xref: /petsc/src/ts/interface/ts.c (revision ba1e01c44f2f740c97c9026fe63e360558b7709b)
1 
2 #include <petsc/private/tsimpl.h>        /*I "petscts.h"  I*/
3 #include <petscdmshell.h>
4 #include <petscdmda.h>
5 #include <petscviewer.h>
6 #include <petscdraw.h>
7 
8 /* Logging support */
9 PetscClassId  TS_CLASSID, DMTS_CLASSID;
10 PetscLogEvent TS_AdjointStep, TS_Step, TS_PseudoComputeTimeStep, TS_FunctionEval, TS_JacobianEval;
11 
12 const char *const TSExactFinalTimeOptions[] = {"UNSPECIFIED","STEPOVER","INTERPOLATE","MATCHSTEP","TSExactFinalTimeOption","TS_EXACTFINALTIME_",0};
13 
14 struct _n_TSMonitorDrawCtx {
15   PetscViewer   viewer;
16   Vec           initialsolution;
17   PetscBool     showinitial;
18   PetscInt      howoften;  /* when > 0 uses step % howoften, when negative only final solution plotted */
19   PetscBool     showtimestepandtime;
20 };
21 
22 #undef __FUNCT__
23 #define __FUNCT__ "TSMonitorSetFromOptions"
24 /*@C
25    TSMonitorSetFromOptions - Sets a monitor function and viewer appropriate for the type indicated by the user
26 
27    Collective on TS
28 
29    Input Parameters:
30 +  ts - TS object you wish to monitor
31 .  name - the monitor type one is seeking
32 .  help - message indicating what monitoring is done
33 .  manual - manual page for the monitor
34 .  monitor - the monitor function
35 -  monitorsetup - a function that is called once ONLY if the user selected this monitor that may set additional features of the TS or PetscViewer objects
36 
37    Level: developer
38 
39 .seealso: PetscOptionsGetViewer(), PetscOptionsGetReal(), PetscOptionsHasName(), PetscOptionsGetString(),
40           PetscOptionsGetIntArray(), PetscOptionsGetRealArray(), PetscOptionsBool()
41           PetscOptionsInt(), PetscOptionsString(), PetscOptionsReal(), PetscOptionsBool(),
42           PetscOptionsName(), PetscOptionsBegin(), PetscOptionsEnd(), PetscOptionsHead(),
43           PetscOptionsStringArray(),PetscOptionsRealArray(), PetscOptionsScalar(),
44           PetscOptionsBoolGroupBegin(), PetscOptionsBoolGroup(), PetscOptionsBoolGroupEnd(),
45           PetscOptionsFList(), PetscOptionsEList()
46 @*/
47 PetscErrorCode  TSMonitorSetFromOptions(TS ts,const char name[],const char help[], const char manual[],PetscErrorCode (*monitor)(TS,PetscInt,PetscReal,Vec,PetscViewerAndFormat*),PetscErrorCode (*monitorsetup)(TS,PetscViewerAndFormat*))
48 {
49   PetscErrorCode    ierr;
50   PetscViewer       viewer;
51   PetscViewerFormat format;
52   PetscBool         flg;
53 
54   PetscFunctionBegin;
55   ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject)ts),((PetscObject)ts)->prefix,name,&viewer,&format,&flg);CHKERRQ(ierr);
56   if (flg) {
57     PetscViewerAndFormat *vf;
58     ierr = PetscViewerAndFormatCreate(viewer,format,&vf);CHKERRQ(ierr);
59     ierr = PetscObjectDereference((PetscObject)viewer);CHKERRQ(ierr);
60     if (monitorsetup) {
61       ierr = (*monitorsetup)(ts,vf);CHKERRQ(ierr);
62     }
63     ierr = TSMonitorSet(ts,(PetscErrorCode (*)(TS,PetscInt,PetscReal,Vec,void*))monitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);CHKERRQ(ierr);
64   }
65   PetscFunctionReturn(0);
66 }
67 
68 #undef __FUNCT__
69 #define __FUNCT__ "TSAdjointMonitorSetFromOptions"
70 /*@C
71    TSAdjointMonitorSetFromOptions - Sets a monitor function and viewer appropriate for the type indicated by the user
72 
73    Collective on TS
74 
75    Input Parameters:
76 +  ts - TS object you wish to monitor
77 .  name - the monitor type one is seeking
78 .  help - message indicating what monitoring is done
79 .  manual - manual page for the monitor
80 .  monitor - the monitor function
81 -  monitorsetup - a function that is called once ONLY if the user selected this monitor that may set additional features of the TS or PetscViewer objects
82 
83    Level: developer
84 
85 .seealso: PetscOptionsGetViewer(), PetscOptionsGetReal(), PetscOptionsHasName(), PetscOptionsGetString(),
86           PetscOptionsGetIntArray(), PetscOptionsGetRealArray(), PetscOptionsBool()
87           PetscOptionsInt(), PetscOptionsString(), PetscOptionsReal(), PetscOptionsBool(),
88           PetscOptionsName(), PetscOptionsBegin(), PetscOptionsEnd(), PetscOptionsHead(),
89           PetscOptionsStringArray(),PetscOptionsRealArray(), PetscOptionsScalar(),
90           PetscOptionsBoolGroupBegin(), PetscOptionsBoolGroup(), PetscOptionsBoolGroupEnd(),
91           PetscOptionsFList(), PetscOptionsEList()
92 @*/
93 PetscErrorCode  TSAdjointMonitorSetFromOptions(TS ts,const char name[],const char help[], const char manual[],PetscErrorCode (*monitor)(TS,PetscInt,PetscReal,Vec,PetscInt,Vec*,Vec*,PetscViewerAndFormat*),PetscErrorCode (*monitorsetup)(TS,PetscViewerAndFormat*))
94 {
95   PetscErrorCode    ierr;
96   PetscViewer       viewer;
97   PetscViewerFormat format;
98   PetscBool         flg;
99 
100   PetscFunctionBegin;
101   ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject)ts),((PetscObject)ts)->prefix,name,&viewer,&format,&flg);CHKERRQ(ierr);
102   if (flg) {
103     PetscViewerAndFormat *vf;
104     ierr = PetscViewerAndFormatCreate(viewer,format,&vf);CHKERRQ(ierr);
105     ierr = PetscObjectDereference((PetscObject)viewer);CHKERRQ(ierr);
106     if (monitorsetup) {
107       ierr = (*monitorsetup)(ts,vf);CHKERRQ(ierr);
108     }
109     ierr = TSAdjointMonitorSet(ts,(PetscErrorCode (*)(TS,PetscInt,PetscReal,Vec,PetscInt,Vec*,Vec*,void*))monitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);CHKERRQ(ierr);
110   }
111   PetscFunctionReturn(0);
112 }
113 
114 #undef __FUNCT__
115 #define __FUNCT__ "TSSetFromOptions"
116 /*@
117    TSSetFromOptions - Sets various TS parameters from user options.
118 
119    Collective on TS
120 
121    Input Parameter:
122 .  ts - the TS context obtained from TSCreate()
123 
124    Options Database Keys:
125 +  -ts_type <type> - TSEULER, TSBEULER, TSSUNDIALS, TSPSEUDO, TSCN, TSRK, TSTHETA, TSALPHA, TSGLLE, TSSSP, TSGLEE
126 .  -ts_save_trajectory - checkpoint the solution at each time-step
127 .  -ts_max_steps <maxsteps> - maximum number of time-steps to take
128 .  -ts_final_time <time> - maximum time to compute to
129 .  -ts_dt <dt> - initial time step
130 .  -ts_exact_final_time <stepover,interpolate,matchstep> whether to stop at the exact given final time and how to compute the solution at that ti,e
131 .  -ts_max_snes_failures <maxfailures> - Maximum number of nonlinear solve failures allowed
132 .  -ts_max_reject <maxrejects> - Maximum number of step rejections before step fails
133 .  -ts_error_if_step_fails <true,false> - Error if no step succeeds
134 .  -ts_rtol <rtol> - relative tolerance for local truncation error
135 .  -ts_atol <atol> Absolute tolerance for local truncation error
136 .  -ts_adjoint_solve <yes,no> After solving the ODE/DAE solve the adjoint problem (requires -ts_save_trajectory)
137 .  -ts_fd_color - Use finite differences with coloring to compute IJacobian
138 .  -ts_monitor - print information at each timestep
139 .  -ts_monitor_lg_solution - Monitor solution graphically
140 .  -ts_monitor_lg_error - Monitor error graphically
141 .  -ts_monitor_lg_timestep - Monitor timestep size graphically
142 .  -ts_monitor_lg_snes_iterations - Monitor number nonlinear iterations for each timestep graphically
143 .  -ts_monitor_lg_ksp_iterations - Monitor number nonlinear iterations for each timestep graphically
144 .  -ts_monitor_sp_eig - Monitor eigenvalues of linearized operator graphically
145 .  -ts_monitor_draw_solution - Monitor solution graphically
146 .  -ts_monitor_draw_solution_phase  <xleft,yleft,xright,yright> - Monitor solution graphically with phase diagram, requires problem with exactly 2 degrees of freedom
147 .  -ts_monitor_draw_error - Monitor error graphically, requires use to have provided TSSetSolutionFunction()
148 .  -ts_monitor_solution [ascii binary draw][:filename][:viewerformat] - monitors the solution at each timestep
149 .  -ts_monitor_solution_vtk <filename.vts> - Save each time step to a binary file, use filename-%%03D.vts
150 .  -ts_monitor_envelope - determine maximum and minimum value of each component of the solution over the solution time
151 .  -ts_adjoint_monitor - print information at each adjoint time step
152 -  -ts_adjoint_monitor_draw_sensi - monitor the sensitivity of the first cost function wrt initial conditions (lambda[0]) graphically
153 
154    Developer Note: We should unify all the -ts_monitor options in the way that -xxx_view has been unified
155 
156    Level: beginner
157 
158 .keywords: TS, timestep, set, options, database
159 
160 .seealso: TSGetType()
161 @*/
162 PetscErrorCode  TSSetFromOptions(TS ts)
163 {
164   PetscBool              opt,flg,tflg;
165   PetscErrorCode         ierr;
166   char                   monfilename[PETSC_MAX_PATH_LEN];
167   PetscReal              time_step;
168   TSExactFinalTimeOption eftopt;
169   char                   dir[16];
170   TSIFunction            ifun;
171   const char             *defaultType;
172   char                   typeName[256];
173 
174   PetscFunctionBegin;
175   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
176 
177   ierr = TSRegisterAll();CHKERRQ(ierr);
178   ierr = TSGetIFunction(ts,NULL,&ifun,NULL);CHKERRQ(ierr);
179 
180   ierr = PetscObjectOptionsBegin((PetscObject)ts);CHKERRQ(ierr);
181   if (((PetscObject)ts)->type_name)
182     defaultType = ((PetscObject)ts)->type_name;
183   else
184     defaultType = ifun ? TSBEULER : TSEULER;
185   ierr = PetscOptionsFList("-ts_type","TS method","TSSetType",TSList,defaultType,typeName,256,&opt);CHKERRQ(ierr);
186   if (opt) {
187     ierr = TSSetType(ts,typeName);CHKERRQ(ierr);
188   } else {
189     ierr = TSSetType(ts,defaultType);CHKERRQ(ierr);
190   }
191 
192   /* Handle generic TS options */
193   ierr = PetscOptionsInt("-ts_max_steps","Maximum number of time steps","TSSetDuration",ts->max_steps,&ts->max_steps,NULL);CHKERRQ(ierr);
194   ierr = PetscOptionsReal("-ts_final_time","Time to run to","TSSetDuration",ts->max_time,&ts->max_time,NULL);CHKERRQ(ierr);
195   ierr = PetscOptionsReal("-ts_init_time","Initial time","TSSetTime",ts->ptime,&ts->ptime,NULL);CHKERRQ(ierr);
196   ierr = PetscOptionsReal("-ts_dt","Initial time step","TSSetTimeStep",ts->time_step,&time_step,&flg);CHKERRQ(ierr);
197   if (flg) {ierr = TSSetTimeStep(ts,time_step);CHKERRQ(ierr);}
198   ierr = PetscOptionsEnum("-ts_exact_final_time","Option for handling of final time step","TSSetExactFinalTime",TSExactFinalTimeOptions,(PetscEnum)ts->exact_final_time,(PetscEnum*)&eftopt,&flg);CHKERRQ(ierr);
199   if (flg) {ierr = TSSetExactFinalTime(ts,eftopt);CHKERRQ(ierr);}
200   ierr = PetscOptionsInt("-ts_max_snes_failures","Maximum number of nonlinear solve failures","TSSetMaxSNESFailures",ts->max_snes_failures,&ts->max_snes_failures,NULL);CHKERRQ(ierr);
201   ierr = PetscOptionsInt("-ts_max_reject","Maximum number of step rejections before step fails","TSSetMaxStepRejections",ts->max_reject,&ts->max_reject,NULL);CHKERRQ(ierr);
202   ierr = PetscOptionsBool("-ts_error_if_step_fails","Error if no step succeeds","TSSetErrorIfStepFails",ts->errorifstepfailed,&ts->errorifstepfailed,NULL);CHKERRQ(ierr);
203   ierr = PetscOptionsReal("-ts_rtol","Relative tolerance for local truncation error","TSSetTolerances",ts->rtol,&ts->rtol,NULL);CHKERRQ(ierr);
204   ierr = PetscOptionsReal("-ts_atol","Absolute tolerance for local truncation error","TSSetTolerances",ts->atol,&ts->atol,NULL);CHKERRQ(ierr);
205 
206 #if defined(PETSC_HAVE_SAWS)
207   {
208   PetscBool set;
209   flg  = PETSC_FALSE;
210   ierr = PetscOptionsBool("-ts_saws_block","Block for SAWs memory snooper at end of TSSolve","PetscObjectSAWsBlock",((PetscObject)ts)->amspublishblock,&flg,&set);CHKERRQ(ierr);
211   if (set) {
212     ierr = PetscObjectSAWsSetBlock((PetscObject)ts,flg);CHKERRQ(ierr);
213   }
214   }
215 #endif
216 
217   /* Monitor options */
218   ierr = TSMonitorSetFromOptions(ts,"-ts_monitor","Monitor time and timestep size","TSMonitorDefault",TSMonitorDefault,NULL);CHKERRQ(ierr);
219   ierr = TSMonitorSetFromOptions(ts,"-ts_monitor_solution","View the solution at each timestep","TSMonitorSolution",TSMonitorSolution,NULL);CHKERRQ(ierr);
220   ierr = TSAdjointMonitorSetFromOptions(ts,"-ts_adjoint_monitor","Monitor adjoint timestep size","TSAdjointMonitorDefault",TSAdjointMonitorDefault,NULL);CHKERRQ(ierr);
221 
222   ierr = PetscOptionsString("-ts_monitor_python","Use Python function","TSMonitorSet",0,monfilename,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
223   if (flg) {ierr = PetscPythonMonitorSet((PetscObject)ts,monfilename);CHKERRQ(ierr);}
224 
225   ierr = PetscOptionsName("-ts_monitor_lg_solution","Monitor solution graphically","TSMonitorLGSolution",&opt);CHKERRQ(ierr);
226   if (opt) {
227     TSMonitorLGCtx ctx;
228     PetscInt       howoften = 1;
229 
230     ierr = PetscOptionsInt("-ts_monitor_lg_solution","Monitor solution graphically","TSMonitorLGSolution",howoften,&howoften,NULL);CHKERRQ(ierr);
231     ierr = TSMonitorLGCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
232     ierr = TSMonitorSet(ts,TSMonitorLGSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
233   }
234 
235   ierr = PetscOptionsName("-ts_monitor_lg_error","Monitor error graphically","TSMonitorLGError",&opt);CHKERRQ(ierr);
236   if (opt) {
237     TSMonitorLGCtx ctx;
238     PetscInt       howoften = 1;
239 
240     ierr = PetscOptionsInt("-ts_monitor_lg_error","Monitor error graphically","TSMonitorLGError",howoften,&howoften,NULL);CHKERRQ(ierr);
241     ierr = TSMonitorLGCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
242     ierr = TSMonitorSet(ts,TSMonitorLGError,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
243   }
244 
245   ierr = PetscOptionsName("-ts_monitor_lg_timestep","Monitor timestep size graphically","TSMonitorLGTimeStep",&opt);CHKERRQ(ierr);
246   if (opt) {
247     TSMonitorLGCtx ctx;
248     PetscInt       howoften = 1;
249 
250     ierr = PetscOptionsInt("-ts_monitor_lg_timestep","Monitor timestep size graphically","TSMonitorLGTimeStep",howoften,&howoften,NULL);CHKERRQ(ierr);
251     ierr = TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
252     ierr = TSMonitorSet(ts,TSMonitorLGTimeStep,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
253   }
254   ierr = PetscOptionsName("-ts_monitor_lg_snes_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGSNESIterations",&opt);CHKERRQ(ierr);
255   if (opt) {
256     TSMonitorLGCtx ctx;
257     PetscInt       howoften = 1;
258 
259     ierr = PetscOptionsInt("-ts_monitor_lg_snes_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGSNESIterations",howoften,&howoften,NULL);CHKERRQ(ierr);
260     ierr = TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
261     ierr = TSMonitorSet(ts,TSMonitorLGSNESIterations,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
262   }
263   ierr = PetscOptionsName("-ts_monitor_lg_ksp_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGKSPIterations",&opt);CHKERRQ(ierr);
264   if (opt) {
265     TSMonitorLGCtx ctx;
266     PetscInt       howoften = 1;
267 
268     ierr = PetscOptionsInt("-ts_monitor_lg_ksp_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGKSPIterations",howoften,&howoften,NULL);CHKERRQ(ierr);
269     ierr = TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
270     ierr = TSMonitorSet(ts,TSMonitorLGKSPIterations,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
271   }
272   ierr = PetscOptionsName("-ts_monitor_sp_eig","Monitor eigenvalues of linearized operator graphically","TSMonitorSPEig",&opt);CHKERRQ(ierr);
273   if (opt) {
274     TSMonitorSPEigCtx ctx;
275     PetscInt          howoften = 1;
276 
277     ierr = PetscOptionsInt("-ts_monitor_sp_eig","Monitor eigenvalues of linearized operator graphically","TSMonitorSPEig",howoften,&howoften,NULL);CHKERRQ(ierr);
278     ierr = TSMonitorSPEigCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
279     ierr = TSMonitorSet(ts,TSMonitorSPEig,ctx,(PetscErrorCode (*)(void**))TSMonitorSPEigCtxDestroy);CHKERRQ(ierr);
280   }
281   opt  = PETSC_FALSE;
282   ierr = PetscOptionsName("-ts_monitor_draw_solution","Monitor solution graphically","TSMonitorDrawSolution",&opt);CHKERRQ(ierr);
283   if (opt) {
284     TSMonitorDrawCtx ctx;
285     PetscInt         howoften = 1;
286 
287     ierr = PetscOptionsInt("-ts_monitor_draw_solution","Monitor solution graphically","TSMonitorDrawSolution",howoften,&howoften,NULL);CHKERRQ(ierr);
288     ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
289     ierr = TSMonitorSet(ts,TSMonitorDrawSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
290   }
291   opt  = PETSC_FALSE;
292   ierr = PetscOptionsName("-ts_adjoint_monitor_draw_sensi","Monitor adjoint sensitivities (lambda only) graphically","TSAdjointMonitorDrawSensi",&opt);CHKERRQ(ierr);
293   if (opt) {
294     TSMonitorDrawCtx ctx;
295     PetscInt         howoften = 1;
296 
297     ierr = PetscOptionsInt("-ts_adjoint_monitor_draw_sensi","Monitor adjoint sensitivities (lambda only) graphically","TSAdjointMonitorDrawSensi",howoften,&howoften,NULL);CHKERRQ(ierr);
298     ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
299     ierr = TSAdjointMonitorSet(ts,TSAdjointMonitorDrawSensi,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
300   }
301   opt  = PETSC_FALSE;
302   ierr = PetscOptionsName("-ts_monitor_draw_solution_phase","Monitor solution graphically","TSMonitorDrawSolutionPhase",&opt);CHKERRQ(ierr);
303   if (opt) {
304     TSMonitorDrawCtx ctx;
305     PetscReal        bounds[4];
306     PetscInt         n = 4;
307     PetscDraw        draw;
308     PetscDrawAxis    axis;
309 
310     ierr = PetscOptionsRealArray("-ts_monitor_draw_solution_phase","Monitor solution graphically","TSMonitorDrawSolutionPhase",bounds,&n,NULL);CHKERRQ(ierr);
311     if (n != 4) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Must provide bounding box of phase field");
312     ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,1,&ctx);CHKERRQ(ierr);
313     ierr = PetscViewerDrawGetDraw(ctx->viewer,0,&draw);CHKERRQ(ierr);
314     ierr = PetscViewerDrawGetDrawAxis(ctx->viewer,0,&axis);CHKERRQ(ierr);
315     ierr = PetscDrawAxisSetLimits(axis,bounds[0],bounds[2],bounds[1],bounds[3]);CHKERRQ(ierr);
316     ierr = PetscDrawAxisSetLabels(axis,"Phase Diagram","Variable 1","Variable 2");CHKERRQ(ierr);
317     ierr = TSMonitorSet(ts,TSMonitorDrawSolutionPhase,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
318   }
319   opt  = PETSC_FALSE;
320   ierr = PetscOptionsName("-ts_monitor_draw_error","Monitor error graphically","TSMonitorDrawError",&opt);CHKERRQ(ierr);
321   if (opt) {
322     TSMonitorDrawCtx ctx;
323     PetscInt         howoften = 1;
324 
325     ierr = PetscOptionsInt("-ts_monitor_draw_error","Monitor error graphically","TSMonitorDrawError",howoften,&howoften,NULL);CHKERRQ(ierr);
326     ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
327     ierr = TSMonitorSet(ts,TSMonitorDrawError,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
328   }
329 
330   opt  = PETSC_FALSE;
331   ierr = PetscOptionsString("-ts_monitor_solution_vtk","Save each time step to a binary file, use filename-%%03D.vts","TSMonitorSolutionVTK",0,monfilename,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
332   if (flg) {
333     const char *ptr,*ptr2;
334     char       *filetemplate;
335     if (!monfilename[0]) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"-ts_monitor_solution_vtk requires a file template, e.g. filename-%%03D.vts");
336     /* Do some cursory validation of the input. */
337     ierr = PetscStrstr(monfilename,"%",(char**)&ptr);CHKERRQ(ierr);
338     if (!ptr) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"-ts_monitor_solution_vtk requires a file template, e.g. filename-%%03D.vts");
339     for (ptr++; ptr && *ptr; ptr++) {
340       ierr = PetscStrchr("DdiouxX",*ptr,(char**)&ptr2);CHKERRQ(ierr);
341       if (!ptr2 && (*ptr < '0' || '9' < *ptr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Invalid file template argument to -ts_monitor_solution_vtk, should look like filename-%%03D.vts");
342       if (ptr2) break;
343     }
344     ierr = PetscStrallocpy(monfilename,&filetemplate);CHKERRQ(ierr);
345     ierr = TSMonitorSet(ts,TSMonitorSolutionVTK,filetemplate,(PetscErrorCode (*)(void**))TSMonitorSolutionVTKDestroy);CHKERRQ(ierr);
346   }
347 
348   ierr = PetscOptionsString("-ts_monitor_dmda_ray","Display a ray of the solution","None","y=0",dir,16,&flg);CHKERRQ(ierr);
349   if (flg) {
350     TSMonitorDMDARayCtx *rayctx;
351     int                  ray = 0;
352     DMDADirection        ddir;
353     DM                   da;
354     PetscMPIInt          rank;
355 
356     if (dir[1] != '=') SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Unknown ray %s",dir);
357     if (dir[0] == 'x') ddir = DMDA_X;
358     else if (dir[0] == 'y') ddir = DMDA_Y;
359     else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Unknown ray %s",dir);
360     sscanf(dir+2,"%d",&ray);
361 
362     ierr = PetscInfo2(((PetscObject)ts),"Displaying DMDA ray %c = %D\n",dir[0],ray);CHKERRQ(ierr);
363     ierr = PetscNew(&rayctx);CHKERRQ(ierr);
364     ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
365     ierr = DMDAGetRay(da,ddir,ray,&rayctx->ray,&rayctx->scatter);CHKERRQ(ierr);
366     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)ts),&rank);CHKERRQ(ierr);
367     if (!rank) {
368       ierr = PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,0,0,600,300,&rayctx->viewer);CHKERRQ(ierr);
369     }
370     rayctx->lgctx = NULL;
371     ierr = TSMonitorSet(ts,TSMonitorDMDARay,rayctx,TSMonitorDMDARayDestroy);CHKERRQ(ierr);
372   }
373   ierr = PetscOptionsString("-ts_monitor_lg_dmda_ray","Display a ray of the solution","None","x=0",dir,16,&flg);CHKERRQ(ierr);
374   if (flg) {
375     TSMonitorDMDARayCtx *rayctx;
376     int                 ray = 0;
377     DMDADirection       ddir;
378     DM                  da;
379     PetscInt            howoften = 1;
380 
381     if (dir[1] != '=') SETERRQ1(PetscObjectComm((PetscObject) ts), PETSC_ERR_ARG_WRONG, "Malformed ray %s", dir);
382     if      (dir[0] == 'x') ddir = DMDA_X;
383     else if (dir[0] == 'y') ddir = DMDA_Y;
384     else SETERRQ1(PetscObjectComm((PetscObject) ts), PETSC_ERR_ARG_WRONG, "Unknown ray direction %s", dir);
385     sscanf(dir+2, "%d", &ray);
386 
387     ierr = PetscInfo2(((PetscObject) ts),"Displaying LG DMDA ray %c = %D\n", dir[0], ray);CHKERRQ(ierr);
388     ierr = PetscNew(&rayctx);CHKERRQ(ierr);
389     ierr = TSGetDM(ts, &da);CHKERRQ(ierr);
390     ierr = DMDAGetRay(da, ddir, ray, &rayctx->ray, &rayctx->scatter);CHKERRQ(ierr);
391     ierr = TSMonitorLGCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,600,400,howoften,&rayctx->lgctx);CHKERRQ(ierr);
392     ierr = TSMonitorSet(ts, TSMonitorLGDMDARay, rayctx, TSMonitorDMDARayDestroy);CHKERRQ(ierr);
393   }
394 
395   ierr = PetscOptionsName("-ts_monitor_envelope","Monitor maximum and minimum value of each component of the solution","TSMonitorEnvelope",&opt);CHKERRQ(ierr);
396   if (opt) {
397     TSMonitorEnvelopeCtx ctx;
398 
399     ierr = TSMonitorEnvelopeCtxCreate(ts,&ctx);CHKERRQ(ierr);
400     ierr = TSMonitorSet(ts,TSMonitorEnvelope,ctx,(PetscErrorCode (*)(void**))TSMonitorEnvelopeCtxDestroy);CHKERRQ(ierr);
401   }
402 
403   flg  = PETSC_FALSE;
404   ierr = PetscOptionsBool("-ts_fd_color", "Use finite differences with coloring to compute IJacobian", "TSComputeJacobianDefaultColor", flg, &flg, NULL);CHKERRQ(ierr);
405   if (flg) {
406     DM   dm;
407     DMTS tdm;
408 
409     ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
410     ierr = DMGetDMTS(dm, &tdm);CHKERRQ(ierr);
411     tdm->ijacobianctx = NULL;
412     ierr = TSSetIJacobian(ts, NULL, NULL, TSComputeIJacobianDefaultColor, 0);CHKERRQ(ierr);
413     ierr = PetscInfo(ts, "Setting default finite difference coloring Jacobian matrix\n");CHKERRQ(ierr);
414   }
415 
416   if (ts->adapt) {
417     ierr = TSAdaptSetFromOptions(PetscOptionsObject,ts->adapt);CHKERRQ(ierr);
418   }
419 
420   /* Handle specific TS options */
421   if (ts->ops->setfromoptions) {
422     ierr = (*ts->ops->setfromoptions)(PetscOptionsObject,ts);CHKERRQ(ierr);
423   }
424 
425   /* TS trajectory must be set after TS, since it may use some TS options above */
426   tflg = ts->trajectory ? PETSC_TRUE : PETSC_FALSE;
427   ierr = PetscOptionsBool("-ts_save_trajectory","Save the solution at each timestep","TSSetSaveTrajectory",tflg,&tflg,NULL);CHKERRQ(ierr);
428   if (tflg) {
429     ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
430   }
431   tflg = ts->adjoint_solve ? PETSC_TRUE : PETSC_FALSE;
432   ierr = PetscOptionsBool("-ts_adjoint_solve","Solve the adjoint problem immediately after solving the forward problem","",tflg,&tflg,&flg);CHKERRQ(ierr);
433   if (flg) {
434     ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
435     ts->adjoint_solve = tflg;
436   }
437 
438   /* process any options handlers added with PetscObjectAddOptionsHandler() */
439   ierr = PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject)ts);CHKERRQ(ierr);
440   ierr = PetscOptionsEnd();CHKERRQ(ierr);
441 
442   if (ts->trajectory) {
443     ierr = TSTrajectorySetFromOptions(ts->trajectory,ts);CHKERRQ(ierr);
444   }
445 
446   ierr = TSGetSNES(ts,&ts->snes);CHKERRQ(ierr);
447   if (ts->problem_type == TS_LINEAR) {ierr = SNESSetType(ts->snes,SNESKSPONLY);CHKERRQ(ierr);}
448   ierr = SNESSetFromOptions(ts->snes);CHKERRQ(ierr);
449   PetscFunctionReturn(0);
450 }
451 
452 #undef __FUNCT__
453 #define __FUNCT__ "TSSetSaveTrajectory"
454 /*@
455    TSSetSaveTrajectory - Causes the TS to save its solutions as it iterates forward in time in a TSTrajectory object
456 
457    Collective on TS
458 
459    Input Parameters:
460 .  ts - the TS context obtained from TSCreate()
461 
462 Note: This routine should be called after all TS options have been set
463 
464    Level: intermediate
465 
466 .seealso: TSGetTrajectory(), TSAdjointSolve()
467 
468 .keywords: TS, set, checkpoint,
469 @*/
470 PetscErrorCode  TSSetSaveTrajectory(TS ts)
471 {
472   PetscErrorCode ierr;
473 
474   PetscFunctionBegin;
475   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
476   if (!ts->trajectory) {
477     ierr = TSTrajectoryCreate(PetscObjectComm((PetscObject)ts),&ts->trajectory);CHKERRQ(ierr);
478     ierr = TSTrajectorySetFromOptions(ts->trajectory,ts);CHKERRQ(ierr);
479   }
480   PetscFunctionReturn(0);
481 }
482 
483 #undef __FUNCT__
484 #define __FUNCT__ "TSComputeRHSJacobian"
485 /*@
486    TSComputeRHSJacobian - Computes the Jacobian matrix that has been
487       set with TSSetRHSJacobian().
488 
489    Collective on TS and Vec
490 
491    Input Parameters:
492 +  ts - the TS context
493 .  t - current timestep
494 -  U - input vector
495 
496    Output Parameters:
497 +  A - Jacobian matrix
498 .  B - optional preconditioning matrix
499 -  flag - flag indicating matrix structure
500 
501    Notes:
502    Most users should not need to explicitly call this routine, as it
503    is used internally within the nonlinear solvers.
504 
505    See KSPSetOperators() for important information about setting the
506    flag parameter.
507 
508    Level: developer
509 
510 .keywords: SNES, compute, Jacobian, matrix
511 
512 .seealso:  TSSetRHSJacobian(), KSPSetOperators()
513 @*/
514 PetscErrorCode  TSComputeRHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B)
515 {
516   PetscErrorCode ierr;
517   PetscObjectState Ustate;
518   DM             dm;
519   DMTS           tsdm;
520   TSRHSJacobian  rhsjacobianfunc;
521   void           *ctx;
522   TSIJacobian    ijacobianfunc;
523   TSRHSFunction  rhsfunction;
524 
525   PetscFunctionBegin;
526   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
527   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
528   PetscCheckSameComm(ts,1,U,3);
529   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
530   ierr = DMGetDMTS(dm,&tsdm);CHKERRQ(ierr);
531   ierr = DMTSGetRHSJacobian(dm,&rhsjacobianfunc,&ctx);CHKERRQ(ierr);
532   ierr = DMTSGetIJacobian(dm,&ijacobianfunc,NULL);CHKERRQ(ierr);
533   ierr = DMTSGetRHSFunction(dm,&rhsfunction,&ctx);CHKERRQ(ierr);
534   ierr = PetscObjectStateGet((PetscObject)U,&Ustate);CHKERRQ(ierr);
535   if (ts->rhsjacobian.time == t && (ts->problem_type == TS_LINEAR || (ts->rhsjacobian.X == U && ts->rhsjacobian.Xstate == Ustate)) && (rhsfunction != TSComputeRHSFunctionLinear)) {
536     PetscFunctionReturn(0);
537   }
538 
539   if (!rhsjacobianfunc && !ijacobianfunc) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSJacobian() and / or TSSetIJacobian()");
540 
541   if (ts->rhsjacobian.reuse) {
542     ierr = MatShift(A,-ts->rhsjacobian.shift);CHKERRQ(ierr);
543     ierr = MatScale(A,1./ts->rhsjacobian.scale);CHKERRQ(ierr);
544     if (A != B) {
545       ierr = MatShift(B,-ts->rhsjacobian.shift);CHKERRQ(ierr);
546       ierr = MatScale(B,1./ts->rhsjacobian.scale);CHKERRQ(ierr);
547     }
548     ts->rhsjacobian.shift = 0;
549     ts->rhsjacobian.scale = 1.;
550   }
551 
552   if (rhsjacobianfunc) {
553     PetscBool missing;
554     ierr = PetscLogEventBegin(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
555     PetscStackPush("TS user Jacobian function");
556     ierr = (*rhsjacobianfunc)(ts,t,U,A,B,ctx);CHKERRQ(ierr);
557     PetscStackPop;
558     ierr = PetscLogEventEnd(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
559     if (A) {
560       ierr = MatMissingDiagonal(A,&missing,NULL);CHKERRQ(ierr);
561       if (missing) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Amat passed to TSSetRHSJacobian() must have all diagonal entries set, if they are zero you must still set them with a zero value");
562     }
563     if (B && B != A) {
564       ierr = MatMissingDiagonal(B,&missing,NULL);CHKERRQ(ierr);
565       if (missing) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Bmat passed to TSSetRHSJacobian() must have all diagonal entries set, if they are zero you must still set them with a zero value");
566     }
567   } else {
568     ierr = MatZeroEntries(A);CHKERRQ(ierr);
569     if (A != B) {ierr = MatZeroEntries(B);CHKERRQ(ierr);}
570   }
571   ts->rhsjacobian.time       = t;
572   ts->rhsjacobian.X          = U;
573   ierr                       = PetscObjectStateGet((PetscObject)U,&ts->rhsjacobian.Xstate);CHKERRQ(ierr);
574   PetscFunctionReturn(0);
575 }
576 
577 #undef __FUNCT__
578 #define __FUNCT__ "TSComputeRHSFunction"
579 /*@
580    TSComputeRHSFunction - Evaluates the right-hand-side function.
581 
582    Collective on TS and Vec
583 
584    Input Parameters:
585 +  ts - the TS context
586 .  t - current time
587 -  U - state vector
588 
589    Output Parameter:
590 .  y - right hand side
591 
592    Note:
593    Most users should not need to explicitly call this routine, as it
594    is used internally within the nonlinear solvers.
595 
596    Level: developer
597 
598 .keywords: TS, compute
599 
600 .seealso: TSSetRHSFunction(), TSComputeIFunction()
601 @*/
602 PetscErrorCode TSComputeRHSFunction(TS ts,PetscReal t,Vec U,Vec y)
603 {
604   PetscErrorCode ierr;
605   TSRHSFunction  rhsfunction;
606   TSIFunction    ifunction;
607   void           *ctx;
608   DM             dm;
609 
610   PetscFunctionBegin;
611   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
612   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
613   PetscValidHeaderSpecific(y,VEC_CLASSID,4);
614   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
615   ierr = DMTSGetRHSFunction(dm,&rhsfunction,&ctx);CHKERRQ(ierr);
616   ierr = DMTSGetIFunction(dm,&ifunction,NULL);CHKERRQ(ierr);
617 
618   if (!rhsfunction && !ifunction) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSFunction() and / or TSSetIFunction()");
619 
620   ierr = PetscLogEventBegin(TS_FunctionEval,ts,U,y,0);CHKERRQ(ierr);
621   if (rhsfunction) {
622     PetscStackPush("TS user right-hand-side function");
623     ierr = (*rhsfunction)(ts,t,U,y,ctx);CHKERRQ(ierr);
624     PetscStackPop;
625   } else {
626     ierr = VecZeroEntries(y);CHKERRQ(ierr);
627   }
628 
629   ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,y,0);CHKERRQ(ierr);
630   PetscFunctionReturn(0);
631 }
632 
633 #undef __FUNCT__
634 #define __FUNCT__ "TSComputeSolutionFunction"
635 /*@
636    TSComputeSolutionFunction - Evaluates the solution function.
637 
638    Collective on TS and Vec
639 
640    Input Parameters:
641 +  ts - the TS context
642 -  t - current time
643 
644    Output Parameter:
645 .  U - the solution
646 
647    Note:
648    Most users should not need to explicitly call this routine, as it
649    is used internally within the nonlinear solvers.
650 
651    Level: developer
652 
653 .keywords: TS, compute
654 
655 .seealso: TSSetSolutionFunction(), TSSetRHSFunction(), TSComputeIFunction()
656 @*/
657 PetscErrorCode TSComputeSolutionFunction(TS ts,PetscReal t,Vec U)
658 {
659   PetscErrorCode     ierr;
660   TSSolutionFunction solutionfunction;
661   void               *ctx;
662   DM                 dm;
663 
664   PetscFunctionBegin;
665   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
666   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
667   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
668   ierr = DMTSGetSolutionFunction(dm,&solutionfunction,&ctx);CHKERRQ(ierr);
669 
670   if (solutionfunction) {
671     PetscStackPush("TS user solution function");
672     ierr = (*solutionfunction)(ts,t,U,ctx);CHKERRQ(ierr);
673     PetscStackPop;
674   }
675   PetscFunctionReturn(0);
676 }
677 #undef __FUNCT__
678 #define __FUNCT__ "TSComputeForcingFunction"
679 /*@
680    TSComputeForcingFunction - Evaluates the forcing function.
681 
682    Collective on TS and Vec
683 
684    Input Parameters:
685 +  ts - the TS context
686 -  t - current time
687 
688    Output Parameter:
689 .  U - the function value
690 
691    Note:
692    Most users should not need to explicitly call this routine, as it
693    is used internally within the nonlinear solvers.
694 
695    Level: developer
696 
697 .keywords: TS, compute
698 
699 .seealso: TSSetSolutionFunction(), TSSetRHSFunction(), TSComputeIFunction()
700 @*/
701 PetscErrorCode TSComputeForcingFunction(TS ts,PetscReal t,Vec U)
702 {
703   PetscErrorCode     ierr, (*forcing)(TS,PetscReal,Vec,void*);
704   void               *ctx;
705   DM                 dm;
706 
707   PetscFunctionBegin;
708   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
709   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
710   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
711   ierr = DMTSGetForcingFunction(dm,&forcing,&ctx);CHKERRQ(ierr);
712 
713   if (forcing) {
714     PetscStackPush("TS user forcing function");
715     ierr = (*forcing)(ts,t,U,ctx);CHKERRQ(ierr);
716     PetscStackPop;
717   }
718   PetscFunctionReturn(0);
719 }
720 
721 #undef __FUNCT__
722 #define __FUNCT__ "TSGetRHSVec_Private"
723 static PetscErrorCode TSGetRHSVec_Private(TS ts,Vec *Frhs)
724 {
725   Vec            F;
726   PetscErrorCode ierr;
727 
728   PetscFunctionBegin;
729   *Frhs = NULL;
730   ierr  = TSGetIFunction(ts,&F,NULL,NULL);CHKERRQ(ierr);
731   if (!ts->Frhs) {
732     ierr = VecDuplicate(F,&ts->Frhs);CHKERRQ(ierr);
733   }
734   *Frhs = ts->Frhs;
735   PetscFunctionReturn(0);
736 }
737 
738 #undef __FUNCT__
739 #define __FUNCT__ "TSGetRHSMats_Private"
740 static PetscErrorCode TSGetRHSMats_Private(TS ts,Mat *Arhs,Mat *Brhs)
741 {
742   Mat            A,B;
743   PetscErrorCode ierr;
744 
745   PetscFunctionBegin;
746   if (Arhs) *Arhs = NULL;
747   if (Brhs) *Brhs = NULL;
748   ierr = TSGetIJacobian(ts,&A,&B,NULL,NULL);CHKERRQ(ierr);
749   if (Arhs) {
750     if (!ts->Arhs) {
751       ierr = MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&ts->Arhs);CHKERRQ(ierr);
752     }
753     *Arhs = ts->Arhs;
754   }
755   if (Brhs) {
756     if (!ts->Brhs) {
757       if (A != B) {
758         ierr = MatDuplicate(B,MAT_DO_NOT_COPY_VALUES,&ts->Brhs);CHKERRQ(ierr);
759       } else {
760         ierr = PetscObjectReference((PetscObject)ts->Arhs);CHKERRQ(ierr);
761         ts->Brhs = ts->Arhs;
762       }
763     }
764     *Brhs = ts->Brhs;
765   }
766   PetscFunctionReturn(0);
767 }
768 
769 #undef __FUNCT__
770 #define __FUNCT__ "TSComputeIFunction"
771 /*@
772    TSComputeIFunction - Evaluates the DAE residual written in implicit form F(t,U,Udot)=0
773 
774    Collective on TS and Vec
775 
776    Input Parameters:
777 +  ts - the TS context
778 .  t - current time
779 .  U - state vector
780 .  Udot - time derivative of state vector
781 -  imex - flag indicates if the method is IMEX so that the RHSFunction should be kept separate
782 
783    Output Parameter:
784 .  Y - right hand side
785 
786    Note:
787    Most users should not need to explicitly call this routine, as it
788    is used internally within the nonlinear solvers.
