xref: /petsc/src/ts/interface/ts.c (revision 4cdd57e5d74e338dd6722c4f54249377c94f1cf6)
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   ierr = (*ts->ops->getauxsolution)(ts,v);CHKERRQ(ierr);
2311   PetscFunctionReturn(0);
2312 }
2313 
2314 #undef __FUNCT__
2315 #define __FUNCT__ "TSGetTimeError"
2316 /*@
2317    TSGetTimeError - Returns the estimated error vector, if the chosen
2318    TSType has an error estimation functionality.
2319 
2320    Not Collective, but Vec returned is parallel if TS is parallel
2321 
2322    Parameters :
2323 .  ts - the TS context obtained from TSCreate() (input parameter).
2324 .  v - the vector containing the error (same size as the solution).
2325 
2326    Level: intermediate
2327 
2328 .seealso: TSGetSolution()
2329 
2330 .keywords: TS, timestep, get, error
2331 @*/
2332 PetscErrorCode  TSGetTimeError(TS ts,Vec *v)
2333 {
2334   PetscErrorCode ierr;
2335 
2336   PetscFunctionBegin;
2337   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2338   ierr = (*ts->ops->gettimeerror)(ts,v);CHKERRQ(ierr);
2339   PetscFunctionReturn(0);
2340 }
2341 
2342 #undef __FUNCT__
2343 #define __FUNCT__ "TSGetCostGradients"
2344 /*@
2345    TSGetCostGradients - Returns the gradients from the TSAdjointSolve()
2346 
2347    Not Collective, but Vec returned is parallel if TS is parallel
2348 
2349    Input Parameter:
2350 .  ts - the TS context obtained from TSCreate()
2351 
2352    Output Parameter:
2353 +  lambda - vectors containing the gradients of the cost functions with respect to the ODE/DAE solution variables
2354 -  mu - vectors containing the gradients of the cost functions with respect to the problem parameters
2355 
2356    Level: intermediate
2357 
2358 .seealso: TSGetTimeStep()
2359 
2360 .keywords: TS, timestep, get, sensitivity
2361 @*/
2362 PetscErrorCode  TSGetCostGradients(TS ts,PetscInt *numcost,Vec **lambda,Vec **mu)
2363 {
2364   PetscFunctionBegin;
2365   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2366   if (numcost) *numcost = ts->numcost;
2367   if (lambda)  *lambda  = ts->vecs_sensi;
2368   if (mu)      *mu      = ts->vecs_sensip;
2369   PetscFunctionReturn(0);
2370 }
2371 
2372 /* ----- Routines to initialize and destroy a timestepper ---- */
2373 #undef __FUNCT__
2374 #define __FUNCT__ "TSSetProblemType"
2375 /*@
2376   TSSetProblemType - Sets the type of problem to be solved.
2377 
2378   Not collective
2379 
2380   Input Parameters:
2381 + ts   - The TS
2382 - type - One of TS_LINEAR, TS_NONLINEAR where these types refer to problems of the forms
2383 .vb
2384          U_t - A U = 0      (linear)
2385          U_t - A(t) U = 0   (linear)
2386          F(t,U,U_t) = 0     (nonlinear)
2387 .ve
2388 
2389    Level: beginner
2390 
2391 .keywords: TS, problem type
2392 .seealso: TSSetUp(), TSProblemType, TS
2393 @*/
2394 PetscErrorCode  TSSetProblemType(TS ts, TSProblemType type)
2395 {
2396   PetscErrorCode ierr;
2397 
2398   PetscFunctionBegin;
2399   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
2400   ts->problem_type = type;
2401   if (type == TS_LINEAR) {
2402     SNES snes;
2403     ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
2404     ierr = SNESSetType(snes,SNESKSPONLY);CHKERRQ(ierr);
2405   }
2406   PetscFunctionReturn(0);
2407 }
2408 
2409 #undef __FUNCT__
2410 #define __FUNCT__ "TSGetProblemType"
2411 /*@C
2412   TSGetProblemType - Gets the type of problem to be solved.
2413 
2414   Not collective
2415 
2416   Input Parameter:
2417 . ts   - The TS
2418 
2419   Output Parameter:
2420 . type - One of TS_LINEAR, TS_NONLINEAR where these types refer to problems of the forms
2421 .vb
2422          M U_t = A U
2423          M(t) U_t = A(t) U
2424          F(t,U,U_t)
2425 .ve
2426 
2427    Level: beginner
2428 
2429 .keywords: TS, problem type
2430 .seealso: TSSetUp(), TSProblemType, TS
2431 @*/
2432 PetscErrorCode  TSGetProblemType(TS ts, TSProblemType *type)
2433 {
2434   PetscFunctionBegin;
2435   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
2436   PetscValidIntPointer(type,2);
2437   *type = ts->problem_type;
2438   PetscFunctionReturn(0);
2439 }
2440 
2441 #undef __FUNCT__
2442 #define __FUNCT__ "TSSetUp"
2443 /*@
2444    TSSetUp - Sets up the internal data structures for the later use
2445    of a timestepper.
2446 
2447    Collective on TS
2448 
2449    Input Parameter:
2450 .  ts - the TS context obtained from TSCreate()
2451 
2452    Notes:
2453    For basic use of the TS solvers the user need not explicitly call
2454    TSSetUp(), since these actions will automatically occur during
2455    the call to TSStep().  However, if one wishes to control this
2456    phase separately, TSSetUp() should be called after TSCreate()
2457    and optional routines of the form TSSetXXX(), but before TSStep().
2458 
2459    Level: advanced
2460 
2461 .keywords: TS, timestep, setup
2462 
2463 .seealso: TSCreate(), TSStep(), TSDestroy()
2464 @*/
2465 PetscErrorCode  TSSetUp(TS ts)
2466 {
2467   PetscErrorCode ierr;
2468   DM             dm;
2469   PetscErrorCode (*func)(SNES,Vec,Vec,void*);
2470   PetscErrorCode (*jac)(SNES,Vec,Mat,Mat,void*);
2471   TSIFunction    ifun;
2472   TSIJacobian    ijac;
2473   TSI2Jacobian   i2jac;
2474   TSRHSJacobian  rhsjac;
2475 
2476   PetscFunctionBegin;
2477   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2478   if (ts->setupcalled) PetscFunctionReturn(0);
2479 
2480   ts->total_steps = 0;
2481   if (!((PetscObject)ts)->type_name) {
2482     ierr = TSGetIFunction(ts,NULL,&ifun,NULL);CHKERRQ(ierr);
2483     ierr = TSSetType(ts,ifun ? TSBEULER : TSEULER);CHKERRQ(ierr);
2484   }
2485 
2486   if (!ts->vec_sol) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetSolution() first");
2487 
2488   if (ts->rhsjacobian.reuse) {
2489     Mat Amat,Pmat;
2490     SNES snes;
2491     ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
2492     ierr = SNESGetJacobian(snes,&Amat,&Pmat,NULL,NULL);CHKERRQ(ierr);
2493     /* Matching matrices implies that an IJacobian is NOT set, because if it had been set, the IJacobian's matrix would
2494      * have displaced the RHS matrix */
2495     if (Amat == ts->Arhs) {
2496       ierr = MatDuplicate(ts->Arhs,MAT_DO_NOT_COPY_VALUES,&Amat);CHKERRQ(ierr);
2497       ierr = SNESSetJacobian(snes,Amat,NULL,NULL,NULL);CHKERRQ(ierr);
2498       ierr = MatDestroy(&Amat);CHKERRQ(ierr);
2499     }
2500     if (Pmat == ts->Brhs) {
2501       ierr = MatDuplicate(ts->Brhs,MAT_DO_NOT_COPY_VALUES,&Pmat);CHKERRQ(ierr);
2502       ierr = SNESSetJacobian(snes,NULL,Pmat,NULL,NULL);CHKERRQ(ierr);
2503       ierr = MatDestroy(&Pmat);CHKERRQ(ierr);
2504     }
2505   }
2506   if (ts->ops->setup) {
2507     ierr = (*ts->ops->setup)(ts);CHKERRQ(ierr);
2508   }
2509 
2510   /* In the case where we've set a DMTSFunction or what have you, we need the default SNESFunction
2511      to be set right but can't do it elsewhere due to the overreliance on ctx=ts.
2512    */
2513   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
2514   ierr = DMSNESGetFunction(dm,&func,NULL);CHKERRQ(ierr);
2515   if (!func) {
2516     ierr = DMSNESSetFunction(dm,SNESTSFormFunction,ts);CHKERRQ(ierr);
2517   }
2518   /* If the SNES doesn't have a jacobian set and the TS has an ijacobian or rhsjacobian set, set the SNES to use it.
2519      Otherwise, the SNES will use coloring internally to form the Jacobian.
2520    */
2521   ierr = DMSNESGetJacobian(dm,&jac,NULL);CHKERRQ(ierr);
2522   ierr = DMTSGetIJacobian(dm,&ijac,NULL);CHKERRQ(ierr);
2523   ierr = DMTSGetI2Jacobian(dm,&i2jac,NULL);CHKERRQ(ierr);
2524   ierr = DMTSGetRHSJacobian(dm,&rhsjac,NULL);CHKERRQ(ierr);
2525   if (!jac && (ijac || i2jac || rhsjac)) {
2526     ierr = DMSNESSetJacobian(dm,SNESTSFormJacobian,ts);CHKERRQ(ierr);
2527   }
2528 
2529   /* if time integration scheme has a starting method, call it */
2530   if (ts->ops->startingmethod) {
2531     ierr = (*ts->ops->startingmethod)(ts);CHKERRQ(ierr);
2532   }
2533 
2534   ts->setupcalled = PETSC_TRUE;
2535   PetscFunctionReturn(0);
2536 }
2537 
2538 #undef __FUNCT__
2539 #define __FUNCT__ "TSAdjointSetUp"
2540 /*@
2541    TSAdjointSetUp - Sets up the internal data structures for the later use
2542    of an adjoint solver
2543 
2544    Collective on TS
2545 
2546    Input Parameter:
2547 .  ts - the TS context obtained from TSCreate()
2548 
2549    Level: advanced
2550 
2551 .keywords: TS, timestep, setup
2552 
2553 .seealso: TSCreate(), TSAdjointStep(), TSSetCostGradients()
2554 @*/
2555 PetscErrorCode  TSAdjointSetUp(TS ts)
2556 {
2557   PetscErrorCode ierr;
2558 
2559   PetscFunctionBegin;
2560   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2561   if (ts->adjointsetupcalled) PetscFunctionReturn(0);
2562   if (!ts->vecs_sensi) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetCostGradients() first");
2563 
2564   if (ts->vec_costintegral) { /* if there is integral in the cost function*/
2565     ierr = VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&ts->vecs_drdy);CHKERRQ(ierr);
2566     if (ts->vecs_sensip){
2567       ierr = VecDuplicateVecs(ts->vecs_sensip[0],ts->numcost,&ts->vecs_drdp);CHKERRQ(ierr);
2568     }
2569   }
2570 
2571   if (ts->ops->adjointsetup) {
2572     ierr = (*ts->ops->adjointsetup)(ts);CHKERRQ(ierr);
2573   }
2574   ts->adjointsetupcalled = PETSC_TRUE;
2575   PetscFunctionReturn(0);
2576 }
2577 
2578 #undef __FUNCT__
2579 #define __FUNCT__ "TSReset"
2580 /*@
2581    TSReset - Resets a TS context and removes any allocated Vecs and Mats.
2582 
2583    Collective on TS
2584 
2585    Input Parameter:
2586 .  ts - the TS context obtained from TSCreate()
2587 
2588    Level: beginner
2589 
2590 .keywords: TS, timestep, reset
2591 
2592 .seealso: TSCreate(), TSSetup(), TSDestroy()
2593 @*/
2594 PetscErrorCode  TSReset(TS ts)
2595 {
2596   PetscErrorCode ierr;
2597 
2598   PetscFunctionBegin;
2599   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2600 
2601   if (ts->ops->reset) {
2602     ierr = (*ts->ops->reset)(ts);CHKERRQ(ierr);
2603   }
2604   if (ts->snes) {ierr = SNESReset(ts->snes);CHKERRQ(ierr);}
2605   if (ts->adapt) {ierr = TSAdaptReset(ts->adapt);CHKERRQ(ierr);}
2606 
2607   ierr = MatDestroy(&ts->Arhs);CHKERRQ(ierr);
2608   ierr = MatDestroy(&ts->Brhs);CHKERRQ(ierr);
2609   ierr = VecDestroy(&ts->Frhs);CHKERRQ(ierr);
2610   ierr = VecDestroy(&ts->vec_sol);CHKERRQ(ierr);
2611   ierr = VecDestroy(&ts->vec_dot);CHKERRQ(ierr);
2612   ierr = VecDestroy(&ts->vatol);CHKERRQ(ierr);
2613   ierr = VecDestroy(&ts->vrtol);CHKERRQ(ierr);
2614   ierr = VecDestroyVecs(ts->nwork,&ts->work);CHKERRQ(ierr);
2615 
2616  if (ts->vec_costintegral) {
2617     ierr = VecDestroyVecs(ts->numcost,&ts->vecs_drdy);CHKERRQ(ierr);
2618     if (ts->vecs_drdp){
2619       ierr = VecDestroyVecs(ts->numcost,&ts->vecs_drdp);CHKERRQ(ierr);
2620     }
2621   }
2622   ts->vecs_sensi  = NULL;
2623   ts->vecs_sensip = NULL;
2624   ierr = MatDestroy(&ts->Jacp);CHKERRQ(ierr);
2625   ierr = VecDestroy(&ts->vec_costintegral);CHKERRQ(ierr);
2626   ierr = VecDestroy(&ts->vec_costintegrand);CHKERRQ(ierr);
2627   ts->setupcalled = PETSC_FALSE;
2628   PetscFunctionReturn(0);
2629 }
2630 
2631 #undef __FUNCT__
2632 #define __FUNCT__ "TSDestroy"
2633 /*@
2634    TSDestroy - Destroys the timestepper context that was created
2635    with TSCreate().
2636 
2637    Collective on TS
2638 
2639    Input Parameter:
2640 .  ts - the TS context obtained from TSCreate()
2641 
2642    Level: beginner
2643 
2644 .keywords: TS, timestepper, destroy
2645 
2646 .seealso: TSCreate(), TSSetUp(), TSSolve()
2647 @*/
2648 PetscErrorCode  TSDestroy(TS *ts)
2649 {
2650   PetscErrorCode ierr;
2651 
2652   PetscFunctionBegin;
2653   if (!*ts) PetscFunctionReturn(0);
2654   PetscValidHeaderSpecific((*ts),TS_CLASSID,1);
2655   if (--((PetscObject)(*ts))->refct > 0) {*ts = 0; PetscFunctionReturn(0);}
2656 
2657   ierr = TSReset((*ts));CHKERRQ(ierr);
2658 
2659   /* if memory was published with SAWs then destroy it */
2660   ierr = PetscObjectSAWsViewOff((PetscObject)*ts);CHKERRQ(ierr);
2661   if ((*ts)->ops->destroy) {ierr = (*(*ts)->ops->destroy)((*ts));CHKERRQ(ierr);}
2662 
2663   ierr = TSTrajectoryDestroy(&(*ts)->trajectory);CHKERRQ(ierr);
2664 
2665   ierr = TSAdaptDestroy(&(*ts)->adapt);CHKERRQ(ierr);
2666   ierr = TSEventDestroy(&(*ts)->event);CHKERRQ(ierr);
2667 
2668   ierr = SNESDestroy(&(*ts)->snes);CHKERRQ(ierr);
2669   ierr = DMDestroy(&(*ts)->dm);CHKERRQ(ierr);
2670   ierr = TSMonitorCancel((*ts));CHKERRQ(ierr);
2671   ierr = TSAdjointMonitorCancel((*ts));CHKERRQ(ierr);
2672 
2673   ierr = PetscHeaderDestroy(ts);CHKERRQ(ierr);
2674   PetscFunctionReturn(0);
2675 }
2676 
2677 #undef __FUNCT__
2678 #define __FUNCT__ "TSGetSNES"
2679 /*@
2680    TSGetSNES - Returns the SNES (nonlinear solver) associated with
2681    a TS (timestepper) context. Valid only for nonlinear problems.
2682 
2683    Not Collective, but SNES is parallel if TS is parallel
2684 
2685    Input Parameter:
2686 .  ts - the TS context obtained from TSCreate()
2687 
2688    Output Parameter:
2689 .  snes - the nonlinear solver context
2690 
2691    Notes:
2692    The user can then directly manipulate the SNES context to set various
2693    options, etc.  Likewise, the user can then extract and manipulate the
2694    KSP, KSP, and PC contexts as well.
2695 
2696    TSGetSNES() does not work for integrators that do not use SNES; in
2697    this case TSGetSNES() returns NULL in snes.
2698 
2699    Level: beginner
2700 
2701 .keywords: timestep, get, SNES
2702 @*/
2703 PetscErrorCode  TSGetSNES(TS ts,SNES *snes)
2704 {
2705   PetscErrorCode ierr;
2706 
2707   PetscFunctionBegin;
2708   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2709   PetscValidPointer(snes,2);
2710   if (!ts->snes) {
2711     ierr = SNESCreate(PetscObjectComm((PetscObject)ts),&ts->snes);CHKERRQ(ierr);
2712     ierr = SNESSetFunction(ts->snes,NULL,SNESTSFormFunction,ts);CHKERRQ(ierr);
2713     ierr = PetscLogObjectParent((PetscObject)ts,(PetscObject)ts->snes);CHKERRQ(ierr);
2714     ierr = PetscObjectIncrementTabLevel((PetscObject)ts->snes,(PetscObject)ts,1);CHKERRQ(ierr);
2715     if (ts->dm) {ierr = SNESSetDM(ts->snes,ts->dm);CHKERRQ(ierr);}
2716     if (ts->problem_type == TS_LINEAR) {
2717       ierr = SNESSetType(ts->snes,SNESKSPONLY);CHKERRQ(ierr);
2718     }
2719   }
2720   *snes = ts->snes;
2721   PetscFunctionReturn(0);
2722 }
2723 
2724 #undef __FUNCT__
2725 #define __FUNCT__ "TSSetSNES"
2726 /*@
2727    TSSetSNES - Set the SNES (nonlinear solver) to be used by the timestepping context
2728 
2729    Collective
2730 
2731    Input Parameter:
2732 +  ts - the TS context obtained from TSCreate()
2733 -  snes - the nonlinear solver context
2734 
2735    Notes:
2736    Most users should have the TS created by calling TSGetSNES()
2737 
2738    Level: developer
2739 
2740 .keywords: timestep, set, SNES
2741 @*/
2742 PetscErrorCode TSSetSNES(TS ts,SNES snes)
2743 {
2744   PetscErrorCode ierr;
2745   PetscErrorCode (*func)(SNES,Vec,Mat,Mat,void*);
2746 
2747   PetscFunctionBegin;
2748   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2749   PetscValidHeaderSpecific(snes,SNES_CLASSID,2);
2750   ierr = PetscObjectReference((PetscObject)snes);CHKERRQ(ierr);
2751   ierr = SNESDestroy(&ts->snes);CHKERRQ(ierr);
2752 
2753   ts->snes = snes;
2754 
2755   ierr = SNESSetFunction(ts->snes,NULL,SNESTSFormFunction,ts);CHKERRQ(ierr);
2756   ierr = SNESGetJacobian(ts->snes,NULL,NULL,&func,NULL);CHKERRQ(ierr);
2757   if (func == SNESTSFormJacobian) {
2758     ierr = SNESSetJacobian(ts->snes,NULL,NULL,SNESTSFormJacobian,ts);CHKERRQ(ierr);
2759   }
2760   PetscFunctionReturn(0);
2761 }
2762 
2763 #undef __FUNCT__
2764 #define __FUNCT__ "TSGetKSP"
2765 /*@
2766    TSGetKSP - Returns the KSP (linear solver) associated with
2767    a TS (timestepper) context.
2768 
2769    Not Collective, but KSP is parallel if TS is parallel
2770 
2771    Input Parameter:
2772 .  ts - the TS context obtained from TSCreate()
2773 
2774    Output Parameter:
2775 .  ksp - the nonlinear solver context
2776 
2777    Notes:
2778    The user can then directly manipulate the KSP context to set various
2779    options, etc.  Likewise, the user can then extract and manipulate the
2780    KSP and PC contexts as well.
2781 
2782    TSGetKSP() does not work for integrators that do not use KSP;
2783    in this case TSGetKSP() returns NULL in ksp.
2784 
2785    Level: beginner
2786 
2787 .keywords: timestep, get, KSP
2788 @*/
2789 PetscErrorCode  TSGetKSP(TS ts,KSP *ksp)
2790 {
2791   PetscErrorCode ierr;
2792   SNES           snes;
2793 
2794   PetscFunctionBegin;
2795   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2796   PetscValidPointer(ksp,2);
2797   if (!((PetscObject)ts)->type_name) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"KSP is not created yet. Call TSSetType() first");
2798   if (ts->problem_type != TS_LINEAR) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Linear only; use TSGetSNES()");
2799   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
2800   ierr = SNESGetKSP(snes,ksp);CHKERRQ(ierr);
2801   PetscFunctionReturn(0);
2802 }
2803 
2804 /* ----------- Routines to set solver parameters ---------- */
2805 
2806 #undef __FUNCT__
2807 #define __FUNCT__ "TSGetDuration"
2808 /*@
2809    TSGetDuration - Gets the maximum number of timesteps to use and
2810    maximum time for iteration.
2811 
2812    Not Collective
2813 
2814    Input Parameters:
2815 +  ts       - the TS context obtained from TSCreate()
2816 .  maxsteps - maximum number of iterations to use, or NULL
2817 -  maxtime  - final time to iterate to, or NULL
2818 
2819    Level: intermediate
2820 
2821 .keywords: TS, timestep, get, maximum, iterations, time
2822 @*/
2823 PetscErrorCode  TSGetDuration(TS ts, PetscInt *maxsteps, PetscReal *maxtime)
2824 {
2825   PetscFunctionBegin;
2826   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
2827   if (maxsteps) {
2828     PetscValidIntPointer(maxsteps,2);
2829     *maxsteps = ts->max_steps;
2830   }
2831   if (maxtime) {
2832     PetscValidScalarPointer(maxtime,3);
2833     *maxtime = ts->max_time;
2834   }
2835   PetscFunctionReturn(0);
2836 }
2837 
2838 #undef __FUNCT__
2839 #define __FUNCT__ "TSSetDuration"
2840 /*@
2841    TSSetDuration - Sets the maximum number of timesteps to use and
2842    maximum time for iteration.
2843 
2844    Logically Collective on TS
2845 
2846    Input Parameters:
2847 +  ts - the TS context obtained from TSCreate()
2848 .  maxsteps - maximum number of iterations to use
2849 -  maxtime - final time to iterate to
2850 
2851    Options Database Keys:
2852 .  -ts_max_steps <maxsteps> - Sets maxsteps
2853 .  -ts_final_time <maxtime> - Sets maxtime
2854 
2855    Notes:
2856    The default maximum number of iterations is 5000. Default time is 5.0
2857 
2858    Level: intermediate
2859 
2860 .keywords: TS, timestep, set, maximum, iterations
2861 
2862 .seealso: TSSetExactFinalTime()
2863 @*/
2864 PetscErrorCode  TSSetDuration(TS ts,PetscInt maxsteps,PetscReal maxtime)
2865 {
2866   PetscFunctionBegin;
2867   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2868   PetscValidLogicalCollectiveInt(ts,maxsteps,2);
2869   PetscValidLogicalCollectiveReal(ts,maxtime,2);
2870   if (maxsteps >= 0) ts->max_steps = maxsteps;
2871   if (maxtime != PETSC_DEFAULT) ts->max_time = maxtime;
2872   PetscFunctionReturn(0);
2873 }
2874 
2875 #undef __FUNCT__
2876 #define __FUNCT__ "TSSetSolution"
2877 /*@
2878    TSSetSolution - Sets the initial solution vector
2879    for use by the TS routines.
2880 
2881    Logically Collective on TS and Vec
2882 
2883    Input Parameters:
2884 +  ts - the TS context obtained from TSCreate()
2885 -  u - the solution vector
2886 
2887    Level: beginner
2888 
2889 .keywords: TS, timestep, set, solution, initial conditions
2890 @*/
2891 PetscErrorCode  TSSetSolution(TS ts,Vec u)
2892 {
2893   PetscErrorCode ierr;
2894   DM             dm;
2895 
2896   PetscFunctionBegin;
2897   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2898   PetscValidHeaderSpecific(u,VEC_CLASSID,2);
2899   ierr = PetscObjectReference((PetscObject)u);CHKERRQ(ierr);
2900   ierr = VecDestroy(&ts->vec_sol);CHKERRQ(ierr);
2901   ts->vec_sol = u;
2902 
2903   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
2904   ierr = DMShellSetGlobalVector(dm,u);CHKERRQ(ierr);
2905   PetscFunctionReturn(0);
2906 }
2907 
2908 #undef __FUNCT__
2909 #define __FUNCT__ "TSAdjointSetSteps"
2910 /*@
2911    TSAdjointSetSteps - Sets the number of steps the adjoint solver should take backward in time
2912 
2913    Logically Collective on TS
2914 
2915    Input Parameters:
2916 +  ts - the TS context obtained from TSCreate()
2917 .  steps - number of steps to use
2918 
2919    Level: intermediate
2920 
2921    Notes: Normally one does not call this and TSAdjointSolve() integrates back to the original timestep. One can call this
2922           so as to integrate back to less than the original timestep
2923 
2924 .keywords: TS, timestep, set, maximum, iterations
2925 
2926 .seealso: TSSetExactFinalTime()
2927 @*/
2928 PetscErrorCode  TSAdjointSetSteps(TS ts,PetscInt steps)
2929 {
2930   PetscFunctionBegin;
2931   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2932   PetscValidLogicalCollectiveInt(ts,steps,2);
2933   if (steps < 0) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Cannot step back a negative number of steps");
2934   if (steps > ts->total_steps) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Cannot step back more than the total number of forward steps");
2935   ts->adjoint_max_steps = steps;
2936   PetscFunctionReturn(0);
2937 }
2938 
2939 #undef __FUNCT__
2940 #define __FUNCT__ "TSSetCostGradients"
2941 /*@
2942    TSSetCostGradients - Sets the initial value of the gradients of the cost function w.r.t. initial conditions and w.r.t. the problem parameters
2943       for use by the TSAdjoint routines.
