> - Save each time step to a binary file, use filename-%%03D.vts
150 .  -ts_monitor_envelope - determine maximum and minimum value of each component of the solution over the solution time
151 .  -ts_adjoint_monitor - print information at each adjoint time step
152 -  -ts_adjoint_monitor_draw_sensi - monitor the sensitivity of the first cost function wrt initial conditions (lambda[0]) graphically
153 
154    Developer Note: We should unify all the -ts_monitor options in the way that -xxx_view has been unified
155 
156    Level: beginner
157 
158 .keywords: TS, timestep, set, options, database
159 
160 .seealso: TSGetType()
161 @*/
162 PetscErrorCode  TSSetFromOptions(TS ts)
163 {
164   PetscBool              opt,flg,tflg;
165   PetscErrorCode         ierr;
166   char                   monfilename[PETSC_MAX_PATH_LEN];
167   PetscReal              time_step;
168   TSExactFinalTimeOption eftopt;
169   char                   dir[16];
170   TSIFunction            ifun;
171   const char             *defaultType;
172   char                   typeName[256];
173 
174   PetscFunctionBegin;
175   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
176 
177   ierr = TSRegisterAll();CHKERRQ(ierr);
178   ierr = TSGetIFunction(ts,NULL,&ifun,NULL);CHKERRQ(ierr);
179 
180   ierr = PetscObjectOptionsBegin((PetscObject)ts);CHKERRQ(ierr);
181   if (((PetscObject)ts)->type_name)
182     defaultType = ((PetscObject)ts)->type_name;
183   else
184     defaultType = ifun ? TSBEULER : TSEULER;
185   ierr = PetscOptionsFList("-ts_type","TS method","TSSetType",TSList,defaultType,typeName,256,&opt);CHKERRQ(ierr);
186   if (opt) {
187     ierr = TSSetType(ts,typeName);CHKERRQ(ierr);
188   } else {
189     ierr = TSSetType(ts,defaultType);CHKERRQ(ierr);
190   }
191 
192   /* Handle generic TS options */
193   ierr = PetscOptionsInt("-ts_max_steps","Maximum number of time steps","TSSetDuration",ts->max_steps,&ts->max_steps,NULL);CHKERRQ(ierr);
194   ierr = PetscOptionsReal("-ts_final_time","Time to run to","TSSetDuration",ts->max_time,&ts->max_time,NULL);CHKERRQ(ierr);
195   ierr = PetscOptionsReal("-ts_init_time","Initial time","TSSetTime",ts->ptime,&ts->ptime,NULL);CHKERRQ(ierr);
196   ierr = PetscOptionsReal("-ts_dt","Initial time step","TSSetTimeStep",ts->time_step,&time_step,&flg);CHKERRQ(ierr);
197   if (flg) {ierr = TSSetTimeStep(ts,time_step);CHKERRQ(ierr);}
198   ierr = PetscOptionsEnum("-ts_exact_final_time","Option for handling of final time step","TSSetExactFinalTime",TSExactFinalTimeOptions,(PetscEnum)ts->exact_final_time,(PetscEnum*)&eftopt,&flg);CHKERRQ(ierr);
199   if (flg) {ierr = TSSetExactFinalTime(ts,eftopt);CHKERRQ(ierr);}
200   ierr = PetscOptionsInt("-ts_max_snes_failures","Maximum number of nonlinear solve failures","TSSetMaxSNESFailures",ts->max_snes_failures,&ts->max_snes_failures,NULL);CHKERRQ(ierr);
201   ierr = PetscOptionsInt("-ts_max_reject","Maximum number of step rejections before step fails","TSSetMaxStepRejections",ts->max_reject,&ts->max_reject,NULL);CHKERRQ(ierr);
202   ierr = PetscOptionsBool("-ts_error_if_step_fails","Error if no step succeeds","TSSetErrorIfStepFails",ts->errorifstepfailed,&ts->errorifstepfailed,NULL);CHKERRQ(ierr);
203   ierr = PetscOptionsReal("-ts_rtol","Relative tolerance for local truncation error","TSSetTolerances",ts->rtol,&ts->rtol,NULL);CHKERRQ(ierr);
204   ierr = PetscOptionsReal("-ts_atol","Absolute tolerance for local truncation error","TSSetTolerances",ts->atol,&ts->atol,NULL);CHKERRQ(ierr);
205 
206 #if defined(PETSC_HAVE_SAWS)
207   {
208   PetscBool set;
209   flg  = PETSC_FALSE;
210   ierr = PetscOptionsBool("-ts_saws_block","Block for SAWs memory snooper at end of TSSolve","PetscObjectSAWsBlock",((PetscObject)ts)->amspublishblock,&flg,&set);CHKERRQ(ierr);
211   if (set) {
212     ierr = PetscObjectSAWsSetBlock((PetscObject)ts,flg);CHKERRQ(ierr);
213   }
214   }
215 #endif
216 
217   /* Monitor options */
218   ierr = TSMonitorSetFromOptions(ts,"-ts_monitor","Monitor time and timestep size","TSMonitorDefault",TSMonitorDefault,NULL);CHKERRQ(ierr);
219   ierr = TSMonitorSetFromOptions(ts,"-ts_monitor_solution","View the solution at each timestep","TSMonitorSolution",TSMonitorSolution,NULL);CHKERRQ(ierr);
220   ierr = TSAdjointMonitorSetFromOptions(ts,"-ts_adjoint_monitor","Monitor adjoint timestep size","TSAdjointMonitorDefault",TSAdjointMonitorDefault,NULL);CHKERRQ(ierr);
221 
222   ierr = PetscOptionsString("-ts_monitor_python","Use Python function","TSMonitorSet",0,monfilename,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
223   if (flg) {ierr = PetscPythonMonitorSet((PetscObject)ts,monfilename);CHKERRQ(ierr);}
224 
225   ierr = PetscOptionsName("-ts_monitor_lg_solution","Monitor solution graphically","TSMonitorLGSolution",&opt);CHKERRQ(ierr);
226   if (opt) {
227     TSMonitorLGCtx ctx;
228     PetscInt       howoften = 1;
229 
230     ierr = PetscOptionsInt("-ts_monitor_lg_solution","Monitor solution graphically","TSMonitorLGSolution",howoften,&howoften,NULL);CHKERRQ(ierr);
231     ierr = TSMonitorLGCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
232     ierr = TSMonitorSet(ts,TSMonitorLGSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
233   }
234 
235   ierr = PetscOptionsName("-ts_monitor_lg_error","Monitor error graphically","TSMonitorLGError",&opt);CHKERRQ(ierr);
236   if (opt) {
237     TSMonitorLGCtx ctx;
238     PetscInt       howoften = 1;
239 
240     ierr = PetscOptionsInt("-ts_monitor_lg_error","Monitor error graphically","TSMonitorLGError",howoften,&howoften,NULL);CHKERRQ(ierr);
241     ierr = TSMonitorLGCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
242     ierr = TSMonitorSet(ts,TSMonitorLGError,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
243   }
244 
245   ierr = PetscOptionsName("-ts_monitor_lg_timestep","Monitor timestep size graphically","TSMonitorLGTimeStep",&opt);CHKERRQ(ierr);
246   if (opt) {
247     TSMonitorLGCtx ctx;
248     PetscInt       howoften = 1;
249 
250     ierr = PetscOptionsInt("-ts_monitor_lg_timestep","Monitor timestep size graphically","TSMonitorLGTimeStep",howoften,&howoften,NULL);CHKERRQ(ierr);
251     ierr = TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
252     ierr = TSMonitorSet(ts,TSMonitorLGTimeStep,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
253   }
254   ierr = PetscOptionsName("-ts_monitor_lg_snes_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGSNESIterations",&opt);CHKERRQ(ierr);
255   if (opt) {
256     TSMonitorLGCtx ctx;
257     PetscInt       howoften = 1;
258 
259     ierr = PetscOptionsInt("-ts_monitor_lg_snes_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGSNESIterations",howoften,&howoften,NULL);CHKERRQ(ierr);
260     ierr = TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
261     ierr = TSMonitorSet(ts,TSMonitorLGSNESIterations,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
262   }
263   ierr = PetscOptionsName("-ts_monitor_lg_ksp_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGKSPIterations",&opt);CHKERRQ(ierr);
264   if (opt) {
265     TSMonitorLGCtx ctx;
266     PetscInt       howoften = 1;
267 
268     ierr = PetscOptionsInt("-ts_monitor_lg_ksp_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGKSPIterations",howoften,&howoften,NULL);CHKERRQ(ierr);
269     ierr = TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
270     ierr = TSMonitorSet(ts,TSMonitorLGKSPIterations,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
271   }
272   ierr = PetscOptionsName("-ts_monitor_sp_eig","Monitor eigenvalues of linearized operator graphically","TSMonitorSPEig",&opt);CHKERRQ(ierr);
273   if (opt) {
274     TSMonitorSPEigCtx ctx;
275     PetscInt          howoften = 1;
276 
277     ierr = PetscOptionsInt("-ts_monitor_sp_eig","Monitor eigenvalues of linearized operator graphically","TSMonitorSPEig",howoften,&howoften,NULL);CHKERRQ(ierr);
278     ierr = TSMonitorSPEigCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
279     ierr = TSMonitorSet(ts,TSMonitorSPEig,ctx,(PetscErrorCode (*)(void**))TSMonitorSPEigCtxDestroy);CHKERRQ(ierr);
280   }
281   opt  = PETSC_FALSE;
282   ierr = PetscOptionsName("-ts_monitor_draw_solution","Monitor solution graphically","TSMonitorDrawSolution",&opt);CHKERRQ(ierr);
283   if (opt) {
284     TSMonitorDrawCtx ctx;
285     PetscInt         howoften = 1;
286 
287     ierr = PetscOptionsInt("-ts_monitor_draw_solution","Monitor solution graphically","TSMonitorDrawSolution",howoften,&howoften,NULL);CHKERRQ(ierr);
288     ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
289     ierr = TSMonitorSet(ts,TSMonitorDrawSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
290   }
291   opt  = PETSC_FALSE;
292   ierr = PetscOptionsName("-ts_adjoint_monitor_draw_sensi","Monitor adjoint sensitivities (lambda only) graphically","TSAdjointMonitorDrawSensi",&opt);CHKERRQ(ierr);
293   if (opt) {
294     TSMonitorDrawCtx ctx;
295     PetscInt         howoften = 1;
296 
297     ierr = PetscOptionsInt("-ts_adjoint_monitor_draw_sensi","Monitor adjoint sensitivities (lambda only) graphically","TSAdjointMonitorDrawSensi",howoften,&howoften,NULL);CHKERRQ(ierr);
298     ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
299     ierr = TSAdjointMonitorSet(ts,TSAdjointMonitorDrawSensi,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
300   }
301   opt  = PETSC_FALSE;
302   ierr = PetscOptionsName("-ts_monitor_draw_solution_phase","Monitor solution graphically","TSMonitorDrawSolutionPhase",&opt);CHKERRQ(ierr);
303   if (opt) {
304     TSMonitorDrawCtx ctx;
305     PetscReal        bounds[4];
306     PetscInt         n = 4;
307     PetscDraw        draw;
308     PetscDrawAxis    axis;
309 
310     ierr = PetscOptionsRealArray("-ts_monitor_draw_solution_phase","Monitor solution graphically","TSMonitorDrawSolutionPhase",bounds,&n,NULL);CHKERRQ(ierr);
311     if (n != 4) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Must provide bounding box of phase field");
312     ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,1,&ctx);CHKERRQ(ierr);
313     ierr = PetscViewerDrawGetDraw(ctx->viewer,0,&draw);CHKERRQ(ierr);
314     ierr = PetscViewerDrawGetDrawAxis(ctx->viewer,0,&axis);CHKERRQ(ierr);
315     ierr = PetscDrawAxisSetLimits(axis,bounds[0],bounds[2],bounds[1],bounds[3]);CHKERRQ(ierr);
316     ierr = PetscDrawAxisSetLabels(axis,"Phase Diagram","Variable 1","Variable 2");CHKERRQ(ierr);
317     ierr = TSMonitorSet(ts,TSMonitorDrawSolutionPhase,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
318   }
319   opt  = PETSC_FALSE;
320   ierr = PetscOptionsName("-ts_monitor_draw_error","Monitor error graphically","TSMonitorDrawError",&opt);CHKERRQ(ierr);
321   if (opt) {
322     TSMonitorDrawCtx ctx;
323     PetscInt         howoften = 1;
324 
325     ierr = PetscOptionsInt("-ts_monitor_draw_error","Monitor error graphically","TSMonitorDrawError",howoften,&howoften,NULL);CHKERRQ(ierr);
326     ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
327     ierr = TSMonitorSet(ts,TSMonitorDrawError,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
328   }
329 
330   opt  = PETSC_FALSE;
331   ierr = PetscOptionsString("-ts_monitor_solution_vtk","Save each time step to a binary file, use filename-%%03D.vts","TSMonitorSolutionVTK",0,monfilename,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
332   if (flg) {
333     const char *ptr,*ptr2;
334     char       *filetemplate;
335     if (!monfilename[0]) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"-ts_monitor_solution_vtk requires a file template, e.g. filename-%%03D.vts");
336     /* Do some cursory validation of the input. */
337     ierr = PetscStrstr(monfilename,"%",(char**)&ptr);CHKERRQ(ierr);
338     if (!ptr) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"-ts_monitor_solution_vtk requires a file template, e.g. filename-%%03D.vts");
339     for (ptr++; ptr && *ptr; ptr++) {
340       ierr = PetscStrchr("DdiouxX",*ptr,(char**)&ptr2);CHKERRQ(ierr);
341       if (!ptr2 && (*ptr < '0' || '9' < *ptr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Invalid file template argument to -ts_monitor_solution_vtk, should look like filename-%%03D.vts");
342       if (ptr2) break;
343     }
344     ierr = PetscStrallocpy(monfilename,&filetemplate);CHKERRQ(ierr);
345     ierr = TSMonitorSet(ts,TSMonitorSolutionVTK,filetemplate,(PetscErrorCode (*)(void**))TSMonitorSolutionVTKDestroy);CHKERRQ(ierr);
346   }
347 
348   ierr = PetscOptionsString("-ts_monitor_dmda_ray","Display a ray of the solution","None","y=0",dir,16,&flg);CHKERRQ(ierr);
349   if (flg) {
350     TSMonitorDMDARayCtx *rayctx;
351     int                  ray = 0;
352     DMDADirection        ddir;
353     DM                   da;
354     PetscMPIInt          rank;
355 
356     if (dir[1] != '=') SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Unknown ray %s",dir);
357     if (dir[0] == 'x') ddir = DMDA_X;
358     else if (dir[0] == 'y') ddir = DMDA_Y;
359     else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Unknown ray %s",dir);
360     sscanf(dir+2,"%d",&ray);
361 
362     ierr = PetscInfo2(((PetscObject)ts),"Displaying DMDA ray %c = %D\n",dir[0],ray);CHKERRQ(ierr);
363     ierr = PetscNew(&rayctx);CHKERRQ(ierr);
364     ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
365     ierr = DMDAGetRay(da,ddir,ray,&rayctx->ray,&rayctx->scatter);CHKERRQ(ierr);
366     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)ts),&rank);CHKERRQ(ierr);
367     if (!rank) {
368       ierr = PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,0,0,600,300,&rayctx->viewer);CHKERRQ(ierr);
369     }
370     rayctx->lgctx = NULL;
371     ierr = TSMonitorSet(ts,TSMonitorDMDARay,rayctx,TSMonitorDMDARayDestroy);CHKERRQ(ierr);
372   }
373   ierr = PetscOptionsString("-ts_monitor_lg_dmda_ray","Display a ray of the solution","None","x=0",dir,16,&flg);CHKERRQ(ierr);
374   if (flg) {
375     TSMonitorDMDARayCtx *rayctx;
376     int                 ray = 0;
377     DMDADirection       ddir;
378     DM                  da;
379     PetscInt            howoften = 1;
380 
381     if (dir[1] != '=') SETERRQ1(PetscObjectComm((PetscObject) ts), PETSC_ERR_ARG_WRONG, "Malformed ray %s", dir);
382     if      (dir[0] == 'x') ddir = DMDA_X;
383     else if (dir[0] == 'y') ddir = DMDA_Y;
384     else SETERRQ1(PetscObjectComm((PetscObject) ts), PETSC_ERR_ARG_WRONG, "Unknown ray direction %s", dir);
385     sscanf(dir+2, "%d", &ray);
386 
387     ierr = PetscInfo2(((PetscObject) ts),"Displaying LG DMDA ray %c = %D\n", dir[0], ray);CHKERRQ(ierr);
388     ierr = PetscNew(&rayctx);CHKERRQ(ierr);
389     ierr = TSGetDM(ts, &da);CHKERRQ(ierr);
390     ierr = DMDAGetRay(da, ddir, ray, &rayctx->ray, &rayctx->scatter);CHKERRQ(ierr);
391     ierr = TSMonitorLGCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,600,400,howoften,&rayctx->lgctx);CHKERRQ(ierr);
392     ierr = TSMonitorSet(ts, TSMonitorLGDMDARay, rayctx, TSMonitorDMDARayDestroy);CHKERRQ(ierr);
393   }
394 
395   ierr = PetscOptionsName("-ts_monitor_envelope","Monitor maximum and minimum value of each component of the solution","TSMonitorEnvelope",&opt);CHKERRQ(ierr);
396   if (opt) {
397     TSMonitorEnvelopeCtx ctx;
398 
399     ierr = TSMonitorEnvelopeCtxCreate(ts,&ctx);CHKERRQ(ierr);
400     ierr = TSMonitorSet(ts,TSMonitorEnvelope,ctx,(PetscErrorCode (*)(void**))TSMonitorEnvelopeCtxDestroy);CHKERRQ(ierr);
401   }
402 
403   flg  = PETSC_FALSE;
404   ierr = PetscOptionsBool("-ts_fd_color", "Use finite differences with coloring to compute IJacobian", "TSComputeJacobianDefaultColor", flg, &flg, NULL);CHKERRQ(ierr);
405   if (flg) {
406     DM   dm;
407     DMTS tdm;
408 
409     ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
410     ierr = DMGetDMTS(dm, &tdm);CHKERRQ(ierr);
411     tdm->ijacobianctx = NULL;
412     ierr = TSSetIJacobian(ts, NULL, NULL, TSComputeIJacobianDefaultColor, 0);CHKERRQ(ierr);
413     ierr = PetscInfo(ts, "Setting default finite difference coloring Jacobian matrix\n");CHKERRQ(ierr);
414   }
415 
416   if (ts->adapt) {
417     ierr = TSAdaptSetFromOptions(PetscOptionsObject,ts->adapt);CHKERRQ(ierr);
418   }
419 
420   /* Handle specific TS options */
421   if (ts->ops->setfromoptions) {
422     ierr = (*ts->ops->setfromoptions)(PetscOptionsObject,ts);CHKERRQ(ierr);
423   }
424 
425   /* TS trajectory must be set after TS, since it may use some TS options above */
426   tflg = ts->trajectory ? PETSC_TRUE : PETSC_FALSE;
427   ierr = PetscOptionsBool("-ts_save_trajectory","Save the solution at each timestep","TSSetSaveTrajectory",tflg,&tflg,NULL);CHKERRQ(ierr);
428   if (tflg) {
429     ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
430   }
431   tflg = ts->adjoint_solve ? PETSC_TRUE : PETSC_FALSE;
432   ierr = PetscOptionsBool("-ts_adjoint_solve","Solve the adjoint problem immediately after solving the forward problem","",tflg,&tflg,&flg);CHKERRQ(ierr);
433   if (flg) {
434     ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
435     ts->adjoint_solve = tflg;
436   }
437 
438   /* process any options handlers added with PetscObjectAddOptionsHandler() */
439   ierr = PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject)ts);CHKERRQ(ierr);
440   ierr = PetscOptionsEnd();CHKERRQ(ierr);
441 
442   if (ts->trajectory) {
443     ierr = TSTrajectorySetFromOptions(ts->trajectory,ts);CHKERRQ(ierr);
444   }
445 
446   ierr = TSGetSNES(ts,&ts->snes);CHKERRQ(ierr);
447   if (ts->problem_type == TS_LINEAR) {ierr = SNESSetType(ts->snes,SNESKSPONLY);CHKERRQ(ierr);}
448   ierr = SNESSetFromOptions(ts->snes);CHKERRQ(ierr);
449   PetscFunctionReturn(0);
450 }
451 
452 #undef __FUNCT__
453 #define __FUNCT__ "TSSetSaveTrajectory"
454 /*@
455    TSSetSaveTrajectory - Causes the TS to save its solutions as it iterates forward in time in a TSTrajectory object
456 
457    Collective on TS
458 
459    Input Parameters:
460 .  ts - the TS context obtained from TSCreate()
461 
462 Note: This routine should be called after all TS options have been set
463 
464    Level: intermediate
465 
466 .seealso: TSGetTrajectory(), TSAdjointSolve()
467 
468 .keywords: TS, set, checkpoint,
469 @*/
470 PetscErrorCode  TSSetSaveTrajectory(TS ts)
471 {
472   PetscErrorCode ierr;
473 
474   PetscFunctionBegin;
475   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
476   if (!ts->trajectory) {
477     ierr = TSTrajectoryCreate(PetscObjectComm((PetscObject)ts),&ts->trajectory);CHKERRQ(ierr);
478     ierr = TSTrajectorySetFromOptions(ts->trajectory,ts);CHKERRQ(ierr);
479   }
480   PetscFunctionReturn(0);
481 }
482 
483 #undef __FUNCT__
484 #define __FUNCT__ "TSComputeRHSJacobian"
485 /*@
486    TSComputeRHSJacobian - Computes the Jacobian matrix that has been
487       set with TSSetRHSJacobian().
488 
489    Collective on TS and Vec
490 
491    Input Parameters:
492 +  ts - the TS context
493 .  t - current timestep
494 -  U - input vector
495 
496    Output Parameters:
497 +  A - Jacobian matrix
498 .  B - optional preconditioning matrix
499 -  flag - flag indicating matrix structure
500 
501    Notes:
502    Most users should not need to explicitly call this routine, as it
503    is used internally within the nonlinear solvers.
504 
505    See KSPSetOperators() for important information about setting the
506    flag parameter.
507 
508    Level: developer
509 
510 .keywords: SNES, compute, Jacobian, matrix
511 
512 .seealso:  TSSetRHSJacobian(), KSPSetOperators()
513 @*/
514 PetscErrorCode  TSComputeRHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B)
515 {
516   PetscErrorCode ierr;
517   PetscObjectState Ustate;
518   DM             dm;
519   DMTS           tsdm;
520   TSRHSJacobian  rhsjacobianfunc;
521   void           *ctx;
522   TSIJacobian    ijacobianfunc;
523   TSRHSFunction  rhsfunction;
524 
525   PetscFunctionBegin;
526   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
527   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
528   PetscCheckSameComm(ts,1,U,3);
529   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
530   ierr = DMGetDMTS(dm,&tsdm);CHKERRQ(ierr);
531   ierr = DMTSGetRHSJacobian(dm,&rhsjacobianfunc,&ctx);CHKERRQ(ierr);
532   ierr = DMTSGetIJacobian(dm,&ijacobianfunc,NULL);CHKERRQ(ierr);
533   ierr = DMTSGetRHSFunction(dm,&rhsfunction,&ctx);CHKERRQ(ierr);
534   ierr = PetscObjectStateGet((PetscObject)U,&Ustate);CHKERRQ(ierr);
535   if (ts->rhsjacobian.time == t && (ts->problem_type == TS_LINEAR || (ts->rhsjacobian.X == U && ts->rhsjacobian.Xstate == Ustate)) && (rhsfunction != TSComputeRHSFunctionLinear)) {
536     PetscFunctionReturn(0);
537   }
538 
539   if (!rhsjacobianfunc && !ijacobianfunc) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSJacobian() and / or TSSetIJacobian()");
540 
541   if (ts->rhsjacobian.reuse) {
542     ierr = MatShift(A,-ts->rhsjacobian.shift);CHKERRQ(ierr);
543     ierr = MatScale(A,1./ts->rhsjacobian.scale);CHKERRQ(ierr);
544     if (A != B) {
545       ierr = MatShift(B,-ts->rhsjacobian.shift);CHKERRQ(ierr);
546       ierr = MatScale(B,1./ts->rhsjacobian.scale);CHKERRQ(ierr);
547     }
548     ts->rhsjacobian.shift = 0;
549     ts->rhsjacobian.scale = 1.;
550   }
551 
552   if (rhsjacobianfunc) {
553     PetscBool missing;
554     ierr = PetscLogEventBegin(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
555     PetscStackPush("TS user Jacobian function");
556     ierr = (*rhsjacobianfunc)(ts,t,U,A,B,ctx);CHKERRQ(ierr);
557     PetscStackPop;
558     ierr = PetscLogEventEnd(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
559     if (A) {
560       ierr = MatMissingDiagonal(A,&missing,NULL);CHKERRQ(ierr);
561       if (missing) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Amat passed to TSSetRHSJacobian() must have all diagonal entries set, if they are zero you must still set them with a zero value");
562     }
563     if (B && B != A) {
564       ierr = MatMissingDiagonal(B,&missing,NULL);CHKERRQ(ierr);
565       if (missing) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Bmat passed to TSSetRHSJacobian() must have all diagonal entries set, if they are zero you must still set them with a zero value");
566     }
567   } else {
568     ierr = MatZeroEntries(A);CHKERRQ(ierr);
569     if (A != B) {ierr = MatZeroEntries(B);CHKERRQ(ierr);}
570   }
571   ts->rhsjacobian.time       = t;
572   ts->rhsjacobian.X          = U;
573   ierr                       = PetscObjectStateGet((PetscObject)U,&ts->rhsjacobian.Xstate);CHKERRQ(ierr);
574   PetscFunctionReturn(0);
575 }
576 
577 #undef __FUNCT__
578 #define __FUNCT__ "TSComputeRHSFunction"
579 /*@
580    TSComputeRHSFunction - Evaluates the right-hand-side function.
581 
582    Collective on TS and Vec
583 
584    Input Parameters:
585 +  ts - the TS context
586 .  t - current time
587 -  U - state vector
588 
589    Output Parameter:
590 .  y - right hand side
591 
592    Note:
593    Most users should not need to explicitly call this routine, as it
594    is used internally within the nonlinear solvers.
595 
596    Level: developer
597 
598 .keywords: TS, compute
599 
600 .seealso: TSSetRHSFunction(), TSComputeIFunction()
601 @*/
602 PetscErrorCode TSComputeRHSFunction(TS ts,PetscReal t,Vec U,Vec y)
603 {
604   PetscErrorCode ierr;
605   TSRHSFunction  rhsfunction;
606   TSIFunction    ifunction;
607   void           *ctx;
608   DM             dm;
609 
610   PetscFunctionBegin;
611   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
612   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
613   PetscValidHeaderSpecific(y,VEC_CLASSID,4);
614   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
615   ierr = DMTSGetRHSFunction(dm,&rhsfunction,&ctx);CHKERRQ(ierr);
616   ierr = DMTSGetIFunction(dm,&ifunction,NULL);CHKERRQ(ierr);
617 
618   if (!rhsfunction && !ifunction) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSFunction() and / or TSSetIFunction()");
619 
620   ierr = PetscLogEventBegin(TS_FunctionEval,ts,U,y,0);CHKERRQ(ierr);
621   if (rhsfunction) {
622     PetscStackPush("TS user right-hand-side function");
623     ierr = (*rhsfunction)(ts,t,U,y,ctx);CHKERRQ(ierr);
624     PetscStackPop;
625   } else {
626     ierr = VecZeroEntries(y);CHKERRQ(ierr);
627   }
628 
629   ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,y,0);CHKERRQ(ierr);
630   PetscFunctionReturn(0);
631 }
632 
633 #undef __FUNCT__
634 #define __FUNCT__ "TSComputeSolutionFunction"
635 /*@
636    TSComputeSolutionFunction - Evaluates the solution function.
637 
638    Collective on TS and Vec
639 
640    Input Parameters:
641 +  ts - the TS context
642 -  t - current time
643 
644    Output Parameter:
645 .  U - the solution
646 
647    Note:
648    Most users should not need to explicitly call this routine, as it
649    is used internally within the nonlinear solvers.
650 
651    Level: developer
652 
653 .keywords: TS, compute
654 
655 .seealso: TSSetSolutionFunction(), TSSetRHSFunction(), TSComputeIFunction()
656 @*/
657 PetscErrorCode TSComputeSolutionFunction(TS ts,PetscReal t,Vec U)
658 {
659   PetscErrorCode     ierr;
660   TSSolutionFunction solutionfunction;
661   void               *ctx;
662   DM                 dm;
663 
664   PetscFunctionBegin;
665   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
666   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
667   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
668   ierr = DMTSGetSolutionFunction(dm,&solutionfunction,&ctx);CHKERRQ(ierr);
669 
670   if (solutionfunction) {
671     PetscStackPush("TS user solution function");
672     ierr = (*solutionfunction)(ts,t,U,ctx);CHKERRQ(ierr);
673     PetscStackPop;
674   }
675   PetscFunctionReturn(0);
676 }
677 #undef __FUNCT__
678 #define __FUNCT__ "TSComputeForcingFunction"
679 /*@
680    TSComputeForcingFunction - Evaluates the forcing function.
681 
682    Collective on TS and Vec
683 
684    Input Parameters:
685 +  ts - the TS context
686 -  t - current time
687 
688    Output Parameter:
689 .  U - the function value
690 
691    Note:
692    Most users should not need to explicitly call this routine, as it
693    is used internally within the nonlinear solvers.
694 
695    Level: developer
696 
697 .keywords: TS, compute
698 
699 .seealso: TSSetSolutionFunction(), TSSetRHSFunction(), TSComputeIFunction()
700 @*/
701 PetscErrorCode TSComputeForcingFunction(TS ts,PetscReal t,Vec U)
702 {
703   PetscErrorCode     ierr, (*forcing)(TS,PetscReal,Vec,void*);
704   void               *ctx;
705   DM                 dm;
706 
707   PetscFunctionBegin;
708   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
709   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
710   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
711   ierr = DMTSGetForcingFunction(dm,&forcing,&ctx);CHKERRQ(ierr);
712 
713   if (forcing) {
714     PetscStackPush("TS user forcing function");
715     ierr = (*forcing)(ts,t,U,ctx);CHKERRQ(ierr);
716     PetscStackPop;
717   }
718   PetscFunctionReturn(0);
719 }
720 
721 #undef __FUNCT__
722 #define __FUNCT__ "TSGetRHSVec_Private"
723 static PetscErrorCode TSGetRHSVec_Private(TS ts,Vec *Frhs)
724 {
725   Vec            F;
726   PetscErrorCode ierr;
727 
728   PetscFunctionBegin;
729   *Frhs = NULL;
730   ierr  = TSGetIFunction(ts,&F,NULL,NULL);CHKERRQ(ierr);
731   if (!ts->Frhs) {
732     ierr = VecDuplicate(F,&ts->Frhs);CHKERRQ(ierr);
733   }
734   *Frhs = ts->Frhs;
735   PetscFunctionReturn(0);
736 }
737 
738 #undef __FUNCT__
739 #define __FUNCT__ "TSGetRHSMats_Private"
740 static PetscErrorCode TSGetRHSMats_Private(TS ts,Mat *Arhs,Mat *Brhs)
741 {
742   Mat            A,B;
743   PetscErrorCode ierr;
744 
745   PetscFunctionBegin;
746   if (Arhs) *Arhs = NULL;
747   if (Brhs) *Brhs = NULL;
748   ierr = TSGetIJacobian(ts,&A,&B,NULL,NULL);CHKERRQ(ierr);
749   if (Arhs) {
750     if (!ts->Arhs) {
751       ierr = MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&ts->Arhs);CHKERRQ(ierr);
752     }
753     *Arhs = ts->Arhs;
754   }
755   if (Brhs) {
756     if (!ts->Brhs) {
757       if (A != B) {
758         ierr = MatDuplicate(B,MAT_DO_NOT_COPY_VALUES,&ts->Brhs);CHKERRQ(ierr);
759       } else {
760         ierr = PetscObjectReference((PetscObject)ts->Arhs);CHKERRQ(ierr);
761         ts->Brhs = ts->Arhs;
762       }
763     }
764     *Brhs = ts->Brhs;
765   }
766   PetscFunctionReturn(0);
767 }
768 
769 #undef __FUNCT__
770 #define __FUNCT__ "TSComputeIFunction"
771 /*@
772    TSComputeIFunction - Evaluates the DAE residual written in implicit form F(t,U,Udot)=0
773 
774    Collective on TS and Vec
775 
776    Input Parameters:
777 +  ts - the TS context
778 .  t - current time
779 .  U - state vector
780 .  Udot - time derivative of state vector
781 -  imex - flag indicates if the method is IMEX so that the RHSFunction should be kept separate
782 
783    Output Parameter:
784 .  Y - right hand side
785 
786    Note:
787    Most users should not need to explicitly call this routine, as it
788    is used internally within the nonlinear solvers.
789 
790    If the user did did not write their equations in implicit form, this
791    function recasts them in implicit form.
792 
793    Level: developer
794 
795 .keywords: TS, compute
796 
797 .seealso: TSSetIFunction(), TSComputeRHSFunction()
798 @*/
799 PetscErrorCode TSComputeIFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec Y,PetscBool imex)
800 {
801   PetscErrorCode ierr;
802   TSIFunction    ifunction;
803   TSRHSFunction  rhsfunction;
804   void           *ctx;
805   DM             dm;
806 
807   PetscFunctionBegin;
808   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
809   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
810   PetscValidHeaderSpecific(Udot,VEC_CLASSID,4);
811   PetscValidHeaderSpecific(Y,VEC_CLASSID,5);
812 
813   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
814   ierr = DMTSGetIFunction(dm,&ifunction,&ctx);CHKERRQ(ierr);
815   ierr = DMTSGetRHSFunction(dm,&rhsfunction,NULL);CHKERRQ(ierr);
816 
817   if (!rhsfunction && !ifunction) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSFunction() and / or TSSetIFunction()");
818 
819   ierr = PetscLogEventBegin(TS_FunctionEval,ts,U,Udot,Y);CHKERRQ(ierr);
820   if (ifunction) {
821     PetscStackPush("TS user implicit function");
822     ierr = (*ifunction)(ts,t,U,Udot,Y,ctx);CHKERRQ(ierr);
823     PetscStackPop;
824   }
825   if (imex) {
826     if (!ifunction) {
827       ierr = VecCopy(Udot,Y);CHKERRQ(ierr);
828     }
829   } else if (rhsfunction) {
830     if (ifunction) {
831       Vec Frhs;
832       ierr = TSGetRHSVec_Private(ts,&Frhs);CHKERRQ(ierr);
833       ierr = TSComputeRHSFunction(ts,t,U,Frhs);CHKERRQ(ierr);
834       ierr = VecAXPY(Y,-1,Frhs);CHKERRQ(ierr);
835     } else {
836       ierr = TSComputeRHSFunction(ts,t,U,Y);CHKERRQ(ierr);
837       ierr = VecAYPX(Y,-1,Udot);CHKERRQ(ierr);
838     }
839   }
840   ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,Udot,Y);CHKERRQ(ierr);
841   PetscFunctionReturn(0);
842 }
843 
844 #undef __FUNCT__
845 #define __FUNCT__ "TSComputeIJacobian"
846 /*@
847    TSComputeIJacobian - Evaluates the Jacobian of the DAE
848 
849    Collective on TS and Vec
850 
851    Input
852       Input Parameters:
853 +  ts - the TS context
854 .  t - current timestep
855 .  U - state vector
856 .  Udot - time derivative of state vector
857 .  shift - shift to apply, see note below
858 -  imex - flag indicates if the method is IMEX so that the RHSJacobian should be kept separate
859 
860    Output Parameters:
861 +  A - Jacobian matrix
862 .  B - optional preconditioning matrix
863 -  flag - flag indicating matrix structure
864 
865    Notes:
866    If F(t,U,Udot)=0 is the DAE, the required Jacobian is
867 
868    dF/dU + shift*dF/dUdot
869 
870    Most users should not need to explicitly call this routine, as it
871    is used internally within the nonlinear solvers.
872 
873    Level: developer
874 
875 .keywords: TS, compute, Jacobian, matrix
876 
877 .seealso:  TSSetIJacobian()
878 @*/
879 PetscErrorCode TSComputeIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat A,Mat B,PetscBool imex)
880 {
881   PetscErrorCode ierr;
882   TSIJacobian    ijacobian;
883   TSRHSJacobian  rhsjacobian;
884   DM             dm;
885   void           *ctx;
886 
887   PetscFunctionBegin;
888   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
889   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
890   PetscValidHeaderSpecific(Udot,VEC_CLASSID,4);
891   PetscValidPointer(A,6);
892   PetscValidHeaderSpecific(A,MAT_CLASSID,6);
893   PetscValidPointer(B,7);
894   PetscValidHeaderSpecific(B,MAT_CLASSID,7);
895 
896   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
897   ierr = DMTSGetIJacobian(dm,&ijacobian,&ctx);CHKERRQ(ierr);
898   ierr = DMTSGetRHSJacobian(dm,&rhsjacobian,NULL);CHKERRQ(ierr);
899 
900   if (!rhsjacobian && !ijacobian) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSJacobian() and / or TSSetIJacobian()");
901 
902   ierr = PetscLogEventBegin(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
903   if (ijacobian) {
904     PetscBool missing;
905     PetscStackPush("TS user implicit Jacobian");
906     ierr = (*ijacobian)(ts,t,U,Udot,shift,A,B,ctx);CHKERRQ(ierr);
907     PetscStackPop;
908     if (A) {
909       ierr = MatMissingDiagonal(A,&missing,NULL);CHKERRQ(ierr);
910       if (missing) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Amat passed to TSSetIJacobian() must have all diagonal entries set, if they are zero you must still set them with a zero value");
911     }
912     if (B && B != A) {
913       ierr = MatMissingDiagonal(B,&missing,NULL);CHKERRQ(ierr);
914       if (missing) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Bmat passed to TSSetIJacobian() must have all diagonal entries set, if they are zero you must still set them with a zero value");
915     }
916   }
917   if (imex) {
918     if (!ijacobian) {  /* system was written as Udot = G(t,U) */
919       ierr = MatZeroEntries(A);CHKERRQ(ierr);
920       ierr = MatShift(A,shift);CHKERRQ(ierr);
921       if (A != B) {
922         ierr = MatZeroEntries(B);CHKERRQ(ierr);
923         ierr = MatShift(B,shift);CHKERRQ(ierr);
924       }
925     }
926   } else {
927     Mat Arhs = NULL,Brhs = NULL;
928     if (rhsjacobian) {
929       ierr = TSGetRHSMats_Private(ts,&Arhs,&Brhs);CHKERRQ(ierr);
930       ierr = TSComputeRHSJacobian(ts,t,U,Arhs,Brhs);CHKERRQ(ierr);
931     }
932     if (Arhs == A) {           /* No IJacobian, so we only have the RHS matrix */
933       ts->rhsjacobian.scale = -1;
934       ts->rhsjacobian.shift = shift;
935       ierr = MatScale(A,-1);CHKERRQ(ierr);
936       ierr = MatShift(A,shift);CHKERRQ(ierr);
937       if (A != B) {
938         ierr = MatScale(B,-1);CHKERRQ(ierr);
939         ierr = MatShift(B,shift);CHKERRQ(ierr);
940       }
941     } else if (Arhs) {          /* Both IJacobian and RHSJacobian */
942       MatStructure axpy = DIFFERENT_NONZERO_PATTERN;
943       if (!ijacobian) {         /* No IJacobian provided, but we have a separate RHS matrix */
944         ierr = MatZeroEntries(A);CHKERRQ(ierr);
945         ierr = MatShift(A,shift);CHKERRQ(ierr);
946         if (A != B) {
947           ierr = MatZeroEntries(B);CHKERRQ(ierr);
948           ierr = MatShift(B,shift);CHKERRQ(ierr);
949         }
950       }
951       ierr = MatAXPY(A,-1,Arhs,axpy);CHKERRQ(ierr);
952       if (A != B) {
953         ierr = MatAXPY(B,-1,Brhs,axpy);CHKERRQ(ierr);
954       }
955     }
956   }
957   ierr = PetscLogEventEnd(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
958   PetscFunctionReturn(0);
959 }
960 
961 #undef __FUNCT__
962 #define __FUNCT__ "TSSetRHSFunction"
963 /*@C
964     TSSetRHSFunction - Sets the routine for evaluating the function,
965     where U_t = G(t,u).
966 
967     Logically Collective on TS
968 
969     Input Parameters:
970 +   ts - the TS context obtained from TSCreate()
971 .   r - vector to put the computed right hand side (or NULL to have it created)
972 .   f - routine for evaluating the right-hand-side function
973 -   ctx - [optional] user-defined context for private data for the
974           function evaluation routine (may be NULL)
975 
976     Calling sequence of func:
977 $     func (TS ts,PetscReal t,Vec u,Vec F,void *ctx);
978 
979 +   t - current timestep
980 .   u - input vector
981 .   F - function vector
982 -   ctx - [optional] user-defined function context
983 
984     Level: beginner
985 
986     Notes: You must call this function or TSSetIFunction() to define your ODE. You cannot use this function when solving a DAE.