789 
790    If the user did did not write their equations in implicit form, this
791    function recasts them in implicit form.
792 
793    Level: developer
794 
795 .keywords: TS, compute
796 
797 .seealso: TSSetIFunction(), TSComputeRHSFunction()
798 @*/
799 PetscErrorCode TSComputeIFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec Y,PetscBool imex)
800 {
801   PetscErrorCode ierr;
802   TSIFunction    ifunction;
803   TSRHSFunction  rhsfunction;
804   void           *ctx;
805   DM             dm;
806 
807   PetscFunctionBegin;
808   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
809   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
810   PetscValidHeaderSpecific(Udot,VEC_CLASSID,4);
811   PetscValidHeaderSpecific(Y,VEC_CLASSID,5);
812 
813   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
814   ierr = DMTSGetIFunction(dm,&ifunction,&ctx);CHKERRQ(ierr);
815   ierr = DMTSGetRHSFunction(dm,&rhsfunction,NULL);CHKERRQ(ierr);
816 
817   if (!rhsfunction && !ifunction) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSFunction() and / or TSSetIFunction()");
818 
819   ierr = PetscLogEventBegin(TS_FunctionEval,ts,U,Udot,Y);CHKERRQ(ierr);
820   if (ifunction) {
821     PetscStackPush("TS user implicit function");
822     ierr = (*ifunction)(ts,t,U,Udot,Y,ctx);CHKERRQ(ierr);
823     PetscStackPop;
824   }
825   if (imex) {
826     if (!ifunction) {
827       ierr = VecCopy(Udot,Y);CHKERRQ(ierr);
828     }
829   } else if (rhsfunction) {
830     if (ifunction) {
831       Vec Frhs;
832       ierr = TSGetRHSVec_Private(ts,&Frhs);CHKERRQ(ierr);
833       ierr = TSComputeRHSFunction(ts,t,U,Frhs);CHKERRQ(ierr);
834       ierr = VecAXPY(Y,-1,Frhs);CHKERRQ(ierr);
835     } else {
836       ierr = TSComputeRHSFunction(ts,t,U,Y);CHKERRQ(ierr);
837       ierr = VecAYPX(Y,-1,Udot);CHKERRQ(ierr);
838     }
839   }
840   ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,Udot,Y);CHKERRQ(ierr);
841   PetscFunctionReturn(0);
842 }
843 
844 #undef __FUNCT__
845 #define __FUNCT__ "TSComputeIJacobian"
846 /*@
847    TSComputeIJacobian - Evaluates the Jacobian of the DAE
848 
849    Collective on TS and Vec
850 
851    Input
852       Input Parameters:
853 +  ts - the TS context
854 .  t - current timestep
855 .  U - state vector
856 .  Udot - time derivative of state vector
857 .  shift - shift to apply, see note below
858 -  imex - flag indicates if the method is IMEX so that the RHSJacobian should be kept separate
859 
860    Output Parameters:
861 +  A - Jacobian matrix
862 .  B - optional preconditioning matrix
863 -  flag - flag indicating matrix structure
864 
865    Notes:
866    If F(t,U,Udot)=0 is the DAE, the required Jacobian is
867 
868    dF/dU + shift*dF/dUdot
869 
870    Most users should not need to explicitly call this routine, as it
871    is used internally within the nonlinear solvers.
872 
873    Level: developer
874 
875 .keywords: TS, compute, Jacobian, matrix
876 
877 .seealso:  TSSetIJacobian()
878 @*/
879 PetscErrorCode TSComputeIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat A,Mat B,PetscBool imex)
880 {
881   PetscErrorCode ierr;
882   TSIJacobian    ijacobian;
883   TSRHSJacobian  rhsjacobian;
884   DM             dm;
885   void           *ctx;
886 
887   PetscFunctionBegin;
888   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
889   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
890   PetscValidHeaderSpecific(Udot,VEC_CLASSID,4);
891   PetscValidPointer(A,6);
892   PetscValidHeaderSpecific(A,MAT_CLASSID,6);
893   PetscValidPointer(B,7);
894   PetscValidHeaderSpecific(B,MAT_CLASSID,7);
895 
896   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
897   ierr = DMTSGetIJacobian(dm,&ijacobian,&ctx);CHKERRQ(ierr);
898   ierr = DMTSGetRHSJacobian(dm,&rhsjacobian,NULL);CHKERRQ(ierr);
899 
900   if (!rhsjacobian && !ijacobian) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSJacobian() and / or TSSetIJacobian()");
901 
902   ierr = PetscLogEventBegin(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
903   if (ijacobian) {
904     PetscBool missing;
905     PetscStackPush("TS user implicit Jacobian");
906     ierr = (*ijacobian)(ts,t,U,Udot,shift,A,B,ctx);CHKERRQ(ierr);
907     PetscStackPop;
908     if (A) {
909       ierr = MatMissingDiagonal(A,&missing,NULL);CHKERRQ(ierr);
910       if (missing) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Amat passed to TSSetIJacobian() must have all diagonal entries set, if they are zero you must still set them with a zero value");
911     }
912     if (B && B != A) {
913       ierr = MatMissingDiagonal(B,&missing,NULL);CHKERRQ(ierr);
914       if (missing) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Bmat passed to TSSetIJacobian() must have all diagonal entries set, if they are zero you must still set them with a zero value");
915     }
916   }
917   if (imex) {
918     if (!ijacobian) {  /* system was written as Udot = G(t,U) */
919       ierr = MatZeroEntries(A);CHKERRQ(ierr);
920       ierr = MatShift(A,shift);CHKERRQ(ierr);
921       if (A != B) {
922         ierr = MatZeroEntries(B);CHKERRQ(ierr);
923         ierr = MatShift(B,shift);CHKERRQ(ierr);
924       }
925     }
926   } else {
927     Mat Arhs = NULL,Brhs = NULL;
928     if (rhsjacobian) {
929       ierr = TSGetRHSMats_Private(ts,&Arhs,&Brhs);CHKERRQ(ierr);
930       ierr = TSComputeRHSJacobian(ts,t,U,Arhs,Brhs);CHKERRQ(ierr);
931     }
932     if (Arhs == A) {           /* No IJacobian, so we only have the RHS matrix */
933       ts->rhsjacobian.scale = -1;
934       ts->rhsjacobian.shift = shift;
935       ierr = MatScale(A,-1);CHKERRQ(ierr);
936       ierr = MatShift(A,shift);CHKERRQ(ierr);
937       if (A != B) {
938         ierr = MatScale(B,-1);CHKERRQ(ierr);
939         ierr = MatShift(B,shift);CHKERRQ(ierr);
940       }
941     } else if (Arhs) {          /* Both IJacobian and RHSJacobian */
942       MatStructure axpy = DIFFERENT_NONZERO_PATTERN;
943       if (!ijacobian) {         /* No IJacobian provided, but we have a separate RHS matrix */
944         ierr = MatZeroEntries(A);CHKERRQ(ierr);
945         ierr = MatShift(A,shift);CHKERRQ(ierr);
946         if (A != B) {
947           ierr = MatZeroEntries(B);CHKERRQ(ierr);
948           ierr = MatShift(B,shift);CHKERRQ(ierr);
949         }
950       }
951       ierr = MatAXPY(A,-1,Arhs,axpy);CHKERRQ(ierr);
952       if (A != B) {
953         ierr = MatAXPY(B,-1,Brhs,axpy);CHKERRQ(ierr);
954       }
955     }
956   }
957   ierr = PetscLogEventEnd(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
958   PetscFunctionReturn(0);
959 }
960 
961 #undef __FUNCT__
962 #define __FUNCT__ "TSSetRHSFunction"
963 /*@C
964     TSSetRHSFunction - Sets the routine for evaluating the function,
965     where U_t = G(t,u).
966 
967     Logically Collective on TS
968 
969     Input Parameters:
970 +   ts - the TS context obtained from TSCreate()
971 .   r - vector to put the computed right hand side (or NULL to have it created)
972 .   f - routine for evaluating the right-hand-side function
973 -   ctx - [optional] user-defined context for private data for the
974           function evaluation routine (may be NULL)
975 
976     Calling sequence of func:
977 $     func (TS ts,PetscReal t,Vec u,Vec F,void *ctx);
978 
979 +   t - current timestep
980 .   u - input vector
981 .   F - function vector
982 -   ctx - [optional] user-defined function context
983 
984     Level: beginner
985 
986     Notes: You must call this function or TSSetIFunction() to define your ODE. You cannot use this function when solving a DAE.
987 
988 .keywords: TS, timestep, set, right-hand-side, function
989 
990 .seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSSetIFunction()
991 @*/
992 PetscErrorCode  TSSetRHSFunction(TS ts,Vec r,PetscErrorCode (*f)(TS,PetscReal,Vec,Vec,void*),void *ctx)
993 {
994   PetscErrorCode ierr;
995   SNES           snes;
996   Vec            ralloc = NULL;
997   DM             dm;
998 
999   PetscFunctionBegin;
1000   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1001   if (r) PetscValidHeaderSpecific(r,VEC_CLASSID,2);
1002 
1003   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1004   ierr = DMTSSetRHSFunction(dm,f,ctx);CHKERRQ(ierr);
1005   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1006   if (!r && !ts->dm && ts->vec_sol) {
1007     ierr = VecDuplicate(ts->vec_sol,&ralloc);CHKERRQ(ierr);
1008     r = ralloc;
1009   }
1010   ierr = SNESSetFunction(snes,r,SNESTSFormFunction,ts);CHKERRQ(ierr);
1011   ierr = VecDestroy(&ralloc);CHKERRQ(ierr);
1012   PetscFunctionReturn(0);
1013 }
1014 
1015 #undef __FUNCT__
1016 #define __FUNCT__ "TSSetSolutionFunction"
1017 /*@C
1018     TSSetSolutionFunction - Provide a function that computes the solution of the ODE or DAE
1019 
1020     Logically Collective on TS
1021 
1022     Input Parameters:
1023 +   ts - the TS context obtained from TSCreate()
1024 .   f - routine for evaluating the solution
1025 -   ctx - [optional] user-defined context for private data for the
1026           function evaluation routine (may be NULL)
1027 
1028     Calling sequence of func:
1029 $     func (TS ts,PetscReal t,Vec u,void *ctx);
1030 
1031 +   t - current timestep
1032 .   u - output vector
1033 -   ctx - [optional] user-defined function context
1034 
1035     Notes:
1036     This routine is used for testing accuracy of time integration schemes when you already know the solution.
1037     If analytic solutions are not known for your system, consider using the Method of Manufactured Solutions to
1038     create closed-form solutions with non-physical forcing terms.
1039 
1040     For low-dimensional problems solved in serial, such as small discrete systems, TSMonitorLGError() can be used to monitor the error history.
1041 
1042     Level: beginner
1043 
1044 .keywords: TS, timestep, set, right-hand-side, function
1045 
1046 .seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSComputeSolutionFunction(), TSSetForcingFunction()
1047 @*/
1048 PetscErrorCode  TSSetSolutionFunction(TS ts,PetscErrorCode (*f)(TS,PetscReal,Vec,void*),void *ctx)
1049 {
1050   PetscErrorCode ierr;
1051   DM             dm;
1052 
1053   PetscFunctionBegin;
1054   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1055   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1056   ierr = DMTSSetSolutionFunction(dm,f,ctx);CHKERRQ(ierr);
1057   PetscFunctionReturn(0);
1058 }
1059 
1060 #undef __FUNCT__
1061 #define __FUNCT__ "TSSetForcingFunction"
1062 /*@C
1063     TSSetForcingFunction - Provide a function that computes a forcing term for a ODE or PDE
1064 
1065     Logically Collective on TS
1066 
1067     Input Parameters:
1068 +   ts - the TS context obtained from TSCreate()
1069 .   f - routine for evaluating the forcing function
1070 -   ctx - [optional] user-defined context for private data for the
1071           function evaluation routine (may be NULL)
1072 
1073     Calling sequence of func:
1074 $     func (TS ts,PetscReal t,Vec u,void *ctx);
1075 
1076 +   t - current timestep
1077 .   u - output vector
1078 -   ctx - [optional] user-defined function context
1079 
1080     Notes:
1081     This routine is useful for testing accuracy of time integration schemes when using the Method of Manufactured Solutions to
1082     create closed-form solutions with a non-physical forcing term.
1083 
1084     For low-dimensional problems solved in serial, such as small discrete systems, TSMonitorLGError() can be used to monitor the error history.
1085 
1086     Level: beginner
1087 
1088 .keywords: TS, timestep, set, right-hand-side, function
1089 
1090 .seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSComputeSolutionFunction(), TSSetSolutionFunction()
1091 @*/
1092 PetscErrorCode  TSSetForcingFunction(TS ts,TSForcingFunction f,void *ctx)
1093 {
1094   PetscErrorCode ierr;
1095   DM             dm;
1096 
1097   PetscFunctionBegin;
1098   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1099   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1100   ierr = DMTSSetForcingFunction(dm,f,ctx);CHKERRQ(ierr);
1101   PetscFunctionReturn(0);
1102 }
1103 
1104 #undef __FUNCT__
1105 #define __FUNCT__ "TSSetRHSJacobian"
1106 /*@C
1107    TSSetRHSJacobian - Sets the function to compute the Jacobian of G,
1108    where U_t = G(U,t), as well as the location to store the matrix.
1109 
1110    Logically Collective on TS
1111 
1112    Input Parameters:
1113 +  ts  - the TS context obtained from TSCreate()
1114 .  Amat - (approximate) Jacobian matrix
1115 .  Pmat - matrix from which preconditioner is to be constructed (usually the same as Amat)
1116 .  f   - the Jacobian evaluation routine
1117 -  ctx - [optional] user-defined context for private data for the
1118          Jacobian evaluation routine (may be NULL)
1119 
1120    Calling sequence of f:
1121 $     func (TS ts,PetscReal t,Vec u,Mat A,Mat B,void *ctx);
1122 
1123 +  t - current timestep
1124 .  u - input vector
1125 .  Amat - (approximate) Jacobian matrix
1126 .  Pmat - matrix from which preconditioner is to be constructed (usually the same as Amat)
1127 -  ctx - [optional] user-defined context for matrix evaluation routine
1128 
1129    Notes:
1130    You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value
1131 
1132    The TS solver may modify the nonzero structure and the entries of the matrices Amat and Pmat between the calls to f()
1133    You should not assume the values are the same in the next call to f() as you set them in the previous call.
1134 
1135    Level: beginner
1136 
1137 .keywords: TS, timestep, set, right-hand-side, Jacobian
1138 
1139 .seealso: SNESComputeJacobianDefaultColor(), TSSetRHSFunction(), TSRHSJacobianSetReuse(), TSSetIJacobian()
1140 
1141 @*/
1142 PetscErrorCode  TSSetRHSJacobian(TS ts,Mat Amat,Mat Pmat,TSRHSJacobian f,void *ctx)
1143 {
1144   PetscErrorCode ierr;
1145   SNES           snes;
1146   DM             dm;
1147   TSIJacobian    ijacobian;
1148 
1149   PetscFunctionBegin;
1150   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1151   if (Amat) PetscValidHeaderSpecific(Amat,MAT_CLASSID,2);
1152   if (Pmat) PetscValidHeaderSpecific(Pmat,MAT_CLASSID,3);
1153   if (Amat) PetscCheckSameComm(ts,1,Amat,2);
1154   if (Pmat) PetscCheckSameComm(ts,1,Pmat,3);
1155 
1156   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1157   ierr = DMTSSetRHSJacobian(dm,f,ctx);CHKERRQ(ierr);
1158   if (f == TSComputeRHSJacobianConstant) {
1159     /* Handle this case automatically for the user; otherwise user should call themselves. */
1160     ierr = TSRHSJacobianSetReuse(ts,PETSC_TRUE);CHKERRQ(ierr);
1161   }
1162   ierr = DMTSGetIJacobian(dm,&ijacobian,NULL);CHKERRQ(ierr);
1163   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1164   if (!ijacobian) {
1165     ierr = SNESSetJacobian(snes,Amat,Pmat,SNESTSFormJacobian,ts);CHKERRQ(ierr);
1166   }
1167   if (Amat) {
1168     ierr = PetscObjectReference((PetscObject)Amat);CHKERRQ(ierr);
1169     ierr = MatDestroy(&ts->Arhs);CHKERRQ(ierr);
1170     ts->Arhs = Amat;
1171   }
1172   if (Pmat) {
1173     ierr = PetscObjectReference((PetscObject)Pmat);CHKERRQ(ierr);
1174     ierr = MatDestroy(&ts->Brhs);CHKERRQ(ierr);
1175     ts->Brhs = Pmat;
1176   }
1177   PetscFunctionReturn(0);
1178 }
1179 
1180 
1181 #undef __FUNCT__
1182 #define __FUNCT__ "TSSetIFunction"
1183 /*@C
1184    TSSetIFunction - Set the function to compute F(t,U,U_t) where F() = 0 is the DAE to be solved.
1185 
1186    Logically Collective on TS
1187 
1188    Input Parameters:
1189 +  ts  - the TS context obtained from TSCreate()
1190 .  r   - vector to hold the residual (or NULL to have it created internally)
1191 .  f   - the function evaluation routine
1192 -  ctx - user-defined context for private data for the function evaluation routine (may be NULL)
1193 
1194    Calling sequence of f:
1195 $  f(TS ts,PetscReal t,Vec u,Vec u_t,Vec F,ctx);
1196 
1197 +  t   - time at step/stage being solved
1198 .  u   - state vector
1199 .  u_t - time derivative of state vector
1200 .  F   - function vector
1201 -  ctx - [optional] user-defined context for matrix evaluation routine
1202 
1203    Important:
1204    The user MUST call either this routine or TSSetRHSFunction() to define the ODE.  When solving DAEs you must use this function.
1205 
1206    Level: beginner
1207 
1208 .keywords: TS, timestep, set, DAE, Jacobian
1209 
1210 .seealso: TSSetRHSJacobian(), TSSetRHSFunction(), TSSetIJacobian()
1211 @*/
1212 PetscErrorCode  TSSetIFunction(TS ts,Vec r,TSIFunction f,void *ctx)
1213 {
1214   PetscErrorCode ierr;
1215   SNES           snes;
1216   Vec            ralloc = NULL;
1217   DM             dm;
1218 
1219   PetscFunctionBegin;
1220   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1221   if (r) PetscValidHeaderSpecific(r,VEC_CLASSID,2);
1222 
1223   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1224   ierr = DMTSSetIFunction(dm,f,ctx);CHKERRQ(ierr);
1225 
1226   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1227   if (!r && !ts->dm && ts->vec_sol) {
1228     ierr = VecDuplicate(ts->vec_sol,&ralloc);CHKERRQ(ierr);
1229     r  = ralloc;
1230   }
1231   ierr = SNESSetFunction(snes,r,SNESTSFormFunction,ts);CHKERRQ(ierr);
1232   ierr = VecDestroy(&ralloc);CHKERRQ(ierr);
1233   PetscFunctionReturn(0);
1234 }
1235 
1236 #undef __FUNCT__
1237 #define __FUNCT__ "TSGetIFunction"
1238 /*@C
1239    TSGetIFunction - Returns the vector where the implicit residual is stored and the function/contex to compute it.
1240 
1241    Not Collective
1242 
1243    Input Parameter:
1244 .  ts - the TS context
1245 
1246    Output Parameter:
1247 +  r - vector to hold residual (or NULL)
1248 .  func - the function to compute residual (or NULL)
1249 -  ctx - the function context (or NULL)
1250 
1251    Level: advanced
1252 
1253 .keywords: TS, nonlinear, get, function
1254 
1255 .seealso: TSSetIFunction(), SNESGetFunction()
1256 @*/
1257 PetscErrorCode TSGetIFunction(TS ts,Vec *r,TSIFunction *func,void **ctx)
1258 {
1259   PetscErrorCode ierr;
1260   SNES           snes;
1261   DM             dm;
1262 
1263   PetscFunctionBegin;
1264   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1265   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1266   ierr = SNESGetFunction(snes,r,NULL,NULL);CHKERRQ(ierr);
1267   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1268   ierr = DMTSGetIFunction(dm,func,ctx);CHKERRQ(ierr);
1269   PetscFunctionReturn(0);
1270 }
1271 
1272 #undef __FUNCT__
1273 #define __FUNCT__ "TSGetRHSFunction"
1274 /*@C
1275    TSGetRHSFunction - Returns the vector where the right hand side is stored and the function/context to compute it.
1276 
1277    Not Collective
1278 
1279    Input Parameter:
1280 .  ts - the TS context
1281 
1282    Output Parameter:
1283 +  r - vector to hold computed right hand side (or NULL)
1284 .  func - the function to compute right hand side (or NULL)
1285 -  ctx - the function context (or NULL)
1286 
1287    Level: advanced
1288 
1289 .keywords: TS, nonlinear, get, function
1290 
1291 .seealso: TSSetRHSFunction(), SNESGetFunction()
1292 @*/
1293 PetscErrorCode TSGetRHSFunction(TS ts,Vec *r,TSRHSFunction *func,void **ctx)
1294 {
1295   PetscErrorCode ierr;
1296   SNES           snes;
1297   DM             dm;
1298 
1299   PetscFunctionBegin;
1300   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1301   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1302   ierr = SNESGetFunction(snes,r,NULL,NULL);CHKERRQ(ierr);
1303   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1304   ierr = DMTSGetRHSFunction(dm,func,ctx);CHKERRQ(ierr);
1305   PetscFunctionReturn(0);
1306 }
1307 
1308 #undef __FUNCT__
1309 #define __FUNCT__ "TSSetIJacobian"
1310 /*@C
1311    TSSetIJacobian - Set the function to compute the matrix dF/dU + a*dF/dU_t where F(t,U,U_t) is the function
1312         provided with TSSetIFunction().
1313 
1314    Logically Collective on TS
1315 
1316    Input Parameters:
1317 +  ts  - the TS context obtained from TSCreate()
1318 .  Amat - (approximate) Jacobian matrix
1319 .  Pmat - matrix used to compute preconditioner (usually the same as Amat)
1320 .  f   - the Jacobian evaluation routine
1321 -  ctx - user-defined context for private data for the Jacobian evaluation routine (may be NULL)
1322 
1323    Calling sequence of f:
1324 $  f(TS ts,PetscReal t,Vec U,Vec U_t,PetscReal a,Mat Amat,Mat Pmat,void *ctx);
1325 
1326 +  t    - time at step/stage being solved
1327 .  U    - state vector
1328 .  U_t  - time derivative of state vector
1329 .  a    - shift
1330 .  Amat - (approximate) Jacobian of F(t,U,W+a*U), equivalent to dF/dU + a*dF/dU_t
1331 .  Pmat - matrix used for constructing preconditioner, usually the same as Amat
1332 -  ctx  - [optional] user-defined context for matrix evaluation routine
1333 
1334    Notes:
1335    The matrices Amat and Pmat are exactly the matrices that are used by SNES for the nonlinear solve.
1336 
1337    If you know the operator Amat has a null space you can use MatSetNullSpace() and MatSetTransposeNullSpace() to supply the null
1338    space to Amat and the KSP solvers will automatically use that null space as needed during the solution process.
1339 
1340    The matrix dF/dU + a*dF/dU_t you provide turns out to be
1341    the Jacobian of F(t,U,W+a*U) where F(t,U,U_t) = 0 is the DAE to be solved.
1342    The time integrator internally approximates U_t by W+a*U where the positive "shift"
1343    a and vector W depend on the integration method, step size, and past states. For example with
1344    the backward Euler method a = 1/dt and W = -a*U(previous timestep) so
1345    W + a*U = a*(U - U(previous timestep)) = (U - U(previous timestep))/dt
1346 
1347    You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value
1348 
1349    The TS solver may modify the nonzero structure and the entries of the matrices Amat and Pmat between the calls to f()
1350    You should not assume the values are the same in the next call to f() as you set them in the previous call.
1351 
1352    Level: beginner
1353 
1354 .keywords: TS, timestep, DAE, Jacobian
1355 
1356 .seealso: TSSetIFunction(), TSSetRHSJacobian(), SNESComputeJacobianDefaultColor(), SNESComputeJacobianDefault(), TSSetRHSFunction()
1357 
1358 @*/
1359 PetscErrorCode  TSSetIJacobian(TS ts,Mat Amat,Mat Pmat,TSIJacobian f,void *ctx)
1360 {
1361   PetscErrorCode ierr;
1362   SNES           snes;
1363   DM             dm;
1364 
1365   PetscFunctionBegin;
1366   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1367   if (Amat) PetscValidHeaderSpecific(Amat,MAT_CLASSID,2);
1368   if (Pmat) PetscValidHeaderSpecific(Pmat,MAT_CLASSID,3);
1369   if (Amat) PetscCheckSameComm(ts,1,Amat,2);
1370   if (Pmat) PetscCheckSameComm(ts,1,Pmat,3);
1371 
1372   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1373   ierr = DMTSSetIJacobian(dm,f,ctx);CHKERRQ(ierr);
1374 
1375   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1376   ierr = SNESSetJacobian(snes,Amat,Pmat,SNESTSFormJacobian,ts);CHKERRQ(ierr);
1377   PetscFunctionReturn(0);
1378 }
1379 
1380 #undef __FUNCT__
1381 #define __FUNCT__ "TSRHSJacobianSetReuse"
1382 /*@
1383    TSRHSJacobianSetReuse - restore RHS Jacobian before re-evaluating.  Without this flag, TS will change the sign and
1384    shift the RHS Jacobian for a finite-time-step implicit solve, in which case the user function will need to recompute
1385    the entire Jacobian.  The reuse flag must be set if the evaluation function will assume that the matrix entries have
1386    not been changed by the TS.
1387 
1388    Logically Collective
1389 
1390    Input Arguments:
1391 +  ts - TS context obtained from TSCreate()
1392 -  reuse - PETSC_TRUE if the RHS Jacobian
1393 
1394    Level: intermediate
1395 
1396 .seealso: TSSetRHSJacobian(), TSComputeRHSJacobianConstant()
1397 @*/
1398 PetscErrorCode TSRHSJacobianSetReuse(TS ts,PetscBool reuse)
1399 {
1400   PetscFunctionBegin;
1401   ts->rhsjacobian.reuse = reuse;
1402   PetscFunctionReturn(0);
1403 }
1404 
1405 #undef __FUNCT__
1406 #define __FUNCT__ "TSSetI2Function"
1407 /*@C
1408    TSSetI2Function - Set the function to compute F(t,U,U_t,U_tt) where F = 0 is the DAE to be solved.
1409 
1410    Logically Collective on TS
1411 
1412    Input Parameters:
1413 +  ts  - the TS context obtained from TSCreate()
1414 .  F   - vector to hold the residual (or NULL to have it created internally)
1415 .  fun - the function evaluation routine
1416 -  ctx - user-defined context for private data for the function evaluation routine (may be NULL)
1417 
1418    Calling sequence of fun:
1419 $  fun(TS ts,PetscReal t,Vec U,Vec U_t,Vec U_tt,Vec F,ctx);
1420 
1421 +  t    - time at step/stage being solved
1422 .  U    - state vector
1423 .  U_t  - time derivative of state vector
1424 .  U_tt - second time derivative of state vector
1425 .  F    - function vector
1426 -  ctx  - [optional] user-defined context for matrix evaluation routine (may be NULL)
1427 
1428    Level: beginner
1429 
1430 .keywords: TS, timestep, set, ODE, DAE, Function
1431 
1432 .seealso: TSSetI2Jacobian()
1433 @*/
1434 PetscErrorCode TSSetI2Function(TS ts,Vec F,TSI2Function fun,void *ctx)
1435 {
1436   DM             dm;
1437   PetscErrorCode ierr;
1438 
1439   PetscFunctionBegin;
1440   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1441   if (F) PetscValidHeaderSpecific(F,VEC_CLASSID,2);
1442   ierr = TSSetIFunction(ts,F,NULL,NULL);CHKERRQ(ierr);
1443   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1444   ierr = DMTSSetI2Function(dm,fun,ctx);CHKERRQ(ierr);
1445   PetscFunctionReturn(0);
1446 }
1447 
1448 #undef __FUNCT__
1449 #define __FUNCT__ "TSGetI2Function"
1450 /*@C
1451   TSGetI2Function - Returns the vector where the implicit residual is stored and the function/contex to compute it.
1452 
1453   Not Collective
1454 
1455   Input Parameter:
1456 . ts - the TS context
1457 
1458   Output Parameter:
1459 + r - vector to hold residual (or NULL)
1460 . fun - the function to compute residual (or NULL)
1461 - ctx - the function context (or NULL)
1462 
1463   Level: advanced
1464 
1465 .keywords: TS, nonlinear, get, function
1466 
1467 .seealso: TSSetI2Function(), SNESGetFunction()
1468 @*/
1469 PetscErrorCode TSGetI2Function(TS ts,Vec *r,TSI2Function *fun,void **ctx)
1470 {
1471   PetscErrorCode ierr;
1472   SNES           snes;
1473   DM             dm;
1474 
1475   PetscFunctionBegin;
1476   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1477   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1478   ierr = SNESGetFunction(snes,r,NULL,NULL);CHKERRQ(ierr);
1479   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1480   ierr = DMTSGetI2Function(dm,fun,ctx);CHKERRQ(ierr);
1481   PetscFunctionReturn(0);
1482 }
1483 
1484 #undef __FUNCT__
1485 #define __FUNCT__ "TSSetI2Jacobian"
1486 /*@C
1487    TSSetI2Jacobian - Set the function to compute the matrix dF/dU + v*dF/dU_t  + a*dF/dU_tt
1488         where F(t,U,U_t,U_tt) is the function you provided with TSSetI2Function().
1489 
1490    Logically Collective on TS
1491 
1492    Input Parameters:
1493 +  ts  - the TS context obtained from TSCreate()
1494 .  J   - Jacobian matrix
1495 .  P   - preconditioning matrix for J (may be same as J)
1496 .  jac - the Jacobian evaluation routine
1497 -  ctx - user-defined context for private data for the Jacobian evaluation routine (may be NULL)
1498 
1499    Calling sequence of jac:
1500 $  jac(TS ts,PetscReal t,Vec U,Vec U_t,Vec U_tt,PetscReal v,PetscReal a,Mat J,Mat P,void *ctx);
1501 
1502 +  t    - time at step/stage being solved
1503 .  U    - state vector
1504 .  U_t  - time derivative of state vector
1505 .  U_tt - second time derivative of state vector
1506 .  v    - shift for U_t
1507 .  a    - shift for U_tt
1508 .  J    - Jacobian of G(U) = F(t,U,W+v*U,W'+a*U), equivalent to dF/dU + v*dF/dU_t  + a*dF/dU_tt
1509 .  P    - preconditioning matrix for J, may be same as J
1510 -  ctx  - [optional] user-defined context for matrix evaluation routine
1511 
1512    Notes:
1513    The matrices J and P are exactly the matrices that are used by SNES for the nonlinear solve.
1514 
1515    The matrix dF/dU + v*dF/dU_t + a*dF/dU_tt you provide turns out to be
1516    the Jacobian of G(U) = F(t,U,W+v*U,W'+a*U) where F(t,U,U_t,U_tt) = 0 is the DAE to be solved.
1517    The time integrator internally approximates U_t by W+v*U and U_tt by W'+a*U  where the positive "shift"
1518    parameters 'v' and 'a' and vectors W, W' depend on the integration method, step size, and past states.
1519 
1520    Level: beginner
1521 
1522 .keywords: TS, timestep, set, ODE, DAE, Jacobian
1523 
1524 .seealso: TSSetI2Function()
1525 @*/
1526 PetscErrorCode TSSetI2Jacobian(TS ts,Mat J,Mat P,TSI2Jacobian jac,void *ctx)
1527 {
1528   DM             dm;
1529   PetscErrorCode ierr;
1530 
1531   PetscFunctionBegin;
1532   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1533   if (J) PetscValidHeaderSpecific(J,MAT_CLASSID,2);
1534   if (P) PetscValidHeaderSpecific(P,MAT_CLASSID,3);
1535   ierr = TSSetIJacobian(ts,J,P,NULL,NULL);CHKERRQ(ierr);
1536   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1537   ierr = DMTSSetI2Jacobian(dm,jac,ctx);CHKERRQ(ierr);
1538   PetscFunctionReturn(0);
1539 }
1540 
1541 #undef __FUNCT__
1542 #define __FUNCT__ "TSGetI2Jacobian"
1543 /*@C
1544   TSGetI2Jacobian - Returns the implicit Jacobian at the present timestep.
1545 
1546   Not Collective, but parallel objects are returned if TS is parallel
1547 
1548   Input Parameter:
1549 . ts  - The TS context obtained from TSCreate()
1550 
1551   Output Parameters:
1552 + J  - The (approximate) Jacobian of F(t,U,U_t,U_tt)
1553 . P - The matrix from which the preconditioner is constructed, often the same as J
1554 . jac - The function to compute the Jacobian matrices
1555 - ctx - User-defined context for Jacobian evaluation routine
1556 
1557   Notes: You can pass in NULL for any return argument you do not need.
1558 
1559   Level: advanced
1560 
1561 .seealso: TSGetTimeStep(), TSGetMatrices(), TSGetTime(), TSGetTimeStepNumber()
1562 
1563 .keywords: TS, timestep, get, matrix, Jacobian
1564 @*/
1565 PetscErrorCode  TSGetI2Jacobian(TS ts,Mat *J,Mat *P,TSI2Jacobian *jac,void **ctx)
1566 {
1567   PetscErrorCode ierr;
1568   SNES           snes;
1569   DM             dm;
1570 
1571   PetscFunctionBegin;
1572   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
1573   ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr);
1574   ierr = SNESGetJacobian(snes,J,P,NULL,NULL);CHKERRQ(ierr);
1575   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1576   ierr = DMTSGetI2Jacobian(dm,jac,ctx);CHKERRQ(ierr);
1577   PetscFunctionReturn(0);
1578 }
1579 
1580 #undef __FUNCT__
1581 #define __FUNCT__ "TSComputeI2Function"
1582 /*@
1583   TSComputeI2Function - Evaluates the DAE residual written in implicit form F(t,U,U_t,U_tt) = 0
1584 
1585   Collective on TS and Vec
1586 
1587   Input Parameters:
1588 + ts - the TS context
1589 . t - current time
1590 . U - state vector
1591 . V - time derivative of state vector (U_t)
1592 - A - second time derivative of state vector (U_tt)
1593 
1594   Output Parameter:
1595 . F - the residual vector
1596 
1597   Note:
1598   Most users should not need to explicitly call this routine, as it
1599   is used internally within the nonlinear solvers.
1600 
1601   Level: developer
1602 
1603 .keywords: TS, compute, function, vector
1604 
1605 .seealso: TSSetI2Function()
1606 @*/
1607 PetscErrorCode TSComputeI2Function(TS ts,PetscReal t,Vec U,Vec V,Vec A,Vec F)
1608 {
1609   DM             dm;
1610   TSI2Function   I2Function;
1611   void           *ctx;
1612   TSRHSFunction  rhsfunction;
1613   PetscErrorCode ierr;
1614 
1615   PetscFunctionBegin;
1616   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1617   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
1618   PetscValidHeaderSpecific(V,VEC_CLASSID,4);
1619   PetscValidHeaderSpecific(A,VEC_CLASSID,5);
1620   PetscValidHeaderSpecific(F,VEC_CLASSID,6);
1621 
1622   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1623   ierr = DMTSGetI2Function(dm,&I2Function,&ctx);CHKERRQ(ierr);
1624   ierr = DMTSGetRHSFunction(dm,&rhsfunction,NULL);CHKERRQ(ierr);
1625 
1626   if (!I2Function) {
1627     ierr = TSComputeIFunction(ts,t,U,A,F,PETSC_FALSE);CHKERRQ(ierr);
1628     PetscFunctionReturn(0);
1629   }
1630 
1631   ierr = PetscLogEventBegin(TS_FunctionEval,ts,U,V,F);CHKERRQ(ierr);
1632 
1633   PetscStackPush("TS user implicit function");
1634   ierr = I2Function(ts,t,U,V,A,F,ctx);CHKERRQ(ierr);
1635   PetscStackPop;
1636 
1637   if (rhsfunction) {
1638     Vec Frhs;
1639     ierr = TSGetRHSVec_Private(ts,&Frhs);CHKERRQ(ierr);
1640     ierr = TSComputeRHSFunction(ts,t,U,Frhs);CHKERRQ(ierr);
1641     ierr = VecAXPY(F,-1,Frhs);CHKERRQ(ierr);
1642   }
1643 
1644   ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,V,F);CHKERRQ(ierr);
1645   PetscFunctionReturn(0);
1646 }
1647 
1648 #undef __FUNCT__
1649 #define __FUNCT__ "TSComputeI2Jacobian"
1650 /*@
1651   TSComputeI2Jacobian - Evaluates the Jacobian of the DAE
1652 
1653   Collective on TS and Vec
1654 
1655   Input Parameters:
1656 + ts - the TS context
1657 . t - current timestep
1658 . U - state vector
1659 . V - time derivative of state vector
1660 . A - second time derivative of state vector
1661 . shiftV - shift to apply, see note below
1662 - shiftA - shift to apply, see note below
1663 
1664   Output Parameters:
1665 + J - Jacobian matrix
1666 - P - optional preconditioning matrix
1667 
1668   Notes:
1669   If F(t,U,V,A)=0 is the DAE, the required Jacobian is
1670 
1671   dF/dU + shiftV*dF/dV + shiftA*dF/dA
1672 
1673   Most users should not need to explicitly call this routine, as it
1674   is used internally within the nonlinear solvers.
1675 
1676   Level: developer
1677 
1678 .keywords: TS, compute, Jacobian, matrix
1679 
1680 .seealso:  TSSetI2Jacobian()
1681 @*/
1682 PetscErrorCode TSComputeI2Jacobian(TS ts,PetscReal t,Vec U,Vec V,Vec A,PetscReal shiftV,PetscReal shiftA,Mat J,Mat P)
1683 {
1684   DM             dm;
1685   TSI2Jacobian   I2Jacobian;
1686   void           *ctx;
1687   TSRHSJacobian  rhsjacobian;
1688   PetscErrorCode ierr;
1689 
1690   PetscFunctionBegin;
1691   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1692   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
1693   PetscValidHeaderSpecific(V,VEC_CLASSID,4);
1694   PetscValidHeaderSpecific(A,VEC_CLASSID,5);
1695   PetscValidHeaderSpecific(J,MAT_CLASSID,8);
1696   PetscValidHeaderSpecific(P,MAT_CLASSID,9);
1697 
1698   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
1699   ierr = DMTSGetI2Jacobian(dm,&I2Jacobian,&ctx);CHKERRQ(ierr);
1700   ierr = DMTSGetRHSJacobian(dm,&rhsjacobian,NULL);CHKERRQ(ierr);
1701 
1702   if (!I2Jacobian) {
1703     ierr = TSComputeIJacobian(ts,t,U,A,shiftA,J,P,PETSC_FALSE);CHKERRQ(ierr);
1704     PetscFunctionReturn(0);
1705   }
1706 
1707   ierr = PetscLogEventBegin(TS_JacobianEval,ts,U,J,P);CHKERRQ(ierr);
1708 
1709   PetscStackPush("TS user implicit Jacobian");
1710   ierr = I2Jacobian(ts,t,U,V,A,shiftV,shiftA,J,P,ctx);CHKERRQ(ierr);
1711   PetscStackPop;
1712 
1713   if (rhsjacobian) {
1714     Mat Jrhs,Prhs; MatStructure axpy = DIFFERENT_NONZERO_PATTERN;
1715     ierr = TSGetRHSMats_Private(ts,&Jrhs,&Prhs);CHKERRQ(ierr);
1716     ierr = TSComputeRHSJacobian(ts,t,U,Jrhs,Prhs);CHKERRQ(ierr);
1717     ierr = MatAXPY(J,-1,Jrhs,axpy);CHKERRQ(ierr);
1718     if (P != J) {ierr = MatAXPY(P,-1,Prhs,axpy);CHKERRQ(ierr);}
1719   }
1720 
1721   ierr = PetscLogEventEnd(TS_JacobianEval,ts,U,J,P);CHKERRQ(ierr);
1722   PetscFunctionReturn(0);
1723 }
1724 
1725 #undef __FUNCT__
1726 #define __FUNCT__ "TS2SetSolution"
1727 /*@
1728    TS2SetSolution - Sets the initial solution and time derivative vectors
1729    for use by the TS routines handling second order equations.
1730 
1731    Logically Collective on TS and Vec
1732 
1733    Input Parameters:
1734 +  ts - the TS context obtained from TSCreate()
1735 .  u - the solution vector
1736 -  v - the time derivative vector
1737 
1738    Level: beginner
1739 
1740 .keywords: TS, timestep, set, solution, initial conditions
1741 @*/
1742 PetscErrorCode  TS2SetSolution(TS ts,Vec u,Vec v)
1743 {
1744   PetscErrorCode ierr;
1745 
1746   PetscFunctionBegin;
1747   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1748   PetscValidHeaderSpecific(u,VEC_CLASSID,2);
1749   PetscValidHeaderSpecific(v,VEC_CLASSID,3);
1750   ierr = TSSetSolution(ts,u);CHKERRQ(ierr);
1751   ierr = PetscObjectReference((PetscObject)v);CHKERRQ(ierr);
1752   ierr = VecDestroy(&ts->vec_dot);CHKERRQ(ierr);
1753   ts->vec_dot = v;
1754   PetscFunctionReturn(0);
1755 }
1756 
1757 #undef __FUNCT__
1758 #define __FUNCT__ "TS2GetSolution"
1759 /*@
1760    TS2GetSolution - Returns the solution and time derivative at the present timestep
1761    for second order equations. It is valid to call this routine inside the function
1762    that you are evaluating in order to move to the new timestep. This vector not
1763    changed until the solution at the next timestep has been calculated.