2944 
2945    Logically Collective on TS and Vec
2946 
2947    Input Parameters:
2948 +  ts - the TS context obtained from TSCreate()
2949 .  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
2950 -  mu - gradients with respect to the parameters, the number of entries in these vectors is the same as the number of parameters
2951 
2952    Level: beginner
2953 
2954    Notes: the entries in these vectors must be correctly initialized with the values lamda_i = df/dy|finaltime  mu_i = df/dp|finaltime
2955 
2956 .keywords: TS, timestep, set, sensitivity, initial conditions
2957 @*/
2958 PetscErrorCode  TSSetCostGradients(TS ts,PetscInt numcost,Vec *lambda,Vec *mu)
2959 {
2960   PetscFunctionBegin;
2961   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2962   PetscValidPointer(lambda,2);
2963   ts->vecs_sensi  = lambda;
2964   ts->vecs_sensip = mu;
2965   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");
2966   ts->numcost  = numcost;
2967   PetscFunctionReturn(0);
2968 }
2969 
2970 #undef __FUNCT__
2971 #define __FUNCT__ "TSAdjointSetRHSJacobian"
2972 /*@C
2973   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.
2974 
2975   Logically Collective on TS
2976 
2977   Input Parameters:
2978 + ts   - The TS context obtained from TSCreate()
2979 - func - The function
2980 
2981   Calling sequence of func:
2982 $ func (TS ts,PetscReal t,Vec y,Mat A,void *ctx);
2983 +   t - current timestep
2984 .   y - input vector (current ODE solution)
2985 .   A - output matrix
2986 -   ctx - [optional] user-defined function context
2987 
2988   Level: intermediate
2989 
2990   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
2991 
2992 .keywords: TS, sensitivity
2993 .seealso:
2994 @*/
2995 PetscErrorCode  TSAdjointSetRHSJacobian(TS ts,Mat Amat,PetscErrorCode (*func)(TS,PetscReal,Vec,Mat,void*),void *ctx)
2996 {
2997   PetscErrorCode ierr;
2998 
2999   PetscFunctionBegin;
3000   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3001   if (Amat) PetscValidHeaderSpecific(Amat,MAT_CLASSID,2);
3002 
3003   ts->rhsjacobianp    = func;
3004   ts->rhsjacobianpctx = ctx;
3005   if(Amat) {
3006     ierr = PetscObjectReference((PetscObject)Amat);CHKERRQ(ierr);
3007     ierr = MatDestroy(&ts->Jacp);CHKERRQ(ierr);
3008     ts->Jacp = Amat;
3009   }
3010   PetscFunctionReturn(0);
3011 }
3012 
3013 #undef __FUNCT__
3014 #define __FUNCT__ "TSAdjointComputeRHSJacobian"
3015 /*@C
3016   TSAdjointComputeRHSJacobian - Runs the user-defined Jacobian function.
3017 
3018   Collective on TS
3019 
3020   Input Parameters:
3021 . ts   - The TS context obtained from TSCreate()
3022 
3023   Level: developer
3024 
3025 .keywords: TS, sensitivity
3026 .seealso: TSAdjointSetRHSJacobian()
3027 @*/
3028 PetscErrorCode  TSAdjointComputeRHSJacobian(TS ts,PetscReal t,Vec X,Mat Amat)
3029 {
3030   PetscErrorCode ierr;
3031 
3032   PetscFunctionBegin;
3033   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3034   PetscValidHeaderSpecific(X,VEC_CLASSID,3);
3035   PetscValidPointer(Amat,4);
3036 
3037   PetscStackPush("TS user JacobianP function for sensitivity analysis");
3038   ierr = (*ts->rhsjacobianp)(ts,t,X,Amat,ts->rhsjacobianpctx); CHKERRQ(ierr);
3039   PetscStackPop;
3040   PetscFunctionReturn(0);
3041 }
3042 
3043 #undef __FUNCT__
3044 #define __FUNCT__ "TSSetCostIntegrand"
3045 /*@C
3046     TSSetCostIntegrand - Sets the routine for evaluating the integral term in one or more cost functions
3047 
3048     Logically Collective on TS
3049 
3050     Input Parameters:
3051 +   ts - the TS context obtained from TSCreate()
3052 .   numcost - number of gradients to be computed, this is the number of cost functions
3053 .   rf - routine for evaluating the integrand function
3054 .   drdyf - function that computes the gradients of the r's with respect to y,NULL if not a function y
3055 .   drdpf - function that computes the gradients of the r's with respect to p, NULL if not a function of p
3056 .   fwd - flag indicating whether to evaluate cost integral in the forward run or the adjoint run
3057 -   ctx - [optional] user-defined context for private data for the function evaluation routine (may be NULL)
3058 
3059     Calling sequence of rf:
3060 $     rf(TS ts,PetscReal t,Vec y,Vec f[],void *ctx);
3061 
3062 +   t - current timestep
3063 .   y - input vector
3064 .   f - function result; one vector entry for each cost function
3065 -   ctx - [optional] user-defined function context
3066 
3067    Calling sequence of drdyf:
3068 $    PetscErroCode drdyf(TS ts,PetscReal t,Vec y,Vec *drdy,void *ctx);
3069 
3070    Calling sequence of drdpf:
3071 $    PetscErroCode drdpf(TS ts,PetscReal t,Vec y,Vec *drdp,void *ctx);
3072 
3073     Level: intermediate
3074 
3075     Notes: For optimization there is generally a single cost function, numcost = 1. For sensitivities there may be multiple cost functions
3076 
3077 .keywords: TS, sensitivity analysis, timestep, set, quadrature, function
3078 
3079 .seealso: TSAdjointSetRHSJacobian(),TSGetCostGradients(), TSSetCostGradients()
3080 @*/
3081 PetscErrorCode  TSSetCostIntegrand(TS ts,PetscInt numcost,PetscErrorCode (*rf)(TS,PetscReal,Vec,Vec,void*),
3082                                                           PetscErrorCode (*drdyf)(TS,PetscReal,Vec,Vec*,void*),
3083                                                           PetscErrorCode (*drdpf)(TS,PetscReal,Vec,Vec*,void*),
3084                                                           PetscBool fwd,void *ctx)
3085 {
3086   PetscErrorCode ierr;
3087 
3088   PetscFunctionBegin;
3089   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3090   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()");
3091   if (!ts->numcost) ts->numcost=numcost;
3092 
3093   ts->costintegralfwd  = fwd; /* Evaluate the cost integral in forward run if fwd is true */
3094   ierr                 = VecCreateSeq(PETSC_COMM_SELF,numcost,&ts->vec_costintegral);CHKERRQ(ierr);
3095   ierr                 = VecDuplicate(ts->vec_costintegral,&ts->vec_costintegrand);CHKERRQ(ierr);
3096   ts->costintegrand    = rf;
3097   ts->costintegrandctx = ctx;
3098   ts->drdyfunction     = drdyf;
3099   ts->drdpfunction     = drdpf;
3100   PetscFunctionReturn(0);
3101 }
3102 
3103 #undef __FUNCT__
3104 #define __FUNCT__ "TSGetCostIntegral"
3105 /*@
3106    TSGetCostIntegral - Returns the values of the integral term in the cost functions.
3107    It is valid to call the routine after a backward run.
3108 
3109    Not Collective
3110 
3111    Input Parameter:
3112 .  ts - the TS context obtained from TSCreate()
3113 
3114    Output Parameter:
3115 .  v - the vector containing the integrals for each cost function
3116 
3117    Level: intermediate
3118 
3119 .seealso: TSSetCostIntegrand()
3120 
3121 .keywords: TS, sensitivity analysis
3122 @*/
3123 PetscErrorCode  TSGetCostIntegral(TS ts,Vec *v)
3124 {
3125   PetscFunctionBegin;
3126   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3127   PetscValidPointer(v,2);
3128   *v = ts->vec_costintegral;
3129   PetscFunctionReturn(0);
3130 }
3131 
3132 #undef __FUNCT__
3133 #define __FUNCT__ "TSAdjointComputeCostIntegrand"
3134 /*@
3135    TSAdjointComputeCostIntegrand - Evaluates the integral function in the cost functions.
3136 
3137    Input Parameters:
3138 +  ts - the TS context
3139 .  t - current time
3140 -  y - state vector, i.e. current solution
3141 
3142    Output Parameter:
3143 .  q - vector of size numcost to hold the outputs
3144 
3145    Note:
3146    Most users should not need to explicitly call this routine, as it
3147    is used internally within the sensitivity analysis context.
3148 
3149    Level: developer
3150 
3151 .keywords: TS, compute
3152 
3153 .seealso: TSSetCostIntegrand()
3154 @*/
3155 PetscErrorCode TSAdjointComputeCostIntegrand(TS ts,PetscReal t,Vec y,Vec q)
3156 {
3157   PetscErrorCode ierr;
3158 
3159   PetscFunctionBegin;
3160   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3161   PetscValidHeaderSpecific(y,VEC_CLASSID,3);
3162   PetscValidHeaderSpecific(q,VEC_CLASSID,4);
3163 
3164   ierr = PetscLogEventBegin(TS_FunctionEval,ts,y,q,0);CHKERRQ(ierr);
3165   if (ts->costintegrand) {
3166     PetscStackPush("TS user integrand in the cost function");
3167     ierr = (*ts->costintegrand)(ts,t,y,q,ts->costintegrandctx);CHKERRQ(ierr);
3168     PetscStackPop;
3169   } else {
3170     ierr = VecZeroEntries(q);CHKERRQ(ierr);
3171   }
3172 
3173   ierr = PetscLogEventEnd(TS_FunctionEval,ts,y,q,0);CHKERRQ(ierr);
3174   PetscFunctionReturn(0);
3175 }
3176 
3177 #undef __FUNCT__
3178 #define __FUNCT__ "TSAdjointComputeDRDYFunction"
3179 /*@
3180   TSAdjointComputeDRDYFunction - Runs the user-defined DRDY function.
3181 
3182   Collective on TS
3183 
3184   Input Parameters:
3185 . ts   - The TS context obtained from TSCreate()
3186 
3187   Notes:
3188   TSAdjointComputeDRDYFunction() is typically used for sensitivity implementation,
3189   so most users would not generally call this routine themselves.
3190 
3191   Level: developer
3192 
3193 .keywords: TS, sensitivity
3194 .seealso: TSAdjointComputeDRDYFunction()
3195 @*/
3196 PetscErrorCode  TSAdjointComputeDRDYFunction(TS ts,PetscReal t,Vec y,Vec *drdy)
3197 {
3198   PetscErrorCode ierr;
3199 
3200   PetscFunctionBegin;
3201   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3202   PetscValidHeaderSpecific(y,VEC_CLASSID,3);
3203 
3204   PetscStackPush("TS user DRDY function for sensitivity analysis");
3205   ierr = (*ts->drdyfunction)(ts,t,y,drdy,ts->costintegrandctx); CHKERRQ(ierr);
3206   PetscStackPop;
3207   PetscFunctionReturn(0);
3208 }
3209 
3210 #undef __FUNCT__
3211 #define __FUNCT__ "TSAdjointComputeDRDPFunction"
3212 /*@
3213   TSAdjointComputeDRDPFunction - Runs the user-defined DRDP function.
3214 
3215   Collective on TS
3216 
3217   Input Parameters:
3218 . ts   - The TS context obtained from TSCreate()
3219 
3220   Notes:
3221   TSDRDPFunction() is typically used for sensitivity implementation,
3222   so most users would not generally call this routine themselves.
3223 
3224   Level: developer
3225 
3226 .keywords: TS, sensitivity
3227 .seealso: TSAdjointSetDRDPFunction()
3228 @*/
3229 PetscErrorCode  TSAdjointComputeDRDPFunction(TS ts,PetscReal t,Vec y,Vec *drdp)
3230 {
3231   PetscErrorCode ierr;
3232 
3233   PetscFunctionBegin;
3234   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3235   PetscValidHeaderSpecific(y,VEC_CLASSID,3);
3236 
3237   PetscStackPush("TS user DRDP function for sensitivity analysis");
3238   ierr = (*ts->drdpfunction)(ts,t,y,drdp,ts->costintegrandctx); CHKERRQ(ierr);
3239   PetscStackPop;
3240   PetscFunctionReturn(0);
3241 }
3242 
3243 #undef __FUNCT__
3244 #define __FUNCT__ "TSSetPreStep"
3245 /*@C
3246   TSSetPreStep - Sets the general-purpose function
3247   called once at the beginning of each time step.
3248 
3249   Logically Collective on TS
3250 
3251   Input Parameters:
3252 + ts   - The TS context obtained from TSCreate()
3253 - func - The function
3254 
3255   Calling sequence of func:
3256 . func (TS ts);
3257 
3258   Level: intermediate
3259 
3260   Note:
3261   If a step is rejected, TSStep() will call this routine again before each attempt.
3262   The last completed time step number can be queried using TSGetTimeStepNumber(), the
3263   size of the step being attempted can be obtained using TSGetTimeStep().
3264 
3265 .keywords: TS, timestep
3266 .seealso: TSSetPreStage(), TSSetPostStage(), TSSetPostStep(), TSStep()
3267 @*/
3268 PetscErrorCode  TSSetPreStep(TS ts, PetscErrorCode (*func)(TS))
3269 {
3270   PetscFunctionBegin;
3271   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3272   ts->prestep = func;
3273   PetscFunctionReturn(0);
3274 }
3275 
3276 #undef __FUNCT__
3277 #define __FUNCT__ "TSPreStep"
3278 /*@
3279   TSPreStep - Runs the user-defined pre-step function.
3280 
3281   Collective on TS
3282 
3283   Input Parameters:
3284 . ts   - The TS context obtained from TSCreate()
3285 
3286   Notes:
3287   TSPreStep() is typically used within time stepping implementations,
3288   so most users would not generally call this routine themselves.
3289 
3290   Level: developer
3291 
3292 .keywords: TS, timestep
3293 .seealso: TSSetPreStep(), TSPreStage(), TSPostStage(), TSPostStep()
3294 @*/
3295 PetscErrorCode  TSPreStep(TS ts)
3296 {
3297   PetscErrorCode ierr;
3298 
3299   PetscFunctionBegin;
3300   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3301   if (ts->prestep) {
3302     PetscStackCallStandard((*ts->prestep),(ts));
3303   }
3304   PetscFunctionReturn(0);
3305 }
3306 
3307 #undef __FUNCT__
3308 #define __FUNCT__ "TSSetPreStage"
3309 /*@C
3310   TSSetPreStage - Sets the general-purpose function
3311   called once at the beginning of each stage.
3312 
3313   Logically Collective on TS
3314 
3315   Input Parameters:
3316 + ts   - The TS context obtained from TSCreate()
3317 - func - The function
3318 
3319   Calling sequence of func:
3320 . PetscErrorCode func(TS ts, PetscReal stagetime);
3321 
3322   Level: intermediate
3323 
3324   Note:
3325   There may be several stages per time step. If the solve for a given stage fails, the step may be rejected and retried.
3326   The time step number being computed can be queried using TSGetTimeStepNumber() and the total size of the step being
3327   attempted can be obtained using TSGetTimeStep(). The time at the start of the step is available via TSGetTime().
3328 
3329 .keywords: TS, timestep
3330 .seealso: TSSetPostStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
3331 @*/
3332 PetscErrorCode  TSSetPreStage(TS ts, PetscErrorCode (*func)(TS,PetscReal))
3333 {
3334   PetscFunctionBegin;
3335   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3336   ts->prestage = func;
3337   PetscFunctionReturn(0);
3338 }
3339 
3340 #undef __FUNCT__
3341 #define __FUNCT__ "TSSetPostStage"
3342 /*@C
3343   TSSetPostStage - Sets the general-purpose function
3344   called once at the end of each stage.
3345 
3346   Logically Collective on TS
3347 
3348   Input Parameters:
3349 + ts   - The TS context obtained from TSCreate()
3350 - func - The function
3351 
3352   Calling sequence of func:
3353 . PetscErrorCode func(TS ts, PetscReal stagetime, PetscInt stageindex, Vec* Y);
3354 
3355   Level: intermediate
3356 
3357   Note:
3358   There may be several stages per time step. If the solve for a given stage fails, the step may be rejected and retried.
3359   The time step number being computed can be queried using TSGetTimeStepNumber() and the total size of the step being
3360   attempted can be obtained using TSGetTimeStep(). The time at the start of the step is available via TSGetTime().
3361 
3362 .keywords: TS, timestep
3363 .seealso: TSSetPreStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
3364 @*/
3365 PetscErrorCode  TSSetPostStage(TS ts, PetscErrorCode (*func)(TS,PetscReal,PetscInt,Vec*))
3366 {
3367   PetscFunctionBegin;
3368   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3369   ts->poststage = func;
3370   PetscFunctionReturn(0);
3371 }
3372 
3373 #undef __FUNCT__
3374 #define __FUNCT__ "TSSetPostEvaluate"
3375 /*@C
3376   TSSetPostEvaluate - Sets the general-purpose function
3377   called once at the end of each step evaluation.
3378 
3379   Logically Collective on TS
3380 
3381   Input Parameters:
3382 + ts   - The TS context obtained from TSCreate()
3383 - func - The function
3384 
3385   Calling sequence of func:
3386 . PetscErrorCode func(TS ts);
3387 
3388   Level: intermediate
3389 
3390   Note:
3391   Semantically, TSSetPostEvaluate() differs from TSSetPostStep() since the function it sets is called before event-handling
3392   thus guaranteeing the same solution (computed by the time-stepper) will be passed to it. On the other hand, TSPostStep()
3393   may be passed a different solution, possibly changed by the event handler. TSPostEvaluate() is called after the next step
3394   solution is evaluated allowing to modify it, if need be. The solution can be obtained with TSGetSolution(), the time step
3395   with TSGetTimeStep(), and the time at the start of the step is available via TSGetTime()
3396 
3397 .keywords: TS, timestep
3398 .seealso: TSSetPreStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
3399 @*/
3400 PetscErrorCode  TSSetPostEvaluate(TS ts, PetscErrorCode (*func)(TS))
3401 {
3402   PetscFunctionBegin;
3403   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3404   ts->postevaluate = func;
3405   PetscFunctionReturn(0);
3406 }
3407 
3408 #undef __FUNCT__
3409 #define __FUNCT__ "TSPreStage"
3410 /*@
3411   TSPreStage - Runs the user-defined pre-stage function set using TSSetPreStage()
3412 
3413   Collective on TS
3414 
3415   Input Parameters:
3416 . ts          - The TS context obtained from TSCreate()
3417   stagetime   - The absolute time of the current stage
3418 
3419   Notes:
3420   TSPreStage() is typically used within time stepping implementations,
3421   most users would not generally call this routine themselves.
3422 
3423   Level: developer
3424 
3425 .keywords: TS, timestep
3426 .seealso: TSPostStage(), TSSetPreStep(), TSPreStep(), TSPostStep()
3427 @*/
3428 PetscErrorCode  TSPreStage(TS ts, PetscReal stagetime)
3429 {
3430   PetscErrorCode ierr;
3431 
3432   PetscFunctionBegin;
3433   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3434   if (ts->prestage) {
3435     PetscStackCallStandard((*ts->prestage),(ts,stagetime));
3436   }
3437   PetscFunctionReturn(0);
3438 }
3439 
3440 #undef __FUNCT__
3441 #define __FUNCT__ "TSPostStage"
3442 /*@
3443   TSPostStage - Runs the user-defined post-stage function set using TSSetPostStage()
3444 
3445   Collective on TS
3446 
3447   Input Parameters:
3448 . ts          - The TS context obtained from TSCreate()
3449   stagetime   - The absolute time of the current stage
3450   stageindex  - Stage number
3451   Y           - Array of vectors (of size = total number
3452                 of stages) with the stage solutions
3453 
3454   Notes:
3455   TSPostStage() is typically used within time stepping implementations,
3456   most users would not generally call this routine themselves.
3457 
3458   Level: developer
3459 
3460 .keywords: TS, timestep
3461 .seealso: TSPreStage(), TSSetPreStep(), TSPreStep(), TSPostStep()
3462 @*/
3463 PetscErrorCode  TSPostStage(TS ts, PetscReal stagetime, PetscInt stageindex, Vec *Y)
3464 {
3465   PetscErrorCode ierr;
3466 
3467   PetscFunctionBegin;
3468   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3469   if (ts->poststage) {
3470     PetscStackCallStandard((*ts->poststage),(ts,stagetime,stageindex,Y));
3471   }
3472   PetscFunctionReturn(0);
3473 }
3474 
3475 #undef __FUNCT__
3476 #define __FUNCT__ "TSPostEvaluate"
3477 /*@
3478   TSPostEvaluate - Runs the user-defined post-evaluate function set using TSSetPostEvaluate()
3479 
3480   Collective on TS
3481 
3482   Input Parameters:
3483 . ts          - The TS context obtained from TSCreate()
3484 
3485   Notes:
3486   TSPostEvaluate() is typically used within time stepping implementations,
3487   most users would not generally call this routine themselves.
3488 
3489   Level: developer
3490 
3491 .keywords: TS, timestep
3492 .seealso: TSSetPostEvaluate(), TSSetPreStep(), TSPreStep(), TSPostStep()
3493 @*/
3494 PetscErrorCode  TSPostEvaluate(TS ts)
3495 {
3496   PetscErrorCode ierr;
3497 
3498   PetscFunctionBegin;
3499   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3500   if (ts->postevaluate) {
3501     PetscStackCallStandard((*ts->postevaluate),(ts));
3502   }
3503   PetscFunctionReturn(0);
3504 }
3505 
3506 #undef __FUNCT__
3507 #define __FUNCT__ "TSSetPostStep"
3508 /*@C
3509   TSSetPostStep - Sets the general-purpose function
3510   called once at the end of each time step.
3511 
3512   Logically Collective on TS
3513 
3514   Input Parameters:
3515 + ts   - The TS context obtained from TSCreate()
3516 - func - The function
3517 
3518   Calling sequence of func:
3519 $ func (TS ts);
3520 
3521   Notes:
3522   The function set by TSSetPostStep() is called after each successful step. The solution vector X
3523   obtained by TSGetSolution() may be different than that computed at the step end if the event handler
3524   locates an event and TSPostEvent() modifies it. Use TSSetPostEvaluate() if an unmodified solution is needed instead.
3525 
3526   Level: intermediate
3527 
3528 .keywords: TS, timestep
3529 .seealso: TSSetPreStep(), TSSetPreStage(), TSSetPostEvaluate(), TSGetTimeStep(), TSGetTimeStepNumber(), TSGetTime()
3530 @*/
3531 PetscErrorCode  TSSetPostStep(TS ts, PetscErrorCode (*func)(TS))
3532 {
3533   PetscFunctionBegin;
3534   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3535   ts->poststep = func;
3536   PetscFunctionReturn(0);
3537 }
3538 
3539 #undef __FUNCT__
3540 #define __FUNCT__ "TSPostStep"
3541 /*@
3542   TSPostStep - Runs the user-defined post-step function.
3543 
3544   Collective on TS
3545 
3546   Input Parameters:
3547 . ts   - The TS context obtained from TSCreate()
3548 
3549   Notes:
3550   TSPostStep() is typically used within time stepping implementations,
3551   so most users would not generally call this routine themselves.
3552 
3553   Level: developer
3554 
3555 .keywords: TS, timestep
3556 @*/
3557 PetscErrorCode  TSPostStep(TS ts)
3558 {
3559   PetscErrorCode ierr;
3560 
3561   PetscFunctionBegin;
3562   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3563   if (ts->poststep) {
3564     PetscStackCallStandard((*ts->poststep),(ts));
3565   }
3566   PetscFunctionReturn(0);
3567 }
3568 
3569 /* ------------ Routines to set performance monitoring options ----------- */
3570 
3571 #undef __FUNCT__
3572 #define __FUNCT__ "TSMonitorSet"
3573 /*@C
3574    TSMonitorSet - Sets an ADDITIONAL function that is to be used at every
3575    timestep to display the iteration's  progress.
3576 
3577    Logically Collective on TS
3578 
3579    Input Parameters:
3580 +  ts - the TS context obtained from TSCreate()
3581 .  monitor - monitoring routine
3582 .  mctx - [optional] user-defined context for private data for the
3583              monitor routine (use NULL if no context is desired)
3584 -  monitordestroy - [optional] routine that frees monitor context
3585           (may be NULL)
3586 
3587    Calling sequence of monitor:
3588 $    int monitor(TS ts,PetscInt steps,PetscReal time,Vec u,void *mctx)
3589 
3590 +    ts - the TS context
3591 .    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)
3592 .    time - current time
3593 .    u - current iterate
3594 -    mctx - [optional] monitoring context
3595 
3596    Notes:
3597    This routine adds an additional monitor to the list of monitors that
3598    already has been loaded.