987 
988 .keywords: TS, timestep, set, right-hand-side, function
989 
990 .seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSSetIFunction()
991 @*/
992 PetscErrorCode  TSSetRHSFunction(TS ts,Vec r,PetscErrorCode (*f)(TS,PetscReal,Vec,Vec,void*),void *ctx)
993 {
994   PetscErrorCode ierr;
995   SNES           snes;
996   Vec            ralloc = NULL;
997   DM             dm;
998 
999   PetscFunctionBegin;
1000   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1001   if (r) PetscValidHeaderSpecific(r,VEC_CLASSID,2);
1002 
1003   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1004   ierr = DMTSSetRHSFunction(dm,f,ctx);CHKERRQ(ierr);
1005   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1006   if (!r && !ts->dm && ts->vec_sol) {
1007     ierr = VecDuplicate(ts->vec_sol,&ralloc);CHKERRQ(ierr);
1008     r = ralloc;
1009   }
1010   ierr = SNESSetFunction(snes,r,SNESTSFormFunction,ts);CHKERRQ(ierr);
1011   ierr = VecDestroy(&ralloc);CHKERRQ(ierr);
1012   PetscFunctionReturn(0);
1013 }
1014 
1015 #undef __FUNCT__
1016 #define __FUNCT__ "TSSetSolutionFunction"
1017 /*@C
1018     TSSetSolutionFunction - Provide a function that computes the solution of the ODE or DAE
1019 
1020     Logically Collective on TS
1021 
1022     Input Parameters:
1023 +   ts - the TS context obtained from TSCreate()
1024 .   f - routine for evaluating the solution
1025 -   ctx - [optional] user-defined context for private data for the
1026           function evaluation routine (may be NULL)
1027 
1028     Calling sequence of func:
1029 $     func (TS ts,PetscReal t,Vec u,void *ctx);
1030 
1031 +   t - current timestep
1032 .   u - output vector
1033 -   ctx - [optional] user-defined function context
1034 
1035     Notes:
1036     This routine is used for testing accuracy of time integration schemes when you already know the solution.
1037     If analytic solutions are not known for your system, consider using the Method of Manufactured Solutions to
1038     create closed-form solutions with non-physical forcing terms.
1039 
1040     For low-dimensional problems solved in serial, such as small discrete systems, TSMonitorLGError() can be used to monitor the error history.
1041 
1042     Level: beginner
1043 
1044 .keywords: TS, timestep, set, right-hand-side, function
1045 
1046 .seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSComputeSolutionFunction(), TSSetForcingFunction()
1047 @*/
1048 PetscErrorCode  TSSetSolutionFunction(TS ts,PetscErrorCode (*f)(TS,PetscReal,Vec,void*),void *ctx)
1049 {
1050   PetscErrorCode ierr;
1051   DM             dm;
1052 
1053   PetscFunctionBegin;
1054   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1055   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1056   ierr = DMTSSetSolutionFunction(dm,f,ctx);CHKERRQ(ierr);
1057   PetscFunctionReturn(0);
1058 }
1059 
1060 #undef __FUNCT__
1061 #define __FUNCT__ "TSSetForcingFunction"
1062 /*@C
1063     TSSetForcingFunction - Provide a function that computes a forcing term for a ODE or PDE
1064 
1065     Logically Collective on TS
1066 
1067     Input Parameters:
1068 +   ts - the TS context obtained from TSCreate()
1069 .   f - routine for evaluating the forcing function
1070 -   ctx - [optional] user-defined context for private data for the
1071           function evaluation routine (may be NULL)
1072 
1073     Calling sequence of func:
1074 $     func (TS ts,PetscReal t,Vec u,void *ctx);
1075 
1076 +   t - current timestep
1077 .   u - output vector
1078 -   ctx - [optional] user-defined function context
1079 
1080     Notes:
1081     This routine is useful for testing accuracy of time integration schemes when using the Method of Manufactured Solutions to
1082     create closed-form solutions with a non-physical forcing term.
1083 
1084     For low-dimensional problems solved in serial, such as small discrete systems, TSMonitorLGError() can be used to monitor the error history.
1085 
1086     Level: beginner
1087 
1088 .keywords: TS, timestep, set, right-hand-side, function
1089 
1090 .seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSComputeSolutionFunction(), TSSetSolutionFunction()
1091 @*/
1092 PetscErrorCode  TSSetForcingFunction(TS ts,TSForcingFunction f,void *ctx)
1093 {
1094   PetscErrorCode ierr;
1095   DM             dm;
1096 
1097   PetscFunctionBegin;
1098   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1099   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1100   ierr = DMTSSetForcingFunction(dm,f,ctx);CHKERRQ(ierr);
1101   PetscFunctionReturn(0);
1102 }
1103 
1104 #undef __FUNCT__
1105 #define __FUNCT__ "TSSetRHSJacobian"
1106 /*@C
1107    TSSetRHSJacobian - Sets the function to compute the Jacobian of G,
1108    where U_t = G(U,t), as well as the location to store the matrix.
1109 
1110    Logically Collective on TS
1111 
1112    Input Parameters:
1113 +  ts  - the TS context obtained from TSCreate()
1114 .  Amat - (approximate) Jacobian matrix
1115 .  Pmat - matrix from which preconditioner is to be constructed (usually the same as Amat)
1116 .  f   - the Jacobian evaluation routine
1117 -  ctx - [optional] user-defined context for private data for the
1118          Jacobian evaluation routine (may be NULL)
1119 
1120    Calling sequence of f:
1121 $     func (TS ts,PetscReal t,Vec u,Mat A,Mat B,void *ctx);
1122 
1123 +  t - current timestep
1124 .  u - input vector
1125 .  Amat - (approximate) Jacobian matrix
1126 .  Pmat - matrix from which preconditioner is to be constructed (usually the same as Amat)
1127 -  ctx - [optional] user-defined context for matrix evaluation routine
1128 
1129    Notes:
1130    You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value
1131 
1132    The TS solver may modify the nonzero structure and the entries of the matrices Amat and Pmat between the calls to f()
1133    You should not assume the values are the same in the next call to f() as you set them in the previous call.
1134 
1135    Level: beginner
1136 
1137 .keywords: TS, timestep, set, right-hand-side, Jacobian
1138 
1139 .seealso: SNESComputeJacobianDefaultColor(), TSSetRHSFunction(), TSRHSJacobianSetReuse(), TSSetIJacobian()
1140 
1141 @*/
1142 PetscErrorCode  TSSetRHSJacobian(TS ts,Mat Amat,Mat Pmat,TSRHSJacobian f,void *ctx)
1143 {
1144   PetscErrorCode ierr;
1145   SNES           snes;
1146   DM             dm;
1147   TSIJacobian    ijacobian;
1148 
1149   PetscFunctionBegin;
1150   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1151   if (Amat) PetscValidHeaderSpecific(Amat,MAT_CLASSID,2);
1152   if (Pmat) PetscValidHeaderSpecific(Pmat,MAT_CLASSID,3);
1153   if (Amat) PetscCheckSameComm(ts,1,Amat,2);
1154   if (Pmat) PetscCheckSameComm(ts,1,Pmat,3);
1155 
1156   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1157   ierr = DMTSSetRHSJacobian(dm,f,ctx);CHKERRQ(ierr);
1158   if (f == TSComputeRHSJacobianConstant) {
1159     /* Handle this case automatically for the user; otherwise user should call themselves. */
1160     ierr = TSRHSJacobianSetReuse(ts,PETSC_TRUE);CHKERRQ(ierr);
1161   }
1162   ierr = DMTSGetIJacobian(dm,&ijacobian,NULL);CHKERRQ(ierr);
1163   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1164   if (!ijacobian) {
1165     ierr = SNESSetJacobian(snes,Amat,Pmat,SNESTSFormJacobian,ts);CHKERRQ(ierr);
1166   }
1167   if (Amat) {
1168     ierr = PetscObjectReference((PetscObject)Amat);CHKERRQ(ierr);
1169     ierr = MatDestroy(&ts->Arhs);CHKERRQ(ierr);
1170     ts->Arhs = Amat;
1171   }
1172   if (Pmat) {
1173     ierr = PetscObjectReference((PetscObject)Pmat);CHKERRQ(ierr);
1174     ierr = MatDestroy(&ts->Brhs);CHKERRQ(ierr);
1175     ts->Brhs = Pmat;
1176   }
1177   PetscFunctionReturn(0);
1178 }
1179 
1180 
1181 #undef __FUNCT__
1182 #define __FUNCT__ "TSSetIFunction"
1183 /*@C
1184    TSSetIFunction - Set the function to compute F(t,U,U_t) where F() = 0 is the DAE to be solved.
1185 
1186    Logically Collective on TS
1187 
1188    Input Parameters:
1189 +  ts  - the TS context obtained from TSCreate()
1190 .  r   - vector to hold the residual (or NULL to have it created internally)
1191 .  f   - the function evaluation routine
1192 -  ctx - user-defined context for private data for the function evaluation routine (may be NULL)
1193 
1194    Calling sequence of f:
1195 $  f(TS ts,PetscReal t,Vec u,Vec u_t,Vec F,ctx);
1196 
1197 +  t   - time at step/stage being solved
1198 .  u   - state vector
1199 .  u_t - time derivative of state vector
1200 .  F   - function vector
1201 -  ctx - [optional] user-defined context for matrix evaluation routine
1202 
1203    Important:
1204    The user MUST call either this routine or TSSetRHSFunction() to define the ODE.  When solving DAEs you must use this function.
1205 
1206    Level: beginner
1207 
1208 .keywords: TS, timestep, set, DAE, Jacobian
1209 
1210 .seealso: TSSetRHSJacobian(), TSSetRHSFunction(), TSSetIJacobian()
1211 @*/
1212 PetscErrorCode  TSSetIFunction(TS ts,Vec r,TSIFunction f,void *ctx)
1213 {
1214   PetscErrorCode ierr;
1215   SNES           snes;
1216   Vec            ralloc = NULL;
1217   DM             dm;
1218 
1219   PetscFunctionBegin;
1220   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1221   if (r) PetscValidHeaderSpecific(r,VEC_CLASSID,2);
1222 
1223   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1224   ierr = DMTSSetIFunction(dm,f,ctx);CHKERRQ(ierr);
1225 
1226   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1227   if (!r && !ts->dm && ts->vec_sol) {
1228     ierr = VecDuplicate(ts->vec_sol,&ralloc);CHKERRQ(ierr);
1229     r  = ralloc;
1230   }
1231   ierr = SNESSetFunction(snes,r,SNESTSFormFunction,ts);CHKERRQ(ierr);
1232   ierr = VecDestroy(&ralloc);CHKERRQ(ierr);
1233   PetscFunctionReturn(0);
1234 }
1235 
1236 #undef __FUNCT__
1237 #define __FUNCT__ "TSGetIFunction"
1238 /*@C
1239    TSGetIFunction - Returns the vector where the implicit residual is stored and the function/contex to compute it.
1240 
1241    Not Collective
1242 
1243    Input Parameter:
1244 .  ts - the TS context
1245 
1246    Output Parameter:
1247 +  r - vector to hold residual (or NULL)
1248 .  func - the function to compute residual (or NULL)
1249 -  ctx - the function context (or NULL)
1250 
1251    Level: advanced
1252 
1253 .keywords: TS, nonlinear, get, function
1254 
1255 .seealso: TSSetIFunction(), SNESGetFunction()
1256 @*/
1257 PetscErrorCode TSGetIFunction(TS ts,Vec *r,TSIFunction *func,void **ctx)
1258 {
1259   PetscErrorCode ierr;
1260   SNES           snes;
1261   DM             dm;
1262 
1263   PetscFunctionBegin;
1264   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1265   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1266   ierr = SNESGetFunction(snes,r,NULL,NULL);CHKERRQ(ierr);
1267   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1268   ierr = DMTSGetIFunction(dm,func,ctx);CHKERRQ(ierr);
1269   PetscFunctionReturn(0);
1270 }
1271 
1272 #undef __FUNCT__
1273 #define __FUNCT__ "TSGetRHSFunction"
1274 /*@C
1275    TSGetRHSFunction - Returns the vector where the right hand side is stored and the function/context to compute it.
1276 
1277    Not Collective
1278 
1279    Input Parameter:
1280 .  ts - the TS context
1281 
1282    Output Parameter:
1283 +  r - vector to hold computed right hand side (or NULL)
1284 .  func - the function to compute right hand side (or NULL)
1285 -  ctx - the function context (or NULL)
1286 
1287    Level: advanced
1288 
1289 .keywords: TS, nonlinear, get, function
1290 
1291 .seealso: TSSetRHSFunction(), SNESGetFunction()
1292 @*/
1293 PetscErrorCode TSGetRHSFunction(TS ts,Vec *r,TSRHSFunction *func,void **ctx)
1294 {
1295   PetscErrorCode ierr;
1296   SNES           snes;
1297   DM             dm;
1298 
1299   PetscFunctionBegin;
1300   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1301   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1302   ierr = SNESGetFunction(snes,r,NULL,NULL);CHKERRQ(ierr);
1303   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1304   ierr = DMTSGetRHSFunction(dm,func,ctx);CHKERRQ(ierr);
1305   PetscFunctionReturn(0);
1306 }
1307 
1308 #undef __FUNCT__
1309 #define __FUNCT__ "TSSetIJacobian"
1310 /*@C
1311    TSSetIJacobian - Set the function to compute the matrix dF/dU + a*dF/dU_t where F(t,U,U_t) is the function
1312         provided with TSSetIFunction().
1313 
1314    Logically Collective on TS
1315 
1316    Input Parameters:
1317 +  ts  - the TS context obtained from TSCreate()
1318 .  Amat - (approximate) Jacobian matrix
1319 .  Pmat - matrix used to compute preconditioner (usually the same as Amat)
1320 .  f   - the Jacobian evaluation routine
1321 -  ctx - user-defined context for private data for the Jacobian evaluation routine (may be NULL)
1322 
1323    Calling sequence of f:
1324 $  f(TS ts,PetscReal t,Vec U,Vec U_t,PetscReal a,Mat Amat,Mat Pmat,void *ctx);
1325 
1326 +  t    - time at step/stage being solved
1327 .  U    - state vector
1328 .  U_t  - time derivative of state vector
1329 .  a    - shift
1330 .  Amat - (approximate) Jacobian of F(t,U,W+a*U), equivalent to dF/dU + a*dF/dU_t
1331 .  Pmat - matrix used for constructing preconditioner, usually the same as Amat
1332 -  ctx  - [optional] user-defined context for matrix evaluation routine
1333 
1334    Notes:
1335    The matrices Amat and Pmat are exactly the matrices that are used by SNES for the nonlinear solve.
1336 
1337    If you know the operator Amat has a null space you can use MatSetNullSpace() and MatSetTransposeNullSpace() to supply the null
1338    space to Amat and the KSP solvers will automatically use that null space as needed during the solution process.
1339 
1340    The matrix dF/dU + a*dF/dU_t you provide turns out to be
1341    the Jacobian of F(t,U,W+a*U) where F(t,U,U_t) = 0 is the DAE to be solved.
1342    The time integrator internally approximates U_t by W+a*U where the positive "shift"
1343    a and vector W depend on the integration method, step size, and past states. For example with
1344    the backward Euler method a = 1/dt and W = -a*U(previous timestep) so
1345    W + a*U = a*(U - U(previous timestep)) = (U - U(previous timestep))/dt
1346 
1347    You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value
1348 
1349    The TS solver may modify the nonzero structure and the entries of the matrices Amat and Pmat between the calls to f()
1350    You should not assume the values are the same in the next call to f() as you set them in the previous call.
1351 
1352    Level: beginner
1353 
1354 .keywords: TS, timestep, DAE, Jacobian
1355 
1356 .seealso: TSSetIFunction(), TSSetRHSJacobian(), SNESComputeJacobianDefaultColor(), SNESComputeJacobianDefault(), TSSetRHSFunction()
1357 
1358 @*/
1359 PetscErrorCode  TSSetIJacobian(TS ts,Mat Amat,Mat Pmat,TSIJacobian f,void *ctx)
1360 {
1361   PetscErrorCode ierr;
1362   SNES           snes;
1363   DM             dm;
1364 
1365   PetscFunctionBegin;
1366   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1367   if (Amat) PetscValidHeaderSpecific(Amat,MAT_CLASSID,2);
1368   if (Pmat) PetscValidHeaderSpecific(Pmat,MAT_CLASSID,3);
1369   if (Amat) PetscCheckSameComm(ts,1,Amat,2);
1370   if (Pmat) PetscCheckSameComm(ts,1,Pmat,3);
1371 
1372   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1373   ierr = DMTSSetIJacobian(dm,f,ctx);CHKERRQ(ierr);
1374 
1375   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1376   ierr = SNESSetJacobian(snes,Amat,Pmat,SNESTSFormJacobian,ts);CHKERRQ(ierr);
1377   PetscFunctionReturn(0);
1378 }
1379 
1380 #undef __FUNCT__
1381 #define __FUNCT__ "TSRHSJacobianSetReuse"
1382 /*@
1383    TSRHSJacobianSetReuse - restore RHS Jacobian before re-evaluating.  Without this flag, TS will change the sign and
1384    shift the RHS Jacobian for a finite-time-step implicit solve, in which case the user function will need to recompute
1385    the entire Jacobian.  The reuse flag must be set if the evaluation function will assume that the matrix entries have
1386    not been changed by the TS.
1387 
1388    Logically Collective
1389 
1390    Input Arguments:
1391 +  ts - TS context obtained from TSCreate()
1392 -  reuse - PETSC_TRUE if the RHS Jacobian
1393 
1394    Level: intermediate
1395 
1396 .seealso: TSSetRHSJacobian(), TSComputeRHSJacobianConstant()
1397 @*/
1398 PetscErrorCode TSRHSJacobianSetReuse(TS ts,PetscBool reuse)
1399 {
1400   PetscFunctionBegin;
1401   ts->rhsjacobian.reuse = reuse;
1402   PetscFunctionReturn(0);
1403 }
1404 
1405 #undef __FUNCT__
1406 #define __FUNCT__ "TSSetI2Function"
1407 /*@C
1408    TSSetI2Function - Set the function to compute F(t,U,U_t,U_tt) where F = 0 is the DAE to be solved.
1409 
1410    Logically Collective on TS
1411 
1412    Input Parameters:
1413 +  ts  - the TS context obtained from TSCreate()
1414 .  F   - vector to hold the residual (or NULL to have it created internally)
1415 .  fun - the function evaluation routine
1416 -  ctx - user-defined context for private data for the function evaluation routine (may be NULL)
1417 
1418    Calling sequence of fun:
1419 $  fun(TS ts,PetscReal t,Vec U,Vec U_t,Vec U_tt,Vec F,ctx);
1420 
1421 +  t    - time at step/stage being solved
1422 .  U    - state vector
1423 .  U_t  - time derivative of state vector
1424 .  U_tt - second time derivative of state vector
1425 .  F    - function vector
1426 -  ctx  - [optional] user-defined context for matrix evaluation routine (may be NULL)
1427 
1428    Level: beginner
1429 
1430 .keywords: TS, timestep, set, ODE, DAE, Function
1431 
1432 .seealso: TSSetI2Jacobian()
1433 @*/
1434 PetscErrorCode TSSetI2Function(TS ts,Vec F,TSI2Function fun,void *ctx)
1435 {
1436   DM             dm;
1437   PetscErrorCode ierr;
1438 
1439   PetscFunctionBegin;
1440   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1441   if (F) PetscValidHeaderSpecific(F,VEC_CLASSID,2);
1442   ierr = TSSetIFunction(ts,F,NULL,NULL);CHKERRQ(ierr);
1443   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1444   ierr = DMTSSetI2Function(dm,fun,ctx);CHKERRQ(ierr);
1445   PetscFunctionReturn(0);
1446 }
1447 
1448 #undef __FUNCT__
1449 #define __FUNCT__ "TSGetI2Function"
1450 /*@C
1451   TSGetI2Function - Returns the vector where the implicit residual is stored and the function/contex to compute it.
1452 
1453   Not Collective
1454 
1455   Input Parameter:
1456 . ts - the TS context
1457 
1458   Output Parameter:
1459 + r - vector to hold residual (or NULL)
1460 . fun - the function to compute residual (or NULL)
1461 - ctx - the function context (or NULL)
1462 
1463   Level: advanced
1464 
1465 .keywords: TS, nonlinear, get, function
1466 
1467 .seealso: TSSetI2Function(), SNESGetFunction()
1468 @*/
1469 PetscErrorCode TSGetI2Function(TS ts,Vec *r,TSI2Function *fun,void **ctx)
1470 {
1471   PetscErrorCode ierr;
1472   SNES           snes;
1473   DM             dm;
1474 
1475   PetscFunctionBegin;
1476   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1477   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1478   ierr = SNESGetFunction(snes,r,NULL,NULL);CHKERRQ(ierr);
1479   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1480   ierr = DMTSGetI2Function(dm,fun,ctx);CHKERRQ(ierr);
1481   PetscFunctionReturn(0);
1482 }
1483 
1484 #undef __FUNCT__
1485 #define __FUNCT__ "TSSetI2Jacobian"
1486 /*@C
1487    TSSetI2Jacobian - Set the function to compute the matrix dF/dU + v*dF/dU_t  + a*dF/dU_tt
1488         where F(t,U,U_t,U_tt) is the function you provided with TSSetI2Function().
1489 
1490    Logically Collective on TS
1491 
1492    Input Parameters:
1493 +  ts  - the TS context obtained from TSCreate()
1494 .  J   - Jacobian matrix
1495 .  P   - preconditioning matrix for J (may be same as J)
1496 .  jac - the Jacobian evaluation routine
1497 -  ctx - user-defined context for private data for the Jacobian evaluation routine (may be NULL)
1498 
1499    Calling sequence of jac:
1500 $  jac(TS ts,PetscReal t,Vec U,Vec U_t,Vec U_tt,PetscReal v,PetscReal a,Mat J,Mat P,void *ctx);
1501 
1502 +  t    - time at step/stage being solved
1503 .  U    - state vector
1504 .  U_t  - time derivative of state vector
1505 .  U_tt - second time derivative of state vector
1506 .  v    - shift for U_t
1507 .  a    - shift for U_tt
1508 .  J    - Jacobian of G(U) = F(t,U,W+v*U,W'+a*U), equivalent to dF/dU + v*dF/dU_t  + a*dF/dU_tt
1509 .  P    - preconditioning matrix for J, may be same as J
1510 -  ctx  - [optional] user-defined context for matrix evaluation routine
1511 
1512    Notes:
1513    The matrices J and P are exactly the matrices that are used by SNES for the nonlinear solve.
1514 
1515    The matrix dF/dU + v*dF/dU_t + a*dF/dU_tt you provide turns out to be
1516    the Jacobian of G(U) = F(t,U,W+v*U,W'+a*U) where F(t,U,U_t,U_tt) = 0 is the DAE to be solved.
1517    The time integrator internally approximates U_t by W+v*U and U_tt by W'+a*U  where the positive "shift"
1518    parameters 'v' and 'a' and vectors W, W' depend on the integration method, step size, and past states.
1519 
1520    Level: beginner
1521 
1522 .keywords: TS, timestep, set, ODE, DAE, Jacobian
1523 
1524 .seealso: TSSetI2Function()
1525 @*/
1526 PetscErrorCode TSSetI2Jacobian(TS ts,Mat J,Mat P,TSI2Jacobian jac,void *ctx)
1527 {
1528   DM             dm;
1529   PetscErrorCode ierr;
1530 
1531   PetscFunctionBegin;
1532   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1533   if (J) PetscValidHeaderSpecific(J,MAT_CLASSID,2);
1534   if (P) PetscValidHeaderSpecific(P,MAT_CLASSID,3);
1535   ierr = TSSetIJacobian(ts,J,P,NULL,NULL);CHKERRQ(ierr);
1536   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1537   ierr = DMTSSetI2Jacobian(dm,jac,ctx);CHKERRQ(ierr);
1538   PetscFunctionReturn(0);
1539 }
1540 
1541 #undef __FUNCT__
1542 #define __FUNCT__ "TSGetI2Jacobian"
1543 /*@C
1544   TSGetI2Jacobian - Returns the implicit Jacobian at the present timestep.
1545 
1546   Not Collective, but parallel objects are returned if TS is parallel
1547 
1548   Input Parameter:
1549 . ts  - The TS context obtained from TSCreate()
1550 
1551   Output Parameters:
1552 + J  - The (approximate) Jacobian of F(t,U,U_t,U_tt)
1553 . P - The matrix from which the preconditioner is constructed, often the same as J
1554 . jac - The function to compute the Jacobian matrices
1555 - ctx - User-defined context for Jacobian evaluation routine
1556 
1557   Notes: You can pass in NULL for any return argument you do not need.
1558 
1559   Level: advanced
1560 
1561 .seealso: TSGetTimeStep(), TSGetMatrices(), TSGetTime(), TSGetTimeStepNumber()
1562 
1563 .keywords: TS, timestep, get, matrix, Jacobian
1564 @*/
1565 PetscErrorCode  TSGetI2Jacobian(TS ts,Mat *J,Mat *P,TSI2Jacobian *jac,void **ctx)
1566 {
1567   PetscErrorCode ierr;
1568   SNES           snes;
1569   DM             dm;
1570 
1571   PetscFunctionBegin;
1572   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1573   ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr);
1574   ierr = SNESGetJacobian(snes,J,P,NULL,NULL);CHKERRQ(ierr);
1575   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1576   ierr = DMTSGetI2Jacobian(dm,jac,ctx);CHKERRQ(ierr);
1577   PetscFunctionReturn(0);
1578 }
1579 
1580 #undef __FUNCT__
1581 #define __FUNCT__ "TSComputeI2Function"
1582 /*@
1583   TSComputeI2Function - Evaluates the DAE residual written in implicit form F(t,U,U_t,U_tt) = 0
1584 
1585   Collective on TS and Vec
1586 
1587   Input Parameters:
1588 + ts - the TS context
1589 . t - current time
1590 . U - state vector
1591 . V - time derivative of state vector (U_t)
1592 - A - second time derivative of state vector (U_tt)
1593 
1594   Output Parameter:
1595 . F - the residual vector
1596 
1597   Note:
1598   Most users should not need to explicitly call this routine, as it
1599   is used internally within the nonlinear solvers.
1600 
1601   Level: developer
1602 
1603 .keywords: TS, compute, function, vector
1604 
1605 .seealso: TSSetI2Function()
1606 @*/
1607 PetscErrorCode TSComputeI2Function(TS ts,PetscReal t,Vec U,Vec V,Vec A,Vec F)
1608 {
1609   DM             dm;
1610   TSI2Function   I2Function;
1611   void           *ctx;
1612   TSRHSFunction  rhsfunction;
1613   PetscErrorCode ierr;
1614 
1615   PetscFunctionBegin;
1616   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1617   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
1618   PetscValidHeaderSpecific(V,VEC_CLASSID,4);
1619   PetscValidHeaderSpecific(A,VEC_CLASSID,5);
1620   PetscValidHeaderSpecific(F,VEC_CLASSID,6);
1621 
1622   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1623   ierr = DMTSGetI2Function(dm,&I2Function,&ctx);CHKERRQ(ierr);
1624   ierr = DMTSGetRHSFunction(dm,&rhsfunction,NULL);CHKERRQ(ierr);
1625 
1626   if (!I2Function) {
1627     ierr = TSComputeIFunction(ts,t,U,A,F,PETSC_FALSE);CHKERRQ(ierr);
1628     PetscFunctionReturn(0);
1629   }
1630 
1631   ierr = PetscLogEventBegin(TS_FunctionEval,ts,U,V,F);CHKERRQ(ierr);
1632 
1633   PetscStackPush("TS user implicit function");
1634   ierr = I2Function(ts,t,U,V,A,F,ctx);CHKERRQ(ierr);
1635   PetscStackPop;
1636 
1637   if (rhsfunction) {
1638     Vec Frhs;
1639     ierr = TSGetRHSVec_Private(ts,&Frhs);CHKERRQ(ierr);
1640     ierr = TSComputeRHSFunction(ts,t,U,Frhs);CHKERRQ(ierr);
1641     ierr = VecAXPY(F,-1,Frhs);CHKERRQ(ierr);
1642   }
1643 
1644   ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,V,F);CHKERRQ(ierr);
1645   PetscFunctionReturn(0);
1646 }
1647 
1648 #undef __FUNCT__
1649 #define __FUNCT__ "TSComputeI2Jacobian"
1650 /*@
1651   TSComputeI2Jacobian - Evaluates the Jacobian of the DAE
1652 
1653   Collective on TS and Vec
1654 
1655   Input Parameters:
1656 + ts - the TS context
1657 . t - current timestep
1658 . U - state vector
1659 . V - time derivative of state vector
1660 . A - second time derivative of state vector
1661 . shiftV - shift to apply, see note below
1662 - shiftA - shift to apply, see note below
1663 
1664   Output Parameters:
1665 + J - Jacobian matrix
1666 - P - optional preconditioning matrix
1667 
1668   Notes:
1669   If F(t,U,V,A)=0 is the DAE, the required Jacobian is
1670 
1671   dF/dU + shiftV*dF/dV + shiftA*dF/dA
1672 
1673   Most users should not need to explicitly call this routine, as it
1674   is used internally within the nonlinear solvers.
1675 
1676   Level: developer
1677 
1678 .keywords: TS, compute, Jacobian, matrix
1679 
1680 .seealso:  TSSetI2Jacobian()
1681 @*/
1682 PetscErrorCode TSComputeI2Jacobian(TS ts,PetscReal t,Vec U,Vec V,Vec A,PetscReal shiftV,PetscReal shiftA,Mat J,Mat P)
1683 {
1684   DM             dm;
1685   TSI2Jacobian   I2Jacobian;
1686   void           *ctx;
1687   TSRHSJacobian  rhsjacobian;
1688   PetscErrorCode ierr;
1689 
1690   PetscFunctionBegin;
1691   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1692   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
1693   PetscValidHeaderSpecific(V,VEC_CLASSID,4);
1694   PetscValidHeaderSpecific(A,VEC_CLASSID,5);
1695   PetscValidHeaderSpecific(J,MAT_CLASSID,8);
1696   PetscValidHeaderSpecific(P,MAT_CLASSID,9);
1697 
1698   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1699   ierr = DMTSGetI2Jacobian(dm,&I2Jacobian,&ctx);CHKERRQ(ierr);
1700   ierr = DMTSGetRHSJacobian(dm,&rhsjacobian,NULL);CHKERRQ(ierr);
1701 
1702   if (!I2Jacobian) {
1703     ierr = TSComputeIJacobian(ts,t,U,A,shiftA,J,P,PETSC_FALSE);CHKERRQ(ierr);
1704     PetscFunctionReturn(0);
1705   }
1706 
1707   ierr = PetscLogEventBegin(TS_JacobianEval,ts,U,J,P);CHKERRQ(ierr);
1708 
1709   PetscStackPush("TS user implicit Jacobian");
1710   ierr = I2Jacobian(ts,t,U,V,A,shiftV,shiftA,J,P,ctx);CHKERRQ(ierr);
1711   PetscStackPop;
1712 
1713   if (rhsjacobian) {
1714     Mat Jrhs,Prhs; MatStructure axpy = DIFFERENT_NONZERO_PATTERN;
1715     ierr = TSGetRHSMats_Private(ts,&Jrhs,&Prhs);CHKERRQ(ierr);
1716     ierr = TSComputeRHSJacobian(ts,t,U,Jrhs,Prhs);CHKERRQ(ierr);
1717     ierr = MatAXPY(J,-1,Jrhs,axpy);CHKERRQ(ierr);
1718     if (P != J) {ierr = MatAXPY(P,-1,Prhs,axpy);CHKERRQ(ierr);}
1719   }
1720 
1721   ierr = PetscLogEventEnd(TS_JacobianEval,ts,U,J,P);CHKERRQ(ierr);
1722   PetscFunctionReturn(0);
1723 }
1724 
1725 #undef __FUNCT__
1726 #define __FUNCT__ "TS2SetSolution"
1727 /*@
1728    TS2SetSolution - Sets the initial solution and time derivative vectors
1729    for use by the TS routines handling second order equations.
1730 
1731    Logically Collective on TS and Vec
1732 
1733    Input Parameters:
1734 +  ts - the TS context obtained from TSCreate()
1735 .  u - the solution vector
1736 -  v - the time derivative vector
1737 
1738    Level: beginner
1739 
1740 .keywords: TS, timestep, set, solution, initial conditions
1741 @*/
1742 PetscErrorCode  TS2SetSolution(TS ts,Vec u,Vec v)
1743 {
1744   PetscErrorCode ierr;
1745 
1746   PetscFunctionBegin;
1747   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1748   PetscValidHeaderSpecific(u,VEC_CLASSID,2);
1749   PetscValidHeaderSpecific(v,VEC_CLASSID,3);
1750   ierr = TSSetSolution(ts,u);CHKERRQ(ierr);
1751   ierr = PetscObjectReference((PetscObject)v);CHKERRQ(ierr);
1752   ierr = VecDestroy(&ts->vec_dot);CHKERRQ(ierr);
1753   ts->vec_dot = v;
1754   PetscFunctionReturn(0);
1755 }
1756 
1757 #undef __FUNCT__
1758 #define __FUNCT__ "TS2GetSolution"
1759 /*@
1760    TS2GetSolution - Returns the solution and time derivative at the present timestep
1761    for second order equations. It is valid to call this routine inside the function
1762    that you are evaluating in order to move to the new timestep. This vector not
1763    changed until the solution at the next timestep has been calculated.
1764 
1765    Not Collective, but Vec returned is parallel if TS is parallel
1766 
1767    Input Parameter:
1768 .  ts - the TS context obtained from TSCreate()
1769 
1770    Output Parameter:
1771 +  u - the vector containing the solution
1772 -  v - the vector containing the time derivative
1773 
1774    Level: intermediate
1775 
1776 .seealso: TS2SetSolution(), TSGetTimeStep(), TSGetTime()
1777 
1778 .keywords: TS, timestep, get, solution
1779 @*/
1780 PetscErrorCode  TS2GetSolution(TS ts,Vec *u,Vec *v)
1781 {
1782   PetscFunctionBegin;
1783   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1784   if (u) PetscValidPointer(u,2);
1785   if (v) PetscValidPointer(v,3);
1786   if (u) *u = ts->vec_sol;
1787   if (v) *v = ts->vec_dot;
1788   PetscFunctionReturn(0);
1789 }
1790 
1791 #undef __FUNCT__
1792 #define __FUNCT__ "TSLoad"
1793 /*@C
1794   TSLoad - Loads a KSP that has been stored in binary  with KSPView().
1795 
1796   Collective on PetscViewer
1797 
1798   Input Parameters:
1799 + newdm - the newly loaded TS, this needs to have been created with TSCreate() or
1800            some related function before a call to TSLoad().
1801 - viewer - binary file viewer, obtained from PetscViewerBinaryOpen()
1802 
1803    Level: intermediate
1804 
1805   Notes:
1806    The type is determined by the data in the file, any type set into the TS before this call is ignored.
1807 
1808   Notes for advanced users:
1809   Most users should not need to know the details of the binary storage
1810   format, since TSLoad() and TSView() completely hide these details.
1811   But for anyone who's interested, the standard binary matrix storage
1812   format is
1813 .vb
1814      has not yet been determined
1815 .ve
1816 
1817 .seealso: PetscViewerBinaryOpen(), TSView(), MatLoad(), VecLoad()
1818 @*/
1819 PetscErrorCode  TSLoad(TS ts, PetscViewer viewer)
1820 {
1821   PetscErrorCode ierr;
1822   PetscBool      isbinary;
1823   PetscInt       classid;
1824   char           type[256];
1825   DMTS           sdm;
1826   DM             dm;
1827 
1828   PetscFunctionBegin;
1829   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1830   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
1831   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1832   if (!isbinary) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid viewer; open viewer with PetscViewerBinaryOpen()");
1833 
1834   ierr = PetscViewerBinaryRead(viewer,&classid,1,NULL,PETSC_INT);CHKERRQ(ierr);
1835   if (classid != TS_FILE_CLASSID) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Not TS next in file");
1836   ierr = PetscViewerBinaryRead(viewer,type,256,NULL,PETSC_CHAR);CHKERRQ(ierr);
1837   ierr = TSSetType(ts, type);CHKERRQ(ierr);
1838   if (ts->ops->load) {
1839     ierr = (*ts->ops->load)(ts,viewer);CHKERRQ(ierr);
1840   }
1841   ierr = DMCreate(PetscObjectComm((PetscObject)ts),&dm);CHKERRQ(ierr);
1842   ierr = DMLoad(dm,viewer);CHKERRQ(ierr);
1843   ierr = TSSetDM(ts,dm);CHKERRQ(ierr);
1844   ierr = DMCreateGlobalVector(ts->dm,&ts->vec_sol);CHKERRQ(ierr);
1845   ierr = VecLoad(ts->vec_sol,viewer);CHKERRQ(ierr);
1846   ierr = DMGetDMTS(ts->dm,&sdm);CHKERRQ(ierr);
1847   ierr = DMTSLoad(sdm,viewer);CHKERRQ(ierr);
1848   PetscFunctionReturn(0);
1849 }
1850 
1851 #include <petscdraw.h>
1852 #if defined(PETSC_HAVE_SAWS)
1853 #include <petscviewersaws.h>
1854 #endif
1855 #undef __FUNCT__
1856 #define __FUNCT__ "TSView"
1857 /*@C
1858     TSView - Prints the TS data structure.
1859 
1860     Collective on TS
1861 
1862     Input Parameters:
1863 +   ts - the TS context obtained from TSCreate()
1864 -   viewer - visualization context
1865 
1866     Options Database Key:
1867 .   -ts_view - calls TSView() at end of TSStep()
1868 
1869     Notes:
1870     The available visualization contexts include
1871 +     PETSC_VIEWER_STDOUT_SELF - standard output (default)
1872 -     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
1873          output where only the first processor opens
1874          the file.  All other processors send their
1875          data to the first processor to print.