1764 
1765    Not Collective, but Vec returned is parallel if TS is parallel
1766 
1767    Input Parameter:
1768 .  ts - the TS context obtained from TSCreate()
1769 
1770    Output Parameter:
1771 +  u - the vector containing the solution
1772 -  v - the vector containing the time derivative
1773 
1774    Level: intermediate
1775 
1776 .seealso: TS2SetSolution(), TSGetTimeStep(), TSGetTime()
1777 
1778 .keywords: TS, timestep, get, solution
1779 @*/
1780 PetscErrorCode  TS2GetSolution(TS ts,Vec *u,Vec *v)
1781 {
1782   PetscFunctionBegin;
1783   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1784   if (u) PetscValidPointer(u,2);
1785   if (v) PetscValidPointer(v,3);
1786   if (u) *u = ts->vec_sol;
1787   if (v) *v = ts->vec_dot;
1788   PetscFunctionReturn(0);
1789 }
1790 
1791 #undef __FUNCT__
1792 #define __FUNCT__ "TSLoad"
1793 /*@C
1794   TSLoad - Loads a KSP that has been stored in binary  with KSPView().
1795 
1796   Collective on PetscViewer
1797 
1798   Input Parameters:
1799 + newdm - the newly loaded TS, this needs to have been created with TSCreate() or
1800            some related function before a call to TSLoad().
1801 - viewer - binary file viewer, obtained from PetscViewerBinaryOpen()
1802 
1803    Level: intermediate
1804 
1805   Notes:
1806    The type is determined by the data in the file, any type set into the TS before this call is ignored.
1807 
1808   Notes for advanced users:
1809   Most users should not need to know the details of the binary storage
1810   format, since TSLoad() and TSView() completely hide these details.
1811   But for anyone who's interested, the standard binary matrix storage
1812   format is
1813 .vb
1814      has not yet been determined
1815 .ve
1816 
1817 .seealso: PetscViewerBinaryOpen(), TSView(), MatLoad(), VecLoad()
1818 @*/
1819 PetscErrorCode  TSLoad(TS ts, PetscViewer viewer)
1820 {
1821   PetscErrorCode ierr;
1822   PetscBool      isbinary;
1823   PetscInt       classid;
1824   char           type[256];
1825   DMTS           sdm;
1826   DM             dm;
1827 
1828   PetscFunctionBegin;
1829   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1830   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
1831   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1832   if (!isbinary) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid viewer; open viewer with PetscViewerBinaryOpen()");
1833 
1834   ierr = PetscViewerBinaryRead(viewer,&classid,1,NULL,PETSC_INT);CHKERRQ(ierr);
1835   if (classid != TS_FILE_CLASSID) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Not TS next in file");
1836   ierr = PetscViewerBinaryRead(viewer,type,256,NULL,PETSC_CHAR);CHKERRQ(ierr);
1837   ierr = TSSetType(ts, type);CHKERRQ(ierr);
1838   if (ts->ops->load) {
1839     ierr = (*ts->ops->load)(ts,viewer);CHKERRQ(ierr);
1840   }
1841   ierr = DMCreate(PetscObjectComm((PetscObject)ts),&dm);CHKERRQ(ierr);
1842   ierr = DMLoad(dm,viewer);CHKERRQ(ierr);
1843   ierr = TSSetDM(ts,dm);CHKERRQ(ierr);
1844   ierr = DMCreateGlobalVector(ts->dm,&ts->vec_sol);CHKERRQ(ierr);
1845   ierr = VecLoad(ts->vec_sol,viewer);CHKERRQ(ierr);
1846   ierr = DMGetDMTS(ts->dm,&sdm);CHKERRQ(ierr);
1847   ierr = DMTSLoad(sdm,viewer);CHKERRQ(ierr);
1848   PetscFunctionReturn(0);
1849 }
1850 
1851 #include <petscdraw.h>
1852 #if defined(PETSC_HAVE_SAWS)
1853 #include <petscviewersaws.h>
1854 #endif
1855 #undef __FUNCT__
1856 #define __FUNCT__ "TSView"
1857 /*@C
1858     TSView - Prints the TS data structure.
1859 
1860     Collective on TS
1861 
1862     Input Parameters:
1863 +   ts - the TS context obtained from TSCreate()
1864 -   viewer - visualization context
1865 
1866     Options Database Key:
1867 .   -ts_view - calls TSView() at end of TSStep()
1868 
1869     Notes:
1870     The available visualization contexts include
1871 +     PETSC_VIEWER_STDOUT_SELF - standard output (default)
1872 -     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
1873          output where only the first processor opens
1874          the file.  All other processors send their
1875          data to the first processor to print.
1876 
1877     The user can open an alternative visualization context with
1878     PetscViewerASCIIOpen() - output to a specified file.
1879 
1880     Level: beginner
1881 
1882 .keywords: TS, timestep, view
1883 
1884 .seealso: PetscViewerASCIIOpen()
1885 @*/
1886 PetscErrorCode  TSView(TS ts,PetscViewer viewer)
1887 {
1888   PetscErrorCode ierr;
1889   TSType         type;
1890   PetscBool      iascii,isstring,isundials,isbinary,isdraw;
1891   DMTS           sdm;
1892 #if defined(PETSC_HAVE_SAWS)
1893   PetscBool      issaws;
1894 #endif
1895 
1896   PetscFunctionBegin;
1897   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
1898   if (!viewer) {
1899     ierr = PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)ts),&viewer);CHKERRQ(ierr);
1900   }
1901   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
1902   PetscCheckSameComm(ts,1,viewer,2);
1903 
1904   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1905   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);CHKERRQ(ierr);
1906   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1907   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1908 #if defined(PETSC_HAVE_SAWS)
1909   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSAWS,&issaws);CHKERRQ(ierr);
1910 #endif
1911   if (iascii) {
1912     ierr = PetscObjectPrintClassNamePrefixType((PetscObject)ts,viewer);CHKERRQ(ierr);
1913     ierr = PetscViewerASCIIPrintf(viewer,"  maximum steps=%D\n",ts->max_steps);CHKERRQ(ierr);
1914     ierr = PetscViewerASCIIPrintf(viewer,"  maximum time=%g\n",(double)ts->max_time);CHKERRQ(ierr);
1915     if (ts->problem_type == TS_NONLINEAR) {
1916       ierr = PetscViewerASCIIPrintf(viewer,"  total number of nonlinear solver iterations=%D\n",ts->snes_its);CHKERRQ(ierr);
1917       ierr = PetscViewerASCIIPrintf(viewer,"  total number of nonlinear solve failures=%D\n",ts->num_snes_failures);CHKERRQ(ierr);
1918     }
1919     ierr = PetscViewerASCIIPrintf(viewer,"  total number of linear solver iterations=%D\n",ts->ksp_its);CHKERRQ(ierr);
1920     ierr = PetscViewerASCIIPrintf(viewer,"  total number of rejected steps=%D\n",ts->reject);CHKERRQ(ierr);
1921     if (ts->vrtol) {
1922       ierr = PetscViewerASCIIPrintf(viewer,"  using vector of relative error tolerances, ");CHKERRQ(ierr);
1923     } else {
1924       ierr = PetscViewerASCIIPrintf(viewer,"  using relative error tolerance of %g, ",(double)ts->rtol);CHKERRQ(ierr);
1925     }
1926     if (ts->vatol) {
1927       ierr = PetscViewerASCIIPrintf(viewer,"  using vector of absolute error tolerances\n");CHKERRQ(ierr);
1928     } else {
1929       ierr = PetscViewerASCIIPrintf(viewer,"  using absolute error tolerance of %g\n",(double)ts->atol);CHKERRQ(ierr);
1930     }
1931     ierr = DMGetDMTS(ts->dm,&sdm);CHKERRQ(ierr);
1932     ierr = DMTSView(sdm,viewer);CHKERRQ(ierr);
1933     if (ts->ops->view) {
1934       ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
1935       ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
1936       ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
1937     }
1938   } else if (isstring) {
1939     ierr = TSGetType(ts,&type);CHKERRQ(ierr);
1940     ierr = PetscViewerStringSPrintf(viewer," %-7.7s",type);CHKERRQ(ierr);
1941   } else if (isbinary) {
1942     PetscInt    classid = TS_FILE_CLASSID;
1943     MPI_Comm    comm;
1944     PetscMPIInt rank;
1945     char        type[256];
1946 
1947     ierr = PetscObjectGetComm((PetscObject)ts,&comm);CHKERRQ(ierr);
1948     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1949     if (!rank) {
1950       ierr = PetscViewerBinaryWrite(viewer,&classid,1,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
1951       ierr = PetscStrncpy(type,((PetscObject)ts)->type_name,256);CHKERRQ(ierr);
1952       ierr = PetscViewerBinaryWrite(viewer,type,256,PETSC_CHAR,PETSC_FALSE);CHKERRQ(ierr);
1953     }
1954     if (ts->ops->view) {
1955       ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
1956     }
1957     ierr = DMView(ts->dm,viewer);CHKERRQ(ierr);
1958     ierr = VecView(ts->vec_sol,viewer);CHKERRQ(ierr);
1959     ierr = DMGetDMTS(ts->dm,&sdm);CHKERRQ(ierr);
1960     ierr = DMTSView(sdm,viewer);CHKERRQ(ierr);
1961   } else if (isdraw) {
1962     PetscDraw draw;
1963     char      str[36];
1964     PetscReal x,y,bottom,h;
1965 
1966     ierr   = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1967     ierr   = PetscDrawGetCurrentPoint(draw,&x,&y);CHKERRQ(ierr);
1968     ierr   = PetscStrcpy(str,"TS: ");CHKERRQ(ierr);
1969     ierr   = PetscStrcat(str,((PetscObject)ts)->type_name);CHKERRQ(ierr);
1970     ierr   = PetscDrawStringBoxed(draw,x,y,PETSC_DRAW_BLACK,PETSC_DRAW_BLACK,str,NULL,&h);CHKERRQ(ierr);
1971     bottom = y - h;
1972     ierr   = PetscDrawPushCurrentPoint(draw,x,bottom);CHKERRQ(ierr);
1973     if (ts->ops->view) {
1974       ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
1975     }
1976     ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
1977 #if defined(PETSC_HAVE_SAWS)
1978   } else if (issaws) {
1979     PetscMPIInt rank;
1980     const char  *name;
1981 
1982     ierr = PetscObjectGetName((PetscObject)ts,&name);CHKERRQ(ierr);
1983     ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
1984     if (!((PetscObject)ts)->amsmem && !rank) {
1985       char       dir[1024];
1986 
1987       ierr = PetscObjectViewSAWs((PetscObject)ts,viewer);CHKERRQ(ierr);
1988       ierr = PetscSNPrintf(dir,1024,"/PETSc/Objects/%s/time_step",name);CHKERRQ(ierr);
1989       PetscStackCallSAWs(SAWs_Register,(dir,&ts->steps,1,SAWs_READ,SAWs_INT));
1990       ierr = PetscSNPrintf(dir,1024,"/PETSc/Objects/%s/time",name);CHKERRQ(ierr);
1991       PetscStackCallSAWs(SAWs_Register,(dir,&ts->ptime,1,SAWs_READ,SAWs_DOUBLE));
1992     }
1993     if (ts->ops->view) {
1994       ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
1995     }
1996 #endif
1997   }
1998 
1999   ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
2000   ierr = PetscObjectTypeCompare((PetscObject)ts,TSSUNDIALS,&isundials);CHKERRQ(ierr);
2001   ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
2002   PetscFunctionReturn(0);
2003 }
2004 
2005 
2006 #undef __FUNCT__
2007 #define __FUNCT__ "TSSetApplicationContext"
2008 /*@
2009    TSSetApplicationContext - Sets an optional user-defined context for
2010    the timesteppers.
2011 
2012    Logically Collective on TS
2013 
2014    Input Parameters:
2015 +  ts - the TS context obtained from TSCreate()
2016 -  usrP - optional user context
2017 
2018    Fortran Notes: To use this from Fortran you must write a Fortran interface definition for this
2019     function that tells Fortran the Fortran derived data type that you are passing in as the ctx argument.
2020 
2021    Level: intermediate
2022 
2023 .keywords: TS, timestep, set, application, context
2024 
2025 .seealso: TSGetApplicationContext()
2026 @*/
2027 PetscErrorCode  TSSetApplicationContext(TS ts,void *usrP)
2028 {
2029   PetscFunctionBegin;
2030   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2031   ts->user = usrP;
2032   PetscFunctionReturn(0);
2033 }
2034 
2035 #undef __FUNCT__
2036 #define __FUNCT__ "TSGetApplicationContext"
2037 /*@
2038     TSGetApplicationContext - Gets the user-defined context for the
2039     timestepper.
2040 
2041     Not Collective
2042 
2043     Input Parameter:
2044 .   ts - the TS context obtained from TSCreate()
2045 
2046     Output Parameter:
2047 .   usrP - user context
2048 
2049    Fortran Notes: To use this from Fortran you must write a Fortran interface definition for this
2050     function that tells Fortran the Fortran derived data type that you are passing in as the ctx argument.
2051 
2052     Level: intermediate
2053 
2054 .keywords: TS, timestep, get, application, context
2055 
2056 .seealso: TSSetApplicationContext()
2057 @*/
2058 PetscErrorCode  TSGetApplicationContext(TS ts,void *usrP)
2059 {
2060   PetscFunctionBegin;
2061   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2062   *(void**)usrP = ts->user;
2063   PetscFunctionReturn(0);
2064 }
2065 
2066 #undef __FUNCT__
2067 #define __FUNCT__ "TSGetTimeStepNumber"
2068 /*@
2069    TSGetTimeStepNumber - Gets the number of time steps completed.
2070 
2071    Not Collective
2072 
2073    Input Parameter:
2074 .  ts - the TS context obtained from TSCreate()
2075 
2076    Output Parameter:
2077 .  iter - number of steps completed so far
2078 
2079    Level: intermediate
2080 
2081 .keywords: TS, timestep, get, iteration, number
2082 .seealso: TSGetTime(), TSGetTimeStep(), TSSetPreStep(), TSSetPreStage(), TSSetPostStage(), TSSetPostStep()
2083 @*/
2084 PetscErrorCode  TSGetTimeStepNumber(TS ts,PetscInt *iter)
2085 {
2086   PetscFunctionBegin;
2087   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2088   PetscValidIntPointer(iter,2);
2089   *iter = ts->steps;
2090   PetscFunctionReturn(0);
2091 }
2092 
2093 #undef __FUNCT__
2094 #define __FUNCT__ "TSSetInitialTimeStep"
2095 /*@
2096    TSSetInitialTimeStep - Sets the initial timestep to be used,
2097    as well as the initial time.
2098 
2099    Logically Collective on TS
2100 
2101    Input Parameters:
2102 +  ts - the TS context obtained from TSCreate()
2103 .  initial_time - the initial time
2104 -  time_step - the size of the timestep
2105 
2106    Level: intermediate
2107 
2108 .seealso: TSSetTimeStep(), TSGetTimeStep()
2109 
2110 .keywords: TS, set, initial, timestep
2111 @*/
2112 PetscErrorCode  TSSetInitialTimeStep(TS ts,PetscReal initial_time,PetscReal time_step)
2113 {
2114   PetscErrorCode ierr;
2115 
2116   PetscFunctionBegin;
2117   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2118   ierr = TSSetTimeStep(ts,time_step);CHKERRQ(ierr);
2119   ierr = TSSetTime(ts,initial_time);CHKERRQ(ierr);
2120   PetscFunctionReturn(0);
2121 }
2122 
2123 #undef __FUNCT__
2124 #define __FUNCT__ "TSSetTimeStep"
2125 /*@
2126    TSSetTimeStep - Allows one to reset the timestep at any time,
2127    useful for simple pseudo-timestepping codes.
2128 
2129    Logically Collective on TS
2130 
2131    Input Parameters:
2132 +  ts - the TS context obtained from TSCreate()
2133 -  time_step - the size of the timestep
2134 
2135    Level: intermediate
2136 
2137 .seealso: TSSetInitialTimeStep(), TSGetTimeStep()
2138 
2139 .keywords: TS, set, timestep
2140 @*/
2141 PetscErrorCode  TSSetTimeStep(TS ts,PetscReal time_step)
2142 {
2143   PetscFunctionBegin;
2144   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2145   PetscValidLogicalCollectiveReal(ts,time_step,2);
2146   ts->time_step = time_step;
2147   PetscFunctionReturn(0);
2148 }
2149 
2150 #undef __FUNCT__
2151 #define __FUNCT__ "TSSetExactFinalTime"
2152 /*@
2153    TSSetExactFinalTime - Determines whether to adapt the final time step to
2154      match the exact final time, interpolate solution to the exact final time,
2155      or just return at the final time TS computed.
2156 
2157   Logically Collective on TS
2158 
2159    Input Parameter:
2160 +   ts - the time-step context
2161 -   eftopt - exact final time option
2162 
2163 $  TS_EXACTFINALTIME_STEPOVER    - Don't do anything if final time is exceeded
2164 $  TS_EXACTFINALTIME_INTERPOLATE - Interpolate back to final time
2165 $  TS_EXACTFINALTIME_MATCHSTEP - Adapt final time step to match the final time
2166 
2167    Options Database:
2168 .   -ts_exact_final_time <stepover,interpolate,matchstep> - select the final step at runtime
2169 
2170    Warning: If you use the option TS_EXACTFINALTIME_STEPOVER the solution may be at a very different time
2171     then the final time you selected.
2172 
2173    Level: beginner
2174 
2175 .seealso: TSExactFinalTimeOption
2176 @*/
2177 PetscErrorCode  TSSetExactFinalTime(TS ts,TSExactFinalTimeOption eftopt)
2178 {
2179   PetscFunctionBegin;
2180   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2181   PetscValidLogicalCollectiveEnum(ts,eftopt,2);
2182   ts->exact_final_time = eftopt;
2183   PetscFunctionReturn(0);
2184 }
2185 
2186 #undef __FUNCT__
2187 #define __FUNCT__ "TSGetTimeStep"
2188 /*@
2189    TSGetTimeStep - Gets the current timestep size.
2190 
2191    Not Collective
2192 
2193    Input Parameter:
2194 .  ts - the TS context obtained from TSCreate()
2195 
2196    Output Parameter:
2197 .  dt - the current timestep size
2198 
2199    Level: intermediate
2200 
2201 .seealso: TSSetInitialTimeStep(), TSGetTimeStep()
2202 
2203 .keywords: TS, get, timestep
2204 @*/
2205 PetscErrorCode  TSGetTimeStep(TS ts,PetscReal *dt)
2206 {
2207   PetscFunctionBegin;
2208   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2209   PetscValidRealPointer(dt,2);
2210   *dt = ts->time_step;
2211   PetscFunctionReturn(0);
2212 }
2213 
2214 #undef __FUNCT__
2215 #define __FUNCT__ "TSGetSolution"
2216 /*@
2217    TSGetSolution - Returns the solution at the present timestep. It
2218    is valid to call this routine inside the function that you are evaluating
2219    in order to move to the new timestep. This vector not changed until
2220    the solution at the next timestep has been calculated.
2221 
2222    Not Collective, but Vec returned is parallel if TS is parallel
2223 
2224    Input Parameter:
2225 .  ts - the TS context obtained from TSCreate()
2226 
2227    Output Parameter:
2228 .  v - the vector containing the solution
2229 
2230    Note: If you used TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP); this does not return the solution at the requested
2231    final time. It returns the solution at the next timestep.
2232 
2233    Level: intermediate
2234 
2235 .seealso: TSGetTimeStep(), TSGetTime(), TSGetSolveTime(), TSGetSolutionComponents()
2236 
2237 .keywords: TS, timestep, get, solution
2238 @*/
2239 PetscErrorCode  TSGetSolution(TS ts,Vec *v)
2240 {
2241   PetscFunctionBegin;
2242   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2243   PetscValidPointer(v,2);
2244   *v = ts->vec_sol;
2245   PetscFunctionReturn(0);
2246 }
2247 
2248 #undef __FUNCT__
2249 #define __FUNCT__ "TSGetSolutionComponents"
2250 /*@
2251    TSGetSolutionComponents - Returns any solution components at the present
2252    timestep, if available for the time integration method being used.
2253    Solution components are quantities that share the same size and
2254    structure as the solution vector.
2255 
2256    Not Collective, but Vec returned is parallel if TS is parallel
2257 
2258    Parameters :
2259 .  ts - the TS context obtained from TSCreate() (input parameter).
2260 .  n - If v is PETSC_NULL, then the number of solution components is
2261        returned through n, else the n-th solution component is
2262        returned in v.
2263 .  v - the vector containing the n-th solution component
2264        (may be PETSC_NULL to use this function to find out
2265         the number of solutions components).
2266 
2267    Level: advanced
2268 
2269 .seealso: TSGetSolution()
2270 
2271 .keywords: TS, timestep, get, solution
2272 @*/
2273 PetscErrorCode  TSGetSolutionComponents(TS ts,PetscInt *n,Vec *v)
2274 {
2275   PetscErrorCode ierr;
2276 
2277   PetscFunctionBegin;
2278   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2279   if (!ts->ops->getsolutioncomponents) *n = 0;
2280   else {
2281     ierr = (*ts->ops->getsolutioncomponents)(ts,n,v);CHKERRQ(ierr);
2282   }
2283   PetscFunctionReturn(0);
2284 }
2285 
2286 #undef __FUNCT__
2287 #define __FUNCT__ "TSGetAuxSolution"
2288 /*@
2289    TSGetAuxSolution - Returns an auxiliary solution at the present
2290    timestep, if available for the time integration method being used.
2291 
2292    Not Collective, but Vec returned is parallel if TS is parallel
2293 
2294    Parameters :
2295 .  ts - the TS context obtained from TSCreate() (input parameter).
2296 .  v - the vector containing the auxiliary solution
2297 
2298    Level: intermediate
2299 
2300 .seealso: TSGetSolution()
2301 
2302 .keywords: TS, timestep, get, solution
2303 @*/
2304 PetscErrorCode  TSGetAuxSolution(TS ts,Vec *v)
2305 {
2306   PetscErrorCode ierr;
2307 
2308   PetscFunctionBegin;
2309   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2310   if (ts->ops->getauxsolution) {
2311     ierr = (*ts->ops->getauxsolution)(ts,v);CHKERRQ(ierr);
2312   } else {
2313     ierr = VecZeroEntries(*v); CHKERRQ(ierr);
2314   }
2315   PetscFunctionReturn(0);
2316 }
2317 
2318 #undef __FUNCT__
2319 #define __FUNCT__ "TSGetTimeError"
2320 /*@
2321    TSGetTimeError - Returns the estimated error vector, if the chosen
2322    TSType has an error estimation functionality.
2323 
2324    Not Collective, but Vec returned is parallel if TS is parallel
2325 
2326    Note: MUST call after TSSetUp()
2327 
2328    Parameters :
2329 .  ts - the TS context obtained from TSCreate() (input parameter).
2330 .  n - current estimate (n=0) or previous one (n=-1)
2331 .  v - the vector containing the error (same size as the solution).
2332 
2333    Level: intermediate
2334 
2335 .seealso: TSGetSolution(), TSSetTimeError()
2336 
2337 .keywords: TS, timestep, get, error
2338 @*/
2339 PetscErrorCode  TSGetTimeError(TS ts,PetscInt n,Vec *v)
2340 {
2341   PetscErrorCode ierr;
2342 
2343   PetscFunctionBegin;
2344   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2345   if (ts->ops->gettimeerror) {
2346     ierr = (*ts->ops->gettimeerror)(ts,n,v);CHKERRQ(ierr);
2347   } else {
2348     ierr = VecZeroEntries(*v);CHKERRQ(ierr);
2349   }
2350   PetscFunctionReturn(0);
2351 }
2352 
2353 #undef __FUNCT__
2354 #define __FUNCT__ "TSSetTimeError"
2355 /*@
2356    TSSetTimeError - Sets the estimated error vector, if the chosen
2357    TSType has an error estimation functionality. This can be used
2358    to restart such a time integrator with a given error vector.
2359 
2360    Not Collective, but Vec returned is parallel if TS is parallel
2361 
2362    Parameters :
2363 .  ts - the TS context obtained from TSCreate() (input parameter).
2364 .  v - the vector containing the error (same size as the solution).
2365 
2366    Level: intermediate
2367 
2368 .seealso: TSSetSolution(), TSGetTimeError)
2369 
2370 .keywords: TS, timestep, get, error
2371 @*/
2372 PetscErrorCode  TSSetTimeError(TS ts,Vec v)
2373 {
2374   PetscErrorCode ierr;
2375 
2376   PetscFunctionBegin;
2377   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2378   if (!ts->setupcalled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetUp() first");
2379   if (ts->ops->settimeerror) {
2380     ierr = (*ts->ops->settimeerror)(ts,v);CHKERRQ(ierr);
2381   }
2382   PetscFunctionReturn(0);
2383 }
2384 
2385 #undef __FUNCT__
2386 #define __FUNCT__ "TSGetCostGradients"
2387 /*@
2388    TSGetCostGradients - Returns the gradients from the TSAdjointSolve()
2389 
2390    Not Collective, but Vec returned is parallel if TS is parallel
2391 
2392    Input Parameter:
2393 .  ts - the TS context obtained from TSCreate()
2394 
2395    Output Parameter:
2396 +  lambda - vectors containing the gradients of the cost functions with respect to the ODE/DAE solution variables
2397 -  mu - vectors containing the gradients of the cost functions with respect to the problem parameters
2398 
2399    Level: intermediate
2400 
2401 .seealso: TSGetTimeStep()
2402 
2403 .keywords: TS, timestep, get, sensitivity
2404 @*/
2405 PetscErrorCode  TSGetCostGradients(TS ts,PetscInt *numcost,Vec **lambda,Vec **mu)
2406 {
2407   PetscFunctionBegin;
2408   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2409   if (numcost) *numcost = ts->numcost;
2410   if (lambda)  *lambda  = ts->vecs_sensi;
2411   if (mu)      *mu      = ts->vecs_sensip;
2412   PetscFunctionReturn(0);
2413 }
2414 
2415 /* ----- Routines to initialize and destroy a timestepper ---- */
2416 #undef __FUNCT__
2417 #define __FUNCT__ "TSSetProblemType"
2418 /*@
2419   TSSetProblemType - Sets the type of problem to be solved.
2420 
2421   Not collective
2422 
2423   Input Parameters:
2424 + ts   - The TS
2425 - type - One of TS_LINEAR, TS_NONLINEAR where these types refer to problems of the forms
2426 .vb
2427          U_t - A U = 0      (linear)
2428          U_t - A(t) U = 0   (linear)
2429          F(t,U,U_t) = 0     (nonlinear)
2430 .ve
2431 
2432    Level: beginner
2433 
2434 .keywords: TS, problem type
2435 .seealso: TSSetUp(), TSProblemType, TS
2436 @*/
2437 PetscErrorCode  TSSetProblemType(TS ts, TSProblemType type)
2438 {
2439   PetscErrorCode ierr;
2440 
2441   PetscFunctionBegin;
2442   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
2443   ts->problem_type = type;
2444   if (type == TS_LINEAR) {
2445     SNES snes;
2446     ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
2447     ierr = SNESSetType(snes,SNESKSPONLY);CHKERRQ(ierr);
2448   }
2449   PetscFunctionReturn(0);
2450 }
2451 
2452 #undef __FUNCT__
2453 #define __FUNCT__ "TSGetProblemType"
2454 /*@C
2455   TSGetProblemType - Gets the type of problem to be solved.
2456 
2457   Not collective
2458 
2459   Input Parameter:
2460 . ts   - The TS
2461 
2462   Output Parameter:
2463 . type - One of TS_LINEAR, TS_NONLINEAR where these types refer to problems of the forms
2464 .vb
2465          M U_t = A U
2466          M(t) U_t = A(t) U
2467          F(t,U,U_t)
2468 .ve
2469 
2470    Level: beginner
2471 
2472 .keywords: TS, problem type
2473 .seealso: TSSetUp(), TSProblemType, TS
2474 @*/
2475 PetscErrorCode  TSGetProblemType(TS ts, TSProblemType *type)
2476 {
2477   PetscFunctionBegin;
2478   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
2479   PetscValidIntPointer(type,2);
2480   *type = ts->problem_type;
2481   PetscFunctionReturn(0);
2482 }
2483 
2484 #undef __FUNCT__
2485 #define __FUNCT__ "TSSetUp"
2486 /*@
2487    TSSetUp - Sets up the internal data structures for the later use
2488    of a timestepper.
2489 
2490    Collective on TS
2491 
2492    Input Parameter:
2493 .  ts - the TS context obtained from TSCreate()
2494 
2495    Notes:
2496    For basic use of the TS solvers the user need not explicitly call
2497    TSSetUp(), since these actions will automatically occur during
2498    the call to TSStep().  However, if one wishes to control this
2499    phase separately, TSSetUp() should be called after TSCreate()
2500    and optional routines of the form TSSetXXX(), but before TSStep().
2501 
2502    Level: advanced
2503 
2504 .keywords: TS, timestep, setup
2505 
2506 .seealso: TSCreate(), TSStep(), TSDestroy()
2507 @*/
2508 PetscErrorCode  TSSetUp(TS ts)
2509 {
2510   PetscErrorCode ierr;
2511   DM             dm;
2512   PetscErrorCode (*func)(SNES,Vec,Vec,void*);
2513   PetscErrorCode (*jac)(SNES,Vec,Mat,Mat,void*);
2514   TSIFunction    ifun;
2515   TSIJacobian    ijac;
2516   TSI2Jacobian   i2jac;
2517   TSRHSJacobian  rhsjac;
2518 
2519   PetscFunctionBegin;
2520   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2521   if (ts->setupcalled) PetscFunctionReturn(0);
2522 
2523   ts->total_steps = 0;
2524   if (!((PetscObject)ts)->type_name) {
2525     ierr = TSGetIFunction(ts,NULL,&ifun,NULL);CHKERRQ(ierr);
2526     ierr = TSSetType(ts,ifun ? TSBEULER : TSEULER);CHKERRQ(ierr);
2527   }
2528 
2529   if (!ts->vec_sol) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetSolution() first");
2530 
2531   if (ts->rhsjacobian.reuse) {
2532     Mat Amat,Pmat;
2533     SNES snes;
2534     ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
2535     ierr = SNESGetJacobian(snes,&Amat,&Pmat,NULL,NULL);CHKERRQ(ierr);
2536     /* Matching matrices implies that an IJacobian is NOT set, because if it had been set, the IJacobian's matrix would
2537      * have displaced the RHS matrix */
2538     if (Amat == ts->Arhs) {
2539       ierr = MatDuplicate(ts->Arhs,MAT_DO_NOT_COPY_VALUES,&Amat);CHKERRQ(ierr);
2540       ierr = SNESSetJacobian(snes,Amat,NULL,NULL,NULL);CHKERRQ(ierr);
2541       ierr = MatDestroy(&Amat);CHKERRQ(ierr);
2542     }
2543     if (Pmat == ts->Brhs) {
2544       ierr = MatDuplicate(ts->Brhs,MAT_DO_NOT_COPY_VALUES,&Pmat);CHKERRQ(ierr);
2545       ierr = SNESSetJacobian(snes,NULL,Pmat,NULL,NULL);CHKERRQ(ierr);
2546       ierr = MatDestroy(&Pmat);CHKERRQ(ierr);
2547     }
2548   }
2549   if (ts->ops->setup) {
2550     ierr = (*ts->ops->setup)(ts);CHKERRQ(ierr);
2551   }
2552 
2553   /* In the case where we've set a DMTSFunction or what have you, we need the default SNESFunction
2554      to be set right but can't do it elsewhere due to the overreliance on ctx=ts.
2555    */
2556   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
2557   ierr = DMSNESGetFunction(dm,&func,NULL);CHKERRQ(ierr);
2558   if (!func) {
2559     ierr = DMSNESSetFunction(dm,SNESTSFormFunction,ts);CHKERRQ(ierr);
2560   }
2561   /* If the SNES doesn't have a jacobian set and the TS has an ijacobian or rhsjacobian set, set the SNES to use it.
2562      Otherwise, the SNES will use coloring internally to form the Jacobian.
2563    */
2564   ierr = DMSNESGetJacobian(dm,&jac,NULL);CHKERRQ(ierr);
2565   ierr = DMTSGetIJacobian(dm,&ijac,NULL);CHKERRQ(ierr);
2566   ierr = DMTSGetI2Jacobian(dm,&i2jac,NULL);CHKERRQ(ierr);
2567   ierr = DMTSGetRHSJacobian(dm,&rhsjac,NULL);CHKERRQ(ierr);
2568   if (!jac && (ijac || i2jac || rhsjac)) {
2569     ierr = DMSNESSetJacobian(dm,SNESTSFormJacobian,ts);CHKERRQ(ierr);
2570   }
2571 
2572   /* if time integration scheme has a starting method, call it */
2573   if (ts->ops->startingmethod) {
2574     ierr = (*ts->ops->startingmethod)(ts);CHKERRQ(ierr);
2575   }
2576 
2577   ts->setupcalled = PETSC_TRUE;
2578   PetscFunctionReturn(0);
2579 }
2580 
2581 #undef __FUNCT__
2582 #define __FUNCT__ "TSAdjointSetUp"
2583 /*@
2584    TSAdjointSetUp - Sets up the internal data structures for the later use
2585    of an adjoint solver
2586 
2587    Collective on TS
2588 
2589    Input Parameter:
2590 .  ts - the TS context obtained from TSCreate()
2591 
2592    Level: advanced
2593 
2594 .keywords: TS, timestep, setup
2595 
2596 .seealso: TSCreate(), TSAdjointStep(), TSSetCostGradients()
2597 @*/
2598 PetscErrorCode  TSAdjointSetUp(TS ts)
2599 {
2600   PetscErrorCode ierr;
2601 
2602   PetscFunctionBegin;
2603   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2604   if (ts->adjointsetupcalled) PetscFunctionReturn(0);
2605   if (!ts->vecs_sensi) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetCostGradients() first");
2606 
2607   if (ts->vec_costintegral) { /* if there is integral in the cost function*/
2608     ierr = VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&ts->vecs_drdy);CHKERRQ(ierr);
2609     if (ts->vecs_sensip){
2610       ierr = VecDuplicateVecs(ts->vecs_sensip[0],ts->numcost,&ts->vecs_drdp);CHKERRQ(ierr);
2611     }
2612   }
2613 
2614   if (ts->ops->adjointsetup) {
2615     ierr = (*ts->ops->adjointsetup)(ts);CHKERRQ(ierr);
2616   }
2617   ts->adjointsetupcalled = PETSC_TRUE;
2618   PetscFunctionReturn(0);
2619 }
2620 
2621 #undef __FUNCT__
2622 #define __FUNCT__ "TSReset"
2623 /*@
2624    TSReset - Resets a TS context and removes any allocated Vecs and Mats.
2625 
2626    Collective on TS
2627 
2628    Input Parameter:
2629 .  ts - the TS context obtained from TSCreate()
2630 
2631    Level: beginner
2632 
2633 .keywords: TS, timestep, reset
2634 
2635 .seealso: TSCreate(), TSSetup(), TSDestroy()
2636 @*/
2637 PetscErrorCode  TSReset(TS ts)
2638 {
2639   PetscErrorCode ierr;
2640 
2641   PetscFunctionBegin;
2642   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2643 
2644   if (ts->ops->reset) {
2645     ierr = (*ts->ops->reset)(ts);CHKERRQ(ierr);
2646   }
2647   if (ts->snes) {ierr = SNESReset(ts->snes);CHKERRQ(ierr);}
2648   if (ts->adapt) {ierr = TSAdaptReset(ts->adapt);CHKERRQ(ierr);}
2649 
2650   ierr = MatDestroy(&ts->Arhs);CHKERRQ(ierr);
2651   ierr = MatDestroy(&ts->Brhs);CHKERRQ(ierr);
2652   ierr = VecDestroy(&ts->Frhs);CHKERRQ(ierr);
2653   ierr = VecDestroy(&ts->vec_sol);CHKERRQ(ierr);
2654   ierr = VecDestroy(&ts->vec_dot);CHKERRQ(ierr);
2655   ierr = VecDestroy(&ts->vatol);CHKERRQ(ierr);
2656   ierr = VecDestroy(&ts->vrtol);CHKERRQ(ierr);
2657   ierr = VecDestroyVecs(ts->nwork,&ts->work);CHKERRQ(ierr);
2658 
2659  if (ts->vec_costintegral) {
2660     ierr = VecDestroyVecs(ts->numcost,&ts->vecs_drdy);CHKERRQ(ierr);
2661     if (ts->vecs_drdp){
2662       ierr = VecDestroyVecs(ts->numcost,&ts->vecs_drdp);CHKERRQ(ierr);
2663     }
2664   }
2665   ts->vecs_sensi  = NULL;
2666   ts->vecs_sensip = NULL;
2667   ierr = MatDestroy(&ts->Jacp);CHKERRQ(ierr);
2668   ierr = VecDestroy(&ts->vec_costintegral);CHKERRQ(ierr);
2669   ierr = VecDestroy(&ts->vec_costintegrand);CHKERRQ(ierr);
2670   ts->setupcalled = PETSC_FALSE;
2671   PetscFunctionReturn(0);
2672 }
2673 
2674 #undef __FUNCT__
2675 #define __FUNCT__ "TSDestroy"
2676 /*@
2677    TSDestroy - Destroys the timestepper context that was created
2678    with TSCreate().
2679 
2680    Collective on TS
2681 
2682    Input Parameter:
2683 .  ts - the TS context obtained from TSCreate()
2684 
2685    Level: beginner
2686 
2687 .keywords: TS, timestepper, destroy
2688 
2689 .seealso: TSCreate(), TSSetUp(), TSSolve()
2690 @*/
2691 PetscErrorCode  TSDestroy(TS *ts)
2692 {
2693   PetscErrorCode ierr;
2694 
2695   PetscFunctionBegin;
2696   if (!*ts) PetscFunctionReturn(0);
2697   PetscValidHeaderSpecific((*ts),TS_CLASSID,1);
2698   if (--((PetscObject)(*ts))->refct > 0) {*ts = 0; PetscFunctionReturn(0);}
2699 
2700   ierr = TSReset((*ts));CHKERRQ(ierr);
2701 
2702   /* if memory was published with SAWs then destroy it */
2703   ierr = PetscObjectSAWsViewOff((PetscObject)*ts);CHKERRQ(ierr);
2704   if ((*ts)->ops->destroy) {ierr = (*(*ts)->ops->destroy)((*ts));CHKERRQ(ierr);}
2705 
2706   ierr = TSTrajectoryDestroy(&(*ts)->trajectory);CHKERRQ(ierr);
2707 
2708   ierr = TSAdaptDestroy(&(*ts)->adapt);CHKERRQ(ierr);
2709   ierr = TSEventDestroy(&(*ts)->event);CHKERRQ(ierr);
2710 
2711   ierr = SNESDestroy(&(*ts)->snes);CHKERRQ(ierr);
2712   ierr = DMDestroy(&(*ts)->dm);CHKERRQ(ierr);
2713   ierr = TSMonitorCancel((*ts));CHKERRQ(ierr);
2714   ierr = TSAdjointMonitorCancel((*ts));CHKERRQ(ierr);
2715 
2716   ierr = PetscHeaderDestroy(ts);CHKERRQ(ierr);
2717   PetscFunctionReturn(0);
2718 }
2719 
2720 #undef __FUNCT__
2721 #define __FUNCT__ "TSGetSNES"
2722 /*@
2723    TSGetSNES - Returns the SNES (nonlinear solver) associated with
2724    a TS (timestepper) context. Valid only for nonlinear problems.
2725 
2726    Not Collective, but SNES is parallel if TS is parallel
2727 
2728    Input Parameter:
2729 .  ts - the TS context obtained from TSCreate()
2730 
2731    Output Parameter:
2732 .  snes - the nonlinear solver context
2733 
2734    Notes:
2735    The user can then directly manipulate the SNES context to set various
2736    options, etc.  Likewise, the user can then extract and manipulate the
2737    KSP, KSP, and PC contexts as well.
2738 
2739    TSGetSNES() does not work for integrators that do not use SNES; in
2740    this case TSGetSNES() returns NULL in snes.
2741 
2742    Level: beginner
2743 
2744 .keywords: timestep, get, SNES
2745 @*/
2746 PetscErrorCode  TSGetSNES(TS ts,SNES *snes)
2747 {
2748   PetscErrorCode ierr;
2749 
2750   PetscFunctionBegin;
2751   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2752   PetscValidPointer(snes,2);
2753   if (!ts->snes) {
2754     ierr = SNESCreate(PetscObjectComm((PetscObject)ts),&ts->snes);CHKERRQ(ierr);
2755     ierr = SNESSetFunction(ts->snes,NULL,SNESTSFormFunction,ts);CHKERRQ(ierr);
2756     ierr = PetscLogObjectParent((PetscObject)ts,(PetscObject)ts->snes);CHKERRQ(ierr);
2757     ierr = PetscObjectIncrementTabLevel((PetscObject)ts->snes,(PetscObject)ts,1);CHKERRQ(ierr);
2758     if (ts->dm) {ierr = SNESSetDM(ts->snes,ts->dm);CHKERRQ(ierr);}
2759     if (ts->problem_type == TS_LINEAR) {
2760       ierr = SNESSetType(ts->snes,SNESKSPONLY);CHKERRQ(ierr);
2761     }
2762   }
2763   *snes = ts->snes;
2764   PetscFunctionReturn(0);
2765 }
2766 
2767 #undef __FUNCT__
2768 #define __FUNCT__ "TSSetSNES"
2769 /*@
2770    TSSetSNES - Set the SNES (nonlinear solver) to be used by the timestepping context
2771 
2772    Collective
2773 
2774    Input Parameter:
2775 +  ts - the TS context obtained from TSCreate()
2776 -  snes - the nonlinear solver context
2777 
2778    Notes:
2779    Most users should have the TS created by calling TSGetSNES()
2780 
2781    Level: developer
2782 
2783 .keywords: timestep, set, SNES
2784 @*/
2785 PetscErrorCode TSSetSNES(TS ts,SNES snes)
2786 {
2787   PetscErrorCode ierr;
2788   PetscErrorCode (*func)(SNES,Vec,Mat,Mat,void*);
2789 
2790   PetscFunctionBegin;
2791   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2792   PetscValidHeaderSpecific(snes,SNES_CLASSID,2);
2793   ierr = PetscObjectReference((PetscObject)snes);CHKERRQ(ierr);
2794   ierr = SNESDestroy(&ts->snes);CHKERRQ(ierr);
2795 
2796   ts->snes = snes;
2797 
2798   ierr = SNESSetFunction(ts->snes,NULL,SNESTSFormFunction,ts);CHKERRQ(ierr);
2799   ierr = SNESGetJacobian(ts->snes,NULL,NULL,&func,NULL);CHKERRQ(ierr);
2800   if (func == SNESTSFormJacobian) {
2801     ierr = SNESSetJacobian(ts->snes,NULL,NULL,SNESTSFormJacobian,ts);CHKERRQ(ierr);
2802   }
2803   PetscFunctionReturn(0);
2804 }
2805 
2806 #undef __FUNCT__
2807 #define __FUNCT__ "TSGetKSP"
2808 /*@
2809    TSGetKSP - Returns the KSP (linear solver) associated with
2810    a TS (timestepper) context.