3599 
3600    Fortran notes: Only a single monitor function can be set for each TS object
3601 
3602    Level: intermediate
3603 
3604 .keywords: TS, timestep, set, monitor
3605 
3606 .seealso: TSMonitorDefault(), TSMonitorCancel()
3607 @*/
3608 PetscErrorCode  TSMonitorSet(TS ts,PetscErrorCode (*monitor)(TS,PetscInt,PetscReal,Vec,void*),void *mctx,PetscErrorCode (*mdestroy)(void**))
3609 {
3610   PetscErrorCode ierr;
3611   PetscInt       i;
3612   PetscBool      identical;
3613 
3614   PetscFunctionBegin;
3615   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3616   for (i=0; i<ts->numbermonitors;i++) {
3617     ierr = PetscMonitorCompare((PetscErrorCode (*)(void))monitor,mctx,mdestroy,(PetscErrorCode (*)(void))ts->monitor[i],ts->monitorcontext[i],ts->monitordestroy[i],&identical);CHKERRQ(ierr);
3618     if (identical) PetscFunctionReturn(0);
3619   }
3620   if (ts->numbermonitors >= MAXTSMONITORS) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many monitors set");
3621   ts->monitor[ts->numbermonitors]          = monitor;
3622   ts->monitordestroy[ts->numbermonitors]   = mdestroy;
3623   ts->monitorcontext[ts->numbermonitors++] = (void*)mctx;
3624   PetscFunctionReturn(0);
3625 }
3626 
3627 #undef __FUNCT__
3628 #define __FUNCT__ "TSMonitorCancel"
3629 /*@C
3630    TSMonitorCancel - Clears all the monitors that have been set on a time-step object.
3631 
3632    Logically Collective on TS
3633 
3634    Input Parameters:
3635 .  ts - the TS context obtained from TSCreate()
3636 
3637    Notes:
3638    There is no way to remove a single, specific monitor.
3639 
3640    Level: intermediate
3641 
3642 .keywords: TS, timestep, set, monitor
3643 
3644 .seealso: TSMonitorDefault(), TSMonitorSet()
3645 @*/
3646 PetscErrorCode  TSMonitorCancel(TS ts)
3647 {
3648   PetscErrorCode ierr;
3649   PetscInt       i;
3650 
3651   PetscFunctionBegin;
3652   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3653   for (i=0; i<ts->numbermonitors; i++) {
3654     if (ts->monitordestroy[i]) {
3655       ierr = (*ts->monitordestroy[i])(&ts->monitorcontext[i]);CHKERRQ(ierr);
3656     }
3657   }
3658   ts->numbermonitors = 0;
3659   PetscFunctionReturn(0);
3660 }
3661 
3662 #undef __FUNCT__
3663 #define __FUNCT__ "TSMonitorDefault"
3664 /*@C
3665    TSMonitorDefault - The Default monitor, prints the timestep and time for each step
3666 
3667    Level: intermediate
3668 
3669 .keywords: TS, set, monitor
3670 
3671 .seealso:  TSMonitorSet()
3672 @*/
3673 PetscErrorCode TSMonitorDefault(TS ts,PetscInt step,PetscReal ptime,Vec v,PetscViewerAndFormat *vf)
3674 {
3675   PetscErrorCode ierr;
3676   PetscViewer    viewer =  vf->viewer;
3677   PetscBool      iascii,ibinary;
3678 
3679   PetscFunctionBegin;
3680   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
3681   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
3682   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&ibinary);CHKERRQ(ierr);
3683   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
3684   if (iascii) {
3685     ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3686     if (step == -1){ /* this indicates it is an interpolated solution */
3687       ierr = PetscViewerASCIIPrintf(viewer,"Interpolated solution at time %g between steps %D and %D\n",(double)ptime,ts->steps-1,ts->steps);CHKERRQ(ierr);
3688     } else {
3689       ierr = PetscViewerASCIIPrintf(viewer,"%D TS dt %g time %g%s",step,(double)ts->time_step,(double)ptime,ts->steprollback ? " (r)\n" : "\n");CHKERRQ(ierr);
3690     }
3691     ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3692   } else if (ibinary) {
3693     PetscMPIInt rank;
3694     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)viewer),&rank);CHKERRQ(ierr);
3695     if (!rank) {
3696       PetscBool skipHeader;
3697       PetscInt  classid = REAL_FILE_CLASSID;
3698 
3699       ierr = PetscViewerBinaryGetSkipHeader(viewer,&skipHeader);CHKERRQ(ierr);
3700       if (!skipHeader) {
3701          ierr = PetscViewerBinaryWrite(viewer,&classid,1,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
3702        }
3703       ierr = PetscRealView(1,&ptime,viewer);CHKERRQ(ierr);
3704     } else {
3705       ierr = PetscRealView(0,&ptime,viewer);CHKERRQ(ierr);
3706     }
3707   }
3708   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
3709   PetscFunctionReturn(0);
3710 }
3711 
3712 #undef __FUNCT__
3713 #define __FUNCT__ "TSAdjointMonitorSet"
3714 /*@C
3715    TSAdjointMonitorSet - Sets an ADDITIONAL function that is to be used at every
3716    timestep to display the iteration's  progress.
3717 
3718    Logically Collective on TS
3719 
3720    Input Parameters:
3721 +  ts - the TS context obtained from TSCreate()
3722 .  adjointmonitor - monitoring routine
3723 .  adjointmctx - [optional] user-defined context for private data for the
3724              monitor routine (use NULL if no context is desired)
3725 -  adjointmonitordestroy - [optional] routine that frees monitor context
3726           (may be NULL)
3727 
3728    Calling sequence of monitor:
3729 $    int adjointmonitor(TS ts,PetscInt steps,PetscReal time,Vec u,PetscInt numcost,Vec *lambda, Vec *mu,void *adjointmctx)
3730 
3731 +    ts - the TS context
3732 .    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
3733                                been interpolated to)
3734 .    time - current time
3735 .    u - current iterate
3736 .    numcost - number of cost functionos
3737 .    lambda - sensitivities to initial conditions
3738 .    mu - sensitivities to parameters
3739 -    adjointmctx - [optional] adjoint monitoring context
3740 
3741    Notes:
3742    This routine adds an additional monitor to the list of monitors that
3743    already has been loaded.
3744 
3745    Fortran notes: Only a single monitor function can be set for each TS object
3746 
3747    Level: intermediate
3748 
3749 .keywords: TS, timestep, set, adjoint, monitor
3750 
3751 .seealso: TSAdjointMonitorCancel()
3752 @*/
3753 PetscErrorCode  TSAdjointMonitorSet(TS ts,PetscErrorCode (*adjointmonitor)(TS,PetscInt,PetscReal,Vec,PetscInt,Vec*,Vec*,void*),void *adjointmctx,PetscErrorCode (*adjointmdestroy)(void**))
3754 {
3755   PetscErrorCode ierr;
3756   PetscInt       i;
3757   PetscBool      identical;
3758 
3759   PetscFunctionBegin;
3760   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3761   for (i=0; i<ts->numbermonitors;i++) {
3762     ierr = PetscMonitorCompare((PetscErrorCode (*)(void))adjointmonitor,adjointmctx,adjointmdestroy,(PetscErrorCode (*)(void))ts->adjointmonitor[i],ts->adjointmonitorcontext[i],ts->adjointmonitordestroy[i],&identical);CHKERRQ(ierr);
3763     if (identical) PetscFunctionReturn(0);
3764   }
3765   if (ts->numberadjointmonitors >= MAXTSMONITORS) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many adjoint monitors set");
3766   ts->adjointmonitor[ts->numberadjointmonitors]          = adjointmonitor;
3767   ts->adjointmonitordestroy[ts->numberadjointmonitors]   = adjointmdestroy;
3768   ts->adjointmonitorcontext[ts->numberadjointmonitors++] = (void*)adjointmctx;
3769   PetscFunctionReturn(0);
3770 }
3771 
3772 #undef __FUNCT__
3773 #define __FUNCT__ "TSAdjointMonitorCancel"
3774 /*@C
3775    TSAdjointMonitorCancel - Clears all the adjoint monitors that have been set on a time-step object.
3776 
3777    Logically Collective on TS
3778 
3779    Input Parameters:
3780 .  ts - the TS context obtained from TSCreate()
3781 
3782    Notes:
3783    There is no way to remove a single, specific monitor.
3784 
3785    Level: intermediate
3786 
3787 .keywords: TS, timestep, set, adjoint, monitor
3788 
3789 .seealso: TSAdjointMonitorSet()
3790 @*/
3791 PetscErrorCode  TSAdjointMonitorCancel(TS ts)
3792 {
3793   PetscErrorCode ierr;
3794   PetscInt       i;
3795 
3796   PetscFunctionBegin;
3797   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3798   for (i=0; i<ts->numberadjointmonitors; i++) {
3799     if (ts->adjointmonitordestroy[i]) {
3800       ierr = (*ts->adjointmonitordestroy[i])(&ts->adjointmonitorcontext[i]);CHKERRQ(ierr);
3801     }
3802   }
3803   ts->numberadjointmonitors = 0;
3804   PetscFunctionReturn(0);
3805 }
3806 
3807 #undef __FUNCT__
3808 #define __FUNCT__ "TSAdjointMonitorDefault"
3809 /*@C
3810    TSAdjointMonitorDefault - the default monitor of adjoint computations
3811 
3812    Level: intermediate
3813 
3814 .keywords: TS, set, monitor
3815 
3816 .seealso: TSAdjointMonitorSet()
3817 @*/
3818 PetscErrorCode TSAdjointMonitorDefault(TS ts,PetscInt step,PetscReal ptime,Vec v,PetscInt numcost,Vec *lambda,Vec *mu,PetscViewerAndFormat *vf)
3819 {
3820   PetscErrorCode ierr;
3821   PetscViewer    viewer = vf->viewer;
3822 
3823   PetscFunctionBegin;
3824   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
3825   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
3826   ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3827   ierr = PetscViewerASCIIPrintf(viewer,"%D TS dt %g time %g%s",step,(double)ts->time_step,(double)ptime,ts->steprollback ? " (r)\n" : "\n");CHKERRQ(ierr);
3828   ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3829   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
3830   PetscFunctionReturn(0);
3831 }
3832 
3833 #undef __FUNCT__
3834 #define __FUNCT__ "TSInterpolate"
3835 /*@
3836    TSInterpolate - Interpolate the solution computed during the previous step to an arbitrary location in the interval
3837 
3838    Collective on TS
3839 
3840    Input Argument:
3841 +  ts - time stepping context
3842 -  t - time to interpolate to
3843 
3844    Output Argument:
3845 .  U - state at given time
3846 
3847    Level: intermediate
3848 
3849    Developer Notes:
3850    TSInterpolate() and the storing of previous steps/stages should be generalized to support delay differential equations and continuous adjoints.
3851 
3852 .keywords: TS, set
3853 
3854 .seealso: TSSetExactFinalTime(), TSSolve()
3855 @*/
3856 PetscErrorCode TSInterpolate(TS ts,PetscReal t,Vec U)
3857 {
3858   PetscErrorCode ierr;
3859 
3860   PetscFunctionBegin;
3861   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3862   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
3863   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);
3864   if (!ts->ops->interpolate) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"%s does not provide interpolation",((PetscObject)ts)->type_name);
3865   ierr = (*ts->ops->interpolate)(ts,t,U);CHKERRQ(ierr);
3866   PetscFunctionReturn(0);
3867 }
3868 
3869 #undef __FUNCT__
3870 #define __FUNCT__ "TSStep"
3871 /*@
3872    TSStep - Steps one time step
3873 
3874    Collective on TS
3875 
3876    Input Parameter:
3877 .  ts - the TS context obtained from TSCreate()
3878 
3879    Level: developer
3880 
3881    Notes:
3882    The public interface for the ODE/DAE solvers is TSSolve(), you should almost for sure be using that routine and not this routine.
3883 
3884    The hook set using TSSetPreStep() is called before each attempt to take the step. In general, the time step size may
3885    be changed due to adaptive error controller or solve failures. Note that steps may contain multiple stages.
3886 
3887    This may over-step the final time provided in TSSetDuration() depending on the time-step used. TSSolve() interpolates to exactly the
3888    time provided in TSSetDuration(). One can use TSInterpolate() to determine an interpolated solution within the final timestep.
3889 
3890 .keywords: TS, timestep, solve
3891 
3892 .seealso: TSCreate(), TSSetUp(), TSDestroy(), TSSolve(), TSSetPreStep(), TSSetPreStage(), TSSetPostStage(), TSInterpolate()
3893 @*/
3894 PetscErrorCode  TSStep(TS ts)
3895 {
3896   PetscErrorCode   ierr;
3897   static PetscBool cite = PETSC_FALSE;
3898   PetscReal        ptime;
3899 
3900   PetscFunctionBegin;
3901   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3902   ierr = PetscCitationsRegister("@techreport{tspaper,\n"
3903                                 "  title       = {{PETSc/TS}: A Modern Scalable {DAE/ODE} Solver Library},\n"
3904                                 "  author      = {Shrirang Abhyankar and Jed Brown and Emil Constantinescu and Debojyoti Ghosh and Barry F. Smith},\n"
3905                                 "  type        = {Preprint},\n"
3906                                 "  number      = {ANL/MCS-P5061-0114},\n"
3907                                 "  institution = {Argonne National Laboratory},\n"
3908                                 "  year        = {2014}\n}\n",&cite);CHKERRQ(ierr);
3909 
3910   ierr = TSSetUp(ts);CHKERRQ(ierr);
3911   ierr = TSTrajectorySetUp(ts->trajectory,ts);CHKERRQ(ierr);
3912 
3913   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()");
3914   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");
3915 
3916   if (!ts->steps) ts->ptime_prev = ts->ptime;
3917   ts->reason = TS_CONVERGED_ITERATING;
3918   ptime = ts->ptime; ts->ptime_prev_rollback = ts->ptime_prev;
3919   if (!ts->ops->step) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSStep not implemented for type '%s'",((PetscObject)ts)->type_name);
3920   ierr = PetscLogEventBegin(TS_Step,ts,0,0,0);CHKERRQ(ierr);
3921   ierr = (*ts->ops->step)(ts);CHKERRQ(ierr);
3922   ierr = PetscLogEventEnd(TS_Step,ts,0,0,0);CHKERRQ(ierr);
3923   ts->ptime_prev = ptime;
3924   ts->steps++; ts->total_steps++;
3925   ts->steprollback = PETSC_FALSE;
3926   ts->steprestart  = PETSC_FALSE;
3927 
3928   if (ts->reason < 0) {
3929     if (ts->errorifstepfailed) {
3930       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]);
3931       else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s",TSConvergedReasons[ts->reason]);
3932     }
3933   } else if (!ts->reason) {
3934     if (ts->steps >= ts->max_steps)     ts->reason = TS_CONVERGED_ITS;
3935     else if (ts->ptime >= ts->max_time) ts->reason = TS_CONVERGED_TIME;
3936   }
3937   PetscFunctionReturn(0);
3938 }
3939 
3940 #undef __FUNCT__
3941 #define __FUNCT__ "TSAdjointStep"
3942 /*@
3943    TSAdjointStep - Steps one time step backward in the adjoint run
3944 
3945    Collective on TS
3946 
3947    Input Parameter:
3948 .  ts - the TS context obtained from TSCreate()
3949 
3950    Level: intermediate
3951 
3952 .keywords: TS, adjoint, step
3953 
3954 .seealso: TSAdjointSetUp(), TSAdjointSolve()
3955 @*/
3956 PetscErrorCode  TSAdjointStep(TS ts)
3957 {
3958   DM               dm;
3959   PetscErrorCode   ierr;
3960 
3961   PetscFunctionBegin;
3962   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3963   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
3964   ierr = TSAdjointSetUp(ts);CHKERRQ(ierr);
3965 
3966   ierr = VecViewFromOptions(ts->vec_sol,(PetscObject)ts,"-ts_view_solution");CHKERRQ(ierr);
3967 
3968   ts->reason = TS_CONVERGED_ITERATING;
3969   ts->ptime_prev = ts->ptime;
3970   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);
3971   ierr = PetscLogEventBegin(TS_AdjointStep,ts,0,0,0);CHKERRQ(ierr);
3972   ierr = (*ts->ops->adjointstep)(ts);CHKERRQ(ierr);
3973   ierr = PetscLogEventEnd(TS_AdjointStep,ts,0,0,0);CHKERRQ(ierr);
3974   ts->steps++; ts->total_steps--;
3975 
3976   if (ts->reason < 0) {
3977     if (ts->errorifstepfailed) {
3978       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]);
3979       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]);
3980       else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s",TSConvergedReasons[ts->reason]);
3981     }
3982   } else if (!ts->reason) {
3983     if (ts->steps >= ts->adjoint_max_steps) ts->reason = TS_CONVERGED_ITS;
3984   }
3985   PetscFunctionReturn(0);
3986 }
3987 
3988 #undef __FUNCT__
3989 #define __FUNCT__ "TSEvaluateWLTE"
3990 /*@
3991    TSEvaluateWLTE - Evaluate the weighted local truncation error norm
3992    at the end of a time step with a given order of accuracy.
3993 
3994    Collective on TS
3995 
3996    Input Arguments:
3997 +  ts - time stepping context
3998 .  wnormtype - norm type, either NORM_2 or NORM_INFINITY
3999 -  order - optional, desired order for the error evaluation or PETSC_DECIDE
4000 
4001    Output Arguments:
4002 +  order - optional, the actual order of the error evaluation
4003 -  wlte - the weighted local truncation error norm
4004 
4005    Level: advanced
4006 
4007    Notes:
4008    If the timestepper cannot evaluate the error in a particular step
4009    (eg. in the first step or restart steps after event handling),
4010    this routine returns wlte=-1.0 .
4011 
4012 .seealso: TSStep(), TSAdapt, TSErrorWeightedNorm()
4013 @*/
4014 PetscErrorCode TSEvaluateWLTE(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
4015 {
4016   PetscErrorCode ierr;
4017 
4018   PetscFunctionBegin;
4019   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4020   PetscValidType(ts,1);
4021   PetscValidLogicalCollectiveEnum(ts,wnormtype,4);
4022   if (order) PetscValidIntPointer(order,3);
4023   if (order) PetscValidLogicalCollectiveInt(ts,*order,3);
4024   PetscValidRealPointer(wlte,4);
4025   if (wnormtype != NORM_2 && wnormtype != NORM_INFINITY) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
4026   if (!ts->ops->evaluatewlte) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSEvaluateWLTE not implemented for type '%s'",((PetscObject)ts)->type_name);
4027   ierr = (*ts->ops->evaluatewlte)(ts,wnormtype,order,wlte);CHKERRQ(ierr);
4028   PetscFunctionReturn(0);
4029 }
4030 
4031 #undef __FUNCT__
4032 #define __FUNCT__ "TSEvaluateStep"
4033 /*@
4034    TSEvaluateStep - Evaluate the solution at the end of a time step with a given order of accuracy.
4035 
4036    Collective on TS
4037 
4038    Input Arguments:
4039 +  ts - time stepping context
4040 .  order - desired order of accuracy
4041 -  done - whether the step was evaluated at this order (pass NULL to generate an error if not available)
4042 
4043    Output Arguments:
4044 .  U - state at the end of the current step
4045 
4046    Level: advanced
4047 
4048    Notes:
4049    This function cannot be called until all stages have been evaluated.
4050    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.
4051 
4052 .seealso: TSStep(), TSAdapt
4053 @*/
4054 PetscErrorCode TSEvaluateStep(TS ts,PetscInt order,Vec U,PetscBool *done)
4055 {
4056   PetscErrorCode ierr;
4057 
4058   PetscFunctionBegin;
4059   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4060   PetscValidType(ts,1);
4061   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
4062   if (!ts->ops->evaluatestep) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSEvaluateStep not implemented for type '%s'",((PetscObject)ts)->type_name);
4063   ierr = (*ts->ops->evaluatestep)(ts,order,U,done);CHKERRQ(ierr);
4064   PetscFunctionReturn(0);
4065 }
4066 
4067 #undef __FUNCT__
4068 #define __FUNCT__ "TSForwardCostIntegral"
4069 /*@
4070  TSForwardCostIntegral - Evaluate the cost integral in the forward run.
4071 
4072  Collective on TS
4073 
4074  Input Arguments:
4075  .  ts - time stepping context
4076 
4077  Level: advanced
4078 
4079  Notes:
4080  This function cannot be called until TSStep() has been completed.
4081 
4082  .seealso: TSSolve(), TSAdjointCostIntegral()
4083  @*/
4084 PetscErrorCode TSForwardCostIntegral(TS ts)
4085 {
4086     PetscErrorCode ierr;
4087     PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4088     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);
4089     ierr = (*ts->ops->forwardintegral)(ts);CHKERRQ(ierr);
4090     PetscFunctionReturn(0);
4091 }
4092 
4093 #undef __FUNCT__
4094 #define __FUNCT__ "TSSolve"
4095 /*@
4096    TSSolve - Steps the requested number of timesteps.
4097 
4098    Collective on TS
4099 
4100    Input Parameter:
4101 +  ts - the TS context obtained from TSCreate()
4102 -  u - the solution vector  (can be null if TSSetSolution() was used and TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP) was not used,
4103                              otherwise must contain the initial conditions and will contain the solution at the final requested time
4104 
4105    Level: beginner
4106 
4107    Notes:
4108    The final time returned by this function may be different from the time of the internally
4109    held state accessible by TSGetSolution() and TSGetTime() because the method may have
4110    stepped over the final time.
4111 
4112 .keywords: TS, timestep, solve
4113 
4114 .seealso: TSCreate(), TSSetSolution(), TSStep(), TSGetTime(), TSGetSolveTime()
4115 @*/
4116 PetscErrorCode TSSolve(TS ts,Vec u)
4117 {
4118   Vec               solution;
4119   PetscErrorCode    ierr;
4120 
4121   PetscFunctionBegin;
4122   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4123   if (u) PetscValidHeaderSpecific(u,VEC_CLASSID,2);
4124 
4125   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 */
4126     PetscValidHeaderSpecific(u,VEC_CLASSID,2);
4127     if (!ts->vec_sol || u == ts->vec_sol) {
4128       ierr = VecDuplicate(u,&solution);CHKERRQ(ierr);
4129       ierr = TSSetSolution(ts,solution);CHKERRQ(ierr);
4130       ierr = VecDestroy(&solution);CHKERRQ(ierr); /* grant ownership */
4131     }
4132     ierr = VecCopy(u,ts->vec_sol);CHKERRQ(ierr);
4133   } else if (u) {
4134     ierr = TSSetSolution(ts,u);CHKERRQ(ierr);
4135   }
4136   ierr = TSSetUp(ts);CHKERRQ(ierr);
4137   ierr = TSTrajectorySetUp(ts->trajectory,ts);CHKERRQ(ierr);
4138 
4139   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()");
4140   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");
4141 
4142   /* reset time step and iteration counters */
4143   ts->steps             = 0;
4144   ts->ksp_its           = 0;
4145   ts->snes_its          = 0;
4146   ts->num_snes_failures = 0;
4147   ts->reject            = 0;
4148   ts->reason            = TS_CONVERGED_ITERATING;
4149 
4150   ierr = TSViewFromOptions(ts,NULL,"-ts_view_pre");CHKERRQ(ierr);
4151 
4152   if (ts->ops->solve) { /* This private interface is transitional and should be removed when all implementations are updated. */
4153     ierr = (*ts->ops->solve)(ts);CHKERRQ(ierr);
4154     if (u) {ierr = VecCopy(ts->vec_sol,u);CHKERRQ(ierr);}
4155     ts->solvetime = ts->ptime;
4156     solution = ts->vec_sol;
4157   } else { /* Step the requested number of timesteps. */
4158     if (ts->steps >= ts->max_steps)     ts->reason = TS_CONVERGED_ITS;
4159     else if (ts->ptime >= ts->max_time) ts->reason = TS_CONVERGED_TIME;
4160     ierr = TSTrajectorySet(ts->trajectory,ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4161     ierr = TSEventInitialize(ts->event,ts,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4162     ts->steprollback = PETSC_FALSE;
4163     ts->steprestart  = PETSC_TRUE;
4164 
4165     while (!ts->reason) {
4166       ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4167       if (!ts->steprollback) {
4168         ierr = TSPreStep(ts);CHKERRQ(ierr);
4169       }
4170       ierr = TSStep(ts);CHKERRQ(ierr);
4171       if (ts->vec_costintegral && ts->costintegralfwd) { /* Must evaluate the cost integral before event is handled. The cost integral value can also be rolled back. */
4172         ierr = TSForwardCostIntegral(ts);CHKERRQ(ierr);
4173       }
4174       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. */
4175       if (!ts->steprollback) {
4176         ierr = TSTrajectorySet(ts->trajectory,ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4177         ierr = TSPostStep(ts);CHKERRQ(ierr);
4178       }
4179     }
4180     ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4181 
4182     if (ts->exact_final_time == TS_EXACTFINALTIME_INTERPOLATE && ts->ptime > ts->max_time) {
4183       ierr = TSInterpolate(ts,ts->max_time,u);CHKERRQ(ierr);
4184       ts->solvetime = ts->max_time;
4185       solution = u;
4186       ierr = TSMonitor(ts,-1,ts->solvetime,solution);CHKERRQ(ierr);
4187     } else {
4188       if (u) {ierr = VecCopy(ts->vec_sol,u);CHKERRQ(ierr);}
4189       ts->solvetime = ts->ptime;
4190       solution = ts->vec_sol;
4191     }
4192   }
4193 
4194   ierr = TSViewFromOptions(ts,NULL,"-ts_view");CHKERRQ(ierr);
4195   ierr = VecViewFromOptions(solution,NULL,"-ts_view_solution");CHKERRQ(ierr);
4196   ierr = PetscObjectSAWsBlock((PetscObject)ts);CHKERRQ(ierr);
4197   if (ts->adjoint_solve) {
4198     ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
4199   }
4200   PetscFunctionReturn(0);
4201 }
4202 
4203 #undef __FUNCT__
4204 #define __FUNCT__ "TSAdjointCostIntegral"