1876 
1877     The user can open an alternative visualization context with
1878     PetscViewerASCIIOpen() - output to a specified file.
1879 
1880     Level: beginner
1881 
1882 .keywords: TS, timestep, view
1883 
1884 .seealso: PetscViewerASCIIOpen()
1885 @*/
1886 PetscErrorCode  TSView(TS ts,PetscViewer viewer)
1887 {
1888   PetscErrorCode ierr;
1889   TSType         type;
1890   PetscBool      iascii,isstring,isundials,isbinary,isdraw;
1891   DMTS           sdm;
1892 #if defined(PETSC_HAVE_SAWS)
1893   PetscBool      issaws;
1894 #endif
1895 
1896   PetscFunctionBegin;
1897   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1898   if (!viewer) {
1899     ierr = PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)ts),&viewer);CHKERRQ(ierr);
1900   }
1901   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
1902   PetscCheckSameComm(ts,1,viewer,2);
1903 
1904   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1905   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);CHKERRQ(ierr);
1906   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1907   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1908 #if defined(PETSC_HAVE_SAWS)
1909   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSAWS,&issaws);CHKERRQ(ierr);
1910 #endif
1911   if (iascii) {
1912     ierr = PetscObjectPrintClassNamePrefixType((PetscObject)ts,viewer);CHKERRQ(ierr);
1913     ierr = PetscViewerASCIIPrintf(viewer,"  maximum steps=%D\n",ts->max_steps);CHKERRQ(ierr);
1914     ierr = PetscViewerASCIIPrintf(viewer,"  maximum time=%g\n",(double)ts->max_time);CHKERRQ(ierr);
1915     if (ts->problem_type == TS_NONLINEAR) {
1916       ierr = PetscViewerASCIIPrintf(viewer,"  total number of nonlinear solver iterations=%D\n",ts->snes_its);CHKERRQ(ierr);
1917       ierr = PetscViewerASCIIPrintf(viewer,"  total number of nonlinear solve failures=%D\n",ts->num_snes_failures);CHKERRQ(ierr);
1918     }
1919     ierr = PetscViewerASCIIPrintf(viewer,"  total number of linear solver iterations=%D\n",ts->ksp_its);CHKERRQ(ierr);
1920     ierr = PetscViewerASCIIPrintf(viewer,"  total number of rejected steps=%D\n",ts->reject);CHKERRQ(ierr);
1921     if (ts->vrtol) {
1922       ierr = PetscViewerASCIIPrintf(viewer,"  using vector of relative error tolerances, ");CHKERRQ(ierr);
1923     } else {
1924       ierr = PetscViewerASCIIPrintf(viewer,"  using relative error tolerance of %g, ",(double)ts->rtol);CHKERRQ(ierr);
1925     }
1926     if (ts->vatol) {
1927       ierr = PetscViewerASCIIPrintf(viewer,"  using vector of absolute error tolerances\n");CHKERRQ(ierr);
1928     } else {
1929       ierr = PetscViewerASCIIPrintf(viewer,"  using absolute error tolerance of %g\n",(double)ts->atol);CHKERRQ(ierr);
1930     }
1931     ierr = DMGetDMTS(ts->dm,&sdm);CHKERRQ(ierr);
1932     ierr = DMTSView(sdm,viewer);CHKERRQ(ierr);
1933     if (ts->ops->view) {
1934       ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1935       ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
1936       ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1937     }
1938   } else if (isstring) {
1939     ierr = TSGetType(ts,&type);CHKERRQ(ierr);
1940     ierr = PetscViewerStringSPrintf(viewer," %-7.7s",type);CHKERRQ(ierr);
1941   } else if (isbinary) {
1942     PetscInt    classid = TS_FILE_CLASSID;
1943     MPI_Comm    comm;
1944     PetscMPIInt rank;
1945     char        type[256];
1946 
1947     ierr = PetscObjectGetComm((PetscObject)ts,&comm);CHKERRQ(ierr);
1948     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1949     if (!rank) {
1950       ierr = PetscViewerBinaryWrite(viewer,&classid,1,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
1951       ierr = PetscStrncpy(type,((PetscObject)ts)->type_name,256);CHKERRQ(ierr);
1952       ierr = PetscViewerBinaryWrite(viewer,type,256,PETSC_CHAR,PETSC_FALSE);CHKERRQ(ierr);
1953     }
1954     if (ts->ops->view) {
1955       ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
1956     }
1957     ierr = DMView(ts->dm,viewer);CHKERRQ(ierr);
1958     ierr = VecView(ts->vec_sol,viewer);CHKERRQ(ierr);
1959     ierr = DMGetDMTS(ts->dm,&sdm);CHKERRQ(ierr);
1960     ierr = DMTSView(sdm,viewer);CHKERRQ(ierr);
1961   } else if (isdraw) {
1962     PetscDraw draw;
1963     char      str[36];
1964     PetscReal x,y,bottom,h;
1965 
1966     ierr   = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1967     ierr   = PetscDrawGetCurrentPoint(draw,&x,&y);CHKERRQ(ierr);
1968     ierr   = PetscStrcpy(str,"TS: ");CHKERRQ(ierr);
1969     ierr   = PetscStrcat(str,((PetscObject)ts)->type_name);CHKERRQ(ierr);
1970     ierr   = PetscDrawStringBoxed(draw,x,y,PETSC_DRAW_BLACK,PETSC_DRAW_BLACK,str,NULL,&h);CHKERRQ(ierr);
1971     bottom = y - h;
1972     ierr   = PetscDrawPushCurrentPoint(draw,x,bottom);CHKERRQ(ierr);
1973     if (ts->ops->view) {
1974       ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
1975     }
1976     ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
1977 #if defined(PETSC_HAVE_SAWS)
1978   } else if (issaws) {
1979     PetscMPIInt rank;
1980     const char  *name;
1981 
1982     ierr = PetscObjectGetName((PetscObject)ts,&name);CHKERRQ(ierr);
1983     ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
1984     if (!((PetscObject)ts)->amsmem && !rank) {
1985       char       dir[1024];
1986 
1987       ierr = PetscObjectViewSAWs((PetscObject)ts,viewer);CHKERRQ(ierr);
1988       ierr = PetscSNPrintf(dir,1024,"/PETSc/Objects/%s/time_step",name);CHKERRQ(ierr);
1989       PetscStackCallSAWs(SAWs_Register,(dir,&ts->steps,1,SAWs_READ,SAWs_INT));
1990       ierr = PetscSNPrintf(dir,1024,"/PETSc/Objects/%s/time",name);CHKERRQ(ierr);
1991       PetscStackCallSAWs(SAWs_Register,(dir,&ts->ptime,1,SAWs_READ,SAWs_DOUBLE));
1992     }
1993     if (ts->ops->view) {
1994       ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
1995     }
1996 #endif
1997   }
1998 
1999   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
2000   ierr = PetscObjectTypeCompare((PetscObject)ts,TSSUNDIALS,&isundials);CHKERRQ(ierr);
2001   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
2002   PetscFunctionReturn(0);
2003 }
2004 
2005 
2006 #undef __FUNCT__
2007 #define __FUNCT__ "TSSetApplicationContext"
2008 /*@
2009    TSSetApplicationContext - Sets an optional user-defined context for
2010    the timesteppers.
2011 
2012    Logically Collective on TS
2013 
2014    Input Parameters:
2015 +  ts - the TS context obtained from TSCreate()
2016 -  usrP - optional user context
2017 
2018    Fortran Notes: To use this from Fortran you must write a Fortran interface definition for this
2019     function that tells Fortran the Fortran derived data type that you are passing in as the ctx argument.
2020 
2021    Level: intermediate
2022 
2023 .keywords: TS, timestep, set, application, context
2024 
2025 .seealso: TSGetApplicationContext()
2026 @*/
2027 PetscErrorCode  TSSetApplicationContext(TS ts,void *usrP)
2028 {
2029   PetscFunctionBegin;
2030   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2031   ts->user = usrP;
2032   PetscFunctionReturn(0);
2033 }
2034 
2035 #undef __FUNCT__
2036 #define __FUNCT__ "TSGetApplicationContext"
2037 /*@
2038     TSGetApplicationContext - Gets the user-defined context for the
2039     timestepper.
2040 
2041     Not Collective
2042 
2043     Input Parameter:
2044 .   ts - the TS context obtained from TSCreate()
2045 
2046     Output Parameter:
2047 .   usrP - user context
2048 
2049    Fortran Notes: To use this from Fortran you must write a Fortran interface definition for this
2050     function that tells Fortran the Fortran derived data type that you are passing in as the ctx argument.
2051 
2052     Level: intermediate
2053 
2054 .keywords: TS, timestep, get, application, context
2055 
2056 .seealso: TSSetApplicationContext()
2057 @*/
2058 PetscErrorCode  TSGetApplicationContext(TS ts,void *usrP)
2059 {
2060   PetscFunctionBegin;
2061   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2062   *(void**)usrP = ts->user;
2063   PetscFunctionReturn(0);
2064 }
2065 
2066 #undef __FUNCT__
2067 #define __FUNCT__ "TSGetTimeStepNumber"
2068 /*@
2069    TSGetTimeStepNumber - Gets the number of time steps completed.
2070 
2071    Not Collective
2072 
2073    Input Parameter:
2074 .  ts - the TS context obtained from TSCreate()
2075 
2076    Output Parameter:
2077 .  iter - number of steps completed so far
2078 
2079    Level: intermediate
2080 
2081 .keywords: TS, timestep, get, iteration, number
2082 .seealso: TSGetTime(), TSGetTimeStep(), TSSetPreStep(), TSSetPreStage(), TSSetPostStage(), TSSetPostStep()
2083 @*/
2084 PetscErrorCode  TSGetTimeStepNumber(TS ts,PetscInt *iter)
2085 {
2086   PetscFunctionBegin;
2087   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2088   PetscValidIntPointer(iter,2);
2089   *iter = ts->steps;
2090   PetscFunctionReturn(0);
2091 }
2092 
2093 #undef __FUNCT__
2094 #define __FUNCT__ "TSSetInitialTimeStep"
2095 /*@
2096    TSSetInitialTimeStep - Sets the initial timestep to be used,
2097    as well as the initial time.
2098 
2099    Logically Collective on TS
2100 
2101    Input Parameters:
2102 +  ts - the TS context obtained from TSCreate()
2103 .  initial_time - the initial time
2104 -  time_step - the size of the timestep
2105 
2106    Level: intermediate
2107 
2108 .seealso: TSSetTimeStep(), TSGetTimeStep()
2109 
2110 .keywords: TS, set, initial, timestep
2111 @*/
2112 PetscErrorCode  TSSetInitialTimeStep(TS ts,PetscReal initial_time,PetscReal time_step)
2113 {
2114   PetscErrorCode ierr;
2115 
2116   PetscFunctionBegin;
2117   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2118   ierr = TSSetTimeStep(ts,time_step);CHKERRQ(ierr);
2119   ierr = TSSetTime(ts,initial_time);CHKERRQ(ierr);
2120   PetscFunctionReturn(0);
2121 }
2122 
2123 #undef __FUNCT__
2124 #define __FUNCT__ "TSSetTimeStep"
2125 /*@
2126    TSSetTimeStep - Allows one to reset the timestep at any time,
2127    useful for simple pseudo-timestepping codes.
2128 
2129    Logically Collective on TS
2130 
2131    Input Parameters:
2132 +  ts - the TS context obtained from TSCreate()
2133 -  time_step - the size of the timestep
2134 
2135    Level: intermediate
2136 
2137 .seealso: TSSetInitialTimeStep(), TSGetTimeStep()
2138 
2139 .keywords: TS, set, timestep
2140 @*/
2141 PetscErrorCode  TSSetTimeStep(TS ts,PetscReal time_step)
2142 {
2143   PetscFunctionBegin;
2144   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2145   PetscValidLogicalCollectiveReal(ts,time_step,2);
2146   ts->time_step = time_step;
2147   PetscFunctionReturn(0);
2148 }
2149 
2150 #undef __FUNCT__
2151 #define __FUNCT__ "TSSetExactFinalTime"
2152 /*@
2153    TSSetExactFinalTime - Determines whether to adapt the final time step to
2154      match the exact final time, interpolate solution to the exact final time,
2155      or just return at the final time TS computed.
2156 
2157   Logically Collective on TS
2158 
2159    Input Parameter:
2160 +   ts - the time-step context
2161 -   eftopt - exact final time option
2162 
2163 $  TS_EXACTFINALTIME_STEPOVER    - Don't do anything if final time is exceeded
2164 $  TS_EXACTFINALTIME_INTERPOLATE - Interpolate back to final time
2165 $  TS_EXACTFINALTIME_MATCHSTEP - Adapt final time step to match the final time
2166 
2167    Options Database:
2168 .   -ts_exact_final_time <stepover,interpolate,matchstep> - select the final step at runtime
2169 
2170    Warning: If you use the option TS_EXACTFINALTIME_STEPOVER the solution may be at a very different time
2171     then the final time you selected.
2172 
2173    Level: beginner
2174 
2175 .seealso: TSExactFinalTimeOption
2176 @*/
2177 PetscErrorCode  TSSetExactFinalTime(TS ts,TSExactFinalTimeOption eftopt)
2178 {
2179   PetscFunctionBegin;
2180   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2181   PetscValidLogicalCollectiveEnum(ts,eftopt,2);
2182   ts->exact_final_time = eftopt;
2183   PetscFunctionReturn(0);
2184 }
2185 
2186 #undef __FUNCT__
2187 #define __FUNCT__ "TSGetTimeStep"
2188 /*@
2189    TSGetTimeStep - Gets the current timestep size.
2190 
2191    Not Collective
2192 
2193    Input Parameter:
2194 .  ts - the TS context obtained from TSCreate()
2195 
2196    Output Parameter:
2197 .  dt - the current timestep size
2198 
2199    Level: intermediate
2200 
2201 .seealso: TSSetInitialTimeStep(), TSGetTimeStep()
2202 
2203 .keywords: TS, get, timestep
2204 @*/
2205 PetscErrorCode  TSGetTimeStep(TS ts,PetscReal *dt)
2206 {
2207   PetscFunctionBegin;
2208   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2209   PetscValidRealPointer(dt,2);
2210   *dt = ts->time_step;
2211   PetscFunctionReturn(0);
2212 }
2213 
2214 #undef __FUNCT__
2215 #define __FUNCT__ "TSGetSolution"
2216 /*@
2217    TSGetSolution - Returns the solution at the present timestep. It
2218    is valid to call this routine inside the function that you are evaluating
2219    in order to move to the new timestep. This vector not changed until
2220    the solution at the next timestep has been calculated.
2221 
2222    Not Collective, but Vec returned is parallel if TS is parallel
2223 
2224    Input Parameter:
2225 .  ts - the TS context obtained from TSCreate()
2226 
2227    Output Parameter:
2228 .  v - the vector containing the solution
2229 
2230    Note: If you used TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP); this does not return the solution at the requested
2231    final time. It returns the solution at the next timestep.
2232 
2233    Level: intermediate
2234 
2235 .seealso: TSGetTimeStep(), TSGetTime(), TSGetSolveTime(), TSGetSolutionComponents()
2236 
2237 .keywords: TS, timestep, get, solution
2238 @*/
2239 PetscErrorCode  TSGetSolution(TS ts,Vec *v)
2240 {
2241   PetscFunctionBegin;
2242   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2243   PetscValidPointer(v,2);
2244   *v = ts->vec_sol;
2245   PetscFunctionReturn(0);
2246 }
2247 
2248 #undef __FUNCT__
2249 #define __FUNCT__ "TSGetSolutionComponents"
2250 /*@
2251    TSGetSolutionComponents - Returns any solution components at the present
2252    timestep, if available for the time integration method being used.
2253    Solution components are quantities that share the same size and
2254    structure as the solution vector.
2255 
2256    Not Collective, but Vec returned is parallel if TS is parallel
2257 
2258    Parameters :
2259 .  ts - the TS context obtained from TSCreate() (input parameter).
2260 .  n - If v is PETSC_NULL, then the number of solution components is
2261        returned through n, else the n-th solution component is
2262        returned in v.
2263 .  v - the vector containing the n-th solution component
2264        (may be PETSC_NULL to use this function to find out
2265         the number of solutions components).
2266 
2267    Level: advanced
2268 
2269 .seealso: TSGetSolution()
2270 
2271 .keywords: TS, timestep, get, solution
2272 @*/
2273 PetscErrorCode  TSGetSolutionComponents(TS ts,PetscInt *n,Vec *v)
2274 {
2275   PetscErrorCode ierr;
2276 
2277   PetscFunctionBegin;
2278   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2279   if (!ts->ops->getsolutioncomponents) *n = 0;
2280   else {
2281     ierr = (*ts->ops->getsolutioncomponents)(ts,n,v);CHKERRQ(ierr);
2282   }
2283   PetscFunctionReturn(0);
2284 }
2285 
2286 #undef __FUNCT__
2287 #define __FUNCT__ "TSGetAuxSolution"
2288 /*@
2289    TSGetAuxSolution - Returns an auxiliary solution at the present
2290    timestep, if available for the time integration method being used.
2291 
2292    Not Collective, but Vec returned is parallel if TS is parallel
2293 
2294    Parameters :
2295 .  ts - the TS context obtained from TSCreate() (input parameter).
2296 .  v - the vector containing the auxiliary solution
2297 
2298    Level: intermediate
2299 
2300 .seealso: TSGetSolution()
2301 
2302 .keywords: TS, timestep, get, solution
2303 @*/
2304 PetscErrorCode  TSGetAuxSolution(TS ts,Vec *v)
2305 {
2306   PetscErrorCode ierr;
2307 
2308   PetscFunctionBegin;
2309   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2310   if (ts->ops->getauxsolution) {
2311     ierr = (*ts->ops->getauxsolution)(ts,v);CHKERRQ(ierr);
2312   } else {
2313     ierr = VecZeroEntries(*v); CHKERRQ(ierr);
2314   }
2315   PetscFunctionReturn(0);
2316 }
2317 
2318 #undef __FUNCT__
2319 #define __FUNCT__ "TSGetTimeError"
2320 /*@
2321    TSGetTimeError - Returns the estimated error vector, if the chosen
2322    TSType has an error estimation functionality.
2323 
2324    Not Collective, but Vec returned is parallel if TS is parallel
2325 
2326    Note: MUST call after TSSetUp()
2327 
2328    Parameters :
2329 .  ts - the TS context obtained from TSCreate() (input parameter).
2330 .  n - current estimate (n=0) or previous one (n=-1)
2331 .  v - the vector containing the error (same size as the solution).
2332 
2333    Level: intermediate
2334 
2335 .seealso: TSGetSolution(), TSSetTimeError()
2336 
2337 .keywords: TS, timestep, get, error
2338 @*/
2339 PetscErrorCode  TSGetTimeError(TS ts,PetscInt n,Vec *v)
2340 {
2341   PetscErrorCode ierr;
2342 
2343   PetscFunctionBegin;
2344   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2345   if (ts->ops->gettimeerror) {
2346     ierr = (*ts->ops->gettimeerror)(ts,n,v);CHKERRQ(ierr);
2347   } else {
2348     ierr = VecZeroEntries(*v);CHKERRQ(ierr);
2349   }
2350   PetscFunctionReturn(0);
2351 }
2352 
2353 #undef __FUNCT__
2354 #define __FUNCT__ "TSSetTimeError"
2355 /*@
2356    TSSetTimeError - Sets the estimated error vector, if the chosen
2357    TSType has an error estimation functionality. This can be used
2358    to restart such a time integrator with a given error vector.
2359 
2360    Not Collective, but Vec returned is parallel if TS is parallel
2361 
2362    Parameters :
2363 .  ts - the TS context obtained from TSCreate() (input parameter).
2364 .  v - the vector containing the error (same size as the solution).
2365 
2366    Level: intermediate
2367 
2368 .seealso: TSSetSolution(), TSGetTimeError)
2369 
2370 .keywords: TS, timestep, get, error
2371 @*/
2372 PetscErrorCode  TSSetTimeError(TS ts,Vec v)
2373 {
2374   PetscErrorCode ierr;
2375 
2376   PetscFunctionBegin;
2377   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2378   if (!ts->setupcalled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetUp() first");
2379   if (ts->ops->settimeerror) {
2380     ierr = (*ts->ops->settimeerror)(ts,v);CHKERRQ(ierr);
2381   }
2382   PetscFunctionReturn(0);
2383 }
2384 
2385 #undef __FUNCT__
2386 #define __FUNCT__ "TSGetCostGradients"
2387 /*@
2388    TSGetCostGradients - Returns the gradients from the TSAdjointSolve()
2389 
2390    Not Collective, but Vec returned is parallel if TS is parallel
2391 
2392    Input Parameter:
2393 .  ts - the TS context obtained from TSCreate()
2394 
2395    Output Parameter:
2396 +  lambda - vectors containing the gradients of the cost functions with respect to the ODE/DAE solution variables
2397 -  mu - vectors containing the gradients of the cost functions with respect to the problem parameters
2398 
2399    Level: intermediate
2400 
2401 .seealso: TSGetTimeStep()
2402 
2403 .keywords: TS, timestep, get, sensitivity
2404 @*/
2405 PetscErrorCode  TSGetCostGradients(TS ts,PetscInt *numcost,Vec **lambda,Vec **mu)
2406 {
2407   PetscFunctionBegin;
2408   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2409   if (numcost) *numcost = ts->numcost;
2410   if (lambda)  *lambda  = ts->vecs_sensi;
2411   if (mu)      *mu      = ts->vecs_sensip;
2412   PetscFunctionReturn(0);
2413 }
2414 
2415 /* ----- Routines to initialize and destroy a timestepper ---- */
2416 #undef __FUNCT__
2417 #define __FUNCT__ "TSSetProblemType"
2418 /*@
2419   TSSetProblemType - Sets the type of problem to be solved.
2420 
2421   Not collective
2422 
2423   Input Parameters:
2424 + ts   - The TS
2425 - type - One of TS_LINEAR, TS_NONLINEAR where these types refer to problems of the forms
2426 .vb
2427          U_t - A U = 0      (linear)
2428          U_t - A(t) U = 0   (linear)
2429          F(t,U,U_t) = 0     (nonlinear)
2430 .ve
2431 
2432    Level: beginner
2433 
2434 .keywords: TS, problem type
2435 .seealso: TSSetUp(), TSProblemType, TS
2436 @*/
2437 PetscErrorCode  TSSetProblemType(TS ts, TSProblemType type)
2438 {
2439   PetscErrorCode ierr;
2440 
2441   PetscFunctionBegin;
2442   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
2443   ts->problem_type = type;
2444   if (type == TS_LINEAR) {
2445     SNES snes;
2446     ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
2447     ierr = SNESSetType(snes,SNESKSPONLY);CHKERRQ(ierr);
2448   }
2449   PetscFunctionReturn(0);
2450 }
2451 
2452 #undef __FUNCT__
2453 #define __FUNCT__ "TSGetProblemType"
2454 /*@C
2455   TSGetProblemType - Gets the type of problem to be solved.
2456 
2457   Not collective
2458 
2459   Input Parameter:
2460 . ts   - The TS
2461 
2462   Output Parameter:
2463 . type - One of TS_LINEAR, TS_NONLINEAR where these types refer to problems of the forms
2464 .vb
2465          M U_t = A U
2466          M(t) U_t = A(t) U
2467          F(t,U,U_t)
2468 .ve
2469 
2470    Level: beginner
2471 
2472 .keywords: TS, problem type
2473 .seealso: TSSetUp(), TSProblemType, TS
2474 @*/
2475 PetscErrorCode  TSGetProblemType(TS ts, TSProblemType *type)
2476 {
2477   PetscFunctionBegin;
2478   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
2479   PetscValidIntPointer(type,2);
2480   *type = ts->problem_type;
2481   PetscFunctionReturn(0);
2482 }
2483 
2484 #undef __FUNCT__
2485 #define __FUNCT__ "TSSetUp"
2486 /*@
2487    TSSetUp - Sets up the internal data structures for the later use
2488    of a timestepper.
2489 
2490    Collective on TS
2491 
2492    Input Parameter:
2493 .  ts - the TS context obtained from TSCreate()
2494 
2495    Notes:
2496    For basic use of the TS solvers the user need not explicitly call
2497    TSSetUp(), since these actions will automatically occur during
2498    the call to TSStep().  However, if one wishes to control this
2499    phase separately, TSSetUp() should be called after TSCreate()
2500    and optional routines of the form TSSetXXX(), but before TSStep().
2501 
2502    Level: advanced
2503 
2504 .keywords: TS, timestep, setup
2505 
2506 .seealso: TSCreate(), TSStep(), TSDestroy()
2507 @*/
2508 PetscErrorCode  TSSetUp(TS ts)
2509 {
2510   PetscErrorCode ierr;
2511   DM             dm;
2512   PetscErrorCode (*func)(SNES,Vec,Vec,void*);
2513   PetscErrorCode (*jac)(SNES,Vec,Mat,Mat,void*);
2514   TSIFunction    ifun;
2515   TSIJacobian    ijac;
2516   TSI2Jacobian   i2jac;
2517   TSRHSJacobian  rhsjac;
2518 
2519   PetscFunctionBegin;
2520   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2521   if (ts->setupcalled) PetscFunctionReturn(0);
2522 
2523   ts->total_steps = 0;
2524   if (!((PetscObject)ts)->type_name) {
2525     ierr = TSGetIFunction(ts,NULL,&ifun,NULL);CHKERRQ(ierr);
2526     ierr = TSSetType(ts,ifun ? TSBEULER : TSEULER);CHKERRQ(ierr);
2527   }
2528 
2529   if (!ts->vec_sol) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetSolution() first");
2530 
2531   if (ts->rhsjacobian.reuse) {
2532     Mat Amat,Pmat;
2533     SNES snes;
2534     ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
2535     ierr = SNESGetJacobian(snes,&Amat,&Pmat,NULL,NULL);CHKERRQ(ierr);
2536     /* Matching matrices implies that an IJacobian is NOT set, because if it had been set, the IJacobian's matrix would
2537      * have displaced the RHS matrix */
2538     if (Amat == ts->Arhs) {
2539       ierr = MatDuplicate(ts->Arhs,MAT_DO_NOT_COPY_VALUES,&Amat);CHKERRQ(ierr);
2540       ierr = SNESSetJacobian(snes,Amat,NULL,NULL,NULL);CHKERRQ(ierr);
2541       ierr = MatDestroy(&Amat);CHKERRQ(ierr);
2542     }
2543     if (Pmat == ts->Brhs) {
2544       ierr = MatDuplicate(ts->Brhs,MAT_DO_NOT_COPY_VALUES,&Pmat);CHKERRQ(ierr);
2545       ierr = SNESSetJacobian(snes,NULL,Pmat,NULL,NULL);CHKERRQ(ierr);
2546       ierr = MatDestroy(&Pmat);CHKERRQ(ierr);
2547     }
2548   }
2549   if (ts->ops->setup) {
2550     ierr = (*ts->ops->setup)(ts);CHKERRQ(ierr);
2551   }
2552 
2553   /* In the case where we've set a DMTSFunction or what have you, we need the default SNESFunction
2554      to be set right but can't do it elsewhere due to the overreliance on ctx=ts.
2555    */
2556   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
2557   ierr = DMSNESGetFunction(dm,&func,NULL);CHKERRQ(ierr);
2558   if (!func) {
2559     ierr = DMSNESSetFunction(dm,SNESTSFormFunction,ts);CHKERRQ(ierr);
2560   }
2561   /* If the SNES doesn't have a jacobian set and the TS has an ijacobian or rhsjacobian set, set the SNES to use it.
2562      Otherwise, the SNES will use coloring internally to form the Jacobian.
2563    */
2564   ierr = DMSNESGetJacobian(dm,&jac,NULL);CHKERRQ(ierr);
2565   ierr = DMTSGetIJacobian(dm,&ijac,NULL);CHKERRQ(ierr);
2566   ierr = DMTSGetI2Jacobian(dm,&i2jac,NULL);CHKERRQ(ierr);
2567   ierr = DMTSGetRHSJacobian(dm,&rhsjac,NULL);CHKERRQ(ierr);
2568   if (!jac && (ijac || i2jac || rhsjac)) {
2569     ierr = DMSNESSetJacobian(dm,SNESTSFormJacobian,ts);CHKERRQ(ierr);
2570   }
2571 
2572   /* if time integration scheme has a starting method, call it */
2573   if (ts->ops->startingmethod) {
2574     ierr = (*ts->ops->startingmethod)(ts);CHKERRQ(ierr);
2575   }
2576 
2577   ts->setupcalled = PETSC_TRUE;
2578   PetscFunctionReturn(0);
2579 }
2580 
2581 #undef __FUNCT__
2582 #define __FUNCT__ "TSAdjointSetUp"
2583 /*@
2584    TSAdjointSetUp - Sets up the internal data structures for the later use
2585    of an adjoint solver
2586 
2587    Collective on TS
2588 
2589    Input Parameter:
2590 .  ts - the TS context obtained from TSCreate()
2591 
2592    Level: advanced
2593 
2594 .keywords: TS, timestep, setup
2595 
2596 .seealso: TSCreate(), TSAdjointStep(), TSSetCostGradients()
2597 @*/
2598 PetscErrorCode  TSAdjointSetUp(TS ts)
2599 {
2600   PetscErrorCode ierr;
2601 
2602   PetscFunctionBegin;
2603   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2604   if (ts->adjointsetupcalled) PetscFunctionReturn(0);
2605   if (!ts->vecs_sensi) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetCostGradients() first");
2606 
2607   if (ts->vec_costintegral) { /* if there is integral in the cost function*/
2608     ierr = VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&ts->vecs_drdy);CHKERRQ(ierr);
2609     if (ts->vecs_sensip){
2610       ierr = VecDuplicateVecs(ts->vecs_sensip[0],ts->numcost,&ts->vecs_drdp);CHKERRQ(ierr);
2611     }
2612   }
2613 
2614   if (ts->ops->adjointsetup) {
2615     ierr = (*ts->ops->adjointsetup)(ts);CHKERRQ(ierr);
2616   }
2617   ts->adjointsetupcalled = PETSC_TRUE;
2618   PetscFunctionReturn(0);
2619 }
2620 
2621 #undef __FUNCT__
2622 #define __FUNCT__ "TSReset"
2623 /*@
2624    TSReset - Resets a TS context and removes any allocated Vecs and Mats.
2625 
2626    Collective on TS
2627 
2628    Input Parameter:
2629 .  ts - the TS context obtained from TSCreate()
2630 
2631    Level: beginner
2632 
2633 .keywords: TS, timestep, reset
2634 
2635 .seealso: TSCreate(), TSSetup(), TSDestroy()
2636 @*/
2637 PetscErrorCode  TSReset(TS ts)
2638 {
2639   PetscErrorCode ierr;
2640 
2641   PetscFunctionBegin;
2642   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2643 
2644   if (ts->ops->reset) {
2645     ierr = (*ts->ops->reset)(ts);CHKERRQ(ierr);
2646   }
2647   if (ts->snes) {ierr = SNESReset(ts->snes);CHKERRQ(ierr);}
2648   if (ts->adapt) {ierr = TSAdaptReset(ts->adapt);CHKERRQ(ierr);}
2649 
2650   ierr = MatDestroy(&ts->Arhs);CHKERRQ(ierr);
2651   ierr = MatDestroy(&ts->Brhs);CHKERRQ(ierr);
2652   ierr = VecDestroy(&ts->Frhs);CHKERRQ(ierr);
2653   ierr = VecDestroy(&ts->vec_sol);CHKERRQ(ierr);
2654   ierr = VecDestroy(&ts->vec_dot);CHKERRQ(ierr);
2655   ierr = VecDestroy(&ts->vatol);CHKERRQ(ierr);
2656   ierr = VecDestroy(&ts->vrtol);CHKERRQ(ierr);
2657   ierr = VecDestroyVecs(ts->nwork,&ts->work);CHKERRQ(ierr);
2658 
2659  if (ts->vec_costintegral) {
2660     ierr = VecDestroyVecs(ts->numcost,&ts->vecs_drdy);CHKERRQ(ierr);
2661     if (ts->vecs_drdp){
2662       ierr = VecDestroyVecs(ts->numcost,&ts->vecs_drdp);CHKERRQ(ierr);
2663     }
2664   }
2665   ts->vecs_sensi  = NULL;
2666   ts->vecs_sensip = NULL;
2667   ierr = MatDestroy(&ts->Jacp);CHKERRQ(ierr);
2668   ierr = VecDestroy(&ts->vec_costintegral);CHKERRQ(ierr);
2669   ierr = VecDestroy(&ts->vec_costintegrand);CHKERRQ(ierr);
2670   ts->setupcalled = PETSC_FALSE;
2671   PetscFunctionReturn(0);
2672 }
2673 
2674 #undef __FUNCT__
2675 #define __FUNCT__ "TSDestroy"
2676 /*@
2677    TSDestroy - Destroys the timestepper context that was created
2678    with TSCreate().
2679 
2680    Collective on TS
2681 
2682    Input Parameter:
2683 .  ts - the TS context obtained from TSCreate()
2684 
2685    Level: beginner
2686 
2687 .keywords: TS, timestepper, destroy
2688 
2689 .seealso: TSCreate(), TSSetUp(), TSSolve()
2690 @*/
2691 PetscErrorCode  TSDestroy(TS *ts)
2692 {
2693   PetscErrorCode ierr;
2694 
2695   PetscFunctionBegin;
2696   if (!*ts) PetscFunctionReturn(0);
2697   PetscValidHeaderSpecific((*ts),TS_CLASSID,1);
2698   if (--((PetscObject)(*ts))->refct > 0) {*ts = 0; PetscFunctionReturn(0);}
2699 
2700   ierr = TSReset((*ts));CHKERRQ(ierr);
2701 
2702   /* if memory was published with SAWs then destroy it */
2703   ierr = PetscObjectSAWsViewOff((PetscObject)*ts);CHKERRQ(ierr);
2704   if ((*ts)->ops->destroy) {ierr = (*(*ts)->ops->destroy)((*ts));CHKERRQ(ierr);}
2705 
2706   ierr = TSTrajectoryDestroy(&(*ts)->trajectory);CHKERRQ(ierr);
2707 
2708   ierr = TSAdaptDestroy(&(*ts)->adapt);CHKERRQ(ierr);
2709   ierr = TSEventDestroy(&(*ts)->event);CHKERRQ(ierr);
2710 
2711   ierr = SNESDestroy(&(*ts)->snes);CHKERRQ(ierr);
2712   ierr = DMDestroy(&(*ts)->dm);CHKERRQ(ierr);
2713   ierr = TSMonitorCancel((*ts));CHKERRQ(ierr);
2714   ierr = TSAdjointMonitorCancel((*ts));CHKERRQ(ierr);
2715 
2716   ierr = PetscHeaderDestroy(ts);CHKERRQ(ierr);
2717   PetscFunctionReturn(0);
2718 }
2719 
2720 #undef __FUNCT__
2721 #define __FUNCT__ "TSGetSNES"
2722 /*@
2723    TSGetSNES - Returns the SNES (nonlinear solver) associated with
2724    a TS (timestepper) context. Valid only for nonlinear problems.
2725 
2726    Not Collective, but SNES is parallel if TS is parallel
2727 
2728    Input Parameter:
2729 .  ts - the TS context obtained from TSCreate()
2730 
2731    Output Parameter:
2732 .  snes - the nonlinear solver context
2733 
2734    Notes:
2735    The user can then directly manipulate the SNES context to set various
2736    options, etc.  Likewise, the user can then extract and manipulate the
2737    KSP, KSP, and PC contexts as well.
2738 
2739    TSGetSNES() does not work for integrators that do not use SNES; in
2740    this case TSGetSNES() returns NULL in snes.
2741 
2742    Level: beginner
2743 
2744 .keywords: timestep, get, SNES
2745 @*/
2746 PetscErrorCode  TSGetSNES(TS ts,SNES *snes)
2747 {
2748   PetscErrorCode ierr;
2749 
2750   PetscFunctionBegin;
2751   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2752   PetscValidPointer(snes,2);
2753   if (!ts->snes) {
2754     ierr = SNESCreate(PetscObjectComm((PetscObject)ts),&ts->snes);CHKERRQ(ierr);
2755     ierr = SNESSetFunction(ts->snes,NULL,SNESTSFormFunction,ts);CHKERRQ(ierr);
2756     ierr = PetscLogObjectParent((PetscObject)ts,(PetscObject)ts->snes);CHKERRQ(ierr);
2757     ierr = PetscObjectIncrementTabLevel((PetscObject)ts->snes,(PetscObject)ts,1);CHKERRQ(ierr);
2758     if (ts->dm) {ierr = SNESSetDM(ts->snes,ts->dm);CHKERRQ(ierr);}
2759     if (ts->problem_type == TS_LINEAR) {
2760       ierr = SNESSetType(ts->snes,SNESKSPONLY);CHKERRQ(ierr);
2761     }
2762   }
2763   *snes = ts->snes;
2764   PetscFunctionReturn(0);
2765 }
2766 
2767 #undef __FUNCT__
2768 #define __FUNCT__ "TSSetSNES"
2769 /*@
2770    TSSetSNES - Set the SNES (nonlinear solver) to be used by the timestepping context
2771 
2772    Collective
2773 
2774    Input Parameter:
2775 +  ts - the TS context obtained from TSCreate()
2776 -  snes - the nonlinear solver context
2777 
2778    Notes:
2779    Most users should have the TS created by calling TSGetSNES()
2780 
2781    Level: developer
2782 
2783 .keywords: timestep, set, SNES
2784 @*/
2785 PetscErrorCode TSSetSNES(TS ts,SNES snes)
2786 {
2787   PetscErrorCode ierr;
2788   PetscErrorCode (*func)(SNES,Vec,Mat,Mat,void*);
2789 
2790   PetscFunctionBegin;
2791   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2792   PetscValidHeaderSpecific(snes,SNES_CLASSID,2);
2793   ierr = PetscObjectReference((PetscObject)snes);CHKERRQ(ierr);
2794   ierr = SNESDestroy(&ts->snes);CHKERRQ(ierr);
2795 
2796   ts->snes = snes;
2797 
2798   ierr = SNESSetFunction(ts->snes,NULL,SNESTSFormFunction,ts);CHKERRQ(ierr);
2799   ierr = SNESGetJacobian(ts->snes,NULL,NULL,&func,NULL);CHKERRQ(ierr);
2800   if (func == SNESTSFormJacobian) {
2801     ierr = SNESSetJacobian(ts->snes,NULL,NULL,SNESTSFormJacobian,ts);CHKERRQ(ierr);
2802   }
2803   PetscFunctionReturn(0);
2804 }
2805 
2806 #undef __FUNCT__
2807 #define __FUNCT__ "TSGetKSP"
2808 /*@
2809    TSGetKSP - Returns the KSP (linear solver) associated with
2810    a TS (timestepper) context.
2811 
2812    Not Collective, but KSP is parallel if TS is parallel
2813 
2814    Input Parameter:
2815 .  ts - the TS context obtained from TSCreate()
2816 
2817    Output Parameter:
2818 .  ksp - the nonlinear solver context
2819 
2820    Notes:
2821    The user can then directly manipulate the KSP context to set various
2822    options, etc.  Likewise, the user can then extract and manipulate the
2823    KSP and PC contexts as well.
2824 
2825    TSGetKSP() does not work for integrators that do not use KSP;
2826    in this case TSGetKSP() returns NULL in ksp.
2827 
2828    Level: beginner
2829 
2830 .keywords: timestep, get, KSP
2831 @*/
2832 PetscErrorCode  TSGetKSP(TS ts,KSP *ksp)
2833 {
2834   PetscErrorCode ierr;
2835   SNES           snes;
2836 
2837   PetscFunctionBegin;
2838   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2839   PetscValidPointer(ksp,2);
2840   if (!((PetscObject)ts)->type_name) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"KSP is not created yet. Call TSSetType() first");
2841   if (ts->problem_type != TS_LINEAR) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Linear only; use TSGetSNES()");
2842   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
2843   ierr = SNESGetKSP(snes,ksp);CHKERRQ(ierr);
2844   PetscFunctionReturn(0);
2845 }
2846 
2847 /* ----------- Routines to set solver parameters ---------- */
2848 
2849 #undef __FUNCT__
2850 #define __FUNCT__ "TSGetDuration"
2851 /*@
2852    TSGetDuration - Gets the maximum number of timesteps to use and
2853    maximum time for iteration.
2854 
2855    Not Collective
2856 
2857    Input Parameters:
2858 +  ts       - the TS context obtained from TSCreate()
2859 .  maxsteps - maximum number of iterations to use, or NULL
2860 -  maxtime  - final time to iterate to, or NULL
2861 
2862    Level: intermediate
2863 
2864 .keywords: TS, timestep, get, maximum, iterations, time
2865 @*/
2866 PetscErrorCode  TSGetDuration(TS ts, PetscInt *maxsteps, PetscReal *maxtime)
2867 {
2868   PetscFunctionBegin;
2869   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
2870   if (maxsteps) {
2871     PetscValidIntPointer(maxsteps,2);
2872     *maxsteps = ts->max_steps;
2873   }
2874   if (maxtime) {
2875     PetscValidScalarPointer(maxtime,3);
2876     *maxtime = ts->max_time;
2877   }
2878   PetscFunctionReturn(0);
2879 }
2880 
2881 #undef __FUNCT__
2882 #define __FUNCT__ "TSSetDuration"
2883 /*@
2884    TSSetDuration - Sets the maximum number of timesteps to use and
2885    maximum time for iteration.
2886 
2887    Logically Collective on TS
2888 
2889    Input Parameters:
2890 +  ts - the TS context obtained from TSCreate()
2891 .  maxsteps - maximum number of iterations to use
2892 -  maxtime - final time to iterate to
2893 
2894    Options Database Keys:
2895 .  -ts_max_steps <maxsteps> - Sets maxsteps
2896 .  -ts_final_time <maxtime> - Sets maxtime
2897 
2898    Notes:
2899    The default maximum number of iterations is 5000. Default time is 5.0
2900 
2901    Level: intermediate
2902 
2903 .keywords: TS, timestep, set, maximum, iterations
2904 
2905 .seealso: TSSetExactFinalTime()
2906 @*/
2907 PetscErrorCode  TSSetDuration(TS ts,PetscInt maxsteps,PetscReal maxtime)
2908 {
2909   PetscFunctionBegin;
2910   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2911   PetscValidLogicalCollectiveInt(ts,maxsteps,2);
2912   PetscValidLogicalCollectiveReal(ts,maxtime,2);
2913   if (maxsteps >= 0) ts->max_steps = maxsteps;
2914   if (maxtime != PETSC_DEFAULT) ts->max_time = maxtime;
2915   PetscFunctionReturn(0);
2916 }
2917 
2918 #undef __FUNCT__
2919 #define __FUNCT__ "TSSetSolution"
2920 /*@
2921    TSSetSolution - Sets the initial solution vector
2922    for use by the TS routines.
