xref: /petsc/src/ts/interface/ts.c (revision 6f25b0d859dac903ff686d220b65c3e0af8b9181)

#include <petsc/private/tsimpl.h>        /*I "petscts.h"  I*/
#include <petscdmshell.h>
#include <petscdmda.h>
#include <petscviewer.h>
#include <petscdraw.h>

/* Logging support */
PetscClassId  TS_CLASSID, DMTS_CLASSID;
PetscLogEvent TS_AdjointStep, TS_Step, TS_PseudoComputeTimeStep, TS_FunctionEval, TS_JacobianEval;

const char *const TSExactFinalTimeOptions[] = {"UNSPECIFIED","STEPOVER","INTERPOLATE","MATCHSTEP","TSExactFinalTimeOption","TS_EXACTFINALTIME_",0};

struct _n_TSMonitorDrawCtx {
  PetscViewer   viewer;
  Vec           initialsolution;
  PetscBool     showinitial;
  PetscInt      howoften;  /* when > 0 uses step % howoften, when negative only final solution plotted */
  PetscBool     showtimestepandtime;
};

/*@C
   TSMonitorSetFromOptions - Sets a monitor function and viewer appropriate for the type indicated by the user

   Collective on TS

   Input Parameters:
+  ts - TS object you wish to monitor
.  name - the monitor type one is seeking
.  help - message indicating what monitoring is done
.  manual - manual page for the monitor
.  monitor - the monitor function
-  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

   Level: developer

.seealso: PetscOptionsGetViewer(), PetscOptionsGetReal(), PetscOptionsHasName(), PetscOptionsGetString(),
          PetscOptionsGetIntArray(), PetscOptionsGetRealArray(), PetscOptionsBool()
          PetscOptionsInt(), PetscOptionsString(), PetscOptionsReal(), PetscOptionsBool(),
          PetscOptionsName(), PetscOptionsBegin(), PetscOptionsEnd(), PetscOptionsHead(),
          PetscOptionsStringArray(),PetscOptionsRealArray(), PetscOptionsScalar(),
          PetscOptionsBoolGroupBegin(), PetscOptionsBoolGroup(), PetscOptionsBoolGroupEnd(),
          PetscOptionsFList(), PetscOptionsEList()
@*/
PetscErrorCode  TSMonitorSetFromOptions(TS ts,const char name[],const char help[], const char manual[],PetscErrorCode (*monitor)(TS,PetscInt,PetscReal,Vec,PetscViewerAndFormat*),PetscErrorCode (*monitorsetup)(TS,PetscViewerAndFormat*))
{
  PetscErrorCode    ierr;
  PetscViewer       viewer;
  PetscViewerFormat format;
  PetscBool         flg;

  PetscFunctionBegin;
  ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject)ts),((PetscObject)ts)->prefix,name,&viewer,&format,&flg);CHKERRQ(ierr);
  if (flg) {
    PetscViewerAndFormat *vf;
    ierr = PetscViewerAndFormatCreate(viewer,format,&vf);CHKERRQ(ierr);
    ierr = PetscObjectDereference((PetscObject)viewer);CHKERRQ(ierr);
    if (monitorsetup) {
      ierr = (*monitorsetup)(ts,vf);CHKERRQ(ierr);
    }
    ierr = TSMonitorSet(ts,(PetscErrorCode (*)(TS,PetscInt,PetscReal,Vec,void*))monitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@C
   TSAdjointMonitorSensi - monitors the first lambda sensitivity

   Level: intermediate

.keywords: TS, set, monitor

.seealso: TSAdjointMonitorSet()
@*/
PetscErrorCode TSAdjointMonitorSensi(TS ts,PetscInt step,PetscReal ptime,Vec v,PetscInt numcost,Vec *lambda,Vec *mu,PetscViewerAndFormat *vf)
{
  PetscErrorCode ierr;
  PetscViewer    viewer = vf->viewer;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
  ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
  ierr = VecView(lambda[0],viewer);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSAdjointMonitorSetFromOptions - Sets a monitor function and viewer appropriate for the type indicated by the user

   Collective on TS

   Input Parameters:
+  ts - TS object you wish to monitor
.  name - the monitor type one is seeking
.  help - message indicating what monitoring is done
.  manual - manual page for the monitor
.  monitor - the monitor function
-  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