4205 /*@
4206  TSAdjointCostIntegral - Evaluate the cost integral in the adjoint run.
4207 
4208  Collective on TS
4209 
4210  Input Arguments:
4211  .  ts - time stepping context
4212 
4213  Level: advanced
4214 
4215  Notes:
4216  This function cannot be called until TSAdjointStep() has been completed.
4217 
4218  .seealso: TSAdjointSolve(), TSAdjointStep
4219  @*/
4220 PetscErrorCode TSAdjointCostIntegral(TS ts)
4221 {
4222     PetscErrorCode ierr;
4223     PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4224     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);
4225     ierr = (*ts->ops->adjointintegral)(ts);CHKERRQ(ierr);
4226     PetscFunctionReturn(0);
4227 }
4228 
4229 #undef __FUNCT__
4230 #define __FUNCT__ "TSAdjointSolve"
4231 /*@
4232    TSAdjointSolve - Solves the discrete ajoint problem for an ODE/DAE
4233 
4234    Collective on TS
4235 
4236    Input Parameter:
4237 .  ts - the TS context obtained from TSCreate()
4238 
4239    Options Database:
4240 . -ts_adjoint_view_solution <viewerinfo> - views the first gradient with respect to the initial conditions
4241 
4242    Level: intermediate
4243 
4244    Notes:
4245    This must be called after a call to TSSolve() that solves the forward problem
4246 
4247    By default this will integrate back to the initial time, one can use TSAdjointSetSteps() to step back to a later time
4248 
4249 .keywords: TS, timestep, solve
4250 
4251 .seealso: TSCreate(), TSSetCostGradients(), TSSetSolution(), TSAdjointStep()
4252 @*/
4253 PetscErrorCode TSAdjointSolve(TS ts)
4254 {
4255   PetscErrorCode    ierr;
4256 
4257   PetscFunctionBegin;
4258   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4259   ierr = TSAdjointSetUp(ts);CHKERRQ(ierr);
4260 
4261   /* reset time step and iteration counters */
4262   ts->steps             = 0;
4263   ts->ksp_its           = 0;
4264   ts->snes_its          = 0;
4265   ts->num_snes_failures = 0;
4266   ts->reject            = 0;
4267   ts->reason            = TS_CONVERGED_ITERATING;
4268 
4269   if (!ts->adjoint_max_steps) ts->adjoint_max_steps = ts->total_steps;
4270 
4271   if (ts->steps >= ts->adjoint_max_steps)     ts->reason = TS_CONVERGED_ITS;
4272   while (!ts->reason) {
4273     ierr = TSTrajectoryGet(ts->trajectory,ts,ts->total_steps,&ts->ptime);CHKERRQ(ierr);
4274     ierr = TSAdjointMonitor(ts,ts->total_steps,ts->ptime,ts->vec_sol,ts->numcost,ts->vecs_sensi,ts->vecs_sensip);CHKERRQ(ierr);
4275     ierr = TSAdjointEventHandler(ts);CHKERRQ(ierr);
4276     ierr = TSAdjointStep(ts);CHKERRQ(ierr);
4277     if (ts->vec_costintegral && !ts->costintegralfwd) {
4278       ierr = TSAdjointCostIntegral(ts);CHKERRQ(ierr);
4279     }
4280   }
4281   ierr = TSTrajectoryGet(ts->trajectory,ts,ts->total_steps,&ts->ptime);CHKERRQ(ierr);
4282   ierr = TSAdjointMonitor(ts,ts->total_steps,ts->ptime,ts->vec_sol,ts->numcost,ts->vecs_sensi,ts->vecs_sensip);CHKERRQ(ierr);
4283   ts->solvetime = ts->ptime;
4284   ierr = TSTrajectoryViewFromOptions(ts->trajectory,NULL,"-ts_trajectory_view");CHKERRQ(ierr);
4285   ierr = VecViewFromOptions(ts->vecs_sensi[0],(PetscObject) ts, "-ts_adjoint_view_solution");CHKERRQ(ierr);
4286   PetscFunctionReturn(0);
4287 }
4288 
4289 #undef __FUNCT__
4290 #define __FUNCT__ "TSMonitor"
4291 /*@C
4292    TSMonitor - Runs all user-provided monitor routines set using TSMonitorSet()
4293 
4294    Collective on TS
4295 
4296    Input Parameters:
4297 +  ts - time stepping context obtained from TSCreate()
4298 .  step - step number that has just completed
4299 .  ptime - model time of the state
4300 -  u - state at the current model time
4301 
4302    Notes:
4303    TSMonitor() is typically used automatically within the time stepping implementations.
4304    Users would almost never call this routine directly.
4305 
4306    A step of -1 indicates that the monitor is being called on a solution obtained by interpolating from computed solutions
4307 
4308    Level: developer
4309 
4310 .keywords: TS, timestep
4311 @*/
4312 PetscErrorCode TSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec u)
4313 {
4314   DM             dm;
4315   PetscInt       i,n = ts->numbermonitors;
4316   PetscErrorCode ierr;
4317 
4318   PetscFunctionBegin;
4319   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4320   PetscValidHeaderSpecific(u,VEC_CLASSID,4);
4321 
4322   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4323   ierr = DMSetOutputSequenceNumber(dm,step,ptime);CHKERRQ(ierr);
4324 
4325   ierr = VecLockPush(u);CHKERRQ(ierr);
4326   for (i=0; i<n; i++) {
4327     ierr = (*ts->monitor[i])(ts,step,ptime,u,ts->monitorcontext[i]);CHKERRQ(ierr);
4328   }
4329   ierr = VecLockPop(u);CHKERRQ(ierr);
4330   PetscFunctionReturn(0);
4331 }
4332 
4333 #undef __FUNCT__
4334 #define __FUNCT__ "TSAdjointMonitor"
4335 /*@C
4336    TSAdjointMonitor - Runs all user-provided adjoint monitor routines set using TSAdjointMonitorSet()
4337 
4338    Collective on TS
4339 
4340    Input Parameters:
4341 +  ts - time stepping context obtained from TSCreate()
4342 .  step - step number that has just completed
4343 .  ptime - model time of the state
4344 .  u - state at the current model time
4345 .  numcost - number of cost functions (dimension of lambda  or mu)
4346 .  lambda - vectors containing the gradients of the cost functions with respect to the ODE/DAE solution variables
4347 -  mu - vectors containing the gradients of the cost functions with respect to the problem parameters
4348 
4349    Notes:
4350    TSAdjointMonitor() is typically used automatically within the time stepping implementations.
4351    Users would almost never call this routine directly.
4352 
4353    Level: developer
4354 
4355 .keywords: TS, timestep
4356 @*/
4357 PetscErrorCode TSAdjointMonitor(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscInt numcost,Vec *lambda, Vec *mu)
4358 {
4359   PetscErrorCode ierr;
4360   PetscInt       i,n = ts->numberadjointmonitors;
4361 
4362   PetscFunctionBegin;
4363   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4364   PetscValidHeaderSpecific(u,VEC_CLASSID,4);
4365   ierr = VecLockPush(u);CHKERRQ(ierr);
4366   for (i=0; i<n; i++) {
4367     ierr = (*ts->adjointmonitor[i])(ts,step,ptime,u,numcost,lambda,mu,ts->adjointmonitorcontext[i]);CHKERRQ(ierr);
4368   }
4369   ierr = VecLockPop(u);CHKERRQ(ierr);
4370   PetscFunctionReturn(0);
4371 }
4372 
4373 /* ------------------------------------------------------------------------*/
4374 #undef __FUNCT__
4375 #define __FUNCT__ "TSMonitorLGCtxCreate"
4376 /*@C
4377    TSMonitorLGCtxCreate - Creates a TSMonitorLGCtx context for use with
4378    TS to monitor the solution process graphically in various ways
4379 
4380    Collective on TS
4381 
4382    Input Parameters:
4383 +  host - the X display to open, or null for the local machine
4384 .  label - the title to put in the title bar
4385 .  x, y - the screen coordinates of the upper left coordinate of the window
4386 .  m, n - the screen width and height in pixels
4387 -  howoften - if positive then determines the frequency of the plotting, if -1 then only at the final time
4388 
4389    Output Parameter:
4390 .  ctx - the context
4391 
4392    Options Database Key:
4393 +  -ts_monitor_lg_timestep - automatically sets line graph monitor
4394 .  -ts_monitor_lg_solution - monitor the solution (or certain values of the solution by calling TSMonitorLGSetDisplayVariables() or TSMonitorLGCtxSetDisplayVariables())
4395 .  -ts_monitor_lg_error -  monitor the error
4396 .  -ts_monitor_lg_ksp_iterations - monitor the number of KSP iterations needed for each timestep
4397 .  -ts_monitor_lg_snes_iterations - monitor the number of SNES iterations needed for each timestep
4398 -  -lg_use_markers <true,false> - mark the data points (at each time step) on the plot; default is true
4399 
4400    Notes:
4401    Use TSMonitorLGCtxDestroy() to destroy.
4402 
4403    One can provide a function that transforms the solution before plotting it with TSMonitorLGCtxSetTransform() or TSMonitorLGSetTransform()
4404 
4405    Many of the functions that control the monitoring have two forms: TSMonitorLGSet/GetXXXX() and TSMonitorLGCtxSet/GetXXXX() the first take a TS object as the
4406    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
4407    as the first argument.
4408 
4409    One can control the names displayed for each solution or error variable with TSMonitorLGCtxSetVariableNames() or TSMonitorLGSetVariableNames()
4410 
4411 
4412    Level: intermediate
4413 
4414 .keywords: TS, monitor, line graph, residual
4415 
4416 .seealso: TSMonitorLGTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError(), TSMonitorDefault(), VecView(),
4417            TSMonitorLGCtxCreate(), TSMonitorLGCtxSetVariableNames(), TSMonitorLGCtxGetVariableNames(),
4418            TSMonitorLGSetVariableNames(), TSMonitorLGGetVariableNames(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetDisplayVariables(),
4419            TSMonitorLGCtxSetTransform(), TSMonitorLGSetTransform(), TSMonitorLGError(), TSMonitorLGSNESIterations(), TSMonitorLGKSPIterations(),
4420            TSMonitorEnvelopeCtxCreate(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxDestroy(), TSMonitorEnvelop()
4421 
4422 @*/
4423 PetscErrorCode  TSMonitorLGCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorLGCtx *ctx)
4424 {
4425   PetscDraw      draw;
4426   PetscErrorCode ierr;
4427 
4428   PetscFunctionBegin;
4429   ierr = PetscNew(ctx);CHKERRQ(ierr);
4430   ierr = PetscDrawCreate(comm,host,label,x,y,m,n,&draw);CHKERRQ(ierr);
4431   ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
4432   ierr = PetscDrawLGCreate(draw,1,&(*ctx)->lg);CHKERRQ(ierr);
4433   ierr = PetscDrawLGSetFromOptions((*ctx)->lg);CHKERRQ(ierr);
4434   ierr = PetscDrawDestroy(&draw);CHKERRQ(ierr);
4435   (*ctx)->howoften = howoften;
4436   PetscFunctionReturn(0);
4437 }
4438 
4439 #undef __FUNCT__
4440 #define __FUNCT__ "TSMonitorLGTimeStep"
4441 PetscErrorCode TSMonitorLGTimeStep(TS ts,PetscInt step,PetscReal ptime,Vec v,void *monctx)
4442 {
4443   TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
4444   PetscReal      x   = ptime,y;
4445   PetscErrorCode ierr;
4446 
4447   PetscFunctionBegin;
4448   if (step < 0) PetscFunctionReturn(0); /* -1 indicates an interpolated solution */
4449   if (!step) {
4450     PetscDrawAxis axis;
4451     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
4452     ierr = PetscDrawAxisSetLabels(axis,"Timestep as function of time","Time","Time Step");CHKERRQ(ierr);
4453     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
4454   }
4455   ierr = TSGetTimeStep(ts,&y);CHKERRQ(ierr);
4456   ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
4457   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
4458     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
4459     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
4460   }
4461   PetscFunctionReturn(0);
4462 }
4463 
4464 #undef __FUNCT__
4465 #define __FUNCT__ "TSMonitorLGCtxDestroy"
4466 /*@C
4467    TSMonitorLGCtxDestroy - Destroys a line graph context that was created
4468    with TSMonitorLGCtxCreate().
4469 
4470    Collective on TSMonitorLGCtx
4471 
4472    Input Parameter:
4473 .  ctx - the monitor context
4474 
4475    Level: intermediate
4476 
4477 .keywords: TS, monitor, line graph, destroy
4478 
4479 .seealso: TSMonitorLGCtxCreate(),  TSMonitorSet(), TSMonitorLGTimeStep();
4480 @*/
4481 PetscErrorCode  TSMonitorLGCtxDestroy(TSMonitorLGCtx *ctx)
4482 {
4483   PetscErrorCode ierr;
4484 
4485   PetscFunctionBegin;
4486   if ((*ctx)->transformdestroy) {
4487     ierr = ((*ctx)->transformdestroy)((*ctx)->transformctx);CHKERRQ(ierr);
4488   }
4489   ierr = PetscDrawLGDestroy(&(*ctx)->lg);CHKERRQ(ierr);
4490   ierr = PetscStrArrayDestroy(&(*ctx)->names);CHKERRQ(ierr);
4491   ierr = PetscStrArrayDestroy(&(*ctx)->displaynames);CHKERRQ(ierr);
4492   ierr = PetscFree((*ctx)->displayvariables);CHKERRQ(ierr);
4493   ierr = PetscFree((*ctx)->displayvalues);CHKERRQ(ierr);
4494   ierr = PetscFree(*ctx);CHKERRQ(ierr);
4495   PetscFunctionReturn(0);
4496 }
4497 
4498 #undef __FUNCT__
4499 #define __FUNCT__ "TSGetTime"
4500 /*@
4501    TSGetTime - Gets the time of the most recently completed step.
4502 
4503    Not Collective
4504 
4505    Input Parameter:
4506 .  ts - the TS context obtained from TSCreate()
4507 
4508    Output Parameter:
4509 .  t  - the current time. This time may not corresponds to the final time set with TSSetDuration(), use TSGetSolveTime().
4510 
4511    Level: beginner
4512 
4513    Note:
4514    When called during time step evaluation (e.g. during residual evaluation or via hooks set using TSSetPreStep(),
4515    TSSetPreStage(), TSSetPostStage(), or TSSetPostStep()), the time is the time at the start of the step being evaluated.
4516 
4517 .seealso: TSSetInitialTimeStep(), TSGetTimeStep(), TSGetSolveTime()
4518 
4519 .keywords: TS, get, time
4520 @*/
4521 PetscErrorCode  TSGetTime(TS ts,PetscReal *t)
4522 {
4523   PetscFunctionBegin;
4524   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4525   PetscValidRealPointer(t,2);
4526   *t = ts->ptime;
4527   PetscFunctionReturn(0);
4528 }
4529 
4530 #undef __FUNCT__
4531 #define __FUNCT__ "TSGetPrevTime"
4532 /*@
4533    TSGetPrevTime - Gets the starting time of the previously completed step.
4534 
4535    Not Collective
4536 
4537    Input Parameter:
4538 .  ts - the TS context obtained from TSCreate()
4539 
4540    Output Parameter:
4541 .  t  - the previous time
4542 
4543    Level: beginner
4544 
4545 .seealso: TSSetInitialTimeStep(), TSGetTimeStep()
4546 
4547 .keywords: TS, get, time
4548 @*/
4549 PetscErrorCode  TSGetPrevTime(TS ts,PetscReal *t)
4550 {
4551   PetscFunctionBegin;
4552   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4553   PetscValidRealPointer(t,2);
4554   *t = ts->ptime_prev;
4555   PetscFunctionReturn(0);
4556 }
4557 
4558 #undef __FUNCT__
4559 #define __FUNCT__ "TSSetTime"
4560 /*@
4561    TSSetTime - Allows one to reset the time.
4562 
4563    Logically Collective on TS
4564 
4565    Input Parameters:
4566 +  ts - the TS context obtained from TSCreate()
4567 -  time - the time
4568 
4569    Level: intermediate
4570 
4571 .seealso: TSGetTime(), TSSetDuration()
4572 
4573 .keywords: TS, set, time
4574 @*/
4575 PetscErrorCode  TSSetTime(TS ts, PetscReal t)
4576 {
4577   PetscFunctionBegin;
4578   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4579   PetscValidLogicalCollectiveReal(ts,t,2);
4580   ts->ptime = t;
4581   PetscFunctionReturn(0);
4582 }
4583 
4584 #undef __FUNCT__
4585 #define __FUNCT__ "TSSetOptionsPrefix"
4586 /*@C
4587    TSSetOptionsPrefix - Sets the prefix used for searching for all
4588    TS options in the database.
4589 
4590    Logically Collective on TS
4591 
4592    Input Parameter:
4593 +  ts     - The TS context
4594 -  prefix - The prefix to prepend to all option names
4595 
4596    Notes:
4597    A hyphen (-) must NOT be given at the beginning of the prefix name.
4598    The first character of all runtime options is AUTOMATICALLY the
4599    hyphen.
4600 
4601    Level: advanced
4602 
4603 .keywords: TS, set, options, prefix, database
4604 
4605 .seealso: TSSetFromOptions()
4606 
4607 @*/
4608 PetscErrorCode  TSSetOptionsPrefix(TS ts,const char prefix[])
4609 {
4610   PetscErrorCode ierr;
4611   SNES           snes;
4612 
4613   PetscFunctionBegin;
4614   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4615   ierr = PetscObjectSetOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
4616   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4617   ierr = SNESSetOptionsPrefix(snes,prefix);CHKERRQ(ierr);
4618   PetscFunctionReturn(0);
4619 }
4620 
4621 
4622 #undef __FUNCT__
4623 #define __FUNCT__ "TSAppendOptionsPrefix"
4624 /*@C
4625    TSAppendOptionsPrefix - Appends to the prefix used for searching for all
4626    TS options in the database.
4627 
4628    Logically Collective on TS
4629 
4630    Input Parameter:
4631 +  ts     - The TS context
4632 -  prefix - The prefix to prepend to all option names
4633 
4634    Notes:
4635    A hyphen (-) must NOT be given at the beginning of the prefix name.
4636    The first character of all runtime options is AUTOMATICALLY the
4637    hyphen.
4638 
4639    Level: advanced
4640 
4641 .keywords: TS, append, options, prefix, database
4642 
4643 .seealso: TSGetOptionsPrefix()
4644 
4645 @*/
4646 PetscErrorCode  TSAppendOptionsPrefix(TS ts,const char prefix[])
4647 {
4648   PetscErrorCode ierr;
4649   SNES           snes;
4650 
4651   PetscFunctionBegin;
4652   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4653   ierr = PetscObjectAppendOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
4654   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4655   ierr = SNESAppendOptionsPrefix(snes,prefix);CHKERRQ(ierr);
4656   PetscFunctionReturn(0);
4657 }
4658 
4659 #undef __FUNCT__
4660 #define __FUNCT__ "TSGetOptionsPrefix"
4661 /*@C
4662    TSGetOptionsPrefix - Sets the prefix used for searching for all
4663    TS options in the database.
4664 
4665    Not Collective
4666 
4667    Input Parameter:
4668 .  ts - The TS context
4669 
4670    Output Parameter:
4671 .  prefix - A pointer to the prefix string used
4672 
4673    Notes: On the fortran side, the user should pass in a string 'prifix' of
4674    sufficient length to hold the prefix.
4675 
4676    Level: intermediate
4677 
4678 .keywords: TS, get, options, prefix, database
4679 
4680 .seealso: TSAppendOptionsPrefix()
4681 @*/
4682 PetscErrorCode  TSGetOptionsPrefix(TS ts,const char *prefix[])
4683 {
4684   PetscErrorCode ierr;
4685 
4686   PetscFunctionBegin;
4687   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4688   PetscValidPointer(prefix,2);
4689   ierr = PetscObjectGetOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
4690   PetscFunctionReturn(0);
4691 }
4692 
4693 #undef __FUNCT__
4694 #define __FUNCT__ "TSGetRHSJacobian"
4695 /*@C
4696    TSGetRHSJacobian - Returns the Jacobian J at the present timestep.
4697 
4698    Not Collective, but parallel objects are returned if TS is parallel
4699 
4700    Input Parameter:
4701 .  ts  - The TS context obtained from TSCreate()
4702 
4703    Output Parameters:
4704 +  Amat - The (approximate) Jacobian J of G, where U_t = G(U,t)  (or NULL)
4705 .  Pmat - The matrix from which the preconditioner is constructed, usually the same as Amat  (or NULL)
4706 .  func - Function to compute the Jacobian of the RHS  (or NULL)
4707 -  ctx - User-defined context for Jacobian evaluation routine  (or NULL)
4708 
4709    Notes: You can pass in NULL for any return argument you do not need.
4710 
4711    Level: intermediate
4712 
4713 .seealso: TSGetTimeStep(), TSGetMatrices(), TSGetTime(), TSGetTimeStepNumber()
4714 
4715 .keywords: TS, timestep, get, matrix, Jacobian
4716 @*/
4717 PetscErrorCode  TSGetRHSJacobian(TS ts,Mat *Amat,Mat *Pmat,TSRHSJacobian *func,void **ctx)
4718 {
4719   PetscErrorCode ierr;
4720   SNES           snes;
4721   DM             dm;
4722 
4723   PetscFunctionBegin;
4724   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4725   ierr = SNESGetJacobian(snes,Amat,Pmat,NULL,NULL);CHKERRQ(ierr);
4726   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4727   ierr = DMTSGetRHSJacobian(dm,func,ctx);CHKERRQ(ierr);
4728   PetscFunctionReturn(0);
4729 }
4730 
4731 #undef __FUNCT__
4732 #define __FUNCT__ "TSGetIJacobian"
4733 /*@C
4734    TSGetIJacobian - Returns the implicit Jacobian at the present timestep.
4735 
4736    Not Collective, but parallel objects are returned if TS is parallel
4737 
4738    Input Parameter:
4739 .  ts  - The TS context obtained from TSCreate()
4740 
4741    Output Parameters:
4742 +  Amat  - The (approximate) Jacobian of F(t,U,U_t)
4743 .  Pmat - The matrix from which the preconditioner is constructed, often the same as Amat