2811 
2812    Not Collective, but KSP is parallel if TS is parallel
2813 
2814    Input Parameter:
2815 .  ts - the TS context obtained from TSCreate()
2816 
2817    Output Parameter:
2818 .  ksp - the nonlinear solver context
2819 
2820    Notes:
2821    The user can then directly manipulate the KSP context to set various
2822    options, etc.  Likewise, the user can then extract and manipulate the
2823    KSP and PC contexts as well.
2824 
2825    TSGetKSP() does not work for integrators that do not use KSP;
2826    in this case TSGetKSP() returns NULL in ksp.
2827 
2828    Level: beginner
2829 
2830 .keywords: timestep, get, KSP
2831 @*/
2832 PetscErrorCode  TSGetKSP(TS ts,KSP *ksp)
2833 {
2834   PetscErrorCode ierr;
2835   SNES           snes;
2836 
2837   PetscFunctionBegin;
2838   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2839   PetscValidPointer(ksp,2);
2840   if (!((PetscObject)ts)->type_name) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"KSP is not created yet. Call TSSetType() first");
2841   if (ts->problem_type != TS_LINEAR) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Linear only; use TSGetSNES()");
2842   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
2843   ierr = SNESGetKSP(snes,ksp);CHKERRQ(ierr);
2844   PetscFunctionReturn(0);
2845 }
2846 
2847 /* ----------- Routines to set solver parameters ---------- */
2848 
2849 #undef __FUNCT__
2850 #define __FUNCT__ "TSGetDuration"
2851 /*@
2852    TSGetDuration - Gets the maximum number of timesteps to use and
2853    maximum time for iteration.
2854 
2855    Not Collective
2856 
2857    Input Parameters:
2858 +  ts       - the TS context obtained from TSCreate()
2859 .  maxsteps - maximum number of iterations to use, or NULL
2860 -  maxtime  - final time to iterate to, or NULL
2861 
2862    Level: intermediate
2863 
2864 .keywords: TS, timestep, get, maximum, iterations, time
2865 @*/
2866 PetscErrorCode  TSGetDuration(TS ts, PetscInt *maxsteps, PetscReal *maxtime)
2867 {
2868   PetscFunctionBegin;
2869   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
2870   if (maxsteps) {
2871     PetscValidIntPointer(maxsteps,2);
2872     *maxsteps = ts->max_steps;
2873   }
2874   if (maxtime) {
2875     PetscValidScalarPointer(maxtime,3);
2876     *maxtime = ts->max_time;
2877   }
2878   PetscFunctionReturn(0);
2879 }
2880 
2881 #undef __FUNCT__
2882 #define __FUNCT__ "TSSetDuration"
2883 /*@
2884    TSSetDuration - Sets the maximum number of timesteps to use and
2885    maximum time for iteration.
2886 
2887    Logically Collective on TS
2888 
2889    Input Parameters:
2890 +  ts - the TS context obtained from TSCreate()
2891 .  maxsteps - maximum number of iterations to use
2892 -  maxtime - final time to iterate to
2893 
2894    Options Database Keys:
2895 .  -ts_max_steps <maxsteps> - Sets maxsteps
2896 .  -ts_final_time <maxtime> - Sets maxtime
2897 
2898    Notes:
2899    The default maximum number of iterations is 5000. Default time is 5.0
2900 
2901    Level: intermediate
2902 
2903 .keywords: TS, timestep, set, maximum, iterations
2904 
2905 .seealso: TSSetExactFinalTime()
2906 @*/
2907 PetscErrorCode  TSSetDuration(TS ts,PetscInt maxsteps,PetscReal maxtime)
2908 {
2909   PetscFunctionBegin;
2910   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2911   PetscValidLogicalCollectiveInt(ts,maxsteps,2);
2912   PetscValidLogicalCollectiveReal(ts,maxtime,2);
2913   if (maxsteps >= 0) ts->max_steps = maxsteps;
2914   if (maxtime != PETSC_DEFAULT) ts->max_time = maxtime;
2915   PetscFunctionReturn(0);
2916 }
2917 
2918 #undef __FUNCT__
2919 #define __FUNCT__ "TSSetSolution"
2920 /*@
2921    TSSetSolution - Sets the initial solution vector
2922    for use by the TS routines.
2923 
2924    Logically Collective on TS and Vec
2925 
2926    Input Parameters:
2927 +  ts - the TS context obtained from TSCreate()
2928 -  u - the solution vector
2929 
2930    Level: beginner
2931 
2932 .keywords: TS, timestep, set, solution, initial conditions
2933 @*/
2934 PetscErrorCode  TSSetSolution(TS ts,Vec u)
2935 {
2936   PetscErrorCode ierr;
2937   DM             dm;
2938 
2939   PetscFunctionBegin;
2940   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2941   PetscValidHeaderSpecific(u,VEC_CLASSID,2);
2942   ierr = PetscObjectReference((PetscObject)u);CHKERRQ(ierr);
2943   ierr = VecDestroy(&ts->vec_sol);CHKERRQ(ierr);
2944   ts->vec_sol = u;
2945 
2946   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
2947   ierr = DMShellSetGlobalVector(dm,u);CHKERRQ(ierr);
2948   PetscFunctionReturn(0);
2949 }
2950 
2951 #undef __FUNCT__
2952 #define __FUNCT__ "TSAdjointSetSteps"
2953 /*@
2954    TSAdjointSetSteps - Sets the number of steps the adjoint solver should take backward in time
2955 
2956    Logically Collective on TS
2957 
2958    Input Parameters:
2959 +  ts - the TS context obtained from TSCreate()
2960 .  steps - number of steps to use
2961 
2962    Level: intermediate
2963 
2964    Notes: Normally one does not call this and TSAdjointSolve() integrates back to the original timestep. One can call this
2965           so as to integrate back to less than the original timestep
2966 
2967 .keywords: TS, timestep, set, maximum, iterations
2968 
2969 .seealso: TSSetExactFinalTime()
2970 @*/
2971 PetscErrorCode  TSAdjointSetSteps(TS ts,PetscInt steps)
2972 {
2973   PetscFunctionBegin;
2974   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
2975   PetscValidLogicalCollectiveInt(ts,steps,2);
2976   if (steps < 0) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Cannot step back a negative number of steps");
2977   if (steps > ts->total_steps) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Cannot step back more than the total number of forward steps");
2978   ts->adjoint_max_steps = steps;
2979   PetscFunctionReturn(0);
2980 }
2981 
2982 #undef __FUNCT__
2983 #define __FUNCT__ "TSSetCostGradients"
2984 /*@
2985    TSSetCostGradients - Sets the initial value of the gradients of the cost function w.r.t. initial conditions and w.r.t. the problem parameters
2986       for use by the TSAdjoint routines.
2987 
2988    Logically Collective on TS and Vec
2989 
2990    Input Parameters:
2991 +  ts - the TS context obtained from TSCreate()
2992 .  lambda - gradients with respect to the initial condition variables, the dimension and parallel layout of these vectors is the same as the ODE solution vector
2993 -  mu - gradients with respect to the parameters, the number of entries in these vectors is the same as the number of parameters
2994 
2995    Level: beginner
2996 
2997    Notes: the entries in these vectors must be correctly initialized with the values lamda_i = df/dy|finaltime  mu_i = df/dp|finaltime
2998 
2999 .keywords: TS, timestep, set, sensitivity, initial conditions
3000 @*/
3001 PetscErrorCode  TSSetCostGradients(TS ts,PetscInt numcost,Vec *lambda,Vec *mu)
3002 {
3003   PetscFunctionBegin;
3004   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3005   PetscValidPointer(lambda,2);
3006   ts->vecs_sensi  = lambda;
3007   ts->vecs_sensip = mu;
3008   if (ts->numcost && ts->numcost!=numcost) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"The number of cost functions (2rd parameter of TSSetCostIntegrand()) is inconsistent with the one set by TSSetCostIntegrand");
3009   ts->numcost  = numcost;
3010   PetscFunctionReturn(0);
3011 }
3012 
3013 #undef __FUNCT__
3014 #define __FUNCT__ "TSAdjointSetRHSJacobian"
3015 /*@C
3016   TSAdjointSetRHSJacobian - Sets the function that computes the Jacobian of G w.r.t. the parameters p where y_t = G(y,p,t), as well as the location to store the matrix.
3017 
3018   Logically Collective on TS
3019 
3020   Input Parameters:
3021 + ts   - The TS context obtained from TSCreate()
3022 - func - The function
3023 
3024   Calling sequence of func:
3025 $ func (TS ts,PetscReal t,Vec y,Mat A,void *ctx);
3026 +   t - current timestep
3027 .   y - input vector (current ODE solution)
3028 .   A - output matrix
3029 -   ctx - [optional] user-defined function context
3030 
3031   Level: intermediate
3032 
3033   Notes: Amat has the same number of rows and the same row parallel layout as u, Amat has the same number of columns and parallel layout as p
3034 
3035 .keywords: TS, sensitivity
3036 .seealso:
3037 @*/
3038 PetscErrorCode  TSAdjointSetRHSJacobian(TS ts,Mat Amat,PetscErrorCode (*func)(TS,PetscReal,Vec,Mat,void*),void *ctx)
3039 {
3040   PetscErrorCode ierr;
3041 
3042   PetscFunctionBegin;
3043   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3044   if (Amat) PetscValidHeaderSpecific(Amat,MAT_CLASSID,2);
3045 
3046   ts->rhsjacobianp    = func;
3047   ts->rhsjacobianpctx = ctx;
3048   if(Amat) {
3049     ierr = PetscObjectReference((PetscObject)Amat);CHKERRQ(ierr);
3050     ierr = MatDestroy(&ts->Jacp);CHKERRQ(ierr);
3051     ts->Jacp = Amat;
3052   }
3053   PetscFunctionReturn(0);
3054 }
3055 
3056 #undef __FUNCT__
3057 #define __FUNCT__ "TSAdjointComputeRHSJacobian"
3058 /*@C
3059   TSAdjointComputeRHSJacobian - Runs the user-defined Jacobian function.
3060 
3061   Collective on TS
3062 
3063   Input Parameters:
3064 . ts   - The TS context obtained from TSCreate()
3065 
3066   Level: developer
3067 
3068 .keywords: TS, sensitivity
3069 .seealso: TSAdjointSetRHSJacobian()
3070 @*/
3071 PetscErrorCode  TSAdjointComputeRHSJacobian(TS ts,PetscReal t,Vec X,Mat Amat)
3072 {
3073   PetscErrorCode ierr;
3074 
3075   PetscFunctionBegin;
3076   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3077   PetscValidHeaderSpecific(X,VEC_CLASSID,3);
3078   PetscValidPointer(Amat,4);
3079 
3080   PetscStackPush("TS user JacobianP function for sensitivity analysis");
3081   ierr = (*ts->rhsjacobianp)(ts,t,X,Amat,ts->rhsjacobianpctx); CHKERRQ(ierr);
3082   PetscStackPop;
3083   PetscFunctionReturn(0);
3084 }
3085 
3086 #undef __FUNCT__
3087 #define __FUNCT__ "TSSetCostIntegrand"
3088 /*@C
3089     TSSetCostIntegrand - Sets the routine for evaluating the integral term in one or more cost functions
3090 
3091     Logically Collective on TS
3092 
3093     Input Parameters:
3094 +   ts - the TS context obtained from TSCreate()
3095 .   numcost - number of gradients to be computed, this is the number of cost functions
3096 .   rf - routine for evaluating the integrand function
3097 .   drdyf - function that computes the gradients of the r's with respect to y,NULL if not a function y
3098 .   drdpf - function that computes the gradients of the r's with respect to p, NULL if not a function of p
3099 .   fwd - flag indicating whether to evaluate cost integral in the forward run or the adjoint run
3100 -   ctx - [optional] user-defined context for private data for the function evaluation routine (may be NULL)
3101 
3102     Calling sequence of rf:
3103 $     rf(TS ts,PetscReal t,Vec y,Vec f[],void *ctx);
3104 
3105 +   t - current timestep
3106 .   y - input vector
3107 .   f - function result; one vector entry for each cost function
3108 -   ctx - [optional] user-defined function context
3109 
3110    Calling sequence of drdyf:
3111 $    PetscErroCode drdyf(TS ts,PetscReal t,Vec y,Vec *drdy,void *ctx);
3112 
3113    Calling sequence of drdpf:
3114 $    PetscErroCode drdpf(TS ts,PetscReal t,Vec y,Vec *drdp,void *ctx);
3115 
3116     Level: intermediate
3117 
3118     Notes: For optimization there is generally a single cost function, numcost = 1. For sensitivities there may be multiple cost functions
3119 
3120 .keywords: TS, sensitivity analysis, timestep, set, quadrature, function
3121 
3122 .seealso: TSAdjointSetRHSJacobian(),TSGetCostGradients(), TSSetCostGradients()
3123 @*/
3124 PetscErrorCode  TSSetCostIntegrand(TS ts,PetscInt numcost,PetscErrorCode (*rf)(TS,PetscReal,Vec,Vec,void*),
3125                                                           PetscErrorCode (*drdyf)(TS,PetscReal,Vec,Vec*,void*),
3126                                                           PetscErrorCode (*drdpf)(TS,PetscReal,Vec,Vec*,void*),
3127                                                           PetscBool fwd,void *ctx)
3128 {
3129   PetscErrorCode ierr;
3130 
3131   PetscFunctionBegin;
3132   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3133   if (ts->numcost && ts->numcost!=numcost) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"The number of cost functions (2rd parameter of TSSetCostIntegrand()) is inconsistent with the one set by TSSetCostGradients()");
3134   if (!ts->numcost) ts->numcost=numcost;
3135 
3136   ts->costintegralfwd  = fwd; /* Evaluate the cost integral in forward run if fwd is true */
3137   ierr                 = VecCreateSeq(PETSC_COMM_SELF,numcost,&ts->vec_costintegral);CHKERRQ(ierr);
3138   ierr                 = VecDuplicate(ts->vec_costintegral,&ts->vec_costintegrand);CHKERRQ(ierr);
3139   ts->costintegrand    = rf;
3140   ts->costintegrandctx = ctx;
3141   ts->drdyfunction     = drdyf;
3142   ts->drdpfunction     = drdpf;
3143   PetscFunctionReturn(0);
3144 }
3145 
3146 #undef __FUNCT__
3147 #define __FUNCT__ "TSGetCostIntegral"
3148 /*@
3149    TSGetCostIntegral - Returns the values of the integral term in the cost functions.
3150    It is valid to call the routine after a backward run.
3151 
3152    Not Collective
3153 
3154    Input Parameter:
3155 .  ts - the TS context obtained from TSCreate()
3156 
3157    Output Parameter:
3158 .  v - the vector containing the integrals for each cost function
3159 
3160    Level: intermediate
3161 
3162 .seealso: TSSetCostIntegrand()
3163 
3164 .keywords: TS, sensitivity analysis
3165 @*/
3166 PetscErrorCode  TSGetCostIntegral(TS ts,Vec *v)
3167 {
3168   PetscFunctionBegin;
3169   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3170   PetscValidPointer(v,2);
3171   *v = ts->vec_costintegral;
3172   PetscFunctionReturn(0);
3173 }
3174 
3175 #undef __FUNCT__
3176 #define __FUNCT__ "TSAdjointComputeCostIntegrand"
3177 /*@
3178    TSAdjointComputeCostIntegrand - Evaluates the integral function in the cost functions.
3179 
3180    Input Parameters:
3181 +  ts - the TS context
3182 .  t - current time
3183 -  y - state vector, i.e. current solution
3184 
3185    Output Parameter:
3186 .  q - vector of size numcost to hold the outputs
3187 
3188    Note:
3189    Most users should not need to explicitly call this routine, as it
3190    is used internally within the sensitivity analysis context.
3191 
3192    Level: developer
3193 
3194 .keywords: TS, compute
3195 
3196 .seealso: TSSetCostIntegrand()
3197 @*/
3198 PetscErrorCode TSAdjointComputeCostIntegrand(TS ts,PetscReal t,Vec y,Vec q)
3199 {
3200   PetscErrorCode ierr;
3201 
3202   PetscFunctionBegin;
3203   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3204   PetscValidHeaderSpecific(y,VEC_CLASSID,3);
3205   PetscValidHeaderSpecific(q,VEC_CLASSID,4);
3206 
3207   ierr = PetscLogEventBegin(TS_FunctionEval,ts,y,q,0);CHKERRQ(ierr);
3208   if (ts->costintegrand) {
3209     PetscStackPush("TS user integrand in the cost function");
3210     ierr = (*ts->costintegrand)(ts,t,y,q,ts->costintegrandctx);CHKERRQ(ierr);
3211     PetscStackPop;
3212   } else {
3213     ierr = VecZeroEntries(q);CHKERRQ(ierr);
3214   }
3215 
3216   ierr = PetscLogEventEnd(TS_FunctionEval,ts,y,q,0);CHKERRQ(ierr);
3217   PetscFunctionReturn(0);
3218 }
3219 
3220 #undef __FUNCT__
3221 #define __FUNCT__ "TSAdjointComputeDRDYFunction"
3222 /*@
3223   TSAdjointComputeDRDYFunction - Runs the user-defined DRDY function.
3224 
3225   Collective on TS
3226 
3227   Input Parameters:
3228 . ts   - The TS context obtained from TSCreate()
3229 
3230   Notes:
3231   TSAdjointComputeDRDYFunction() is typically used for sensitivity implementation,
3232   so most users would not generally call this routine themselves.
3233 
3234   Level: developer
3235 
3236 .keywords: TS, sensitivity
3237 .seealso: TSAdjointComputeDRDYFunction()
3238 @*/
3239 PetscErrorCode  TSAdjointComputeDRDYFunction(TS ts,PetscReal t,Vec y,Vec *drdy)
3240 {
3241   PetscErrorCode ierr;
3242 
3243   PetscFunctionBegin;
3244   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3245   PetscValidHeaderSpecific(y,VEC_CLASSID,3);
3246 
3247   PetscStackPush("TS user DRDY function for sensitivity analysis");
3248   ierr = (*ts->drdyfunction)(ts,t,y,drdy,ts->costintegrandctx); CHKERRQ(ierr);
3249   PetscStackPop;
3250   PetscFunctionReturn(0);
3251 }
3252 
3253 #undef __FUNCT__
3254 #define __FUNCT__ "TSAdjointComputeDRDPFunction"
3255 /*@
3256   TSAdjointComputeDRDPFunction - Runs the user-defined DRDP function.
3257 
3258   Collective on TS
3259 
3260   Input Parameters:
3261 . ts   - The TS context obtained from TSCreate()
3262 
3263   Notes:
3264   TSDRDPFunction() is typically used for sensitivity implementation,
3265   so most users would not generally call this routine themselves.
3266 
3267   Level: developer
3268 
3269 .keywords: TS, sensitivity
3270 .seealso: TSAdjointSetDRDPFunction()
3271 @*/
3272 PetscErrorCode  TSAdjointComputeDRDPFunction(TS ts,PetscReal t,Vec y,Vec *drdp)
3273 {
3274   PetscErrorCode ierr;
3275 
3276   PetscFunctionBegin;
3277   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3278   PetscValidHeaderSpecific(y,VEC_CLASSID,3);
3279 
3280   PetscStackPush("TS user DRDP function for sensitivity analysis");
3281   ierr = (*ts->drdpfunction)(ts,t,y,drdp,ts->costintegrandctx); CHKERRQ(ierr);
3282   PetscStackPop;
3283   PetscFunctionReturn(0);
3284 }
3285 
3286 #undef __FUNCT__
3287 #define __FUNCT__ "TSSetPreStep"
3288 /*@C
3289   TSSetPreStep - Sets the general-purpose function
3290   called once at the beginning of each time step.
3291 
3292   Logically Collective on TS
3293 
3294   Input Parameters:
3295 + ts   - The TS context obtained from TSCreate()
3296 - func - The function
3297 
3298   Calling sequence of func:
3299 . func (TS ts);
3300 
3301   Level: intermediate
3302 
3303   Note:
3304   If a step is rejected, TSStep() will call this routine again before each attempt.
3305   The last completed time step number can be queried using TSGetTimeStepNumber(), the
3306   size of the step being attempted can be obtained using TSGetTimeStep().
3307 
3308 .keywords: TS, timestep
3309 .seealso: TSSetPreStage(), TSSetPostStage(), TSSetPostStep(), TSStep()
3310 @*/
3311 PetscErrorCode  TSSetPreStep(TS ts, PetscErrorCode (*func)(TS))
3312 {
3313   PetscFunctionBegin;
3314   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3315   ts->prestep = func;
3316   PetscFunctionReturn(0);
3317 }
3318 
3319 #undef __FUNCT__
3320 #define __FUNCT__ "TSPreStep"
3321 /*@
3322   TSPreStep - Runs the user-defined pre-step function.
3323 
3324   Collective on TS
3325 
3326   Input Parameters:
3327 . ts   - The TS context obtained from TSCreate()
3328 
3329   Notes:
3330   TSPreStep() is typically used within time stepping implementations,
3331   so most users would not generally call this routine themselves.
3332 
3333   Level: developer
3334 
3335 .keywords: TS, timestep
3336 .seealso: TSSetPreStep(), TSPreStage(), TSPostStage(), TSPostStep()
3337 @*/
3338 PetscErrorCode  TSPreStep(TS ts)
3339 {
3340   PetscErrorCode ierr;
3341 
3342   PetscFunctionBegin;
3343   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3344   if (ts->prestep) {
3345     PetscStackCallStandard((*ts->prestep),(ts));
3346   }
3347   PetscFunctionReturn(0);
3348 }
3349 
3350 #undef __FUNCT__
3351 #define __FUNCT__ "TSSetPreStage"
3352 /*@C
3353   TSSetPreStage - Sets the general-purpose function
3354   called once at the beginning of each stage.
3355 
3356   Logically Collective on TS
3357 
3358   Input Parameters:
3359 + ts   - The TS context obtained from TSCreate()
3360 - func - The function
3361 
3362   Calling sequence of func:
3363 . PetscErrorCode func(TS ts, PetscReal stagetime);
3364 
3365   Level: intermediate
3366 
3367   Note:
3368   There may be several stages per time step. If the solve for a given stage fails, the step may be rejected and retried.
3369   The time step number being computed can be queried using TSGetTimeStepNumber() and the total size of the step being
3370   attempted can be obtained using TSGetTimeStep(). The time at the start of the step is available via TSGetTime().
3371 
3372 .keywords: TS, timestep
3373 .seealso: TSSetPostStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
3374 @*/
3375 PetscErrorCode  TSSetPreStage(TS ts, PetscErrorCode (*func)(TS,PetscReal))
3376 {
3377   PetscFunctionBegin;
3378   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3379   ts->prestage = func;
3380   PetscFunctionReturn(0);
3381 }
3382 
3383 #undef __FUNCT__
3384 #define __FUNCT__ "TSSetPostStage"
3385 /*@C
3386   TSSetPostStage - Sets the general-purpose function
3387   called once at the end of each stage.
3388 
3389   Logically Collective on TS
3390 
3391   Input Parameters:
3392 + ts   - The TS context obtained from TSCreate()
3393 - func - The function
3394 
3395   Calling sequence of func:
3396 . PetscErrorCode func(TS ts, PetscReal stagetime, PetscInt stageindex, Vec* Y);
3397 
3398   Level: intermediate
3399 
3400   Note:
3401   There may be several stages per time step. If the solve for a given stage fails, the step may be rejected and retried.
3402   The time step number being computed can be queried using TSGetTimeStepNumber() and the total size of the step being
3403   attempted can be obtained using TSGetTimeStep(). The time at the start of the step is available via TSGetTime().
3404 
3405 .keywords: TS, timestep
3406 .seealso: TSSetPreStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
3407 @*/
3408 PetscErrorCode  TSSetPostStage(TS ts, PetscErrorCode (*func)(TS,PetscReal,PetscInt,Vec*))
3409 {
3410   PetscFunctionBegin;
3411   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3412   ts->poststage = func;
3413   PetscFunctionReturn(0);
3414 }
3415 
3416 #undef __FUNCT__
3417 #define __FUNCT__ "TSSetPostEvaluate"
3418 /*@C
3419   TSSetPostEvaluate - Sets the general-purpose function
3420   called once at the end of each step evaluation.
3421 
3422   Logically Collective on TS
3423 
3424   Input Parameters:
3425 + ts   - The TS context obtained from TSCreate()
3426 - func - The function
3427 
3428   Calling sequence of func:
3429 . PetscErrorCode func(TS ts);
3430 
3431   Level: intermediate
3432 
3433   Note:
3434   Semantically, TSSetPostEvaluate() differs from TSSetPostStep() since the function it sets is called before event-handling
3435   thus guaranteeing the same solution (computed by the time-stepper) will be passed to it. On the other hand, TSPostStep()
3436   may be passed a different solution, possibly changed by the event handler. TSPostEvaluate() is called after the next step
3437   solution is evaluated allowing to modify it, if need be. The solution can be obtained with TSGetSolution(), the time step
3438   with TSGetTimeStep(), and the time at the start of the step is available via TSGetTime()
3439 
3440 .keywords: TS, timestep
3441 .seealso: TSSetPreStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
3442 @*/
3443 PetscErrorCode  TSSetPostEvaluate(TS ts, PetscErrorCode (*func)(TS))
3444 {
3445   PetscFunctionBegin;
3446   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3447   ts->postevaluate = func;
3448   PetscFunctionReturn(0);
3449 }
3450 
3451 #undef __FUNCT__
3452 #define __FUNCT__ "TSPreStage"
3453 /*@
3454   TSPreStage - Runs the user-defined pre-stage function set using TSSetPreStage()
3455 
3456   Collective on TS
3457 
3458   Input Parameters:
3459 . ts          - The TS context obtained from TSCreate()
3460   stagetime   - The absolute time of the current stage
3461 
3462   Notes:
3463   TSPreStage() is typically used within time stepping implementations,
3464   most users would not generally call this routine themselves.
3465 
3466   Level: developer
3467 
3468 .keywords: TS, timestep
3469 .seealso: TSPostStage(), TSSetPreStep(), TSPreStep(), TSPostStep()
3470 @*/
3471 PetscErrorCode  TSPreStage(TS ts, PetscReal stagetime)
3472 {
3473   PetscErrorCode ierr;
3474 
3475   PetscFunctionBegin;
3476   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3477   if (ts->prestage) {
3478     PetscStackCallStandard((*ts->prestage),(ts,stagetime));
3479   }
3480   PetscFunctionReturn(0);
3481 }
3482 
3483 #undef __FUNCT__
3484 #define __FUNCT__ "TSPostStage"
3485 /*@
3486   TSPostStage - Runs the user-defined post-stage function set using TSSetPostStage()
3487 
3488   Collective on TS
3489 
3490   Input Parameters:
3491 . ts          - The TS context obtained from TSCreate()
3492   stagetime   - The absolute time of the current stage
3493   stageindex  - Stage number
3494   Y           - Array of vectors (of size = total number
3495                 of stages) with the stage solutions
3496 
3497   Notes:
3498   TSPostStage() is typically used within time stepping implementations,
3499   most users would not generally call this routine themselves.
3500 
3501   Level: developer
3502 
3503 .keywords: TS, timestep
3504 .seealso: TSPreStage(), TSSetPreStep(), TSPreStep(), TSPostStep()
3505 @*/
3506 PetscErrorCode  TSPostStage(TS ts, PetscReal stagetime, PetscInt stageindex, Vec *Y)
3507 {
3508   PetscErrorCode ierr;
3509 
3510   PetscFunctionBegin;
3511   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3512   if (ts->poststage) {
3513     PetscStackCallStandard((*ts->poststage),(ts,stagetime,stageindex,Y));
3514   }
3515   PetscFunctionReturn(0);
3516 }
3517 
3518 #undef __FUNCT__
3519 #define __FUNCT__ "TSPostEvaluate"
3520 /*@
3521   TSPostEvaluate - Runs the user-defined post-evaluate function set using TSSetPostEvaluate()
3522 
3523   Collective on TS
3524 
3525   Input Parameters:
3526 . ts          - The TS context obtained from TSCreate()
3527 
3528   Notes:
3529   TSPostEvaluate() is typically used within time stepping implementations,
3530   most users would not generally call this routine themselves.
3531 
3532   Level: developer
3533 
3534 .keywords: TS, timestep
3535 .seealso: TSSetPostEvaluate(), TSSetPreStep(), TSPreStep(), TSPostStep()
3536 @*/
3537 PetscErrorCode  TSPostEvaluate(TS ts)
3538 {
3539   PetscErrorCode ierr;
3540 
3541   PetscFunctionBegin;
3542   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3543   if (ts->postevaluate) {
3544     PetscStackCallStandard((*ts->postevaluate),(ts));
3545   }
3546   PetscFunctionReturn(0);
3547 }
3548 
3549 #undef __FUNCT__
3550 #define __FUNCT__ "TSSetPostStep"
3551 /*@C
3552   TSSetPostStep - Sets the general-purpose function
3553   called once at the end of each time step.
3554 
3555   Logically Collective on TS
3556 
3557   Input Parameters:
3558 + ts   - The TS context obtained from TSCreate()
3559 - func - The function
3560 
3561   Calling sequence of func:
3562 $ func (TS ts);
3563 
3564   Notes:
3565   The function set by TSSetPostStep() is called after each successful step. The solution vector X
3566   obtained by TSGetSolution() may be different than that computed at the step end if the event handler
3567   locates an event and TSPostEvent() modifies it. Use TSSetPostEvaluate() if an unmodified solution is needed instead.
3568 
3569   Level: intermediate
3570 
3571 .keywords: TS, timestep
3572 .seealso: TSSetPreStep(), TSSetPreStage(), TSSetPostEvaluate(), TSGetTimeStep(), TSGetTimeStepNumber(), TSGetTime()
3573 @*/
3574 PetscErrorCode  TSSetPostStep(TS ts, PetscErrorCode (*func)(TS))
3575 {
3576   PetscFunctionBegin;
3577   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
3578   ts->poststep = func;
3579   PetscFunctionReturn(0);
3580 }
3581 
3582 #undef __FUNCT__
3583 #define __FUNCT__ "TSPostStep"
3584 /*@
3585   TSPostStep - Runs the user-defined post-step function.
3586 
3587   Collective on TS
3588 
3589   Input Parameters:
3590 . ts   - The TS context obtained from TSCreate()
3591 
3592   Notes:
3593   TSPostStep() is typically used within time stepping implementations,
3594   so most users would not generally call this routine themselves.
3595 
3596   Level: developer
3597 
3598 .keywords: TS, timestep
3599 @*/
3600 PetscErrorCode  TSPostStep(TS ts)
3601 {
3602   PetscErrorCode ierr;
3603 
3604   PetscFunctionBegin;
3605   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3606   if (ts->poststep) {
3607     PetscStackCallStandard((*ts->poststep),(ts));
3608   }
3609   PetscFunctionReturn(0);
3610 }
3611 
3612 /* ------------ Routines to set performance monitoring options ----------- */
3613 
3614 #undef __FUNCT__
3615 #define __FUNCT__ "TSMonitorSet"
3616 /*@C
3617    TSMonitorSet - Sets an ADDITIONAL function that is to be used at every
3618    timestep to display the iteration's  progress.
3619 
3620    Logically Collective on TS
3621 
3622    Input Parameters:
3623 +  ts - the TS context obtained from TSCreate()
3624 .  monitor - monitoring routine
3625 .  mctx - [optional] user-defined context for private data for the
3626              monitor routine (use NULL if no context is desired)
3627 -  monitordestroy - [optional] routine that frees monitor context
3628           (may be NULL)
3629 
3630    Calling sequence of monitor:
3631 $    int monitor(TS ts,PetscInt steps,PetscReal time,Vec u,void *mctx)
3632 
3633 +    ts - the TS context
3634 .    steps - iteration number (after the final time step the monitor routine may be called with a step of -1, this indicates the solution has been interpolated to this time)
3635 .    time - current time
3636 .    u - current iterate
3637 -    mctx - [optional] monitoring context
3638 
3639    Notes:
3640    This routine adds an additional monitor to the list of monitors that
3641    already has been loaded.
3642 
3643    Fortran notes: Only a single monitor function can be set for each TS object
3644 
3645    Level: intermediate
3646 
3647 .keywords: TS, timestep, set, monitor
3648 
3649 .seealso: TSMonitorDefault(), TSMonitorCancel()
3650 @*/
3651 PetscErrorCode  TSMonitorSet(TS ts,PetscErrorCode (*monitor)(TS,PetscInt,PetscReal,Vec,void*),void *mctx,PetscErrorCode (*mdestroy)(void**))
3652 {
3653   PetscErrorCode ierr;
3654   PetscInt       i;
3655   PetscBool      identical;
3656 
3657   PetscFunctionBegin;
3658   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3659   for (i=0; i<ts->numbermonitors;i++) {
3660     ierr = PetscMonitorCompare((PetscErrorCode (*)(void))monitor,mctx,mdestroy,(PetscErrorCode (*)(void))ts->monitor[i],ts->monitorcontext[i],ts->monitordestroy[i],&identical);CHKERRQ(ierr);
3661     if (identical) PetscFunctionReturn(0);
3662   }
3663   if (ts->numbermonitors >= MAXTSMONITORS) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many monitors set");
3664   ts->monitor[ts->numbermonitors]          = monitor;
3665   ts->monitordestroy[ts->numbermonitors]   = mdestroy;
3666   ts->monitorcontext[ts->numbermonitors++] = (void*)mctx;
3667   PetscFunctionReturn(0);
3668 }
3669 
3670 #undef __FUNCT__
3671 #define __FUNCT__ "TSMonitorCancel"
3672 /*@C
3673    TSMonitorCancel - Clears all the monitors that have been set on a time-step object.
3674 
3675    Logically Collective on TS
3676 
3677    Input Parameters:
3678 .  ts - the TS context obtained from TSCreate()
3679 
3680    Notes:
3681    There is no way to remove a single, specific monitor.
3682 
3683    Level: intermediate
3684 
3685 .keywords: TS, timestep, set, monitor
3686 
3687 .seealso: TSMonitorDefault(), TSMonitorSet()
3688 @*/
3689 PetscErrorCode  TSMonitorCancel(TS ts)
3690 {
3691   PetscErrorCode ierr;
3692   PetscInt       i;
3693 
3694   PetscFunctionBegin;
3695   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3696   for (i=0; i<ts->numbermonitors; i++) {
3697     if (ts->monitordestroy[i]) {
3698       ierr = (*ts->monitordestroy[i])(&ts->monitorcontext[i]);CHKERRQ(ierr);
3699     }
3700   }
3701   ts->numbermonitors = 0;
3702   PetscFunctionReturn(0);
3703 }
3704 
3705 #undef __FUNCT__
3706 #define __FUNCT__ "TSMonitorDefault"
3707 /*@C
3708    TSMonitorDefault - The Default monitor, prints the timestep and time for each step
3709 
3710    Level: intermediate
3711 
3712 .keywords: TS, set, monitor
3713 
3714 .seealso:  TSMonitorSet()
3715 @*/
3716 PetscErrorCode TSMonitorDefault(TS ts,PetscInt step,PetscReal ptime,Vec v,PetscViewerAndFormat *vf)
3717 {
3718   PetscErrorCode ierr;
3719   PetscViewer    viewer =  vf->viewer;
3720   PetscBool      iascii,ibinary;
3721 
3722   PetscFunctionBegin;
3723   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
3724   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
3725   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&ibinary);CHKERRQ(ierr);
3726   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
3727   if (iascii) {
3728     ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3729     if (step == -1){ /* this indicates it is an interpolated solution */
3730       ierr = PetscViewerASCIIPrintf(viewer,"Interpolated solution at time %g between steps %D and %D\n",(double)ptime,ts->steps-1,ts->steps);CHKERRQ(ierr);
3731     } else {
3732       ierr = PetscViewerASCIIPrintf(viewer,"%D TS dt %g time %g%s",step,(double)ts->time_step,(double)ptime,ts->steprollback ? " (r)\n" : "\n");CHKERRQ(ierr);
3733     }
3734     ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3735   } else if (ibinary) {
3736     PetscMPIInt rank;
3737     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)viewer),&rank);CHKERRQ(ierr);
3738     if (!rank) {
3739       PetscBool skipHeader;
3740       PetscInt  classid = REAL_FILE_CLASSID;
3741 
3742       ierr = PetscViewerBinaryGetSkipHeader(viewer,&skipHeader);CHKERRQ(ierr);
3743       if (!skipHeader) {
3744          ierr = PetscViewerBinaryWrite(viewer,&classid,1,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
3745        }
3746       ierr = PetscRealView(1,&ptime,viewer);CHKERRQ(ierr);
3747     } else {
3748       ierr = PetscRealView(0,&ptime,viewer);CHKERRQ(ierr);
3749     }
3750   }
3751   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
3752   PetscFunctionReturn(0);
3753 }
3754 
3755 #undef __FUNCT__
3756 #define __FUNCT__ "TSAdjointMonitorSet"
3757 /*@C
3758    TSAdjointMonitorSet - Sets an ADDITIONAL function that is to be used at every
3759    timestep to display the iteration's  progress.
3760 
3761    Logically Collective on TS
3762 
3763    Input Parameters:
3764 +  ts - the TS context obtained from TSCreate()
3765 .  adjointmonitor - monitoring routine
3766 .  adjointmctx - [optional] user-defined context for private data for the
3767              monitor routine (use NULL if no context is desired)
3768 -  adjointmonitordestroy - [optional] routine that frees monitor context
3769           (may be NULL)
3770 
3771    Calling sequence of monitor:
3772 $    int adjointmonitor(TS ts,PetscInt steps,PetscReal time,Vec u,PetscInt numcost,Vec *lambda, Vec *mu,void *adjointmctx)
3773 
3774 +    ts - the TS context
3775 .    steps - iteration number (after the final time step the monitor routine is called with a step of -1, this is at the final time which may have
3776                                been interpolated to)
3777 .    time - current time
3778 .    u - current iterate
3779 .    numcost - number of cost functionos
3780 .    lambda - sensitivities to initial conditions
3781 .    mu - sensitivities to parameters
3782 -    adjointmctx - [optional] adjoint monitoring context
3783 
3784    Notes:
3785    This routine adds an additional monitor to the list of monitors that
3786    already has been loaded.
3787 
3788    Fortran notes: Only a single monitor function can be set for each TS object
3789 
3790    Level: intermediate
3791 
3792 .keywords: TS, timestep, set, adjoint, monitor
3793 
3794 .seealso: TSAdjointMonitorCancel()
3795 @*/
3796 PetscErrorCode  TSAdjointMonitorSet(TS ts,PetscErrorCode (*adjointmonitor)(TS,PetscInt,PetscReal,Vec,PetscInt,Vec*,Vec*,void*),void *adjointmctx,PetscErrorCode (*adjointmdestroy)(void**))
3797 {
3798   PetscErrorCode ierr;
3799   PetscInt       i;
3800   PetscBool      identical;
3801 
3802   PetscFunctionBegin;
3803   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3804   for (i=0; i<ts->numbermonitors;i++) {
3805     ierr = PetscMonitorCompare((PetscErrorCode (*)(void))adjointmonitor,adjointmctx,adjointmdestroy,(PetscErrorCode (*)(void))ts->adjointmonitor[i],ts->adjointmonitorcontext[i],ts->adjointmonitordestroy[i],&identical);CHKERRQ(ierr);
3806     if (identical) PetscFunctionReturn(0);
3807   }
3808   if (ts->numberadjointmonitors >= MAXTSMONITORS) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many adjoint monitors set");
3809   ts->adjointmonitor[ts->numberadjointmonitors]          = adjointmonitor;
3810   ts->adjointmonitordestroy[ts->numberadjointmonitors]   = adjointmdestroy;
3811   ts->adjointmonitorcontext[ts->numberadjointmonitors++] = (void*)adjointmctx;
3812   PetscFunctionReturn(0);
3813 }
3814 
3815 #undef __FUNCT__
3816 #define __FUNCT__ "TSAdjointMonitorCancel"
3817 /*@C
3818    TSAdjointMonitorCancel - Clears all the adjoint monitors that have been set on a time-step object.
3819 
3820    Logically Collective on TS
3821 
3822    Input Parameters:
3823 .  ts - the TS context obtained from TSCreate()
3824 
3825    Notes:
3826    There is no way to remove a single, specific monitor.
3827 
3828    Level: intermediate
3829 
3830 .keywords: TS, timestep, set, adjoint, monitor
3831 
3832 .seealso: TSAdjointMonitorSet()
3833 @*/
3834 PetscErrorCode  TSAdjointMonitorCancel(TS ts)
3835 {
3836   PetscErrorCode ierr;
3837   PetscInt       i;
3838 
3839   PetscFunctionBegin;
3840   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3841   for (i=0; i<ts->numberadjointmonitors; i++) {
3842     if (ts->adjointmonitordestroy[i]) {
3843       ierr = (*ts->adjointmonitordestroy[i])(&ts->adjointmonitorcontext[i]);CHKERRQ(ierr);
3844     }
3845   }
3846   ts->numberadjointmonitors = 0;
3847   PetscFunctionReturn(0);
3848 }
3849 
3850 #undef __FUNCT__
3851 #define __FUNCT__ "TSAdjointMonitorDefault"
3852 /*@C
3853    TSAdjointMonitorDefault - the default monitor of adjoint computations
3854 
3855    Level: intermediate
3856 
3857 .keywords: TS, set, monitor
3858 
3859 .seealso: TSAdjointMonitorSet()
3860 @*/
3861 PetscErrorCode TSAdjointMonitorDefault(TS ts,PetscInt step,PetscReal ptime,Vec v,PetscInt numcost,Vec *lambda,Vec *mu,PetscViewerAndFormat *vf)
3862 {
3863   PetscErrorCode ierr;
3864   PetscViewer    viewer = vf->viewer;
3865 
3866   PetscFunctionBegin;
3867   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
3868   ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
3869   ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3870   ierr = PetscViewerASCIIPrintf(viewer,"%D TS dt %g time %g%s",step,(double)ts->time_step,(double)ptime,ts->steprollback ? " (r)\n" : "\n");CHKERRQ(ierr);
3871   ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
3872   ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
3873   PetscFunctionReturn(0);
3874 }
3875 
3876 #undef __FUNCT__
3877 #define __FUNCT__ "TSInterpolate"
3878 /*@
3879    TSInterpolate - Interpolate the solution computed during the previous step to an arbitrary location in the interval
3880 
3881    Collective on TS
3882 
3883    Input Argument:
3884 +  ts - time stepping context
3885 -  t - time to interpolate to
3886 
3887    Output Argument:
3888 .  U - state at given time
3889 
3890    Level: intermediate
3891 
3892    Developer Notes:
3893    TSInterpolate() and the storing of previous steps/stages should be generalized to support delay differential equations and continuous adjoints.