2923 
2924    Logically Collective on TS and Vec
2925 
2926    Input Parameters:
2927 +  ts - the TS context obtained from TSCreate()
2928 -  u - the solution vector
2929 
2930    Level: beginner
2931 
2932 .keywords: TS, timestep, set, solution, initial conditions
2933 @*/
2934 PetscErrorCode  TSSetSolution(TS ts,Vec u)
2935 {
2936   PetscErrorCode ierr;
2937   DM             dm;
2938 
2939   PetscFunctionBegin;
2940   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2941   PetscValidHeaderSpecific(u,VEC_CLASSID,2);
2942   ierr = PetscObjectReference((PetscObject)u);CHKERRQ(ierr);
2943   ierr = VecDestroy(&ts->vec_sol);CHKERRQ(ierr);
2944   ts->vec_sol = u;
2945 
2946   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
2947   ierr = DMShellSetGlobalVector(dm,u);CHKERRQ(ierr);
2948   PetscFunctionReturn(0);
2949 }
2950 
2951 #undef __FUNCT__
2952 #define __FUNCT__ "TSAdjointSetSteps"
2953 /*@
2954    TSAdjointSetSteps - Sets the number of steps the adjoint solver should take backward in time
2955 
2956    Logically Collective on TS
2957 
2958    Input Parameters:
2959 +  ts - the TS context obtained from TSCreate()
2960 .  steps - number of steps to use
2961 
2962    Level: intermediate
2963 
2964    Notes: Normally one does not call this and TSAdjointSolve() integrates back to the original timestep. One can call this
2965           so as to integrate back to less than the original timestep
2966 
2967 .keywords: TS, timestep, set, maximum, iterations
2968 
2969 .seealso: TSSetExactFinalTime()
2970 @*/
2971 PetscErrorCode  TSAdjointSetSteps(TS ts,PetscInt steps)
2972 {
2973   PetscFunctionBegin;
2974   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2975   PetscValidLogicalCollectiveInt(ts,steps,2);
2976   if (steps < 0) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Cannot step back a negative number of steps");
2977   if (steps > ts->total_steps) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Cannot step back more than the total number of forward steps");
2978   ts->adjoint_max_steps = steps;
2979   PetscFunctionReturn(0);
2980 }
2981 
2982 #undef __FUNCT__
2983 #define __FUNCT__ "TSSetCostGradients"
2984 /*@
2985    TSSetCostGradients - Sets the initial value of the gradients of the cost function w.r.t. initial conditions and w.r.t. the problem parameters
2986       for use by the TSAdjoint routines.
2987 
2988    Logically Collective on TS and Vec
2989 
2990    Input Parameters:
2991 +  ts - the TS context obtained from TSCreate()
2992 .  lambda - gradients with respect to the initial condition variables, the dimension and parallel layout of these vectors is the same as the ODE solution vector
2993 -  mu - gradients with respect to the parameters, the number of entries in these vectors is the same as the number of parameters
2994 
2995    Level: beginner
2996 
2997    Notes: the entries in these vectors must be correctly initialized with the values lamda_i = df/dy|finaltime  mu_i = df/dp|finaltime
2998 
2999 .keywords: TS, timestep, set, sensitivity, initial conditions
3000 @*/
3001 PetscErrorCode  TSSetCostGradients(TS ts,PetscInt numcost,Vec *lambda,Vec *mu)
3002 {
3003   PetscFunctionBegin;
3004   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3005   PetscValidPointer(lambda,2);
3006   ts->vecs_sensi  = lambda;
3007   ts->vecs_sensip = mu;
3008   if (ts->numcost && ts->numcost!=numcost) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"The number of cost functions (2rd parameter of TSSetCostIntegrand()) is inconsistent with the one set by TSSetCostIntegrand");
3009   ts->numcost  = numcost;
3010   PetscFunctionReturn(0);
3011 }
3012 
3013 #undef __FUNCT__
3014 #define __FUNCT__ "TSAdjointSetRHSJacobian"
3015 /*@C
3016   TSAdjointSetRHSJacobian - Sets the function that computes the Jacobian of G w.r.t. the parameters p where y_t = G(y,p,t), as well as the location to store the matrix.
3017 
3018   Logically Collective on TS
3019 
3020   Input Parameters:
3021 + ts   - The TS context obtained from TSCreate()
3022 - func - The function
3023 
3024   Calling sequence of func:
3025 $ func (TS ts,PetscReal t,Vec y,Mat A,void *ctx);
3026 +   t - current timestep
3027 .   y - input vector (current ODE solution)
3028 .   A - output matrix
3029 -   ctx - [optional] user-defined function context
3030 
3031   Level: intermediate
3032 
3033   Notes: Amat has the same number of rows and the same row parallel layout as u, Amat has the same number of columns and parallel layout as p
3034 
3035 .keywords: TS, sensitivity
3036 .seealso:
3037 @*/
3038 PetscErrorCode  TSAdjointSetRHSJacobian(TS ts,Mat Amat,PetscErrorCode (*func)(TS,PetscReal,Vec,Mat,void*),void *ctx)
3039 {
3040   PetscErrorCode ierr;
3041 
3042   PetscFunctionBegin;
3043   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3044   if (Amat) PetscValidHeaderSpecific(Amat,MAT_CLASSID,2);
3045 
3046   ts->rhsjacobianp    = func;
3047   ts->rhsjacobianpctx = ctx;
3048   if(Amat) {
3049     ierr = PetscObjectReference((PetscObject)Amat);CHKERRQ(ierr);
3050     ierr = MatDestroy(&ts->Jacp);CHKERRQ(ierr);
3051     ts->Jacp = Amat;
3052   }
3053   PetscFunctionReturn(0);
3054 }
3055 
3056 #undef __FUNCT__
3057 #define __FUNCT__ "TSAdjointComputeRHSJacobian"
3058 /*@C
3059   TSAdjointComputeRHSJacobian - Runs the user-defined Jacobian function.
3060 
3061   Collective on TS
3062 
3063   Input Parameters:
3064 . ts   - The TS context obtained from TSCreate()
3065 
3066   Level: developer
3067 
3068 .keywords: TS, sensitivity
3069 .seealso: TSAdjointSetRHSJacobian()
3070 @*/
3071 PetscErrorCode  TSAdjointComputeRHSJacobian(TS ts,PetscReal t,Vec X,Mat Amat)
3072 {
3073   PetscErrorCode ierr;
3074 
3075   PetscFunctionBegin;
3076   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3077   PetscValidHeaderSpecific(X,VEC_CLASSID,3);
3078   PetscValidPointer(Amat,4);
3079 
3080   PetscStackPush("TS user JacobianP function for sensitivity analysis");
3081   ierr = (*ts->rhsjacobianp)(ts,t,X,Amat,ts->rhsjacobianpctx); CHKERRQ(ierr);
3082   PetscStackPop;
3083   PetscFunctionReturn(0);
3084 }
3085 
3086 #undef __FUNCT__
3087 #define __FUNCT__ "TSSetCostIntegrand"
3088 /*@C
3089     TSSetCostIntegrand - Sets the routine for evaluating the integral term in one or more cost functions
3090 
3091     Logically Collective on TS
3092 
3093     Input Parameters:
3094 +   ts - the TS context obtained from TSCreate()
3095 .   numcost - number of gradients to be computed, this is the number of cost functions
3096 .   rf - routine for evaluating the integrand function
3097 .   drdyf - function that computes the gradients of the r's with respect to y,NULL if not a function y
3098 .   drdpf - function that computes the gradients of the r's with respect to p, NULL if not a function of p
3099 .   fwd - flag indicating whether to evaluate cost integral in the forward run or the adjoint run
3100 -   ctx - [optional] user-defined context for private data for the function evaluation routine (may be NULL)
3101 
3102     Calling sequence of rf:
3103 $     rf(TS ts,PetscReal t,Vec y,Vec f[],void *ctx);
3104 
3105 +   t - current timestep
3106 .   y - input vector
3107 .   f - function result; one vector entry for each cost function
3108 -   ctx - [optional] user-defined function context
3109 
3110    Calling sequence of drdyf:
3111 $    PetscErroCode drdyf(TS ts,PetscReal t,Vec y,Vec *drdy,void *ctx);
3112 
3113    Calling sequence of drdpf:
3114 $    PetscErroCode drdpf(TS ts,PetscReal t,Vec y,Vec *drdp,void *ctx);
3115 
3116     Level: intermediate
3117 
3118     Notes: For optimization there is generally a single cost function, numcost = 1. For sensitivities there may be multiple cost functions
3119 
3120 .keywords: TS, sensitivity analysis, timestep, set, quadrature, function
3121 
3122 .seealso: TSAdjointSetRHSJacobian(),TSGetCostGradients(), TSSetCostGradients()
3123 @*/
3124 PetscErrorCode  TSSetCostIntegrand(TS ts,PetscInt numcost,PetscErrorCode (*rf)(TS,PetscReal,Vec,Vec,void*),
3125                                                           PetscErrorCode (*drdyf)(TS,PetscReal,Vec,Vec*,void*),
3126                                                           PetscErrorCode (*drdpf)(TS,PetscReal,Vec,Vec*,void*),
3127                                                           PetscBool fwd,void *ctx)
3128 {
3129   PetscErrorCode ierr;
3130 
3131   PetscFunctionBegin;
3132   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3133   if (ts->numcost && ts->numcost!=numcost) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"The number of cost functions (2rd parameter of TSSetCostIntegrand()) is inconsistent with the one set by TSSetCostGradients()");
3134   if (!ts->numcost) ts->numcost=numcost;
3135 
3136   ts->costintegralfwd  = fwd; /* Evaluate the cost integral in forward run if fwd is true */
3137   ierr                 = VecCreateSeq(PETSC_COMM_SELF,numcost,&ts->vec_costintegral);CHKERRQ(ierr);
3138   ierr                 = VecDuplicate(ts->vec_costintegral,&ts->vec_costintegrand);CHKERRQ(ierr);
3139   ts->costintegrand    = rf;
3140   ts->costintegrandctx = ctx;
3141   ts->drdyfunction     = drdyf;
3142   ts->drdpfunction     = drdpf;
3143   PetscFunctionReturn(0);
3144 }
3145 
3146 #undef __FUNCT__
3147 #define __FUNCT__ "TSGetCostIntegral"
3148 /*@
3149    TSGetCostIntegral - Returns the values of the integral term in the cost functions.
3150    It is valid to call the routine after a backward run.
3151 
3152    Not Collective
3153 
3154    Input Parameter:
3155 .  ts - the TS context obtained from TSCreate()
3156 
3157    Output Parameter:
3158 .  v - the vector containing the integrals for each cost function
3159 
3160    Level: intermediate
3161 
3162 .seealso: TSSetCostIntegrand()
3163 
3164 .keywords: TS, sensitivity analysis
3165 @*/
3166 PetscErrorCode  TSGetCostIntegral(TS ts,Vec *v)
3167 {
3168   PetscFunctionBegin;
3169   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3170   PetscValidPointer(v,2);
3171   *v = ts->vec_costintegral;
3172   PetscFunctionReturn(0);
3173 }
3174 
3175 #undef __FUNCT__
3176 #define __FUNCT__ "TSAdjointComputeCostIntegrand"
3177 /*@
3178    TSAdjointComputeCostIntegrand - Evaluates the integral function in the cost functions.
3179 
3180    Input Parameters:
3181 +  ts - the TS context
3182 .  t - current time
3183 -  y - state vector, i.e. current solution
3184 
3185    Output Parameter:
3186 .  q - vector of size numcost to hold the outputs
3187 
3188    Note:
3189    Most users should not need to explicitly call this routine, as it
3190    is used internally within the sensitivity analysis context.
3191 
3192    Level: developer
3193 
3194 .keywords: TS, compute
3195 
3196 .seealso: TSSetCostIntegrand()
3197 @*/
3198 PetscErrorCode TSAdjointComputeCostIntegrand(TS ts,PetscReal t,Vec y,Vec q)
3199 {
3200   PetscErrorCode ierr;
3201 
3202   PetscFunctionBegin;
3203   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3204   PetscValidHeaderSpecific(y,VEC_CLASSID,3);
3205   PetscValidHeaderSpecific(q,VEC_CLASSID,4);
3206 
3207   ierr = PetscLogEventBegin(TS_FunctionEval,ts,y,q,0);CHKERRQ(ierr);
3208   if (ts->costintegrand) {
3209     PetscStackPush("TS user integrand in the cost function");
3210     ierr = (*ts->costintegrand)(ts,t,y,q,ts->costintegrandctx);CHKERRQ(ierr);
3211     PetscStackPop;
3212   } else {
3213     ierr = VecZeroEntries(q);CHKERRQ(ierr);
3214   }
3215 
3216   ierr = PetscLogEventEnd(TS_FunctionEval,ts,y,q,0);CHKERRQ(ierr);
3217   PetscFunctionReturn(0);
3218 }
3219 
3220 #undef __FUNCT__
3221 #define __FUNCT__ "TSAdjointComputeDRDYFunction"
3222 /*@
3223   TSAdjointComputeDRDYFunction - Runs the user-defined DRDY function.
3224 
3225   Collective on TS
3226 
3227   Input Parameters:
3228 . ts   - The TS context obtained from TSCreate()
3229 
3230   Notes:
3231   TSAdjointComputeDRDYFunction() is typically used for sensitivity implementation,
3232   so most users would not generally call this routine themselves.
3233 
3234   Level: developer
3235 
3236 .keywords: TS, sensitivity
3237 .seealso: TSAdjointComputeDRDYFunction()
3238 @*/
3239 PetscErrorCode  TSAdjointComputeDRDYFunction(TS ts,PetscReal t,Vec y,Vec *drdy)
3240 {
3241   PetscErrorCode ierr;
3242 
3243   PetscFunctionBegin;
3244   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3245   PetscValidHeaderSpecific(y,VEC_CLASSID,3);
3246 
3247   PetscStackPush("TS user DRDY function for sensitivity analysis");
3248   ierr = (*ts->drdyfunction)(ts,t,y,drdy,ts->costintegrandctx); CHKERRQ(ierr);
3249   PetscStackPop;
3250   PetscFunctionReturn(0);
3251 }
3252 
3253 #undef __FUNCT__
3254 #define __FUNCT__ "TSAdjointComputeDRDPFunction"
3255 /*@
3256   TSAdjointComputeDRDPFunction - Runs the user-defined DRDP function.
3257 
3258   Collective on TS
3259 
3260   Input Parameters:
3261 . ts   - The TS context obtained from TSCreate()
3262 
3263   Notes:
3264   TSDRDPFunction() is typically used for sensitivity implementation,
3265   so most users would not generally call this routine themselves.
3266 
3267   Level: developer
3268 
3269 .keywords: TS, sensitivity
3270 .seealso: TSAdjointSetDRDPFunction()
3271 @*/
3272 PetscErrorCode  TSAdjointComputeDRDPFunction(TS ts,PetscReal t,Vec y,Vec *drdp)
3273 {
3274   PetscErrorCode ierr;
3275 
3276   PetscFunctionBegin;
3277   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3278   PetscValidHeaderSpecific(y,VEC_CLASSID,3);
3279 
3280   PetscStackPush("TS user DRDP function for sensitivity analysis");
3281   ierr = (*ts->drdpfunction)(ts,t,y,drdp,ts->costintegrandctx); CHKERRQ(ierr);
3282   PetscStackPop;
3283   PetscFunctionReturn(0);
3284 }
3285 
3286 #undef __FUNCT__
3287 #define __FUNCT__ "TSSetPreStep"
3288 /*@C
3289   TSSetPreStep - Sets the general-purpose function
3290   called once at the beginning of each time step.
3291 
3292   Logically Collective on TS
3293 
3294   Input Parameters:
3295 + ts   - The TS context obtained from TSCreate()
3296 - func - The function
3297 
3298   Calling sequence of func:
3299 . func (TS ts);
3300 
3301   Level: intermediate
3302 
3303   Note:
3304   If a step is rejected, TSStep() will call this routine again before each attempt.
3305   The last completed time step number can be queried using TSGetTimeStepNumber(), the
3306   size of the step being attempted can be obtained using TSGetTimeStep().
3307 
3308 .keywords: TS, timestep
3309 .seealso: TSSetPreStage(), TSSetPostStage(), TSSetPostStep(), TSStep()
3310 @*/
3311 PetscErrorCode  TSSetPreStep(TS ts, PetscErrorCode (*func)(TS))
3312 {
3313   PetscFunctionBegin;
3314   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3315   ts->prestep = func;
3316   PetscFunctionReturn(0);
3317 }
3318 
3319 #undef __FUNCT__
3320 #define __FUNCT__ "TSPreStep"
3321 /*@
3322   TSPreStep - Runs the user-defined pre-step function.
3323 
3324   Collective on TS
3325 
3326   Input Parameters:
3327 . ts   - The TS context obtained from TSCreate()
3328 
3329   Notes:
3330   TSPreStep() is typically used within time stepping implementations,
3331   so most users would not generally call this routine themselves.
3332 
3333   Level: developer
3334 
3335 .keywords: TS, timestep
3336 .seealso: TSSetPreStep(), TSPreStage(), TSPostStage(), TSPostStep()
3337 @*/
3338 PetscErrorCode  TSPreStep(TS ts)
3339 {
3340   PetscErrorCode ierr;
3341 
3342   PetscFunctionBegin;
3343   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3344   if (ts->prestep) {
3345     PetscStackCallStandard((*ts->prestep),(ts));
3346   }
3347   PetscFunctionReturn(0);
3348 }
3349 
3350 #undef __FUNCT__
3351 #define __FUNCT__ "TSSetPreStage"
3352 /*@C
3353   TSSetPreStage - Sets the general-purpose function
3354   called once at the beginning of each stage.
3355 
3356   Logically Collective on TS
3357 
3358   Input Parameters:
3359 + ts   - The TS context obtained from TSCreate()
3360 - func - The function
3361 
3362   Calling sequence of func:
3363 . PetscErrorCode func(TS ts, PetscReal stagetime);
3364 
3365   Level: intermediate
3366 
3367   Note:
3368   There may be several stages per time step. If the solve for a given stage fails, the step may be rejected and retried.
3369   The time step number being computed can be queried using TSGetTimeStepNumber() and the total size of the step being
3370   attempted can be obtained using TSGetTimeStep(). The time at the start of the step is available via TSGetTime().
3371 
3372 .keywords: TS, timestep
3373 .seealso: TSSetPostStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
3374 @*/
3375 PetscErrorCode  TSSetPreStage(TS ts, PetscErrorCode (*func)(TS,PetscReal))
3376 {
3377   PetscFunctionBegin;
3378   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3379   ts->prestage = func;
3380   PetscFunctionReturn(0);
3381 }
3382 
3383 #undef __FUNCT__
3384 #define __FUNCT__ "TSSetPostStage"
3385 /*@C
3386   TSSetPostStage - Sets the general-purpose function
3387   called once at the end of each stage.
3388 
3389   Logically Collective on TS
3390 
3391   Input Parameters:
3392 + ts   - The TS context obtained from TSCreate()
3393 - func - The function
3394 
3395   Calling sequence of func:
3396 . PetscErrorCode func(TS ts, PetscReal stagetime, PetscInt stageindex, Vec* Y);
3397 
3398   Level: intermediate
3399 
3400   Note:
3401   There may be several stages per time step. If the solve for a given stage fails, the step may be rejected and retried.
3402   The time step number being computed can be queried using TSGetTimeStepNumber() and the total size of the step being
3403   attempted can be obtained using TSGetTimeStep(). The time at the start of the step is available via TSGetTime().
3404 
3405 .keywords: TS, timestep
3406 .seealso: TSSetPreStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
3407 @*/
3408 PetscErrorCode  TSSetPostStage(TS ts, PetscErrorCode (*func)(TS,PetscReal,PetscInt,Vec*))
3409 {
3410   PetscFunctionBegin;
3411   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3412   ts->poststage = func;
3413   PetscFunctionReturn(0);
3414 }
3415 
3416 #undef __FUNCT__
3417 #define __FUNCT__ "TSSetPostEvaluate"
3418 /*@C
3419   TSSetPostEvaluate - Sets the general-purpose function
3420   called once at the end of each step evaluation.
3421 
3422   Logically Collective on TS
3423 
3424   Input Parameters:
3425 + ts   - The TS context obtained from TSCreate()
3426 - func - The function
3427 
3428   Calling sequence of func:
3429 . PetscErrorCode func(TS ts);
3430 
3431   Level: intermediate
3432 
3433   Note:
3434   Semantically, TSSetPostEvaluate() differs from TSSetPostStep() since the function it sets is called before event-handling
3435   thus guaranteeing the same solution (computed by the time-stepper) will be passed to it. On the other hand, TSPostStep()
3436   may be passed a different solution, possibly changed by the event handler. TSPostEvaluate() is called after the next step
3437   solution is evaluated allowing to modify it, if need be. The solution can be obtained with TSGetSolution(), the time step
3438   with TSGetTimeStep(), and the time at the start of the step is available via TSGetTime()
3439 
3440 .keywords: TS, timestep
3441 .seealso: TSSetPreStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
3442 @*/
3443 PetscErrorCode  TSSetPostEvaluate(TS ts, PetscErrorCode (*func)(TS))
3444 {
3445   PetscFunctionBegin;
3446   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3447   ts->postevaluate = func;
3448   PetscFunctionReturn(0);
3449 }
3450 
3451 #undef __FUNCT__
3452 #define __FUNCT__ "TSPreStage"
3453 /*@
3454   TSPreStage - Runs the user-defined pre-stage function set using TSSetPreStage()
3455 
3456   Collective on TS
3457 
3458   Input Parameters:
3459 . ts          - The TS context obtained from TSCreate()
3460   stagetime   - The absolute time of the current stage
3461 
3462   Notes:
3463   TSPreStage() is typically used within time stepping implementations,
3464   most users would not generally call this routine themselves.
3465 
3466   Level: developer
3467 
3468 .keywords: TS, timestep
3469 .seealso: TSPostStage(), TSSetPreStep(), TSPreStep(), TSPostStep()
3470 @*/
3471 PetscErrorCode  TSPreStage(TS ts, PetscReal stagetime)
3472 {
3473   PetscErrorCode ierr;
3474 
3475   PetscFunctionBegin;
3476   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3477   if (ts->prestage) {
3478     PetscStackCallStandard((*ts->prestage),(ts,stagetime));
3479   }
3480   PetscFunctionReturn(0);
3481 }
3482 
3483 #undef __FUNCT__
3484 #define __FUNCT__ "TSPostStage"
3485 /*@
3486   TSPostStage - Runs the user-defined post-stage function set using TSSetPostStage()
3487 
3488   Collective on TS
3489 
3490   Input Parameters:
3491 . ts          - The TS context obtained from TSCreate()
3492   stagetime   - The absolute time of the current stage
3493   stageindex  - Stage number
3494   Y           - Array of vectors (of size = total number
3495                 of stages) with the stage solutions
3496 
3497   Notes:
3498   TSPostStage() is typically used within time stepping implementations,
3499   most users would not generally call this routine themselves.
3500 
3501   Level: developer
3502 
3503 .keywords: TS, timestep
3504 .seealso: TSPreStage(), TSSetPreStep(), TSPreStep(), TSPostStep()
3505 @*/
3506 PetscErrorCode  TSPostStage(TS ts, PetscReal stagetime, PetscInt stageindex, Vec *Y)
3507 {
3508   PetscErrorCode ierr;
3509 
3510   PetscFunctionBegin;
3511   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3512   if (ts->poststage) {
3513     PetscStackCallStandard((*ts->poststage),(ts,stagetime,stageindex,Y));
3514   }
3515   PetscFunctionReturn(0);
3516 }
3517 
3518 #undef __FUNCT__
3519 #define __FUNCT__ "TSPostEvaluate"
3520 /*@
3521   TSPostEvaluate - Runs the user-defined post-evaluate function set using TSSetPostEvaluate()
3522 
3523   Collective on TS
3524 
3525   Input Parameters:
3526 . ts          - The TS context obtained from TSCreate()
3527 
3528   Notes:
3529   TSPostEvaluate() is typically used within time stepping implementations,
3530   most users would not generally call this routine themselves.
3531 
3532   Level: developer
3533 
3534 .keywords: TS, timestep
3535 .seealso: TSSetPostEvaluate(), TSSetPreStep(), TSPreStep(), TSPostStep()
3536 @*/
3537 PetscErrorCode  TSPostEvaluate(TS ts)
3538 {
3539   PetscErrorCode ierr;
3540 
3541   PetscFunctionBegin;
3542   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3543   if (ts->postevaluate) {
3544     PetscStackCallStandard((*ts->postevaluate),(ts));
3545   }
3546   PetscFunctionReturn(0);
3547 }
3548 
3549 #undef __FUNCT__
3550 #define __FUNCT__ "TSSetPostStep"
3551 /*@C
3552   TSSetPostStep - Sets the general-purpose function
3553   called once at the end of each time step.
3554 
3555   Logically Collective on TS
3556 
3557   Input Parameters:
3558 + ts   - The TS context obtained from TSCreate()
3559 - func - The function
3560 
3561   Calling sequence of func:
3562 $ func (TS ts);
3563 
3564   Notes:
3565   The function set by TSSetPostStep() is called after each successful step. The solution vector X
3566   obtained by TSGetSolution() may be different than that computed at the step end if the event handler
3567   locates an event and TSPostEvent() modifies it. Use TSSetPostEvaluate() if an unmodified solution is needed instead.
3568 
3569   Level: intermediate
3570 
3571 .keywords: TS, timestep
3572 .seealso: TSSetPreStep(), TSSetPreStage(), TSSetPostEvaluate(), TSGetTimeStep(), TSGetTimeStepNumber(), TSGetTime()
3573 @*/
3574 PetscErrorCode  TSSetPostStep(TS ts, PetscErrorCode (*func)(TS))
3575 {
3576   PetscFunctionBegin;
3577   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3578   ts->poststep = func;
3579   PetscFunctionReturn(0);
3580 }
3581 
3582 #undef __FUNCT__
3583 #define __FUNCT__ "TSPostStep"
3584 /*@
3585   TSPostStep - Runs the user-defined post-step function.
3586 
3587   Collective on TS
3588 
3589   Input Parameters:
3590 . ts   - The TS context obtained from TSCreate()
3591 
3592   Notes:
3593   TSPostStep() is typically used within time stepping implementations,
3594   so most users would not generally call this routine themselves.
3595 
3596   Level: developer
3597 
3598 .keywords: TS, timestep
3599 @*/
3600 PetscErrorCode  TSPostStep(TS ts)
3601 {
3602   PetscErrorCode ierr;
3603 
3604   PetscFunctionBegin;
3605   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3606   if (ts->poststep) {
3607     PetscStackCallStandard((*ts->poststep),(ts));
3608   }
3609   PetscFunctionReturn(0);
3610 }
3611 
3612 /* ------------ Routines to set performance monitoring options ----------- */
3613 
3614 #undef __FUNCT__
3615 #define __FUNCT__ "TSMonitorSet"
3616 /*@C
3617    TSMonitorSet - Sets an ADDITIONAL function that is to be used at every
3618    timestep to display the iteration's  progress.
3619 
3620    Logically Collective on TS
3621 
3622    Input Parameters:
3623 +  ts - the TS context obtained from TSCreate()
3624 .  monitor - monitoring routine
3625 .  mctx - [optional] user-defined context for private data for the
3626              monitor routine (use NULL if no context is desired)
3627 -  monitordestroy - [optional] routine that frees monitor context
3628           (may be NULL)
3629 
3630    Calling sequence of monitor:
3631 $    int monitor(TS ts,PetscInt steps,PetscReal time,Vec u,void *mctx)
3632 
3633 +    ts - the TS context
3634 .    steps - iteration number (after the final time step the monitor routine may be called with a step of -1, this indicates the solution has been interpolated to this time)
3635 .    time - current time
3636 .    u - current iterate
3637 -    mctx - [optional] monitoring context
3638 
3639    Notes:
3640    This routine adds an additional monitor to the list of monitors that
3641    already has been loaded.
3642 
3643    Fortran notes: Only a single monitor function can be set for each TS object
3644 
3645    Level: intermediate
3646 
3647 .keywords: TS, timestep, set, monitor
3648 
3649 .seealso: TSMonitorDefault(), TSMonitorCancel()
3650 @*/
3651 PetscErrorCode  TSMonitorSet(TS ts,PetscErrorCode (*monitor)(TS,PetscInt,PetscReal,Vec,void*),void *mctx,PetscErrorCode (*mdestroy)(void**))
3652 {
3653   PetscErrorCode ierr;
3654   PetscInt       i;
3655   PetscBool      identical;
3656 
3657   PetscFunctionBegin;
3658   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3659   for (i=0; i<ts->numbermonitors;i++) {
3660     ierr = PetscMonitorCompare((PetscErrorCode (*)(void))monitor,mctx,mdestroy,(PetscErrorCode (*)(void))ts->monitor[i],ts->monitorcontext[i],ts->monitordestroy[i],&identical);CHKERRQ(ierr);
3661     if (identical) PetscFunctionReturn(0);
3662   }
3663   if (ts->numbermonitors >= MAXTSMONITORS) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many monitors set");
3664   ts->monitor[ts->numbermonitors]          = monitor;
3665   ts->monitordestroy[ts->numbermonitors]   = mdestroy;
3666   ts->monitorcontext[ts->numbermonitors++] = (void*)mctx;
3667   PetscFunctionReturn(0);
3668 }
3669 
3670 #undef __FUNCT__
3671 #define __FUNCT__ "TSMonitorCancel"
3672 /*@C
3673    TSMonitorCancel - Clears all the monitors that have been set on a time-step object.
3674 
3675    Logically Collective on TS
3676 
3677    Input Parameters:
3678 .  ts - the TS context obtained from TSCreate()
3679 
3680    Notes:
3681    There is no way to remove a single, specific monitor.
3682 
3683    Level: intermediate
3684 
3685 .keywords: TS, timestep, set, monitor
3686 
3687 .seealso: TSMonitorDefault(), TSMonitorSet()
3688 @*/
3689 PetscErrorCode  TSMonitorCancel(TS ts)
3690 {
3691   PetscErrorCode ierr;
3692   PetscInt       i;
3693 
3694   PetscFunctionBegin;
3695   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3696   for (i=0; i<ts->numbermonitors; i++) {
3697     if (ts->monitordestroy[i]) {
3698       ierr = (*ts->monitordestroy[i])(&ts->monitorcontext[i]);CHKERRQ(ierr);
3699     }
3700   }
3701   ts->numbermonitors = 0;
3702   PetscFunctionReturn(0);
3703 }
3704 
3705 #undef __FUNCT__
3706 #define __FUNCT__ "TSMonitorDefault"
3707 /*@C
3708    TSMonitorDefault - The Default monitor, prints the timestep and time for each step
3709 
3710    Level: intermediate
3711 
3712 .keywords: TS, set, monitor
3713 
3714 .seealso:  TSMonitorSet()
3715 @*/
3716 PetscErrorCode TSMonitorDefault(TS ts,PetscInt step,PetscReal ptime,Vec v,PetscViewerAndFormat *vf)
3717 {
3718   PetscErrorCode ierr;
3719   PetscViewer    viewer =  vf->viewer;
3720   PetscBool      iascii,ibinary;
3721 
3722   PetscFunctionBegin;
3723   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
3724   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
3725   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&ibinary);CHKERRQ(ierr);
3726   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
3727   if (iascii) {
3728     ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3729     if (step == -1){ /* this indicates it is an interpolated solution */
3730       ierr = PetscViewerASCIIPrintf(viewer,"Interpolated solution at time %g between steps %D and %D\n",(double)ptime,ts->steps-1,ts->steps);CHKERRQ(ierr);
3731     } else {
3732       ierr = PetscViewerASCIIPrintf(viewer,"%D TS dt %g time %g%s",step,(double)ts->time_step,(double)ptime,ts->steprollback ? " (r)\n" : "\n");CHKERRQ(ierr);
3733     }
3734     ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3735   } else if (ibinary) {
3736     PetscMPIInt rank;
3737     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)viewer),&rank);CHKERRQ(ierr);
3738     if (!rank) {
3739       PetscBool skipHeader;
3740       PetscInt  classid = REAL_FILE_CLASSID;
3741 
3742       ierr = PetscViewerBinaryGetSkipHeader(viewer,&skipHeader);CHKERRQ(ierr);
3743       if (!skipHeader) {
3744          ierr = PetscViewerBinaryWrite(viewer,&classid,1,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
3745        }
3746       ierr = PetscRealView(1,&ptime,viewer);CHKERRQ(ierr);
3747     } else {
3748       ierr = PetscRealView(0,&ptime,viewer);CHKERRQ(ierr);
3749     }
3750   }
3751   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
3752   PetscFunctionReturn(0);
3753 }
3754 
3755 #undef __FUNCT__
3756 #define __FUNCT__ "TSAdjointMonitorSet"
3757 /*@C
3758    TSAdjointMonitorSet - Sets an ADDITIONAL function that is to be used at every
3759    timestep to display the iteration's  progress.
3760 
3761    Logically Collective on TS
3762 
3763    Input Parameters:
3764 +  ts - the TS context obtained from TSCreate()
3765 .  adjointmonitor - monitoring routine
3766 .  adjointmctx - [optional] user-defined context for private data for the
3767              monitor routine (use NULL if no context is desired)
3768 -  adjointmonitordestroy - [optional] routine that frees monitor context
3769           (may be NULL)
3770 
3771    Calling sequence of monitor:
3772 $    int adjointmonitor(TS ts,PetscInt steps,PetscReal time,Vec u,PetscInt numcost,Vec *lambda, Vec *mu,void *adjointmctx)
3773 
3774 +    ts - the TS context
3775 .    steps - iteration number (after the final time step the monitor routine is called with a step of -1, this is at the final time which may have
3776                                been interpolated to)
3777 .    time - current time
3778 .    u - current iterate
3779 .    numcost - number of cost functionos
3780 .    lambda - sensitivities to initial conditions
3781 .    mu - sensitivities to parameters
3782 -    adjointmctx - [optional] adjoint monitoring context
3783 
3784    Notes:
3785    This routine adds an additional monitor to the list of monitors that
3786    already has been loaded.
3787 
3788    Fortran notes: Only a single monitor function can be set for each TS object
3789 
3790    Level: intermediate
3791 
3792 .keywords: TS, timestep, set, adjoint, monitor
3793 
3794 .seealso: TSAdjointMonitorCancel()
3795 @*/
3796 PetscErrorCode  TSAdjointMonitorSet(TS ts,PetscErrorCode (*adjointmonitor)(TS,PetscInt,PetscReal,Vec,PetscInt,Vec*,Vec*,void*),void *adjointmctx,PetscErrorCode (*adjointmdestroy)(void**))
3797 {
3798   PetscErrorCode ierr;
3799   PetscInt       i;
3800   PetscBool      identical;
3801 
3802   PetscFunctionBegin;
3803   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3804   for (i=0; i<ts->numbermonitors;i++) {
3805     ierr = PetscMonitorCompare((PetscErrorCode (*)(void))adjointmonitor,adjointmctx,adjointmdestroy,(PetscErrorCode (*)(void))ts->adjointmonitor[i],ts->adjointmonitorcontext[i],ts->adjointmonitordestroy[i],&identical);CHKERRQ(ierr);
3806     if (identical) PetscFunctionReturn(0);
3807   }
3808   if (ts->numberadjointmonitors >= MAXTSMONITORS) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many adjoint monitors set");
3809   ts->adjointmonitor[ts->numberadjointmonitors]          = adjointmonitor;
3810   ts->adjointmonitordestroy[ts->numberadjointmonitors]   = adjointmdestroy;
3811   ts->adjointmonitorcontext[ts->numberadjointmonitors++] = (void*)adjointmctx;
3812   PetscFunctionReturn(0);
3813 }
3814 
3815 #undef __FUNCT__
3816 #define __FUNCT__ "TSAdjointMonitorCancel"
3817 /*@C
3818    TSAdjointMonitorCancel - Clears all the adjoint monitors that have been set on a time-step object.
3819 
3820    Logically Collective on TS
3821 
3822    Input Parameters:
3823 .  ts - the TS context obtained from TSCreate()
3824 
3825    Notes:
3826    There is no way to remove a single, specific monitor.
3827 
3828    Level: intermediate
3829 
3830 .keywords: TS, timestep, set, adjoint, monitor
3831 
3832 .seealso: TSAdjointMonitorSet()
3833 @*/
3834 PetscErrorCode  TSAdjointMonitorCancel(TS ts)
3835 {
3836   PetscErrorCode ierr;
3837   PetscInt       i;
3838 
3839   PetscFunctionBegin;
3840   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3841   for (i=0; i<ts->numberadjointmonitors; i++) {
3842     if (ts->adjointmonitordestroy[i]) {
3843       ierr = (*ts->adjointmonitordestroy[i])(&ts->adjointmonitorcontext[i]);CHKERRQ(ierr);
3844     }
3845   }
3846   ts->numberadjointmonitors = 0;
3847   PetscFunctionReturn(0);
3848 }
3849 
3850 #undef __FUNCT__
3851 #define __FUNCT__ "TSAdjointMonitorDefault"
3852 /*@C
3853    TSAdjointMonitorDefault - the default monitor of adjoint computations
3854 
3855    Level: intermediate
3856 
3857 .keywords: TS, set, monitor
3858 
3859 .seealso: TSAdjointMonitorSet()
3860 @*/
3861 PetscErrorCode TSAdjointMonitorDefault(TS ts,PetscInt step,PetscReal ptime,Vec v,PetscInt numcost,Vec *lambda,Vec *mu,PetscViewerAndFormat *vf)
3862 {
3863   PetscErrorCode ierr;
3864   PetscViewer    viewer = vf->viewer;
3865 
3866   PetscFunctionBegin;
3867   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
3868   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
3869   ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3870   ierr = PetscViewerASCIIPrintf(viewer,"%D TS dt %g time %g%s",step,(double)ts->time_step,(double)ptime,ts->steprollback ? " (r)\n" : "\n");CHKERRQ(ierr);
3871   ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3872   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
3873   PetscFunctionReturn(0);
3874 }
3875 
3876 #undef __FUNCT__
3877 #define __FUNCT__ "TSInterpolate"
3878 /*@
3879    TSInterpolate - Interpolate the solution computed during the previous step to an arbitrary location in the interval
3880 
3881    Collective on TS
3882 
3883    Input Argument:
3884 +  ts - time stepping context
3885 -  t - time to interpolate to
3886 
3887    Output Argument:
3888 .  U - state at given time
3889 
3890    Level: intermediate
3891 
3892    Developer Notes:
3893    TSInterpolate() and the storing of previous steps/stages should be generalized to support delay differential equations and continuous adjoints.
3894 
3895 .keywords: TS, set
3896 
3897 .seealso: TSSetExactFinalTime(), TSSolve()
3898 @*/
3899 PetscErrorCode TSInterpolate(TS ts,PetscReal t,Vec U)
3900 {
3901   PetscErrorCode ierr;
3902 
3903   PetscFunctionBegin;
3904   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3905   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
3906   if (t < ts->ptime_prev || t > ts->ptime) SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Requested time %g not in last time steps [%g,%g]",t,(double)ts->ptime_prev,(double)ts->ptime);
3907   if (!ts->ops->interpolate) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"%s does not provide interpolation",((PetscObject)ts)->type_name);
3908   ierr = (*ts->ops->interpolate)(ts,t,U);CHKERRQ(ierr);
3909   PetscFunctionReturn(0);
3910 }
3911 
3912 #undef __FUNCT__
3913 #define __FUNCT__ "TSStep"
3914 /*@
3915    TSStep - Steps one time step
3916 
3917    Collective on TS
3918 
3919    Input Parameter:
3920 .  ts - the TS context obtained from TSCreate()
3921 
3922    Level: developer
3923 
3924    Notes:
3925    The public interface for the ODE/DAE solvers is TSSolve(), you should almost for sure be using that routine and not this routine.
3926 
3927    The hook set using TSSetPreStep() is called before each attempt to take the step. In general, the time step size may
3928    be changed due to adaptive error controller or solve failures. Note that steps may contain multiple stages.
3929 
3930    This may over-step the final time provided in TSSetDuration() depending on the time-step used. TSSolve() interpolates to exactly the
3931    time provided in TSSetDuration(). One can use TSInterpolate() to determine an interpolated solution within the final timestep.