4744 .  f   - The function to compute the matrices
4745 - ctx - User-defined context for Jacobian evaluation routine
4746 
4747    Notes: You can pass in NULL for any return argument you do not need.
4748 
4749    Level: advanced
4750 
4751 .seealso: TSGetTimeStep(), TSGetRHSJacobian(), TSGetMatrices(), TSGetTime(), TSGetTimeStepNumber()
4752 
4753 .keywords: TS, timestep, get, matrix, Jacobian
4754 @*/
4755 PetscErrorCode  TSGetIJacobian(TS ts,Mat *Amat,Mat *Pmat,TSIJacobian *f,void **ctx)
4756 {
4757   PetscErrorCode ierr;
4758   SNES           snes;
4759   DM             dm;
4760 
4761   PetscFunctionBegin;
4762   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4763   ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr);
4764   ierr = SNESGetJacobian(snes,Amat,Pmat,NULL,NULL);CHKERRQ(ierr);
4765   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4766   ierr = DMTSGetIJacobian(dm,f,ctx);CHKERRQ(ierr);
4767   PetscFunctionReturn(0);
4768 }
4769 
4770 
4771 #undef __FUNCT__
4772 #define __FUNCT__ "TSMonitorDrawSolution"
4773 /*@C
4774    TSMonitorDrawSolution - Monitors progress of the TS solvers by calling
4775    VecView() for the solution at each timestep
4776 
4777    Collective on TS
4778 
4779    Input Parameters:
4780 +  ts - the TS context
4781 .  step - current time-step
4782 .  ptime - current time
4783 -  dummy - either a viewer or NULL
4784 
4785    Options Database:
4786 .   -ts_monitor_draw_solution_initial - show initial solution as well as current solution
4787 
4788    Notes: the initial solution and current solution are not display with a common axis scaling so generally the option -ts_monitor_draw_solution_initial
4789        will look bad
4790 
4791    Level: intermediate
4792 
4793 .keywords: TS,  vector, monitor, view
4794 
4795 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
4796 @*/
4797 PetscErrorCode  TSMonitorDrawSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
4798 {
4799   PetscErrorCode   ierr;
4800   TSMonitorDrawCtx ictx = (TSMonitorDrawCtx)dummy;
4801   PetscDraw        draw;
4802 
4803   PetscFunctionBegin;
4804   if (!step && ictx->showinitial) {
4805     if (!ictx->initialsolution) {
4806       ierr = VecDuplicate(u,&ictx->initialsolution);CHKERRQ(ierr);
4807     }
4808     ierr = VecCopy(u,ictx->initialsolution);CHKERRQ(ierr);
4809   }
4810   if (!(((ictx->howoften > 0) && (!(step % ictx->howoften))) || ((ictx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);
4811 
4812   if (ictx->showinitial) {
4813     PetscReal pause;
4814     ierr = PetscViewerDrawGetPause(ictx->viewer,&pause);CHKERRQ(ierr);
4815     ierr = PetscViewerDrawSetPause(ictx->viewer,0.0);CHKERRQ(ierr);
4816     ierr = VecView(ictx->initialsolution,ictx->viewer);CHKERRQ(ierr);
4817     ierr = PetscViewerDrawSetPause(ictx->viewer,pause);CHKERRQ(ierr);
4818     ierr = PetscViewerDrawSetHold(ictx->viewer,PETSC_TRUE);CHKERRQ(ierr);
4819   }
4820   ierr = VecView(u,ictx->viewer);CHKERRQ(ierr);
4821   if (ictx->showtimestepandtime) {
4822     PetscReal xl,yl,xr,yr,h;
4823     char      time[32];
4824 
4825     ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
4826     ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
4827     ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
4828     h    = yl + .95*(yr - yl);
4829     ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
4830     ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
4831   }
4832 
4833   if (ictx->showinitial) {
4834     ierr = PetscViewerDrawSetHold(ictx->viewer,PETSC_FALSE);CHKERRQ(ierr);
4835   }
4836   PetscFunctionReturn(0);
4837 }
4838 
4839 #undef __FUNCT__
4840 #define __FUNCT__ "TSAdjointMonitorDrawSensi"
4841 /*@C
4842    TSAdjointMonitorDrawSensi - Monitors progress of the adjoint TS solvers by calling
4843    VecView() for the sensitivities to initial states at each timestep
4844 
4845    Collective on TS
4846 
4847    Input Parameters:
4848 +  ts - the TS context
4849 .  step - current time-step
4850 .  ptime - current time
4851 .  u - current state
4852 .  numcost - number of cost functions
4853 .  lambda - sensitivities to initial conditions
4854 .  mu - sensitivities to parameters
4855 -  dummy - either a viewer or NULL
4856 
4857    Level: intermediate
4858 
4859 .keywords: TS,  vector, adjoint, monitor, view
4860 
4861 .seealso: TSAdjointMonitorSet(), TSAdjointMonitorDefault(), VecView()
4862 @*/
4863 PetscErrorCode  TSAdjointMonitorDrawSensi(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscInt numcost,Vec *lambda,Vec *mu,void *dummy)
4864 {
4865   PetscErrorCode   ierr;
4866   TSMonitorDrawCtx ictx = (TSMonitorDrawCtx)dummy;
4867   PetscDraw        draw;
4868   PetscReal        xl,yl,xr,yr,h;
4869   char             time[32];
4870 
4871   PetscFunctionBegin;
4872   if (!(((ictx->howoften > 0) && (!(step % ictx->howoften))) || ((ictx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);
4873 
4874   ierr = VecView(lambda[0],ictx->viewer);CHKERRQ(ierr);
4875   ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
4876   ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
4877   ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
4878   h    = yl + .95*(yr - yl);
4879   ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
4880   ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
4881   PetscFunctionReturn(0);
4882 }
4883 
4884 #undef __FUNCT__
4885 #define __FUNCT__ "TSMonitorDrawSolutionPhase"
4886 /*@C
4887    TSMonitorDrawSolutionPhase - Monitors progress of the TS solvers by plotting the solution as a phase diagram
4888 
4889    Collective on TS
4890 
4891    Input Parameters:
4892 +  ts - the TS context
4893 .  step - current time-step
4894 .  ptime - current time
4895 -  dummy - either a viewer or NULL
4896 
4897    Level: intermediate
4898 
4899 .keywords: TS,  vector, monitor, view
4900 
4901 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
4902 @*/
4903 PetscErrorCode  TSMonitorDrawSolutionPhase(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
4904 {
4905   PetscErrorCode    ierr;
4906   TSMonitorDrawCtx  ictx = (TSMonitorDrawCtx)dummy;
4907   PetscDraw         draw;
4908   PetscDrawAxis     axis;
4909   PetscInt          n;
4910   PetscMPIInt       size;
4911   PetscReal         U0,U1,xl,yl,xr,yr,h;
4912   char              time[32];
4913   const PetscScalar *U;
4914 
4915   PetscFunctionBegin;
4916   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)ts),&size);CHKERRQ(ierr);
4917   if (size != 1) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Only allowed for sequential runs");
4918   ierr = VecGetSize(u,&n);CHKERRQ(ierr);
4919   if (n != 2) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Only for ODEs with two unknowns");
4920 
4921   ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
4922   ierr = PetscViewerDrawGetDrawAxis(ictx->viewer,0,&axis);CHKERRQ(ierr);
4923   ierr = PetscDrawAxisGetLimits(axis,&xl,&xr,&yl,&yr);CHKERRQ(ierr);
4924   if (!step) {
4925     ierr = PetscDrawClear(draw);CHKERRQ(ierr);
4926     ierr = PetscDrawAxisDraw(axis);CHKERRQ(ierr);
4927   }
4928 
4929   ierr = VecGetArrayRead(u,&U);CHKERRQ(ierr);
4930   U0 = PetscRealPart(U[0]);
4931   U1 = PetscRealPart(U[1]);
4932   ierr = VecRestoreArrayRead(u,&U);CHKERRQ(ierr);
4933   if ((U0 < xl) || (U1 < yl) || (U0 > xr) || (U1 > yr)) PetscFunctionReturn(0);
4934 
4935   ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
4936   ierr = PetscDrawPoint(draw,U0,U1,PETSC_DRAW_BLACK);CHKERRQ(ierr);
4937   if (ictx->showtimestepandtime) {
4938     ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
4939     ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
4940     h    = yl + .95*(yr - yl);
4941     ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
4942   }
4943   ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
4944   ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
4945   ierr = PetscDrawSave(draw);CHKERRQ(ierr);
4946   PetscFunctionReturn(0);
4947 }
4948 
4949 
4950 #undef __FUNCT__
4951 #define __FUNCT__ "TSMonitorDrawCtxDestroy"
4952 /*@C
4953    TSMonitorDrawCtxDestroy - Destroys the monitor context for TSMonitorDrawSolution()
4954 
4955    Collective on TS
4956 
4957    Input Parameters:
4958 .    ctx - the monitor context
4959 
4960    Level: intermediate
4961 
4962 .keywords: TS,  vector, monitor, view
4963 
4964 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorDrawSolution(), TSMonitorDrawError()
4965 @*/
4966 PetscErrorCode  TSMonitorDrawCtxDestroy(TSMonitorDrawCtx *ictx)
4967 {
4968   PetscErrorCode ierr;
4969 
4970   PetscFunctionBegin;
4971   ierr = PetscViewerDestroy(&(*ictx)->viewer);CHKERRQ(ierr);
4972   ierr = VecDestroy(&(*ictx)->initialsolution);CHKERRQ(ierr);
4973   ierr = PetscFree(*ictx);CHKERRQ(ierr);
4974   PetscFunctionReturn(0);
4975 }
4976 
4977 #undef __FUNCT__
4978 #define __FUNCT__ "TSMonitorDrawCtxCreate"
4979 /*@C
4980    TSMonitorDrawCtxCreate - Creates the monitor context for TSMonitorDrawCtx
4981 
4982    Collective on TS
4983 
4984    Input Parameter:
4985 .    ts - time-step context
4986 
4987    Output Patameter:
4988 .    ctx - the monitor context
4989 
4990    Options Database:
4991 .   -ts_monitor_draw_solution_initial - show initial solution as well as current solution
4992 
4993    Level: intermediate
4994 
4995 .keywords: TS,  vector, monitor, view
4996 
4997 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorDrawCtx()
4998 @*/
4999 PetscErrorCode  TSMonitorDrawCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorDrawCtx *ctx)
5000 {
5001   PetscErrorCode   ierr;
5002 
5003   PetscFunctionBegin;
5004   ierr = PetscNew(ctx);CHKERRQ(ierr);
5005   ierr = PetscViewerDrawOpen(comm,host,label,x,y,m,n,&(*ctx)->viewer);CHKERRQ(ierr);
5006   ierr = PetscViewerSetFromOptions((*ctx)->viewer);CHKERRQ(ierr);
5007 
5008   (*ctx)->howoften    = howoften;
5009   (*ctx)->showinitial = PETSC_FALSE;
5010   ierr = PetscOptionsGetBool(NULL,NULL,"-ts_monitor_draw_solution_initial",&(*ctx)->showinitial,NULL);CHKERRQ(ierr);
5011 
5012   (*ctx)->showtimestepandtime = PETSC_FALSE;
5013   ierr = PetscOptionsGetBool(NULL,NULL,"-ts_monitor_draw_solution_show_time",&(*ctx)->showtimestepandtime,NULL);CHKERRQ(ierr);
5014   PetscFunctionReturn(0);
5015 }
5016 
5017 #undef __FUNCT__
5018 #define __FUNCT__ "TSMonitorDrawError"
5019 /*@C
5020    TSMonitorDrawError - Monitors progress of the TS solvers by calling
5021    VecView() for the error at each timestep
5022 
5023    Collective on TS
5024 
5025    Input Parameters:
5026 +  ts - the TS context
5027 .  step - current time-step
5028 .  ptime - current time
5029 -  dummy - either a viewer or NULL
5030 
5031    Level: intermediate
5032 
5033 .keywords: TS,  vector, monitor, view
5034 
5035 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
5036 @*/
5037 PetscErrorCode  TSMonitorDrawError(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
5038 {
5039   PetscErrorCode   ierr;
5040   TSMonitorDrawCtx ctx    = (TSMonitorDrawCtx)dummy;
5041   PetscViewer      viewer = ctx->viewer;
5042   Vec              work;
5043 
5044   PetscFunctionBegin;
5045   if (!(((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);
5046   ierr = VecDuplicate(u,&work);CHKERRQ(ierr);
5047   ierr = TSComputeSolutionFunction(ts,ptime,work);CHKERRQ(ierr);
5048   ierr = VecAXPY(work,-1.0,u);CHKERRQ(ierr);
5049   ierr = VecView(work,viewer);CHKERRQ(ierr);
5050   ierr = VecDestroy(&work);CHKERRQ(ierr);
5051   PetscFunctionReturn(0);
5052 }
5053 
5054 #include <petsc/private/dmimpl.h>
5055 #undef __FUNCT__
5056 #define __FUNCT__ "TSSetDM"
5057 /*@
5058    TSSetDM - Sets the DM that may be used by some nonlinear solvers or preconditioners under the TS
5059 
5060    Logically Collective on TS and DM
5061 
5062    Input Parameters:
5063 +  ts - the ODE integrator object
5064 -  dm - the dm, cannot be NULL
5065 
5066    Level: intermediate
5067 
5068 
5069 .seealso: TSGetDM(), SNESSetDM(), SNESGetDM()
5070 @*/
5071 PetscErrorCode  TSSetDM(TS ts,DM dm)
5072 {
5073   PetscErrorCode ierr;
5074   SNES           snes;
5075   DMTS           tsdm;
5076 
5077   PetscFunctionBegin;
5078   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5079   PetscValidHeaderSpecific(dm,DM_CLASSID,2);
5080   ierr = PetscObjectReference((PetscObject)dm);CHKERRQ(ierr);
5081   if (ts->dm) {               /* Move the DMTS context over to the new DM unless the new DM already has one */
5082     if (ts->dm->dmts && !dm->dmts) {
5083       ierr = DMCopyDMTS(ts->dm,dm);CHKERRQ(ierr);
5084       ierr = DMGetDMTS(ts->dm,&tsdm);CHKERRQ(ierr);
5085       if (tsdm->originaldm == ts->dm) { /* Grant write privileges to the replacement DM */
5086         tsdm->originaldm = dm;
5087       }
5088     }
5089     ierr = DMDestroy(&ts->dm);CHKERRQ(ierr);
5090   }
5091   ts->dm = dm;
5092 
5093   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
5094   ierr = SNESSetDM(snes,dm);CHKERRQ(ierr);
5095   PetscFunctionReturn(0);
5096 }
5097 
5098 #undef __FUNCT__
5099 #define __FUNCT__ "TSGetDM"
5100 /*@
5101    TSGetDM - Gets the DM that may be used by some preconditioners
5102 
5103    Not Collective
5104 
5105    Input Parameter:
5106 . ts - the preconditioner context
5107 
5108    Output Parameter:
5109 .  dm - the dm
5110 
5111    Level: intermediate
5112 
5113 
5114 .seealso: TSSetDM(), SNESSetDM(), SNESGetDM()
5115 @*/
5116 PetscErrorCode  TSGetDM(TS ts,DM *dm)
5117 {
5118   PetscErrorCode ierr;
5119 
5120   PetscFunctionBegin;
5121   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5122   if (!ts->dm) {
5123     ierr = DMShellCreate(PetscObjectComm((PetscObject)ts),&ts->dm);CHKERRQ(ierr);
5124     if (ts->snes) {ierr = SNESSetDM(ts->snes,ts->dm);CHKERRQ(ierr);}
5125   }
5126   *dm = ts->dm;
5127   PetscFunctionReturn(0);
5128 }
5129 
5130 #undef __FUNCT__
5131 #define __FUNCT__ "SNESTSFormFunction"
5132 /*@
5133    SNESTSFormFunction - Function to evaluate nonlinear residual
5134 
5135    Logically Collective on SNES
5136 
5137    Input Parameter:
5138 + snes - nonlinear solver
5139 . U - the current state at which to evaluate the residual
5140 - ctx - user context, must be a TS
5141 
5142    Output Parameter:
5143 . F - the nonlinear residual
5144 
5145    Notes:
5146    This function is not normally called by users and is automatically registered with the SNES used by TS.
5147    It is most frequently passed to MatFDColoringSetFunction().
5148 
5149    Level: advanced
5150 
5151 .seealso: SNESSetFunction(), MatFDColoringSetFunction()
5152 @*/
5153 PetscErrorCode  SNESTSFormFunction(SNES snes,Vec U,Vec F,void *ctx)
5154 {
5155   TS             ts = (TS)ctx;
5156   PetscErrorCode ierr;
5157 
5158   PetscFunctionBegin;
5159   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
5160   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
5161   PetscValidHeaderSpecific(F,VEC_CLASSID,3);
5162   PetscValidHeaderSpecific(ts,TS_CLASSID,4);
5163   ierr = (ts->ops->snesfunction)(snes,U,F,ts);CHKERRQ(ierr);
5164   PetscFunctionReturn(0);
5165 }
5166 
5167 #undef __FUNCT__
5168 #define __FUNCT__ "SNESTSFormJacobian"
5169 /*@
5170    SNESTSFormJacobian - Function to evaluate the Jacobian
5171 
5172    Collective on SNES
5173 
5174    Input Parameter:
5175 + snes - nonlinear solver
5176 . U - the current state at which to evaluate the residual
5177 - ctx - user context, must be a TS
5178 
5179    Output Parameter:
5180 + A - the Jacobian
5181 . B - the preconditioning matrix (may be the same as A)
5182 - flag - indicates any structure change in the matrix
5183 
5184    Notes:
5185    This function is not normally called by users and is automatically registered with the SNES used by TS.
5186 
5187    Level: developer
5188 
5189 .seealso: SNESSetJacobian()
5190 @*/
5191 PetscErrorCode  SNESTSFormJacobian(SNES snes,Vec U,Mat A,Mat B,void *ctx)
5192 {
5193   TS             ts = (TS)ctx;
5194   PetscErrorCode ierr;
5195 
5196   PetscFunctionBegin;
5197   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
5198   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
5199   PetscValidPointer(A,3);
5200   PetscValidHeaderSpecific(A,MAT_CLASSID,3);
5201   PetscValidPointer(B,4);
5202   PetscValidHeaderSpecific(B,MAT_CLASSID,4);
5203   PetscValidHeaderSpecific(ts,TS_CLASSID,6);
5204   ierr = (ts->ops->snesjacobian)(snes,U,A,B,ts);CHKERRQ(ierr);
5205   PetscFunctionReturn(0);
5206 }
5207 
5208 #undef __FUNCT__
5209 #define __FUNCT__ "TSComputeRHSFunctionLinear"
5210 /*@C
5211    TSComputeRHSFunctionLinear - Evaluate the right hand side via the user-provided Jacobian, for linear problems Udot = A U only
5212 
5213    Collective on TS
5214 
5215    Input Arguments:
5216 +  ts - time stepping context
5217 .  t - time at which to evaluate
5218 .  U - state at which to evaluate
5219 -  ctx - context
5220 
5221    Output Arguments:
5222 .  F - right hand side
5223 
5224    Level: intermediate
5225 
5226    Notes:
5227    This function is intended to be passed to TSSetRHSFunction() to evaluate the right hand side for linear problems.
5228    The matrix (and optionally the evaluation context) should be passed to TSSetRHSJacobian().
5229 
5230 .seealso: TSSetRHSFunction(), TSSetRHSJacobian(), TSComputeRHSJacobianConstant()
5231 @*/
5232 PetscErrorCode TSComputeRHSFunctionLinear(TS ts,PetscReal t,Vec U,Vec F,void *ctx)
5233 {
5234   PetscErrorCode ierr;
5235   Mat            Arhs,Brhs;
5236 
5237   PetscFunctionBegin;
5238   ierr = TSGetRHSMats_Private(ts,&Arhs,&Brhs);CHKERRQ(ierr);
5239   ierr = TSComputeRHSJacobian(ts,t,U,Arhs,Brhs);CHKERRQ(ierr);
5240   ierr = MatMult(Arhs,U,F);CHKERRQ(ierr);
5241   PetscFunctionReturn(0);
5242 }
5243 
5244 #undef __FUNCT__
5245 #define __FUNCT__ "TSComputeRHSJacobianConstant"
5246 /*@C
5247    TSComputeRHSJacobianConstant - Reuses a Jacobian that is time-independent.
5248 
5249    Collective on TS
5250 
5251    Input Arguments:
5252 +  ts - time stepping context
5253 .  t - time at which to evaluate
5254 .  U - state at which to evaluate
5255 -  ctx - context
5256 
5257    Output Arguments:
5258 +  A - pointer to operator
5259 .  B - pointer to preconditioning matrix
5260 -  flg - matrix structure flag
5261 
5262    Level: intermediate
5263 
5264    Notes:
5265    This function is intended to be passed to TSSetRHSJacobian() to evaluate the Jacobian for linear time-independent problems.
5266 
5267 .seealso: TSSetRHSFunction(), TSSetRHSJacobian(), TSComputeRHSFunctionLinear()
5268 @*/
5269 PetscErrorCode TSComputeRHSJacobianConstant(TS ts,PetscReal t,Vec U,Mat A,Mat B,void *ctx)
5270 {
5271   PetscFunctionBegin;
5272   PetscFunctionReturn(0);
5273 }
5274 
5275 #undef __FUNCT__
5276 #define __FUNCT__ "TSComputeIFunctionLinear"
5277 /*@C
5278    TSComputeIFunctionLinear - Evaluate the left hand side via the user-provided Jacobian, for linear problems only
5279 
5280    Collective on TS
5281 
5282    Input Arguments:
5283 +  ts - time stepping context
5284 .  t - time at which to evaluate
5285 .  U - state at which to evaluate
5286 .  Udot - time derivative of state vector
5287 -  ctx - context
5288 
5289    Output Arguments:
5290 .  F - left hand side
5291 
5292    Level: intermediate
5293 
5294    Notes:
5295    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
5296    user is required to write their own TSComputeIFunction.
5297    This function is intended to be passed to TSSetIFunction() to evaluate the left hand side for linear problems.
5298    The matrix (and optionally the evaluation context) should be passed to TSSetIJacobian().
5299 
5300    Note that using this function is NOT equivalent to using TSComputeRHSFunctionLinear() since that solves Udot = A U
5301 
5302 .seealso: TSSetIFunction(), TSSetIJacobian(), TSComputeIJacobianConstant(), TSComputeRHSFunctionLinear()
5303 @*/
5304 PetscErrorCode TSComputeIFunctionLinear(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
5305 {
5306   PetscErrorCode ierr;
5307   Mat            A,B;
5308 
5309   PetscFunctionBegin;
5310   ierr = TSGetIJacobian(ts,&A,&B,NULL,NULL);CHKERRQ(ierr);
5311   ierr = TSComputeIJacobian(ts,t,U,Udot,1.0,A,B,PETSC_TRUE);CHKERRQ(ierr);
5312   ierr = MatMult(A,Udot,F);CHKERRQ(ierr);
5313   PetscFunctionReturn(0);
5314 }
5315 
5316 #undef __FUNCT__
5317 #define __FUNCT__ "TSComputeIJacobianConstant"
5318 /*@C
5319    TSComputeIJacobianConstant - Reuses a time-independent for a semi-implicit DAE or ODE
5320 
5321    Collective on TS
5322 
5323    Input Arguments:
5324 +  ts - time stepping context
5325 .  t - time at which to evaluate
5326 .  U - state at which to evaluate
5327 .  Udot - time derivative of state vector
5328 .  shift - shift to apply
5329 -  ctx - context
5330 
5331    Output Arguments:
5332 +  A - pointer to operator
5333 .  B - pointer to preconditioning matrix
5334 -  flg - matrix structure flag
5335 
5336    Level: advanced
5337 
5338    Notes:
5339    This function is intended to be passed to TSSetIJacobian() to evaluate the Jacobian for linear time-independent problems.
5340 
5341    It is only appropriate for problems of the form
5342 
5343 $     M Udot = F(U,t)
5344 
5345   where M is constant and F is non-stiff.  The user must pass M to TSSetIJacobian().  The current implementation only
5346   works with IMEX time integration methods such as TSROSW and TSARKIMEX, since there is no support for de-constructing
5347   an implicit operator of the form
5348 
5349 $    shift*M + J
5350 
5351   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
5352   a copy of M or reassemble it when requested.
5353 
5354 .seealso: TSSetIFunction(), TSSetIJacobian(), TSComputeIFunctionLinear()
5355 @*/
5356 PetscErrorCode TSComputeIJacobianConstant(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat A,Mat B,void *ctx)
5357 {
5358   PetscErrorCode ierr;
5359 
5360   PetscFunctionBegin;
5361   ierr = MatScale(A, shift / ts->ijacobian.shift);CHKERRQ(ierr);
5362   ts->ijacobian.shift = shift;
5363   PetscFunctionReturn(0);
5364 }
5365 
5366 #undef __FUNCT__
5367 #define __FUNCT__ "TSGetEquationType"
5368 /*@
5369    TSGetEquationType - Gets the type of the equation that TS is solving.
5370 
5371    Not Collective
5372 
5373    Input Parameter:
5374 .  ts - the TS context
5375 
5376    Output Parameter:
5377 .  equation_type - see TSEquationType
5378 
5379    Level: beginner
5380 
5381 .keywords: TS, equation type
5382 
5383 .seealso: TSSetEquationType(), TSEquationType
5384 @*/
5385 PetscErrorCode  TSGetEquationType(TS ts,TSEquationType *equation_type)
5386 {
5387   PetscFunctionBegin;
5388   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5389   PetscValidPointer(equation_type,2);
5390   *equation_type = ts->equation_type;
5391   PetscFunctionReturn(0);
5392 }
5393 
5394 #undef __FUNCT__
5395 #define __FUNCT__ "TSSetEquationType"
5396 /*@
5397    TSSetEquationType - Sets the type of the equation that TS is solving.
5398 
5399    Not Collective
5400 
5401    Input Parameter:
5402 +  ts - the TS context
5403 -  equation_type - see TSEquationType
5404 
5405    Level: advanced
5406 
5407 .keywords: TS, equation type
5408 
5409 .seealso: TSGetEquationType(), TSEquationType
5410 @*/
5411 PetscErrorCode  TSSetEquationType(TS ts,TSEquationType equation_type)
5412 {
5413   PetscFunctionBegin;
5414   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5415   ts->equation_type = equation_type;
5416   PetscFunctionReturn(0);
5417 }
5418 
5419 #undef __FUNCT__
5420 #define __FUNCT__ "TSGetConvergedReason"
5421 /*@
5422    TSGetConvergedReason - Gets the reason the TS iteration was stopped.
5423 
5424    Not Collective
5425 
5426    Input Parameter:
5427 .  ts - the TS context
5428 
5429    Output Parameter:
5430 .  reason - negative value indicates diverged, positive value converged, see TSConvergedReason or the
5431             manual pages for the individual convergence tests for complete lists
5432 
5433    Level: beginner
5434 
5435    Notes:
5436    Can only be called after the call to TSSolve() is complete.
5437 
5438 .keywords: TS, nonlinear, set, convergence, test
5439 
5440 .seealso: TSSetConvergenceTest(), TSConvergedReason
5441 @*/
5442 PetscErrorCode  TSGetConvergedReason(TS ts,TSConvergedReason *reason)
5443 {
5444   PetscFunctionBegin;
5445   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5446   PetscValidPointer(reason,2);
5447   *reason = ts->reason;
5448   PetscFunctionReturn(0);
5449 }
5450 
5451 #undef __FUNCT__
5452 #define __FUNCT__ "TSSetConvergedReason"
5453 /*@
5454    TSSetConvergedReason - Sets the reason for handling the convergence of TSSolve.
5455 
5456    Not Collective
5457 
5458    Input Parameter:
5459 +  ts - the TS context
5460 .  reason - negative value indicates diverged, positive value converged, see TSConvergedReason or the
5461             manual pages for the individual convergence tests for complete lists
5462 
5463    Level: advanced
5464 
5465    Notes:
5466    Can only be called during TSSolve() is active.
5467 
5468 .keywords: TS, nonlinear, set, convergence, test
5469 
5470 .seealso: TSConvergedReason
5471 @*/
5472 PetscErrorCode  TSSetConvergedReason(TS ts,TSConvergedReason reason)
5473 {
5474   PetscFunctionBegin;
5475   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5476   ts->reason = reason;
5477   PetscFunctionReturn(0);
5478 }
5479 
5480 #undef __FUNCT__
5481 #define __FUNCT__ "TSGetSolveTime"
5482 /*@
5483    TSGetSolveTime - Gets the time after a call to TSSolve()
5484 
5485    Not Collective
5486 
5487    Input Parameter:
5488 .  ts - the TS context
5489 
5490    Output Parameter:
5491 .  ftime - the final time. This time corresponds to the final time set with TSSetDuration()
5492 
5493    Level: beginner
5494 
5495    Notes:
5496    Can only be called after the call to TSSolve() is complete.
5497 
5498 .keywords: TS, nonlinear, set, convergence, test
5499 
5500 .seealso: TSSetConvergenceTest(), TSConvergedReason
5501 @*/
5502 PetscErrorCode  TSGetSolveTime(TS ts,PetscReal *ftime)
5503 {
5504   PetscFunctionBegin;
5505   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5506   PetscValidPointer(ftime,2);
5507   *ftime = ts->solvetime;
5508   PetscFunctionReturn(0);
5509 }
5510 
5511 #undef __FUNCT__
5512 #define __FUNCT__ "TSGetTotalSteps"
5513 /*@
5514    TSGetTotalSteps - Gets the total number of steps done since the last call to TSSetUp() or TSCreate()
5515 
5516    Not Collective
5517 
5518    Input Parameter:
5519 .  ts - the TS context
5520 
5521    Output Parameter:
5522 .  steps - the number of steps
5523 
5524    Level: beginner
5525 
5526    Notes:
5527    Includes the number of steps for all calls to TSSolve() since TSSetUp() was called
5528 
5529 .keywords: TS, nonlinear, set, convergence, test
5530 
5531 .seealso: TSSetConvergenceTest(), TSConvergedReason
5532 @*/
5533 PetscErrorCode  TSGetTotalSteps(TS ts,PetscInt *steps)
5534 {
5535   PetscFunctionBegin;
5536   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5537   PetscValidPointer(steps,2);
5538   *steps = ts->total_steps;
5539   PetscFunctionReturn(0);
5540 }
5541 
5542 #undef __FUNCT__
5543 #define __FUNCT__ "TSGetSNESIterations"
5544 /*@
5545    TSGetSNESIterations - Gets the total number of nonlinear iterations
5546    used by the time integrator.
5547 
5548    Not Collective
5549 
5550    Input Parameter:
5551 .  ts - TS context
5552 
5553    Output Parameter:
5554 .  nits - number of nonlinear iterations
5555 
5556    Notes:
5557    This counter is reset to zero for each successive call to TSSolve().
5558 
5559    Level: intermediate
5560 
5561 .keywords: TS, get, number, nonlinear, iterations
5562 
5563 .seealso:  TSGetKSPIterations()
5564 @*/
5565 PetscErrorCode TSGetSNESIterations(TS ts,PetscInt *nits)
5566 {
5567   PetscFunctionBegin;
5568   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5569   PetscValidIntPointer(nits,2);
5570   *nits = ts->snes_its;
5571   PetscFunctionReturn(0);
5572 }
5573 
5574 #undef __FUNCT__
5575 #define __FUNCT__ "TSGetKSPIterations"
5576 /*@
5577    TSGetKSPIterations - Gets the total number of linear iterations
5578    used by the time integrator.