3894 
3895 .keywords: TS, set
3896 
3897 .seealso: TSSetExactFinalTime(), TSSolve()
3898 @*/
3899 PetscErrorCode TSInterpolate(TS ts,PetscReal t,Vec U)
3900 {
3901   PetscErrorCode ierr;
3902 
3903   PetscFunctionBegin;
3904   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3905   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
3906   if (t < ts->ptime_prev || t > ts->ptime) SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Requested time %g not in last time steps [%g,%g]",t,(double)ts->ptime_prev,(double)ts->ptime);
3907   if (!ts->ops->interpolate) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"%s does not provide interpolation",((PetscObject)ts)->type_name);
3908   ierr = (*ts->ops->interpolate)(ts,t,U);CHKERRQ(ierr);
3909   PetscFunctionReturn(0);
3910 }
3911 
3912 #undef __FUNCT__
3913 #define __FUNCT__ "TSStep"
3914 /*@
3915    TSStep - Steps one time step
3916 
3917    Collective on TS
3918 
3919    Input Parameter:
3920 .  ts - the TS context obtained from TSCreate()
3921 
3922    Level: developer
3923 
3924    Notes:
3925    The public interface for the ODE/DAE solvers is TSSolve(), you should almost for sure be using that routine and not this routine.
3926 
3927    The hook set using TSSetPreStep() is called before each attempt to take the step. In general, the time step size may
3928    be changed due to adaptive error controller or solve failures. Note that steps may contain multiple stages.
3929 
3930    This may over-step the final time provided in TSSetDuration() depending on the time-step used. TSSolve() interpolates to exactly the
3931    time provided in TSSetDuration(). One can use TSInterpolate() to determine an interpolated solution within the final timestep.
3932 
3933 .keywords: TS, timestep, solve
3934 
3935 .seealso: TSCreate(), TSSetUp(), TSDestroy(), TSSolve(), TSSetPreStep(), TSSetPreStage(), TSSetPostStage(), TSInterpolate()
3936 @*/
3937 PetscErrorCode  TSStep(TS ts)
3938 {
3939   PetscErrorCode   ierr;
3940   static PetscBool cite = PETSC_FALSE;
3941   PetscReal        ptime;
3942 
3943   PetscFunctionBegin;
3944   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
3945   ierr = PetscCitationsRegister("@techreport{tspaper,\n"
3946                                 "  title       = {{PETSc/TS}: A Modern Scalable {DAE/ODE} Solver Library},\n"
3947                                 "  author      = {Shrirang Abhyankar and Jed Brown and Emil Constantinescu and Debojyoti Ghosh and Barry F. Smith},\n"
3948                                 "  type        = {Preprint},\n"
3949                                 "  number      = {ANL/MCS-P5061-0114},\n"
3950                                 "  institution = {Argonne National Laboratory},\n"
3951                                 "  year        = {2014}\n}\n",&cite);CHKERRQ(ierr);
3952 
3953   ierr = TSSetUp(ts);CHKERRQ(ierr);
3954   ierr = TSTrajectorySetUp(ts->trajectory,ts);CHKERRQ(ierr);
3955 
3956   if (ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"You must call TSSetExactFinalTime() or use -ts_exact_final_time <stepover,interpolate,matchstep> before calling TSStep()");
3957   if (ts->exact_final_time == TS_EXACTFINALTIME_MATCHSTEP && !ts->adapt) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Since TS is not adaptive you cannot use TS_EXACTFINALTIME_MATCHSTEP, suggest TS_EXACTFINALTIME_INTERPOLATE");
3958 
3959   if (!ts->steps) ts->ptime_prev = ts->ptime;
3960   ts->reason = TS_CONVERGED_ITERATING;
3961   ptime = ts->ptime; ts->ptime_prev_rollback = ts->ptime_prev;
3962   if (!ts->ops->step) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSStep not implemented for type '%s'",((PetscObject)ts)->type_name);
3963   ierr = PetscLogEventBegin(TS_Step,ts,0,0,0);CHKERRQ(ierr);
3964   ierr = (*ts->ops->step)(ts);CHKERRQ(ierr);
3965   ierr = PetscLogEventEnd(TS_Step,ts,0,0,0);CHKERRQ(ierr);
3966   ts->ptime_prev = ptime;
3967   ts->steps++; ts->total_steps++;
3968   ts->steprollback = PETSC_FALSE;
3969   ts->steprestart  = PETSC_FALSE;
3970 
3971   if (ts->reason < 0) {
3972     if (ts->errorifstepfailed) {
3973       if (ts->reason == TS_DIVERGED_NONLINEAR_SOLVE) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s, increase -ts_max_snes_failures or make negative to attempt recovery",TSConvergedReasons[ts->reason]);
3974       else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s",TSConvergedReasons[ts->reason]);
3975     }
3976   } else if (!ts->reason) {
3977     if (ts->steps >= ts->max_steps)     ts->reason = TS_CONVERGED_ITS;
3978     else if (ts->ptime >= ts->max_time) ts->reason = TS_CONVERGED_TIME;
3979   }
3980   PetscFunctionReturn(0);
3981 }
3982 
3983 #undef __FUNCT__
3984 #define __FUNCT__ "TSAdjointStep"
3985 /*@
3986    TSAdjointStep - Steps one time step backward in the adjoint run
3987 
3988    Collective on TS
3989 
3990    Input Parameter:
3991 .  ts - the TS context obtained from TSCreate()
3992 
3993    Level: intermediate
3994 
3995 .keywords: TS, adjoint, step
3996 
3997 .seealso: TSAdjointSetUp(), TSAdjointSolve()
3998 @*/
3999 PetscErrorCode  TSAdjointStep(TS ts)
4000 {
4001   DM               dm;
4002   PetscErrorCode   ierr;
4003 
4004   PetscFunctionBegin;
4005   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4006   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4007   ierr = TSAdjointSetUp(ts);CHKERRQ(ierr);
4008 
4009   ierr = VecViewFromOptions(ts->vec_sol,(PetscObject)ts,"-ts_view_solution");CHKERRQ(ierr);
4010 
4011   ts->reason = TS_CONVERGED_ITERATING;
4012   ts->ptime_prev = ts->ptime;
4013   if (!ts->ops->adjointstep) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed because the adjoint of  %s has not been implemented, try other time stepping methods for adjoint sensitivity analysis",((PetscObject)ts)->type_name);
4014   ierr = PetscLogEventBegin(TS_AdjointStep,ts,0,0,0);CHKERRQ(ierr);
4015   ierr = (*ts->ops->adjointstep)(ts);CHKERRQ(ierr);
4016   ierr = PetscLogEventEnd(TS_AdjointStep,ts,0,0,0);CHKERRQ(ierr);
4017   ts->steps++; ts->total_steps--;
4018 
4019   if (ts->reason < 0) {
4020     if (ts->errorifstepfailed) {
4021       if (ts->reason == TS_DIVERGED_NONLINEAR_SOLVE) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s, increase -ts_max_snes_failures or make negative to attempt recovery",TSConvergedReasons[ts->reason]);
4022       else if (ts->reason == TS_DIVERGED_STEP_REJECTED) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s, increase -ts_max_reject or make negative to attempt recovery",TSConvergedReasons[ts->reason]);
4023       else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s",TSConvergedReasons[ts->reason]);
4024     }
4025   } else if (!ts->reason) {
4026     if (ts->steps >= ts->adjoint_max_steps) ts->reason = TS_CONVERGED_ITS;
4027   }
4028   PetscFunctionReturn(0);
4029 }
4030 
4031 #undef __FUNCT__
4032 #define __FUNCT__ "TSEvaluateWLTE"
4033 /*@
4034    TSEvaluateWLTE - Evaluate the weighted local truncation error norm
4035    at the end of a time step with a given order of accuracy.
4036 
4037    Collective on TS
4038 
4039    Input Arguments:
4040 +  ts - time stepping context
4041 .  wnormtype - norm type, either NORM_2 or NORM_INFINITY
4042 -  order - optional, desired order for the error evaluation or PETSC_DECIDE
4043 
4044    Output Arguments:
4045 +  order - optional, the actual order of the error evaluation
4046 -  wlte - the weighted local truncation error norm
4047 
4048    Level: advanced
4049 
4050    Notes:
4051    If the timestepper cannot evaluate the error in a particular step
4052    (eg. in the first step or restart steps after event handling),
4053    this routine returns wlte=-1.0 .
4054 
4055 .seealso: TSStep(), TSAdapt, TSErrorWeightedNorm()
4056 @*/
4057 PetscErrorCode TSEvaluateWLTE(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
4058 {
4059   PetscErrorCode ierr;
4060 
4061   PetscFunctionBegin;
4062   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4063   PetscValidType(ts,1);
4064   PetscValidLogicalCollectiveEnum(ts,wnormtype,4);
4065   if (order) PetscValidIntPointer(order,3);
4066   if (order) PetscValidLogicalCollectiveInt(ts,*order,3);
4067   PetscValidRealPointer(wlte,4);
4068   if (wnormtype != NORM_2 && wnormtype != NORM_INFINITY) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
4069   if (!ts->ops->evaluatewlte) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSEvaluateWLTE not implemented for type '%s'",((PetscObject)ts)->type_name);
4070   ierr = (*ts->ops->evaluatewlte)(ts,wnormtype,order,wlte);CHKERRQ(ierr);
4071   PetscFunctionReturn(0);
4072 }
4073 
4074 #undef __FUNCT__
4075 #define __FUNCT__ "TSEvaluateStep"
4076 /*@
4077    TSEvaluateStep - Evaluate the solution at the end of a time step with a given order of accuracy.
4078 
4079    Collective on TS
4080 
4081    Input Arguments:
4082 +  ts - time stepping context
4083 .  order - desired order of accuracy
4084 -  done - whether the step was evaluated at this order (pass NULL to generate an error if not available)
4085 
4086    Output Arguments:
4087 .  U - state at the end of the current step
4088 
4089    Level: advanced
4090 
4091    Notes:
4092    This function cannot be called until all stages have been evaluated.
4093    It is normally called by adaptive controllers before a step has been accepted and may also be called by the user after TSStep() has returned.
4094 
4095 .seealso: TSStep(), TSAdapt
4096 @*/
4097 PetscErrorCode TSEvaluateStep(TS ts,PetscInt order,Vec U,PetscBool *done)
4098 {
4099   PetscErrorCode ierr;
4100 
4101   PetscFunctionBegin;
4102   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4103   PetscValidType(ts,1);
4104   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
4105   if (!ts->ops->evaluatestep) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSEvaluateStep not implemented for type '%s'",((PetscObject)ts)->type_name);
4106   ierr = (*ts->ops->evaluatestep)(ts,order,U,done);CHKERRQ(ierr);
4107   PetscFunctionReturn(0);
4108 }
4109 
4110 #undef __FUNCT__
4111 #define __FUNCT__ "TSForwardCostIntegral"
4112 /*@
4113  TSForwardCostIntegral - Evaluate the cost integral in the forward run.
4114 
4115  Collective on TS
4116 
4117  Input Arguments:
4118  .  ts - time stepping context
4119 
4120  Level: advanced
4121 
4122  Notes:
4123  This function cannot be called until TSStep() has been completed.
4124 
4125  .seealso: TSSolve(), TSAdjointCostIntegral()
4126  @*/
4127 PetscErrorCode TSForwardCostIntegral(TS ts)
4128 {
4129     PetscErrorCode ierr;
4130     PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4131     if (!ts->ops->forwardintegral) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"%s does not provide integral evaluation in the forward run",((PetscObject)ts)->type_name);
4132     ierr = (*ts->ops->forwardintegral)(ts);CHKERRQ(ierr);
4133     PetscFunctionReturn(0);
4134 }
4135 
4136 #undef __FUNCT__
4137 #define __FUNCT__ "TSSolve"
4138 /*@
4139    TSSolve - Steps the requested number of timesteps.
4140 
4141    Collective on TS
4142 
4143    Input Parameter:
4144 +  ts - the TS context obtained from TSCreate()
4145 -  u - the solution vector  (can be null if TSSetSolution() was used and TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP) was not used,
4146                              otherwise must contain the initial conditions and will contain the solution at the final requested time
4147 
4148    Level: beginner
4149 
4150    Notes:
4151    The final time returned by this function may be different from the time of the internally
4152    held state accessible by TSGetSolution() and TSGetTime() because the method may have
4153    stepped over the final time.
4154 
4155 .keywords: TS, timestep, solve
4156 
4157 .seealso: TSCreate(), TSSetSolution(), TSStep(), TSGetTime(), TSGetSolveTime()
4158 @*/
4159 PetscErrorCode TSSolve(TS ts,Vec u)
4160 {
4161   Vec               solution;
4162   PetscErrorCode    ierr;
4163 
4164   PetscFunctionBegin;
4165   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4166   if (u) PetscValidHeaderSpecific(u,VEC_CLASSID,2);
4167 
4168   if (ts->exact_final_time == TS_EXACTFINALTIME_INTERPOLATE) {   /* Need ts->vec_sol to be distinct so it is not overwritten when we interpolate at the end */
4169     PetscValidHeaderSpecific(u,VEC_CLASSID,2);
4170     if (!ts->vec_sol || u == ts->vec_sol) {
4171       ierr = VecDuplicate(u,&solution);CHKERRQ(ierr);
4172       ierr = TSSetSolution(ts,solution);CHKERRQ(ierr);
4173       ierr = VecDestroy(&solution);CHKERRQ(ierr); /* grant ownership */
4174     }
4175     ierr = VecCopy(u,ts->vec_sol);CHKERRQ(ierr);
4176   } else if (u) {
4177     ierr = TSSetSolution(ts,u);CHKERRQ(ierr);
4178   }
4179   ierr = TSSetUp(ts);CHKERRQ(ierr);
4180   ierr = TSTrajectorySetUp(ts->trajectory,ts);CHKERRQ(ierr);
4181 
4182   if (ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"You must call TSSetExactFinalTime() or use -ts_exact_final_time <stepover,interpolate,matchstep> before calling TSSolve()");
4183   if (ts->exact_final_time == TS_EXACTFINALTIME_MATCHSTEP && !ts->adapt) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Since TS is not adaptive you cannot use TS_EXACTFINALTIME_MATCHSTEP, suggest TS_EXACTFINALTIME_INTERPOLATE");
4184 
4185   /* reset time step and iteration counters */
4186   ts->steps             = 0;
4187   ts->ksp_its           = 0;
4188   ts->snes_its          = 0;
4189   ts->num_snes_failures = 0;
4190   ts->reject            = 0;
4191   ts->reason            = TS_CONVERGED_ITERATING;
4192 
4193   ierr = TSViewFromOptions(ts,NULL,"-ts_view_pre");CHKERRQ(ierr);
4194 
4195   if (ts->ops->solve) { /* This private interface is transitional and should be removed when all implementations are updated. */
4196     ierr = (*ts->ops->solve)(ts);CHKERRQ(ierr);
4197     if (u) {ierr = VecCopy(ts->vec_sol,u);CHKERRQ(ierr);}
4198     ts->solvetime = ts->ptime;
4199     solution = ts->vec_sol;
4200   } else { /* Step the requested number of timesteps. */
4201     if (ts->steps >= ts->max_steps)     ts->reason = TS_CONVERGED_ITS;
4202     else if (ts->ptime >= ts->max_time) ts->reason = TS_CONVERGED_TIME;
4203     ierr = TSTrajectorySet(ts->trajectory,ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4204     ierr = TSEventInitialize(ts->event,ts,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4205     ts->steprollback = PETSC_FALSE;
4206     ts->steprestart  = PETSC_TRUE;
4207 
4208     while (!ts->reason) {
4209       ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4210       if (!ts->steprollback) {
4211         ierr = TSPreStep(ts);CHKERRQ(ierr);
4212       }
4213       ierr = TSStep(ts);CHKERRQ(ierr);
4214       if (ts->vec_costintegral && ts->costintegralfwd) { /* Must evaluate the cost integral before event is handled. The cost integral value can also be rolled back. */
4215         ierr = TSForwardCostIntegral(ts);CHKERRQ(ierr);
4216       }
4217       ierr = TSPostEvaluate(ts);CHKERRQ(ierr);
4218       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. */
4219       if (!ts->steprollback) {
4220         ierr = TSTrajectorySet(ts->trajectory,ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4221         ierr = TSPostStep(ts);CHKERRQ(ierr);
4222       }
4223     }
4224     ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
4225 
4226     if (ts->exact_final_time == TS_EXACTFINALTIME_INTERPOLATE && ts->ptime > ts->max_time) {
4227       ierr = TSInterpolate(ts,ts->max_time,u);CHKERRQ(ierr);
4228       ts->solvetime = ts->max_time;
4229       solution = u;
4230       ierr = TSMonitor(ts,-1,ts->solvetime,solution);CHKERRQ(ierr);
4231     } else {
4232       if (u) {ierr = VecCopy(ts->vec_sol,u);CHKERRQ(ierr);}
4233       ts->solvetime = ts->ptime;
4234       solution = ts->vec_sol;
4235     }
4236   }
4237 
4238   ierr = TSViewFromOptions(ts,NULL,"-ts_view");CHKERRQ(ierr);
4239   ierr = VecViewFromOptions(solution,NULL,"-ts_view_solution");CHKERRQ(ierr);
4240   ierr = PetscObjectSAWsBlock((PetscObject)ts);CHKERRQ(ierr);
4241   if (ts->adjoint_solve) {
4242     ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
4243   }
4244   PetscFunctionReturn(0);
4245 }
4246 
4247 #undef __FUNCT__
4248 #define __FUNCT__ "TSAdjointCostIntegral"
4249 /*@
4250  TSAdjointCostIntegral - Evaluate the cost integral in the adjoint run.
4251 
4252  Collective on TS
4253 
4254  Input Arguments:
4255  .  ts - time stepping context
4256 
4257  Level: advanced
4258 
4259  Notes:
4260  This function cannot be called until TSAdjointStep() has been completed.
4261 
4262  .seealso: TSAdjointSolve(), TSAdjointStep
4263  @*/
4264 PetscErrorCode TSAdjointCostIntegral(TS ts)
4265 {
4266     PetscErrorCode ierr;
4267     PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4268     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);
4269     ierr = (*ts->ops->adjointintegral)(ts);CHKERRQ(ierr);
4270     PetscFunctionReturn(0);
4271 }
4272 
4273 #undef __FUNCT__
4274 #define __FUNCT__ "TSAdjointSolve"
4275 /*@
4276    TSAdjointSolve - Solves the discrete ajoint problem for an ODE/DAE
4277 
4278    Collective on TS
4279 
4280    Input Parameter:
4281 .  ts - the TS context obtained from TSCreate()
4282 
4283    Options Database:
4284 . -ts_adjoint_view_solution <viewerinfo> - views the first gradient with respect to the initial conditions
4285 
4286    Level: intermediate
4287 
4288    Notes:
4289    This must be called after a call to TSSolve() that solves the forward problem
4290 
4291    By default this will integrate back to the initial time, one can use TSAdjointSetSteps() to step back to a later time
4292 
4293 .keywords: TS, timestep, solve
4294 
4295 .seealso: TSCreate(), TSSetCostGradients(), TSSetSolution(), TSAdjointStep()
4296 @*/
4297 PetscErrorCode TSAdjointSolve(TS ts)
4298 {
4299   PetscErrorCode    ierr;
4300 
4301   PetscFunctionBegin;
4302   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4303   ierr = TSAdjointSetUp(ts);CHKERRQ(ierr);
4304 
4305   /* reset time step and iteration counters */
4306   ts->steps             = 0;
4307   ts->ksp_its           = 0;
4308   ts->snes_its          = 0;
4309   ts->num_snes_failures = 0;
4310   ts->reject            = 0;
4311   ts->reason            = TS_CONVERGED_ITERATING;
4312 
4313   if (!ts->adjoint_max_steps) ts->adjoint_max_steps = ts->total_steps;
4314 
4315   if (ts->steps >= ts->adjoint_max_steps)     ts->reason = TS_CONVERGED_ITS;
4316   while (!ts->reason) {
4317     ierr = TSTrajectoryGet(ts->trajectory,ts,ts->total_steps,&ts->ptime);CHKERRQ(ierr);
4318     ierr = TSAdjointMonitor(ts,ts->total_steps,ts->ptime,ts->vec_sol,ts->numcost,ts->vecs_sensi,ts->vecs_sensip);CHKERRQ(ierr);
4319     ierr = TSAdjointEventHandler(ts);CHKERRQ(ierr);
4320     ierr = TSAdjointStep(ts);CHKERRQ(ierr);
4321     if (ts->vec_costintegral && !ts->costintegralfwd) {
4322       ierr = TSAdjointCostIntegral(ts);CHKERRQ(ierr);
4323     }
4324   }
4325   ierr = TSTrajectoryGet(ts->trajectory,ts,ts->total_steps,&ts->ptime);CHKERRQ(ierr);
4326   ierr = TSAdjointMonitor(ts,ts->total_steps,ts->ptime,ts->vec_sol,ts->numcost,ts->vecs_sensi,ts->vecs_sensip);CHKERRQ(ierr);
4327   ts->solvetime = ts->ptime;
4328   ierr = TSTrajectoryViewFromOptions(ts->trajectory,NULL,"-ts_trajectory_view");CHKERRQ(ierr);
4329   ierr = VecViewFromOptions(ts->vecs_sensi[0],(PetscObject) ts, "-ts_adjoint_view_solution");CHKERRQ(ierr);
4330   PetscFunctionReturn(0);
4331 }
4332 
4333 #undef __FUNCT__
4334 #define __FUNCT__ "TSMonitor"
4335 /*@C
4336    TSMonitor - Runs all user-provided monitor routines set using TSMonitorSet()
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 
4346    Notes:
4347    TSMonitor() is typically used automatically within the time stepping implementations.
4348    Users would almost never call this routine directly.
4349 
4350    A step of -1 indicates that the monitor is being called on a solution obtained by interpolating from computed solutions
4351 
4352    Level: developer
4353 
4354 .keywords: TS, timestep
4355 @*/
4356 PetscErrorCode TSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec u)
4357 {
4358   DM             dm;
4359   PetscInt       i,n = ts->numbermonitors;
4360   PetscErrorCode ierr;
4361 
4362   PetscFunctionBegin;
4363   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4364   PetscValidHeaderSpecific(u,VEC_CLASSID,4);
4365 
4366   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4367   ierr = DMSetOutputSequenceNumber(dm,step,ptime);CHKERRQ(ierr);
4368 
4369   ierr = VecLockPush(u);CHKERRQ(ierr);
4370   for (i=0; i<n; i++) {
4371     ierr = (*ts->monitor[i])(ts,step,ptime,u,ts->monitorcontext[i]);CHKERRQ(ierr);
4372   }
4373   ierr = VecLockPop(u);CHKERRQ(ierr);
4374   PetscFunctionReturn(0);
4375 }
4376 
4377 #undef __FUNCT__
4378 #define __FUNCT__ "TSAdjointMonitor"
4379 /*@C
4380    TSAdjointMonitor - Runs all user-provided adjoint monitor routines set using TSAdjointMonitorSet()
4381 
4382    Collective on TS
4383 
4384    Input Parameters:
4385 +  ts - time stepping context obtained from TSCreate()
4386 .  step - step number that has just completed
4387 .  ptime - model time of the state
4388 .  u - state at the current model time
4389 .  numcost - number of cost functions (dimension of lambda  or mu)
4390 .  lambda - vectors containing the gradients of the cost functions with respect to the ODE/DAE solution variables
4391 -  mu - vectors containing the gradients of the cost functions with respect to the problem parameters
4392 
4393    Notes:
4394    TSAdjointMonitor() is typically used automatically within the time stepping implementations.
4395    Users would almost never call this routine directly.
4396 
4397    Level: developer
4398 
4399 .keywords: TS, timestep
4400 @*/
4401 PetscErrorCode TSAdjointMonitor(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscInt numcost,Vec *lambda, Vec *mu)
4402 {
4403   PetscErrorCode ierr;
4404   PetscInt       i,n = ts->numberadjointmonitors;
4405 
4406   PetscFunctionBegin;
4407   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4408   PetscValidHeaderSpecific(u,VEC_CLASSID,4);
4409   ierr = VecLockPush(u);CHKERRQ(ierr);
4410   for (i=0; i<n; i++) {
4411     ierr = (*ts->adjointmonitor[i])(ts,step,ptime,u,numcost,lambda,mu,ts->adjointmonitorcontext[i]);CHKERRQ(ierr);
4412   }
4413   ierr = VecLockPop(u);CHKERRQ(ierr);
4414   PetscFunctionReturn(0);
4415 }
4416 
4417 /* ------------------------------------------------------------------------*/
4418 #undef __FUNCT__
4419 #define __FUNCT__ "TSMonitorLGCtxCreate"
4420 /*@C
4421    TSMonitorLGCtxCreate - Creates a TSMonitorLGCtx context for use with
4422    TS to monitor the solution process graphically in various ways
4423 
4424    Collective on TS
4425 
4426    Input Parameters:
4427 +  host - the X display to open, or null for the local machine
4428 .  label - the title to put in the title bar
4429 .  x, y - the screen coordinates of the upper left coordinate of the window
4430 .  m, n - the screen width and height in pixels
4431 -  howoften - if positive then determines the frequency of the plotting, if -1 then only at the final time
4432 
4433    Output Parameter:
4434 .  ctx - the context
4435 
4436    Options Database Key:
4437 +  -ts_monitor_lg_timestep - automatically sets line graph monitor
4438 .  -ts_monitor_lg_solution - monitor the solution (or certain values of the solution by calling TSMonitorLGSetDisplayVariables() or TSMonitorLGCtxSetDisplayVariables())
4439 .  -ts_monitor_lg_error -  monitor the error
4440 .  -ts_monitor_lg_ksp_iterations - monitor the number of KSP iterations needed for each timestep
4441 .  -ts_monitor_lg_snes_iterations - monitor the number of SNES iterations needed for each timestep
4442 -  -lg_use_markers <true,false> - mark the data points (at each time step) on the plot; default is true
4443 
4444    Notes:
4445    Use TSMonitorLGCtxDestroy() to destroy.
4446 
4447    One can provide a function that transforms the solution before plotting it with TSMonitorLGCtxSetTransform() or TSMonitorLGSetTransform()
4448 
4449    Many of the functions that control the monitoring have two forms: TSMonitorLGSet/GetXXXX() and TSMonitorLGCtxSet/GetXXXX() the first take a TS object as the
4450    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
4451    as the first argument.
4452 
4453    One can control the names displayed for each solution or error variable with TSMonitorLGCtxSetVariableNames() or TSMonitorLGSetVariableNames()
4454 
4455 
4456    Level: intermediate
4457 
4458 .keywords: TS, monitor, line graph, residual
4459 
4460 .seealso: TSMonitorLGTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError(), TSMonitorDefault(), VecView(),
4461            TSMonitorLGCtxCreate(), TSMonitorLGCtxSetVariableNames(), TSMonitorLGCtxGetVariableNames(),
4462            TSMonitorLGSetVariableNames(), TSMonitorLGGetVariableNames(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetDisplayVariables(),
4463            TSMonitorLGCtxSetTransform(), TSMonitorLGSetTransform(), TSMonitorLGError(), TSMonitorLGSNESIterations(), TSMonitorLGKSPIterations(),
4464            TSMonitorEnvelopeCtxCreate(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxDestroy(), TSMonitorEnvelop()
4465 
4466 @*/
4467 PetscErrorCode  TSMonitorLGCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorLGCtx *ctx)
4468 {
4469   PetscDraw      draw;
4470   PetscErrorCode ierr;
4471 
4472   PetscFunctionBegin;
4473   ierr = PetscNew(ctx);CHKERRQ(ierr);
4474   ierr = PetscDrawCreate(comm,host,label,x,y,m,n,&draw);CHKERRQ(ierr);
4475   ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
4476   ierr = PetscDrawLGCreate(draw,1,&(*ctx)->lg);CHKERRQ(ierr);
4477   ierr = PetscDrawLGSetFromOptions((*ctx)->lg);CHKERRQ(ierr);
4478   ierr = PetscDrawDestroy(&draw);CHKERRQ(ierr);
4479   (*ctx)->howoften = howoften;
4480   PetscFunctionReturn(0);
4481 }
4482 
4483 #undef __FUNCT__
4484 #define __FUNCT__ "TSMonitorLGTimeStep"
4485 PetscErrorCode TSMonitorLGTimeStep(TS ts,PetscInt step,PetscReal ptime,Vec v,void *monctx)
4486 {
4487   TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
4488   PetscReal      x   = ptime,y;
4489   PetscErrorCode ierr;
4490 
4491   PetscFunctionBegin;
4492   if (step < 0) PetscFunctionReturn(0); /* -1 indicates an interpolated solution */
4493   if (!step) {
4494     PetscDrawAxis axis;
4495     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
4496     ierr = PetscDrawAxisSetLabels(axis,"Timestep as function of time","Time","Time Step");CHKERRQ(ierr);
4497     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
4498   }
4499   ierr = TSGetTimeStep(ts,&y);CHKERRQ(ierr);
4500   ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
4501   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
4502     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
4503     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
4504   }
4505   PetscFunctionReturn(0);
4506 }
4507 
4508 #undef __FUNCT__
4509 #define __FUNCT__ "TSMonitorLGCtxDestroy"
4510 /*@C
4511    TSMonitorLGCtxDestroy - Destroys a line graph context that was created
4512    with TSMonitorLGCtxCreate().
4513 
4514    Collective on TSMonitorLGCtx
4515 
4516    Input Parameter:
4517 .  ctx - the monitor context
4518 
4519    Level: intermediate
4520 
4521 .keywords: TS, monitor, line graph, destroy
4522 
4523 .seealso: TSMonitorLGCtxCreate(),  TSMonitorSet(), TSMonitorLGTimeStep();
4524 @*/
4525 PetscErrorCode  TSMonitorLGCtxDestroy(TSMonitorLGCtx *ctx)
4526 {
4527   PetscErrorCode ierr;
4528 
4529   PetscFunctionBegin;
4530   if ((*ctx)->transformdestroy) {
4531     ierr = ((*ctx)->transformdestroy)((*ctx)->transformctx);CHKERRQ(ierr);
4532   }
4533   ierr = PetscDrawLGDestroy(&(*ctx)->lg);CHKERRQ(ierr);
4534   ierr = PetscStrArrayDestroy(&(*ctx)->names);CHKERRQ(ierr);
4535   ierr = PetscStrArrayDestroy(&(*ctx)->displaynames);CHKERRQ(ierr);
4536   ierr = PetscFree((*ctx)->displayvariables);CHKERRQ(ierr);
4537   ierr = PetscFree((*ctx)->displayvalues);CHKERRQ(ierr);
4538   ierr = PetscFree(*ctx);CHKERRQ(ierr);
4539   PetscFunctionReturn(0);
4540 }
4541 
4542 #undef __FUNCT__
4543 #define __FUNCT__ "TSGetTime"
4544 /*@
4545    TSGetTime - Gets the time of the most recently completed step.
4546 
4547    Not Collective
4548 
4549    Input Parameter:
4550 .  ts - the TS context obtained from TSCreate()
4551 
4552    Output Parameter:
4553 .  t  - the current time. This time may not corresponds to the final time set with TSSetDuration(), use TSGetSolveTime().
4554 
4555    Level: beginner
4556 
4557    Note:
4558    When called during time step evaluation (e.g. during residual evaluation or via hooks set using TSSetPreStep(),
4559    TSSetPreStage(), TSSetPostStage(), or TSSetPostStep()), the time is the time at the start of the step being evaluated.
4560 
4561 .seealso: TSSetInitialTimeStep(), TSGetTimeStep(), TSGetSolveTime()
4562 
4563 .keywords: TS, get, time
4564 @*/
4565 PetscErrorCode  TSGetTime(TS ts,PetscReal *t)
4566 {
4567   PetscFunctionBegin;
4568   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4569   PetscValidRealPointer(t,2);
4570   *t = ts->ptime;
4571   PetscFunctionReturn(0);
4572 }
4573 
4574 #undef __FUNCT__
4575 #define __FUNCT__ "TSGetPrevTime"
4576 /*@
4577    TSGetPrevTime - Gets the starting time of the previously completed step.
4578 
4579    Not Collective
4580 
4581    Input Parameter:
4582 .  ts - the TS context obtained from TSCreate()
4583 
4584    Output Parameter:
4585 .  t  - the previous time
4586 
4587    Level: beginner
4588 
4589 .seealso: TSSetInitialTimeStep(), TSGetTimeStep()
4590 
4591 .keywords: TS, get, time
4592 @*/
4593 PetscErrorCode  TSGetPrevTime(TS ts,PetscReal *t)
4594 {
4595   PetscFunctionBegin;
4596   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4597   PetscValidRealPointer(t,2);
4598   *t = ts->ptime_prev;
4599   PetscFunctionReturn(0);
4600 }
4601 
4602 #undef __FUNCT__
4603 #define __FUNCT__ "TSSetTime"
4604 /*@
4605    TSSetTime - Allows one to reset the time.
4606 
4607    Logically Collective on TS
4608 
4609    Input Parameters:
4610 +  ts - the TS context obtained from TSCreate()
4611 -  time - the time
4612 
4613    Level: intermediate
4614 
4615 .seealso: TSGetTime(), TSSetDuration()
4616 
4617 .keywords: TS, set, time
4618 @*/
4619 PetscErrorCode  TSSetTime(TS ts, PetscReal t)
4620 {
4621   PetscFunctionBegin;
4622   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4623   PetscValidLogicalCollectiveReal(ts,t,2);
4624   ts->ptime = t;
4625   PetscFunctionReturn(0);
4626 }
4627 
4628 #undef __FUNCT__
4629 #define __FUNCT__ "TSSetOptionsPrefix"
4630 /*@C
4631    TSSetOptionsPrefix - Sets the prefix used for searching for all
4632    TS options in the database.
4633 
4634    Logically Collective on TS
4635 
4636    Input Parameter:
4637 +  ts     - The TS context
4638 -  prefix - The prefix to prepend to all option names
4639 
4640    Notes:
4641    A hyphen (-) must NOT be given at the beginning of the prefix name.
4642    The first character of all runtime options is AUTOMATICALLY the
4643    hyphen.
4644 
4645    Level: advanced
4646 
4647 .keywords: TS, set, options, prefix, database
4648 
4649 .seealso: TSSetFromOptions()
4650 
4651 @*/
4652 PetscErrorCode  TSSetOptionsPrefix(TS ts,const char prefix[])
4653 {
4654   PetscErrorCode ierr;
4655   SNES           snes;
4656 
4657   PetscFunctionBegin;
4658   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4659   ierr = PetscObjectSetOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
4660   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4661   ierr = SNESSetOptionsPrefix(snes,prefix);CHKERRQ(ierr);
4662   PetscFunctionReturn(0);
4663 }
4664 
4665 
4666 #undef __FUNCT__
4667 #define __FUNCT__ "TSAppendOptionsPrefix"
4668 /*@C
4669    TSAppendOptionsPrefix - Appends to the prefix used for searching for all
4670    TS options in the database.
4671 
4672    Logically Collective on TS
4673 
4674    Input Parameter:
4675 +  ts     - The TS context
4676 -  prefix - The prefix to prepend to all option names
4677 
4678    Notes:
4679    A hyphen (-) must NOT be given at the beginning of the prefix name.
4680    The first character of all runtime options is AUTOMATICALLY the
4681    hyphen.
4682 
4683    Level: advanced
4684 
4685 .keywords: TS, append, options, prefix, database
4686 
4687 .seealso: TSGetOptionsPrefix()
4688 
4689 @*/
4690 PetscErrorCode  TSAppendOptionsPrefix(TS ts,const char prefix[])
4691 {
4692   PetscErrorCode ierr;
4693   SNES           snes;
4694 
4695   PetscFunctionBegin;
4696   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4697   ierr = PetscObjectAppendOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
4698   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4699   ierr = SNESAppendOptionsPrefix(snes,prefix);CHKERRQ(ierr);
4700   PetscFunctionReturn(0);
4701 }
4702 
4703 #undef __FUNCT__
4704 #define __FUNCT__ "TSGetOptionsPrefix"
4705 /*@C
4706    TSGetOptionsPrefix - Sets the prefix used for searching for all
4707    TS options in the database.
4708 
4709    Not Collective
4710 
4711    Input Parameter:
4712 .  ts - The TS context
4713 
4714    Output Parameter:
4715 .  prefix - A pointer to the prefix string used
4716 
4717    Notes: On the fortran side, the user should pass in a string 'prifix' of
4718    sufficient length to hold the prefix.