3932 
3933 .keywords: TS, timestep, solve
3934 
3935 .seealso: TSCreate(), TSSetUp(), TSDestroy(), TSSolve(), TSSetPreStep(), TSSetPreStage(), TSSetPostStage(), TSInterpolate()
3936 @*/
3937 PetscErrorCode  TSStep(TS ts)
3938 {
3939   PetscErrorCode   ierr;
3940   static PetscBool cite = PETSC_FALSE;
3941   PetscReal        ptime;
3942 
3943   PetscFunctionBegin;
3944   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3945   ierr = PetscCitationsRegister("@techreport{tspaper,\n"
3946                                 "  title       = {{PETSc/TS}: A Modern Scalable {DAE/ODE} Solver Library},\n"
3947                                 "  author      = {Shrirang Abhyankar and Jed Brown and Emil Constantinescu and Debojyoti Ghosh and Barry F. Smith},\n"
3948                                 "  type        = {Preprint},\n"
3949                                 "  number      = {ANL/MCS-P5061-0114},\n"
3950                                 "  institution = {Argonne National Laboratory},\n"
3951                                 "  year        = {2014}\n}\n",&cite);CHKERRQ(ierr);
3952 
3953   ierr = TSSetUp(ts);CHKERRQ(ierr);
3954   ierr = TSTrajectorySetUp(ts->trajectory,ts);CHKERRQ(ierr);
3955 
3956   if (ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"You must call TSSetExactFinalTime() or use -ts_exact_final_time <stepover,interpolate,matchstep> before calling TSStep()");
3957   if (ts->exact_final_time == TS_EXACTFINALTIME_MATCHSTEP && !ts->adapt) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Since TS is not adaptive you cannot use TS_EXACTFINALTIME_MATCHSTEP, suggest TS_EXACTFINALTIME_INTERPOLATE");
3958 
3959   if (!ts->steps) ts->ptime_prev = ts->ptime;
3960   ts->reason = TS_CONVERGED_ITERATING;
3961   ptime = ts->ptime; ts->ptime_prev_rollback = ts->ptime_prev;
3962   if (!ts->ops->step) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSStep not implemented for type '%s'",((PetscObject)ts)->type_name);
3963   ierr = PetscLogEventBegin(TS_Step,ts,0,0,0);CHKERRQ(ierr);
3964   ierr = (*ts->ops->step)(ts);CHKERRQ(ierr);
3965   ierr = PetscLogEventEnd(TS_Step,ts,0,0,0);CHKERRQ(ierr);
3966   ts->ptime_prev = ptime;
3967   ts->steps++; ts->total_steps++;
3968   ts->steprollback = PETSC_FALSE;
3969   ts->steprestart  = PETSC_FALSE;
3970 
3971   if (ts->reason < 0) {
3972     if (ts->errorifstepfailed) {
3973       if (ts->reason == TS_DIVERGED_NONLINEAR_SOLVE) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s, increase -ts_max_snes_failures or make negative to attempt recovery",TSConvergedReasons[ts->reason]);
3974       else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s",TSConvergedReasons[ts->reason]);
3975     }
3976   } else if (!ts->reason) {
3977     if (ts->steps >= ts->max_steps)     ts->reason = TS_CONVERGED_ITS;
3978     else if (ts->ptime >= ts->max_time) ts->reason = TS_CONVERGED_TIME;
3979   }
3980   PetscFunctionReturn(0);
3981 }
3982 
3983 #undef __FUNCT__
3984 #define __FUNCT__ "TSAdjointStep"
3985 /*@
3986    TSAdjointStep - Steps one time step backward in the adjoint run
3987 
3988    Collective on TS
3989 
3990    Input Parameter:
3991 .  ts - the TS context obtained from TSCreate()
3992 
3993    Level: intermediate
3994 
3995 .keywords: TS, adjoint, step
3996 
3997 .seealso: TSAdjointSetUp(), TSAdjointSolve()
3998 @*/
3999 PetscErrorCode  TSAdjointStep(TS ts)
4000 {
4001   DM               dm;
4002   PetscErrorCode   ierr;
4003 
4004   PetscFunctionBegin;
4005   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4006   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4007   ierr = TSAdjointSetUp(ts);CHKERRQ(ierr);
4008 
4009   ierr = VecViewFromOptions(ts->vec_sol,(PetscObject)ts,"-ts_view_solution");CHKERRQ(ierr);
4010 
4011   ts->reason = TS_CONVERGED_ITERATING;
4012   ts->ptime_prev = ts->ptime;
4013   if (!ts->ops->adjointstep) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed because the adjoint of  %s has not been implemented, try other time stepping methods for adjoint sensitivity analysis",((PetscObject)ts)->type_name);
4014   ierr = PetscLogEventBegin(TS_AdjointStep,ts,0,0,0);CHKERRQ(ierr);
4015   ierr = (*ts->ops->adjointstep)(ts);CHKERRQ(ierr);
4016   ierr = PetscLogEventEnd(TS_AdjointStep,ts,0,0,0);CHKERRQ(ierr);
4017   ts->steps++; ts->total_steps--;
4018 
4019   if (ts->reason < 0) {
4020     if (ts->errorifstepfailed) {
4021       if (ts->reason == TS_DIVERGED_NONLINEAR_SOLVE) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s, increase -ts_max_snes_failures or make negative to attempt recovery",TSConvergedReasons[ts->reason]);
4022       else if (ts->reason == TS_DIVERGED_STEP_REJECTED) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s, increase -ts_max_reject or make negative to attempt recovery",TSConvergedReasons[ts->reason]);
4023       else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s",TSConvergedReasons[ts->reason]);
4024     }
4025   } else if (!ts->reason) {
4026     if (ts->steps >= ts->adjoint_max_steps) ts->reason = TS_CONVERGED_ITS;
4027   }
4028   PetscFunctionReturn(0);
4029 }
4030 
4031 #undef __FUNCT__
4032 #define __FUNCT__ "TSEvaluateWLTE"
4033 /*@
4034    TSEvaluateWLTE - Evaluate the weighted local truncation error norm
4035    at the end of a time step with a given order of accuracy.
4036 
4037    Collective on TS
4038 
4039    Input Arguments:
4040 +  ts - time stepping context
4041 .  wnormtype - norm type, either NORM_2 or NORM_INFINITY
4042 -  order - optional, desired order for the error evaluation or PETSC_DECIDE
4043 
4044    Output Arguments:
4045 +  order - optional, the actual order of the error evaluation
4046 -  wlte - the weighted local truncation error norm
4047 
4048    Level: advanced
4049 
4050    Notes:
4051    If the timestepper cannot evaluate the error in a particular step
4052    (eg. in the first step or restart steps after event handling),
4053    this routine returns wlte=-1.0 .
4054 
4055 .seealso: TSStep(), TSAdapt, TSErrorWeightedNorm()
4056 @*/
4057 PetscErrorCode TSEvaluateWLTE(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
4058 {
4059   PetscErrorCode ierr;
4060 
4061   PetscFunctionBegin;
4062   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4063   PetscValidType(ts,1);
4064   PetscValidLogicalCollectiveEnum(ts,wnormtype,4);
4065   if (order) PetscValidIntPointer(order,3);
4066   if (order) PetscValidLogicalCollectiveInt(ts,*order,3);
4067   PetscValidRealPointer(wlte,4);
4068   if (wnormtype != NORM_2 && wnormtype != NORM_INFINITY) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
4069   if (!ts->ops->evaluatewlte) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSEvaluateWLTE not implemented for type '%s'",((PetscObject)ts)->type_name);
4070   ierr = (*ts->ops->evaluatewlte)(ts,wnormtype,order,wlte);CHKERRQ(ierr);
4071   PetscFunctionReturn(0);
4072 }
4073 
4074 #undef __FUNCT__
4075 #define __FUNCT__ "TSEvaluateStep"
4076 /*@
4077    TSEvaluateStep - Evaluate the solution at the end of a time step with a given order of accuracy.
4078 
4079    Collective on TS
4080 
4081    Input Arguments:
4082 +  ts - time stepping context
4083 .  order - desired order of accuracy
4084 -  done - whether the step was evaluated at this order (pass NULL to generate an error if not available)
4085 
4086    Output Arguments:
4087 .  U - state at the end of the current step
4088 
4089    Level: advanced
4090 
4091    Notes:
4092    This function cannot be called until all stages have been evaluated.
4093    It is normally called by adaptive controllers before a step has been accepted and may also be called by the user after TSStep() has returned.
4094 
4095 .seealso: TSStep(), TSAdapt
4096 @*/
4097 PetscErrorCode TSEvaluateStep(TS ts,PetscInt order,Vec U,PetscBool *done)
4098 {
4099   PetscErrorCode ierr;
4100 
4101   PetscFunctionBegin;
4102   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4103   PetscValidType(ts,1);
4104   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
4105   if (!ts->ops->evaluatestep) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSEvaluateStep not implemented for type '%s'",((PetscObject)ts)->type_name);
4106   ierr = (*ts->ops->evaluatestep)(ts,order,U,done);CHKERRQ(ierr);
4107   PetscFunctionReturn(0);
4108 }
4109 
4110 #undef __FUNCT__
4111 #define __FUNCT__ "TSForwardCostIntegral"
4112 /*@
4113  TSForwardCostIntegral - Evaluate the cost integral in the forward run.
4114 
4115  Collective on TS
4116 
4117  Input Arguments:
4118  .  ts - time stepping context
4119 
4120  Level: advanced
4121 
4122  Notes:
4123  This function cannot be called until TSStep() has been completed.
4124 
4125  .seealso: TSSolve(), TSAdjointCostIntegral()
4126  @*/
4127 PetscErrorCode TSForwardCostIntegral(TS ts)
4128 {
4129     PetscErrorCode ierr;
4130     PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4131     if (!ts->ops->forwardintegral) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"%s does not provide integral evaluation in the forward run",((PetscObject)ts)->type_name);
4132     ierr = (*ts->ops->forwardintegral)(ts);CHKERRQ(ierr);
4133     PetscFunctionReturn(0);
4134 }
4135 
4136 #undef __FUNCT__
4137 #define __FUNCT__ "TSSolve"
4138 /*@
4139    TSSolve - Steps the requested number of timesteps.
4140 
4141    Collective on TS
4142 
4143    Input Parameter:
4144 +  ts - the TS context obtained from TSCreate()
4145 -  u - the solution vector  (can be null if TSSetSolution() was used and TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP) was not used,
4146                              otherwise must contain the initial conditions and will contain the solution at the final requested time
4147 
4148    Level: beginner
4149 
4150    Notes:
4151    The final time returned by this function may be different from the time of the internally
4152    held state accessible by TSGetSolution() and TSGetTime() because the method may have
4153    stepped over the final time.
4154 
4155 .keywords: TS, timestep, solve
4156 
4157 .seealso: TSCreate(), TSSetSolution(), TSStep(), TSGetTime(), TSGetSolveTime()
4158 @*/
4159 PetscErrorCode TSSolve(TS ts,Vec u)
4160 {
4161   Vec               solution;
4162   PetscErrorCode    ierr;
4163 
4164   PetscFunctionBegin;
4165   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4166   if (u) PetscValidHeaderSpecific(u,VEC_CLASSID,2);
4167 
4168   if (ts->exact_final_time == TS_EXACTFINALTIME_INTERPOLATE) {   /* Need ts->vec_sol to be distinct so it is not overwritten when we interpolate at the end */
4169     PetscValidHeaderSpecific(u,VEC_CLASSID,2);
4170     if (!ts->vec_sol || u == ts->vec_sol) {
4171       ierr = VecDuplicate(u,&solution);CHKERRQ(ierr);
4172       ierr = TSSetSolution(ts,solution);CHKERRQ(ierr);
4173       ierr = VecDestroy(&solution);CHKERRQ(ierr); /* grant ownership */
4174     }
4175     ierr = VecCopy(u,ts->vec_sol);CHKERRQ(ierr);
4176   } else if (u) {
4177     ierr = TSSetSolution(ts,u);CHKERRQ(ierr);
4178   }
4179   ierr = TSSetUp(ts);CHKERRQ(ierr);
4180   ierr = TSTrajectorySetUp(ts->trajectory,ts);CHKERRQ(ierr);
4181 
4182   if (ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"You must call TSSetExactFinalTime() or use -ts_exact_final_time <stepover,interpolate,matchstep> before calling TSSolve()");
4183   if (ts->exact_final_time == TS_EXACTFINALTIME_MATCHSTEP && !ts->adapt) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Since TS is not adaptive you cannot use TS_EXACTFINALTIME_MATCHSTEP, suggest TS_EXACTFINALTIME_INTERPOLATE");
4184 
4185   /* reset time step and iteration counters */
4186   ts->steps             = 0;
4187   ts->ksp_its           = 0;
4188   ts->snes_its          = 0;
4189   ts->num_snes_failures = 0;
4190   ts->reject            = 0;
4191   ts->reason            = TS_CONVERGED_ITERATING;
4192 
4193   ierr = TSViewFromOptions(ts,NULL,"-ts_view_pre");CHKERRQ(ierr);
4194 
4195   if (ts->ops->solve) { /* This private interface is transitional and should be removed when all implementations are updated. */
4196     ierr = (*ts->ops->solve)(ts);CHKERRQ(ierr);
4197     if (u) {ierr = VecCopy(ts->vec_sol,u);CHKERRQ(ierr);}
4198     ts->solvetime = ts->ptime;
4199     solution = ts->vec_sol;
4200   } else { /* Step the requested number of timesteps. */
4201     if (ts->steps >= ts->max_steps)     ts->reason = TS_CONVERGED_ITS;
4202     else if (ts->ptime >= ts->max_time) ts->reason = TS_CONVERGED_TIME;
4203     ierr = TSTrajectorySet(ts->trajectory,ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4204     ierr = TSEventInitialize(ts->event,ts,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4205     ts->steprollback = PETSC_FALSE;
4206     ts->steprestart  = PETSC_TRUE;
4207 
4208     while (!ts->reason) {
4209       ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4210       if (!ts->steprollback) {
4211         ierr = TSPreStep(ts);CHKERRQ(ierr);
4212       }
4213       ierr = TSStep(ts);CHKERRQ(ierr);
4214       if (ts->vec_costintegral && ts->costintegralfwd) { /* Must evaluate the cost integral before event is handled. The cost integral value can also be rolled back. */
4215         ierr = TSForwardCostIntegral(ts);CHKERRQ(ierr);
4216       }
4217       ierr = TSEventHandler(ts);CHKERRQ(ierr); /* The right-hand side may be changed due to event. Be careful with Any computation using the RHS information after this point. */
4218       if (!ts->steprollback) {
4219         ierr = TSTrajectorySet(ts->trajectory,ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4220         ierr = TSPostStep(ts);CHKERRQ(ierr);
4221       }
4222     }
4223     ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4224 
4225     if (ts->exact_final_time == TS_EXACTFINALTIME_INTERPOLATE && ts->ptime > ts->max_time) {
4226       ierr = TSInterpolate(ts,ts->max_time,u);CHKERRQ(ierr);
4227       ts->solvetime = ts->max_time;
4228       solution = u;
4229       ierr = TSMonitor(ts,-1,ts->solvetime,solution);CHKERRQ(ierr);
4230     } else {
4231       if (u) {ierr = VecCopy(ts->vec_sol,u);CHKERRQ(ierr);}
4232       ts->solvetime = ts->ptime;
4233       solution = ts->vec_sol;
4234     }
4235   }
4236 
4237   ierr = TSViewFromOptions(ts,NULL,"-ts_view");CHKERRQ(ierr);
4238   ierr = VecViewFromOptions(solution,NULL,"-ts_view_solution");CHKERRQ(ierr);
4239   ierr = PetscObjectSAWsBlock((PetscObject)ts);CHKERRQ(ierr);
4240   if (ts->adjoint_solve) {
4241     ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
4242   }
4243   PetscFunctionReturn(0);
4244 }
4245 
4246 #undef __FUNCT__
4247 #define __FUNCT__ "TSAdjointCostIntegral"
4248 /*@
4249  TSAdjointCostIntegral - Evaluate the cost integral in the adjoint run.
4250 
4251  Collective on TS
4252 
4253  Input Arguments:
4254  .  ts - time stepping context
4255 
4256  Level: advanced
4257 
4258  Notes:
4259  This function cannot be called until TSAdjointStep() has been completed.
4260 
4261  .seealso: TSAdjointSolve(), TSAdjointStep
4262  @*/
4263 PetscErrorCode TSAdjointCostIntegral(TS ts)
4264 {
4265     PetscErrorCode ierr;
4266     PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4267     if (!ts->ops->adjointintegral) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"%s does not provide integral evaluation in the adjoint run",((PetscObject)ts)->type_name);
4268     ierr = (*ts->ops->adjointintegral)(ts);CHKERRQ(ierr);
4269     PetscFunctionReturn(0);
4270 }
4271 
4272 #undef __FUNCT__
4273 #define __FUNCT__ "TSAdjointSolve"
4274 /*@
4275    TSAdjointSolve - Solves the discrete ajoint problem for an ODE/DAE
4276 
4277    Collective on TS
4278 
4279    Input Parameter:
4280 .  ts - the TS context obtained from TSCreate()
4281 
4282    Options Database:
4283 . -ts_adjoint_view_solution <viewerinfo> - views the first gradient with respect to the initial conditions
4284 
4285    Level: intermediate
4286 
4287    Notes:
4288    This must be called after a call to TSSolve() that solves the forward problem
4289 
4290    By default this will integrate back to the initial time, one can use TSAdjointSetSteps() to step back to a later time
4291 
4292 .keywords: TS, timestep, solve
4293 
4294 .seealso: TSCreate(), TSSetCostGradients(), TSSetSolution(), TSAdjointStep()
4295 @*/
4296 PetscErrorCode TSAdjointSolve(TS ts)
4297 {
4298   PetscErrorCode    ierr;
4299 
4300   PetscFunctionBegin;
4301   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4302   ierr = TSAdjointSetUp(ts);CHKERRQ(ierr);
4303 
4304   /* reset time step and iteration counters */
4305   ts->steps             = 0;
4306   ts->ksp_its           = 0;
4307   ts->snes_its          = 0;
4308   ts->num_snes_failures = 0;
4309   ts->reject            = 0;
4310   ts->reason            = TS_CONVERGED_ITERATING;
4311 
4312   if (!ts->adjoint_max_steps) ts->adjoint_max_steps = ts->total_steps;
4313 
4314   if (ts->steps >= ts->adjoint_max_steps)     ts->reason = TS_CONVERGED_ITS;
4315   while (!ts->reason) {
4316     ierr = TSTrajectoryGet(ts->trajectory,ts,ts->total_steps,&ts->ptime);CHKERRQ(ierr);
4317     ierr = TSAdjointMonitor(ts,ts->total_steps,ts->ptime,ts->vec_sol,ts->numcost,ts->vecs_sensi,ts->vecs_sensip);CHKERRQ(ierr);
4318     ierr = TSAdjointEventHandler(ts);CHKERRQ(ierr);
4319     ierr = TSAdjointStep(ts);CHKERRQ(ierr);
4320     if (ts->vec_costintegral && !ts->costintegralfwd) {
4321       ierr = TSAdjointCostIntegral(ts);CHKERRQ(ierr);
4322     }
4323   }
4324   ierr = TSTrajectoryGet(ts->trajectory,ts,ts->total_steps,&ts->ptime);CHKERRQ(ierr);
4325   ierr = TSAdjointMonitor(ts,ts->total_steps,ts->ptime,ts->vec_sol,ts->numcost,ts->vecs_sensi,ts->vecs_sensip);CHKERRQ(ierr);
4326   ts->solvetime = ts->ptime;
4327   ierr = TSTrajectoryViewFromOptions(ts->trajectory,NULL,"-ts_trajectory_view");CHKERRQ(ierr);
4328   ierr = VecViewFromOptions(ts->vecs_sensi[0],(PetscObject) ts, "-ts_adjoint_view_solution");CHKERRQ(ierr);
4329   PetscFunctionReturn(0);
4330 }
4331 
4332 #undef __FUNCT__
4333 #define __FUNCT__ "TSMonitor"
4334 /*@C
4335    TSMonitor - Runs all user-provided monitor routines set using TSMonitorSet()
4336 
4337    Collective on TS
4338 
4339    Input Parameters:
4340 +  ts - time stepping context obtained from TSCreate()
4341 .  step - step number that has just completed
4342 .  ptime - model time of the state
4343 -  u - state at the current model time
4344 
4345    Notes:
4346    TSMonitor() is typically used automatically within the time stepping implementations.
4347    Users would almost never call this routine directly.
4348 
4349    A step of -1 indicates that the monitor is being called on a solution obtained by interpolating from computed solutions
4350 
4351    Level: developer
4352 
4353 .keywords: TS, timestep
4354 @*/
4355 PetscErrorCode TSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec u)
4356 {
4357   DM             dm;
4358   PetscInt       i,n = ts->numbermonitors;
4359   PetscErrorCode ierr;
4360 
4361   PetscFunctionBegin;
4362   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4363   PetscValidHeaderSpecific(u,VEC_CLASSID,4);
4364 
4365   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4366   ierr = DMSetOutputSequenceNumber(dm,step,ptime);CHKERRQ(ierr);
4367 
4368   ierr = VecLockPush(u);CHKERRQ(ierr);
4369   for (i=0; i<n; i++) {
4370     ierr = (*ts->monitor[i])(ts,step,ptime,u,ts->monitorcontext[i]);CHKERRQ(ierr);
4371   }
4372   ierr = VecLockPop(u);CHKERRQ(ierr);
4373   PetscFunctionReturn(0);
4374 }
4375 
4376 #undef __FUNCT__
4377 #define __FUNCT__ "TSAdjointMonitor"
4378 /*@C
4379    TSAdjointMonitor - Runs all user-provided adjoint monitor routines set using TSAdjointMonitorSet()
4380 
4381    Collective on TS
4382 
4383    Input Parameters:
4384 +  ts - time stepping context obtained from TSCreate()
4385 .  step - step number that has just completed
4386 .  ptime - model time of the state
4387 .  u - state at the current model time
4388 .  numcost - number of cost functions (dimension of lambda  or mu)
4389 .  lambda - vectors containing the gradients of the cost functions with respect to the ODE/DAE solution variables
4390 -  mu - vectors containing the gradients of the cost functions with respect to the problem parameters
4391 
4392    Notes:
4393    TSAdjointMonitor() is typically used automatically within the time stepping implementations.
4394    Users would almost never call this routine directly.
4395 
4396    Level: developer
4397 
4398 .keywords: TS, timestep
4399 @*/
4400 PetscErrorCode TSAdjointMonitor(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscInt numcost,Vec *lambda, Vec *mu)
4401 {
4402   PetscErrorCode ierr;
4403   PetscInt       i,n = ts->numberadjointmonitors;
4404 
4405   PetscFunctionBegin;
4406   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4407   PetscValidHeaderSpecific(u,VEC_CLASSID,4);
4408   ierr = VecLockPush(u);CHKERRQ(ierr);
4409   for (i=0; i<n; i++) {
4410     ierr = (*ts->adjointmonitor[i])(ts,step,ptime,u,numcost,lambda,mu,ts->adjointmonitorcontext[i]);CHKERRQ(ierr);
4411   }
4412   ierr = VecLockPop(u);CHKERRQ(ierr);
4413   PetscFunctionReturn(0);
4414 }
4415 
4416 /* ------------------------------------------------------------------------*/
4417 #undef __FUNCT__
4418 #define __FUNCT__ "TSMonitorLGCtxCreate"
4419 /*@C
4420    TSMonitorLGCtxCreate - Creates a TSMonitorLGCtx context for use with
4421    TS to monitor the solution process graphically in various ways
4422 
4423    Collective on TS
4424 
4425    Input Parameters:
4426 +  host - the X display to open, or null for the local machine
4427 .  label - the title to put in the title bar
4428 .  x, y - the screen coordinates of the upper left coordinate of the window
4429 .  m, n - the screen width and height in pixels
4430 -  howoften - if positive then determines the frequency of the plotting, if -1 then only at the final time
4431 
4432    Output Parameter:
4433 .  ctx - the context
4434 
4435    Options Database Key:
4436 +  -ts_monitor_lg_timestep - automatically sets line graph monitor
4437 .  -ts_monitor_lg_solution - monitor the solution (or certain values of the solution by calling TSMonitorLGSetDisplayVariables() or TSMonitorLGCtxSetDisplayVariables())
4438 .  -ts_monitor_lg_error -  monitor the error
4439 .  -ts_monitor_lg_ksp_iterations - monitor the number of KSP iterations needed for each timestep
4440 .  -ts_monitor_lg_snes_iterations - monitor the number of SNES iterations needed for each timestep
4441 -  -lg_use_markers <true,false> - mark the data points (at each time step) on the plot; default is true
4442 
4443    Notes:
4444    Use TSMonitorLGCtxDestroy() to destroy.
4445 
4446    One can provide a function that transforms the solution before plotting it with TSMonitorLGCtxSetTransform() or TSMonitorLGSetTransform()
4447 
4448    Many of the functions that control the monitoring have two forms: TSMonitorLGSet/GetXXXX() and TSMonitorLGCtxSet/GetXXXX() the first take a TS object as the
4449    first argument (if that TS object does not have a TSMonitorLGCtx associated with it the function call is ignored) and the second takes a TSMonitorLGCtx object
4450    as the first argument.
4451 
4452    One can control the names displayed for each solution or error variable with TSMonitorLGCtxSetVariableNames() or TSMonitorLGSetVariableNames()
4453 
4454 
4455    Level: intermediate
4456 
4457 .keywords: TS, monitor, line graph, residual
4458 
4459 .seealso: TSMonitorLGTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError(), TSMonitorDefault(), VecView(),
4460            TSMonitorLGCtxCreate(), TSMonitorLGCtxSetVariableNames(), TSMonitorLGCtxGetVariableNames(),
4461            TSMonitorLGSetVariableNames(), TSMonitorLGGetVariableNames(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetDisplayVariables(),
4462            TSMonitorLGCtxSetTransform(), TSMonitorLGSetTransform(), TSMonitorLGError(), TSMonitorLGSNESIterations(), TSMonitorLGKSPIterations(),
4463            TSMonitorEnvelopeCtxCreate(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxDestroy(), TSMonitorEnvelop()
4464 
4465 @*/
4466 PetscErrorCode  TSMonitorLGCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorLGCtx *ctx)
4467 {
4468   PetscDraw      draw;
4469   PetscErrorCode ierr;
4470 
4471   PetscFunctionBegin;
4472   ierr = PetscNew(ctx);CHKERRQ(ierr);
4473   ierr = PetscDrawCreate(comm,host,label,x,y,m,n,&draw);CHKERRQ(ierr);
4474   ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
4475   ierr = PetscDrawLGCreate(draw,1,&(*ctx)->lg);CHKERRQ(ierr);
4476   ierr = PetscDrawLGSetFromOptions((*ctx)->lg);CHKERRQ(ierr);
4477   ierr = PetscDrawDestroy(&draw);CHKERRQ(ierr);
4478   (*ctx)->howoften = howoften;
4479   PetscFunctionReturn(0);
4480 }
4481 
4482 #undef __FUNCT__
4483 #define __FUNCT__ "TSMonitorLGTimeStep"
4484 PetscErrorCode TSMonitorLGTimeStep(TS ts,PetscInt step,PetscReal ptime,Vec v,void *monctx)
4485 {
4486   TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
4487   PetscReal      x   = ptime,y;
4488   PetscErrorCode ierr;
4489 
4490   PetscFunctionBegin;
4491   if (step < 0) PetscFunctionReturn(0); /* -1 indicates an interpolated solution */
4492   if (!step) {
4493     PetscDrawAxis axis;
4494     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
4495     ierr = PetscDrawAxisSetLabels(axis,"Timestep as function of time","Time","Time Step");CHKERRQ(ierr);
4496     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
4497   }
4498   ierr = TSGetTimeStep(ts,&y);CHKERRQ(ierr);
4499   ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
4500   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
4501     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
4502     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
4503   }
4504   PetscFunctionReturn(0);
4505 }
4506 
4507 #undef __FUNCT__
4508 #define __FUNCT__ "TSMonitorLGCtxDestroy"
4509 /*@C
4510    TSMonitorLGCtxDestroy - Destroys a line graph context that was created
4511    with TSMonitorLGCtxCreate().
4512 
4513    Collective on TSMonitorLGCtx
4514 
4515    Input Parameter:
4516 .  ctx - the monitor context
4517 
4518    Level: intermediate
4519 
4520 .keywords: TS, monitor, line graph, destroy
4521 
4522 .seealso: TSMonitorLGCtxCreate(),  TSMonitorSet(), TSMonitorLGTimeStep();
4523 @*/
4524 PetscErrorCode  TSMonitorLGCtxDestroy(TSMonitorLGCtx *ctx)
4525 {
4526   PetscErrorCode ierr;
4527 
4528   PetscFunctionBegin;
4529   if ((*ctx)->transformdestroy) {
4530     ierr = ((*ctx)->transformdestroy)((*ctx)->transformctx);CHKERRQ(ierr);
4531   }
4532   ierr = PetscDrawLGDestroy(&(*ctx)->lg);CHKERRQ(ierr);
4533   ierr = PetscStrArrayDestroy(&(*ctx)->names);CHKERRQ(ierr);
4534   ierr = PetscStrArrayDestroy(&(*ctx)->displaynames);CHKERRQ(ierr);
4535   ierr = PetscFree((*ctx)->displayvariables);CHKERRQ(ierr);
4536   ierr = PetscFree((*ctx)->displayvalues);CHKERRQ(ierr);
4537   ierr = PetscFree(*ctx);CHKERRQ(ierr);
4538   PetscFunctionReturn(0);
4539 }
4540 
4541 #undef __FUNCT__
4542 #define __FUNCT__ "TSGetTime"
4543 /*@
4544    TSGetTime - Gets the time of the most recently completed step.
4545 
4546    Not Collective
4547 
4548    Input Parameter:
4549 .  ts - the TS context obtained from TSCreate()
4550 
4551    Output Parameter:
4552 .  t  - the current time. This time may not corresponds to the final time set with TSSetDuration(), use TSGetSolveTime().
4553 
4554    Level: beginner
4555 
4556    Note:
4557    When called during time step evaluation (e.g. during residual evaluation or via hooks set using TSSetPreStep(),
4558    TSSetPreStage(), TSSetPostStage(), or TSSetPostStep()), the time is the time at the start of the step being evaluated.
4559 
4560 .seealso: TSSetInitialTimeStep(), TSGetTimeStep(), TSGetSolveTime()
4561 
4562 .keywords: TS, get, time
4563 @*/
4564 PetscErrorCode  TSGetTime(TS ts,PetscReal *t)
4565 {
4566   PetscFunctionBegin;
4567   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4568   PetscValidRealPointer(t,2);
4569   *t = ts->ptime;
4570   PetscFunctionReturn(0);
4571 }
4572 
4573 #undef __FUNCT__
4574 #define __FUNCT__ "TSGetPrevTime"
4575 /*@
4576    TSGetPrevTime - Gets the starting time of the previously completed step.
4577 
4578    Not Collective
4579 
4580    Input Parameter:
4581 .  ts - the TS context obtained from TSCreate()
4582 
4583    Output Parameter:
4584 .  t  - the previous time
4585 
4586    Level: beginner
4587 
4588 .seealso: TSSetInitialTimeStep(), TSGetTimeStep()
4589 
4590 .keywords: TS, get, time
4591 @*/
4592 PetscErrorCode  TSGetPrevTime(TS ts,PetscReal *t)
4593 {
4594   PetscFunctionBegin;
4595   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4596   PetscValidRealPointer(t,2);
4597   *t = ts->ptime_prev;
4598   PetscFunctionReturn(0);
4599 }
4600 
4601 #undef __FUNCT__
4602 #define __FUNCT__ "TSSetTime"
4603 /*@
4604    TSSetTime - Allows one to reset the time.
4605 
4606    Logically Collective on TS
4607 
4608    Input Parameters:
4609 +  ts - the TS context obtained from TSCreate()
4610 -  time - the time
4611 
4612    Level: intermediate
4613 
4614 .seealso: TSGetTime(), TSSetDuration()
4615 
4616 .keywords: TS, set, time
4617 @*/
4618 PetscErrorCode  TSSetTime(TS ts, PetscReal t)
4619 {
4620   PetscFunctionBegin;
4621   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4622   PetscValidLogicalCollectiveReal(ts,t,2);
4623   ts->ptime = t;
4624   PetscFunctionReturn(0);
4625 }
4626 
4627 #undef __FUNCT__
4628 #define __FUNCT__ "TSSetOptionsPrefix"
4629 /*@C
4630    TSSetOptionsPrefix - Sets the prefix used for searching for all
4631    TS options in the database.
4632 
4633    Logically Collective on TS
4634 
4635    Input Parameter:
4636 +  ts     - The TS context
4637 -  prefix - The prefix to prepend to all option names
4638 
4639    Notes:
4640    A hyphen (-) must NOT be given at the beginning of the prefix name.
4641    The first character of all runtime options is AUTOMATICALLY the
4642    hyphen.
4643 
4644    Level: advanced
4645 
4646 .keywords: TS, set, options, prefix, database
4647 
4648 .seealso: TSSetFromOptions()
4649 
4650 @*/
4651 PetscErrorCode  TSSetOptionsPrefix(TS ts,const char prefix[])
4652 {
4653   PetscErrorCode ierr;
4654   SNES           snes;
4655 
4656   PetscFunctionBegin;
4657   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4658   ierr = PetscObjectSetOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
4659   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4660   ierr = SNESSetOptionsPrefix(snes,prefix);CHKERRQ(ierr);
4661   PetscFunctionReturn(0);
4662 }
4663 
4664 
4665 #undef __FUNCT__
4666 #define __FUNCT__ "TSAppendOptionsPrefix"
4667 /*@C
4668    TSAppendOptionsPrefix - Appends to the prefix used for searching for all
4669    TS options in the database.
4670 
4671    Logically Collective on TS
4672 
4673    Input Parameter:
4674 +  ts     - The TS context
4675 -  prefix - The prefix to prepend to all option names
4676 
4677    Notes:
4678    A hyphen (-) must NOT be given at the beginning of the prefix name.
4679    The first character of all runtime options is AUTOMATICALLY the
4680    hyphen.
4681 
4682    Level: advanced
4683 
4684 .keywords: TS, append, options, prefix, database
4685 
4686 .seealso: TSGetOptionsPrefix()
4687 
4688 @*/
4689 PetscErrorCode  TSAppendOptionsPrefix(TS ts,const char prefix[])
4690 {
4691   PetscErrorCode ierr;
4692   SNES           snes;
4693 
4694   PetscFunctionBegin;
4695   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4696   ierr = PetscObjectAppendOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
4697   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4698   ierr = SNESAppendOptionsPrefix(snes,prefix);CHKERRQ(ierr);
4699   PetscFunctionReturn(0);
4700 }
4701 
4702 #undef __FUNCT__
4703 #define __FUNCT__ "TSGetOptionsPrefix"
4704 /*@C
4705    TSGetOptionsPrefix - Sets the prefix used for searching for all
4706    TS options in the database.
4707 
4708    Not Collective
4709 
4710    Input Parameter:
4711 .  ts - The TS context
4712 
4713    Output Parameter:
4714 .  prefix - A pointer to the prefix string used
4715 
4716    Notes: On the fortran side, the user should pass in a string 'prifix' of
4717    sufficient length to hold the prefix.
4718 
4719    Level: intermediate
4720 
4721 .keywords: TS, get, options, prefix, database
4722 
4723 .seealso: TSAppendOptionsPrefix()
4724 @*/
4725 PetscErrorCode  TSGetOptionsPrefix(TS ts,const char *prefix[])
4726 {
4727   PetscErrorCode ierr;
4728 
4729   PetscFunctionBegin;
4730   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4731   PetscValidPointer(prefix,2);
4732   ierr = PetscObjectGetOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
4733   PetscFunctionReturn(0);
4734 }
4735 
4736 #undef __FUNCT__
4737 #define __FUNCT__ "TSGetRHSJacobian"
4738 /*@C
4739    TSGetRHSJacobian - Returns the Jacobian J at the present timestep.
4740 
4741    Not Collective, but parallel objects are returned if TS is parallel
4742 
4743    Input Parameter:
4744 .  ts  - The TS context obtained from TSCreate()
4745 
4746    Output Parameters:
4747 +  Amat - The (approximate) Jacobian J of G, where U_t = G(U,t)  (or NULL)
4748 .  Pmat - The matrix from which the preconditioner is constructed, usually the same as Amat  (or NULL)
4749 .  func - Function to compute the Jacobian of the RHS  (or NULL)
4750 -  ctx - User-defined context for Jacobian evaluation routine  (or NULL)
4751 
4752    Notes: You can pass in NULL for any return argument you do not need.
4753 
4754    Level: intermediate
4755 
4756 .seealso: TSGetTimeStep(), TSGetMatrices(), TSGetTime(), TSGetTimeStepNumber()
4757 
4758 .keywords: TS, timestep, get, matrix, Jacobian
4759 @*/
4760 PetscErrorCode  TSGetRHSJacobian(TS ts,Mat *Amat,Mat *Pmat,TSRHSJacobian *func,void **ctx)
4761 {
4762   PetscErrorCode ierr;
4763   SNES           snes;
4764   DM             dm;
4765 
4766   PetscFunctionBegin;
4767   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4768   ierr = SNESGetJacobian(snes,Amat,Pmat,NULL,NULL);CHKERRQ(ierr);
4769   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4770   ierr = DMTSGetRHSJacobian(dm,func,ctx);CHKERRQ(ierr);
4771   PetscFunctionReturn(0);
4772 }
4773 
4774 #undef __FUNCT__
4775 #define __FUNCT__ "TSGetIJacobian"
4776 /*@C
4777    TSGetIJacobian - Returns the implicit Jacobian at the present timestep.
4778 
4779    Not Collective, but parallel objects are returned if TS is parallel
4780 
4781    Input Parameter:
4782 .  ts  - The TS context obtained from TSCreate()
4783 
4784    Output Parameters:
4785 +  Amat  - The (approximate) Jacobian of F(t,U,U_t)
4786 .  Pmat - The matrix from which the preconditioner is constructed, often the same as Amat