5579 
5580    Not Collective
5581 
5582    Input Parameter:
5583 .  ts - TS context
5584 
5585    Output Parameter:
5586 .  lits - number of linear iterations
5587 
5588    Notes:
5589    This counter is reset to zero for each successive call to TSSolve().
5590 
5591    Level: intermediate
5592 
5593 .keywords: TS, get, number, linear, iterations
5594 
5595 .seealso:  TSGetSNESIterations(), SNESGetKSPIterations()
5596 @*/
5597 PetscErrorCode TSGetKSPIterations(TS ts,PetscInt *lits)
5598 {
5599   PetscFunctionBegin;
5600   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5601   PetscValidIntPointer(lits,2);
5602   *lits = ts->ksp_its;
5603   PetscFunctionReturn(0);
5604 }
5605 
5606 #undef __FUNCT__
5607 #define __FUNCT__ "TSGetStepRejections"
5608 /*@
5609    TSGetStepRejections - Gets the total number of rejected steps.
5610 
5611    Not Collective
5612 
5613    Input Parameter:
5614 .  ts - TS context
5615 
5616    Output Parameter:
5617 .  rejects - number of steps rejected
5618 
5619    Notes:
5620    This counter is reset to zero for each successive call to TSSolve().
5621 
5622    Level: intermediate
5623 
5624 .keywords: TS, get, number
5625 
5626 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetSNESFailures(), TSSetMaxSNESFailures(), TSSetErrorIfStepFails()
5627 @*/
5628 PetscErrorCode TSGetStepRejections(TS ts,PetscInt *rejects)
5629 {
5630   PetscFunctionBegin;
5631   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5632   PetscValidIntPointer(rejects,2);
5633   *rejects = ts->reject;
5634   PetscFunctionReturn(0);
5635 }
5636 
5637 #undef __FUNCT__
5638 #define __FUNCT__ "TSGetSNESFailures"
5639 /*@
5640    TSGetSNESFailures - Gets the total number of failed SNES solves
5641 
5642    Not Collective
5643 
5644    Input Parameter:
5645 .  ts - TS context
5646 
5647    Output Parameter:
5648 .  fails - number of failed nonlinear solves
5649 
5650    Notes:
5651    This counter is reset to zero for each successive call to TSSolve().
5652 
5653    Level: intermediate
5654 
5655 .keywords: TS, get, number
5656 
5657 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSSetMaxSNESFailures()
5658 @*/
5659 PetscErrorCode TSGetSNESFailures(TS ts,PetscInt *fails)
5660 {
5661   PetscFunctionBegin;
5662   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5663   PetscValidIntPointer(fails,2);
5664   *fails = ts->num_snes_failures;
5665   PetscFunctionReturn(0);
5666 }
5667 
5668 #undef __FUNCT__
5669 #define __FUNCT__ "TSSetMaxStepRejections"
5670 /*@
5671    TSSetMaxStepRejections - Sets the maximum number of step rejections before a step fails
5672 
5673    Not Collective
5674 
5675    Input Parameter:
5676 +  ts - TS context
5677 -  rejects - maximum number of rejected steps, pass -1 for unlimited
5678 
5679    Notes:
5680    The counter is reset to zero for each step
5681 
5682    Options Database Key:
5683  .  -ts_max_reject - Maximum number of step rejections before a step fails
5684 
5685    Level: intermediate
5686 
5687 .keywords: TS, set, maximum, number
5688 
5689 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxSNESFailures(), TSGetStepRejections(), TSGetSNESFailures(), TSSetErrorIfStepFails(), TSGetConvergedReason()
5690 @*/
5691 PetscErrorCode TSSetMaxStepRejections(TS ts,PetscInt rejects)
5692 {
5693   PetscFunctionBegin;
5694   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5695   ts->max_reject = rejects;
5696   PetscFunctionReturn(0);
5697 }
5698 
5699 #undef __FUNCT__
5700 #define __FUNCT__ "TSSetMaxSNESFailures"
5701 /*@
5702    TSSetMaxSNESFailures - Sets the maximum number of failed SNES solves
5703 
5704    Not Collective
5705 
5706    Input Parameter:
5707 +  ts - TS context
5708 -  fails - maximum number of failed nonlinear solves, pass -1 for unlimited
5709 
5710    Notes:
5711    The counter is reset to zero for each successive call to TSSolve().
5712 
5713    Options Database Key:
5714  .  -ts_max_snes_failures - Maximum number of nonlinear solve failures
5715 
5716    Level: intermediate
5717 
5718 .keywords: TS, set, maximum, number
5719 
5720 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSGetSNESFailures(), SNESGetConvergedReason(), TSGetConvergedReason()
5721 @*/
5722 PetscErrorCode TSSetMaxSNESFailures(TS ts,PetscInt fails)
5723 {
5724   PetscFunctionBegin;
5725   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5726   ts->max_snes_failures = fails;
5727   PetscFunctionReturn(0);
5728 }
5729 
5730 #undef __FUNCT__
5731 #define __FUNCT__ "TSSetErrorIfStepFails"
5732 /*@
5733    TSSetErrorIfStepFails - Error if no step succeeds
5734 
5735    Not Collective
5736 
5737    Input Parameter:
5738 +  ts - TS context
5739 -  err - PETSC_TRUE to error if no step succeeds, PETSC_FALSE to return without failure
5740 
5741    Options Database Key:
5742  .  -ts_error_if_step_fails - Error if no step succeeds
5743 
5744    Level: intermediate
5745 
5746 .keywords: TS, set, error
5747 
5748 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSGetSNESFailures(), TSSetErrorIfStepFails(), TSGetConvergedReason()
5749 @*/
5750 PetscErrorCode TSSetErrorIfStepFails(TS ts,PetscBool err)
5751 {
5752   PetscFunctionBegin;
5753   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5754   ts->errorifstepfailed = err;
5755   PetscFunctionReturn(0);
5756 }
5757 
5758 #undef __FUNCT__
5759 #define __FUNCT__ "TSMonitorSolution"
5760 /*@C
5761    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
5762 
5763    Collective on TS
5764 
5765    Input Parameters:
5766 +  ts - the TS context
5767 .  step - current time-step
5768 .  ptime - current time
5769 .  u - current state
5770 -  vf - viewer and its format
5771 
5772    Level: intermediate
5773 
5774 .keywords: TS,  vector, monitor, view
5775 
5776 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
5777 @*/
5778 PetscErrorCode  TSMonitorSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscViewerAndFormat *vf)
5779 {
5780   PetscErrorCode ierr;
5781 
5782   PetscFunctionBegin;
5783   ierr = PetscViewerPushFormat(vf->viewer,vf->format);CHKERRQ(ierr);
5784   ierr = VecView(u,vf->viewer);CHKERRQ(ierr);
5785   ierr = PetscViewerPopFormat(vf->viewer);CHKERRQ(ierr);
5786   PetscFunctionReturn(0);
5787 }
5788 
5789 #undef __FUNCT__
5790 #define __FUNCT__ "TSMonitorSolutionVTK"
5791 /*@C
5792    TSMonitorSolutionVTK - Monitors progress of the TS solvers by VecView() for the solution at each timestep.
5793 
5794    Collective on TS
5795 
5796    Input Parameters:
5797 +  ts - the TS context
5798 .  step - current time-step
5799 .  ptime - current time
5800 .  u - current state
5801 -  filenametemplate - string containing a format specifier for the integer time step (e.g. %03D)
5802 
5803    Level: intermediate
5804 
5805    Notes:
5806    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.
5807    These are named according to the file name template.
5808 
5809    This function is normally passed as an argument to TSMonitorSet() along with TSMonitorSolutionVTKDestroy().
5810 
5811 .keywords: TS,  vector, monitor, view
5812 
5813 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
5814 @*/
5815 PetscErrorCode TSMonitorSolutionVTK(TS ts,PetscInt step,PetscReal ptime,Vec u,void *filenametemplate)
5816 {
5817   PetscErrorCode ierr;
5818   char           filename[PETSC_MAX_PATH_LEN];
5819   PetscViewer    viewer;
5820 
5821   PetscFunctionBegin;
5822   if (step < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
5823   ierr = PetscSNPrintf(filename,sizeof(filename),(const char*)filenametemplate,step);CHKERRQ(ierr);
5824   ierr = PetscViewerVTKOpen(PetscObjectComm((PetscObject)ts),filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
5825   ierr = VecView(u,viewer);CHKERRQ(ierr);
5826   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
5827   PetscFunctionReturn(0);
5828 }
5829 
5830 #undef __FUNCT__
5831 #define __FUNCT__ "TSMonitorSolutionVTKDestroy"
5832 /*@C
5833    TSMonitorSolutionVTKDestroy - Destroy context for monitoring
5834 
5835    Collective on TS
5836 
5837    Input Parameters:
5838 .  filenametemplate - string containing a format specifier for the integer time step (e.g. %03D)
5839 
5840    Level: intermediate
5841 
5842    Note:
5843    This function is normally passed to TSMonitorSet() along with TSMonitorSolutionVTK().
5844 
5845 .keywords: TS,  vector, monitor, view
5846 
5847 .seealso: TSMonitorSet(), TSMonitorSolutionVTK()
5848 @*/
5849 PetscErrorCode TSMonitorSolutionVTKDestroy(void *filenametemplate)
5850 {
5851   PetscErrorCode ierr;
5852 
5853   PetscFunctionBegin;
5854   ierr = PetscFree(*(char**)filenametemplate);CHKERRQ(ierr);
5855   PetscFunctionReturn(0);
5856 }
5857 
5858 #undef __FUNCT__
5859 #define __FUNCT__ "TSGetAdapt"
5860 /*@
5861    TSGetAdapt - Get the adaptive controller context for the current method
5862 
5863    Collective on TS if controller has not been created yet
5864 
5865    Input Arguments:
5866 .  ts - time stepping context
5867 
5868    Output Arguments:
5869 .  adapt - adaptive controller
5870 
5871    Level: intermediate
5872 
5873 .seealso: TSAdapt, TSAdaptSetType(), TSAdaptChoose()
5874 @*/
5875 PetscErrorCode TSGetAdapt(TS ts,TSAdapt *adapt)
5876 {
5877   PetscErrorCode ierr;
5878 
5879   PetscFunctionBegin;
5880   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5881   PetscValidPointer(adapt,2);
5882   if (!ts->adapt) {
5883     ierr = TSAdaptCreate(PetscObjectComm((PetscObject)ts),&ts->adapt);CHKERRQ(ierr);
5884     ierr = PetscLogObjectParent((PetscObject)ts,(PetscObject)ts->adapt);CHKERRQ(ierr);
5885     ierr = PetscObjectIncrementTabLevel((PetscObject)ts->adapt,(PetscObject)ts,1);CHKERRQ(ierr);
5886   }
5887   *adapt = ts->adapt;
5888   PetscFunctionReturn(0);
5889 }
5890 
5891 #undef __FUNCT__
5892 #define __FUNCT__ "TSSetTolerances"
5893 /*@
5894    TSSetTolerances - Set tolerances for local truncation error when using adaptive controller
5895 
5896    Logically Collective
5897 
5898    Input Arguments:
5899 +  ts - time integration context
5900 .  atol - scalar absolute tolerances, PETSC_DECIDE to leave current value
5901 .  vatol - vector of absolute tolerances or NULL, used in preference to atol if present
5902 .  rtol - scalar relative tolerances, PETSC_DECIDE to leave current value
5903 -  vrtol - vector of relative tolerances or NULL, used in preference to atol if present
5904 
5905    Options Database keys:
5906 +  -ts_rtol <rtol> - relative tolerance for local truncation error
5907 -  -ts_atol <atol> Absolute tolerance for local truncation error
5908 
5909    Notes:
5910    With PETSc's implicit schemes for DAE problems, the calculation of the local truncation error
5911    (LTE) includes both the differential and the algebraic variables. If one wants the LTE to be
5912    computed only for the differential or the algebraic part then this can be done using the vector of
5913    tolerances vatol. For example, by setting the tolerance vector with the desired tolerance for the
5914    differential part and infinity for the algebraic part, the LTE calculation will include only the
5915    differential variables.
5916 
5917    Level: beginner
5918 
5919 .seealso: TS, TSAdapt, TSVecNormWRMS(), TSGetTolerances()
5920 @*/
5921 PetscErrorCode TSSetTolerances(TS ts,PetscReal atol,Vec vatol,PetscReal rtol,Vec vrtol)
5922 {
5923   PetscErrorCode ierr;
5924 
5925   PetscFunctionBegin;
5926   if (atol != PETSC_DECIDE && atol != PETSC_DEFAULT) ts->atol = atol;
5927   if (vatol) {
5928     ierr = PetscObjectReference((PetscObject)vatol);CHKERRQ(ierr);
5929     ierr = VecDestroy(&ts->vatol);CHKERRQ(ierr);
5930     ts->vatol = vatol;
5931   }
5932   if (rtol != PETSC_DECIDE && rtol != PETSC_DEFAULT) ts->rtol = rtol;
5933   if (vrtol) {
5934     ierr = PetscObjectReference((PetscObject)vrtol);CHKERRQ(ierr);
5935     ierr = VecDestroy(&ts->vrtol);CHKERRQ(ierr);
5936     ts->vrtol = vrtol;
5937   }
5938   PetscFunctionReturn(0);
5939 }
5940 
5941 #undef __FUNCT__
5942 #define __FUNCT__ "TSGetTolerances"
5943 /*@
5944    TSGetTolerances - Get tolerances for local truncation error when using adaptive controller
5945 
5946    Logically Collective
5947 
5948    Input Arguments:
5949 .  ts - time integration context
5950 
5951    Output Arguments:
5952 +  atol - scalar absolute tolerances, NULL to ignore
5953 .  vatol - vector of absolute tolerances, NULL to ignore
5954 .  rtol - scalar relative tolerances, NULL to ignore
5955 -  vrtol - vector of relative tolerances, NULL to ignore
5956 
5957    Level: beginner
5958 
5959 .seealso: TS, TSAdapt, TSVecNormWRMS(), TSSetTolerances()
5960 @*/
5961 PetscErrorCode TSGetTolerances(TS ts,PetscReal *atol,Vec *vatol,PetscReal *rtol,Vec *vrtol)
5962 {
5963   PetscFunctionBegin;
5964   if (atol)  *atol  = ts->atol;
5965   if (vatol) *vatol = ts->vatol;
5966   if (rtol)  *rtol  = ts->rtol;
5967   if (vrtol) *vrtol = ts->vrtol;
5968   PetscFunctionReturn(0);
5969 }
5970 
5971 #undef __FUNCT__
5972 #define __FUNCT__ "TSErrorWeightedNorm2"
5973 /*@
5974    TSErrorWeightedNorm2 - compute a weighted 2-norm of the difference between two state vectors
5975 
5976    Collective on TS
5977 
5978    Input Arguments:
5979 +  ts - time stepping context
5980 .  U - state vector, usually ts->vec_sol
5981 -  Y - state vector to be compared to U
5982 
5983    Output Arguments:
5984 .  norm - weighted norm, a value of 1.0 is considered small
5985 
5986    Level: developer
5987 
5988 .seealso: TSErrorWeightedNorm(), TSErrorWeightedNormInfinity()
5989 @*/
5990 PetscErrorCode TSErrorWeightedNorm2(TS ts,Vec U,Vec Y,PetscReal *norm)
5991 {
5992   PetscErrorCode    ierr;
5993   PetscInt          i,n,N,rstart;
5994   const PetscScalar *u,*y;
5995   PetscReal         sum,gsum;
5996   PetscReal         tol;
5997 
5998   PetscFunctionBegin;
5999   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6000   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
6001   PetscValidHeaderSpecific(Y,VEC_CLASSID,3);
6002   PetscValidType(U,2);
6003   PetscValidType(Y,3);
6004   PetscCheckSameComm(U,2,Y,3);
6005   PetscValidPointer(norm,4);
6006   if (U == Y) SETERRQ(PetscObjectComm((PetscObject)U),PETSC_ERR_ARG_IDN,"U and Y cannot be the same vector");
6007 
6008   ierr = VecGetSize(U,&N);CHKERRQ(ierr);
6009   ierr = VecGetLocalSize(U,&n);CHKERRQ(ierr);
6010   ierr = VecGetOwnershipRange(U,&rstart,NULL);CHKERRQ(ierr);
6011   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
6012   ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
6013   sum  = 0.;
6014   if (ts->vatol && ts->vrtol) {
6015     const PetscScalar *atol,*rtol;
6016     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6017     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6018     for (i=0; i<n; i++) {
6019       tol = PetscRealPart(atol[i]) + PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6020       sum += PetscSqr(PetscAbsScalar(y[i] - u[i]) / tol);
6021     }
6022     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6023     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6024   } else if (ts->vatol) {       /* vector atol, scalar rtol */
6025     const PetscScalar *atol;
6026     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6027     for (i=0; i<n; i++) {
6028       tol = PetscRealPart(atol[i]) + ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6029       sum += PetscSqr(PetscAbsScalar(y[i] - u[i]) / tol);
6030     }
6031     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6032   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
6033     const PetscScalar *rtol;
6034     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6035     for (i=0; i<n; i++) {
6036       tol = ts->atol + PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6037       sum += PetscSqr(PetscAbsScalar(y[i] - u[i]) / tol);
6038     }
6039     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6040   } else {                      /* scalar atol, scalar rtol */
6041     for (i=0; i<n; i++) {
6042       tol = ts->atol + ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6043       sum += PetscSqr(PetscAbsScalar(y[i] - u[i]) / tol);
6044     }
6045   }
6046   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
6047   ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
6048 
6049   ierr  = MPIU_Allreduce(&sum,&gsum,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6050   *norm = PetscSqrtReal(gsum / N);
6051 
6052   if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
6053   PetscFunctionReturn(0);
6054 }
6055 
6056 #undef __FUNCT__
6057 #define __FUNCT__ "TSErrorWeightedNormInfinity"
6058 /*@
6059    TSErrorWeightedNormInfinity - compute a weighted infinity-norm of the difference between two state vectors
6060 
6061    Collective on TS
6062 
6063    Input Arguments:
6064 +  ts - time stepping context
6065 .  U - state vector, usually ts->vec_sol
6066 -  Y - state vector to be compared to U
6067 
6068    Output Arguments:
6069 .  norm - weighted norm, a value of 1.0 is considered small
6070 
6071    Level: developer
6072 
6073 .seealso: TSErrorWeightedNorm(), TSErrorWeightedNorm2()
6074 @*/
6075 PetscErrorCode TSErrorWeightedNormInfinity(TS ts,Vec U,Vec Y,PetscReal *norm)
6076 {
6077   PetscErrorCode    ierr;
6078   PetscInt          i,n,N,rstart,k;
6079   const PetscScalar *u,*y;
6080   PetscReal         max,gmax;
6081   PetscReal         tol;
6082 
6083   PetscFunctionBegin;
6084   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6085   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
6086   PetscValidHeaderSpecific(Y,VEC_CLASSID,3);
6087   PetscValidType(U,2);
6088   PetscValidType(Y,3);
6089   PetscCheckSameComm(U,2,Y,3);
6090   PetscValidPointer(norm,4);
6091   if (U == Y) SETERRQ(PetscObjectComm((PetscObject)U),PETSC_ERR_ARG_IDN,"U and Y cannot be the same vector");
6092 
6093   ierr = VecGetSize(U,&N);CHKERRQ(ierr);
6094   ierr = VecGetLocalSize(U,&n);CHKERRQ(ierr);
6095   ierr = VecGetOwnershipRange(U,&rstart,NULL);CHKERRQ(ierr);
6096   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
6097   ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
6098   if (ts->vatol && ts->vrtol) {
6099     const PetscScalar *atol,*rtol;
6100     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6101     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6102     k = 0;
6103     tol = PetscRealPart(atol[k]) + PetscRealPart(rtol[k]) * PetscMax(PetscAbsScalar(u[k]),PetscAbsScalar(y[k]));
6104     max = PetscAbsScalar(y[k] - u[k]) / tol;
6105     for (i=1; i<n; i++) {
6106       tol = PetscRealPart(atol[i]) + PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6107       max = PetscMax(max,PetscAbsScalar(y[i] - u[i]) / tol);
6108     }
6109     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6110     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6111   } else if (ts->vatol) {       /* vector atol, scalar rtol */
6112     const PetscScalar *atol;
6113     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6114     k = 0;
6115     tol = PetscRealPart(atol[k]) + ts->rtol * PetscMax(PetscAbsScalar(u[k]),PetscAbsScalar(y[k]));
6116     max = PetscAbsScalar(y[k] - u[k]) / tol;
6117     for (i=1; i<n; i++) {
6118       tol = PetscRealPart(atol[i]) + ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6119       max = PetscMax(max,PetscAbsScalar(y[i] - u[i]) / tol);
6120     }
6121     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6122   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
6123     const PetscScalar *rtol;
6124     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6125     k = 0;
6126     tol = ts->atol + PetscRealPart(rtol[k]) * PetscMax(PetscAbsScalar(u[k]),PetscAbsScalar(y[k]));
6127     max = PetscAbsScalar(y[k] - u[k]) / tol;
6128     for (i=1; i<n; i++) {
6129       tol = ts->atol + PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6130       max = PetscMax(max,PetscAbsScalar(y[i] - u[i]) / tol);
6131     }
6132     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6133   } else {                      /* scalar atol, scalar rtol */
6134     k = 0;
6135     tol = ts->atol + ts->rtol * PetscMax(PetscAbsScalar(u[k]),PetscAbsScalar(y[k]));
6136     max = PetscAbsScalar(y[k] - u[k]) / tol;
6137     for (i=1; i<n; i++) {
6138       tol = ts->atol + ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6139       max = PetscMax(max,PetscAbsScalar(y[i] - u[i]) / tol);
6140     }
6141   }
6142   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
6143   ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
6144 
6145   ierr  = MPIU_Allreduce(&max,&gmax,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6146   *norm = gmax;
6147 
6148   if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
6149   PetscFunctionReturn(0);
6150 }
6151 
6152 #undef __FUNCT__
6153 #define __FUNCT__ "TSErrorWeightedNorm"
6154 /*@
6155    TSErrorWeightedNorm - compute a weighted norm of the difference between two state vectors
6156 
6157    Collective on TS
6158 
6159    Input Arguments:
6160 +  ts - time stepping context
6161 .  U - state vector, usually ts->vec_sol
6162 .  Y - state vector to be compared to U
6163 -  wnormtype - norm type, either NORM_2 or NORM_INFINITY
6164 
6165    Output Arguments:
6166 .  norm - weighted norm, a value of 1.0 is considered small
6167 
6168 
6169    Options Database Keys:
6170 .  -ts_adapt_wnormtype <wnormtype> - 2, INFINITY
6171 
6172    Level: developer
6173 
6174 .seealso: TSErrorWeightedNormInfinity(), TSErrorWeightedNorm2()
6175 @*/
6176 PetscErrorCode TSErrorWeightedNorm(TS ts,Vec U,Vec Y,NormType wnormtype,PetscReal *norm)
6177 {
6178   PetscErrorCode ierr;
6179 
6180   PetscFunctionBegin;
6181   if (wnormtype == NORM_2) {
6182     ierr = TSErrorWeightedNorm2(ts,U,Y,norm);CHKERRQ(ierr);
6183   } else if(wnormtype == NORM_INFINITY) {
6184     ierr = TSErrorWeightedNormInfinity(ts,U,Y,norm);CHKERRQ(ierr);
6185   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
6186   PetscFunctionReturn(0);
6187 }
6188 
6189 #undef __FUNCT__
6190 #define __FUNCT__ "TSSetCFLTimeLocal"
6191 /*@
6192    TSSetCFLTimeLocal - Set the local CFL constraint relative to forward Euler
6193 
6194    Logically Collective on TS
6195 
6196    Input Arguments:
6197 +  ts - time stepping context
6198 -  cfltime - maximum stable time step if using forward Euler (value can be different on each process)
6199 
6200    Note:
6201    After calling this function, the global CFL time can be obtained by calling TSGetCFLTime()
6202 
6203    Level: intermediate
6204 
6205 .seealso: TSGetCFLTime(), TSADAPTCFL
6206 @*/
6207 PetscErrorCode TSSetCFLTimeLocal(TS ts,PetscReal cfltime)
6208 {
6209   PetscFunctionBegin;
6210   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6211   ts->cfltime_local = cfltime;
6212   ts->cfltime       = -1.;
6213   PetscFunctionReturn(0);
6214 }
6215 
6216 #undef __FUNCT__
6217 #define __FUNCT__ "TSGetCFLTime"
6218 /*@
6219    TSGetCFLTime - Get the maximum stable time step according to CFL criteria applied to forward Euler
6220 
6221    Collective on TS
6222 
6223    Input Arguments:
6224 .  ts - time stepping context
6225 
6226    Output Arguments:
6227 .  cfltime - maximum stable time step for forward Euler
6228 
6229    Level: advanced
6230 
6231 .seealso: TSSetCFLTimeLocal()
6232 @*/
6233 PetscErrorCode TSGetCFLTime(TS ts,PetscReal *cfltime)
6234 {
6235   PetscErrorCode ierr;
6236 
6237   PetscFunctionBegin;
6238   if (ts->cfltime < 0) {
6239     ierr = MPIU_Allreduce(&ts->cfltime_local,&ts->cfltime,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6240   }
6241   *cfltime = ts->cfltime;
6242   PetscFunctionReturn(0);
6243 }
6244 
6245 #undef __FUNCT__
6246 #define __FUNCT__ "TSVISetVariableBounds"
6247 /*@
6248    TSVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu
6249 
6250    Input Parameters:
6251 .  ts   - the TS context.
6252 .  xl   - lower bound.
6253 .  xu   - upper bound.