4719 
4720    Level: intermediate
4721 
4722 .keywords: TS, get, options, prefix, database
4723 
4724 .seealso: TSAppendOptionsPrefix()
4725 @*/
4726 PetscErrorCode  TSGetOptionsPrefix(TS ts,const char *prefix[])
4727 {
4728   PetscErrorCode ierr;
4729 
4730   PetscFunctionBegin;
4731   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
4732   PetscValidPointer(prefix,2);
4733   ierr = PetscObjectGetOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
4734   PetscFunctionReturn(0);
4735 }
4736 
4737 #undef __FUNCT__
4738 #define __FUNCT__ "TSGetRHSJacobian"
4739 /*@C
4740    TSGetRHSJacobian - Returns the Jacobian J at the present timestep.
4741 
4742    Not Collective, but parallel objects are returned if TS is parallel
4743 
4744    Input Parameter:
4745 .  ts  - The TS context obtained from TSCreate()
4746 
4747    Output Parameters:
4748 +  Amat - The (approximate) Jacobian J of G, where U_t = G(U,t)  (or NULL)
4749 .  Pmat - The matrix from which the preconditioner is constructed, usually the same as Amat  (or NULL)
4750 .  func - Function to compute the Jacobian of the RHS  (or NULL)
4751 -  ctx - User-defined context for Jacobian evaluation routine  (or NULL)
4752 
4753    Notes: You can pass in NULL for any return argument you do not need.
4754 
4755    Level: intermediate
4756 
4757 .seealso: TSGetTimeStep(), TSGetMatrices(), TSGetTime(), TSGetTimeStepNumber()
4758 
4759 .keywords: TS, timestep, get, matrix, Jacobian
4760 @*/
4761 PetscErrorCode  TSGetRHSJacobian(TS ts,Mat *Amat,Mat *Pmat,TSRHSJacobian *func,void **ctx)
4762 {
4763   PetscErrorCode ierr;
4764   SNES           snes;
4765   DM             dm;
4766 
4767   PetscFunctionBegin;
4768   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4769   ierr = SNESGetJacobian(snes,Amat,Pmat,NULL,NULL);CHKERRQ(ierr);
4770   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4771   ierr = DMTSGetRHSJacobian(dm,func,ctx);CHKERRQ(ierr);
4772   PetscFunctionReturn(0);
4773 }
4774 
4775 #undef __FUNCT__
4776 #define __FUNCT__ "TSGetIJacobian"
4777 /*@C
4778    TSGetIJacobian - Returns the implicit Jacobian at the present timestep.
4779 
4780    Not Collective, but parallel objects are returned if TS is parallel
4781 
4782    Input Parameter:
4783 .  ts  - The TS context obtained from TSCreate()
4784 
4785    Output Parameters:
4786 +  Amat  - The (approximate) Jacobian of F(t,U,U_t)
4787 .  Pmat - The matrix from which the preconditioner is constructed, often the same as Amat
4788 .  f   - The function to compute the matrices
4789 - ctx - User-defined context for Jacobian evaluation routine
4790 
4791    Notes: You can pass in NULL for any return argument you do not need.
4792 
4793    Level: advanced
4794 
4795 .seealso: TSGetTimeStep(), TSGetRHSJacobian(), TSGetMatrices(), TSGetTime(), TSGetTimeStepNumber()
4796 
4797 .keywords: TS, timestep, get, matrix, Jacobian
4798 @*/
4799 PetscErrorCode  TSGetIJacobian(TS ts,Mat *Amat,Mat *Pmat,TSIJacobian *f,void **ctx)
4800 {
4801   PetscErrorCode ierr;
4802   SNES           snes;
4803   DM             dm;
4804 
4805   PetscFunctionBegin;
4806   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
4807   ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr);
4808   ierr = SNESGetJacobian(snes,Amat,Pmat,NULL,NULL);CHKERRQ(ierr);
4809   ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
4810   ierr = DMTSGetIJacobian(dm,f,ctx);CHKERRQ(ierr);
4811   PetscFunctionReturn(0);
4812 }
4813 
4814 
4815 #undef __FUNCT__
4816 #define __FUNCT__ "TSMonitorDrawSolution"
4817 /*@C
4818    TSMonitorDrawSolution - Monitors progress of the TS solvers by calling
4819    VecView() for the solution at each timestep
4820 
4821    Collective on TS
4822 
4823    Input Parameters:
4824 +  ts - the TS context
4825 .  step - current time-step
4826 .  ptime - current time
4827 -  dummy - either a viewer or NULL
4828 
4829    Options Database:
4830 .   -ts_monitor_draw_solution_initial - show initial solution as well as current solution
4831 
4832    Notes: the initial solution and current solution are not display with a common axis scaling so generally the option -ts_monitor_draw_solution_initial
4833        will look bad
4834 
4835    Level: intermediate
4836 
4837 .keywords: TS,  vector, monitor, view
4838 
4839 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
4840 @*/
4841 PetscErrorCode  TSMonitorDrawSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
4842 {
4843   PetscErrorCode   ierr;
4844   TSMonitorDrawCtx ictx = (TSMonitorDrawCtx)dummy;
4845   PetscDraw        draw;
4846 
4847   PetscFunctionBegin;
4848   if (!step && ictx->showinitial) {
4849     if (!ictx->initialsolution) {
4850       ierr = VecDuplicate(u,&ictx->initialsolution);CHKERRQ(ierr);
4851     }
4852     ierr = VecCopy(u,ictx->initialsolution);CHKERRQ(ierr);
4853   }
4854   if (!(((ictx->howoften > 0) && (!(step % ictx->howoften))) || ((ictx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);
4855 
4856   if (ictx->showinitial) {
4857     PetscReal pause;
4858     ierr = PetscViewerDrawGetPause(ictx->viewer,&pause);CHKERRQ(ierr);
4859     ierr = PetscViewerDrawSetPause(ictx->viewer,0.0);CHKERRQ(ierr);
4860     ierr = VecView(ictx->initialsolution,ictx->viewer);CHKERRQ(ierr);
4861     ierr = PetscViewerDrawSetPause(ictx->viewer,pause);CHKERRQ(ierr);
4862     ierr = PetscViewerDrawSetHold(ictx->viewer,PETSC_TRUE);CHKERRQ(ierr);
4863   }
4864   ierr = VecView(u,ictx->viewer);CHKERRQ(ierr);
4865   if (ictx->showtimestepandtime) {
4866     PetscReal xl,yl,xr,yr,h;
4867     char      time[32];
4868 
4869     ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
4870     ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
4871     ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
4872     h    = yl + .95*(yr - yl);
4873     ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
4874     ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
4875   }
4876 
4877   if (ictx->showinitial) {
4878     ierr = PetscViewerDrawSetHold(ictx->viewer,PETSC_FALSE);CHKERRQ(ierr);
4879   }
4880   PetscFunctionReturn(0);
4881 }
4882 
4883 #undef __FUNCT__
4884 #define __FUNCT__ "TSAdjointMonitorDrawSensi"
4885 /*@C
4886    TSAdjointMonitorDrawSensi - Monitors progress of the adjoint TS solvers by calling
4887    VecView() for the sensitivities to initial states at each timestep
4888 
4889    Collective on TS
4890 
4891    Input Parameters:
4892 +  ts - the TS context
4893 .  step - current time-step
4894 .  ptime - current time
4895 .  u - current state
4896 .  numcost - number of cost functions
4897 .  lambda - sensitivities to initial conditions
4898 .  mu - sensitivities to parameters
4899 -  dummy - either a viewer or NULL
4900 
4901    Level: intermediate
4902 
4903 .keywords: TS,  vector, adjoint, monitor, view
4904 
4905 .seealso: TSAdjointMonitorSet(), TSAdjointMonitorDefault(), VecView()
4906 @*/
4907 PetscErrorCode  TSAdjointMonitorDrawSensi(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscInt numcost,Vec *lambda,Vec *mu,void *dummy)
4908 {
4909   PetscErrorCode   ierr;
4910   TSMonitorDrawCtx ictx = (TSMonitorDrawCtx)dummy;
4911   PetscDraw        draw;
4912   PetscReal        xl,yl,xr,yr,h;
4913   char             time[32];
4914 
4915   PetscFunctionBegin;
4916   if (!(((ictx->howoften > 0) && (!(step % ictx->howoften))) || ((ictx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);
4917 
4918   ierr = VecView(lambda[0],ictx->viewer);CHKERRQ(ierr);
4919   ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
4920   ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
4921   ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
4922   h    = yl + .95*(yr - yl);
4923   ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
4924   ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
4925   PetscFunctionReturn(0);
4926 }
4927 
4928 #undef __FUNCT__
4929 #define __FUNCT__ "TSMonitorDrawSolutionPhase"
4930 /*@C
4931    TSMonitorDrawSolutionPhase - Monitors progress of the TS solvers by plotting the solution as a phase diagram
4932 
4933    Collective on TS
4934 
4935    Input Parameters:
4936 +  ts - the TS context
4937 .  step - current time-step
4938 .  ptime - current time
4939 -  dummy - either a viewer or NULL
4940 
4941    Level: intermediate
4942 
4943 .keywords: TS,  vector, monitor, view
4944 
4945 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
4946 @*/
4947 PetscErrorCode  TSMonitorDrawSolutionPhase(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
4948 {
4949   PetscErrorCode    ierr;
4950   TSMonitorDrawCtx  ictx = (TSMonitorDrawCtx)dummy;
4951   PetscDraw         draw;
4952   PetscDrawAxis     axis;
4953   PetscInt          n;
4954   PetscMPIInt       size;
4955   PetscReal         U0,U1,xl,yl,xr,yr,h;
4956   char              time[32];
4957   const PetscScalar *U;
4958 
4959   PetscFunctionBegin;
4960   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)ts),&size);CHKERRQ(ierr);
4961   if (size != 1) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Only allowed for sequential runs");
4962   ierr = VecGetSize(u,&n);CHKERRQ(ierr);
4963   if (n != 2) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Only for ODEs with two unknowns");
4964 
4965   ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
4966   ierr = PetscViewerDrawGetDrawAxis(ictx->viewer,0,&axis);CHKERRQ(ierr);
4967   ierr = PetscDrawAxisGetLimits(axis,&xl,&xr,&yl,&yr);CHKERRQ(ierr);
4968   if (!step) {
4969     ierr = PetscDrawClear(draw);CHKERRQ(ierr);
4970     ierr = PetscDrawAxisDraw(axis);CHKERRQ(ierr);
4971   }
4972 
4973   ierr = VecGetArrayRead(u,&U);CHKERRQ(ierr);
4974   U0 = PetscRealPart(U[0]);
4975   U1 = PetscRealPart(U[1]);
4976   ierr = VecRestoreArrayRead(u,&U);CHKERRQ(ierr);
4977   if ((U0 < xl) || (U1 < yl) || (U0 > xr) || (U1 > yr)) PetscFunctionReturn(0);
4978 
4979   ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
4980   ierr = PetscDrawPoint(draw,U0,U1,PETSC_DRAW_BLACK);CHKERRQ(ierr);
4981   if (ictx->showtimestepandtime) {
4982     ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
4983     ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
4984     h    = yl + .95*(yr - yl);
4985     ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
4986   }
4987   ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
4988   ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
4989   ierr = PetscDrawSave(draw);CHKERRQ(ierr);
4990   PetscFunctionReturn(0);
4991 }
4992 
4993 
4994 #undef __FUNCT__
4995 #define __FUNCT__ "TSMonitorDrawCtxDestroy"
4996 /*@C
4997    TSMonitorDrawCtxDestroy - Destroys the monitor context for TSMonitorDrawSolution()
4998 
4999    Collective on TS
5000 
5001    Input Parameters:
5002 .    ctx - the monitor context
5003 
5004    Level: intermediate
5005 
5006 .keywords: TS,  vector, monitor, view
5007 
5008 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorDrawSolution(), TSMonitorDrawError()
5009 @*/
5010 PetscErrorCode  TSMonitorDrawCtxDestroy(TSMonitorDrawCtx *ictx)
5011 {
5012   PetscErrorCode ierr;
5013 
5014   PetscFunctionBegin;
5015   ierr = PetscViewerDestroy(&(*ictx)->viewer);CHKERRQ(ierr);
5016   ierr = VecDestroy(&(*ictx)->initialsolution);CHKERRQ(ierr);
5017   ierr = PetscFree(*ictx);CHKERRQ(ierr);
5018   PetscFunctionReturn(0);
5019 }
5020 
5021 #undef __FUNCT__
5022 #define __FUNCT__ "TSMonitorDrawCtxCreate"
5023 /*@C
5024    TSMonitorDrawCtxCreate - Creates the monitor context for TSMonitorDrawCtx
5025 
5026    Collective on TS
5027 
5028    Input Parameter:
5029 .    ts - time-step context
5030 
5031    Output Patameter:
5032 .    ctx - the monitor context
5033 
5034    Options Database:
5035 .   -ts_monitor_draw_solution_initial - show initial solution as well as current solution
5036 
5037    Level: intermediate
5038 
5039 .keywords: TS,  vector, monitor, view
5040 
5041 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorDrawCtx()
5042 @*/
5043 PetscErrorCode  TSMonitorDrawCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorDrawCtx *ctx)
5044 {
5045   PetscErrorCode   ierr;
5046 
5047   PetscFunctionBegin;
5048   ierr = PetscNew(ctx);CHKERRQ(ierr);
5049   ierr = PetscViewerDrawOpen(comm,host,label,x,y,m,n,&(*ctx)->viewer);CHKERRQ(ierr);
5050   ierr = PetscViewerSetFromOptions((*ctx)->viewer);CHKERRQ(ierr);
5051 
5052   (*ctx)->howoften    = howoften;
5053   (*ctx)->showinitial = PETSC_FALSE;
5054   ierr = PetscOptionsGetBool(NULL,NULL,"-ts_monitor_draw_solution_initial",&(*ctx)->showinitial,NULL);CHKERRQ(ierr);
5055 
5056   (*ctx)->showtimestepandtime = PETSC_FALSE;
5057   ierr = PetscOptionsGetBool(NULL,NULL,"-ts_monitor_draw_solution_show_time",&(*ctx)->showtimestepandtime,NULL);CHKERRQ(ierr);
5058   PetscFunctionReturn(0);
5059 }
5060 
5061 #undef __FUNCT__
5062 #define __FUNCT__ "TSMonitorDrawError"
5063 /*@C
5064    TSMonitorDrawError - Monitors progress of the TS solvers by calling
5065    VecView() for the error at each timestep
5066 
5067    Collective on TS
5068 
5069    Input Parameters:
5070 +  ts - the TS context
5071 .  step - current time-step
5072 .  ptime - current time
5073 -  dummy - either a viewer or NULL
5074 
5075    Level: intermediate
5076 
5077 .keywords: TS,  vector, monitor, view
5078 
5079 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
5080 @*/
5081 PetscErrorCode  TSMonitorDrawError(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
5082 {
5083   PetscErrorCode   ierr;
5084   TSMonitorDrawCtx ctx    = (TSMonitorDrawCtx)dummy;
5085   PetscViewer      viewer = ctx->viewer;
5086   Vec              work;
5087 
5088   PetscFunctionBegin;
5089   if (!(((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);
5090   ierr = VecDuplicate(u,&work);CHKERRQ(ierr);
5091   ierr = TSComputeSolutionFunction(ts,ptime,work);CHKERRQ(ierr);
5092   ierr = VecAXPY(work,-1.0,u);CHKERRQ(ierr);
5093   ierr = VecView(work,viewer);CHKERRQ(ierr);
5094   ierr = VecDestroy(&work);CHKERRQ(ierr);
5095   PetscFunctionReturn(0);
5096 }
5097 
5098 #include <petsc/private/dmimpl.h>
5099 #undef __FUNCT__
5100 #define __FUNCT__ "TSSetDM"
5101 /*@
5102    TSSetDM - Sets the DM that may be used by some nonlinear solvers or preconditioners under the TS
5103 
5104    Logically Collective on TS and DM
5105 
5106    Input Parameters:
5107 +  ts - the ODE integrator object
5108 -  dm - the dm, cannot be NULL
5109 
5110    Level: intermediate
5111 
5112 
5113 .seealso: TSGetDM(), SNESSetDM(), SNESGetDM()
5114 @*/
5115 PetscErrorCode  TSSetDM(TS ts,DM dm)
5116 {
5117   PetscErrorCode ierr;
5118   SNES           snes;
5119   DMTS           tsdm;
5120 
5121   PetscFunctionBegin;
5122   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5123   PetscValidHeaderSpecific(dm,DM_CLASSID,2);
5124   ierr = PetscObjectReference((PetscObject)dm);CHKERRQ(ierr);
5125   if (ts->dm) {               /* Move the DMTS context over to the new DM unless the new DM already has one */
5126     if (ts->dm->dmts && !dm->dmts) {
5127       ierr = DMCopyDMTS(ts->dm,dm);CHKERRQ(ierr);
5128       ierr = DMGetDMTS(ts->dm,&tsdm);CHKERRQ(ierr);
5129       if (tsdm->originaldm == ts->dm) { /* Grant write privileges to the replacement DM */
5130         tsdm->originaldm = dm;
5131       }
5132     }
5133     ierr = DMDestroy(&ts->dm);CHKERRQ(ierr);
5134   }
5135   ts->dm = dm;
5136 
5137   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
5138   ierr = SNESSetDM(snes,dm);CHKERRQ(ierr);
5139   PetscFunctionReturn(0);
5140 }
5141 
5142 #undef __FUNCT__
5143 #define __FUNCT__ "TSGetDM"
5144 /*@
5145    TSGetDM - Gets the DM that may be used by some preconditioners
5146 
5147    Not Collective
5148 
5149    Input Parameter:
5150 . ts - the preconditioner context
5151 
5152    Output Parameter:
5153 .  dm - the dm
5154 
5155    Level: intermediate
5156 
5157 
5158 .seealso: TSSetDM(), SNESSetDM(), SNESGetDM()
5159 @*/
5160 PetscErrorCode  TSGetDM(TS ts,DM *dm)
5161 {
5162   PetscErrorCode ierr;
5163 
5164   PetscFunctionBegin;
5165   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5166   if (!ts->dm) {
5167     ierr = DMShellCreate(PetscObjectComm((PetscObject)ts),&ts->dm);CHKERRQ(ierr);
5168     if (ts->snes) {ierr = SNESSetDM(ts->snes,ts->dm);CHKERRQ(ierr);}
5169   }
5170   *dm = ts->dm;
5171   PetscFunctionReturn(0);
5172 }
5173 
5174 #undef __FUNCT__
5175 #define __FUNCT__ "SNESTSFormFunction"
5176 /*@
5177    SNESTSFormFunction - Function to evaluate nonlinear residual
5178 
5179    Logically Collective on SNES
5180 
5181    Input Parameter:
5182 + snes - nonlinear solver
5183 . U - the current state at which to evaluate the residual
5184 - ctx - user context, must be a TS
5185 
5186    Output Parameter:
5187 . F - the nonlinear residual
5188 
5189    Notes:
5190    This function is not normally called by users and is automatically registered with the SNES used by TS.
5191    It is most frequently passed to MatFDColoringSetFunction().
5192 
5193    Level: advanced
5194 
5195 .seealso: SNESSetFunction(), MatFDColoringSetFunction()
5196 @*/
5197 PetscErrorCode  SNESTSFormFunction(SNES snes,Vec U,Vec F,void *ctx)
5198 {
5199   TS             ts = (TS)ctx;
5200   PetscErrorCode ierr;
5201 
5202   PetscFunctionBegin;
5203   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
5204   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
5205   PetscValidHeaderSpecific(F,VEC_CLASSID,3);
5206   PetscValidHeaderSpecific(ts,TS_CLASSID,4);
5207   ierr = (ts->ops->snesfunction)(snes,U,F,ts);CHKERRQ(ierr);
5208   PetscFunctionReturn(0);
5209 }
5210 
5211 #undef __FUNCT__
5212 #define __FUNCT__ "SNESTSFormJacobian"
5213 /*@
5214    SNESTSFormJacobian - Function to evaluate the Jacobian
5215 
5216    Collective on SNES
5217 
5218    Input Parameter:
5219 + snes - nonlinear solver
5220 . U - the current state at which to evaluate the residual
5221 - ctx - user context, must be a TS
5222 
5223    Output Parameter:
5224 + A - the Jacobian
5225 . B - the preconditioning matrix (may be the same as A)
5226 - flag - indicates any structure change in the matrix
5227 
5228    Notes:
5229    This function is not normally called by users and is automatically registered with the SNES used by TS.
5230 
5231    Level: developer
5232 
5233 .seealso: SNESSetJacobian()
5234 @*/
5235 PetscErrorCode  SNESTSFormJacobian(SNES snes,Vec U,Mat A,Mat B,void *ctx)
5236 {
5237   TS             ts = (TS)ctx;
5238   PetscErrorCode ierr;
5239 
5240   PetscFunctionBegin;
5241   PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
5242   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
5243   PetscValidPointer(A,3);
5244   PetscValidHeaderSpecific(A,MAT_CLASSID,3);
5245   PetscValidPointer(B,4);
5246   PetscValidHeaderSpecific(B,MAT_CLASSID,4);
5247   PetscValidHeaderSpecific(ts,TS_CLASSID,6);
5248   ierr = (ts->ops->snesjacobian)(snes,U,A,B,ts);CHKERRQ(ierr);
5249   PetscFunctionReturn(0);
5250 }
5251 
5252 #undef __FUNCT__
5253 #define __FUNCT__ "TSComputeRHSFunctionLinear"
5254 /*@C
5255    TSComputeRHSFunctionLinear - Evaluate the right hand side via the user-provided Jacobian, for linear problems Udot = A U only
5256 
5257    Collective on TS
5258 
5259    Input Arguments:
5260 +  ts - time stepping context
5261 .  t - time at which to evaluate
5262 .  U - state at which to evaluate
5263 -  ctx - context
5264 
5265    Output Arguments:
5266 .  F - right hand side
5267 
5268    Level: intermediate
5269 
5270    Notes:
5271    This function is intended to be passed to TSSetRHSFunction() to evaluate the right hand side for linear problems.
5272    The matrix (and optionally the evaluation context) should be passed to TSSetRHSJacobian().
5273 
5274 .seealso: TSSetRHSFunction(), TSSetRHSJacobian(), TSComputeRHSJacobianConstant()
5275 @*/
5276 PetscErrorCode TSComputeRHSFunctionLinear(TS ts,PetscReal t,Vec U,Vec F,void *ctx)
5277 {
5278   PetscErrorCode ierr;
5279   Mat            Arhs,Brhs;
5280 
5281   PetscFunctionBegin;
5282   ierr = TSGetRHSMats_Private(ts,&Arhs,&Brhs);CHKERRQ(ierr);
5283   ierr = TSComputeRHSJacobian(ts,t,U,Arhs,Brhs);CHKERRQ(ierr);
5284   ierr = MatMult(Arhs,U,F);CHKERRQ(ierr);
5285   PetscFunctionReturn(0);
5286 }
5287 
5288 #undef __FUNCT__
5289 #define __FUNCT__ "TSComputeRHSJacobianConstant"
5290 /*@C
5291    TSComputeRHSJacobianConstant - Reuses a Jacobian that is time-independent.
5292 
5293    Collective on TS
5294 
5295    Input Arguments:
5296 +  ts - time stepping context
5297 .  t - time at which to evaluate
5298 .  U - state at which to evaluate
5299 -  ctx - context
5300 
5301    Output Arguments:
5302 +  A - pointer to operator
5303 .  B - pointer to preconditioning matrix
5304 -  flg - matrix structure flag
5305 
5306    Level: intermediate
5307 
5308    Notes:
5309    This function is intended to be passed to TSSetRHSJacobian() to evaluate the Jacobian for linear time-independent problems.
5310 
5311 .seealso: TSSetRHSFunction(), TSSetRHSJacobian(), TSComputeRHSFunctionLinear()
5312 @*/
5313 PetscErrorCode TSComputeRHSJacobianConstant(TS ts,PetscReal t,Vec U,Mat A,Mat B,void *ctx)
5314 {
5315   PetscFunctionBegin;
5316   PetscFunctionReturn(0);
5317 }
5318 
5319 #undef __FUNCT__
5320 #define __FUNCT__ "TSComputeIFunctionLinear"
5321 /*@C
5322    TSComputeIFunctionLinear - Evaluate the left hand side via the user-provided Jacobian, for linear problems only
5323 
5324    Collective on TS
5325 
5326    Input Arguments:
5327 +  ts - time stepping context
5328 .  t - time at which to evaluate
5329 .  U - state at which to evaluate
5330 .  Udot - time derivative of state vector
5331 -  ctx - context
5332 
5333    Output Arguments:
5334 .  F - left hand side
5335 
5336    Level: intermediate
5337 
5338    Notes:
5339    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
5340    user is required to write their own TSComputeIFunction.
5341    This function is intended to be passed to TSSetIFunction() to evaluate the left hand side for linear problems.
5342    The matrix (and optionally the evaluation context) should be passed to TSSetIJacobian().
5343 
5344    Note that using this function is NOT equivalent to using TSComputeRHSFunctionLinear() since that solves Udot = A U
5345 
5346 .seealso: TSSetIFunction(), TSSetIJacobian(), TSComputeIJacobianConstant(), TSComputeRHSFunctionLinear()
5347 @*/
5348 PetscErrorCode TSComputeIFunctionLinear(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
5349 {
5350   PetscErrorCode ierr;
5351   Mat            A,B;
5352 
5353   PetscFunctionBegin;
5354   ierr = TSGetIJacobian(ts,&A,&B,NULL,NULL);CHKERRQ(ierr);
5355   ierr = TSComputeIJacobian(ts,t,U,Udot,1.0,A,B,PETSC_TRUE);CHKERRQ(ierr);
5356   ierr = MatMult(A,Udot,F);CHKERRQ(ierr);
5357   PetscFunctionReturn(0);
5358 }
5359 
5360 #undef __FUNCT__
5361 #define __FUNCT__ "TSComputeIJacobianConstant"
5362 /*@C
5363    TSComputeIJacobianConstant - Reuses a time-independent for a semi-implicit DAE or ODE
5364 
5365    Collective on TS
5366 
5367    Input Arguments:
5368 +  ts - time stepping context
5369 .  t - time at which to evaluate
5370 .  U - state at which to evaluate
5371 .  Udot - time derivative of state vector
5372 .  shift - shift to apply
5373 -  ctx - context
5374 
5375    Output Arguments:
5376 +  A - pointer to operator
5377 .  B - pointer to preconditioning matrix
5378 -  flg - matrix structure flag
5379 
5380    Level: advanced
5381 
5382    Notes:
5383    This function is intended to be passed to TSSetIJacobian() to evaluate the Jacobian for linear time-independent problems.
5384 
5385    It is only appropriate for problems of the form
5386 
5387 $     M Udot = F(U,t)
5388 
5389   where M is constant and F is non-stiff.  The user must pass M to TSSetIJacobian().  The current implementation only
5390   works with IMEX time integration methods such as TSROSW and TSARKIMEX, since there is no support for de-constructing
5391   an implicit operator of the form
5392 
5393 $    shift*M + J
5394 
5395   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
5396   a copy of M or reassemble it when requested.
5397 
5398 .seealso: TSSetIFunction(), TSSetIJacobian(), TSComputeIFunctionLinear()
5399 @*/
5400 PetscErrorCode TSComputeIJacobianConstant(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat A,Mat B,void *ctx)
5401 {
5402   PetscErrorCode ierr;
5403 
5404   PetscFunctionBegin;
5405   ierr = MatScale(A, shift / ts->ijacobian.shift);CHKERRQ(ierr);
5406   ts->ijacobian.shift = shift;
5407   PetscFunctionReturn(0);
5408 }
5409 
5410 #undef __FUNCT__
5411 #define __FUNCT__ "TSGetEquationType"
5412 /*@
5413    TSGetEquationType - Gets the type of the equation that TS is solving.
5414 
5415    Not Collective
5416 
5417    Input Parameter:
5418 .  ts - the TS context
5419 
5420    Output Parameter:
5421 .  equation_type - see TSEquationType
5422 
5423    Level: beginner
5424 
5425 .keywords: TS, equation type
5426 
5427 .seealso: TSSetEquationType(), TSEquationType
5428 @*/
5429 PetscErrorCode  TSGetEquationType(TS ts,TSEquationType *equation_type)
5430 {
5431   PetscFunctionBegin;
5432   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5433   PetscValidPointer(equation_type,2);
5434   *equation_type = ts->equation_type;
5435   PetscFunctionReturn(0);
5436 }
5437 
5438 #undef __FUNCT__
5439 #define __FUNCT__ "TSSetEquationType"
5440 /*@
5441    TSSetEquationType - Sets the type of the equation that TS is solving.
5442 
5443    Not Collective
5444 
5445    Input Parameter:
5446 +  ts - the TS context
5447 -  equation_type - see TSEquationType
5448 
5449    Level: advanced
5450 
5451 .keywords: TS, equation type
5452 
5453 .seealso: TSGetEquationType(), TSEquationType
5454 @*/
5455 PetscErrorCode  TSSetEquationType(TS ts,TSEquationType equation_type)
5456 {
5457   PetscFunctionBegin;
5458   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5459   ts->equation_type = equation_type;
5460   PetscFunctionReturn(0);
5461 }
5462 
5463 #undef __FUNCT__
5464 #define __FUNCT__ "TSGetConvergedReason"
5465 /*@
5466    TSGetConvergedReason - Gets the reason the TS iteration was stopped.
5467 
5468    Not Collective
5469 
5470    Input Parameter:
5471 .  ts - the TS context
5472 
5473    Output Parameter:
5474 .  reason - negative value indicates diverged, positive value converged, see TSConvergedReason or the
5475             manual pages for the individual convergence tests for complete lists
5476 
5477    Level: beginner
5478 
5479    Notes:
5480    Can only be called after the call to TSSolve() is complete.
5481 
5482 .keywords: TS, nonlinear, set, convergence, test
5483 
5484 .seealso: TSSetConvergenceTest(), TSConvergedReason
5485 @*/
5486 PetscErrorCode  TSGetConvergedReason(TS ts,TSConvergedReason *reason)
5487 {
5488   PetscFunctionBegin;
5489   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5490   PetscValidPointer(reason,2);
5491   *reason = ts->reason;
5492   PetscFunctionReturn(0);
5493 }
5494 
5495 #undef __FUNCT__
5496 #define __FUNCT__ "TSSetConvergedReason"
5497 /*@
5498    TSSetConvergedReason - Sets the reason for handling the convergence of TSSolve.
5499 
5500    Not Collective
5501 
5502    Input Parameter:
5503 +  ts - the TS context
5504 .  reason - negative value indicates diverged, positive value converged, see TSConvergedReason or the
5505             manual pages for the individual convergence tests for complete lists
5506 
5507    Level: advanced
5508 
5509    Notes:
5510    Can only be called during TSSolve() is active.
5511 
5512 .keywords: TS, nonlinear, set, convergence, test
5513 
5514 .seealso: TSConvergedReason
5515 @*/
5516 PetscErrorCode  TSSetConvergedReason(TS ts,TSConvergedReason reason)
5517 {
5518   PetscFunctionBegin;
5519   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5520   ts->reason = reason;
5521   PetscFunctionReturn(0);
5522 }
5523 
5524 #undef __FUNCT__
5525 #define __FUNCT__ "TSGetSolveTime"
5526 /*@
5527    TSGetSolveTime - Gets the time after a call to TSSolve()
5528 
5529    Not Collective
5530 
5531    Input Parameter:
5532 .  ts - the TS context
5533 
5534    Output Parameter:
5535 .  ftime - the final time. This time corresponds to the final time set with TSSetDuration()
5536 
5537    Level: beginner
5538 
5539    Notes:
5540    Can only be called after the call to TSSolve() is complete.
5541 
5542 .keywords: TS, nonlinear, set, convergence, test
5543 
5544 .seealso: TSSetConvergenceTest(), TSConvergedReason
5545 @*/
5546 PetscErrorCode  TSGetSolveTime(TS ts,PetscReal *ftime)
5547 {
5548   PetscFunctionBegin;
5549   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5550   PetscValidPointer(ftime,2);
5551   *ftime = ts->solvetime;
5552   PetscFunctionReturn(0);
5553 }
5554 
5555 #undef __FUNCT__
5556 #define __FUNCT__ "TSGetTotalSteps"
5557 /*@
5558    TSGetTotalSteps - Gets the total number of steps done since the last call to TSSetUp() or TSCreate()
5559 
5560    Not Collective
5561 
5562    Input Parameter:
5563 .  ts - the TS context
5564 
5565    Output Parameter:
5566 .  steps - the number of steps
5567 
5568    Level: beginner
5569 
5570    Notes:
5571    Includes the number of steps for all calls to TSSolve() since TSSetUp() was called
5572 
5573 .keywords: TS, nonlinear, set, convergence, test
5574 
5575 .seealso: TSSetConvergenceTest(), TSConvergedReason
5576 @*/
5577 PetscErrorCode  TSGetTotalSteps(TS ts,PetscInt *steps)
5578 {
5579   PetscFunctionBegin;
5580   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5581   PetscValidPointer(steps,2);
5582   *steps = ts->total_steps;
5583   PetscFunctionReturn(0);
5584 }
5585 
5586 #undef __FUNCT__
5587 #define __FUNCT__ "TSGetSNESIterations"
5588 /*@
5589    TSGetSNESIterations - Gets the total number of nonlinear iterations
5590    used by the time integrator.
5591 
5592    Not Collective
5593 
5594    Input Parameter:
5595 .  ts - TS context
5596 
5597    Output Parameter:
5598 .  nits - number of nonlinear iterations
5599 
5600    Notes:
5601    This counter is reset to zero for each successive call to TSSolve().
5602 
5603    Level: intermediate
5604 
5605 .keywords: TS, get, number, nonlinear, iterations
5606 
5607 .seealso:  TSGetKSPIterations()
5608 @*/
5609 PetscErrorCode TSGetSNESIterations(TS ts,PetscInt *nits)
5610 {
5611   PetscFunctionBegin;
5612   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5613   PetscValidIntPointer(nits,2);
5614   *nits = ts->snes_its;
5615   PetscFunctionReturn(0);
5616 }
5617 
5618 #undef __FUNCT__
5619 #define __FUNCT__ "TSGetKSPIterations"
5620 /*@
5621    TSGetKSPIterations - Gets the total number of linear iterations
5622    used by the time integrator.
5623 
5624    Not Collective
5625 
5626    Input Parameter:
5627 .  ts - TS context
5628 
5629    Output Parameter:
5630 .  lits - number of linear iterations
5631 
5632    Notes:
5633    This counter is reset to zero for each successive call to TSSolve().
5634 
5635    Level: intermediate
5636 
5637 .keywords: TS, get, number, linear, iterations
5638 
5639 .seealso:  TSGetSNESIterations(), SNESGetKSPIterations()
5640 @*/
5641 PetscErrorCode TSGetKSPIterations(TS ts,PetscInt *lits)
5642 {
5643   PetscFunctionBegin;
5644   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5645   PetscValidIntPointer(lits,2);
5646   *lits = ts->ksp_its;
5647   PetscFunctionReturn(0);
5648 }
5649 
5650 #undef __FUNCT__
5651 #define __FUNCT__ "TSGetStepRejections"
5652 /*@
5653    TSGetStepRejections - Gets the total number of rejected steps.
5654 
5655    Not Collective
5656 
5657    Input Parameter:
5658 .  ts - TS context
5659 
5660    Output Parameter:
5661 .  rejects - number of steps rejected
5662 
5663    Notes:
5664    This counter is reset to zero for each successive call to TSSolve().
5665 
5666    Level: intermediate
5667 
5668 .keywords: TS, get, number
5669 
5670 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetSNESFailures(), TSSetMaxSNESFailures(), TSSetErrorIfStepFails()
5671 @*/
5672 PetscErrorCode TSGetStepRejections(TS ts,PetscInt *rejects)
5673 {
5674   PetscFunctionBegin;
5675   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5676   PetscValidIntPointer(rejects,2);
5677   *rejects = ts->reject;
5678   PetscFunctionReturn(0);
5679 }
5680 
5681 #undef __FUNCT__
5682 #define __FUNCT__ "TSGetSNESFailures"
5683 /*@
5684    TSGetSNESFailures - Gets the total number of failed SNES solves
5685 
5686    Not Collective
5687 
5688    Input Parameter:
5689 .  ts - TS context
5690 
5691    Output Parameter:
5692 .  fails - number of failed nonlinear solves
5693 
5694    Notes:
5695    This counter is reset to zero for each successive call to TSSolve().
5696 
5697    Level: intermediate
5698 
5699 .keywords: TS, get, number
5700 
5701 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSSetMaxSNESFailures()
5702 @*/
5703 PetscErrorCode TSGetSNESFailures(TS ts,PetscInt *fails)
5704 {
5705   PetscFunctionBegin;
5706   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5707   PetscValidIntPointer(fails,2);
5708   *fails = ts->num_snes_failures;
5709   PetscFunctionReturn(0);
5710 }
5711 
5712 #undef __FUNCT__
5713 #define __FUNCT__ "TSSetMaxStepRejections"
5714 /*@
5715    TSSetMaxStepRejections - Sets the maximum number of step rejections before a step fails
5716 
5717    Not Collective
5718 
5719    Input Parameter:
5720 +  ts - TS context
5721 -  rejects - maximum number of rejected steps, pass -1 for unlimited
5722 
5723    Notes:
5724    The counter is reset to zero for each step
5725 
5726    Options Database Key:
5727  .  -ts_max_reject - Maximum number of step rejections before a step fails
5728 
5729    Level: intermediate
5730 
5731 .keywords: TS, set, maximum, number
5732 
5733 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxSNESFailures(), TSGetStepRejections(), TSGetSNESFailures(), TSSetErrorIfStepFails(), TSGetConvergedReason()
5734 @*/
5735 PetscErrorCode TSSetMaxStepRejections(TS ts,PetscInt rejects)
5736 {
5737   PetscFunctionBegin;
5738   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5739   ts->max_reject = rejects;
5740   PetscFunctionReturn(0);
5741 }
5742 
5743 #undef __FUNCT__
5744 #define __FUNCT__ "TSSetMaxSNESFailures"
5745 /*@
5746    TSSetMaxSNESFailures - Sets the maximum number of failed SNES solves
5747 
5748    Not Collective
5749 
5750    Input Parameter:
5751 +  ts - TS context
5752 -  fails - maximum number of failed nonlinear solves, pass -1 for unlimited
5753 
5754    Notes:
5755    The counter is reset to zero for each successive call to TSSolve().
5756 
5757    Options Database Key:
5758  .  -ts_max_snes_failures - Maximum number of nonlinear solve failures
5759 
5760    Level: intermediate
5761 
5762 .keywords: TS, set, maximum, number
5763 
5764 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSGetSNESFailures(), SNESGetConvergedReason(), TSGetConvergedReason()
5765 @*/
5766 PetscErrorCode TSSetMaxSNESFailures(TS ts,PetscInt fails)
5767 {
5768   PetscFunctionBegin;
5769   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5770   ts->max_snes_failures = fails;
5771   PetscFunctionReturn(0);
5772 }
5773 
5774 #undef __FUNCT__
5775 #define __FUNCT__ "TSSetErrorIfStepFails"
5776 /*@
5777    TSSetErrorIfStepFails - Error if no step succeeds
5778 
5779    Not Collective
5780 
5781    Input Parameter:
5782 +  ts - TS context
5783 -  err - PETSC_TRUE to error if no step succeeds, PETSC_FALSE to return without failure
5784 
5785    Options Database Key:
5786  .  -ts_error_if_step_fails - Error if no step succeeds
5787 
5788    Level: intermediate
5789 
5790 .keywords: TS, set, error
5791 
5792 .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSGetSNESFailures(), TSSetErrorIfStepFails(), TSGetConvergedReason()
5793 @*/
5794 PetscErrorCode TSSetErrorIfStepFails(TS ts,PetscBool err)
5795 {
5796   PetscFunctionBegin;
5797   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5798   ts->errorifstepfailed = err;
5799   PetscFunctionReturn(0);
5800 }
5801 
5802 #undef __FUNCT__
5803 #define __FUNCT__ "TSMonitorSolution"
5804 /*@C
5805    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
5806 
5807    Collective on TS
5808 
5809    Input Parameters:
5810 +  ts - the TS context
5811 .  step - current time-step
5812 .  ptime - current time
5813 .  u - current state
5814 -  vf - viewer and its format
5815 
5816    Level: intermediate
5817 
5818 .keywords: TS,  vector, monitor, view
5819 
5820 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
5821 @*/
5822 PetscErrorCode  TSMonitorSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscViewerAndFormat *vf)
5823 {
5824   PetscErrorCode ierr;
5825 
5826   PetscFunctionBegin;
5827   ierr = PetscViewerPushFormat(vf->viewer,vf->format);CHKERRQ(ierr);
5828   ierr = VecView(u,vf->viewer);CHKERRQ(ierr);
5829   ierr = PetscViewerPopFormat(vf->viewer);CHKERRQ(ierr);
5830   PetscFunctionReturn(0);
5831 }
5832 
5833 #undef __FUNCT__
5834 #define __FUNCT__ "TSMonitorSolutionVTK"
5835 /*@C
5836    TSMonitorSolutionVTK - Monitors progress of the TS solvers by VecView() for the solution at each timestep.
5837 
5838    Collective on TS
5839 
5840    Input Parameters:
5841 +  ts - the TS context
5842 .  step - current time-step
5843 .  ptime - current time
5844 .  u - current state
5845 -  filenametemplate - string containing a format specifier for the integer time step (e.g. %03D)
5846 
5847    Level: intermediate
5848 
5849    Notes:
5850    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.
5851    These are named according to the file name template.
5852 
5853    This function is normally passed as an argument to TSMonitorSet() along with TSMonitorSolutionVTKDestroy().
5854 
5855 .keywords: TS,  vector, monitor, view
5856 
5857 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
5858 @*/
5859 PetscErrorCode TSMonitorSolutionVTK(TS ts,PetscInt step,PetscReal ptime,Vec u,void *filenametemplate)
5860 {
5861   PetscErrorCode ierr;
5862   char           filename[PETSC_MAX_PATH_LEN];
5863   PetscViewer    viewer;
5864 
5865   PetscFunctionBegin;
5866   if (step < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
5867   ierr = PetscSNPrintf(filename,sizeof(filename),(const char*)filenametemplate,step);CHKERRQ(ierr);
5868   ierr = PetscViewerVTKOpen(PetscObjectComm((PetscObject)ts),filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
5869   ierr = VecView(u,viewer);CHKERRQ(ierr);
5870   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
5871   PetscFunctionReturn(0);
5872 }
5873 
5874 #undef __FUNCT__
5875 #define __FUNCT__ "TSMonitorSolutionVTKDestroy"
5876 /*@C
5877    TSMonitorSolutionVTKDestroy - Destroy context for monitoring
5878 
5879    Collective on TS
5880 
5881    Input Parameters:
5882 .  filenametemplate - string containing a format specifier for the integer time step (e.g. %03D)
5883 
5884    Level: intermediate
5885 
5886    Note:
5887    This function is normally passed to TSMonitorSet() along with TSMonitorSolutionVTK().
5888 
5889 .keywords: TS,  vector, monitor, view
5890 
5891 .seealso: TSMonitorSet(), TSMonitorSolutionVTK()
5892 @*/
5893 PetscErrorCode TSMonitorSolutionVTKDestroy(void *filenametemplate)
5894 {
5895   PetscErrorCode ierr;
5896 
5897   PetscFunctionBegin;
5898   ierr = PetscFree(*(char**)filenametemplate);CHKERRQ(ierr);
5899   PetscFunctionReturn(0);
5900 }
5901 
5902 #undef __FUNCT__
5903 #define __FUNCT__ "TSGetAdapt"
5904 /*@
5905    TSGetAdapt - Get the adaptive controller context for the current method
5906 
5907    Collective on TS if controller has not been created yet
5908 
5909    Input Arguments:
5910 .  ts - time stepping context
5911 
5912    Output Arguments:
5913 .  adapt - adaptive controller
5914 
5915    Level: intermediate
5916 
5917 .seealso: TSAdapt, TSAdaptSetType(), TSAdaptChoose()
5918 @*/
5919 PetscErrorCode TSGetAdapt(TS ts,TSAdapt *adapt)
5920 {
5921   PetscErrorCode ierr;
5922 
5923   PetscFunctionBegin;
5924   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
5925   PetscValidPointer(adapt,2);
5926   if (!ts->adapt) {
5927     ierr = TSAdaptCreate(PetscObjectComm((PetscObject)ts),&ts->adapt);CHKERRQ(ierr);
5928     ierr = PetscLogObjectParent((PetscObject)ts,(PetscObject)ts->adapt);CHKERRQ(ierr);
5929     ierr = PetscObjectIncrementTabLevel((PetscObject)ts->adapt,(PetscObject)ts,1);CHKERRQ(ierr);
5930   }
5931   *adapt = ts->adapt;
5932   PetscFunctionReturn(0);
5933 }
5934 
5935 #undef __FUNCT__
5936 #define __FUNCT__ "TSSetTolerances"
5937 /*@
5938    TSSetTolerances - Set tolerances for local truncation error when using adaptive controller
5939 
5940    Logically Collective
5941 
5942    Input Arguments:
5943 +  ts - time integration context
5944 .  atol - scalar absolute tolerances, PETSC_DECIDE to leave current value
5945 .  vatol - vector of absolute tolerances or NULL, used in preference to atol if present
5946 .  rtol - scalar relative tolerances, PETSC_DECIDE to leave current value
5947 -  vrtol - vector of relative tolerances or NULL, used in preference to atol if present
5948 
5949    Options Database keys:
5950 +  -ts_rtol <rtol> - relative tolerance for local truncation error
5951 -  -ts_atol <atol> Absolute tolerance for local truncation error
5952 
5953    Notes:
5954    With PETSc's implicit schemes for DAE problems, the calculation of the local truncation error
5955    (LTE) includes both the differential and the algebraic variables. If one wants the LTE to be
5956    computed only for the differential or the algebraic part then this can be done using the vector of
5957    tolerances vatol. For example, by setting the tolerance vector with the desired tolerance for the
5958    differential part and infinity for the algebraic part, the LTE calculation will include only the
5959    differential variables.