4787 .  f   - The function to compute the matrices
4788 - ctx - User-defined context for Jacobian evaluation routine
4789 
4790    Notes: You can pass in NULL for any return argument you do not need.
4791 
4792    Level: advanced
4793 
4794 .seealso: TSGetTimeStep(), TSGetRHSJacobian(), TSGetMatrices(), TSGetTime(), TSGetTimeStepNumber()
4795 
4796 .keywords: TS, timestep, get, matrix, Jacobian
4797 @*/
4798 PetscErrorCode  TSGetIJacobian(TS ts,Mat *Amat,Mat *Pmat,TSIJacobian *f,void **ctx)
4799 {
4800   PetscErrorCode ierr;
4801   SNES           snes;
4802   DM             dm;
4803 
4804   PetscFunctionBegin;
4805   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4806   ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr);
4807   ierr = SNESGetJacobian(snes,Amat,Pmat,NULL,NULL);CHKERRQ(ierr);
4808   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4809   ierr = DMTSGetIJacobian(dm,f,ctx);CHKERRQ(ierr);
4810   PetscFunctionReturn(0);
4811 }
4812 
4813 
4814 #undef __FUNCT__
4815 #define __FUNCT__ "TSMonitorDrawSolution"
4816 /*@C
4817    TSMonitorDrawSolution - Monitors progress of the TS solvers by calling
4818    VecView() for the solution at each timestep
4819 
4820    Collective on TS
4821 
4822    Input Parameters:
4823 +  ts - the TS context
4824 .  step - current time-step
4825 .  ptime - current time
4826 -  dummy - either a viewer or NULL
4827 
4828    Options Database:
4829 .   -ts_monitor_draw_solution_initial - show initial solution as well as current solution
4830 
4831    Notes: the initial solution and current solution are not display with a common axis scaling so generally the option -ts_monitor_draw_solution_initial
4832        will look bad
4833 
4834    Level: intermediate
4835 
4836 .keywords: TS,  vector, monitor, view
4837 
4838 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
4839 @*/
4840 PetscErrorCode  TSMonitorDrawSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
4841 {
4842   PetscErrorCode   ierr;
4843   TSMonitorDrawCtx ictx = (TSMonitorDrawCtx)dummy;
4844   PetscDraw        draw;
4845 
4846   PetscFunctionBegin;
4847   if (!step && ictx->showinitial) {
4848     if (!ictx->initialsolution) {
4849       ierr = VecDuplicate(u,&ictx->initialsolution);CHKERRQ(ierr);
4850     }
4851     ierr = VecCopy(u,ictx->initialsolution);CHKERRQ(ierr);
4852   }
4853   if (!(((ictx->howoften > 0) && (!(step % ictx->howoften))) || ((ictx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);
4854 
4855   if (ictx->showinitial) {
4856     PetscReal pause;
4857     ierr = PetscViewerDrawGetPause(ictx->viewer,&pause);CHKERRQ(ierr);
4858     ierr = PetscViewerDrawSetPause(ictx->viewer,0.0);CHKERRQ(ierr);
4859     ierr = VecView(ictx->initialsolution,ictx->viewer);CHKERRQ(ierr);
4860     ierr = PetscViewerDrawSetPause(ictx->viewer,pause);CHKERRQ(ierr);
4861     ierr = PetscViewerDrawSetHold(ictx->viewer,PETSC_TRUE);CHKERRQ(ierr);
4862   }
4863   ierr = VecView(u,ictx->viewer);CHKERRQ(ierr);
4864   if (ictx->showtimestepandtime) {
4865     PetscReal xl,yl,xr,yr,h;
4866     char      time[32];
4867 
4868     ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
4869     ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
4870     ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
4871     h    = yl + .95*(yr - yl);
4872     ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
4873     ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
4874   }
4875 
4876   if (ictx->showinitial) {
4877     ierr = PetscViewerDrawSetHold(ictx->viewer,PETSC_FALSE);CHKERRQ(ierr);
4878   }
4879   PetscFunctionReturn(0);
4880 }
4881 
4882 #undef __FUNCT__
4883 #define __FUNCT__ "TSAdjointMonitorDrawSensi"
4884 /*@C
4885    TSAdjointMonitorDrawSensi - Monitors progress of the adjoint TS solvers by calling
4886    VecView() for the sensitivities to initial states at each timestep
4887 
4888    Collective on TS
4889 
4890    Input Parameters:
4891 +  ts - the TS context
4892 .  step - current time-step
4893 .  ptime - current time
4894 .  u - current state
4895 .  numcost - number of cost functions
4896 .  lambda - sensitivities to initial conditions
4897 .  mu - sensitivities to parameters
4898 -  dummy - either a viewer or NULL
4899 
4900    Level: intermediate
4901 
4902 .keywords: TS,  vector, adjoint, monitor, view
4903 
4904 .seealso: TSAdjointMonitorSet(), TSAdjointMonitorDefault(), VecView()
4905 @*/
4906 PetscErrorCode  TSAdjointMonitorDrawSensi(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscInt numcost,Vec *lambda,Vec *mu,void *dummy)
4907 {
4908   PetscErrorCode   ierr;
4909   TSMonitorDrawCtx ictx = (TSMonitorDrawCtx)dummy;
4910   PetscDraw        draw;
4911   PetscReal        xl,yl,xr,yr,h;
4912   char             time[32];
4913 
4914   PetscFunctionBegin;
4915   if (!(((ictx->howoften > 0) && (!(step % ictx->howoften))) || ((ictx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);
4916 
4917   ierr = VecView(lambda[0],ictx->viewer);CHKERRQ(ierr);
4918   ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
4919   ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
4920   ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
4921   h    = yl + .95*(yr - yl);
4922   ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
4923   ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
4924   PetscFunctionReturn(0);
4925 }
4926 
4927 #undef __FUNCT__
4928 #define __FUNCT__ "TSMonitorDrawSolutionPhase"
4929 /*@C
4930    TSMonitorDrawSolutionPhase - Monitors progress of the TS solvers by plotting the solution as a phase diagram
4931 
4932    Collective on TS
4933 
4934    Input Parameters:
4935 +  ts - the TS context
4936 .  step - current time-step
4937 .  ptime - current time
4938 -  dummy - either a viewer or NULL
4939 
4940    Level: intermediate
4941 
4942 .keywords: TS,  vector, monitor, view
4943 
4944 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
4945 @*/
4946 PetscErrorCode  TSMonitorDrawSolutionPhase(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
4947 {
4948   PetscErrorCode    ierr;
4949   TSMonitorDrawCtx  ictx = (TSMonitorDrawCtx)dummy;
4950   PetscDraw         draw;
4951   PetscDrawAxis     axis;
4952   PetscInt          n;
4953   PetscMPIInt       size;
4954   PetscReal         U0,U1,xl,yl,xr,yr,h;
4955   char              time[32];
4956   const PetscScalar *U;
4957 
4958   PetscFunctionBegin;
4959   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)ts),&size);CHKERRQ(ierr);
4960   if (size != 1) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Only allowed for sequential runs");
4961   ierr = VecGetSize(u,&n);CHKERRQ(ierr);
4962   if (n != 2) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Only for ODEs with two unknowns");
4963 
4964   ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
4965   ierr = PetscViewerDrawGetDrawAxis(ictx->viewer,0,&axis);CHKERRQ(ierr);
4966   ierr = PetscDrawAxisGetLimits(axis,&xl,&xr,&yl,&yr);CHKERRQ(ierr);
4967   if (!step) {
4968     ierr = PetscDrawClear(draw);CHKERRQ(ierr);
4969     ierr = PetscDrawAxisDraw(axis);CHKERRQ(ierr);
4970   }
4971 
4972   ierr = VecGetArrayRead(u,&U);CHKERRQ(ierr);
4973   U0 = PetscRealPart(U[0]);
4974   U1 = PetscRealPart(U[1]);
4975   ierr = VecRestoreArrayRead(u,&U);CHKERRQ(ierr);
4976   if ((U0 < xl) || (U1 < yl) || (U0 > xr) || (U1 > yr)) PetscFunctionReturn(0);
4977 
4978   ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
4979   ierr = PetscDrawPoint(draw,U0,U1,PETSC_DRAW_BLACK);CHKERRQ(ierr);
4980   if (ictx->showtimestepandtime) {
4981     ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
4982     ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
4983     h    = yl + .95*(yr - yl);
4984     ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
4985   }
4986   ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
4987   ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
4988   ierr = PetscDrawSave(draw);CHKERRQ(ierr);
4989   PetscFunctionReturn(0);
4990 }
4991 
4992 
4993 #undef __FUNCT__
4994 #define __FUNCT__ "TSMonitorDrawCtxDestroy"
4995 /*@C
4996    TSMonitorDrawCtxDestroy - Destroys the monitor context for TSMonitorDrawSolution()
4997 
4998    Collective on TS
4999 
5000    Input Parameters:
5001 .    ctx - the monitor context
5002 
5003    Level: intermediate
5004 
5005 .keywords: TS,  vector, monitor, view
5006 
5007 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorDrawSolution(), TSMonitorDrawError()
5008 @*/
5009 PetscErrorCode  TSMonitorDrawCtxDestroy(TSMonitorDrawCtx *ictx)
5010 {
5011   PetscErrorCode ierr;
5012 
5013   PetscFunctionBegin;
5014   ierr = PetscViewerDestroy(&(*ictx)->viewer);CHKERRQ(ierr);
5015   ierr = VecDestroy(&(*ictx)->initialsolution);CHKERRQ(ierr);
5016   ierr = PetscFree(*ictx);CHKERRQ(ierr);
5017   PetscFunctionReturn(0);
5018 }
5019 
5020 #undef __FUNCT__
5021 #define __FUNCT__ "TSMonitorDrawCtxCreate"
5022 /*@C
5023    TSMonitorDrawCtxCreate - Creates the monitor context for TSMonitorDrawCtx
5024 
5025    Collective on TS
5026 
5027    Input Parameter:
5028 .    ts - time-step context
5029 
5030    Output Patameter:
5031 .    ctx - the monitor context
5032 
5033    Options Database:
5034 .   -ts_monitor_draw_solution_initial - show initial solution as well as current solution
5035 
5036    Level: intermediate
5037 
5038 .keywords: TS,  vector, monitor, view
5039 
5040 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorDrawCtx()
5041 @*/
5042 PetscErrorCode  TSMonitorDrawCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorDrawCtx *ctx)
5043 {
5044   PetscErrorCode   ierr;
5045 
5046   PetscFunctionBegin;
5047   ierr = PetscNew(ctx);CHKERRQ(ierr);
5048   ierr = PetscViewerDrawOpen(comm,host,label,x,y,m,n,&(*ctx)->viewer);CHKERRQ(ierr);
5049   ierr = PetscViewerSetFromOptions((*ctx)->viewer);CHKERRQ(ierr);
5050 
5051   (*ctx)->howoften    = howoften;
5052   (*ctx)->showinitial = PETSC_FALSE;
5053   ierr = PetscOptionsGetBool(NULL,NULL,"-ts_monitor_draw_solution_initial",&(*ctx)->showinitial,NULL);CHKERRQ(ierr);
5054 
5055   (*ctx)->showtimestepandtime = PETSC_FALSE;
5056   ierr = PetscOptionsGetBool(NULL,NULL,"-ts_monitor_draw_solution_show_time",&(*ctx)->showtimestepandtime,NULL);CHKERRQ(ierr);
5057   PetscFunctionReturn(0);
5058 }
5059 
5060 #undef __FUNCT__
5061 #define __FUNCT__ "TSMonitorDrawError"
5062 /*@C
5063    TSMonitorDrawError - Monitors progress of the TS solvers by calling
5064    VecView() for the error at each timestep
5065 
5066    Collective on TS
5067 
5068    Input Parameters:
5069 +  ts - the TS context
5070 .  step - current time-step
5071 .  ptime - current time
5072 -  dummy - either a viewer or NULL
5073 
5074    Level: intermediate
5075 
5076 .keywords: TS,  vector, monitor, view
5077 
5078 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
5079 @*/
5080 PetscErrorCode  TSMonitorDrawError(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
5081 {
5082   PetscErrorCode   ierr;
5083   TSMonitorDrawCtx ctx    = (TSMonitorDrawCtx)dummy;
5084   PetscViewer      viewer = ctx->viewer;
5085   Vec              work;
5086 
5087   PetscFunctionBegin;
5088   if (!(((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);
5089   ierr = VecDuplicate(u,&work);CHKERRQ(ierr);
5090   ierr = TSComputeSolutionFunction(ts,ptime,work);CHKERRQ(ierr);
5091   ierr = VecAXPY(work,-1.0,u);CHKERRQ(ierr);
5092   ierr = VecView(work,viewer);CHKERRQ(ierr);
5093   ierr = VecDestroy(&work);CHKERRQ(ierr);
5094   PetscFunctionReturn(0);
5095 }
5096 
5097 #include <petsc/private/dmimpl.h>
5098 #undef __FUNCT__
5099 #define __FUNCT__ "TSSetDM"
5100 /*@
5101    TSSetDM - Sets the DM that may be used by some nonlinear solvers or preconditioners under the TS
5102 
5103    Logically Collective on TS and DM
5104 
5105    Input Parameters:
5106 +  ts - the ODE integrator object
5107 -  dm - the dm, cannot be NULL
5108 
5109    Level: intermediate
5110 
5111 
5112 .seealso: TSGetDM(), SNESSetDM(), SNESGetDM()
5113 @*/
5114 PetscErrorCode  TSSetDM(TS ts,DM dm)
5115 {
5116   PetscErrorCode ierr;
5117   SNES           snes;
5118   DMTS           tsdm;
5119 
5120   PetscFunctionBegin;
5121   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5122   PetscValidHeaderSpecific(dm,DM_CLASSID,2);
5123   ierr = PetscObjectReference((PetscObject)dm);CHKERRQ(ierr);
5124   if (ts->dm) {               /* Move the DMTS context over to the new DM unless the new DM already has one */
5125     if (ts->dm->dmts && !dm->dmts) {
5126       ierr = DMCopyDMTS(ts->dm,dm);CHKERRQ(ierr);
5127       ierr = DMGetDMTS(ts->dm,&tsdm);CHKERRQ(ierr);
5128       if (tsdm->originaldm == ts->dm) { /* Grant write privileges to the replacement DM */
5129         tsdm->originaldm = dm;
5130       }
5131     }
5132     ierr = DMDestroy(&ts->dm);CHKERRQ(ierr);
5133   }
5134   ts->dm = dm;
5135 
5136   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
5137   ierr = SNESSetDM(snes,dm);CHKERRQ(ierr);
5138   PetscFunctionReturn(0);
5139 }
5140 
5141 #undef __FUNCT__
5142 #define __FUNCT__ "TSGetDM"
5143 /*@
5144    TSGetDM - Gets the DM that may be used by some preconditioners
5145 
5146    Not Collective
5147 
5148    Input Parameter:
5149 . ts - the preconditioner context
5150 
5151    Output Parameter:
5152 .  dm - the dm
5153 
5154    Level: intermediate
5155 
5156 
5157 .seealso: TSSetDM(), SNESSetDM(), SNESGetDM()
5158 @*/
5159 PetscErrorCode  TSGetDM(TS ts,DM *dm)
5160 {
5161   PetscErrorCode ierr;
5162 
5163   PetscFunctionBegin;
5164   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5165   if (!ts->dm) {
5166     ierr = DMShellCreate(PetscObjectComm((PetscObject)ts),&ts->dm);CHKERRQ(ierr);
5167     if (ts->snes) {ierr = SNESSetDM(ts->snes,ts->dm);CHKERRQ(ierr);}
5168   }
5169   *dm = ts->dm;
5170   PetscFunctionReturn(0);
5171 }
5172 
5173 #undef __FUNCT__
5174 #define __FUNCT__ "SNESTSFormFunction"
5175 /*@
5176    SNESTSFormFunction - Function to evaluate nonlinear residual
5177 
5178    Logically Collective on SNES
5179 
5180    Input Parameter:
5181 + snes - nonlinear solver
5182 . U - the current state at which to evaluate the residual
5183 - ctx - user context, must be a TS
5184 
5185    Output Parameter:
5186 . F - the nonlinear residual
5187 
5188    Notes:
5189    This function is not normally called by users and is automatically registered with the SNES used by TS.
5190    It is most frequently passed to MatFDColoringSetFunction().
5191 
5192    Level: advanced
5193 
5194 .seealso: SNESSetFunction(), MatFDColoringSetFunction()
5195 @*/
5196 PetscErrorCode  SNESTSFormFunction(SNES snes,Vec U,Vec F,void *ctx)
5197 {
5198   TS             ts = (TS)ctx;
5199   PetscErrorCode ierr;
5200 
5201   PetscFunctionBegin;
5202   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
5203   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
5204   PetscValidHeaderSpecific(F,VEC_CLASSID,3);
5205   PetscValidHeaderSpecific(ts,TS_CLASSID,4);
5206   ierr = (ts->ops->snesfunction)(snes,U,F,ts);CHKERRQ(ierr);
5207   PetscFunctionReturn(0);
5208 }
5209 
5210 #undef __FUNCT__
5211 #define __FUNCT__ "SNESTSFormJacobian"
5212 /*@
5213    SNESTSFormJacobian - Function to evaluate the Jacobian
5214 
5215    Collective on SNES
5216 
5217    Input Parameter:
5218 + snes - nonlinear solver
5219 . U - the current state at which to evaluate the residual
5220 - ctx - user context, must be a TS
5221 
5222    Output Parameter:
5223 + A - the Jacobian
5224 . B - the preconditioning matrix (may be the same as A)
5225 - flag - indicates any structure change in the matrix
5226 
5227    Notes:
5228    This function is not normally called by users and is automatically registered with the SNES used by TS.
5229 
5230    Level: developer
5231 
5232 .seealso: SNESSetJacobian()
5233 @*/
5234 PetscErrorCode  SNESTSFormJacobian(SNES snes,Vec U,Mat A,Mat B,void *ctx)
5235 {
5236   TS             ts = (TS)ctx;
5237   PetscErrorCode ierr;
5238 
5239   PetscFunctionBegin;
5240   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
5241   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
5242   PetscValidPointer(A,3);
5243   PetscValidHeaderSpecific(A,MAT_CLASSID,3);
5244   PetscValidPointer(B,4);
5245   PetscValidHeaderSpecific(B,MAT_CLASSID,4);
5246   PetscValidHeaderSpecific(ts,TS_CLASSID,6);
5247   ierr = (ts->ops->snesjacobian)(snes,U,A,B,ts);CHKERRQ(ierr);
5248   PetscFunctionReturn(0);
5249 }
5250 
5251 #undef __FUNCT__
5252 #define __FUNCT__ "TSComputeRHSFunctionLinear"
5253 /*@C
5254    TSComputeRHSFunctionLinear - Evaluate the right hand side via the user-provided Jacobian, for linear problems Udot = A U only
5255 
5256    Collective on TS
5257 
5258    Input Arguments:
5259 +  ts - time stepping context
5260 .  t - time at which to evaluate
5261 .  U - state at which to evaluate
5262 -  ctx - context
5263 
5264    Output Arguments:
5265 .  F - right hand side
5266 
5267    Level: intermediate
5268 
5269    Notes:
5270    This function is intended to be passed to TSSetRHSFunction() to evaluate the right hand side for linear problems.
5271    The matrix (and optionally the evaluation context) should be passed to TSSetRHSJacobian().
5272 
5273 .seealso: TSSetRHSFunction(), TSSetRHSJacobian(), TSComputeRHSJacobianConstant()
5274 @*/
5275 PetscErrorCode TSComputeRHSFunctionLinear(TS ts,PetscReal t,Vec U,Vec F,void *ctx)
5276 {
5277   PetscErrorCode ierr;
5278   Mat            Arhs,Brhs;
5279 
5280   PetscFunctionBegin;
5281   ierr = TSGetRHSMats_Private(ts,&Arhs,&Brhs);CHKERRQ(ierr);
5282   ierr = TSComputeRHSJacobian(ts,t,U,Arhs,Brhs);CHKERRQ(ierr);
5283   ierr = MatMult(Arhs,U,F);CHKERRQ(ierr);
5284   PetscFunctionReturn(0);
5285 }
5286 
5287 #undef __FUNCT__
5288 #define __FUNCT__ "TSComputeRHSJacobianConstant"
5289 /*@C
5290    TSComputeRHSJacobianConstant - Reuses a Jacobian that is time-independent.
5291 
5292    Collective on TS
5293 
5294    Input Arguments:
5295 +  ts - time stepping context
5296 .  t - time at which to evaluate
5297 .  U - state at which to evaluate
5298 -  ctx - context
5299 
5300    Output Arguments:
5301 +  A - pointer to operator
5302 .  B - pointer to preconditioning matrix
5303 -  flg - matrix structure flag
5304 
5305    Level: intermediate
5306 
5307    Notes:
5308    This function is intended to be passed to TSSetRHSJacobian() to evaluate the Jacobian for linear time-independent problems.
5309 
5310 .seealso: TSSetRHSFunction(), TSSetRHSJacobian(), TSComputeRHSFunctionLinear()
5311 @*/
5312 PetscErrorCode TSComputeRHSJacobianConstant(TS ts,PetscReal t,Vec U,Mat A,Mat B,void *ctx)
5313 {
5314   PetscFunctionBegin;
5315   PetscFunctionReturn(0);
5316 }
5317 
5318 #undef __FUNCT__
5319 #define __FUNCT__ "TSComputeIFunctionLinear"
5320 /*@C
5321    TSComputeIFunctionLinear - Evaluate the left hand side via the user-provided Jacobian, for linear problems only
5322 
5323    Collective on TS
5324 
5325    Input Arguments:
5326 +  ts - time stepping context
5327 .  t - time at which to evaluate
5328 .  U - state at which to evaluate
5329 .  Udot - time derivative of state vector
5330 -  ctx - context
5331 
5332    Output Arguments:
5333 .  F - left hand side
5334 
5335    Level: intermediate
5336 
5337    Notes:
5338    The assumption here is that the left hand side is of the form A*Udot (and not A*Udot + B*U). For other cases, the
5339    user is required to write their own TSComputeIFunction.
5340    This function is intended to be passed to TSSetIFunction() to evaluate the left hand side for linear problems.
5341    The matrix (and optionally the evaluation context) should be passed to TSSetIJacobian().
5342 
5343    Note that using this function is NOT equivalent to using TSComputeRHSFunctionLinear() since that solves Udot = A U
5344 
5345 .seealso: TSSetIFunction(), TSSetIJacobian(), TSComputeIJacobianConstant(), TSComputeRHSFunctionLinear()
5346 @*/
5347 PetscErrorCode TSComputeIFunctionLinear(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
5348 {
5349   PetscErrorCode ierr;
5350   Mat            A,B;
5351 
5352   PetscFunctionBegin;
5353   ierr = TSGetIJacobian(ts,&A,&B,NULL,NULL);CHKERRQ(ierr);
5354   ierr = TSComputeIJacobian(ts,t,U,Udot,1.0,A,B,PETSC_TRUE);CHKERRQ(ierr);
5355   ierr = MatMult(A,Udot,F);CHKERRQ(ierr);
5356   PetscFunctionReturn(0);
5357 }
5358 
5359 #undef __FUNCT__
5360 #define __FUNCT__ "TSComputeIJacobianConstant"
5361 /*@C
5362    TSComputeIJacobianConstant - Reuses a time-independent for a semi-implicit DAE or ODE
5363 
5364    Collective on TS
5365 
5366    Input Arguments:
5367 +  ts - time stepping context
5368 .  t - time at which to evaluate
5369 .  U - state at which to evaluate
5370 .  Udot - time derivative of state vector
5371 .  shift - shift to apply
5372 -  ctx - context
5373 
5374    Output Arguments:
5375 +  A - pointer to operator
5376 .  B - pointer to preconditioning matrix
5377 -  flg - matrix structure flag
5378 
5379    Level: advanced
5380 
5381    Notes:
5382    This function is intended to be passed to TSSetIJacobian() to evaluate the Jacobian for linear time-independent problems.
5383 
5384    It is only appropriate for problems of the form
5385 
5386 $     M Udot = F(U,t)
5387 
5388   where M is constant and F is non-stiff.  The user must pass M to TSSetIJacobian().  The current implementation only
5389   works with IMEX time integration methods such as TSROSW and TSARKIMEX, since there is no support for de-constructing
5390   an implicit operator of the form
5391 
5392 $    shift*M + J
5393 
5394   where J is the Jacobian of -F(U).  Support may be added in a future version of PETSc, but for now, the user must store
5395   a copy of M or reassemble it when requested.
5396 
5397 .seealso: TSSetIFunction(), TSSetIJacobian(), TSComputeIFunctionLinear()
5398 @*/
5399 PetscErrorCode TSComputeIJacobianConstant(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat A,Mat B,void *ctx)
5400 {
5401   PetscErrorCode ierr;
5402 
5403   PetscFunctionBegin;
5404   ierr = MatScale(A, shift / ts->ijacobian.shift);CHKERRQ(ierr);
5405   ts->ijacobian.shift = shift;
5406   PetscFunctionReturn(0);
5407 }
5408 
5409 #undef __FUNCT__
5410 #define __FUNCT__ "TSGetEquationType"
5411 /*@
5412    TSGetEquationType - Gets the type of the equation that TS is solving.
5413 
5414    Not Collective
5415 
5416    Input Parameter:
5417 .  ts - the TS context
5418 
5419    Output Parameter:
5420 .  equation_type - see TSEquationType
5421 
5422    Level: beginner
5423 
5424 .keywords: TS, equation type
5425 
5426 .seealso: TSSetEquationType(), TSEquationType
5427 @*/
5428 PetscErrorCode  TSGetEquationType(TS ts,TSEquationType *equation_type)
5429 {
5430   PetscFunctionBegin;
5431   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5432   PetscValidPointer(equation_type,2);
5433   *equation_type = ts->equation_type;
5434   PetscFunctionReturn(0);
5435 }
5436 
5437 #undef __FUNCT__
5438 #define __FUNCT__ "TSSetEquationType"
5439 /*@
5440    TSSetEquationType - Sets the type of the equation that TS is solving.
5441 
5442    Not Collective
5443 
5444    Input Parameter:
5445 +  ts - the TS context
5446 -  equation_type - see TSEquationType
5447 
5448    Level: advanced
5449 
5450 .keywords: TS, equation type
5451 
5452 .seealso: TSGetEquationType(), TSEquationType
5453 @*/
5454 PetscErrorCode  TSSetEquationType(TS ts,TSEquationType equation_type)
5455 {
5456   PetscFunctionBegin;
5457   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5458   ts->equation_type = equation_type;
5459   PetscFunctionReturn(0);
5460 }
5461 
5462 #undef __FUNCT__
5463 #define __FUNCT__ "TSGetConvergedReason"
5464 /*@
5465    TSGetConvergedReason - Gets the reason the TS iteration was stopped.
5466 
5467    Not Collective
5468 
5469    Input Parameter:
5470 .  ts - the TS context
5471 
5472    Output Parameter:
5473 .  reason - negative value indicates diverged, positive value converged, see TSConvergedReason or the
5474             manual pages for the individual convergence tests for complete lists
5475 
5476    Level: beginner
5477 
5478    Notes:
5479    Can only be called after the call to TSSolve() is complete.
5480 
5481 .keywords: TS, nonlinear, set, convergence, test
5482 
5483 .seealso: TSSetConvergenceTest(), TSConvergedReason
5484 @*/
5485 PetscErrorCode  TSGetConvergedReason(TS ts,TSConvergedReason *reason)
5486 {
5487   PetscFunctionBegin;
5488   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5489   PetscValidPointer(reason,2);
5490   *reason = ts->reason;
5491   PetscFunctionReturn(0);
5492 }
5493 
5494 #undef __FUNCT__
5495 #define __FUNCT__ "TSSetConvergedReason"
5496 /*@
5497    TSSetConvergedReason - Sets the reason for handling the convergence of TSSolve.
5498 
5499    Not Collective
5500 
5501    Input Parameter:
5502 +  ts - the TS context
5503 .  reason - negative value indicates diverged, positive value converged, see TSConvergedReason or the
5504             manual pages for the individual convergence tests for complete lists
5505 
5506    Level: advanced
5507 
5508    Notes:
5509    Can only be called during TSSolve() is active.
5510 
5511 .keywords: TS, nonlinear, set, convergence, test
5512 
5513 .seealso: TSConvergedReason
5514 @*/
5515 PetscErrorCode  TSSetConvergedReason(TS ts,TSConvergedReason reason)
5516 {
5517   PetscFunctionBegin;
5518   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5519   ts->reason = reason;
5520   PetscFunctionReturn(0);
5521 }
5522 
5523 #undef __FUNCT__
5524 #define __FUNCT__ "TSGetSolveTime"
5525 /*@
5526    TSGetSolveTime - Gets the time after a call to TSSolve()
5527 
5528    Not Collective
5529 
5530    Input Parameter:
5531 .  ts - the TS context
5532 
5533    Output Parameter:
5534 .  ftime - the final time. This time corresponds to the final time set with TSSetDuration()
5535 
5536    Level: beginner
5537 
5538    Notes:
5539    Can only be called after the call to TSSolve() is complete.
5540 
5541 .keywords: TS, nonlinear, set, convergence, test
5542 
5543 .seealso: TSSetConvergenceTest(), TSConvergedReason
5544 @*/
5545 PetscErrorCode  TSGetSolveTime(TS ts,PetscReal *ftime)
5546 {
5547   PetscFunctionBegin;
5548   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5549   PetscValidPointer(ftime,2);
5550   *ftime = ts->solvetime;
5551   PetscFunctionReturn(0);
5552 }
5553 
5554 #undef __FUNCT__
5555 #define __FUNCT__ "TSGetTotalSteps"
5556 /*@
5557    TSGetTotalSteps - Gets the total number of steps done since the last call to TSSetUp() or TSCreate()
5558 
5559    Not Collective
5560 
5561    Input Parameter:
5562 .  ts - the TS context
5563 
5564    Output Parameter:
5565 .  steps - the number of steps
5566 
5567    Level: beginner
5568 
5569    Notes:
5570    Includes the number of steps for all calls to TSSolve() since TSSetUp() was called
5571 
5572 .keywords: TS, nonlinear, set, convergence, test
5573 
5574 .seealso: TSSetConvergenceTest(), TSConvergedReason
5575 @*/
5576 PetscErrorCode  TSGetTotalSteps(TS ts,PetscInt *steps)
5577 {
5578   PetscFunctionBegin;
5579   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5580   PetscValidPointer(steps,2);
5581   *steps = ts->total_steps;
5582   PetscFunctionReturn(0);
5583 }
5584 
5585 #undef __FUNCT__
5586 #define __FUNCT__ "TSGetSNESIterations"
5587 /*@
5588    TSGetSNESIterations - Gets the total number of nonlinear iterations
5589    used by the time integrator.
5590 
5591    Not Collective
5592 
5593    Input Parameter:
5594 .  ts - TS context
5595 
5596    Output Parameter:
5597 .  nits - number of nonlinear iterations
5598 
5599    Notes:
5600    This counter is reset to zero for each successive call to TSSolve().
5601 
5602    Level: intermediate
5603 
5604 .keywords: TS, get, number, nonlinear, iterations
5605 
5606 .seealso:  TSGetKSPIterations()
5607 @*/
5608 PetscErrorCode TSGetSNESIterations(TS ts,PetscInt *nits)
5609 {
5610   PetscFunctionBegin;
5611   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5612   PetscValidIntPointer(nits,2);
5613   *nits = ts->snes_its;
5614   PetscFunctionReturn(0);
5615 }
5616 
5617 #undef __FUNCT__
5618 #define __FUNCT__ "TSGetKSPIterations"
5619 /*@
5620    TSGetKSPIterations - Gets the total number of linear iterations
5621    used by the time integrator.
5622 
5623    Not Collective
5624 
5625    Input Parameter:
5626 .  ts - TS context
5627 
5628    Output Parameter:
5629 .  lits - number of linear iterations
5630 
5631    Notes:
5632    This counter is reset to zero for each successive call to TSSolve().
5633 
5634    Level: intermediate
5635 
5636 .keywords: TS, get, number, linear, iterations
5637 
5638 .seealso:  TSGetSNESIterations(), SNESGetKSPIterations()
5639 @*/
5640 PetscErrorCode TSGetKSPIterations(TS ts,PetscInt *lits)
5641 {
5642   PetscFunctionBegin;
5643   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5644   PetscValidIntPointer(lits,2);
5645   *lits = ts->ksp_its;
5646   PetscFunctionReturn(0);
5647 }
5648 
5649 #undef __FUNCT__
5650 #define __FUNCT__ "TSGetStepRejections"
5651 /*@
5652    TSGetStepRejections - Gets the total number of rejected steps.
5653 
5654    Not Collective
5655 
5656    Input Parameter:
5657 .  ts - TS context
5658 
5659    Output Parameter:
5660 .  rejects - number of steps rejected
5661 
5662    Notes:
5663    This counter is reset to zero for each successive call to TSSolve().
5664 
5665    Level: intermediate
5666 
5667 .keywords: TS, get, number
5668 
5669 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetSNESFailures(), TSSetMaxSNESFailures(), TSSetErrorIfStepFails()
5670 @*/
5671 PetscErrorCode TSGetStepRejections(TS ts,PetscInt *rejects)
5672 {
5673   PetscFunctionBegin;
5674   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5675   PetscValidIntPointer(rejects,2);
5676   *rejects = ts->reject;
5677   PetscFunctionReturn(0);
5678 }
5679 
5680 #undef __FUNCT__
5681 #define __FUNCT__ "TSGetSNESFailures"
5682 /*@
5683    TSGetSNESFailures - Gets the total number of failed SNES solves
5684 
5685    Not Collective
5686 
5687    Input Parameter:
5688 .  ts - TS context
5689 
5690    Output Parameter:
5691 .  fails - number of failed nonlinear solves
5692 
5693    Notes:
5694    This counter is reset to zero for each successive call to TSSolve().
5695 
5696    Level: intermediate
5697 
5698 .keywords: TS, get, number
5699 
5700 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSSetMaxSNESFailures()
5701 @*/
5702 PetscErrorCode TSGetSNESFailures(TS ts,PetscInt *fails)
5703 {
5704   PetscFunctionBegin;
5705   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5706   PetscValidIntPointer(fails,2);
5707   *fails = ts->num_snes_failures;
5708   PetscFunctionReturn(0);
5709 }
5710 
5711 #undef __FUNCT__
5712 #define __FUNCT__ "TSSetMaxStepRejections"
5713 /*@
5714    TSSetMaxStepRejections - Sets the maximum number of step rejections before a step fails
5715 
5716    Not Collective
5717 
5718    Input Parameter:
5719 +  ts - TS context
5720 -  rejects - maximum number of rejected steps, pass -1 for unlimited
5721 
5722    Notes:
5723    The counter is reset to zero for each step
5724 
5725    Options Database Key:
5726  .  -ts_max_reject - Maximum number of step rejections before a step fails
5727 
5728    Level: intermediate
5729 
5730 .keywords: TS, set, maximum, number
5731 
5732 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxSNESFailures(), TSGetStepRejections(), TSGetSNESFailures(), TSSetErrorIfStepFails(), TSGetConvergedReason()
5733 @*/
5734 PetscErrorCode TSSetMaxStepRejections(TS ts,PetscInt rejects)
5735 {
5736   PetscFunctionBegin;
5737   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5738   ts->max_reject = rejects;
5739   PetscFunctionReturn(0);
5740 }
5741 
5742 #undef __FUNCT__
5743 #define __FUNCT__ "TSSetMaxSNESFailures"
5744 /*@
5745    TSSetMaxSNESFailures - Sets the maximum number of failed SNES solves
5746 
5747    Not Collective
5748 
5749    Input Parameter:
5750 +  ts - TS context
5751 -  fails - maximum number of failed nonlinear solves, pass -1 for unlimited
5752 
5753    Notes:
5754    The counter is reset to zero for each successive call to TSSolve().
5755 
5756    Options Database Key:
5757  .  -ts_max_snes_failures - Maximum number of nonlinear solve failures
5758 
5759    Level: intermediate
5760 
5761 .keywords: TS, set, maximum, number
5762 
5763 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSGetSNESFailures(), SNESGetConvergedReason(), TSGetConvergedReason()
5764 @*/
5765 PetscErrorCode TSSetMaxSNESFailures(TS ts,PetscInt fails)
5766 {
5767   PetscFunctionBegin;
5768   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5769   ts->max_snes_failures = fails;
5770   PetscFunctionReturn(0);
5771 }
5772 
5773 #undef __FUNCT__
5774 #define __FUNCT__ "TSSetErrorIfStepFails"
5775 /*@
5776    TSSetErrorIfStepFails - Error if no step succeeds
5777 
5778    Not Collective
5779 
5780    Input Parameter:
5781 +  ts - TS context
5782 -  err - PETSC_TRUE to error if no step succeeds, PETSC_FALSE to return without failure
5783 
5784    Options Database Key:
5785  .  -ts_error_if_step_fails - Error if no step succeeds
5786 
5787    Level: intermediate
5788 
5789 .keywords: TS, set, error
5790 
5791 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSGetSNESFailures(), TSSetErrorIfStepFails(), TSGetConvergedReason()
5792 @*/
5793 PetscErrorCode TSSetErrorIfStepFails(TS ts,PetscBool err)
5794 {
5795   PetscFunctionBegin;
5796   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5797   ts->errorifstepfailed = err;
5798   PetscFunctionReturn(0);
5799 }
5800 
5801 #undef __FUNCT__
5802 #define __FUNCT__ "TSMonitorSolution"
5803 /*@C
5804    TSMonitorSolution - Monitors progress of the TS solvers by VecView() for the solution at each timestep. Normally the viewer is a binary file or a PetscDraw object
5805 
5806    Collective on TS
5807 
5808    Input Parameters:
5809 +  ts - the TS context
5810 .  step - current time-step
5811 .  ptime - current time
5812 .  u - current state
5813 -  vf - viewer and its format
5814 
5815    Level: intermediate
5816 
5817 .keywords: TS,  vector, monitor, view
5818 
5819 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
5820 @*/
5821 PetscErrorCode  TSMonitorSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscViewerAndFormat *vf)
5822 {
5823   PetscErrorCode ierr;
5824 
5825   PetscFunctionBegin;
5826   ierr = PetscViewerPushFormat(vf->viewer,vf->format);CHKERRQ(ierr);
5827   ierr = VecView(u,vf->viewer);CHKERRQ(ierr);
5828   ierr = PetscViewerPopFormat(vf->viewer);CHKERRQ(ierr);
5829   PetscFunctionReturn(0);
5830 }
5831 
5832 #undef __FUNCT__
5833 #define __FUNCT__ "TSMonitorSolutionVTK"
5834 /*@C
5835    TSMonitorSolutionVTK - Monitors progress of the TS solvers by VecView() for the solution at each timestep.
5836 
5837    Collective on TS
5838 
5839    Input Parameters:
5840 +  ts - the TS context
5841 .  step - current time-step
5842 .  ptime - current time
5843 .  u - current state
5844 -  filenametemplate - string containing a format specifier for the integer time step (e.g. %03D)
5845 
5846    Level: intermediate
5847 
5848    Notes:
5849    The VTK format does not allow writing multiple time steps in the same file, therefore a different file will be written for each time step.
5850    These are named according to the file name template.
5851 
5852    This function is normally passed as an argument to TSMonitorSet() along with TSMonitorSolutionVTKDestroy().
5853 
5854 .keywords: TS,  vector, monitor, view
5855 
5856 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
5857 @*/
5858 PetscErrorCode TSMonitorSolutionVTK(TS ts,PetscInt step,PetscReal ptime,Vec u,void *filenametemplate)
5859 {
5860   PetscErrorCode ierr;
5861   char           filename[PETSC_MAX_PATH_LEN];
5862   PetscViewer    viewer;
5863 
5864   PetscFunctionBegin;
5865   if (step < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
5866   ierr = PetscSNPrintf(filename,sizeof(filename),(const char*)filenametemplate,step);CHKERRQ(ierr);
5867   ierr = PetscViewerVTKOpen(PetscObjectComm((PetscObject)ts),filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
5868   ierr = VecView(u,viewer);CHKERRQ(ierr);
5869   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
5870   PetscFunctionReturn(0);
5871 }
5872 
5873 #undef __FUNCT__
5874 #define __FUNCT__ "TSMonitorSolutionVTKDestroy"
5875 /*@C
5876    TSMonitorSolutionVTKDestroy - Destroy context for monitoring
5877 
5878    Collective on TS
5879 
5880    Input Parameters:
5881 .  filenametemplate - string containing a format specifier for the integer time step (e.g. %03D)
5882 
5883    Level: intermediate
5884 
5885    Note:
5886    This function is normally passed to TSMonitorSet() along with TSMonitorSolutionVTK().
5887 
5888 .keywords: TS,  vector, monitor, view
5889 
5890 .seealso: TSMonitorSet(), TSMonitorSolutionVTK()
5891 @*/
5892 PetscErrorCode TSMonitorSolutionVTKDestroy(void *filenametemplate)
5893 {
5894   PetscErrorCode ierr;
5895 
5896   PetscFunctionBegin;
5897   ierr = PetscFree(*(char**)filenametemplate);CHKERRQ(ierr);
5898   PetscFunctionReturn(0);
5899 }
5900 
5901 #undef __FUNCT__
5902 #define __FUNCT__ "TSGetAdapt"
5903 /*@
5904    TSGetAdapt - Get the adaptive controller context for the current method
5905 
5906    Collective on TS if controller has not been created yet
5907 
5908    Input Arguments:
5909 .  ts - time stepping context
5910 
5911    Output Arguments:
5912 .  adapt - adaptive controller
5913 
5914    Level: intermediate
5915 
5916 .seealso: TSAdapt, TSAdaptSetType(), TSAdaptChoose()
5917 @*/
5918 PetscErrorCode TSGetAdapt(TS ts,TSAdapt *adapt)
5919 {
5920   PetscErrorCode ierr;
5921 
5922   PetscFunctionBegin;
5923   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5924   PetscValidPointer(adapt,2);
5925   if (!ts->adapt) {
5926     ierr = TSAdaptCreate(PetscObjectComm((PetscObject)ts),&ts->adapt);CHKERRQ(ierr);
5927     ierr = PetscLogObjectParent((PetscObject)ts,(PetscObject)ts->adapt);CHKERRQ(ierr);
5928     ierr = PetscObjectIncrementTabLevel((PetscObject)ts->adapt,(PetscObject)ts,1);CHKERRQ(ierr);
5929   }
5930   *adapt = ts->adapt;
5931   PetscFunctionReturn(0);
5932 }
5933 
5934 #undef __FUNCT__
5935 #define __FUNCT__ "TSSetTolerances"
5936 /*@
5937    TSSetTolerances - Set tolerances for local truncation error when using adaptive controller
5938 
5939    Logically Collective
5940 
5941    Input Arguments:
5942 +  ts - time integration context
5943 .  atol - scalar absolute tolerances, PETSC_DECIDE to leave current value
5944 .  vatol - vector of absolute tolerances or NULL, used in preference to atol if present
5945 .  rtol - scalar relative tolerances, PETSC_DECIDE to leave current value
5946 -  vrtol - vector of relative tolerances or NULL, used in preference to atol if present
5947 
5948    Options Database keys:
5949 +  -ts_rtol <rtol> - relative tolerance for local truncation error
5950 -  -ts_atol <atol> Absolute tolerance for local truncation error
5951 
5952    Notes:
5953    With PETSc's implicit schemes for DAE problems, the calculation of the local truncation error
5954    (LTE) includes both the differential and the algebraic variables. If one wants the LTE to be
5955    computed only for the differential or the algebraic part then this can be done using the vector of
5956    tolerances vatol. For example, by setting the tolerance vector with the desired tolerance for the
5957    differential part and infinity for the algebraic part, the LTE calculation will include only the
5958    differential variables.