6254 
6255    Notes:
6256    If this routine is not called then the lower and upper bounds are set to
6257    PETSC_NINFINITY and PETSC_INFINITY respectively during SNESSetUp().
6258 
6259    Level: advanced
6260 
6261 @*/
6262 PetscErrorCode TSVISetVariableBounds(TS ts, Vec xl, Vec xu)
6263 {
6264   PetscErrorCode ierr;
6265   SNES           snes;
6266 
6267   PetscFunctionBegin;
6268   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
6269   ierr = SNESVISetVariableBounds(snes,xl,xu);CHKERRQ(ierr);
6270   PetscFunctionReturn(0);
6271 }
6272 
6273 #if defined(PETSC_HAVE_MATLAB_ENGINE)
6274 #include <mex.h>
6275 
6276 typedef struct {char *funcname; mxArray *ctx;} TSMatlabContext;
6277 
6278 #undef __FUNCT__
6279 #define __FUNCT__ "TSComputeFunction_Matlab"
6280 /*
6281    TSComputeFunction_Matlab - Calls the function that has been set with
6282                          TSSetFunctionMatlab().
6283 
6284    Collective on TS
6285 
6286    Input Parameters:
6287 +  snes - the TS context
6288 -  u - input vector
6289 
6290    Output Parameter:
6291 .  y - function vector, as set by TSSetFunction()
6292 
6293    Notes:
6294    TSComputeFunction() is typically used within nonlinear solvers
6295    implementations, so most users would not generally call this routine
6296    themselves.
6297 
6298    Level: developer
6299 
6300 .keywords: TS, nonlinear, compute, function
6301 
6302 .seealso: TSSetFunction(), TSGetFunction()
6303 */
6304 PetscErrorCode  TSComputeFunction_Matlab(TS snes,PetscReal time,Vec u,Vec udot,Vec y, void *ctx)
6305 {
6306   PetscErrorCode  ierr;
6307   TSMatlabContext *sctx = (TSMatlabContext*)ctx;
6308   int             nlhs  = 1,nrhs = 7;
6309   mxArray         *plhs[1],*prhs[7];
6310   long long int   lx = 0,lxdot = 0,ly = 0,ls = 0;
6311 
6312   PetscFunctionBegin;
6313   PetscValidHeaderSpecific(snes,TS_CLASSID,1);
6314   PetscValidHeaderSpecific(u,VEC_CLASSID,3);
6315   PetscValidHeaderSpecific(udot,VEC_CLASSID,4);
6316   PetscValidHeaderSpecific(y,VEC_CLASSID,5);
6317   PetscCheckSameComm(snes,1,u,3);
6318   PetscCheckSameComm(snes,1,y,5);
6319 
6320   ierr = PetscMemcpy(&ls,&snes,sizeof(snes));CHKERRQ(ierr);
6321   ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
6322   ierr = PetscMemcpy(&lxdot,&udot,sizeof(udot));CHKERRQ(ierr);
6323   ierr = PetscMemcpy(&ly,&y,sizeof(u));CHKERRQ(ierr);
6324 
6325   prhs[0] =  mxCreateDoubleScalar((double)ls);
6326   prhs[1] =  mxCreateDoubleScalar(time);
6327   prhs[2] =  mxCreateDoubleScalar((double)lx);
6328   prhs[3] =  mxCreateDoubleScalar((double)lxdot);
6329   prhs[4] =  mxCreateDoubleScalar((double)ly);
6330   prhs[5] =  mxCreateString(sctx->funcname);
6331   prhs[6] =  sctx->ctx;
6332   ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSComputeFunctionInternal");CHKERRQ(ierr);
6333   ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
6334   mxDestroyArray(prhs[0]);
6335   mxDestroyArray(prhs[1]);
6336   mxDestroyArray(prhs[2]);
6337   mxDestroyArray(prhs[3]);
6338   mxDestroyArray(prhs[4]);
6339   mxDestroyArray(prhs[5]);
6340   mxDestroyArray(plhs[0]);
6341   PetscFunctionReturn(0);
6342 }
6343 
6344 
6345 #undef __FUNCT__
6346 #define __FUNCT__ "TSSetFunctionMatlab"
6347 /*
6348    TSSetFunctionMatlab - Sets the function evaluation routine and function
6349    vector for use by the TS routines in solving ODEs
6350    equations from MATLAB. Here the function is a string containing the name of a MATLAB function
6351 
6352    Logically Collective on TS
6353 
6354    Input Parameters:
6355 +  ts - the TS context
6356 -  func - function evaluation routine
6357 
6358    Calling sequence of func:
6359 $    func (TS ts,PetscReal time,Vec u,Vec udot,Vec f,void *ctx);
6360 
6361    Level: beginner
6362 
6363 .keywords: TS, nonlinear, set, function
6364 
6365 .seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
6366 */
6367 PetscErrorCode  TSSetFunctionMatlab(TS ts,const char *func,mxArray *ctx)
6368 {
6369   PetscErrorCode  ierr;
6370   TSMatlabContext *sctx;
6371 
6372   PetscFunctionBegin;
6373   /* currently sctx is memory bleed */
6374   ierr = PetscNew(&sctx);CHKERRQ(ierr);
6375   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
6376   /*
6377      This should work, but it doesn't
6378   sctx->ctx = ctx;
6379   mexMakeArrayPersistent(sctx->ctx);
6380   */
6381   sctx->ctx = mxDuplicateArray(ctx);
6382 
6383   ierr = TSSetIFunction(ts,NULL,TSComputeFunction_Matlab,sctx);CHKERRQ(ierr);
6384   PetscFunctionReturn(0);
6385 }
6386 
6387 #undef __FUNCT__
6388 #define __FUNCT__ "TSComputeJacobian_Matlab"
6389 /*
6390    TSComputeJacobian_Matlab - Calls the function that has been set with
6391                          TSSetJacobianMatlab().
6392 
6393    Collective on TS
6394 
6395    Input Parameters:
6396 +  ts - the TS context
6397 .  u - input vector
6398 .  A, B - the matrices
6399 -  ctx - user context
6400 
6401    Level: developer
6402 
6403 .keywords: TS, nonlinear, compute, function
6404 
6405 .seealso: TSSetFunction(), TSGetFunction()
6406 @*/
6407 PetscErrorCode  TSComputeJacobian_Matlab(TS ts,PetscReal time,Vec u,Vec udot,PetscReal shift,Mat A,Mat B,void *ctx)
6408 {
6409   PetscErrorCode  ierr;
6410   TSMatlabContext *sctx = (TSMatlabContext*)ctx;
6411   int             nlhs  = 2,nrhs = 9;
6412   mxArray         *plhs[2],*prhs[9];
6413   long long int   lx = 0,lxdot = 0,lA = 0,ls = 0, lB = 0;
6414 
6415   PetscFunctionBegin;
6416   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6417   PetscValidHeaderSpecific(u,VEC_CLASSID,3);
6418 
6419   /* call Matlab function in ctx with arguments u and y */
6420 
6421   ierr = PetscMemcpy(&ls,&ts,sizeof(ts));CHKERRQ(ierr);
6422   ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
6423   ierr = PetscMemcpy(&lxdot,&udot,sizeof(u));CHKERRQ(ierr);
6424   ierr = PetscMemcpy(&lA,A,sizeof(u));CHKERRQ(ierr);
6425   ierr = PetscMemcpy(&lB,B,sizeof(u));CHKERRQ(ierr);
6426 
6427   prhs[0] =  mxCreateDoubleScalar((double)ls);
6428   prhs[1] =  mxCreateDoubleScalar((double)time);
6429   prhs[2] =  mxCreateDoubleScalar((double)lx);
6430   prhs[3] =  mxCreateDoubleScalar((double)lxdot);
6431   prhs[4] =  mxCreateDoubleScalar((double)shift);
6432   prhs[5] =  mxCreateDoubleScalar((double)lA);
6433   prhs[6] =  mxCreateDoubleScalar((double)lB);
6434   prhs[7] =  mxCreateString(sctx->funcname);
6435   prhs[8] =  sctx->ctx;
6436   ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSComputeJacobianInternal");CHKERRQ(ierr);
6437   ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
6438   mxDestroyArray(prhs[0]);
6439   mxDestroyArray(prhs[1]);
6440   mxDestroyArray(prhs[2]);
6441   mxDestroyArray(prhs[3]);
6442   mxDestroyArray(prhs[4]);
6443   mxDestroyArray(prhs[5]);
6444   mxDestroyArray(prhs[6]);
6445   mxDestroyArray(prhs[7]);
6446   mxDestroyArray(plhs[0]);
6447   mxDestroyArray(plhs[1]);
6448   PetscFunctionReturn(0);
6449 }
6450 
6451 
6452 #undef __FUNCT__
6453 #define __FUNCT__ "TSSetJacobianMatlab"
6454 /*
6455    TSSetJacobianMatlab - Sets the Jacobian function evaluation routine and two empty Jacobian matrices
6456    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
6457 
6458    Logically Collective on TS
6459 
6460    Input Parameters:
6461 +  ts - the TS context
6462 .  A,B - Jacobian matrices
6463 .  func - function evaluation routine
6464 -  ctx - user context
6465 
6466    Calling sequence of func:
6467 $    flag = func (TS ts,PetscReal time,Vec u,Vec udot,Mat A,Mat B,void *ctx);
6468 
6469 
6470    Level: developer
6471 
6472 .keywords: TS, nonlinear, set, function
6473 
6474 .seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
6475 */
6476 PetscErrorCode  TSSetJacobianMatlab(TS ts,Mat A,Mat B,const char *func,mxArray *ctx)
6477 {
6478   PetscErrorCode  ierr;
6479   TSMatlabContext *sctx;
6480 
6481   PetscFunctionBegin;
6482   /* currently sctx is memory bleed */
6483   ierr = PetscNew(&sctx);CHKERRQ(ierr);
6484   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
6485   /*
6486      This should work, but it doesn't
6487   sctx->ctx = ctx;
6488   mexMakeArrayPersistent(sctx->ctx);
6489   */
6490   sctx->ctx = mxDuplicateArray(ctx);
6491 
6492   ierr = TSSetIJacobian(ts,A,B,TSComputeJacobian_Matlab,sctx);CHKERRQ(ierr);
6493   PetscFunctionReturn(0);
6494 }
6495 
6496 #undef __FUNCT__
6497 #define __FUNCT__ "TSMonitor_Matlab"
6498 /*
6499    TSMonitor_Matlab - Calls the function that has been set with TSMonitorSetMatlab().
6500 
6501    Collective on TS
6502 
6503 .seealso: TSSetFunction(), TSGetFunction()
6504 @*/
6505 PetscErrorCode  TSMonitor_Matlab(TS ts,PetscInt it, PetscReal time,Vec u, void *ctx)
6506 {
6507   PetscErrorCode  ierr;
6508   TSMatlabContext *sctx = (TSMatlabContext*)ctx;
6509   int             nlhs  = 1,nrhs = 6;
6510   mxArray         *plhs[1],*prhs[6];
6511   long long int   lx = 0,ls = 0;
6512 
6513   PetscFunctionBegin;
6514   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6515   PetscValidHeaderSpecific(u,VEC_CLASSID,4);
6516 
6517   ierr = PetscMemcpy(&ls,&ts,sizeof(ts));CHKERRQ(ierr);
6518   ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
6519 
6520   prhs[0] =  mxCreateDoubleScalar((double)ls);
6521   prhs[1] =  mxCreateDoubleScalar((double)it);
6522   prhs[2] =  mxCreateDoubleScalar((double)time);
6523   prhs[3] =  mxCreateDoubleScalar((double)lx);
6524   prhs[4] =  mxCreateString(sctx->funcname);
6525   prhs[5] =  sctx->ctx;
6526   ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSMonitorInternal");CHKERRQ(ierr);
6527   ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
6528   mxDestroyArray(prhs[0]);
6529   mxDestroyArray(prhs[1]);
6530   mxDestroyArray(prhs[2]);
6531   mxDestroyArray(prhs[3]);
6532   mxDestroyArray(prhs[4]);
6533   mxDestroyArray(plhs[0]);
6534   PetscFunctionReturn(0);
6535 }
6536 
6537 
6538 #undef __FUNCT__
6539 #define __FUNCT__ "TSMonitorSetMatlab"
6540 /*
6541    TSMonitorSetMatlab - Sets the monitor function from Matlab
6542 
6543    Level: developer
6544 
6545 .keywords: TS, nonlinear, set, function
6546 
6547 .seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
6548 */
6549 PetscErrorCode  TSMonitorSetMatlab(TS ts,const char *func,mxArray *ctx)
6550 {
6551   PetscErrorCode  ierr;
6552   TSMatlabContext *sctx;
6553 
6554   PetscFunctionBegin;
6555   /* currently sctx is memory bleed */
6556   ierr = PetscNew(&sctx);CHKERRQ(ierr);
6557   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
6558   /*
6559      This should work, but it doesn't
6560   sctx->ctx = ctx;
6561   mexMakeArrayPersistent(sctx->ctx);
6562   */
6563   sctx->ctx = mxDuplicateArray(ctx);
6564 
6565   ierr = TSMonitorSet(ts,TSMonitor_Matlab,sctx,NULL);CHKERRQ(ierr);
6566   PetscFunctionReturn(0);
6567 }
6568 #endif
6569 
6570 #undef __FUNCT__
6571 #define __FUNCT__ "TSMonitorLGSolution"
6572 /*@C
6573    TSMonitorLGSolution - Monitors progress of the TS solvers by plotting each component of the solution vector
6574        in a time based line graph
6575 
6576    Collective on TS
6577 
6578    Input Parameters:
6579 +  ts - the TS context
6580 .  step - current time-step
6581 .  ptime - current time
6582 .  u - current solution
6583 -  dctx - the TSMonitorLGCtx object that contains all the options for the monitoring, this is created with TSMonitorLGCtxCreate()
6584 
6585    Options Database:
6586 .   -ts_monitor_lg_solution_variables
6587 
6588    Level: intermediate
6589 
6590    Notes: Each process in a parallel run displays its component solutions in a separate window
6591 
6592 .keywords: TS,  vector, monitor, view
6593 
6594 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGCtxCreate(), TSMonitorLGCtxSetVariableNames(), TSMonitorLGCtxGetVariableNames(),
6595            TSMonitorLGSetVariableNames(), TSMonitorLGGetVariableNames(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetDisplayVariables(),
6596            TSMonitorLGCtxSetTransform(), TSMonitorLGSetTransform(), TSMonitorLGError(), TSMonitorLGSNESIterations(), TSMonitorLGKSPIterations(),
6597            TSMonitorEnvelopeCtxCreate(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxDestroy(), TSMonitorEnvelop()
6598 @*/
6599 PetscErrorCode  TSMonitorLGSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dctx)
6600 {
6601   PetscErrorCode    ierr;
6602   TSMonitorLGCtx    ctx = (TSMonitorLGCtx)dctx;
6603   const PetscScalar *yy;
6604   Vec               v;
6605 
6606   PetscFunctionBegin;
6607   if (step < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
6608   if (!step) {
6609     PetscDrawAxis axis;
6610     PetscInt      dim;
6611     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
6612     ierr = PetscDrawAxisSetLabels(axis,"Solution as function of time","Time","Solution");CHKERRQ(ierr);
6613     if (!ctx->names) {
6614       PetscBool flg;
6615       /* user provides names of variables to plot but no names has been set so assume names are integer values */
6616       ierr = PetscOptionsHasName(((PetscObject)ts)->options,((PetscObject)ts)->prefix,"-ts_monitor_lg_solution_variables",&flg);CHKERRQ(ierr);
6617       if (flg) {
6618         PetscInt i,n;
6619         char     **names;
6620         ierr = VecGetSize(u,&n);CHKERRQ(ierr);
6621         ierr = PetscMalloc1(n+1,&names);CHKERRQ(ierr);
6622         for (i=0; i<n; i++) {
6623           ierr = PetscMalloc1(5,&names[i]);CHKERRQ(ierr);
6624           ierr = PetscSNPrintf(names[i],5,"%D",i);CHKERRQ(ierr);
6625         }
6626         names[n] = NULL;
6627         ctx->names = names;
6628       }
6629     }
6630     if (ctx->names && !ctx->displaynames) {
6631       char      **displaynames;
6632       PetscBool flg;
6633       ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
6634       ierr = PetscMalloc1(dim+1,&displaynames);CHKERRQ(ierr);
6635       ierr = PetscMemzero(displaynames,(dim+1)*sizeof(char*));CHKERRQ(ierr);
6636       ierr = PetscOptionsGetStringArray(((PetscObject)ts)->options,((PetscObject)ts)->prefix,"-ts_monitor_lg_solution_variables",displaynames,&dim,&flg);CHKERRQ(ierr);
6637       if (flg) {
6638         ierr = TSMonitorLGCtxSetDisplayVariables(ctx,(const char *const *)displaynames);CHKERRQ(ierr);
6639       }
6640       ierr = PetscStrArrayDestroy(&displaynames);CHKERRQ(ierr);
6641     }
6642     if (ctx->displaynames) {
6643       ierr = PetscDrawLGSetDimension(ctx->lg,ctx->ndisplayvariables);CHKERRQ(ierr);
6644       ierr = PetscDrawLGSetLegend(ctx->lg,(const char *const *)ctx->displaynames);CHKERRQ(ierr);
6645     } else if (ctx->names) {
6646       ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
6647       ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
6648       ierr = PetscDrawLGSetLegend(ctx->lg,(const char *const *)ctx->names);CHKERRQ(ierr);
6649     } else {
6650       ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
6651       ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
6652     }
6653     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
6654   }
6655 
6656   if (!ctx->transform) v = u;
6657   else {ierr = (*ctx->transform)(ctx->transformctx,u,&v);CHKERRQ(ierr);}
6658   ierr = VecGetArrayRead(v,&yy);CHKERRQ(ierr);
6659   if (ctx->displaynames) {
6660     PetscInt i;
6661     for (i=0; i<ctx->ndisplayvariables; i++)
6662       ctx->displayvalues[i] = PetscRealPart(yy[ctx->displayvariables[i]]);
6663     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,ctx->displayvalues);CHKERRQ(ierr);
6664   } else {
6665 #if defined(PETSC_USE_COMPLEX)
6666     PetscInt  i,n;
6667     PetscReal *yreal;
6668     ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
6669     ierr = PetscMalloc1(n,&yreal);CHKERRQ(ierr);
6670     for (i=0; i<n; i++) yreal[i] = PetscRealPart(yy[i]);
6671     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yreal);CHKERRQ(ierr);
6672     ierr = PetscFree(yreal);CHKERRQ(ierr);
6673 #else
6674     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yy);CHKERRQ(ierr);
6675 #endif
6676   }
6677   ierr = VecRestoreArrayRead(v,&yy);CHKERRQ(ierr);
6678   if (ctx->transform) {ierr = VecDestroy(&v);CHKERRQ(ierr);}
6679 
6680   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
6681     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
6682     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
6683   }
6684   PetscFunctionReturn(0);
6685 }
6686 
6687 
6688 #undef __FUNCT__
6689 #define __FUNCT__ "TSMonitorLGSetVariableNames"
6690 /*@C
6691    TSMonitorLGSetVariableNames - Sets the name of each component in the solution vector so that it may be displayed in the plot
6692 
6693    Collective on TS
6694 
6695    Input Parameters:
6696 +  ts - the TS context
6697 -  names - the names of the components, final string must be NULL
6698 
6699    Level: intermediate
6700 
6701    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
6702 
6703 .keywords: TS,  vector, monitor, view
6704 
6705 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetVariableNames()
6706 @*/
6707 PetscErrorCode  TSMonitorLGSetVariableNames(TS ts,const char * const *names)
6708 {
6709   PetscErrorCode    ierr;
6710   PetscInt          i;
6711 
6712   PetscFunctionBegin;
6713   for (i=0; i<ts->numbermonitors; i++) {
6714     if (ts->monitor[i] == TSMonitorLGSolution) {
6715       ierr = TSMonitorLGCtxSetVariableNames((TSMonitorLGCtx)ts->monitorcontext[i],names);CHKERRQ(ierr);
6716       break;
6717     }
6718   }
6719   PetscFunctionReturn(0);
6720 }
6721 
6722 #undef __FUNCT__
6723 #define __FUNCT__ "TSMonitorLGCtxSetVariableNames"
6724 /*@C
6725    TSMonitorLGCtxSetVariableNames - Sets the name of each component in the solution vector so that it may be displayed in the plot
6726 
6727    Collective on TS
6728 
6729    Input Parameters:
6730 +  ts - the TS context
6731 -  names - the names of the components, final string must be NULL
6732 
6733    Level: intermediate
6734 
6735 .keywords: TS,  vector, monitor, view
6736 
6737 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables(), TSMonitorLGSetVariableNames()
6738 @*/
6739 PetscErrorCode  TSMonitorLGCtxSetVariableNames(TSMonitorLGCtx ctx,const char * const *names)
6740 {
6741   PetscErrorCode    ierr;
6742 
6743   PetscFunctionBegin;
6744   ierr = PetscStrArrayDestroy(&ctx->names);CHKERRQ(ierr);
6745   ierr = PetscStrArrayallocpy(names,&ctx->names);CHKERRQ(ierr);
6746   PetscFunctionReturn(0);
6747 }
6748 
6749 #undef __FUNCT__
6750 #define __FUNCT__ "TSMonitorLGGetVariableNames"
6751 /*@C
6752    TSMonitorLGGetVariableNames - Gets the name of each component in the solution vector so that it may be displayed in the plot
6753 
6754    Collective on TS
6755 
6756    Input Parameter:
6757 .  ts - the TS context
6758 
6759    Output Parameter:
6760 .  names - the names of the components, final string must be NULL
6761 
6762    Level: intermediate
6763 
6764    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
6765 
6766 .keywords: TS,  vector, monitor, view
6767 
6768 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables()
6769 @*/
6770 PetscErrorCode  TSMonitorLGGetVariableNames(TS ts,const char *const **names)
6771 {
6772   PetscInt       i;
6773 
6774   PetscFunctionBegin;
6775   *names = NULL;
6776   for (i=0; i<ts->numbermonitors; i++) {
6777     if (ts->monitor[i] == TSMonitorLGSolution) {
6778       TSMonitorLGCtx  ctx = (TSMonitorLGCtx) ts->monitorcontext[i];
6779       *names = (const char *const *)ctx->names;
6780       break;
6781     }
6782   }
6783   PetscFunctionReturn(0);
6784 }
6785 
6786 #undef __FUNCT__
6787 #define __FUNCT__ "TSMonitorLGCtxSetDisplayVariables"
6788 /*@C
6789    TSMonitorLGCtxSetDisplayVariables - Sets the variables that are to be display in the monitor
6790 
6791    Collective on TS
6792 
6793    Input Parameters:
6794 +  ctx - the TSMonitorLG context
6795 .  displaynames - the names of the components, final string must be NULL
6796 
6797    Level: intermediate
6798 
6799 .keywords: TS,  vector, monitor, view
6800 
6801 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames()
6802 @*/
6803 PetscErrorCode  TSMonitorLGCtxSetDisplayVariables(TSMonitorLGCtx ctx,const char * const *displaynames)
6804 {
6805   PetscInt          j = 0,k;
6806   PetscErrorCode    ierr;
6807 
6808   PetscFunctionBegin;
6809   if (!ctx->names) PetscFunctionReturn(0);
6810   ierr = PetscStrArrayDestroy(&ctx->displaynames);CHKERRQ(ierr);
6811   ierr = PetscStrArrayallocpy(displaynames,&ctx->displaynames);CHKERRQ(ierr);
6812   while (displaynames[j]) j++;
6813   ctx->ndisplayvariables = j;
6814   ierr = PetscMalloc1(ctx->ndisplayvariables,&ctx->displayvariables);CHKERRQ(ierr);
6815   ierr = PetscMalloc1(ctx->ndisplayvariables,&ctx->displayvalues);CHKERRQ(ierr);
6816   j = 0;
6817   while (displaynames[j]) {
6818     k = 0;
6819     while (ctx->names[k]) {
6820       PetscBool flg;
6821       ierr = PetscStrcmp(displaynames[j],ctx->names[k],&flg);CHKERRQ(ierr);
6822       if (flg) {
6823         ctx->displayvariables[j] = k;
6824         break;
6825       }
6826       k++;
6827     }
6828     j++;
6829   }
6830   PetscFunctionReturn(0);
6831 }
6832 
6833 
6834 #undef __FUNCT__
6835 #define __FUNCT__ "TSMonitorLGSetDisplayVariables"
6836 /*@C
6837    TSMonitorLGSetDisplayVariables - Sets the variables that are to be display in the monitor
6838 
6839    Collective on TS
6840 
6841    Input Parameters:
6842 +  ts - the TS context
6843 .  displaynames - the names of the components, final string must be NULL
6844 
6845    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
6846 
6847    Level: intermediate
6848 
6849 .keywords: TS,  vector, monitor, view
6850 
6851 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames()
6852 @*/
6853 PetscErrorCode  TSMonitorLGSetDisplayVariables(TS ts,const char * const *displaynames)
6854 {
6855   PetscInt          i;
6856   PetscErrorCode    ierr;
6857 
6858   PetscFunctionBegin;
6859   for (i=0; i<ts->numbermonitors; i++) {
6860     if (ts->monitor[i] == TSMonitorLGSolution) {
6861       ierr = TSMonitorLGCtxSetDisplayVariables((TSMonitorLGCtx)ts->monitorcontext[i],displaynames);CHKERRQ(ierr);
6862       break;
6863     }
6864   }
6865   PetscFunctionReturn(0);
6866 }
6867 
6868 #undef __FUNCT__
6869 #define __FUNCT__ "TSMonitorLGSetTransform"
6870 /*@C
6871    TSMonitorLGSetTransform - Solution vector will be transformed by provided function before being displayed
6872 
6873    Collective on TS
6874 
6875    Input Parameters:
6876 +  ts - the TS context
6877 .  transform - the transform function
6878 .  destroy - function to destroy the optional context
6879 -  ctx - optional context used by transform function
6880 
6881    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
6882 
6883    Level: intermediate
6884 
6885 .keywords: TS,  vector, monitor, view
6886 
6887 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames(), TSMonitorLGCtxSetTransform()
6888 @*/
6889 PetscErrorCode  TSMonitorLGSetTransform(TS ts,PetscErrorCode (*transform)(void*,Vec,Vec*),PetscErrorCode (*destroy)(void*),void *tctx)
6890 {
6891   PetscInt          i;
6892   PetscErrorCode    ierr;
6893 
6894   PetscFunctionBegin;
6895   for (i=0; i<ts->numbermonitors; i++) {
6896     if (ts->monitor[i] == TSMonitorLGSolution) {
6897       ierr = TSMonitorLGCtxSetTransform((TSMonitorLGCtx)ts->monitorcontext[i],transform,destroy,tctx);CHKERRQ(ierr);
6898     }
6899   }
6900   PetscFunctionReturn(0);
6901 }
6902 
6903 #undef __FUNCT__
6904 #define __FUNCT__ "TSMonitorLGCtxSetTransform"
6905 /*@C
6906    TSMonitorLGCtxSetTransform - Solution vector will be transformed by provided function before being displayed
6907 
6908    Collective on TSLGCtx
6909 
6910    Input Parameters:
6911 +  ts - the TS context
6912 .  transform - the transform function
6913 .  destroy - function to destroy the optional context
6914 -  ctx - optional context used by transform function
6915 
6916    Level: intermediate
6917 
6918 .keywords: TS,  vector, monitor, view
6919 
6920 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames(), TSMonitorLGSetTransform()
6921 @*/
6922 PetscErrorCode  TSMonitorLGCtxSetTransform(TSMonitorLGCtx ctx,PetscErrorCode (*transform)(void*,Vec,Vec*),PetscErrorCode (*destroy)(void*),void *tctx)
6923 {
6924   PetscFunctionBegin;
6925   ctx->transform    = transform;
6926   ctx->transformdestroy = destroy;
6927   ctx->transformctx = tctx;
6928   PetscFunctionReturn(0);
6929 }
6930 
6931 #undef __FUNCT__
6932 #define __FUNCT__ "TSMonitorLGError"
6933 /*@C
6934    TSMonitorLGError - Monitors progress of the TS solvers by plotting each component of the solution vector
6935        in a time based line graph
6936 
6937    Collective on TS
6938 
6939    Input Parameters:
6940 +  ts - the TS context
6941 .  step - current time-step
6942 .  ptime - current time
6943 .  u - current solution
6944 -  dctx - TSMonitorLGCtx object created with TSMonitorLGCtxCreate()