5960 
5961    Level: beginner
5962 
5963 .seealso: TS, TSAdapt, TSVecNormWRMS(), TSGetTolerances()
5964 @*/
5965 PetscErrorCode TSSetTolerances(TS ts,PetscReal atol,Vec vatol,PetscReal rtol,Vec vrtol)
5966 {
5967   PetscErrorCode ierr;
5968 
5969   PetscFunctionBegin;
5970   if (atol != PETSC_DECIDE && atol != PETSC_DEFAULT) ts->atol = atol;
5971   if (vatol) {
5972     ierr = PetscObjectReference((PetscObject)vatol);CHKERRQ(ierr);
5973     ierr = VecDestroy(&ts->vatol);CHKERRQ(ierr);
5974     ts->vatol = vatol;
5975   }
5976   if (rtol != PETSC_DECIDE && rtol != PETSC_DEFAULT) ts->rtol = rtol;
5977   if (vrtol) {
5978     ierr = PetscObjectReference((PetscObject)vrtol);CHKERRQ(ierr);
5979     ierr = VecDestroy(&ts->vrtol);CHKERRQ(ierr);
5980     ts->vrtol = vrtol;
5981   }
5982   PetscFunctionReturn(0);
5983 }
5984 
5985 #undef __FUNCT__
5986 #define __FUNCT__ "TSGetTolerances"
5987 /*@
5988    TSGetTolerances - Get tolerances for local truncation error when using adaptive controller
5989 
5990    Logically Collective
5991 
5992    Input Arguments:
5993 .  ts - time integration context
5994 
5995    Output Arguments:
5996 +  atol - scalar absolute tolerances, NULL to ignore
5997 .  vatol - vector of absolute tolerances, NULL to ignore
5998 .  rtol - scalar relative tolerances, NULL to ignore
5999 -  vrtol - vector of relative tolerances, NULL to ignore
6000 
6001    Level: beginner
6002 
6003 .seealso: TS, TSAdapt, TSVecNormWRMS(), TSSetTolerances()
6004 @*/
6005 PetscErrorCode TSGetTolerances(TS ts,PetscReal *atol,Vec *vatol,PetscReal *rtol,Vec *vrtol)
6006 {
6007   PetscFunctionBegin;
6008   if (atol)  *atol  = ts->atol;
6009   if (vatol) *vatol = ts->vatol;
6010   if (rtol)  *rtol  = ts->rtol;
6011   if (vrtol) *vrtol = ts->vrtol;
6012   PetscFunctionReturn(0);
6013 }
6014 
6015 #undef __FUNCT__
6016 #define __FUNCT__ "TSErrorWeightedNorm2"
6017 /*@
6018    TSErrorWeightedNorm2 - compute a weighted 2-norm of the difference between two state vectors
6019 
6020    Collective on TS
6021 
6022    Input Arguments:
6023 +  ts - time stepping context
6024 .  U - state vector, usually ts->vec_sol
6025 -  Y - state vector to be compared to U
6026 
6027    Output Arguments:
6028 .  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
6029 .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
6030 .  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances
6031 
6032    Level: developer
6033 
6034 .seealso: TSErrorWeightedNorm(), TSErrorWeightedNormInfinity()
6035 @*/
6036 PetscErrorCode TSErrorWeightedNorm2(TS ts,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6037 {
6038   PetscErrorCode    ierr;
6039   PetscInt          i,n,N,rstart;
6040   PetscInt          n_loc,na_loc,nr_loc;
6041   PetscReal         n_glb,na_glb,nr_glb;
6042   const PetscScalar *u,*y;
6043   PetscReal         sum,suma,sumr,gsum,gsuma,gsumr,diff;
6044   PetscReal         tol,tola,tolr;
6045   PetscReal         err_loc[6],err_glb[6];
6046 
6047   PetscFunctionBegin;
6048   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6049   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
6050   PetscValidHeaderSpecific(Y,VEC_CLASSID,3);
6051   PetscValidType(U,2);
6052   PetscValidType(Y,3);
6053   PetscCheckSameComm(U,2,Y,3);
6054   PetscValidPointer(norm,4);
6055   PetscValidPointer(norma,5);
6056   PetscValidPointer(normr,6);
6057   if (U == Y) SETERRQ(PetscObjectComm((PetscObject)U),PETSC_ERR_ARG_IDN,"U and Y cannot be the same vector");
6058 
6059   ierr = VecGetSize(U,&N);CHKERRQ(ierr);
6060   ierr = VecGetLocalSize(U,&n);CHKERRQ(ierr);
6061   ierr = VecGetOwnershipRange(U,&rstart,NULL);CHKERRQ(ierr);
6062   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
6063   ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
6064   sum  = 0.; n_loc  = 0;
6065   suma = 0.; na_loc = 0;
6066   sumr = 0.; nr_loc = 0;
6067   if (ts->vatol && ts->vrtol) {
6068     const PetscScalar *atol,*rtol;
6069     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6070     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6071     for (i=0; i<n; i++) {
6072       diff = PetscAbsScalar(y[i] - u[i]);
6073       tola = PetscRealPart(atol[i]);
6074       if(tola>0.){
6075         suma  += PetscSqr(diff/tola);
6076         na_loc++;
6077       }
6078       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6079       if(tolr>0.){
6080         sumr  += PetscSqr(diff/tolr);
6081         nr_loc++;
6082       }
6083       tol=tola+tolr;
6084       if(tol>0.){
6085         sum  += PetscSqr(diff/tol);
6086         n_loc++;
6087       }
6088     }
6089     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6090     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6091   } else if (ts->vatol) {       /* vector atol, scalar rtol */
6092     const PetscScalar *atol;
6093     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6094     for (i=0; i<n; i++) {
6095       diff = PetscAbsScalar(y[i] - u[i]);
6096       tola = PetscRealPart(atol[i]);
6097       if(tola>0.){
6098         suma  += PetscSqr(diff/tola);
6099         na_loc++;
6100       }
6101       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6102       if(tolr>0.){
6103         sumr  += PetscSqr(diff/tolr);
6104         nr_loc++;
6105       }
6106       tol=tola+tolr;
6107       if(tol>0.){
6108         sum  += PetscSqr(diff/tol);
6109         n_loc++;
6110       }
6111     }
6112     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6113   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
6114     const PetscScalar *rtol;
6115     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6116     for (i=0; i<n; i++) {
6117       diff = PetscAbsScalar(y[i] - u[i]);
6118       tola = ts->atol;
6119       if(tola>0.){
6120         suma  += PetscSqr(diff/tola);
6121         na_loc++;
6122       }
6123       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6124       if(tolr>0.){
6125         sumr  += PetscSqr(diff/tolr);
6126         nr_loc++;
6127       }
6128       tol=tola+tolr;
6129       if(tol>0.){
6130         sum  += PetscSqr(diff/tol);
6131         n_loc++;
6132       }
6133     }
6134     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6135   } else {                      /* scalar atol, scalar rtol */
6136     for (i=0; i<n; i++) {
6137       diff = PetscAbsScalar(y[i] - u[i]);
6138      tola = ts->atol;
6139       if(tola>0.){
6140         suma  += PetscSqr(diff/tola);
6141         na_loc++;
6142       }
6143       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6144       if(tolr>0.){
6145         sumr  += PetscSqr(diff/tolr);
6146         nr_loc++;
6147       }
6148       tol=tola+tolr;
6149       if(tol>0.){
6150         sum  += PetscSqr(diff/tol);
6151         n_loc++;
6152       }
6153     }
6154   }
6155   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
6156   ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
6157 
6158   err_loc[0] = sum;
6159   err_loc[1] = suma;
6160   err_loc[2] = sumr;
6161   err_loc[3] = (PetscReal)n_loc;
6162   err_loc[4] = (PetscReal)na_loc;
6163   err_loc[5] = (PetscReal)nr_loc;
6164 
6165   ierr = MPIU_Allreduce(err_loc,err_glb,6,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6166 
6167   gsum   = err_glb[0];
6168   gsuma  = err_glb[1];
6169   gsumr  = err_glb[2];
6170   n_glb  = err_glb[3];
6171   na_glb = err_glb[4];
6172   nr_glb = err_glb[5];
6173 
6174   *norm  = 0.;
6175   if(n_glb>0. ){*norm  = PetscSqrtReal(gsum  / n_glb );}
6176   *norma = 0.;
6177   if(na_glb>0.){*norma = PetscSqrtReal(gsuma / na_glb);}
6178   *normr = 0.;
6179   if(nr_glb>0.){*normr = PetscSqrtReal(gsumr / nr_glb);}
6180 
6181   if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
6182   if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
6183   if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
6184   PetscFunctionReturn(0);
6185 }
6186 
6187 #undef __FUNCT__
6188 #define __FUNCT__ "TSErrorWeightedNormInfinity"
6189 /*@
6190    TSErrorWeightedNormInfinity - compute a weighted infinity-norm of the difference between two state vectors
6191 
6192    Collective on TS
6193 
6194    Input Arguments:
6195 +  ts - time stepping context
6196 .  U - state vector, usually ts->vec_sol
6197 -  Y - state vector to be compared to U
6198 
6199    Output Arguments:
6200 .  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
6201 .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
6202 .  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances
6203 
6204    Level: developer
6205 
6206 .seealso: TSErrorWeightedNorm(), TSErrorWeightedNorm2()
6207 @*/
6208 PetscErrorCode TSErrorWeightedNormInfinity(TS ts,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6209 {
6210   PetscErrorCode    ierr;
6211   PetscInt          i,n,N,rstart;
6212   const PetscScalar *u,*y;
6213   PetscReal         max,gmax,maxa,gmaxa,maxr,gmaxr;
6214   PetscReal         tol,tola,tolr,diff;
6215   PetscReal         err_loc[3],err_glb[3];
6216 
6217   PetscFunctionBegin;
6218   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6219   PetscValidHeaderSpecific(U,VEC_CLASSID,2);
6220   PetscValidHeaderSpecific(Y,VEC_CLASSID,3);
6221   PetscValidType(U,2);
6222   PetscValidType(Y,3);
6223   PetscCheckSameComm(U,2,Y,3);
6224   PetscValidPointer(norm,4);
6225   PetscValidPointer(norma,5);
6226   PetscValidPointer(normr,6);
6227   if (U == Y) SETERRQ(PetscObjectComm((PetscObject)U),PETSC_ERR_ARG_IDN,"U and Y cannot be the same vector");
6228 
6229   ierr = VecGetSize(U,&N);CHKERRQ(ierr);
6230   ierr = VecGetLocalSize(U,&n);CHKERRQ(ierr);
6231   ierr = VecGetOwnershipRange(U,&rstart,NULL);CHKERRQ(ierr);
6232   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
6233   ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
6234 
6235   max=0.;
6236   maxa=0.;
6237   maxr=0.;
6238 
6239   if (ts->vatol && ts->vrtol) {     /* vector atol, vector rtol */
6240     const PetscScalar *atol,*rtol;
6241     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6242     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6243 
6244     for (i=0; i<n; i++) {
6245       diff = PetscAbsScalar(y[i] - u[i]);
6246       tola = PetscRealPart(atol[i]);
6247       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6248       tol  = tola+tolr;
6249       if(tola>0.){
6250         maxa = PetscMax(maxa,diff / tola);
6251       }
6252       if(tolr>0.){
6253         maxr = PetscMax(maxr,diff / tolr);
6254       }
6255       if(tol>0.){
6256         max = PetscMax(max,diff / tol);
6257       }
6258     }
6259     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6260     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6261   } else if (ts->vatol) {       /* vector atol, scalar rtol */
6262     const PetscScalar *atol;
6263     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6264     for (i=0; i<n; i++) {
6265       diff = PetscAbsScalar(y[i] - u[i]);
6266       tola = PetscRealPart(atol[i]);
6267       tolr = ts->rtol  * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6268       tol  = tola+tolr;
6269       if(tola>0.){
6270         maxa = PetscMax(maxa,diff / tola);
6271       }
6272       if(tolr>0.){
6273         maxr = PetscMax(maxr,diff / tolr);
6274       }
6275       if(tol>0.){
6276         max = PetscMax(max,diff / tol);
6277       }
6278     }
6279     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6280   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
6281     const PetscScalar *rtol;
6282     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6283 
6284     for (i=0; i<n; i++) {
6285       diff = PetscAbsScalar(y[i] - u[i]);
6286       tola = ts->atol;
6287       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6288       tol  = tola+tolr;
6289       if(tola>0.){
6290         maxa = PetscMax(maxa,diff / tola);
6291       }
6292       if(tolr>0.){
6293         maxr = PetscMax(maxr,diff / tolr);
6294       }
6295       if(tol>0.){
6296         max = PetscMax(max,diff / tol);
6297       }
6298     }
6299     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6300   } else {                      /* scalar atol, scalar rtol */
6301 
6302     for (i=0; i<n; i++) {
6303       diff = PetscAbsScalar(y[i] - u[i]);
6304       tola = ts->atol;
6305       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6306       tol  = tola+tolr;
6307       if(tola>0.){
6308         maxa = PetscMax(maxa,diff / tola);
6309       }
6310       if(tolr>0.){
6311         maxr = PetscMax(maxr,diff / tolr);
6312       }
6313       if(tol>0.){
6314         max = PetscMax(max,diff / tol);
6315       }
6316     }
6317   }
6318   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
6319   ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
6320   err_loc[0] = max;
6321   err_loc[1] = maxa;
6322   err_loc[2] = maxr;
6323   ierr  = MPIU_Allreduce(err_loc,err_glb,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6324   gmax   = err_glb[0];
6325   gmaxa  = err_glb[1];
6326   gmaxr  = err_glb[2];
6327 
6328   *norm = gmax;
6329   *norma = gmaxa;
6330   *normr = gmaxr;
6331   if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
6332     if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
6333     if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
6334   PetscFunctionReturn(0);
6335 }
6336 
6337 #undef __FUNCT__
6338 #define __FUNCT__ "TSErrorWeightedNorm"
6339 /*@
6340    TSErrorWeightedNorm - compute a weighted norm of the difference between two state vectors based on supplied absolute and relative tolerances
6341 
6342    Collective on TS
6343 
6344    Input Arguments:
6345 +  ts - time stepping context
6346 .  U - state vector, usually ts->vec_sol
6347 .  Y - state vector to be compared to U
6348 -  wnormtype - norm type, either NORM_2 or NORM_INFINITY
6349 
6350    Output Arguments:
6351 .  norm  - weighted norm, a value of 1.0 achieves a balance between absolute and relative tolerances
6352 .  norma - weighted norm, a value of 1.0 means that the error meets the absolute tolerance set by the user
6353 .  normr - weighted norm, a value of 1.0 means that the error meets the relative tolerance set by the user
6354 
6355    Options Database Keys:
6356 .  -ts_adapt_wnormtype <wnormtype> - 2, INFINITY
6357 
6358    Level: developer
6359 
6360 .seealso: TSErrorWeightedNormInfinity(), TSErrorWeightedNorm2(), TSErrorWeightedENorm
6361 @*/
6362 PetscErrorCode TSErrorWeightedNorm(TS ts,Vec U,Vec Y,NormType wnormtype,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6363 {
6364   PetscErrorCode ierr;
6365 
6366   PetscFunctionBegin;
6367   if (wnormtype == NORM_2) {
6368     ierr = TSErrorWeightedNorm2(ts,U,Y,norm,norma,normr);CHKERRQ(ierr);
6369   } else if(wnormtype == NORM_INFINITY) {
6370     ierr = TSErrorWeightedNormInfinity(ts,U,Y,norm,norma,normr);CHKERRQ(ierr);
6371   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
6372   PetscFunctionReturn(0);
6373 }
6374 
6375 
6376 #undef __FUNCT__
6377 #define __FUNCT__ "TSErrorWeightedENorm2"
6378 /*@
6379    TSErrorWeightedENorm2 - compute a weighted 2 error norm based on supplied absolute and relative tolerances
6380 
6381    Collective on TS
6382 
6383    Input Arguments:
6384 +  ts - time stepping context
6385 .  E - error vector
6386 .  U - state vector, usually ts->vec_sol
6387 -  Y - state vector, previous time step
6388 
6389    Output Arguments:
6390 .  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
6391 .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
6392 .  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances
6393 
6394    Level: developer
6395 
6396 .seealso: TSErrorWeightedENorm(), TSErrorWeightedENormInfinity()
6397 @*/
6398 PetscErrorCode TSErrorWeightedENorm2(TS ts,Vec E,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6399 {
6400   PetscErrorCode    ierr;
6401   PetscInt          i,n,N,rstart;
6402   PetscInt          n_loc,na_loc,nr_loc;
6403   PetscReal         n_glb,na_glb,nr_glb;
6404   const PetscScalar *e,*u,*y;
6405   PetscReal         err,sum,suma,sumr,gsum,gsuma,gsumr;
6406   PetscReal         tol,tola,tolr;
6407   PetscReal         err_loc[6],err_glb[6];
6408 
6409   PetscFunctionBegin;
6410   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6411   PetscValidHeaderSpecific(E,VEC_CLASSID,2);
6412   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
6413   PetscValidHeaderSpecific(Y,VEC_CLASSID,4);
6414   PetscValidType(E,2);
6415   PetscValidType(U,3);
6416   PetscValidType(Y,4);
6417   PetscCheckSameComm(E,2,U,3);
6418   PetscCheckSameComm(U,2,Y,3);
6419   PetscValidPointer(norm,5);
6420   PetscValidPointer(norma,6);
6421   PetscValidPointer(normr,7);
6422 
6423   ierr = VecGetSize(E,&N);CHKERRQ(ierr);
6424   ierr = VecGetLocalSize(E,&n);CHKERRQ(ierr);
6425   ierr = VecGetOwnershipRange(E,&rstart,NULL);CHKERRQ(ierr);
6426   ierr = VecGetArrayRead(E,&e);CHKERRQ(ierr);
6427   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
6428   ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
6429   sum  = 0.; n_loc  = 0;
6430   suma = 0.; na_loc = 0;
6431   sumr = 0.; nr_loc = 0;
6432   if (ts->vatol && ts->vrtol) {
6433     const PetscScalar *atol,*rtol;
6434     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6435     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6436     for (i=0; i<n; i++) {
6437       err = PetscAbsScalar(e[i]);
6438       tola = PetscRealPart(atol[i]);
6439       if(tola>0.){
6440         suma  += PetscSqr(err/tola);
6441         na_loc++;
6442       }
6443       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6444       if(tolr>0.){
6445         sumr  += PetscSqr(err/tolr);
6446         nr_loc++;
6447       }
6448       tol=tola+tolr;
6449       if(tol>0.){
6450         sum  += PetscSqr(err/tol);
6451         n_loc++;
6452       }
6453     }
6454     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6455     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6456   } else if (ts->vatol) {       /* vector atol, scalar rtol */
6457     const PetscScalar *atol;
6458     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6459     for (i=0; i<n; i++) {
6460       err = PetscAbsScalar(e[i]);
6461       tola = PetscRealPart(atol[i]);
6462       if(tola>0.){
6463         suma  += PetscSqr(err/tola);
6464         na_loc++;
6465       }
6466       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6467       if(tolr>0.){
6468         sumr  += PetscSqr(err/tolr);
6469         nr_loc++;
6470       }
6471       tol=tola+tolr;
6472       if(tol>0.){
6473         sum  += PetscSqr(err/tol);
6474         n_loc++;
6475       }
6476     }
6477     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6478   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
6479     const PetscScalar *rtol;
6480     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6481     for (i=0; i<n; i++) {
6482       err = PetscAbsScalar(e[i]);
6483       tola = ts->atol;
6484       if(tola>0.){
6485         suma  += PetscSqr(err/tola);
6486         na_loc++;
6487       }
6488       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6489       if(tolr>0.){
6490         sumr  += PetscSqr(err/tolr);
6491         nr_loc++;
6492       }
6493       tol=tola+tolr;
6494       if(tol>0.){
6495         sum  += PetscSqr(err/tol);
6496         n_loc++;
6497       }
6498     }
6499     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6500   } else {                      /* scalar atol, scalar rtol */
6501     for (i=0; i<n; i++) {
6502       err = PetscAbsScalar(e[i]);
6503      tola = ts->atol;
6504       if(tola>0.){
6505         suma  += PetscSqr(err/tola);
6506         na_loc++;
6507       }
6508       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6509       if(tolr>0.){
6510         sumr  += PetscSqr(err/tolr);
6511         nr_loc++;
6512       }
6513       tol=tola+tolr;
6514       if(tol>0.){
6515         sum  += PetscSqr(err/tol);
6516         n_loc++;
6517       }
6518     }
6519   }
6520   ierr = VecRestoreArrayRead(E,&e);CHKERRQ(ierr);
6521   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
6522   ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
6523 
6524   err_loc[0] = sum;
6525   err_loc[1] = suma;
6526   err_loc[2] = sumr;
6527   err_loc[3] = (PetscReal)n_loc;
6528   err_loc[4] = (PetscReal)na_loc;
6529   err_loc[5] = (PetscReal)nr_loc;
6530 
6531   ierr = MPIU_Allreduce(err_loc,err_glb,6,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6532 
6533   gsum   = err_glb[0];
6534   gsuma  = err_glb[1];
6535   gsumr  = err_glb[2];
6536   n_glb  = err_glb[3];
6537   na_glb = err_glb[4];
6538   nr_glb = err_glb[5];
6539 
6540   *norm  = 0.;
6541   if(n_glb>0. ){*norm  = PetscSqrtReal(gsum  / n_glb );}
6542   *norma = 0.;
6543   if(na_glb>0.){*norma = PetscSqrtReal(gsuma / na_glb);}
6544   *normr = 0.;
6545   if(nr_glb>0.){*normr = PetscSqrtReal(gsumr / nr_glb);}
6546 
6547   if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
6548   if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
6549   if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
6550   PetscFunctionReturn(0);
6551 }
6552 
6553 #undef __FUNCT__
6554 #define __FUNCT__ "TSErrorWeightedENormInfinity"
6555 /*@
6556    TSErrorWeightedENormInfinity - compute a weighted infinity error norm based on supplied absolute and relative tolerances
6557    Collective on TS
6558 
6559    Input Arguments:
6560 +  ts - time stepping context
6561 .  E - error vector
6562 .  U - state vector, usually ts->vec_sol
6563 -  Y - state vector, previous time step
6564 
6565    Output Arguments:
6566 .  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
6567 .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
6568 .  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances
6569 
6570    Level: developer
6571 
6572 .seealso: TSErrorWeightedENorm(), TSErrorWeightedENorm2()
6573 @*/
6574 PetscErrorCode TSErrorWeightedENormInfinity(TS ts,Vec E,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6575 {
6576   PetscErrorCode    ierr;
6577   PetscInt          i,n,N,rstart;
6578   const PetscScalar *e,*u,*y;
6579   PetscReal         err,max,gmax,maxa,gmaxa,maxr,gmaxr;
6580   PetscReal         tol,tola,tolr;
6581   PetscReal         err_loc[3],err_glb[3];
6582 
6583   PetscFunctionBegin;
6584   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6585   PetscValidHeaderSpecific(E,VEC_CLASSID,2);
6586   PetscValidHeaderSpecific(U,VEC_CLASSID,3);
6587   PetscValidHeaderSpecific(Y,VEC_CLASSID,4);
6588   PetscValidType(E,2);
6589   PetscValidType(U,3);
6590   PetscValidType(Y,4);
6591   PetscCheckSameComm(E,2,U,3);
6592   PetscCheckSameComm(U,2,Y,3);
6593   PetscValidPointer(norm,5);
6594   PetscValidPointer(norma,6);
6595   PetscValidPointer(normr,7);
6596 
6597   ierr = VecGetSize(E,&N);CHKERRQ(ierr);
6598   ierr = VecGetLocalSize(E,&n);CHKERRQ(ierr);
6599   ierr = VecGetOwnershipRange(E,&rstart,NULL);CHKERRQ(ierr);
6600   ierr = VecGetArrayRead(E,&e);CHKERRQ(ierr);
6601   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
6602   ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
6603 
6604   max=0.;
6605   maxa=0.;
6606   maxr=0.;
6607 
6608   if (ts->vatol && ts->vrtol) {     /* vector atol, vector rtol */
6609     const PetscScalar *atol,*rtol;
6610     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6611     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6612 
6613     for (i=0; i<n; i++) {
6614       err = PetscAbsScalar(e[i]);
6615       tola = PetscRealPart(atol[i]);
6616       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6617       tol  = tola+tolr;
6618       if(tola>0.){
6619         maxa = PetscMax(maxa,err / tola);
6620       }
6621       if(tolr>0.){
6622         maxr = PetscMax(maxr,err / tolr);
6623       }
6624       if(tol>0.){
6625         max = PetscMax(max,err / tol);
6626       }
6627     }
6628     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6629     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6630   } else if (ts->vatol) {       /* vector atol, scalar rtol */
6631     const PetscScalar *atol;
6632     ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6633     for (i=0; i<n; i++) {
6634       err = PetscAbsScalar(e[i]);
6635       tola = PetscRealPart(atol[i]);
6636       tolr = ts->rtol  * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6637       tol  = tola+tolr;
6638       if(tola>0.){
6639         maxa = PetscMax(maxa,err / tola);
6640       }
6641       if(tolr>0.){
6642         maxr = PetscMax(maxr,err / tolr);
6643       }
6644       if(tol>0.){
6645         max = PetscMax(max,err / tol);
6646       }
6647     }
6648     ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
6649   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
6650     const PetscScalar *rtol;
6651     ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6652 
6653     for (i=0; i<n; i++) {
6654       err = PetscAbsScalar(e[i]);
6655       tola = ts->atol;
6656       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6657       tol  = tola+tolr;
6658       if(tola>0.){
6659         maxa = PetscMax(maxa,err / tola);
6660       }
6661       if(tolr>0.){
6662         maxr = PetscMax(maxr,err / tolr);
6663       }
6664       if(tol>0.){
6665         max = PetscMax(max,err / tol);
6666       }
6667     }
6668     ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
6669   } else {                      /* scalar atol, scalar rtol */
6670 
6671     for (i=0; i<n; i++) {
6672       err = PetscAbsScalar(e[i]);
6673       tola = ts->atol;
6674       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
6675       tol  = tola+tolr;
6676       if(tola>0.){
6677         maxa = PetscMax(maxa,err / tola);
6678       }
6679       if(tolr>0.){
6680         maxr = PetscMax(maxr,err / tolr);
6681       }
6682       if(tol>0.){
6683         max = PetscMax(max,err / tol);
6684       }
6685     }
6686   }
6687   ierr = VecRestoreArrayRead(E,&e);CHKERRQ(ierr);
6688   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
6689   ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
6690   err_loc[0] = max;
6691   err_loc[1] = maxa;
6692   err_loc[2] = maxr;
6693   ierr  = MPIU_Allreduce(err_loc,err_glb,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6694   gmax   = err_glb[0];
6695   gmaxa  = err_glb[1];
6696   gmaxr  = err_glb[2];
6697 
6698   *norm = gmax;
6699   *norma = gmaxa;
6700   *normr = gmaxr;
6701   if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
6702     if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
6703     if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
6704   PetscFunctionReturn(0);
6705 }
6706 
6707 #undef __FUNCT__
6708 #define __FUNCT__ "TSErrorWeightedENorm"
6709 /*@
6710    TSErrorWeightedENorm - compute a weighted error norm based on supplied absolute and relative tolerances
6711 
6712    Collective on TS
6713 
6714    Input Arguments:
6715 +  ts - time stepping context
6716 .  E - error vector
6717 .  U - state vector, usually ts->vec_sol
6718 .  Y - state vector, previous time step
6719 -  wnormtype - norm type, either NORM_2 or NORM_INFINITY
6720 
6721    Output Arguments:
6722 .  norm  - weighted norm, a value of 1.0 achieves a balance between absolute and relative tolerances
6723 .  norma - weighted norm, a value of 1.0 means that the error meets the absolute tolerance set by the user
6724 .  normr - weighted norm, a value of 1.0 means that the error meets the relative tolerance set by the user
6725 
6726    Options Database Keys:
6727 .  -ts_adapt_wnormtype <wnormtype> - 2, INFINITY
6728 
6729    Level: developer
6730 
6731 .seealso: TSErrorWeightedENormInfinity(), TSErrorWeightedENorm2(), TSErrorWeightedNormInfinity(), TSErrorWeightedNorm2()
6732 @*/
6733 PetscErrorCode TSErrorWeightedENorm(TS ts,Vec E,Vec U,Vec Y,NormType wnormtype,PetscReal *norm,PetscReal *norma,PetscReal *normr)
6734 {
6735   PetscErrorCode ierr;
6736 
6737   PetscFunctionBegin;
6738   if (wnormtype == NORM_2) {
6739     ierr = TSErrorWeightedENorm2(ts,E,U,Y,norm,norma,normr);CHKERRQ(ierr);
6740   } else if(wnormtype == NORM_INFINITY) {
6741     ierr = TSErrorWeightedENormInfinity(ts,E,U,Y,norm,norma,normr);CHKERRQ(ierr);
6742   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
6743   PetscFunctionReturn(0);
6744 }
6745 
6746 
6747 #undef __FUNCT__
6748 #define __FUNCT__ "TSSetCFLTimeLocal"
6749 /*@
6750    TSSetCFLTimeLocal - Set the local CFL constraint relative to forward Euler
6751 
6752    Logically Collective on TS
6753 
6754    Input Arguments:
6755 +  ts - time stepping context
6756 -  cfltime - maximum stable time step if using forward Euler (value can be different on each process)
6757 
6758    Note:
6759    After calling this function, the global CFL time can be obtained by calling TSGetCFLTime()
6760 
6761    Level: intermediate
6762 
6763 .seealso: TSGetCFLTime(), TSADAPTCFL
6764 @*/
6765 PetscErrorCode TSSetCFLTimeLocal(TS ts,PetscReal cfltime)
6766 {
6767   PetscFunctionBegin;
6768   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6769   ts->cfltime_local = cfltime;
6770   ts->cfltime       = -1.;
6771   PetscFunctionReturn(0);
6772 }
6773 
6774 #undef __FUNCT__
6775 #define __FUNCT__ "TSGetCFLTime"
6776 /*@
6777    TSGetCFLTime - Get the maximum stable time step according to CFL criteria applied to forward Euler
6778 
6779    Collective on TS
6780 
6781    Input Arguments:
6782 .  ts - time stepping context
6783 
6784    Output Arguments:
6785 .  cfltime - maximum stable time step for forward Euler
6786 
6787    Level: advanced
6788 
6789 .seealso: TSSetCFLTimeLocal()
6790 @*/
6791 PetscErrorCode TSGetCFLTime(TS ts,PetscReal *cfltime)
6792 {
6793   PetscErrorCode ierr;
6794 
6795   PetscFunctionBegin;
6796   if (ts->cfltime < 0) {
6797     ierr = MPIU_Allreduce(&ts->cfltime_local,&ts->cfltime,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
6798   }
6799   *cfltime = ts->cfltime;
6800   PetscFunctionReturn(0);
6801 }
6802 
6803 #undef __FUNCT__
6804 #define __FUNCT__ "TSVISetVariableBounds"
6805 /*@
6806    TSVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu
6807 
6808    Input Parameters:
6809 .  ts   - the TS context.
6810 .  xl   - lower bound.
6811 .  xu   - upper bound.
6812 
6813    Notes:
6814    If this routine is not called then the lower and upper bounds are set to
6815    PETSC_NINFINITY and PETSC_INFINITY respectively during SNESSetUp().
6816 
6817    Level: advanced
6818 
6819 @*/
6820 PetscErrorCode TSVISetVariableBounds(TS ts, Vec xl, Vec xu)
6821 {
6822   PetscErrorCode ierr;
6823   SNES           snes;
6824 
6825   PetscFunctionBegin;
6826   ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
6827   ierr = SNESVISetVariableBounds(snes,xl,xu);CHKERRQ(ierr);
6828   PetscFunctionReturn(0);
6829 }
6830 
6831 #if defined(PETSC_HAVE_MATLAB_ENGINE)
6832 #include <mex.h>
6833 
6834 typedef struct {char *funcname; mxArray *ctx;} TSMatlabContext;
6835 
6836 #undef __FUNCT__
6837 #define __FUNCT__ "TSComputeFunction_Matlab"
6838 /*
6839    TSComputeFunction_Matlab - Calls the function that has been set with
6840                          TSSetFunctionMatlab().
6841 
6842    Collective on TS
6843 
6844    Input Parameters:
6845 +  snes - the TS context
6846 -  u - input vector
6847 
6848    Output Parameter:
6849 .  y - function vector, as set by TSSetFunction()
6850 
6851    Notes:
6852    TSComputeFunction() is typically used within nonlinear solvers
6853    implementations, so most users would not generally call this routine
6854    themselves.
6855 
6856    Level: developer
6857 
6858 .keywords: TS, nonlinear, compute, function
6859 
6860 .seealso: TSSetFunction(), TSGetFunction()
6861 */
6862 PetscErrorCode  TSComputeFunction_Matlab(TS snes,PetscReal time,Vec u,Vec udot,Vec y, void *ctx)
6863 {
6864   PetscErrorCode  ierr;
6865   TSMatlabContext *sctx = (TSMatlabContext*)ctx;
6866   int             nlhs  = 1,nrhs = 7;
6867   mxArray         *plhs[1],*prhs[7];
6868   long long int   lx = 0,lxdot = 0,ly = 0,ls = 0;
6869 
6870   PetscFunctionBegin;
6871   PetscValidHeaderSpecific(snes,TS_CLASSID,1);
6872   PetscValidHeaderSpecific(u,VEC_CLASSID,3);
6873   PetscValidHeaderSpecific(udot,VEC_CLASSID,4);
6874   PetscValidHeaderSpecific(y,VEC_CLASSID,5);
6875   PetscCheckSameComm(snes,1,u,3);
6876   PetscCheckSameComm(snes,1,y,5);
6877 
6878   ierr = PetscMemcpy(&ls,&snes,sizeof(snes));CHKERRQ(ierr);
6879   ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
6880   ierr = PetscMemcpy(&lxdot,&udot,sizeof(udot));CHKERRQ(ierr);
6881   ierr = PetscMemcpy(&ly,&y,sizeof(u));CHKERRQ(ierr);
6882 
6883   prhs[0] =  mxCreateDoubleScalar((double)ls);
6884   prhs[1] =  mxCreateDoubleScalar(time);
6885   prhs[2] =  mxCreateDoubleScalar((double)lx);
6886   prhs[3] =  mxCreateDoubleScalar((double)lxdot);
6887   prhs[4] =  mxCreateDoubleScalar((double)ly);
6888   prhs[5] =  mxCreateString(sctx->funcname);
6889   prhs[6] =  sctx->ctx;
6890   ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSComputeFunctionInternal");CHKERRQ(ierr);
6891   ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
6892   mxDestroyArray(prhs[0]);
6893   mxDestroyArray(prhs[1]);
6894   mxDestroyArray(prhs[2]);
6895   mxDestroyArray(prhs[3]);
6896   mxDestroyArray(prhs[4]);
6897   mxDestroyArray(prhs[5]);
6898   mxDestroyArray(plhs[0]);
6899   PetscFunctionReturn(0);
6900 }
6901 
6902 
6903 #undef __FUNCT__
6904 #define __FUNCT__ "TSSetFunctionMatlab"
6905 /*
6906    TSSetFunctionMatlab - Sets the function evaluation routine and function
6907    vector for use by the TS routines in solving ODEs
6908    equations from MATLAB. Here the function is a string containing the name of a MATLAB function
6909 
6910    Logically Collective on TS
6911 
6912    Input Parameters:
6913 +  ts - the TS context
6914 -  func - function evaluation routine
6915 
6916    Calling sequence of func:
6917 $    func (TS ts,PetscReal time,Vec u,Vec udot,Vec f,void *ctx);
6918 
6919    Level: beginner
6920 
6921 .keywords: TS, nonlinear, set, function
6922 
6923 .seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
6924 */
6925 PetscErrorCode  TSSetFunctionMatlab(TS ts,const char *func,mxArray *ctx)
6926 {
6927   PetscErrorCode  ierr;
6928   TSMatlabContext *sctx;
6929 
6930   PetscFunctionBegin;
6931   /* currently sctx is memory bleed */
6932   ierr = PetscNew(&sctx);CHKERRQ(ierr);
6933   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
6934   /*
6935      This should work, but it doesn't
6936   sctx->ctx = ctx;
6937   mexMakeArrayPersistent(sctx->ctx);
6938   */
6939   sctx->ctx = mxDuplicateArray(ctx);
6940 
6941   ierr = TSSetIFunction(ts,NULL,TSComputeFunction_Matlab,sctx);CHKERRQ(ierr);
6942   PetscFunctionReturn(0);
6943 }
6944 
6945 #undef __FUNCT__
6946 #define __FUNCT__ "TSComputeJacobian_Matlab"
6947 /*
6948    TSComputeJacobian_Matlab - Calls the function that has been set with
6949                          TSSetJacobianMatlab().
6950 
6951    Collective on TS
6952 
6953    Input Parameters:
6954 +  ts - the TS context
6955 .  u - input vector
6956 .  A, B - the matrices
6957 -  ctx - user context
6958 
6959    Level: developer
6960 
6961 .keywords: TS, nonlinear, compute, function
6962 
6963 .seealso: TSSetFunction(), TSGetFunction()
6964 @*/
6965 PetscErrorCode  TSComputeJacobian_Matlab(TS ts,PetscReal time,Vec u,Vec udot,PetscReal shift,Mat A,Mat B,void *ctx)
6966 {
6967   PetscErrorCode  ierr;
6968   TSMatlabContext *sctx = (TSMatlabContext*)ctx;
6969   int             nlhs  = 2,nrhs = 9;
6970   mxArray         *plhs[2],*prhs[9];
6971   long long int   lx = 0,lxdot = 0,lA = 0,ls = 0, lB = 0;
6972 
6973   PetscFunctionBegin;
6974   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
6975   PetscValidHeaderSpecific(u,VEC_CLASSID,3);
6976 
6977   /* call Matlab function in ctx with arguments u and y */
6978 
6979   ierr = PetscMemcpy(&ls,&ts,sizeof(ts));CHKERRQ(ierr);
6980   ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
6981   ierr = PetscMemcpy(&lxdot,&udot,sizeof(u));CHKERRQ(ierr);
6982   ierr = PetscMemcpy(&lA,A,sizeof(u));CHKERRQ(ierr);
6983   ierr = PetscMemcpy(&lB,B,sizeof(u));CHKERRQ(ierr);
6984 
6985   prhs[0] =  mxCreateDoubleScalar((double)ls);
6986   prhs[1] =  mxCreateDoubleScalar((double)time);
6987   prhs[2] =  mxCreateDoubleScalar((double)lx);
6988   prhs[3] =  mxCreateDoubleScalar((double)lxdot);
6989   prhs[4] =  mxCreateDoubleScalar((double)shift);
6990   prhs[5] =  mxCreateDoubleScalar((double)lA);
6991   prhs[6] =  mxCreateDoubleScalar((double)lB);
6992   prhs[7] =  mxCreateString(sctx->funcname);
6993   prhs[8] =  sctx->ctx;
6994   ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSComputeJacobianInternal");CHKERRQ(ierr);
6995   ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
6996   mxDestroyArray(prhs[0]);
6997   mxDestroyArray(prhs[1]);
6998   mxDestroyArray(prhs[2]);
6999   mxDestroyArray(prhs[3]);
7000   mxDestroyArray(prhs[4]);
7001   mxDestroyArray(prhs[5]);
7002   mxDestroyArray(prhs[6]);
7003   mxDestroyArray(prhs[7]);
7004   mxDestroyArray(plhs[0]);
7005   mxDestroyArray(plhs[1]);
7006   PetscFunctionReturn(0);
7007 }
7008 
7009 
7010 #undef __FUNCT__
7011 #define __FUNCT__ "TSSetJacobianMatlab"
7012 /*
7013    TSSetJacobianMatlab - Sets the Jacobian function evaluation routine and two empty Jacobian matrices
7014    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
7015 
7016    Logically Collective on TS
7017 
7018    Input Parameters:
7019 +  ts - the TS context
7020 .  A,B - Jacobian matrices
7021 .  func - function evaluation routine
7022 -  ctx - user context
7023 
7024    Calling sequence of func:
7025 $    flag = func (TS ts,PetscReal time,Vec u,Vec udot,Mat A,Mat B,void *ctx);
7026 
7027 
7028    Level: developer
7029 
7030 .keywords: TS, nonlinear, set, function
7031 
7032 .seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
7033 */
7034 PetscErrorCode  TSSetJacobianMatlab(TS ts,Mat A,Mat B,const char *func,mxArray *ctx)
7035 {
7036   PetscErrorCode  ierr;
7037   TSMatlabContext *sctx;
7038 
7039   PetscFunctionBegin;
7040   /* currently sctx is memory bleed */
7041   ierr = PetscNew(&sctx);CHKERRQ(ierr);
7042   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
7043   /*
7044      This should work, but it doesn't
7045   sctx->ctx = ctx;
7046   mexMakeArrayPersistent(sctx->ctx);
7047   */
7048   sctx->ctx = mxDuplicateArray(ctx);
7049 
7050   ierr = TSSetIJacobian(ts,A,B,TSComputeJacobian_Matlab,sctx);CHKERRQ(ierr);
7051   PetscFunctionReturn(0);
7052 }
7053 
7054 #undef __FUNCT__
7055 #define __FUNCT__ "TSMonitor_Matlab"