5959 
5960    Level: beginner
5961 
5962 .seealso: TS, TSAdapt, TSVecNormWRMS(), TSGetTolerances()
5963 @*/
5964 PetscErrorCode TSSetTolerances(TS ts,PetscReal atol,Vec vatol,PetscReal rtol,Vec vrtol)
5965 {
5966   PetscErrorCode ierr;
5967 
5968   PetscFunctionBegin;
5969   if (atol != PETSC_DECIDE && atol != PETSC_DEFAULT) ts->atol = atol;
5970   if (vatol) {
5971     ierr = PetscObjectReference((PetscObject)vatol);CHKERRQ(ierr);
5972     ierr = VecDestroy(&ts->vatol);CHKERRQ(ierr);
5973     ts->vatol = vatol;
5974   }
5975   if (rtol != PETSC_DECIDE && rtol != PETSC_DEFAULT) ts->rtol = rtol;
5976   if (vrtol) {
5977     ierr = PetscObjectReference((PetscObject)vrtol);CHKERRQ(ierr);
5978     ierr = VecDestroy(&ts->vrtol);CHKERRQ(ierr);
5979     ts->vrtol = vrtol;
5980   }
5981   PetscFunctionReturn(0);
5982 }
5983 
5984 #undef __FUNCT__
5985 #define __FUNCT__ "TSGetTolerances"
5986 /*@
5987    TSGetTolerances - Get tolerances for local truncation error when using adaptive controller
5988 
5989    Logically Collective
5990 
5991    Input Arguments:
5992 .  ts - time integration context
5993 
5994    Output Arguments:
5995 +  atol - scalar absolute tolerances, NULL to ignore
5996 .  vatol - vector of absolute tolerances, NULL to ignore
5997 .  rtol - scalar relative tolerances, NULL to ignore
5998 -  vrtol - vector of relative tolerances, NULL to ignore
5999 
6000    Level: beginner
6001 
6002 .seealso: TS, TSAdapt, TSVecNormWRMS(), TSSetTolerances()
6003 @*/
6004 PetscErrorCode TSGetTolerances(TS ts,PetscReal *atol,Vec *vatol,PetscReal *rtol,Vec *vrtol)
6005 {
6006   PetscFunctionBegin;
6007   if (atol)  *atol  = ts->atol;
6008   if (vatol) *vatol = ts->vatol;
6009   if (rtol)  *rtol  = ts->rtol;
6010   if (vrtol) *vrtol = ts->vrtol;
6011   PetscFunctionReturn(0);
6012 }
6013 
6014 #undef __FUNCT__
6015 #define __FUNCT__ "TSErrorWeightedNorm2"
6016 /*@
6017    TSErrorWeightedNorm2 - compute a weighted 2-norm of the difference between two state vectors
6018 
6019    Collective on TS
6020 
6021    Input Arguments:
6022 +  ts - time stepping context
6023 .  U - state vector, usually ts->vec_sol
6024 -  Y - state vector to be compared to U
6025 
6026    Output Arguments:
6027 .  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
6028 .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
6029 .  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances
6030 
6031    Level: developer
6032 
6033 .seealso: TSErrorWeightedNorm(), TSErrorWeightedNormInfinity()
6034 @*/
6035 PetscErrorCode TSErrorWeightedNorm2(TS ts,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6036 {
6037   PetscErrorCode    ierr;
6038   PetscInt          i,n,N,rstart;
6039   PetscInt          n_loc,na_loc,nr_loc;
6040   PetscReal         n_glb,na_glb,nr_glb;
6041   const PetscScalar *u,*y;
6042   PetscReal         sum,suma,sumr,gsum,gsuma,gsumr,diff;
6043   PetscReal         tol,tola,tolr;
6044   PetscReal         err_loc[6],err_glb[6];
6045 
6046   PetscFunctionBegin;
6047   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6048   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
6049   PetscValidHeaderSpecific(Y,VEC_CLASSID,3);
6050   PetscValidType(U,2);
6051   PetscValidType(Y,3);
6052   PetscCheckSameComm(U,2,Y,3);
6053   PetscValidPointer(norm,4);
6054   PetscValidPointer(norma,5);
6055   PetscValidPointer(normr,6);
6056   if (U == Y) SETERRQ(PetscObjectComm((PetscObject)U),PETSC_ERR_ARG_IDN,"U and Y cannot be the same vector");
6057 
6058   ierr = VecGetSize(U,&N);CHKERRQ(ierr);
6059   ierr = VecGetLocalSize(U,&n);CHKERRQ(ierr);
6060   ierr = VecGetOwnershipRange(U,&rstart,NULL);CHKERRQ(ierr);
6061   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
6062   ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
6063   sum  = 0.; n_loc  = 0;
6064   suma = 0.; na_loc = 0;
6065   sumr = 0.; nr_loc = 0;
6066   if (ts->vatol && ts->vrtol) {
6067     const PetscScalar *atol,*rtol;
6068     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6069     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6070     for (i=0; i<n; i++) {
6071       diff = PetscAbsScalar(y[i] - u[i]);
6072       tola = PetscRealPart(atol[i]);
6073       if(tola>0.){
6074         suma  += PetscSqr(diff/tola);
6075         na_loc++;
6076       }
6077       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6078       if(tolr>0.){
6079         sumr  += PetscSqr(diff/tolr);
6080         nr_loc++;
6081       }
6082       tol=tola+tolr;
6083       if(tol>0.){
6084         sum  += PetscSqr(diff/tol);
6085         n_loc++;
6086       }
6087     }
6088     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6089     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6090   } else if (ts->vatol) {       /* vector atol, scalar rtol */
6091     const PetscScalar *atol;
6092     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6093     for (i=0; i<n; i++) {
6094       diff = PetscAbsScalar(y[i] - u[i]);
6095       tola = PetscRealPart(atol[i]);
6096       if(tola>0.){
6097         suma  += PetscSqr(diff/tola);
6098         na_loc++;
6099       }
6100       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6101       if(tolr>0.){
6102         sumr  += PetscSqr(diff/tolr);
6103         nr_loc++;
6104       }
6105       tol=tola+tolr;
6106       if(tol>0.){
6107         sum  += PetscSqr(diff/tol);
6108         n_loc++;
6109       }
6110     }
6111     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6112   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
6113     const PetscScalar *rtol;
6114     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6115     for (i=0; i<n; i++) {
6116       diff = PetscAbsScalar(y[i] - u[i]);
6117       tola = ts->atol;
6118       if(tola>0.){
6119         suma  += PetscSqr(diff/tola);
6120         na_loc++;
6121       }
6122       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6123       if(tolr>0.){
6124         sumr  += PetscSqr(diff/tolr);
6125         nr_loc++;
6126       }
6127       tol=tola+tolr;
6128       if(tol>0.){
6129         sum  += PetscSqr(diff/tol);
6130         n_loc++;
6131       }
6132     }
6133     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6134   } else {                      /* scalar atol, scalar rtol */
6135     for (i=0; i<n; i++) {
6136       diff = PetscAbsScalar(y[i] - u[i]);
6137      tola = ts->atol;
6138       if(tola>0.){
6139         suma  += PetscSqr(diff/tola);
6140         na_loc++;
6141       }
6142       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6143       if(tolr>0.){
6144         sumr  += PetscSqr(diff/tolr);
6145         nr_loc++;
6146       }
6147       tol=tola+tolr;
6148       if(tol>0.){
6149         sum  += PetscSqr(diff/tol);
6150         n_loc++;
6151       }
6152     }
6153   }
6154   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
6155   ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
6156 
6157   err_loc[0] = sum;
6158   err_loc[1] = suma;
6159   err_loc[2] = sumr;
6160   err_loc[3] = (PetscReal)n_loc;
6161   err_loc[4] = (PetscReal)na_loc;
6162   err_loc[5] = (PetscReal)nr_loc;
6163 
6164   ierr = MPIU_Allreduce(&err_loc,&err_glb,6,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6165 
6166   gsum   = err_glb[0];
6167   gsuma  = err_glb[1];
6168   gsumr  = err_glb[2];
6169   n_glb  = err_glb[3];
6170   na_glb = err_glb[4];
6171   nr_glb = err_glb[5];
6172 
6173   *norm  = 0.;
6174   if(n_glb>0. ){*norm  = PetscSqrtReal(gsum  / n_glb );}
6175   *norma = 0.;
6176   if(na_glb>0.){*norma = PetscSqrtReal(gsuma / na_glb);}
6177   *normr = 0.;
6178   if(nr_glb>0.){*normr = PetscSqrtReal(gsumr / nr_glb);}
6179 
6180   if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
6181   if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
6182   if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
6183   PetscFunctionReturn(0);
6184 }
6185 
6186 #undef __FUNCT__
6187 #define __FUNCT__ "TSErrorWeightedNormInfinity"
6188 /*@
6189    TSErrorWeightedNormInfinity - compute a weighted infinity-norm of the difference between two state vectors
6190 
6191    Collective on TS
6192 
6193    Input Arguments:
6194 +  ts - time stepping context
6195 .  U - state vector, usually ts->vec_sol
6196 -  Y - state vector to be compared to U
6197 
6198    Output Arguments:
6199 .  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
6200 .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
6201 .  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances
6202 
6203    Level: developer
6204 
6205 .seealso: TSErrorWeightedNorm(), TSErrorWeightedNorm2()
6206 @*/
6207 PetscErrorCode TSErrorWeightedNormInfinity(TS ts,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6208 {
6209   PetscErrorCode    ierr;
6210   PetscInt          i,n,N,rstart;
6211   const PetscScalar *u,*y;
6212   PetscReal         max,gmax,maxa,gmaxa,maxr,gmaxr;
6213   PetscReal         tol,tola,tolr,diff;
6214   PetscReal         err_loc[3],err_glb[3];
6215 
6216   PetscFunctionBegin;
6217   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6218   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
6219   PetscValidHeaderSpecific(Y,VEC_CLASSID,3);
6220   PetscValidType(U,2);
6221   PetscValidType(Y,3);
6222   PetscCheckSameComm(U,2,Y,3);
6223   PetscValidPointer(norm,4);
6224   PetscValidPointer(norma,5);
6225   PetscValidPointer(normr,6);
6226   if (U == Y) SETERRQ(PetscObjectComm((PetscObject)U),PETSC_ERR_ARG_IDN,"U and Y cannot be the same vector");
6227 
6228   ierr = VecGetSize(U,&N);CHKERRQ(ierr);
6229   ierr = VecGetLocalSize(U,&n);CHKERRQ(ierr);
6230   ierr = VecGetOwnershipRange(U,&rstart,NULL);CHKERRQ(ierr);
6231   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
6232   ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
6233 
6234   max=0.;
6235   maxa=0.;
6236   maxr=0.;
6237 
6238   if (ts->vatol && ts->vrtol) {     /* vector atol, vector rtol */
6239     const PetscScalar *atol,*rtol;
6240     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6241     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6242 
6243     for (i=0; i<n; i++) {
6244       diff = PetscAbsScalar(y[i] - u[i]);
6245       tola = PetscRealPart(atol[i]);
6246       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6247       tol  = tola+tolr;
6248       if(tola>0.){
6249         maxa = PetscMax(maxa,diff / tola);
6250       }
6251       if(tolr>0.){
6252         maxr = PetscMax(maxr,diff / tolr);
6253       }
6254       if(tol>0.){
6255         max = PetscMax(max,diff / tol);
6256       }
6257     }
6258     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6259     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6260   } else if (ts->vatol) {       /* vector atol, scalar rtol */
6261     const PetscScalar *atol;
6262     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6263     for (i=0; i<n; i++) {
6264       diff = PetscAbsScalar(y[i] - u[i]);
6265       tola = PetscRealPart(atol[i]);
6266       tolr = ts->rtol  * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6267       tol  = tola+tolr;
6268       if(tola>0.){
6269         maxa = PetscMax(maxa,diff / tola);
6270       }
6271       if(tolr>0.){
6272         maxr = PetscMax(maxr,diff / tolr);
6273       }
6274       if(tol>0.){
6275         max = PetscMax(max,diff / tol);
6276       }
6277     }
6278     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6279   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
6280     const PetscScalar *rtol;
6281     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6282 
6283     for (i=0; i<n; i++) {
6284       diff = PetscAbsScalar(y[i] - u[i]);
6285       tola = ts->atol;
6286       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6287       tol  = tola+tolr;
6288       if(tola>0.){
6289         maxa = PetscMax(maxa,diff / tola);
6290       }
6291       if(tolr>0.){
6292         maxr = PetscMax(maxr,diff / tolr);
6293       }
6294       if(tol>0.){
6295         max = PetscMax(max,diff / tol);
6296       }
6297     }
6298     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6299   } else {                      /* scalar atol, scalar rtol */
6300 
6301     for (i=0; i<n; i++) {
6302       diff = PetscAbsScalar(y[i] - u[i]);
6303       tola = ts->atol;
6304       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6305       tol  = tola+tolr;
6306       if(tola>0.){
6307         maxa = PetscMax(maxa,diff / tola);
6308       }
6309       if(tolr>0.){
6310         maxr = PetscMax(maxr,diff / tolr);
6311       }
6312       if(tol>0.){
6313         max = PetscMax(max,diff / tol);
6314       }
6315     }
6316   }
6317   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
6318   ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
6319   err_loc[0] = max;
6320   err_loc[1] = maxa;
6321   err_loc[2] = maxr;
6322   ierr  = MPIU_Allreduce(&err_loc,&err_glb,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6323   gmax   = err_glb[0];
6324   gmaxa  = err_glb[1];
6325   gmaxr  = err_glb[2];
6326 
6327   *norm = gmax;
6328   *norma = gmaxa;
6329   *normr = gmaxr;
6330   if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
6331     if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
6332     if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
6333   PetscFunctionReturn(0);
6334 }
6335 
6336 #undef __FUNCT__
6337 #define __FUNCT__ "TSErrorWeightedNorm"
6338 /*@
6339    TSErrorWeightedNorm - compute a weighted norm of the difference between two state vectors based on supplied absolute and relative tolerances
6340 
6341    Collective on TS
6342 
6343    Input Arguments:
6344 +  ts - time stepping context
6345 .  U - state vector, usually ts->vec_sol
6346 .  Y - state vector to be compared to U
6347 -  wnormtype - norm type, either NORM_2 or NORM_INFINITY
6348 
6349    Output Arguments:
6350 .  norm  - weighted norm, a value of 1.0 achieves a balance between absolute and relative tolerances
6351 .  norma - weighted norm, a value of 1.0 means that the error meets the absolute tolerance set by the user
6352 .  normr - weighted norm, a value of 1.0 means that the error meets the relative tolerance set by the user
6353 
6354    Options Database Keys:
6355 .  -ts_adapt_wnormtype <wnormtype> - 2, INFINITY
6356 
6357    Level: developer
6358 
6359 .seealso: TSErrorWeightedNormInfinity(), TSErrorWeightedNorm2(), TSErrorWeightedENorm
6360 @*/
6361 PetscErrorCode TSErrorWeightedNorm(TS ts,Vec U,Vec Y,NormType wnormtype,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6362 {
6363   PetscErrorCode ierr;
6364 
6365   PetscFunctionBegin;
6366   if (wnormtype == NORM_2) {
6367     ierr = TSErrorWeightedNorm2(ts,U,Y,norm,norma,normr);CHKERRQ(ierr);
6368   } else if(wnormtype == NORM_INFINITY) {
6369     ierr = TSErrorWeightedNormInfinity(ts,U,Y,norm,norma,normr);CHKERRQ(ierr);
6370   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
6371   PetscFunctionReturn(0);
6372 }
6373 
6374 
6375 #undef __FUNCT__
6376 #define __FUNCT__ "TSErrorWeightedENorm2"
6377 /*@
6378    TSErrorWeightedENorm2 - compute a weighted 2 error norm based on supplied absolute and relative tolerances
6379 
6380    Collective on TS
6381 
6382    Input Arguments:
6383 +  ts - time stepping context
6384 .  E - error vector
6385 .  U - state vector, usually ts->vec_sol
6386 -  Y - state vector, previous time step
6387 
6388    Output Arguments:
6389 .  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
6390 .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
6391 .  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances
6392 
6393    Level: developer
6394 
6395 .seealso: TSErrorWeightedENorm(), TSErrorWeightedENormInfinity()
6396 @*/
6397 PetscErrorCode TSErrorWeightedENorm2(TS ts,Vec E,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6398 {
6399   PetscErrorCode    ierr;
6400   PetscInt          i,n,N,rstart;
6401   PetscInt          n_loc,na_loc,nr_loc;
6402   PetscReal         n_glb,na_glb,nr_glb;
6403   const PetscScalar *e,*u,*y;
6404   PetscReal         err,sum,suma,sumr,gsum,gsuma,gsumr;
6405   PetscReal         tol,tola,tolr;
6406   PetscReal         err_loc[6],err_glb[6];
6407 
6408   PetscFunctionBegin;
6409   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6410   PetscValidHeaderSpecific(E,VEC_CLASSID,2);
6411   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
6412   PetscValidHeaderSpecific(Y,VEC_CLASSID,4);
6413   PetscValidType(E,2);
6414   PetscValidType(U,3);
6415   PetscValidType(Y,4);
6416   PetscCheckSameComm(E,2,U,3);
6417   PetscCheckSameComm(U,2,Y,3);
6418   PetscValidPointer(norm,5);
6419   PetscValidPointer(norma,6);
6420   PetscValidPointer(normr,7);
6421 
6422   ierr = VecGetSize(E,&N);CHKERRQ(ierr);
6423   ierr = VecGetLocalSize(E,&n);CHKERRQ(ierr);
6424   ierr = VecGetOwnershipRange(E,&rstart,NULL);CHKERRQ(ierr);
6425   ierr = VecGetArrayRead(E,&e);CHKERRQ(ierr);
6426   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
6427   ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
6428   sum  = 0.; n_loc  = 0;
6429   suma = 0.; na_loc = 0;
6430   sumr = 0.; nr_loc = 0;
6431   if (ts->vatol && ts->vrtol) {
6432     const PetscScalar *atol,*rtol;
6433     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6434     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6435     for (i=0; i<n; i++) {
6436       err = PetscAbsScalar(e[i]);
6437       tola = PetscRealPart(atol[i]);
6438       if(tola>0.){
6439         suma  += PetscSqr(err/tola);
6440         na_loc++;
6441       }
6442       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6443       if(tolr>0.){
6444         sumr  += PetscSqr(err/tolr);
6445         nr_loc++;
6446       }
6447       tol=tola+tolr;
6448       if(tol>0.){
6449         sum  += PetscSqr(err/tol);
6450         n_loc++;
6451       }
6452     }
6453     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6454     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6455   } else if (ts->vatol) {       /* vector atol, scalar rtol */
6456     const PetscScalar *atol;
6457     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6458     for (i=0; i<n; i++) {
6459       err = PetscAbsScalar(e[i]);
6460       tola = PetscRealPart(atol[i]);
6461       if(tola>0.){
6462         suma  += PetscSqr(err/tola);
6463         na_loc++;
6464       }
6465       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6466       if(tolr>0.){
6467         sumr  += PetscSqr(err/tolr);
6468         nr_loc++;
6469       }
6470       tol=tola+tolr;
6471       if(tol>0.){
6472         sum  += PetscSqr(err/tol);
6473         n_loc++;
6474       }
6475     }
6476     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6477   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
6478     const PetscScalar *rtol;
6479     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6480     for (i=0; i<n; i++) {
6481       err = PetscAbsScalar(e[i]);
6482       tola = ts->atol;
6483       if(tola>0.){
6484         suma  += PetscSqr(err/tola);
6485         na_loc++;
6486       }
6487       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6488       if(tolr>0.){
6489         sumr  += PetscSqr(err/tolr);
6490         nr_loc++;
6491       }
6492       tol=tola+tolr;
6493       if(tol>0.){
6494         sum  += PetscSqr(err/tol);
6495         n_loc++;
6496       }
6497     }
6498     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6499   } else {                      /* scalar atol, scalar rtol */
6500     for (i=0; i<n; i++) {
6501       err = PetscAbsScalar(e[i]);
6502      tola = ts->atol;
6503       if(tola>0.){
6504         suma  += PetscSqr(err/tola);
6505         na_loc++;
6506       }
6507       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6508       if(tolr>0.){
6509         sumr  += PetscSqr(err/tolr);
6510         nr_loc++;
6511       }
6512       tol=tola+tolr;
6513       if(tol>0.){
6514         sum  += PetscSqr(err/tol);
6515         n_loc++;
6516       }
6517     }
6518   }
6519   ierr = VecRestoreArrayRead(E,&e);CHKERRQ(ierr);
6520   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
6521   ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
6522 
6523   err_loc[0] = sum;
6524   err_loc[1] = suma;
6525   err_loc[2] = sumr;
6526   err_loc[3] = (PetscReal)n_loc;
6527   err_loc[4] = (PetscReal)na_loc;
6528   err_loc[5] = (PetscReal)nr_loc;
6529 
6530   ierr = MPIU_Allreduce(&err_loc,&err_glb,6,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6531 
6532   gsum   = err_glb[0];
6533   gsuma  = err_glb[1];
6534   gsumr  = err_glb[2];
6535   n_glb  = err_glb[3];
6536   na_glb = err_glb[4];
6537   nr_glb = err_glb[5];
6538 
6539   *norm  = 0.;
6540   if(n_glb>0. ){*norm  = PetscSqrtReal(gsum  / n_glb );}
6541   *norma = 0.;
6542   if(na_glb>0.){*norma = PetscSqrtReal(gsuma / na_glb);}
6543   *normr = 0.;
6544   if(nr_glb>0.){*normr = PetscSqrtReal(gsumr / nr_glb);}
6545 
6546   if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
6547   if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
6548   if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
6549   PetscFunctionReturn(0);
6550 }
6551 
6552 #undef __FUNCT__
6553 #define __FUNCT__ "TSErrorWeightedENormInfinity"
6554 /*@
6555    TSErrorWeightedENormInfinity - compute a weighted infinity error norm based on supplied absolute and relative tolerances
6556    Collective on TS
6557 
6558    Input Arguments:
6559 +  ts - time stepping context
6560 .  E - error vector
6561 .  U - state vector, usually ts->vec_sol
6562 -  Y - state vector, previous time step
6563 
6564    Output Arguments:
6565 .  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
6566 .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
6567 .  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances
6568 
6569    Level: developer
6570 
6571 .seealso: TSErrorWeightedENorm(), TSErrorWeightedENorm2()
6572 @*/
6573 PetscErrorCode TSErrorWeightedENormInfinity(TS ts,Vec E,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6574 {
6575   PetscErrorCode    ierr;
6576   PetscInt          i,n,N,rstart;
6577   const PetscScalar *e,*u,*y;
6578   PetscReal         err,max,gmax,maxa,gmaxa,maxr,gmaxr;
6579   PetscReal         tol,tola,tolr;
6580   PetscReal         err_loc[3],err_glb[3];
6581 
6582   PetscFunctionBegin;
6583   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6584   PetscValidHeaderSpecific(E,VEC_CLASSID,2);
6585   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
6586   PetscValidHeaderSpecific(Y,VEC_CLASSID,4);
6587   PetscValidType(E,2);
6588   PetscValidType(U,3);
6589   PetscValidType(Y,4);
6590   PetscCheckSameComm(E,2,U,3);
6591   PetscCheckSameComm(U,2,Y,3);
6592   PetscValidPointer(norm,5);
6593   PetscValidPointer(norma,6);
6594   PetscValidPointer(normr,7);
6595 
6596   ierr = VecGetSize(E,&N);CHKERRQ(ierr);
6597   ierr = VecGetLocalSize(E,&n);CHKERRQ(ierr);
6598   ierr = VecGetOwnershipRange(E,&rstart,NULL);CHKERRQ(ierr);
6599   ierr = VecGetArrayRead(E,&e);CHKERRQ(ierr);
6600   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
6601   ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
6602 
6603   max=0.;
6604   maxa=0.;
6605   maxr=0.;
6606 
6607   if (ts->vatol && ts->vrtol) {     /* vector atol, vector rtol */
6608     const PetscScalar *atol,*rtol;
6609     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6610     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6611 
6612     for (i=0; i<n; i++) {
6613       err = PetscAbsScalar(e[i]);
6614       tola = PetscRealPart(atol[i]);
6615       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6616       tol  = tola+tolr;
6617       if(tola>0.){
6618         maxa = PetscMax(maxa,err / tola);
6619       }
6620       if(tolr>0.){
6621         maxr = PetscMax(maxr,err / tolr);
6622       }
6623       if(tol>0.){
6624         max = PetscMax(max,err / tol);
6625       }
6626     }
6627     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6628     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6629   } else if (ts->vatol) {       /* vector atol, scalar rtol */
6630     const PetscScalar *atol;
6631     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6632     for (i=0; i<n; i++) {
6633       err = PetscAbsScalar(e[i]);
6634       tola = PetscRealPart(atol[i]);
6635       tolr = ts->rtol  * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6636       tol  = tola+tolr;
6637       if(tola>0.){
6638         maxa = PetscMax(maxa,err / tola);
6639       }
6640       if(tolr>0.){
6641         maxr = PetscMax(maxr,err / tolr);
6642       }
6643       if(tol>0.){
6644         max = PetscMax(max,err / tol);
6645       }
6646     }
6647     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6648   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
6649     const PetscScalar *rtol;
6650     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6651 
6652     for (i=0; i<n; i++) {
6653       err = PetscAbsScalar(e[i]);
6654       tola = ts->atol;
6655       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6656       tol  = tola+tolr;
6657       if(tola>0.){
6658         maxa = PetscMax(maxa,err / tola);
6659       }
6660       if(tolr>0.){
6661         maxr = PetscMax(maxr,err / tolr);
6662       }
6663       if(tol>0.){
6664         max = PetscMax(max,err / tol);
6665       }
6666     }
6667     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6668   } else {                      /* scalar atol, scalar rtol */
6669 
6670     for (i=0; i<n; i++) {
6671       err = PetscAbsScalar(e[i]);
6672       tola = ts->atol;
6673       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6674       tol  = tola+tolr;
6675       if(tola>0.){
6676         maxa = PetscMax(maxa,err / tola);
6677       }
6678       if(tolr>0.){
6679         maxr = PetscMax(maxr,err / tolr);
6680       }
6681       if(tol>0.){
6682         max = PetscMax(max,err / tol);
6683       }
6684     }
6685   }
6686   ierr = VecRestoreArrayRead(E,&e);CHKERRQ(ierr);
6687   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
6688   ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
6689   err_loc[0] = max;
6690   err_loc[1] = maxa;
6691   err_loc[2] = maxr;
6692   ierr  = MPIU_Allreduce(&err_loc,&err_glb,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6693   gmax   = err_glb[0];
6694   gmaxa  = err_glb[1];
6695   gmaxr  = err_glb[2];
6696 
6697   *norm = gmax;
6698   *norma = gmaxa;
6699   *normr = gmaxr;
6700   if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
6701     if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
6702     if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
6703   PetscFunctionReturn(0);
6704 }
6705 
6706 #undef __FUNCT__
6707 #define __FUNCT__ "TSErrorWeightedENorm"
6708 /*@
6709    TSErrorWeightedENorm - compute a weighted error norm based on supplied absolute and relative tolerances
6710 
6711    Collective on TS
6712 
6713    Input Arguments:
6714 +  ts - time stepping context
6715 .  E - error vector
6716 .  U - state vector, usually ts->vec_sol
6717 .  Y - state vector, previous time step
6718 -  wnormtype - norm type, either NORM_2 or NORM_INFINITY
6719 
6720    Output Arguments:
6721 .  norm  - weighted norm, a value of 1.0 achieves a balance between absolute and relative tolerances
6722 .  norma - weighted norm, a value of 1.0 means that the error meets the absolute tolerance set by the user
6723 .  normr - weighted norm, a value of 1.0 means that the error meets the relative tolerance set by the user
6724 
6725    Options Database Keys:
6726 .  -ts_adapt_wnormtype <wnormtype> - 2, INFINITY
6727 
6728    Level: developer
6729 
6730 .seealso: TSErrorWeightedENormInfinity(), TSErrorWeightedENorm2(), TSErrorWeightedNormInfinity(), TSErrorWeightedNorm2()
6731 @*/
6732 PetscErrorCode TSErrorWeightedENorm(TS ts,Vec E,Vec U,Vec Y,NormType wnormtype,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6733 {
6734   PetscErrorCode ierr;
6735 
6736   PetscFunctionBegin;
6737   if (wnormtype == NORM_2) {
6738     ierr = TSErrorWeightedENorm2(ts,E,U,Y,norm,norma,normr);CHKERRQ(ierr);
6739   } else if(wnormtype == NORM_INFINITY) {
6740     ierr = TSErrorWeightedENormInfinity(ts,E,U,Y,norm,norma,normr);CHKERRQ(ierr);
6741   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
6742   PetscFunctionReturn(0);
6743 }
6744 
6745 
6746 #undef __FUNCT__
6747 #define __FUNCT__ "TSSetCFLTimeLocal"
6748 /*@
6749    TSSetCFLTimeLocal - Set the local CFL constraint relative to forward Euler
6750 
6751    Logically Collective on TS
6752 
6753    Input Arguments:
6754 +  ts - time stepping context
6755 -  cfltime - maximum stable time step if using forward Euler (value can be different on each process)
6756 
6757    Note:
6758    After calling this function, the global CFL time can be obtained by calling TSGetCFLTime()
6759 
6760    Level: intermediate
6761 
6762 .seealso: TSGetCFLTime(), TSADAPTCFL
6763 @*/
6764 PetscErrorCode TSSetCFLTimeLocal(TS ts,PetscReal cfltime)
6765 {
6766   PetscFunctionBegin;
6767   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6768   ts->cfltime_local = cfltime;
6769   ts->cfltime       = -1.;
6770   PetscFunctionReturn(0);
6771 }
6772 
6773 #undef __FUNCT__
6774 #define __FUNCT__ "TSGetCFLTime"
6775 /*@
6776    TSGetCFLTime - Get the maximum stable time step according to CFL criteria applied to forward Euler
6777 
6778    Collective on TS
6779 
6780    Input Arguments:
6781 .  ts - time stepping context
6782 
6783    Output Arguments:
6784 .  cfltime - maximum stable time step for forward Euler
6785 
6786    Level: advanced
6787 
6788 .seealso: TSSetCFLTimeLocal()
6789 @*/
6790 PetscErrorCode TSGetCFLTime(TS ts,PetscReal *cfltime)
6791 {
6792   PetscErrorCode ierr;
6793 
6794   PetscFunctionBegin;
6795   if (ts->cfltime < 0) {
6796     ierr = MPIU_Allreduce(&ts->cfltime_local,&ts->cfltime,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6797   }
6798   *cfltime = ts->cfltime;
6799   PetscFunctionReturn(0);
6800 }
6801 
6802 #undef __FUNCT__
6803 #define __FUNCT__ "TSVISetVariableBounds"
6804 /*@
6805    TSVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu
6806 
6807    Input Parameters:
6808 .  ts   - the TS context.
6809 .  xl   - lower bound.
6810 .  xu   - upper bound.
6811 
6812    Notes:
6813    If this routine is not called then the lower and upper bounds are set to
6814    PETSC_NINFINITY and PETSC_INFINITY respectively during SNESSetUp().
6815 
6816    Level: advanced
6817 
6818 @*/
6819 PetscErrorCode TSVISetVariableBounds(TS ts, Vec xl, Vec xu)
6820 {
6821   PetscErrorCode ierr;
6822   SNES           snes;
6823 
6824   PetscFunctionBegin;
6825   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
6826   ierr = SNESVISetVariableBounds(snes,xl,xu);CHKERRQ(ierr);
6827   PetscFunctionReturn(0);
6828 }
6829 
6830 #if defined(PETSC_HAVE_MATLAB_ENGINE)
6831 #include <mex.h>
6832 
6833 typedef struct {char *funcname; mxArray *ctx;} TSMatlabContext;
6834 
6835 #undef __FUNCT__
6836 #define __FUNCT__ "TSComputeFunction_Matlab"
6837 /*
6838    TSComputeFunction_Matlab - Calls the function that has been set with
6839                          TSSetFunctionMatlab().
6840 
6841    Collective on TS
6842 
6843    Input Parameters:
6844 +  snes - the TS context
6845 -  u - input vector
6846 
6847    Output Parameter:
6848 .  y - function vector, as set by TSSetFunction()
6849 
6850    Notes:
6851    TSComputeFunction() is typically used within nonlinear solvers
6852    implementations, so most users would not generally call this routine
6853    themselves.
6854 
6855    Level: developer
6856 
6857 .keywords: TS, nonlinear, compute, function
6858 
6859 .seealso: TSSetFunction(), TSGetFunction()
6860 */
6861 PetscErrorCode  TSComputeFunction_Matlab(TS snes,PetscReal time,Vec u,Vec udot,Vec y, void *ctx)
6862 {
6863   PetscErrorCode  ierr;
6864   TSMatlabContext *sctx = (TSMatlabContext*)ctx;
6865   int             nlhs  = 1,nrhs = 7;
6866   mxArray         *plhs[1],*prhs[7];
6867   long long int   lx = 0,lxdot = 0,ly = 0,ls = 0;
6868 
6869   PetscFunctionBegin;
6870   PetscValidHeaderSpecific(snes,TS_CLASSID,1);
6871   PetscValidHeaderSpecific(u,VEC_CLASSID,3);
6872   PetscValidHeaderSpecific(udot,VEC_CLASSID,4);
6873   PetscValidHeaderSpecific(y,VEC_CLASSID,5);
6874   PetscCheckSameComm(snes,1,u,3);
6875   PetscCheckSameComm(snes,1,y,5);
6876 
6877   ierr = PetscMemcpy(&ls,&snes,sizeof(snes));CHKERRQ(ierr);
6878   ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
6879   ierr = PetscMemcpy(&lxdot,&udot,sizeof(udot));CHKERRQ(ierr);
6880   ierr = PetscMemcpy(&ly,&y,sizeof(u));CHKERRQ(ierr);
6881 
6882   prhs[0] =  mxCreateDoubleScalar((double)ls);
6883   prhs[1] =  mxCreateDoubleScalar(time);
6884   prhs[2] =  mxCreateDoubleScalar((double)lx);
6885   prhs[3] =  mxCreateDoubleScalar((double)lxdot);
6886   prhs[4] =  mxCreateDoubleScalar((double)ly);
6887   prhs[5] =  mxCreateString(sctx->funcname);
6888   prhs[6] =  sctx->ctx;
6889   ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSComputeFunctionInternal");CHKERRQ(ierr);
6890   ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
6891   mxDestroyArray(prhs[0]);
6892   mxDestroyArray(prhs[1]);
6893   mxDestroyArray(prhs[2]);
6894   mxDestroyArray(prhs[3]);
6895   mxDestroyArray(prhs[4]);
6896   mxDestroyArray(prhs[5]);
6897   mxDestroyArray(plhs[0]);
6898   PetscFunctionReturn(0);
6899 }
6900 
6901 
6902 #undef __FUNCT__
6903 #define __FUNCT__ "TSSetFunctionMatlab"
6904 /*
6905    TSSetFunctionMatlab - Sets the function evaluation routine and function
6906    vector for use by the TS routines in solving ODEs
6907    equations from MATLAB. Here the function is a string containing the name of a MATLAB function
6908 
6909    Logically Collective on TS
6910 
6911    Input Parameters:
6912 +  ts - the TS context
6913 -  func - function evaluation routine
6914 
6915    Calling sequence of func:
6916 $    func (TS ts,PetscReal time,Vec u,Vec udot,Vec f,void *ctx);
6917 
6918    Level: beginner
6919 
6920 .keywords: TS, nonlinear, set, function
6921 
6922 .seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
6923 */
6924 PetscErrorCode  TSSetFunctionMatlab(TS ts,const char *func,mxArray *ctx)
6925 {
6926   PetscErrorCode  ierr;
6927   TSMatlabContext *sctx;
6928 
6929   PetscFunctionBegin;
6930   /* currently sctx is memory bleed */
6931   ierr = PetscNew(&sctx);CHKERRQ(ierr);
6932   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
6933   /*
6934      This should work, but it doesn't
6935   sctx->ctx = ctx;
6936   mexMakeArrayPersistent(sctx->ctx);
6937   */
6938   sctx->ctx = mxDuplicateArray(ctx);
6939 
6940   ierr = TSSetIFunction(ts,NULL,TSComputeFunction_Matlab,sctx);CHKERRQ(ierr);
6941   PetscFunctionReturn(0);
6942 }
6943 
6944 #undef __FUNCT__
6945 #define __FUNCT__ "TSComputeJacobian_Matlab"
6946 /*
6947    TSComputeJacobian_Matlab - Calls the function that has been set with
6948                          TSSetJacobianMatlab().
6949 
6950    Collective on TS
6951 
6952    Input Parameters:
6953 +  ts - the TS context
6954 .  u - input vector
6955 .  A, B - the matrices
6956 -  ctx - user context
6957 
6958    Level: developer
6959 
6960 .keywords: TS, nonlinear, compute, function
6961 
6962 .seealso: TSSetFunction(), TSGetFunction()
6963 @*/
6964 PetscErrorCode  TSComputeJacobian_Matlab(TS ts,PetscReal time,Vec u,Vec udot,PetscReal shift,Mat A,Mat B,void *ctx)
6965 {
6966   PetscErrorCode  ierr;
6967   TSMatlabContext *sctx = (TSMatlabContext*)ctx;
6968   int             nlhs  = 2,nrhs = 9;
6969   mxArray         *plhs[2],*prhs[9];
6970   long long int   lx = 0,lxdot = 0,lA = 0,ls = 0, lB = 0;
6971 
6972   PetscFunctionBegin;
6973   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6974   PetscValidHeaderSpecific(u,VEC_CLASSID,3);
6975 
6976   /* call Matlab function in ctx with arguments u and y */
6977 
6978   ierr = PetscMemcpy(&ls,&ts,sizeof(ts));CHKERRQ(ierr);
6979   ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
6980   ierr = PetscMemcpy(&lxdot,&udot,sizeof(u));CHKERRQ(ierr);
6981   ierr = PetscMemcpy(&lA,A,sizeof(u));CHKERRQ(ierr);
6982   ierr = PetscMemcpy(&lB,B,sizeof(u));CHKERRQ(ierr);
6983 
6984   prhs[0] =  mxCreateDoubleScalar((double)ls);
6985   prhs[1] =  mxCreateDoubleScalar((double)time);
6986   prhs[2] =  mxCreateDoubleScalar((double)lx);
6987   prhs[3] =  mxCreateDoubleScalar((double)lxdot);
6988   prhs[4] =  mxCreateDoubleScalar((double)shift);
6989   prhs[5] =  mxCreateDoubleScalar((double)lA);
6990   prhs[6] =  mxCreateDoubleScalar((double)lB);
6991   prhs[7] =  mxCreateString(sctx->funcname);
6992   prhs[8] =  sctx->ctx;
6993   ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSComputeJacobianInternal");CHKERRQ(ierr);
6994   ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
6995   mxDestroyArray(prhs[0]);
6996   mxDestroyArray(prhs[1]);
6997   mxDestroyArray(prhs[2]);
6998   mxDestroyArray(prhs[3]);
6999   mxDestroyArray(prhs[4]);
7000   mxDestroyArray(prhs[5]);
7001   mxDestroyArray(prhs[6]);
7002   mxDestroyArray(prhs[7]);
7003   mxDestroyArray(plhs[0]);
7004   mxDestroyArray(plhs[1]);
7005   PetscFunctionReturn(0);
7006 }
7007 
7008 
7009 #undef __FUNCT__
7010 #define __FUNCT__ "TSSetJacobianMatlab"
7011 /*
7012    TSSetJacobianMatlab - Sets the Jacobian function evaluation routine and two empty Jacobian matrices
7013    vector for use by the TS routines in solving ODEs from MATLAB. Here the function is a string containing the name of a MATLAB function
7014 
7015    Logically Collective on TS
7016 
7017    Input Parameters:
7018 +  ts - the TS context
7019 .  A,B - Jacobian matrices
7020 .  func - function evaluation routine
7021 -  ctx - user context
7022 
7023    Calling sequence of func:
7024 $    flag = func (TS ts,PetscReal time,Vec u,Vec udot,Mat A,Mat B,void *ctx);
7025 
7026 
7027    Level: developer
7028 
7029 .keywords: TS, nonlinear, set, function
7030 
7031 .seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
7032 */
7033 PetscErrorCode  TSSetJacobianMatlab(TS ts,Mat A,Mat B,const char *func,mxArray *ctx)
7034 {
7035   PetscErrorCode  ierr;
7036   TSMatlabContext *sctx;
7037 
7038   PetscFunctionBegin;
7039   /* currently sctx is memory bleed */
7040   ierr = PetscNew(&sctx);CHKERRQ(ierr);
7041   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
7042   /*
7043      This should work, but it doesn't
7044   sctx->ctx = ctx;
7045   mexMakeArrayPersistent(sctx->ctx);
7046   */
7047   sctx->ctx = mxDuplicateArray(ctx);
7048 
7049   ierr = TSSetIJacobian(ts,A,B,TSComputeJacobian_Matlab,sctx);CHKERRQ(ierr);
7050   PetscFunctionReturn(0);
7051 }
7052 
7053 #undef __FUNCT__
7054 #define __FUNCT__ "TSMonitor_Matlab"