6945 
6946    Level: intermediate
6947 
6948    Notes: Each process in a parallel run displays its component errors in a separate window
6949 
6950    The user must provide the solution using TSSetSolutionFunction() to use this monitor.
6951 
6952    Options Database Keys:
6953 .  -ts_monitor_lg_error - create a graphical monitor of error history
6954 
6955 .keywords: TS,  vector, monitor, view
6956 
6957 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSSetSolutionFunction()
6958 @*/
6959 PetscErrorCode  TSMonitorLGError(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
6960 {
6961   PetscErrorCode    ierr;
6962   TSMonitorLGCtx    ctx = (TSMonitorLGCtx)dummy;
6963   const PetscScalar *yy;
6964   Vec               y;
6965 
6966   PetscFunctionBegin;
6967   if (!step) {
6968     PetscDrawAxis axis;
6969     PetscInt      dim;
6970     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
6971     ierr = PetscDrawAxisSetLabels(axis,"Error in solution as function of time","Time","Solution");CHKERRQ(ierr);
6972     ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
6973     ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
6974     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
6975   }
6976   ierr = VecDuplicate(u,&y);CHKERRQ(ierr);
6977   ierr = TSComputeSolutionFunction(ts,ptime,y);CHKERRQ(ierr);
6978   ierr = VecAXPY(y,-1.0,u);CHKERRQ(ierr);
6979   ierr = VecGetArrayRead(y,&yy);CHKERRQ(ierr);
6980 #if defined(PETSC_USE_COMPLEX)
6981   {
6982     PetscReal *yreal;
6983     PetscInt  i,n;
6984     ierr = VecGetLocalSize(y,&n);CHKERRQ(ierr);
6985     ierr = PetscMalloc1(n,&yreal);CHKERRQ(ierr);
6986     for (i=0; i<n; i++) yreal[i] = PetscRealPart(yy[i]);
6987     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yreal);CHKERRQ(ierr);
6988     ierr = PetscFree(yreal);CHKERRQ(ierr);
6989   }
6990 #else
6991   ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yy);CHKERRQ(ierr);
6992 #endif
6993   ierr = VecRestoreArrayRead(y,&yy);CHKERRQ(ierr);
6994   ierr = VecDestroy(&y);CHKERRQ(ierr);
6995   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
6996     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
6997     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
6998   }
6999   PetscFunctionReturn(0);
7000 }
7001 
7002 #undef __FUNCT__
7003 #define __FUNCT__ "TSMonitorLGSNESIterations"
7004 PetscErrorCode TSMonitorLGSNESIterations(TS ts,PetscInt n,PetscReal ptime,Vec v,void *monctx)
7005 {
7006   TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
7007   PetscReal      x   = ptime,y;
7008   PetscErrorCode ierr;
7009   PetscInt       its;
7010 
7011   PetscFunctionBegin;
7012   if (n < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
7013   if (!n) {
7014     PetscDrawAxis axis;
7015     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
7016     ierr = PetscDrawAxisSetLabels(axis,"Nonlinear iterations as function of time","Time","SNES Iterations");CHKERRQ(ierr);
7017     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
7018     ctx->snes_its = 0;
7019   }
7020   ierr = TSGetSNESIterations(ts,&its);CHKERRQ(ierr);
7021   y    = its - ctx->snes_its;
7022   ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
7023   if (((ctx->howoften > 0) && (!(n % ctx->howoften)) && (n > -1)) || ((ctx->howoften == -1) && (n == -1))) {
7024     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
7025     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
7026   }
7027   ctx->snes_its = its;
7028   PetscFunctionReturn(0);
7029 }
7030 
7031 #undef __FUNCT__
7032 #define __FUNCT__ "TSMonitorLGKSPIterations"
7033 PetscErrorCode TSMonitorLGKSPIterations(TS ts,PetscInt n,PetscReal ptime,Vec v,void *monctx)
7034 {
7035   TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
7036   PetscReal      x   = ptime,y;
7037   PetscErrorCode ierr;
7038   PetscInt       its;
7039 
7040   PetscFunctionBegin;
7041   if (n < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
7042   if (!n) {
7043     PetscDrawAxis axis;
7044     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
7045     ierr = PetscDrawAxisSetLabels(axis,"Linear iterations as function of time","Time","KSP Iterations");CHKERRQ(ierr);
7046     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
7047     ctx->ksp_its = 0;
7048   }
7049   ierr = TSGetKSPIterations(ts,&its);CHKERRQ(ierr);
7050   y    = its - ctx->ksp_its;
7051   ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
7052   if (((ctx->howoften > 0) && (!(n % ctx->howoften)) && (n > -1)) || ((ctx->howoften == -1) && (n == -1))) {
7053     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
7054     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
7055   }
7056   ctx->ksp_its = its;
7057   PetscFunctionReturn(0);
7058 }
7059 
7060 #undef __FUNCT__
7061 #define __FUNCT__ "TSComputeLinearStability"
7062 /*@
7063    TSComputeLinearStability - computes the linear stability function at a point
7064 
7065    Collective on TS and Vec
7066 
7067    Input Parameters:
7068 +  ts - the TS context
7069 -  xr,xi - real and imaginary part of input arguments
7070 
7071    Output Parameters:
7072 .  yr,yi - real and imaginary part of function value
7073 
7074    Level: developer
7075 
7076 .keywords: TS, compute
7077 
7078 .seealso: TSSetRHSFunction(), TSComputeIFunction()
7079 @*/
7080 PetscErrorCode TSComputeLinearStability(TS ts,PetscReal xr,PetscReal xi,PetscReal *yr,PetscReal *yi)
7081 {
7082   PetscErrorCode ierr;
7083 
7084   PetscFunctionBegin;
7085   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
7086   if (!ts->ops->linearstability) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Linearized stability function not provided for this method");
7087   ierr = (*ts->ops->linearstability)(ts,xr,xi,yr,yi);CHKERRQ(ierr);
7088   PetscFunctionReturn(0);
7089 }
7090 
7091 /* ------------------------------------------------------------------------*/
7092 #undef __FUNCT__
7093 #define __FUNCT__ "TSMonitorEnvelopeCtxCreate"
7094 /*@C
7095    TSMonitorEnvelopeCtxCreate - Creates a context for use with TSMonitorEnvelope()
7096 
7097    Collective on TS
7098 
7099    Input Parameters:
7100 .  ts  - the ODE solver object
7101 
7102    Output Parameter:
7103 .  ctx - the context
7104 
7105    Level: intermediate
7106 
7107 .keywords: TS, monitor, line graph, residual, seealso
7108 
7109 .seealso: TSMonitorLGTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError()
7110 
7111 @*/
7112 PetscErrorCode  TSMonitorEnvelopeCtxCreate(TS ts,TSMonitorEnvelopeCtx *ctx)
7113 {
7114   PetscErrorCode ierr;
7115 
7116   PetscFunctionBegin;
7117   ierr = PetscNew(ctx);CHKERRQ(ierr);
7118   PetscFunctionReturn(0);
7119 }
7120 
7121 #undef __FUNCT__
7122 #define __FUNCT__ "TSMonitorEnvelope"
7123 /*@C
7124    TSMonitorEnvelope - Monitors the maximum and minimum value of each component of the solution
7125 
7126    Collective on TS
7127 
7128    Input Parameters:
7129 +  ts - the TS context
7130 .  step - current time-step
7131 .  ptime - current time
7132 .  u  - current solution
7133 -  dctx - the envelope context
7134 
7135    Options Database:
7136 .  -ts_monitor_envelope
7137 
7138    Level: intermediate
7139 
7140    Notes: after a solve you can use TSMonitorEnvelopeGetBounds() to access the envelope
7141 
7142 .keywords: TS,  vector, monitor, view
7143 
7144 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxCreate()
7145 @*/
7146 PetscErrorCode  TSMonitorEnvelope(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dctx)
7147 {
7148   PetscErrorCode       ierr;
7149   TSMonitorEnvelopeCtx ctx = (TSMonitorEnvelopeCtx)dctx;
7150 
7151   PetscFunctionBegin;
7152   if (!ctx->max) {
7153     ierr = VecDuplicate(u,&ctx->max);CHKERRQ(ierr);
7154     ierr = VecDuplicate(u,&ctx->min);CHKERRQ(ierr);
7155     ierr = VecCopy(u,ctx->max);CHKERRQ(ierr);
7156     ierr = VecCopy(u,ctx->min);CHKERRQ(ierr);
7157   } else {
7158     ierr = VecPointwiseMax(ctx->max,u,ctx->max);CHKERRQ(ierr);
7159     ierr = VecPointwiseMin(ctx->min,u,ctx->min);CHKERRQ(ierr);
7160   }
7161   PetscFunctionReturn(0);
7162 }
7163 
7164 
7165 #undef __FUNCT__
7166 #define __FUNCT__ "TSMonitorEnvelopeGetBounds"
7167 /*@C
7168    TSMonitorEnvelopeGetBounds - Gets the bounds for the components of the solution
7169 
7170    Collective on TS
7171 
7172    Input Parameter:
7173 .  ts - the TS context
7174 
7175    Output Parameter:
7176 +  max - the maximum values
7177 -  min - the minimum values
7178 
7179    Notes: If the TS does not have a TSMonitorEnvelopeCtx associated with it then this function is ignored
7180 
7181    Level: intermediate
7182 
7183 .keywords: TS,  vector, monitor, view
7184 
7185 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables()
7186 @*/
7187 PetscErrorCode  TSMonitorEnvelopeGetBounds(TS ts,Vec *max,Vec *min)
7188 {
7189   PetscInt i;
7190 
7191   PetscFunctionBegin;
7192   if (max) *max = NULL;
7193   if (min) *min = NULL;
7194   for (i=0; i<ts->numbermonitors; i++) {
7195     if (ts->monitor[i] == TSMonitorEnvelope) {
7196       TSMonitorEnvelopeCtx  ctx = (TSMonitorEnvelopeCtx) ts->monitorcontext[i];
7197       if (max) *max = ctx->max;
7198       if (min) *min = ctx->min;
7199       break;
7200     }
7201   }
7202   PetscFunctionReturn(0);
7203 }
7204 
7205 #undef __FUNCT__
7206 #define __FUNCT__ "TSMonitorEnvelopeCtxDestroy"
7207 /*@C
7208    TSMonitorEnvelopeCtxDestroy - Destroys a context that was created  with TSMonitorEnvelopeCtxCreate().
7209 
7210    Collective on TSMonitorEnvelopeCtx
7211 
7212    Input Parameter:
7213 .  ctx - the monitor context
7214 
7215    Level: intermediate
7216 
7217 .keywords: TS, monitor, line graph, destroy
7218 
7219 .seealso: TSMonitorLGCtxCreate(),  TSMonitorSet(), TSMonitorLGTimeStep()
7220 @*/
7221 PetscErrorCode  TSMonitorEnvelopeCtxDestroy(TSMonitorEnvelopeCtx *ctx)
7222 {
7223   PetscErrorCode ierr;
7224 
7225   PetscFunctionBegin;
7226   ierr = VecDestroy(&(*ctx)->min);CHKERRQ(ierr);
7227   ierr = VecDestroy(&(*ctx)->max);CHKERRQ(ierr);
7228   ierr = PetscFree(*ctx);CHKERRQ(ierr);
7229   PetscFunctionReturn(0);
7230 }
7231 
7232 #undef __FUNCT__
7233 #define __FUNCT__ "TSRollBack"
7234 /*@
7235    TSRollBack - Rolls back one time step
7236 
7237    Collective on TS
7238 
7239    Input Parameter:
7240 .  ts - the TS context obtained from TSCreate()
7241 
7242    Level: advanced
7243 
7244 .keywords: TS, timestep, rollback
7245 
7246 .seealso: TSCreate(), TSSetUp(), TSDestroy(), TSSolve(), TSSetPreStep(), TSSetPreStage(), TSInterpolate()
7247 @*/
7248 PetscErrorCode  TSRollBack(TS ts)
7249 {
7250   PetscErrorCode ierr;
7251 
7252   PetscFunctionBegin;
7253   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
7254   if (ts->steprollback) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"TSRollBack already called");
7255   if (!ts->ops->rollback) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRollBack not implemented for type '%s'",((PetscObject)ts)->type_name);
7256   ierr = (*ts->ops->rollback)(ts);CHKERRQ(ierr);
7257   ts->time_step = ts->ptime - ts->ptime_prev;
7258   ts->ptime = ts->ptime_prev;
7259   ts->ptime_prev = ts->ptime_prev_rollback;
7260   ts->steps--; ts->total_steps--;
7261   ts->steprollback = PETSC_TRUE;
7262   PetscFunctionReturn(0);
7263 }
7264 
7265 #undef __FUNCT__
7266 #define __FUNCT__ "TSGetStages"
7267 /*@
7268    TSGetStages - Get the number of stages and stage values
7269 
7270    Input Parameter:
7271 .  ts - the TS context obtained from TSCreate()
7272 
7273    Level: advanced
7274 
7275 .keywords: TS, getstages
7276 
7277 .seealso: TSCreate()
7278 @*/
7279 PetscErrorCode  TSGetStages(TS ts,PetscInt *ns,Vec **Y)
7280 {
7281   PetscErrorCode ierr;
7282 
7283   PetscFunctionBegin;
7284   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
7285   PetscValidPointer(ns,2);
7286 
7287   if (!ts->ops->getstages) *ns=0;
7288   else {
7289     ierr = (*ts->ops->getstages)(ts,ns,Y);CHKERRQ(ierr);
7290   }
7291   PetscFunctionReturn(0);
7292 }
7293 
7294 #undef __FUNCT__
7295 #define __FUNCT__ "TSComputeIJacobianDefaultColor"
7296 /*@C
7297   TSComputeIJacobianDefaultColor - Computes the Jacobian using finite differences and coloring to exploit matrix sparsity.
7298 
7299   Collective on SNES
7300 
7301   Input Parameters:
7302 + ts - the TS context
7303 . t - current timestep
7304 . U - state vector
7305 . Udot - time derivative of state vector
7306 . shift - shift to apply, see note below
7307 - ctx - an optional user context
7308 
7309   Output Parameters:
7310 + J - Jacobian matrix (not altered in this routine)
7311 - B - newly computed Jacobian matrix to use with preconditioner (generally the same as J)
7312 
7313   Level: intermediate
7314 
7315   Notes:
7316   If F(t,U,Udot)=0 is the DAE, the required Jacobian is
7317 
7318   dF/dU + shift*dF/dUdot
7319 
7320   Most users should not need to explicitly call this routine, as it
7321   is used internally within the nonlinear solvers.
7322 
7323   This will first try to get the coloring from the DM.  If the DM type has no coloring
7324   routine, then it will try to get the coloring from the matrix.  This requires that the
7325   matrix have nonzero entries precomputed.
7326 
7327 .keywords: TS, finite differences, Jacobian, coloring, sparse
7328 .seealso: TSSetIJacobian(), MatFDColoringCreate(), MatFDColoringSetFunction()
7329 @*/
7330 PetscErrorCode TSComputeIJacobianDefaultColor(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat J,Mat B,void *ctx)
7331 {
7332   SNES           snes;
7333   MatFDColoring  color;
7334   PetscBool      hascolor, matcolor = PETSC_FALSE;
7335   PetscErrorCode ierr;
7336 
7337   PetscFunctionBegin;
7338   ierr = PetscOptionsGetBool(((PetscObject)ts)->options,((PetscObject) ts)->prefix, "-ts_fd_color_use_mat", &matcolor, NULL);CHKERRQ(ierr);
7339   ierr = PetscObjectQuery((PetscObject) B, "TSMatFDColoring", (PetscObject *) &color);CHKERRQ(ierr);
7340   if (!color) {
7341     DM         dm;
7342     ISColoring iscoloring;
7343 
7344     ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
7345     ierr = DMHasColoring(dm, &hascolor);CHKERRQ(ierr);
7346     if (hascolor && !matcolor) {
7347       ierr = DMCreateColoring(dm, IS_COLORING_GLOBAL, &iscoloring);CHKERRQ(ierr);
7348       ierr = MatFDColoringCreate(B, iscoloring, &color);CHKERRQ(ierr);
7349       ierr = MatFDColoringSetFunction(color, (PetscErrorCode (*)(void)) SNESTSFormFunction, (void *) ts);CHKERRQ(ierr);
7350       ierr = MatFDColoringSetFromOptions(color);CHKERRQ(ierr);
7351       ierr = MatFDColoringSetUp(B, iscoloring, color);CHKERRQ(ierr);
7352       ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
7353     } else {
7354       MatColoring mc;
7355 
7356       ierr = MatColoringCreate(B, &mc);CHKERRQ(ierr);
7357       ierr = MatColoringSetDistance(mc, 2);CHKERRQ(ierr);
7358       ierr = MatColoringSetType(mc, MATCOLORINGSL);CHKERRQ(ierr);
7359       ierr = MatColoringSetFromOptions(mc);CHKERRQ(ierr);
7360       ierr = MatColoringApply(mc, &iscoloring);CHKERRQ(ierr);
7361       ierr = MatColoringDestroy(&mc);CHKERRQ(ierr);
7362       ierr = MatFDColoringCreate(B, iscoloring, &color);CHKERRQ(ierr);
7363       ierr = MatFDColoringSetFunction(color, (PetscErrorCode (*)(void)) SNESTSFormFunction, (void *) ts);CHKERRQ(ierr);
7364       ierr = MatFDColoringSetFromOptions(color);CHKERRQ(ierr);
7365       ierr = MatFDColoringSetUp(B, iscoloring, color);CHKERRQ(ierr);
7366       ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
7367     }
7368     ierr = PetscObjectCompose((PetscObject) B, "TSMatFDColoring", (PetscObject) color);CHKERRQ(ierr);
7369     ierr = PetscObjectDereference((PetscObject) color);CHKERRQ(ierr);
7370   }
7371   ierr = TSGetSNES(ts, &snes);CHKERRQ(ierr);
7372   ierr = MatFDColoringApply(B, color, U, snes);CHKERRQ(ierr);
7373   if (J != B) {
7374     ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
7375     ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
7376   }
7377   PetscFunctionReturn(0);
7378 }
7379 
7380 #undef __FUNCT__
7381 #define __FUNCT__ "TSSetFunctionDomainError"
7382 /*@
7383     TSSetFunctionDomainError - Set the function testing if the current state vector is valid
7384 
7385     Input Parameters:
7386     ts - the TS context
7387     func - function called within TSFunctionDomainError
7388 
7389     Level: intermediate
7390 
7391 .keywords: TS, state, domain
7392 .seealso: TSAdaptCheckStage(), TSFunctionDomainError()
7393 @*/
7394 
7395 PetscErrorCode TSSetFunctionDomainError(TS ts, PetscErrorCode (*func)(TS,PetscReal,Vec,PetscBool*))
7396 {
7397   PetscFunctionBegin;
7398   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
7399   ts->functiondomainerror = func;
7400   PetscFunctionReturn(0);
7401 }
7402 
7403 #undef __FUNCT__
7404 #define __FUNCT__ "TSFunctionDomainError"
7405 /*@
7406     TSFunctionDomainError - Check if the current state is valid
7407 
7408     Input Parameters:
7409     ts - the TS context
7410     stagetime - time of the simulation
7411     Y - state vector to check.
7412 
7413     Output Parameter:
7414     accept - Set to PETSC_FALSE if the current state vector is valid.
7415 
7416     Note:
7417     This function should be used to ensure the state is in a valid part of the space.
7418     For example, one can ensure here all values are positive.
7419 
7420     Level: advanced
7421 @*/
7422 PetscErrorCode TSFunctionDomainError(TS ts,PetscReal stagetime,Vec Y,PetscBool* accept)
7423 {
7424   PetscErrorCode ierr;
7425 
7426   PetscFunctionBegin;
7427 
7428   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
7429   *accept = PETSC_TRUE;
7430   if (ts->functiondomainerror) {
7431     PetscStackCallStandard((*ts->functiondomainerror),(ts,stagetime,Y,accept));
7432   }
7433   PetscFunctionReturn(0);
7434 }
7435 
7436 #undef  __FUNCT__
7437 #define __FUNCT__ "TSClone"
7438 /*@C
7439   TSClone - This function clones a time step object.
7440 
7441   Collective on MPI_Comm
7442 
7443   Input Parameter:
7444 . tsin    - The input TS
7445 
7446   Output Parameter:
7447 . tsout   - The output TS (cloned)
7448 
7449   Notes:
7450   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.
7451 
7452   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);
7453 
7454   Level: developer
7455 
7456 .keywords: TS, clone
7457 .seealso: TSCreate(), TSSetType(), TSSetUp(), TSDestroy(), TSSetProblemType()
7458 @*/
7459 PetscErrorCode  TSClone(TS tsin, TS *tsout)
7460 {
7461   TS             t;
7462   PetscErrorCode ierr;
7463   SNES           snes_start;
7464   DM             dm;
7465   TSType         type;
7466 
7467   PetscFunctionBegin;
7468   PetscValidPointer(tsin,1);
7469   *tsout = NULL;
7470 
7471   ierr = PetscHeaderCreate(t, TS_CLASSID, "TS", "Time stepping", "TS", PetscObjectComm((PetscObject)tsin), TSDestroy, TSView);CHKERRQ(ierr);
7472 
7473   /* General TS description */
7474   t->numbermonitors    = 0;
7475   t->setupcalled       = 0;
7476   t->ksp_its           = 0;
7477   t->snes_its          = 0;
7478   t->nwork             = 0;
7479   t->rhsjacobian.time  = -1e20;
7480   t->rhsjacobian.scale = 1.;
7481   t->ijacobian.shift   = 1.;
7482 
7483   ierr = TSGetSNES(tsin,&snes_start);CHKERRQ(ierr);
7484   ierr = TSSetSNES(t,snes_start);CHKERRQ(ierr);
7485 
7486   ierr = TSGetDM(tsin,&dm);CHKERRQ(ierr);
7487   ierr = TSSetDM(t,dm);CHKERRQ(ierr);
7488 
7489   t->adapt = tsin->adapt;
7490   ierr = PetscObjectReference((PetscObject)t->adapt);CHKERRQ(ierr);
7491 
7492   t->problem_type      = tsin->problem_type;
7493   t->ptime             = tsin->ptime;
7494   t->time_step         = tsin->time_step;
7495   t->max_time          = tsin->max_time;
7496   t->steps             = tsin->steps;
7497   t->max_steps         = tsin->max_steps;
7498   t->equation_type     = tsin->equation_type;
7499   t->atol              = tsin->atol;
7500   t->rtol              = tsin->rtol;
7501   t->max_snes_failures = tsin->max_snes_failures;
7502   t->max_reject        = tsin->max_reject;
7503   t->errorifstepfailed = tsin->errorifstepfailed;
7504 
7505   ierr = TSGetType(tsin,&type);CHKERRQ(ierr);
7506   ierr = TSSetType(t,type);CHKERRQ(ierr);
7507 
7508   t->vec_sol           = NULL;
7509 
7510   t->cfltime          = tsin->cfltime;
7511   t->cfltime_local    = tsin->cfltime_local;
7512   t->exact_final_time = tsin->exact_final_time;
7513 
7514   ierr = PetscMemcpy(t->ops,tsin->ops,sizeof(struct _TSOps));CHKERRQ(ierr);
7515 
7516   if (((PetscObject)tsin)->fortran_func_pointers) {
7517     PetscInt i;
7518     ierr = PetscMalloc((10)*sizeof(void(*)(void)),&((PetscObject)t)->fortran_func_pointers);CHKERRQ(ierr);
7519     for (i=0; i<10; i++) {
7520       ((PetscObject)t)->fortran_func_pointers[i] = ((PetscObject)tsin)->fortran_func_pointers[i];
7521     }
7522   }
7523   *tsout = t;
7524   PetscFunctionReturn(0);
7525 }
7526