7056 /*
7057    TSMonitor_Matlab - Calls the function that has been set with TSMonitorSetMatlab().
7058 
7059    Collective on TS
7060 
7061 .seealso: TSSetFunction(), TSGetFunction()
7062 @*/
7063 PetscErrorCode  TSMonitor_Matlab(TS ts,PetscInt it, PetscReal time,Vec u, void *ctx)
7064 {
7065   PetscErrorCode  ierr;
7066   TSMatlabContext *sctx = (TSMatlabContext*)ctx;
7067   int             nlhs  = 1,nrhs = 6;
7068   mxArray         *plhs[1],*prhs[6];
7069   long long int   lx = 0,ls = 0;
7070 
7071   PetscFunctionBegin;
7072   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
7073   PetscValidHeaderSpecific(u,VEC_CLASSID,4);
7074 
7075   ierr = PetscMemcpy(&ls,&ts,sizeof(ts));CHKERRQ(ierr);
7076   ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
7077 
7078   prhs[0] =  mxCreateDoubleScalar((double)ls);
7079   prhs[1] =  mxCreateDoubleScalar((double)it);
7080   prhs[2] =  mxCreateDoubleScalar((double)time);
7081   prhs[3] =  mxCreateDoubleScalar((double)lx);
7082   prhs[4] =  mxCreateString(sctx->funcname);
7083   prhs[5] =  sctx->ctx;
7084   ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSMonitorInternal");CHKERRQ(ierr);
7085   ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
7086   mxDestroyArray(prhs[0]);
7087   mxDestroyArray(prhs[1]);
7088   mxDestroyArray(prhs[2]);
7089   mxDestroyArray(prhs[3]);
7090   mxDestroyArray(prhs[4]);
7091   mxDestroyArray(plhs[0]);
7092   PetscFunctionReturn(0);
7093 }
7094 
7095 
7096 #undef __FUNCT__
7097 #define __FUNCT__ "TSMonitorSetMatlab"
7098 /*
7099    TSMonitorSetMatlab - Sets the monitor function from Matlab
7100 
7101    Level: developer
7102 
7103 .keywords: TS, nonlinear, set, function
7104 
7105 .seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
7106 */
7107 PetscErrorCode  TSMonitorSetMatlab(TS ts,const char *func,mxArray *ctx)
7108 {
7109   PetscErrorCode  ierr;
7110   TSMatlabContext *sctx;
7111 
7112   PetscFunctionBegin;
7113   /* currently sctx is memory bleed */
7114   ierr = PetscNew(&sctx);CHKERRQ(ierr);
7115   ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
7116   /*
7117      This should work, but it doesn't
7118   sctx->ctx = ctx;
7119   mexMakeArrayPersistent(sctx->ctx);
7120   */
7121   sctx->ctx = mxDuplicateArray(ctx);
7122 
7123   ierr = TSMonitorSet(ts,TSMonitor_Matlab,sctx,NULL);CHKERRQ(ierr);
7124   PetscFunctionReturn(0);
7125 }
7126 #endif
7127 
7128 #undef __FUNCT__
7129 #define __FUNCT__ "TSMonitorLGSolution"
7130 /*@C
7131    TSMonitorLGSolution - Monitors progress of the TS solvers by plotting each component of the solution vector
7132        in a time based line graph
7133 
7134    Collective on TS
7135 
7136    Input Parameters:
7137 +  ts - the TS context
7138 .  step - current time-step
7139 .  ptime - current time
7140 .  u - current solution
7141 -  dctx - the TSMonitorLGCtx object that contains all the options for the monitoring, this is created with TSMonitorLGCtxCreate()
7142 
7143    Options Database:
7144 .   -ts_monitor_lg_solution_variables
7145 
7146    Level: intermediate
7147 
7148    Notes: Each process in a parallel run displays its component solutions in a separate window
7149 
7150 .keywords: TS,  vector, monitor, view
7151 
7152 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGCtxCreate(), TSMonitorLGCtxSetVariableNames(), TSMonitorLGCtxGetVariableNames(),
7153            TSMonitorLGSetVariableNames(), TSMonitorLGGetVariableNames(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetDisplayVariables(),
7154            TSMonitorLGCtxSetTransform(), TSMonitorLGSetTransform(), TSMonitorLGError(), TSMonitorLGSNESIterations(), TSMonitorLGKSPIterations(),
7155            TSMonitorEnvelopeCtxCreate(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxDestroy(), TSMonitorEnvelop()
7156 @*/
7157 PetscErrorCode  TSMonitorLGSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dctx)
7158 {
7159   PetscErrorCode    ierr;
7160   TSMonitorLGCtx    ctx = (TSMonitorLGCtx)dctx;
7161   const PetscScalar *yy;
7162   Vec               v;
7163 
7164   PetscFunctionBegin;
7165   if (step < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
7166   if (!step) {
7167     PetscDrawAxis axis;
7168     PetscInt      dim;
7169     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
7170     ierr = PetscDrawAxisSetLabels(axis,"Solution as function of time","Time","Solution");CHKERRQ(ierr);
7171     if (!ctx->names) {
7172       PetscBool flg;
7173       /* user provides names of variables to plot but no names has been set so assume names are integer values */
7174       ierr = PetscOptionsHasName(((PetscObject)ts)->options,((PetscObject)ts)->prefix,"-ts_monitor_lg_solution_variables",&flg);CHKERRQ(ierr);
7175       if (flg) {
7176         PetscInt i,n;
7177         char     **names;
7178         ierr = VecGetSize(u,&n);CHKERRQ(ierr);
7179         ierr = PetscMalloc1(n+1,&names);CHKERRQ(ierr);
7180         for (i=0; i<n; i++) {
7181           ierr = PetscMalloc1(5,&names[i]);CHKERRQ(ierr);
7182           ierr = PetscSNPrintf(names[i],5,"%D",i);CHKERRQ(ierr);
7183         }
7184         names[n] = NULL;
7185         ctx->names = names;
7186       }
7187     }
7188     if (ctx->names && !ctx->displaynames) {
7189       char      **displaynames;
7190       PetscBool flg;
7191       ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
7192       ierr = PetscMalloc1(dim+1,&displaynames);CHKERRQ(ierr);
7193       ierr = PetscMemzero(displaynames,(dim+1)*sizeof(char*));CHKERRQ(ierr);
7194       ierr = PetscOptionsGetStringArray(((PetscObject)ts)->options,((PetscObject)ts)->prefix,"-ts_monitor_lg_solution_variables",displaynames,&dim,&flg);CHKERRQ(ierr);
7195       if (flg) {
7196         ierr = TSMonitorLGCtxSetDisplayVariables(ctx,(const char *const *)displaynames);CHKERRQ(ierr);
7197       }
7198       ierr = PetscStrArrayDestroy(&displaynames);CHKERRQ(ierr);
7199     }
7200     if (ctx->displaynames) {
7201       ierr = PetscDrawLGSetDimension(ctx->lg,ctx->ndisplayvariables);CHKERRQ(ierr);
7202       ierr = PetscDrawLGSetLegend(ctx->lg,(const char *const *)ctx->displaynames);CHKERRQ(ierr);
7203     } else if (ctx->names) {
7204       ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
7205       ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
7206       ierr = PetscDrawLGSetLegend(ctx->lg,(const char *const *)ctx->names);CHKERRQ(ierr);
7207     } else {
7208       ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
7209       ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
7210     }
7211     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
7212   }
7213 
7214   if (!ctx->transform) v = u;
7215   else {ierr = (*ctx->transform)(ctx->transformctx,u,&v);CHKERRQ(ierr);}
7216   ierr = VecGetArrayRead(v,&yy);CHKERRQ(ierr);
7217   if (ctx->displaynames) {
7218     PetscInt i;
7219     for (i=0; i<ctx->ndisplayvariables; i++)
7220       ctx->displayvalues[i] = PetscRealPart(yy[ctx->displayvariables[i]]);
7221     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,ctx->displayvalues);CHKERRQ(ierr);
7222   } else {
7223 #if defined(PETSC_USE_COMPLEX)
7224     PetscInt  i,n;
7225     PetscReal *yreal;
7226     ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
7227     ierr = PetscMalloc1(n,&yreal);CHKERRQ(ierr);
7228     for (i=0; i<n; i++) yreal[i] = PetscRealPart(yy[i]);
7229     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yreal);CHKERRQ(ierr);
7230     ierr = PetscFree(yreal);CHKERRQ(ierr);
7231 #else
7232     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yy);CHKERRQ(ierr);
7233 #endif
7234   }
7235   ierr = VecRestoreArrayRead(v,&yy);CHKERRQ(ierr);
7236   if (ctx->transform) {ierr = VecDestroy(&v);CHKERRQ(ierr);}
7237 
7238   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
7239     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
7240     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
7241   }
7242   PetscFunctionReturn(0);
7243 }
7244 
7245 
7246 #undef __FUNCT__
7247 #define __FUNCT__ "TSMonitorLGSetVariableNames"
7248 /*@C
7249    TSMonitorLGSetVariableNames - Sets the name of each component in the solution vector so that it may be displayed in the plot
7250 
7251    Collective on TS
7252 
7253    Input Parameters:
7254 +  ts - the TS context
7255 -  names - the names of the components, final string must be NULL
7256 
7257    Level: intermediate
7258 
7259    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
7260 
7261 .keywords: TS,  vector, monitor, view
7262 
7263 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetVariableNames()
7264 @*/
7265 PetscErrorCode  TSMonitorLGSetVariableNames(TS ts,const char * const *names)
7266 {
7267   PetscErrorCode    ierr;
7268   PetscInt          i;
7269 
7270   PetscFunctionBegin;
7271   for (i=0; i<ts->numbermonitors; i++) {
7272     if (ts->monitor[i] == TSMonitorLGSolution) {
7273       ierr = TSMonitorLGCtxSetVariableNames((TSMonitorLGCtx)ts->monitorcontext[i],names);CHKERRQ(ierr);
7274       break;
7275     }
7276   }
7277   PetscFunctionReturn(0);
7278 }
7279 
7280 #undef __FUNCT__
7281 #define __FUNCT__ "TSMonitorLGCtxSetVariableNames"
7282 /*@C
7283    TSMonitorLGCtxSetVariableNames - Sets the name of each component in the solution vector so that it may be displayed in the plot
7284 
7285    Collective on TS
7286 
7287    Input Parameters:
7288 +  ts - the TS context
7289 -  names - the names of the components, final string must be NULL
7290 
7291    Level: intermediate
7292 
7293 .keywords: TS,  vector, monitor, view
7294 
7295 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables(), TSMonitorLGSetVariableNames()
7296 @*/
7297 PetscErrorCode  TSMonitorLGCtxSetVariableNames(TSMonitorLGCtx ctx,const char * const *names)
7298 {
7299   PetscErrorCode    ierr;
7300 
7301   PetscFunctionBegin;
7302   ierr = PetscStrArrayDestroy(&ctx->names);CHKERRQ(ierr);
7303   ierr = PetscStrArrayallocpy(names,&ctx->names);CHKERRQ(ierr);
7304   PetscFunctionReturn(0);
7305 }
7306 
7307 #undef __FUNCT__
7308 #define __FUNCT__ "TSMonitorLGGetVariableNames"
7309 /*@C
7310    TSMonitorLGGetVariableNames - Gets the name of each component in the solution vector so that it may be displayed in the plot
7311 
7312    Collective on TS
7313 
7314    Input Parameter:
7315 .  ts - the TS context
7316 
7317    Output Parameter:
7318 .  names - the names of the components, final string must be NULL
7319 
7320    Level: intermediate
7321 
7322    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
7323 
7324 .keywords: TS,  vector, monitor, view
7325 
7326 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables()
7327 @*/
7328 PetscErrorCode  TSMonitorLGGetVariableNames(TS ts,const char *const **names)
7329 {
7330   PetscInt       i;
7331 
7332   PetscFunctionBegin;
7333   *names = NULL;
7334   for (i=0; i<ts->numbermonitors; i++) {
7335     if (ts->monitor[i] == TSMonitorLGSolution) {
7336       TSMonitorLGCtx  ctx = (TSMonitorLGCtx) ts->monitorcontext[i];
7337       *names = (const char *const *)ctx->names;
7338       break;
7339     }
7340   }
7341   PetscFunctionReturn(0);
7342 }
7343 
7344 #undef __FUNCT__
7345 #define __FUNCT__ "TSMonitorLGCtxSetDisplayVariables"
7346 /*@C
7347    TSMonitorLGCtxSetDisplayVariables - Sets the variables that are to be display in the monitor
7348 
7349    Collective on TS
7350 
7351    Input Parameters:
7352 +  ctx - the TSMonitorLG context
7353 .  displaynames - the names of the components, final string must be NULL
7354 
7355    Level: intermediate
7356 
7357 .keywords: TS,  vector, monitor, view
7358 
7359 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames()
7360 @*/
7361 PetscErrorCode  TSMonitorLGCtxSetDisplayVariables(TSMonitorLGCtx ctx,const char * const *displaynames)
7362 {
7363   PetscInt          j = 0,k;
7364   PetscErrorCode    ierr;
7365 
7366   PetscFunctionBegin;
7367   if (!ctx->names) PetscFunctionReturn(0);
7368   ierr = PetscStrArrayDestroy(&ctx->displaynames);CHKERRQ(ierr);
7369   ierr = PetscStrArrayallocpy(displaynames,&ctx->displaynames);CHKERRQ(ierr);
7370   while (displaynames[j]) j++;
7371   ctx->ndisplayvariables = j;
7372   ierr = PetscMalloc1(ctx->ndisplayvariables,&ctx->displayvariables);CHKERRQ(ierr);
7373   ierr = PetscMalloc1(ctx->ndisplayvariables,&ctx->displayvalues);CHKERRQ(ierr);
7374   j = 0;
7375   while (displaynames[j]) {
7376     k = 0;
7377     while (ctx->names[k]) {
7378       PetscBool flg;
7379       ierr = PetscStrcmp(displaynames[j],ctx->names[k],&flg);CHKERRQ(ierr);
7380       if (flg) {
7381         ctx->displayvariables[j] = k;
7382         break;
7383       }
7384       k++;
7385     }
7386     j++;
7387   }
7388   PetscFunctionReturn(0);
7389 }
7390 
7391 
7392 #undef __FUNCT__
7393 #define __FUNCT__ "TSMonitorLGSetDisplayVariables"
7394 /*@C
7395    TSMonitorLGSetDisplayVariables - Sets the variables that are to be display in the monitor
7396 
7397    Collective on TS
7398 
7399    Input Parameters:
7400 +  ts - the TS context
7401 .  displaynames - the names of the components, final string must be NULL
7402 
7403    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
7404 
7405    Level: intermediate
7406 
7407 .keywords: TS,  vector, monitor, view
7408 
7409 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames()
7410 @*/
7411 PetscErrorCode  TSMonitorLGSetDisplayVariables(TS ts,const char * const *displaynames)
7412 {
7413   PetscInt          i;
7414   PetscErrorCode    ierr;
7415 
7416   PetscFunctionBegin;
7417   for (i=0; i<ts->numbermonitors; i++) {
7418     if (ts->monitor[i] == TSMonitorLGSolution) {
7419       ierr = TSMonitorLGCtxSetDisplayVariables((TSMonitorLGCtx)ts->monitorcontext[i],displaynames);CHKERRQ(ierr);
7420       break;
7421     }
7422   }
7423   PetscFunctionReturn(0);
7424 }
7425 
7426 #undef __FUNCT__
7427 #define __FUNCT__ "TSMonitorLGSetTransform"
7428 /*@C
7429    TSMonitorLGSetTransform - Solution vector will be transformed by provided function before being displayed
7430 
7431    Collective on TS
7432 
7433    Input Parameters:
7434 +  ts - the TS context
7435 .  transform - the transform function
7436 .  destroy - function to destroy the optional context
7437 -  ctx - optional context used by transform function
7438 
7439    Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored
7440 
7441    Level: intermediate
7442 
7443 .keywords: TS,  vector, monitor, view
7444 
7445 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames(), TSMonitorLGCtxSetTransform()
7446 @*/
7447 PetscErrorCode  TSMonitorLGSetTransform(TS ts,PetscErrorCode (*transform)(void*,Vec,Vec*),PetscErrorCode (*destroy)(void*),void *tctx)
7448 {
7449   PetscInt          i;
7450   PetscErrorCode    ierr;
7451 
7452   PetscFunctionBegin;
7453   for (i=0; i<ts->numbermonitors; i++) {
7454     if (ts->monitor[i] == TSMonitorLGSolution) {
7455       ierr = TSMonitorLGCtxSetTransform((TSMonitorLGCtx)ts->monitorcontext[i],transform,destroy,tctx);CHKERRQ(ierr);
7456     }
7457   }
7458   PetscFunctionReturn(0);
7459 }
7460 
7461 #undef __FUNCT__
7462 #define __FUNCT__ "TSMonitorLGCtxSetTransform"
7463 /*@C
7464    TSMonitorLGCtxSetTransform - Solution vector will be transformed by provided function before being displayed
7465 
7466    Collective on TSLGCtx
7467 
7468    Input Parameters:
7469 +  ts - the TS context
7470 .  transform - the transform function
7471 .  destroy - function to destroy the optional context
7472 -  ctx - optional context used by transform function
7473 
7474    Level: intermediate
7475 
7476 .keywords: TS,  vector, monitor, view
7477 
7478 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames(), TSMonitorLGSetTransform()
7479 @*/
7480 PetscErrorCode  TSMonitorLGCtxSetTransform(TSMonitorLGCtx ctx,PetscErrorCode (*transform)(void*,Vec,Vec*),PetscErrorCode (*destroy)(void*),void *tctx)
7481 {
7482   PetscFunctionBegin;
7483   ctx->transform    = transform;
7484   ctx->transformdestroy = destroy;
7485   ctx->transformctx = tctx;
7486   PetscFunctionReturn(0);
7487 }
7488 
7489 #undef __FUNCT__
7490 #define __FUNCT__ "TSMonitorLGError"
7491 /*@C
7492    TSMonitorLGError - Monitors progress of the TS solvers by plotting each component of the solution vector
7493        in a time based line graph
7494 
7495    Collective on TS
7496 
7497    Input Parameters:
7498 +  ts - the TS context
7499 .  step - current time-step
7500 .  ptime - current time
7501 .  u - current solution
7502 -  dctx - TSMonitorLGCtx object created with TSMonitorLGCtxCreate()
7503 
7504    Level: intermediate
7505 
7506    Notes: Each process in a parallel run displays its component errors in a separate window
7507 
7508    The user must provide the solution using TSSetSolutionFunction() to use this monitor.
7509 
7510    Options Database Keys:
7511 .  -ts_monitor_lg_error - create a graphical monitor of error history
7512 
7513 .keywords: TS,  vector, monitor, view
7514 
7515 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSSetSolutionFunction()
7516 @*/
7517 PetscErrorCode  TSMonitorLGError(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
7518 {
7519   PetscErrorCode    ierr;
7520   TSMonitorLGCtx    ctx = (TSMonitorLGCtx)dummy;
7521   const PetscScalar *yy;
7522   Vec               y;
7523 
7524   PetscFunctionBegin;
7525   if (!step) {
7526     PetscDrawAxis axis;
7527     PetscInt      dim;
7528     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
7529     ierr = PetscDrawAxisSetLabels(axis,"Error in solution as function of time","Time","Solution");CHKERRQ(ierr);
7530     ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
7531     ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
7532     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
7533   }
7534   ierr = VecDuplicate(u,&y);CHKERRQ(ierr);
7535   ierr = TSComputeSolutionFunction(ts,ptime,y);CHKERRQ(ierr);
7536   ierr = VecAXPY(y,-1.0,u);CHKERRQ(ierr);
7537   ierr = VecGetArrayRead(y,&yy);CHKERRQ(ierr);
7538 #if defined(PETSC_USE_COMPLEX)
7539   {
7540     PetscReal *yreal;
7541     PetscInt  i,n;
7542     ierr = VecGetLocalSize(y,&n);CHKERRQ(ierr);
7543     ierr = PetscMalloc1(n,&yreal);CHKERRQ(ierr);
7544     for (i=0; i<n; i++) yreal[i] = PetscRealPart(yy[i]);
7545     ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yreal);CHKERRQ(ierr);
7546     ierr = PetscFree(yreal);CHKERRQ(ierr);
7547   }
7548 #else
7549   ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yy);CHKERRQ(ierr);
7550 #endif
7551   ierr = VecRestoreArrayRead(y,&yy);CHKERRQ(ierr);
7552   ierr = VecDestroy(&y);CHKERRQ(ierr);
7553   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
7554     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
7555     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
7556   }
7557   PetscFunctionReturn(0);
7558 }
7559 
7560 #undef __FUNCT__
7561 #define __FUNCT__ "TSMonitorLGSNESIterations"
7562 PetscErrorCode TSMonitorLGSNESIterations(TS ts,PetscInt n,PetscReal ptime,Vec v,void *monctx)
7563 {
7564   TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
7565   PetscReal      x   = ptime,y;
7566   PetscErrorCode ierr;
7567   PetscInt       its;
7568 
7569   PetscFunctionBegin;
7570   if (n < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
7571   if (!n) {
7572     PetscDrawAxis axis;
7573     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
7574     ierr = PetscDrawAxisSetLabels(axis,"Nonlinear iterations as function of time","Time","SNES Iterations");CHKERRQ(ierr);
7575     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
7576     ctx->snes_its = 0;
7577   }
7578   ierr = TSGetSNESIterations(ts,&its);CHKERRQ(ierr);
7579   y    = its - ctx->snes_its;
7580   ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
7581   if (((ctx->howoften > 0) && (!(n % ctx->howoften)) && (n > -1)) || ((ctx->howoften == -1) && (n == -1))) {
7582     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
7583     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
7584   }
7585   ctx->snes_its = its;
7586   PetscFunctionReturn(0);
7587 }
7588 
7589 #undef __FUNCT__
7590 #define __FUNCT__ "TSMonitorLGKSPIterations"
7591 PetscErrorCode TSMonitorLGKSPIterations(TS ts,PetscInt n,PetscReal ptime,Vec v,void *monctx)
7592 {
7593   TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
7594   PetscReal      x   = ptime,y;
7595   PetscErrorCode ierr;
7596   PetscInt       its;
7597 
7598   PetscFunctionBegin;
7599   if (n < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
7600   if (!n) {
7601     PetscDrawAxis axis;
7602     ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
7603     ierr = PetscDrawAxisSetLabels(axis,"Linear iterations as function of time","Time","KSP Iterations");CHKERRQ(ierr);
7604     ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
7605     ctx->ksp_its = 0;
7606   }
7607   ierr = TSGetKSPIterations(ts,&its);CHKERRQ(ierr);
7608   y    = its - ctx->ksp_its;
7609   ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
7610   if (((ctx->howoften > 0) && (!(n % ctx->howoften)) && (n > -1)) || ((ctx->howoften == -1) && (n == -1))) {
7611     ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
7612     ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
7613   }
7614   ctx->ksp_its = its;
7615   PetscFunctionReturn(0);
7616 }
7617 
7618 #undef __FUNCT__
7619 #define __FUNCT__ "TSComputeLinearStability"
7620 /*@
7621    TSComputeLinearStability - computes the linear stability function at a point
7622 
7623    Collective on TS and Vec
7624 
7625    Input Parameters:
7626 +  ts - the TS context
7627 -  xr,xi - real and imaginary part of input arguments
7628 
7629    Output Parameters:
7630 .  yr,yi - real and imaginary part of function value
7631 
7632    Level: developer
7633 
7634 .keywords: TS, compute
7635 
7636 .seealso: TSSetRHSFunction(), TSComputeIFunction()
7637 @*/
7638 PetscErrorCode TSComputeLinearStability(TS ts,PetscReal xr,PetscReal xi,PetscReal *yr,PetscReal *yi)
7639 {
7640   PetscErrorCode ierr;
7641 
7642   PetscFunctionBegin;
7643   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
7644   if (!ts->ops->linearstability) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Linearized stability function not provided for this method");
7645   ierr = (*ts->ops->linearstability)(ts,xr,xi,yr,yi);CHKERRQ(ierr);
7646   PetscFunctionReturn(0);
7647 }
7648 
7649 /* ------------------------------------------------------------------------*/
7650 #undef __FUNCT__
7651 #define __FUNCT__ "TSMonitorEnvelopeCtxCreate"
7652 /*@C
7653    TSMonitorEnvelopeCtxCreate - Creates a context for use with TSMonitorEnvelope()
7654 
7655    Collective on TS
7656 
7657    Input Parameters:
7658 .  ts  - the ODE solver object
7659 
7660    Output Parameter:
7661 .  ctx - the context
7662 
7663    Level: intermediate
7664 
7665 .keywords: TS, monitor, line graph, residual, seealso
7666 
7667 .seealso: TSMonitorLGTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError()
7668 
7669 @*/
7670 PetscErrorCode  TSMonitorEnvelopeCtxCreate(TS ts,TSMonitorEnvelopeCtx *ctx)
7671 {
7672   PetscErrorCode ierr;
7673 
7674   PetscFunctionBegin;
7675   ierr = PetscNew(ctx);CHKERRQ(ierr);
7676   PetscFunctionReturn(0);
7677 }
7678 
7679 #undef __FUNCT__
7680 #define __FUNCT__ "TSMonitorEnvelope"
7681 /*@C
7682    TSMonitorEnvelope - Monitors the maximum and minimum value of each component of the solution
7683 
7684    Collective on TS
7685 
7686    Input Parameters:
7687 +  ts - the TS context
7688 .  step - current time-step
7689 .  ptime - current time
7690 .  u  - current solution
7691 -  dctx - the envelope context
7692 
7693    Options Database:
7694 .  -ts_monitor_envelope
7695 
7696    Level: intermediate
7697 
7698    Notes: after a solve you can use TSMonitorEnvelopeGetBounds() to access the envelope
7699 
7700 .keywords: TS,  vector, monitor, view
7701 
7702 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxCreate()
7703 @*/
7704 PetscErrorCode  TSMonitorEnvelope(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dctx)
7705 {
7706   PetscErrorCode       ierr;
7707   TSMonitorEnvelopeCtx ctx = (TSMonitorEnvelopeCtx)dctx;
7708 
7709   PetscFunctionBegin;
7710   if (!ctx->max) {
7711     ierr = VecDuplicate(u,&ctx->max);CHKERRQ(ierr);
7712     ierr = VecDuplicate(u,&ctx->min);CHKERRQ(ierr);
7713     ierr = VecCopy(u,ctx->max);CHKERRQ(ierr);
7714     ierr = VecCopy(u,ctx->min);CHKERRQ(ierr);
7715   } else {
7716     ierr = VecPointwiseMax(ctx->max,u,ctx->max);CHKERRQ(ierr);
7717     ierr = VecPointwiseMin(ctx->min,u,ctx->min);CHKERRQ(ierr);
7718   }
7719   PetscFunctionReturn(0);
7720 }
7721 
7722 
7723 #undef __FUNCT__
7724 #define __FUNCT__ "TSMonitorEnvelopeGetBounds"
7725 /*@C
7726    TSMonitorEnvelopeGetBounds - Gets the bounds for the components of the solution
7727 
7728    Collective on TS
7729 
7730    Input Parameter:
7731 .  ts - the TS context
7732 
7733    Output Parameter:
7734 +  max - the maximum values
7735 -  min - the minimum values
7736 
7737    Notes: If the TS does not have a TSMonitorEnvelopeCtx associated with it then this function is ignored
7738 
7739    Level: intermediate
7740 
7741 .keywords: TS,  vector, monitor, view
7742 
7743 .seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables()
7744 @*/
7745 PetscErrorCode  TSMonitorEnvelopeGetBounds(TS ts,Vec *max,Vec *min)
7746 {
7747   PetscInt i;
7748 
7749   PetscFunctionBegin;
7750   if (max) *max = NULL;
7751   if (min) *min = NULL;
7752   for (i=0; i<ts->numbermonitors; i++) {
7753     if (ts->monitor[i] == TSMonitorEnvelope) {
7754       TSMonitorEnvelopeCtx  ctx = (TSMonitorEnvelopeCtx) ts->monitorcontext[i];
7755       if (max) *max = ctx->max;
7756       if (min) *min = ctx->min;
7757       break;
7758     }
7759   }
7760   PetscFunctionReturn(0);
7761 }
7762 
7763 #undef __FUNCT__
7764 #define __FUNCT__ "TSMonitorEnvelopeCtxDestroy"
7765 /*@C
7766    TSMonitorEnvelopeCtxDestroy - Destroys a context that was created  with TSMonitorEnvelopeCtxCreate().
7767 
7768    Collective on TSMonitorEnvelopeCtx
7769 
7770    Input Parameter:
7771 .  ctx - the monitor context
7772 
7773    Level: intermediate
7774 
7775 .keywords: TS, monitor, line graph, destroy
7776 
7777 .seealso: TSMonitorLGCtxCreate(),  TSMonitorSet(), TSMonitorLGTimeStep()
7778 @*/
7779 PetscErrorCode  TSMonitorEnvelopeCtxDestroy(TSMonitorEnvelopeCtx *ctx)
7780 {
7781   PetscErrorCode ierr;
7782 
7783   PetscFunctionBegin;
7784   ierr = VecDestroy(&(*ctx)->min);CHKERRQ(ierr);
7785   ierr = VecDestroy(&(*ctx)->max);CHKERRQ(ierr);
7786   ierr = PetscFree(*ctx);CHKERRQ(ierr);
7787   PetscFunctionReturn(0);
7788 }
7789 
7790 #undef __FUNCT__
7791 #define __FUNCT__ "TSRollBack"
7792 /*@
7793    TSRollBack - Rolls back one time step
7794 
7795    Collective on TS
7796 
7797    Input Parameter:
7798 .  ts - the TS context obtained from TSCreate()
7799 
7800    Level: advanced
7801 
7802 .keywords: TS, timestep, rollback
7803 
7804 .seealso: TSCreate(), TSSetUp(), TSDestroy(), TSSolve(), TSSetPreStep(), TSSetPreStage(), TSInterpolate()
7805 @*/
7806 PetscErrorCode  TSRollBack(TS ts)
7807 {
7808   PetscErrorCode ierr;
7809 
7810   PetscFunctionBegin;
7811   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
7812   if (ts->steprollback) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"TSRollBack already called");
7813   if (!ts->ops->rollback) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRollBack not implemented for type '%s'",((PetscObject)ts)->type_name);
7814   ierr = (*ts->ops->rollback)(ts);CHKERRQ(ierr);
7815   ts->time_step = ts->ptime - ts->ptime_prev;
7816   ts->ptime = ts->ptime_prev;
7817   ts->ptime_prev = ts->ptime_prev_rollback;
7818   ts->steps--; ts->total_steps--;
7819   ierr = TSPostEvaluate(ts);CHKERRQ(ierr);
7820   ts->steprollback = PETSC_TRUE;
7821   PetscFunctionReturn(0);
7822 }
7823 
7824 #undef __FUNCT__
7825 #define __FUNCT__ "TSGetStages"
7826 /*@
7827    TSGetStages - Get the number of stages and stage values
7828 
7829    Input Parameter:
7830 .  ts - the TS context obtained from TSCreate()
7831 
7832    Level: advanced
7833 
7834 .keywords: TS, getstages
7835 
7836 .seealso: TSCreate()
7837 @*/
7838 PetscErrorCode  TSGetStages(TS ts,PetscInt *ns,Vec **Y)
7839 {
7840   PetscErrorCode ierr;
7841 
7842   PetscFunctionBegin;
7843   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
7844   PetscValidPointer(ns,2);
7845 
7846   if (!ts->ops->getstages) *ns=0;
7847   else {
7848     ierr = (*ts->ops->getstages)(ts,ns,Y);CHKERRQ(ierr);
7849   }
7850   PetscFunctionReturn(0);
7851 }
7852 
7853 #undef __FUNCT__
7854 #define __FUNCT__ "TSComputeIJacobianDefaultColor"
7855 /*@C
7856   TSComputeIJacobianDefaultColor - Computes the Jacobian using finite differences and coloring to exploit matrix sparsity.
7857 
7858   Collective on SNES
7859 
7860   Input Parameters:
7861 + ts - the TS context
7862 . t - current timestep
7863 . U - state vector
7864 . Udot - time derivative of state vector
7865 . shift - shift to apply, see note below
7866 - ctx - an optional user context
7867 
7868   Output Parameters:
7869 + J - Jacobian matrix (not altered in this routine)
7870 - B - newly computed Jacobian matrix to use with preconditioner (generally the same as J)
7871 
7872   Level: intermediate
7873 
7874   Notes:
7875   If F(t,U,Udot)=0 is the DAE, the required Jacobian is
7876 
7877   dF/dU + shift*dF/dUdot
7878 
7879   Most users should not need to explicitly call this routine, as it
7880   is used internally within the nonlinear solvers.
7881 
7882   This will first try to get the coloring from the DM.  If the DM type has no coloring
7883   routine, then it will try to get the coloring from the matrix.  This requires that the
7884   matrix have nonzero entries precomputed.
7885 
7886 .keywords: TS, finite differences, Jacobian, coloring, sparse
7887 .seealso: TSSetIJacobian(), MatFDColoringCreate(), MatFDColoringSetFunction()
7888 @*/
7889 PetscErrorCode TSComputeIJacobianDefaultColor(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat J,Mat B,void *ctx)
7890 {
7891   SNES           snes;
7892   MatFDColoring  color;
7893   PetscBool      hascolor, matcolor = PETSC_FALSE;
7894   PetscErrorCode ierr;
7895 
7896   PetscFunctionBegin;
7897   ierr = PetscOptionsGetBool(((PetscObject)ts)->options,((PetscObject) ts)->prefix, "-ts_fd_color_use_mat", &matcolor, NULL);CHKERRQ(ierr);
7898   ierr = PetscObjectQuery((PetscObject) B, "TSMatFDColoring", (PetscObject *) &color);CHKERRQ(ierr);
7899   if (!color) {
7900     DM         dm;
7901     ISColoring iscoloring;
7902 
7903     ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
7904     ierr = DMHasColoring(dm, &hascolor);CHKERRQ(ierr);
7905     if (hascolor && !matcolor) {
7906       ierr = DMCreateColoring(dm, IS_COLORING_GLOBAL, &iscoloring);CHKERRQ(ierr);
7907       ierr = MatFDColoringCreate(B, iscoloring, &color);CHKERRQ(ierr);
7908       ierr = MatFDColoringSetFunction(color, (PetscErrorCode (*)(void)) SNESTSFormFunction, (void *) ts);CHKERRQ(ierr);
7909       ierr = MatFDColoringSetFromOptions(color);CHKERRQ(ierr);
7910       ierr = MatFDColoringSetUp(B, iscoloring, color);CHKERRQ(ierr);
7911       ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
7912     } else {
7913       MatColoring mc;
7914 
7915       ierr = MatColoringCreate(B, &mc);CHKERRQ(ierr);
7916       ierr = MatColoringSetDistance(mc, 2);CHKERRQ(ierr);
7917       ierr = MatColoringSetType(mc, MATCOLORINGSL);CHKERRQ(ierr);
7918       ierr = MatColoringSetFromOptions(mc);CHKERRQ(ierr);
7919       ierr = MatColoringApply(mc, &iscoloring);CHKERRQ(ierr);
7920       ierr = MatColoringDestroy(&mc);CHKERRQ(ierr);
7921       ierr = MatFDColoringCreate(B, iscoloring, &color);CHKERRQ(ierr);
7922       ierr = MatFDColoringSetFunction(color, (PetscErrorCode (*)(void)) SNESTSFormFunction, (void *) ts);CHKERRQ(ierr);
7923       ierr = MatFDColoringSetFromOptions(color);CHKERRQ(ierr);
7924       ierr = MatFDColoringSetUp(B, iscoloring, color);CHKERRQ(ierr);
7925       ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
7926     }
7927     ierr = PetscObjectCompose((PetscObject) B, "TSMatFDColoring", (PetscObject) color);CHKERRQ(ierr);
7928     ierr = PetscObjectDereference((PetscObject) color);CHKERRQ(ierr);
7929   }
7930   ierr = TSGetSNES(ts, &snes);CHKERRQ(ierr);
7931   ierr = MatFDColoringApply(B, color, U, snes);CHKERRQ(ierr);
7932   if (J != B) {
7933     ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
7934     ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
7935   }
7936   PetscFunctionReturn(0);
7937 }
7938 
7939 #undef __FUNCT__
7940 #define __FUNCT__ "TSSetFunctionDomainError"
7941 /*@
7942     TSSetFunctionDomainError - Set the function testing if the current state vector is valid
7943 
7944     Input Parameters:
7945     ts - the TS context
7946     func - function called within TSFunctionDomainError
7947 
7948     Level: intermediate
7949 
7950 .keywords: TS, state, domain
7951 .seealso: TSAdaptCheckStage(), TSFunctionDomainError()
7952 @*/
7953 
7954 PetscErrorCode TSSetFunctionDomainError(TS ts, PetscErrorCode (*func)(TS,PetscReal,Vec,PetscBool*))
7955 {
7956   PetscFunctionBegin;
7957   PetscValidHeaderSpecific(ts, TS_CLASSID,1);
7958   ts->functiondomainerror = func;
7959   PetscFunctionReturn(0);
7960 }
7961 
7962 #undef __FUNCT__
7963 #define __FUNCT__ "TSFunctionDomainError"
7964 /*@
7965     TSFunctionDomainError - Check if the current state is valid
7966 
7967     Input Parameters:
7968     ts - the TS context
7969     stagetime - time of the simulation
7970     Y - state vector to check.
7971 
7972     Output Parameter:
7973     accept - Set to PETSC_FALSE if the current state vector is valid.
7974 
7975     Note:
7976     This function should be used to ensure the state is in a valid part of the space.
7977     For example, one can ensure here all values are positive.
7978 
7979     Level: advanced
7980 @*/
7981 PetscErrorCode TSFunctionDomainError(TS ts,PetscReal stagetime,Vec Y,PetscBool* accept)
7982 {
7983   PetscErrorCode ierr;
7984 
7985   PetscFunctionBegin;
7986 
7987   PetscValidHeaderSpecific(ts,TS_CLASSID,1);
7988   *accept = PETSC_TRUE;
7989   if (ts->functiondomainerror) {
7990     PetscStackCallStandard((*ts->functiondomainerror),(ts,stagetime,Y,accept));
7991   }
7992   PetscFunctionReturn(0);
7993 }
7994 
7995 #undef  __FUNCT__
7996 #define __FUNCT__ "TSClone"
7997 /*@C
7998   TSClone - This function clones a time step object.
7999 
8000   Collective on MPI_Comm
8001 
8002   Input Parameter:
8003 . tsin    - The input TS
8004 
8005   Output Parameter:
8006 . tsout   - The output TS (cloned)
8007 
8008   Notes:
8009   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.
8010 
8011   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);
8012 
8013   Level: developer
8014 
8015 .keywords: TS, clone
8016 .seealso: TSCreate(), TSSetType(), TSSetUp(), TSDestroy(), TSSetProblemType()
8017 @*/
8018 PetscErrorCode  TSClone(TS tsin, TS *tsout)
8019 {
8020   TS             t;
8021   PetscErrorCode ierr;
8022   SNES           snes_start;
8023   DM             dm;
8024   TSType         type;
8025 
8026   PetscFunctionBegin;
8027   PetscValidPointer(tsin,1);
8028   *tsout = NULL;
8029 
8030   ierr = PetscHeaderCreate(t, TS_CLASSID, "TS", "Time stepping", "TS", PetscObjectComm((PetscObject)tsin), TSDestroy, TSView);CHKERRQ(ierr);
8031 
8032   /* General TS description */
8033   t->numbermonitors    = 0;
8034   t->setupcalled       = 0;
8035   t->ksp_its           = 0;
8036   t->snes_its          = 0;
8037   t->nwork             = 0;
8038   t->rhsjacobian.time  = -1e20;
8039   t->rhsjacobian.scale = 1.;
8040   t->ijacobian.shift   = 1.;
8041 
8042   ierr = TSGetSNES(tsin,&snes_start);CHKERRQ(ierr);
8043   ierr = TSSetSNES(t,snes_start);CHKERRQ(ierr);
8044 
8045   ierr = TSGetDM(tsin,&dm);CHKERRQ(ierr);
8046   ierr = TSSetDM(t,dm);CHKERRQ(ierr);
8047 
8048   t->adapt = tsin->adapt;
8049   ierr = PetscObjectReference((PetscObject)t->adapt);CHKERRQ(ierr);
8050 
8051   t->problem_type      = tsin->problem_type;
8052   t->ptime             = tsin->ptime;
8053   t->time_step         = tsin->time_step;
8054   t->max_time          = tsin->max_time;
8055   t->steps             = tsin->steps;
8056   t->max_steps         = tsin->max_steps;
8057   t->equation_type     = tsin->equation_type;
8058   t->atol              = tsin->atol;
8059   t->rtol              = tsin->rtol;
8060   t->max_snes_failures = tsin->max_snes_failures;
8061   t->max_reject        = tsin->max_reject;
8062   t->errorifstepfailed = tsin->errorifstepfailed;
8063 
8064   ierr = TSGetType(tsin,&type);CHKERRQ(ierr);
8065   ierr = TSSetType(t,type);CHKERRQ(ierr);
8066 
8067   t->vec_sol           = NULL;
8068 
8069   t->cfltime          = tsin->cfltime;
8070   t->cfltime_local    = tsin->cfltime_local;
8071   t->exact_final_time = tsin->exact_final_time;
8072 
8073   ierr = PetscMemcpy(t->ops,tsin->ops,sizeof(struct _TSOps));CHKERRQ(ierr);
8074 
8075   if (((PetscObject)tsin)->fortran_func_pointers) {
8076     PetscInt i;
8077     ierr = PetscMalloc((10)*sizeof(void(*)(void)),&((PetscObject)t)->fortran_func_pointers);CHKERRQ(ierr);
8078     for (i=0; i<10; i++) {
8079       ((PetscObject)t)->fortran_func_pointers[i] = ((PetscObject)tsin)->fortran_func_pointers[i];
8080     }
8081   }
8082   *tsout = t;
8083   PetscFunctionReturn(0);
8084 }
8085