7055 /*
7056    TSMonitor_Matlab - Calls the function that has been set with TSMonitorSetMatlab().
7057 
7058    Collective on TS
7059 
7060 .seealso: TSSetFunction(), TSGetFunction()
7061 @*/
7062 PetscErrorCode  TSMonitor_Matlab(TS ts,PetscInt it, PetscReal time,Vec u, void *ctx)
7063 {
7064   PetscErrorCode  ierr;
7065   TSMatlabContext *sctx = (TSMatlabContext*)ctx;
7066   int             nlhs  = 1,nrhs = 6;
7067   mxArray         *plhs[1],*prhs[6];
7068   long long int   lx = 0,ls = 0;
7069 
7070   PetscFunctionBegin;
7071   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
7072   PetscValidHeaderSpecific(u,VEC_CLASSID,4);
7073 
7074   ierr = PetscMemcpy(&ls,&ts,sizeof(ts));CHKERRQ(ierr);
7075   ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
7076 
7077   prhs[0] =  mxCreateDoubleScalar((double)ls);
7078   prhs[1] =  mxCreateDoubleScalar((double)it);
7079   prhs[2] =  mxCreateDoubleScalar((double)time);
7080   prhs[3] =  mxCreateDoubleScalar((double)lx);
7081   prhs[4] =  mxCreateString(sctx->funcname);
7082   prhs[5] =  sctx->ctx;
7083   ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSMonitorInternal");CHKERRQ(ierr);
7084   ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
7085   mxDestroyArray(prhs[0]);
7086   mxDestroyArray(prhs[1]);
7087   mxDestroyArray(prhs[2]);
7088   mxDestroyArray(prhs[3]);
7089   mxDestroyArray(prhs[4]);
7090   mxDestroyArray(plhs[0]);
7091   PetscFunctionReturn(0);
7092 }
7093 
7094 
7095 #undef __FUNCT__
7096 #define __FUNCT__ "TSMonitorSetMatlab"
7097 /*
7098    TSMonitorSetMatlab - Sets the monitor function from Matlab
7099 
7100    Level: developer
7101 
7102 .keywords: TS, nonlinear, set, function
7103 
7104 .seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
7105 */
7106 PetscErrorCode  TSMonitorSetMatlab(TS ts,const char *func,mxArray *ctx)
7107 {
7108   PetscErrorCode  ierr;
7109   TSMatlabContext *sctx;
7110 
7111   PetscFunctionBegin;
7112   /* currently sctx is memory bleed */
7113   ierr = PetscNew(&sctx);CHKERRQ(ierr);
7114   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
7115   /*
7116      This should work, but it doesn't
7117   sctx->ctx = ctx;
7118   mexMakeArrayPersistent(sctx->ctx);
7119   */
7120   sctx->ctx = mxDuplicateArray(ctx);
7121 
7122   ierr = TSMonitorSet(ts,TSMonitor_Matlab,sctx,NULL);CHKERRQ(ierr);
7123   PetscFunctionReturn(0);
7124 }
7125 #endif
7126 
7127 #undef __FUNCT__
7128 #define __FUNCT__ "TSMonitorLGSolution"
7129 /*@C
7130    TSMonitorLGSolution - Monitors progress of the TS solvers by plotting each component of the solution vector
7131        in a time based line graph
7132 
7133    Collective on TS
7134 
7135    Input Parameters:
7136 +  ts - the TS context
7137 .  step - current time-step
7138 .  ptime - current time
7139 .  u - current solution
7140 -  dctx - the TSMonitorLGCtx object that contains all the options for the monitoring, this is created with TSMonitorLGCtxCreate()
7141 
7142    Options Database:
7143 .   -ts_monitor_lg_solution_variables
7144 
7145    Level: intermediate
7146 
7147    Notes: Each process in a parallel run displays its component solutions in a separate window
7148 
7149 .keywords: TS,  vector, monitor, view
7150 
7151 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGCtxCreate(), TSMonitorLGCtxSetVariableNames(), TSMonitorLGCtxGetVariableNames(),
7152            TSMonitorLGSetVariableNames(), TSMonitorLGGetVariableNames(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetDisplayVariables(),
7153            TSMonitorLGCtxSetTransform(), TSMonitorLGSetTransform(), TSMonitorLGError(), TSMonitorLGSNESIterations(), TSMonitorLGKSPIterations(),
7154            TSMonitorEnvelopeCtxCreate(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxDestroy(), TSMonitorEnvelop()
7155 @*/
7156 PetscErrorCode  TSMonitorLGSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dctx)
7157 {
7158   PetscErrorCode    ierr;
7159   TSMonitorLGCtx    ctx = (TSMonitorLGCtx)dctx;
7160   const PetscScalar *yy;
7161   Vec               v;
7162 
7163   PetscFunctionBegin;
7164   if (step < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
7165   if (!step) {
7166     PetscDrawAxis axis;
7167     PetscInt      dim;
7168     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
7169     ierr = PetscDrawAxisSetLabels(axis,"Solution as function of time","Time","Solution");CHKERRQ(ierr);
7170     if (!ctx->names) {
7171       PetscBool flg;
7172       /* user provides names of variables to plot but no names has been set so assume names are integer values */
7173       ierr = PetscOptionsHasName(((PetscObject)ts)->options,((PetscObject)ts)->prefix,"-ts_monitor_lg_solution_variables",&flg);CHKERRQ(ierr);
7174       if (flg) {
7175         PetscInt i,n;
7176         char     **names;
7177         ierr = VecGetSize(u,&n);CHKERRQ(ierr);
7178         ierr = PetscMalloc1(n+1,&names);CHKERRQ(ierr);
7179         for (i=0; i<n; i++) {
7180           ierr = PetscMalloc1(5,&names[i]);CHKERRQ(ierr);
7181           ierr = PetscSNPrintf(names[i],5,"%D",i);CHKERRQ(ierr);
7182         }
7183         names[n] = NULL;
7184         ctx->names = names;
7185       }
7186     }
7187     if (ctx->names && !ctx->displaynames) {
7188       char      **displaynames;
7189       PetscBool flg;
7190       ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
7191       ierr = PetscMalloc1(dim+1,&displaynames);CHKERRQ(ierr);
7192       ierr = PetscMemzero(displaynames,(dim+1)*sizeof(char*));CHKERRQ(ierr);
7193       ierr = PetscOptionsGetStringArray(((PetscObject)ts)->options,((PetscObject)ts)->prefix,"-ts_monitor_lg_solution_variables",displaynames,&dim,&flg);CHKERRQ(ierr);
7194       if (flg) {
7195         ierr = TSMonitorLGCtxSetDisplayVariables(ctx,(const char *const *)displaynames);CHKERRQ(ierr);
7196       }
7197       ierr = PetscStrArrayDestroy(&displaynames);CHKERRQ(ierr);
7198     }
7199     if (ctx->displaynames) {
7200       ierr = PetscDrawLGSetDimension(ctx->lg,ctx->ndisplayvariables);CHKERRQ(ierr);
7201       ierr = PetscDrawLGSetLegend(ctx->lg,(const char *const *)ctx->displaynames);CHKERRQ(ierr);
7202     } else if (ctx->names) {
7203       ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
7204       ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
7205       ierr = PetscDrawLGSetLegend(ctx->lg,(const char *const *)ctx->names);CHKERRQ(ierr);
7206     } else {
7207       ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
7208       ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
7209     }
7210     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
7211   }
7212 
7213   if (!ctx->transform) v = u;
7214   else {ierr = (*ctx->transform)(ctx->transformctx,u,&v);CHKERRQ(ierr);}
7215   ierr = VecGetArrayRead(v,&yy);CHKERRQ(ierr);
7216   if (ctx->displaynames) {
7217     PetscInt i;
7218     for (i=0; i<ctx->ndisplayvariables; i++)
7219       ctx->displayvalues[i] = PetscRealPart(yy[ctx->displayvariables[i]]);
7220     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,ctx->displayvalues);CHKERRQ(ierr);
7221   } else {
7222 #if defined(PETSC_USE_COMPLEX)
7223     PetscInt  i,n;
7224     PetscReal *yreal;
7225     ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
7226     ierr = PetscMalloc1(n,&yreal);CHKERRQ(ierr);
7227     for (i=0; i<n; i++) yreal[i] = PetscRealPart(yy[i]);
7228     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yreal);CHKERRQ(ierr);
7229     ierr = PetscFree(yreal);CHKERRQ(ierr);
7230 #else
7231     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yy);CHKERRQ(ierr);
7232 #endif
7233   }
7234   ierr = VecRestoreArrayRead(v,&yy);CHKERRQ(ierr);
7235   if (ctx->transform) {ierr = VecDestroy(&v);CHKERRQ(ierr);}
7236 
7237   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
7238     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
7239     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
7240   }
7241   PetscFunctionReturn(0);
7242 }
7243 
7244 
7245 #undef __FUNCT__
7246 #define __FUNCT__ "TSMonitorLGSetVariableNames"
7247 /*@C
7248    TSMonitorLGSetVariableNames - Sets the name of each component in the solution vector so that it may be displayed in the plot
7249 
7250    Collective on TS
7251 
7252    Input Parameters:
7253 +  ts - the TS context
7254 -  names - the names of the components, final string must be NULL
7255 
7256    Level: intermediate
7257 
7258    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
7259 
7260 .keywords: TS,  vector, monitor, view
7261 
7262 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetVariableNames()
7263 @*/
7264 PetscErrorCode  TSMonitorLGSetVariableNames(TS ts,const char * const *names)
7265 {
7266   PetscErrorCode    ierr;
7267   PetscInt          i;
7268 
7269   PetscFunctionBegin;
7270   for (i=0; i<ts->numbermonitors; i++) {
7271     if (ts->monitor[i] == TSMonitorLGSolution) {
7272       ierr = TSMonitorLGCtxSetVariableNames((TSMonitorLGCtx)ts->monitorcontext[i],names);CHKERRQ(ierr);
7273       break;
7274     }
7275   }
7276   PetscFunctionReturn(0);
7277 }
7278 
7279 #undef __FUNCT__
7280 #define __FUNCT__ "TSMonitorLGCtxSetVariableNames"
7281 /*@C
7282    TSMonitorLGCtxSetVariableNames - Sets the name of each component in the solution vector so that it may be displayed in the plot
7283 
7284    Collective on TS
7285 
7286    Input Parameters:
7287 +  ts - the TS context
7288 -  names - the names of the components, final string must be NULL
7289 
7290    Level: intermediate
7291 
7292 .keywords: TS,  vector, monitor, view
7293 
7294 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables(), TSMonitorLGSetVariableNames()
7295 @*/
7296 PetscErrorCode  TSMonitorLGCtxSetVariableNames(TSMonitorLGCtx ctx,const char * const *names)
7297 {
7298   PetscErrorCode    ierr;
7299 
7300   PetscFunctionBegin;
7301   ierr = PetscStrArrayDestroy(&ctx->names);CHKERRQ(ierr);
7302   ierr = PetscStrArrayallocpy(names,&ctx->names);CHKERRQ(ierr);
7303   PetscFunctionReturn(0);
7304 }
7305 
7306 #undef __FUNCT__
7307 #define __FUNCT__ "TSMonitorLGGetVariableNames"
7308 /*@C
7309    TSMonitorLGGetVariableNames - Gets the name of each component in the solution vector so that it may be displayed in the plot
7310 
7311    Collective on TS
7312 
7313    Input Parameter:
7314 .  ts - the TS context
7315 
7316    Output Parameter:
7317 .  names - the names of the components, final string must be NULL
7318 
7319    Level: intermediate
7320 
7321    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
7322 
7323 .keywords: TS,  vector, monitor, view
7324 
7325 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables()
7326 @*/
7327 PetscErrorCode  TSMonitorLGGetVariableNames(TS ts,const char *const **names)
7328 {
7329   PetscInt       i;
7330 
7331   PetscFunctionBegin;
7332   *names = NULL;
7333   for (i=0; i<ts->numbermonitors; i++) {
7334     if (ts->monitor[i] == TSMonitorLGSolution) {
7335       TSMonitorLGCtx  ctx = (TSMonitorLGCtx) ts->monitorcontext[i];
7336       *names = (const char *const *)ctx->names;
7337       break;
7338     }
7339   }
7340   PetscFunctionReturn(0);
7341 }
7342 
7343 #undef __FUNCT__
7344 #define __FUNCT__ "TSMonitorLGCtxSetDisplayVariables"
7345 /*@C
7346    TSMonitorLGCtxSetDisplayVariables - Sets the variables that are to be display in the monitor
7347 
7348    Collective on TS
7349 
7350    Input Parameters:
7351 +  ctx - the TSMonitorLG context
7352 .  displaynames - the names of the components, final string must be NULL
7353 
7354    Level: intermediate
7355 
7356 .keywords: TS,  vector, monitor, view
7357 
7358 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames()
7359 @*/
7360 PetscErrorCode  TSMonitorLGCtxSetDisplayVariables(TSMonitorLGCtx ctx,const char * const *displaynames)
7361 {
7362   PetscInt          j = 0,k;
7363   PetscErrorCode    ierr;
7364 
7365   PetscFunctionBegin;
7366   if (!ctx->names) PetscFunctionReturn(0);
7367   ierr = PetscStrArrayDestroy(&ctx->displaynames);CHKERRQ(ierr);
7368   ierr = PetscStrArrayallocpy(displaynames,&ctx->displaynames);CHKERRQ(ierr);
7369   while (displaynames[j]) j++;
7370   ctx->ndisplayvariables = j;
7371   ierr = PetscMalloc1(ctx->ndisplayvariables,&ctx->displayvariables);CHKERRQ(ierr);
7372   ierr = PetscMalloc1(ctx->ndisplayvariables,&ctx->displayvalues);CHKERRQ(ierr);
7373   j = 0;
7374   while (displaynames[j]) {
7375     k = 0;
7376     while (ctx->names[k]) {
7377       PetscBool flg;
7378       ierr = PetscStrcmp(displaynames[j],ctx->names[k],&flg);CHKERRQ(ierr);
7379       if (flg) {
7380         ctx->displayvariables[j] = k;
7381         break;
7382       }
7383       k++;
7384     }
7385     j++;
7386   }
7387   PetscFunctionReturn(0);
7388 }
7389 
7390 
7391 #undef __FUNCT__
7392 #define __FUNCT__ "TSMonitorLGSetDisplayVariables"
7393 /*@C
7394    TSMonitorLGSetDisplayVariables - Sets the variables that are to be display in the monitor
7395 
7396    Collective on TS
7397 
7398    Input Parameters:
7399 +  ts - the TS context
7400 .  displaynames - the names of the components, final string must be NULL
7401 
7402    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
7403 
7404    Level: intermediate
7405 
7406 .keywords: TS,  vector, monitor, view
7407 
7408 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames()
7409 @*/
7410 PetscErrorCode  TSMonitorLGSetDisplayVariables(TS ts,const char * const *displaynames)
7411 {
7412   PetscInt          i;
7413   PetscErrorCode    ierr;
7414 
7415   PetscFunctionBegin;
7416   for (i=0; i<ts->numbermonitors; i++) {
7417     if (ts->monitor[i] == TSMonitorLGSolution) {
7418       ierr = TSMonitorLGCtxSetDisplayVariables((TSMonitorLGCtx)ts->monitorcontext[i],displaynames);CHKERRQ(ierr);
7419       break;
7420     }
7421   }
7422   PetscFunctionReturn(0);
7423 }
7424 
7425 #undef __FUNCT__
7426 #define __FUNCT__ "TSMonitorLGSetTransform"
7427 /*@C
7428    TSMonitorLGSetTransform - Solution vector will be transformed by provided function before being displayed
7429 
7430    Collective on TS
7431 
7432    Input Parameters:
7433 +  ts - the TS context
7434 .  transform - the transform function
7435 .  destroy - function to destroy the optional context
7436 -  ctx - optional context used by transform function
7437 
7438    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
7439 
7440    Level: intermediate
7441 
7442 .keywords: TS,  vector, monitor, view
7443 
7444 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames(), TSMonitorLGCtxSetTransform()
7445 @*/
7446 PetscErrorCode  TSMonitorLGSetTransform(TS ts,PetscErrorCode (*transform)(void*,Vec,Vec*),PetscErrorCode (*destroy)(void*),void *tctx)
7447 {
7448   PetscInt          i;
7449   PetscErrorCode    ierr;
7450 
7451   PetscFunctionBegin;
7452   for (i=0; i<ts->numbermonitors; i++) {
7453     if (ts->monitor[i] == TSMonitorLGSolution) {
7454       ierr = TSMonitorLGCtxSetTransform((TSMonitorLGCtx)ts->monitorcontext[i],transform,destroy,tctx);CHKERRQ(ierr);
7455     }
7456   }
7457   PetscFunctionReturn(0);
7458 }
7459 
7460 #undef __FUNCT__
7461 #define __FUNCT__ "TSMonitorLGCtxSetTransform"
7462 /*@C
7463    TSMonitorLGCtxSetTransform - Solution vector will be transformed by provided function before being displayed
7464 
7465    Collective on TSLGCtx
7466 
7467    Input Parameters:
7468 +  ts - the TS context
7469 .  transform - the transform function
7470 .  destroy - function to destroy the optional context
7471 -  ctx - optional context used by transform function
7472 
7473    Level: intermediate
7474 
7475 .keywords: TS,  vector, monitor, view
7476 
7477 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames(), TSMonitorLGSetTransform()
7478 @*/
7479 PetscErrorCode  TSMonitorLGCtxSetTransform(TSMonitorLGCtx ctx,PetscErrorCode (*transform)(void*,Vec,Vec*),PetscErrorCode (*destroy)(void*),void *tctx)
7480 {
7481   PetscFunctionBegin;
7482   ctx->transform    = transform;
7483   ctx->transformdestroy = destroy;
7484   ctx->transformctx = tctx;
7485   PetscFunctionReturn(0);
7486 }
7487 
7488 #undef __FUNCT__
7489 #define __FUNCT__ "TSMonitorLGError"
7490 /*@C
7491    TSMonitorLGError - Monitors progress of the TS solvers by plotting each component of the solution vector
7492        in a time based line graph
7493 
7494    Collective on TS
7495 
7496    Input Parameters:
7497 +  ts - the TS context
7498 .  step - current time-step
7499 .  ptime - current time
7500 .  u - current solution
7501 -  dctx - TSMonitorLGCtx object created with TSMonitorLGCtxCreate()
7502 
7503    Level: intermediate
7504 
7505    Notes: Each process in a parallel run displays its component errors in a separate window
7506 
7507    The user must provide the solution using TSSetSolutionFunction() to use this monitor.
7508 
7509    Options Database Keys:
7510 .  -ts_monitor_lg_error - create a graphical monitor of error history
7511 
7512 .keywords: TS,  vector, monitor, view
7513 
7514 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSSetSolutionFunction()
7515 @*/
7516 PetscErrorCode  TSMonitorLGError(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
7517 {
7518   PetscErrorCode    ierr;
7519   TSMonitorLGCtx    ctx = (TSMonitorLGCtx)dummy;
7520   const PetscScalar *yy;
7521   Vec               y;
7522 
7523   PetscFunctionBegin;
7524   if (!step) {
7525     PetscDrawAxis axis;
7526     PetscInt      dim;
7527     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
7528     ierr = PetscDrawAxisSetLabels(axis,"Error in solution as function of time","Time","Solution");CHKERRQ(ierr);
7529     ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
7530     ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
7531     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
7532   }
7533   ierr = VecDuplicate(u,&y);CHKERRQ(ierr);
7534   ierr = TSComputeSolutionFunction(ts,ptime,y);CHKERRQ(ierr);
7535   ierr = VecAXPY(y,-1.0,u);CHKERRQ(ierr);
7536   ierr = VecGetArrayRead(y,&yy);CHKERRQ(ierr);
7537 #if defined(PETSC_USE_COMPLEX)
7538   {
7539     PetscReal *yreal;
7540     PetscInt  i,n;
7541     ierr = VecGetLocalSize(y,&n);CHKERRQ(ierr);
7542     ierr = PetscMalloc1(n,&yreal);CHKERRQ(ierr);
7543     for (i=0; i<n; i++) yreal[i] = PetscRealPart(yy[i]);
7544     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yreal);CHKERRQ(ierr);
7545     ierr = PetscFree(yreal);CHKERRQ(ierr);
7546   }
7547 #else
7548   ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yy);CHKERRQ(ierr);
7549 #endif
7550   ierr = VecRestoreArrayRead(y,&yy);CHKERRQ(ierr);
7551   ierr = VecDestroy(&y);CHKERRQ(ierr);
7552   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
7553     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
7554     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
7555   }
7556   PetscFunctionReturn(0);
7557 }
7558 
7559 #undef __FUNCT__
7560 #define __FUNCT__ "TSMonitorLGSNESIterations"
7561 PetscErrorCode TSMonitorLGSNESIterations(TS ts,PetscInt n,PetscReal ptime,Vec v,void *monctx)
7562 {
7563   TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
7564   PetscReal      x   = ptime,y;
7565   PetscErrorCode ierr;
7566   PetscInt       its;
7567 
7568   PetscFunctionBegin;
7569   if (n < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
7570   if (!n) {
7571     PetscDrawAxis axis;
7572     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
7573     ierr = PetscDrawAxisSetLabels(axis,"Nonlinear iterations as function of time","Time","SNES Iterations");CHKERRQ(ierr);
7574     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
7575     ctx->snes_its = 0;
7576   }
7577   ierr = TSGetSNESIterations(ts,&its);CHKERRQ(ierr);
7578   y    = its - ctx->snes_its;
7579   ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
7580   if (((ctx->howoften > 0) && (!(n % ctx->howoften)) && (n > -1)) || ((ctx->howoften == -1) && (n == -1))) {
7581     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
7582     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
7583   }
7584   ctx->snes_its = its;
7585   PetscFunctionReturn(0);
7586 }
7587 
7588 #undef __FUNCT__
7589 #define __FUNCT__ "TSMonitorLGKSPIterations"
7590 PetscErrorCode TSMonitorLGKSPIterations(TS ts,PetscInt n,PetscReal ptime,Vec v,void *monctx)
7591 {
7592   TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
7593   PetscReal      x   = ptime,y;
7594   PetscErrorCode ierr;
7595   PetscInt       its;
7596 
7597   PetscFunctionBegin;
7598   if (n < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
7599   if (!n) {
7600     PetscDrawAxis axis;
7601     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
7602     ierr = PetscDrawAxisSetLabels(axis,"Linear iterations as function of time","Time","KSP Iterations");CHKERRQ(ierr);
7603     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
7604     ctx->ksp_its = 0;
7605   }
7606   ierr = TSGetKSPIterations(ts,&its);CHKERRQ(ierr);
7607   y    = its - ctx->ksp_its;
7608   ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
7609   if (((ctx->howoften > 0) && (!(n % ctx->howoften)) && (n > -1)) || ((ctx->howoften == -1) && (n == -1))) {
7610     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
7611     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
7612   }
7613   ctx->ksp_its = its;
7614   PetscFunctionReturn(0);
7615 }
7616 
7617 #undef __FUNCT__
7618 #define __FUNCT__ "TSComputeLinearStability"
7619 /*@
7620    TSComputeLinearStability - computes the linear stability function at a point
7621 
7622    Collective on TS and Vec
7623 
7624    Input Parameters:
7625 +  ts - the TS context
7626 -  xr,xi - real and imaginary part of input arguments
7627 
7628    Output Parameters:
7629 .  yr,yi - real and imaginary part of function value
7630 
7631    Level: developer
7632 
7633 .keywords: TS, compute
7634 
7635 .seealso: TSSetRHSFunction(), TSComputeIFunction()
7636 @*/
7637 PetscErrorCode TSComputeLinearStability(TS ts,PetscReal xr,PetscReal xi,PetscReal *yr,PetscReal *yi)
7638 {
7639   PetscErrorCode ierr;
7640 
7641   PetscFunctionBegin;
7642   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
7643   if (!ts->ops->linearstability) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Linearized stability function not provided for this method");
7644   ierr = (*ts->ops->linearstability)(ts,xr,xi,yr,yi);CHKERRQ(ierr);
7645   PetscFunctionReturn(0);
7646 }
7647 
7648 /* ------------------------------------------------------------------------*/
7649 #undef __FUNCT__
7650 #define __FUNCT__ "TSMonitorEnvelopeCtxCreate"
7651 /*@C
7652    TSMonitorEnvelopeCtxCreate - Creates a context for use with TSMonitorEnvelope()
7653 
7654    Collective on TS
7655 
7656    Input Parameters:
7657 .  ts  - the ODE solver object
7658 
7659    Output Parameter:
7660 .  ctx - the context
7661 
7662    Level: intermediate
7663 
7664 .keywords: TS, monitor, line graph, residual, seealso
7665 
7666 .seealso: TSMonitorLGTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError()
7667 
7668 @*/
7669 PetscErrorCode  TSMonitorEnvelopeCtxCreate(TS ts,TSMonitorEnvelopeCtx *ctx)
7670 {
7671   PetscErrorCode ierr;
7672 
7673   PetscFunctionBegin;
7674   ierr = PetscNew(ctx);CHKERRQ(ierr);
7675   PetscFunctionReturn(0);
7676 }
7677 
7678 #undef __FUNCT__
7679 #define __FUNCT__ "TSMonitorEnvelope"
7680 /*@C
7681    TSMonitorEnvelope - Monitors the maximum and minimum value of each component of the solution
7682 
7683    Collective on TS
7684 
7685    Input Parameters:
7686 +  ts - the TS context
7687 .  step - current time-step
7688 .  ptime - current time
7689 .  u  - current solution
7690 -  dctx - the envelope context
7691 
7692    Options Database:
7693 .  -ts_monitor_envelope
7694 
7695    Level: intermediate
7696 
7697    Notes: after a solve you can use TSMonitorEnvelopeGetBounds() to access the envelope
7698 
7699 .keywords: TS,  vector, monitor, view
7700 
7701 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxCreate()
7702 @*/
7703 PetscErrorCode  TSMonitorEnvelope(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dctx)
7704 {
7705   PetscErrorCode       ierr;
7706   TSMonitorEnvelopeCtx ctx = (TSMonitorEnvelopeCtx)dctx;
7707 
7708   PetscFunctionBegin;
7709   if (!ctx->max) {
7710     ierr = VecDuplicate(u,&ctx->max);CHKERRQ(ierr);
7711     ierr = VecDuplicate(u,&ctx->min);CHKERRQ(ierr);
7712     ierr = VecCopy(u,ctx->max);CHKERRQ(ierr);
7713     ierr = VecCopy(u,ctx->min);CHKERRQ(ierr);
7714   } else {
7715     ierr = VecPointwiseMax(ctx->max,u,ctx->max);CHKERRQ(ierr);
7716     ierr = VecPointwiseMin(ctx->min,u,ctx->min);CHKERRQ(ierr);
7717   }
7718   PetscFunctionReturn(0);
7719 }
7720 
7721 
7722 #undef __FUNCT__
7723 #define __FUNCT__ "TSMonitorEnvelopeGetBounds"
7724 /*@C
7725    TSMonitorEnvelopeGetBounds - Gets the bounds for the components of the solution
7726 
7727    Collective on TS
7728 
7729    Input Parameter:
7730 .  ts - the TS context
7731 
7732    Output Parameter:
7733 +  max - the maximum values
7734 -  min - the minimum values
7735 
7736    Notes: If the TS does not have a TSMonitorEnvelopeCtx associated with it then this function is ignored
7737 
7738    Level: intermediate
7739 
7740 .keywords: TS,  vector, monitor, view
7741 
7742 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables()
7743 @*/
7744 PetscErrorCode  TSMonitorEnvelopeGetBounds(TS ts,Vec *max,Vec *min)
7745 {
7746   PetscInt i;
7747 
7748   PetscFunctionBegin;
7749   if (max) *max = NULL;
7750   if (min) *min = NULL;
7751   for (i=0; i<ts->numbermonitors; i++) {
7752     if (ts->monitor[i] == TSMonitorEnvelope) {
7753       TSMonitorEnvelopeCtx  ctx = (TSMonitorEnvelopeCtx) ts->monitorcontext[i];
7754       if (max) *max = ctx->max;
7755       if (min) *min = ctx->min;
7756       break;
7757     }
7758   }
7759   PetscFunctionReturn(0);
7760 }
7761 
7762 #undef __FUNCT__
7763 #define __FUNCT__ "TSMonitorEnvelopeCtxDestroy"
7764 /*@C
7765    TSMonitorEnvelopeCtxDestroy - Destroys a context that was created  with TSMonitorEnvelopeCtxCreate().
7766 
7767    Collective on TSMonitorEnvelopeCtx
7768 
7769    Input Parameter:
7770 .  ctx - the monitor context
7771 
7772    Level: intermediate
7773 
7774 .keywords: TS, monitor, line graph, destroy
7775 
7776 .seealso: TSMonitorLGCtxCreate(),  TSMonitorSet(), TSMonitorLGTimeStep()
7777 @*/
7778 PetscErrorCode  TSMonitorEnvelopeCtxDestroy(TSMonitorEnvelopeCtx *ctx)
7779 {
7780   PetscErrorCode ierr;
7781 
7782   PetscFunctionBegin;
7783   ierr = VecDestroy(&(*ctx)->min);CHKERRQ(ierr);
7784   ierr = VecDestroy(&(*ctx)->max);CHKERRQ(ierr);
7785   ierr = PetscFree(*ctx);CHKERRQ(ierr);
7786   PetscFunctionReturn(0);
7787 }
7788 
7789 #undef __FUNCT__
7790 #define __FUNCT__ "TSRollBack"
7791 /*@
7792    TSRollBack - Rolls back one time step
7793 
7794    Collective on TS
7795 
7796    Input Parameter:
7797 .  ts - the TS context obtained from TSCreate()
7798 
7799    Level: advanced
7800 
7801 .keywords: TS, timestep, rollback
7802 
7803 .seealso: TSCreate(), TSSetUp(), TSDestroy(), TSSolve(), TSSetPreStep(), TSSetPreStage(), TSInterpolate()
7804 @*/
7805 PetscErrorCode  TSRollBack(TS ts)
7806 {
7807   PetscErrorCode ierr;
7808 
7809   PetscFunctionBegin;
7810   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
7811   if (ts->steprollback) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"TSRollBack already called");
7812   if (!ts->ops->rollback) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRollBack not implemented for type '%s'",((PetscObject)ts)->type_name);
7813   ierr = (*ts->ops->rollback)(ts);CHKERRQ(ierr);
7814   ts->time_step = ts->ptime - ts->ptime_prev;
7815   ts->ptime = ts->ptime_prev;
7816   ts->ptime_prev = ts->ptime_prev_rollback;
7817   ts->steps--; ts->total_steps--;
7818   ts->steprollback = PETSC_TRUE;
7819   PetscFunctionReturn(0);
7820 }
7821 
7822 #undef __FUNCT__
7823 #define __FUNCT__ "TSGetStages"
7824 /*@
7825    TSGetStages - Get the number of stages and stage values
7826 
7827    Input Parameter:
7828 .  ts - the TS context obtained from TSCreate()
7829 
7830    Level: advanced
7831 
7832 .keywords: TS, getstages
7833 
7834 .seealso: TSCreate()
7835 @*/
7836 PetscErrorCode  TSGetStages(TS ts,PetscInt *ns,Vec **Y)
7837 {
7838   PetscErrorCode ierr;
7839 
7840   PetscFunctionBegin;
7841   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
7842   PetscValidPointer(ns,2);
7843 
7844   if (!ts->ops->getstages) *ns=0;
7845   else {
7846     ierr = (*ts->ops->getstages)(ts,ns,Y);CHKERRQ(ierr);
7847   }
7848   PetscFunctionReturn(0);
7849 }
7850 
7851 #undef __FUNCT__
7852 #define __FUNCT__ "TSComputeIJacobianDefaultColor"
7853 /*@C
7854   TSComputeIJacobianDefaultColor - Computes the Jacobian using finite differences and coloring to exploit matrix sparsity.
7855 
7856   Collective on SNES
7857 
7858   Input Parameters:
7859 + ts - the TS context
7860 . t - current timestep
7861 . U - state vector
7862 . Udot - time derivative of state vector
7863 . shift - shift to apply, see note below
7864 - ctx - an optional user context
7865 
7866   Output Parameters:
7867 + J - Jacobian matrix (not altered in this routine)
7868 - B - newly computed Jacobian matrix to use with preconditioner (generally the same as J)
7869 
7870   Level: intermediate
7871 
7872   Notes:
7873   If F(t,U,Udot)=0 is the DAE, the required Jacobian is
7874 
7875   dF/dU + shift*dF/dUdot
7876 
7877   Most users should not need to explicitly call this routine, as it
7878   is used internally within the nonlinear solvers.
7879 
7880   This will first try to get the coloring from the DM.  If the DM type has no coloring
7881   routine, then it will try to get the coloring from the matrix.  This requires that the
7882   matrix have nonzero entries precomputed.
7883 
7884 .keywords: TS, finite differences, Jacobian, coloring, sparse
7885 .seealso: TSSetIJacobian(), MatFDColoringCreate(), MatFDColoringSetFunction()
7886 @*/
7887 PetscErrorCode TSComputeIJacobianDefaultColor(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat J,Mat B,void *ctx)
7888 {
7889   SNES           snes;
7890   MatFDColoring  color;
7891   PetscBool      hascolor, matcolor = PETSC_FALSE;
7892   PetscErrorCode ierr;
7893 
7894   PetscFunctionBegin;
7895   ierr = PetscOptionsGetBool(((PetscObject)ts)->options,((PetscObject) ts)->prefix, "-ts_fd_color_use_mat", &matcolor, NULL);CHKERRQ(ierr);
7896   ierr = PetscObjectQuery((PetscObject) B, "TSMatFDColoring", (PetscObject *) &color);CHKERRQ(ierr);
7897   if (!color) {
7898     DM         dm;
7899     ISColoring iscoloring;
7900 
7901     ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
7902     ierr = DMHasColoring(dm, &hascolor);CHKERRQ(ierr);
7903     if (hascolor && !matcolor) {
7904       ierr = DMCreateColoring(dm, IS_COLORING_GLOBAL, &iscoloring);CHKERRQ(ierr);
7905       ierr = MatFDColoringCreate(B, iscoloring, &color);CHKERRQ(ierr);
7906       ierr = MatFDColoringSetFunction(color, (PetscErrorCode (*)(void)) SNESTSFormFunction, (void *) ts);CHKERRQ(ierr);
7907       ierr = MatFDColoringSetFromOptions(color);CHKERRQ(ierr);
7908       ierr = MatFDColoringSetUp(B, iscoloring, color);CHKERRQ(ierr);
7909       ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
7910     } else {
7911       MatColoring mc;
7912 
7913       ierr = MatColoringCreate(B, &mc);CHKERRQ(ierr);
7914       ierr = MatColoringSetDistance(mc, 2);CHKERRQ(ierr);
7915       ierr = MatColoringSetType(mc, MATCOLORINGSL);CHKERRQ(ierr);
7916       ierr = MatColoringSetFromOptions(mc);CHKERRQ(ierr);
7917       ierr = MatColoringApply(mc, &iscoloring);CHKERRQ(ierr);
7918       ierr = MatColoringDestroy(&mc);CHKERRQ(ierr);
7919       ierr = MatFDColoringCreate(B, iscoloring, &color);CHKERRQ(ierr);
7920       ierr = MatFDColoringSetFunction(color, (PetscErrorCode (*)(void)) SNESTSFormFunction, (void *) ts);CHKERRQ(ierr);
7921       ierr = MatFDColoringSetFromOptions(color);CHKERRQ(ierr);
7922       ierr = MatFDColoringSetUp(B, iscoloring, color);CHKERRQ(ierr);
7923       ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
7924     }
7925     ierr = PetscObjectCompose((PetscObject) B, "TSMatFDColoring", (PetscObject) color);CHKERRQ(ierr);
7926     ierr = PetscObjectDereference((PetscObject) color);CHKERRQ(ierr);
7927   }
7928   ierr = TSGetSNES(ts, &snes);CHKERRQ(ierr);
7929   ierr = MatFDColoringApply(B, color, U, snes);CHKERRQ(ierr);
7930   if (J != B) {
7931     ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
7932     ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
7933   }
7934   PetscFunctionReturn(0);
7935 }
7936 
7937 #undef __FUNCT__
7938 #define __FUNCT__ "TSSetFunctionDomainError"
7939 /*@
7940     TSSetFunctionDomainError - Set the function testing if the current state vector is valid
7941 
7942     Input Parameters:
7943     ts - the TS context
7944     func - function called within TSFunctionDomainError
7945 
7946     Level: intermediate
7947 
7948 .keywords: TS, state, domain
7949 .seealso: TSAdaptCheckStage(), TSFunctionDomainError()
7950 @*/
7951 
7952 PetscErrorCode TSSetFunctionDomainError(TS ts, PetscErrorCode (*func)(TS,PetscReal,Vec,PetscBool*))
7953 {
7954   PetscFunctionBegin;
7955   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
7956   ts->functiondomainerror = func;
7957   PetscFunctionReturn(0);
7958 }
7959 
7960 #undef __FUNCT__
7961 #define __FUNCT__ "TSFunctionDomainError"
7962 /*@
7963     TSFunctionDomainError - Check if the current state is valid
7964 
7965     Input Parameters:
7966     ts - the TS context
7967     stagetime - time of the simulation
7968     Y - state vector to check.
7969 
7970     Output Parameter:
7971     accept - Set to PETSC_FALSE if the current state vector is valid.
7972 
7973     Note:
7974     This function should be used to ensure the state is in a valid part of the space.
7975     For example, one can ensure here all values are positive.
7976 
7977     Level: advanced
7978 @*/
7979 PetscErrorCode TSFunctionDomainError(TS ts,PetscReal stagetime,Vec Y,PetscBool* accept)
7980 {
7981   PetscErrorCode ierr;
7982 
7983   PetscFunctionBegin;
7984 
7985   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
7986   *accept = PETSC_TRUE;
7987   if (ts->functiondomainerror) {
7988     PetscStackCallStandard((*ts->functiondomainerror),(ts,stagetime,Y,accept));
7989   }
7990   PetscFunctionReturn(0);
7991 }
7992 
7993 #undef  __FUNCT__
7994 #define __FUNCT__ "TSClone"
7995 /*@C
7996   TSClone - This function clones a time step object.
7997 
7998   Collective on MPI_Comm
7999 
8000   Input Parameter:
8001 . tsin    - The input TS
8002 
8003   Output Parameter:
8004 . tsout   - The output TS (cloned)
8005 
8006   Notes:
8007   This function is used to create a clone of a TS object. It is used in ARKIMEX for initializing the slope for first stage explicit methods. It will likely be replaced in the future with a mechanism of switching methods on the fly.
8008 
8009   When using TSDestroy() on a clone the user has to first reset the correct TS reference in the embedded SNES object: e.g.: by running SNES snes_dup=NULL; TSGetSNES(ts,&snes_dup); ierr = TSSetSNES(ts,snes_dup);
8010 
8011   Level: developer
8012 
8013 .keywords: TS, clone
8014 .seealso: TSCreate(), TSSetType(), TSSetUp(), TSDestroy(), TSSetProblemType()
8015 @*/
8016 PetscErrorCode  TSClone(TS tsin, TS *tsout)
8017 {
8018   TS             t;
8019   PetscErrorCode ierr;
8020   SNES           snes_start;
8021   DM             dm;
8022   TSType         type;
8023 
8024   PetscFunctionBegin;
8025   PetscValidPointer(tsin,1);
8026   *tsout = NULL;
8027 
8028   ierr = PetscHeaderCreate(t, TS_CLASSID, "TS", "Time stepping", "TS", PetscObjectComm((PetscObject)tsin), TSDestroy, TSView);CHKERRQ(ierr);
8029 
8030   /* General TS description */
8031   t->numbermonitors    = 0;
8032   t->setupcalled       = 0;
8033   t->ksp_its           = 0;
8034   t->snes_its          = 0;
8035   t->nwork             = 0;
8036   t->rhsjacobian.time  = -1e20;
8037   t->rhsjacobian.scale = 1.;
8038   t->ijacobian.shift   = 1.;
8039 
8040   ierr = TSGetSNES(tsin,&snes_start);CHKERRQ(ierr);
8041   ierr = TSSetSNES(t,snes_start);CHKERRQ(ierr);
8042 
8043   ierr = TSGetDM(tsin,&dm);CHKERRQ(ierr);
8044   ierr = TSSetDM(t,dm);CHKERRQ(ierr);
8045 
8046   t->adapt = tsin->adapt;
8047   ierr = PetscObjectReference((PetscObject)t->adapt);CHKERRQ(ierr);
8048 
8049   t->problem_type      = tsin->problem_type;
8050   t->ptime             = tsin->ptime;
8051   t->time_step         = tsin->time_step;
8052   t->max_time          = tsin->max_time;
8053   t->steps             = tsin->steps;
8054   t->max_steps         = tsin->max_steps;
8055   t->equation_type     = tsin->equation_type;
8056   t->atol              = tsin->atol;
8057   t->rtol              = tsin->rtol;
8058   t->max_snes_failures = tsin->max_snes_failures;
8059   t->max_reject        = tsin->max_reject;
8060   t->errorifstepfailed = tsin->errorifstepfailed;
8061 
8062   ierr = TSGetType(tsin,&type);CHKERRQ(ierr);
8063   ierr = TSSetType(t,type);CHKERRQ(ierr);
8064 
8065   t->vec_sol           = NULL;
8066 
8067   t->cfltime          = tsin->cfltime;
8068   t->cfltime_local    = tsin->cfltime_local;
8069   t->exact_final_time = tsin->exact_final_time;
8070 
8071   ierr = PetscMemcpy(t->ops,tsin->ops,sizeof(struct _TSOps));CHKERRQ(ierr);
8072 
8073   if (((PetscObject)tsin)->fortran_func_pointers) {
8074     PetscInt i;
8075     ierr = PetscMalloc((10)*sizeof(void(*)(void)),&((PetscObject)t)->fortran_func_pointers);CHKERRQ(ierr);
8076     for (i=0; i<10; i++) {
8077       ((PetscObject)t)->fortran_func_pointers[i] = ((PetscObject)tsin)->fortran_func_pointers[i];
8078     }
8079   }
8080   *tsout = t;
8081   PetscFunctionReturn(0);
8082 }
8083