   Level: developer

.seealso: PetscOptionsGetViewer(), PetscOptionsGetReal(), PetscOptionsHasName(), PetscOptionsGetString(),
          PetscOptionsGetIntArray(), PetscOptionsGetRealArray(), PetscOptionsBool()
          PetscOptionsInt(), PetscOptionsString(), PetscOptionsReal(), PetscOptionsBool(),
          PetscOptionsName(), PetscOptionsBegin(), PetscOptionsEnd(), PetscOptionsHead(),
          PetscOptionsStringArray(),PetscOptionsRealArray(), PetscOptionsScalar(),
          PetscOptionsBoolGroupBegin(), PetscOptionsBoolGroup(), PetscOptionsBoolGroupEnd(),
          PetscOptionsFList(), PetscOptionsEList()
@*/
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*))
{
  PetscErrorCode    ierr;
  PetscViewer       viewer;
  PetscViewerFormat format;
  PetscBool         flg;

  PetscFunctionBegin;
  ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject)ts),((PetscObject)ts)->prefix,name,&viewer,&format,&flg);CHKERRQ(ierr);
  if (flg) {
    PetscViewerAndFormat *vf;
    ierr = PetscViewerAndFormatCreate(viewer,format,&vf);CHKERRQ(ierr);
    ierr = PetscObjectDereference((PetscObject)viewer);CHKERRQ(ierr);
    if (monitorsetup) {
      ierr = (*monitorsetup)(ts,vf);CHKERRQ(ierr);
    }
    ierr = TSAdjointMonitorSet(ts,(PetscErrorCode (*)(TS,PetscInt,PetscReal,Vec,PetscInt,Vec*,Vec*,void*))monitor,vf,(PetscErrorCode (*)(void**))PetscViewerAndFormatDestroy);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode TSAdaptSetDefaultType(TSAdapt adapt,TSAdaptType default_type)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(adapt,TSADAPT_CLASSID,1);
  PetscValidCharPointer(default_type,2);
  if (!((PetscObject)adapt)->type_name) {
    ierr = TSAdaptSetType(adapt,default_type);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@
   TSSetFromOptions - Sets various TS parameters from user options.

   Collective on TS

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Options Database Keys:
+  -ts_type <type> - TSEULER, TSBEULER, TSSUNDIALS, TSPSEUDO, TSCN, TSRK, TSTHETA, TSALPHA, TSGLLE, TSSSP, TSGLEE
.  -ts_save_trajectory - checkpoint the solution at each time-step
.  -ts_max_time <time> - maximum time to compute to
.  -ts_max_steps <steps> - maximum number of time-steps to take
.  -ts_init_time <time> - initial time to start computation
.  -ts_final_time <time> - final time to compute to
.  -ts_dt <dt> - initial time step
.  -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
.  -ts_max_snes_failures <maxfailures> - Maximum number of nonlinear solve failures allowed
.  -ts_max_reject <maxrejects> - Maximum number of step rejections before step fails
.  -ts_error_if_step_fails <true,false> - Error if no step succeeds
.  -ts_rtol <rtol> - relative tolerance for local truncation error
.  -ts_atol <atol> Absolute tolerance for local truncation error
.  -ts_adjoint_solve <yes,no> After solving the ODE/DAE solve the adjoint problem (requires -ts_save_trajectory)
.  -ts_fd_color - Use finite differences with coloring to compute IJacobian
.  -ts_monitor - print information at each timestep
.  -ts_monitor_lg_solution - Monitor solution graphically
.  -ts_monitor_lg_error - Monitor error graphically
.  -ts_monitor_lg_timestep - Monitor timestep size graphically
.  -ts_monitor_lg_timestep_log - Monitor log timestep size graphically
.  -ts_monitor_lg_snes_iterations - Monitor number nonlinear iterations for each timestep graphically
.  -ts_monitor_lg_ksp_iterations - Monitor number nonlinear iterations for each timestep graphically
.  -ts_monitor_sp_eig - Monitor eigenvalues of linearized operator graphically
.  -ts_monitor_draw_solution - Monitor solution graphically
.  -ts_monitor_draw_solution_phase  <xleft,yleft,xright,yright> - Monitor solution graphically with phase diagram, requires problem with exactly 2 degrees of freedom
.  -ts_monitor_draw_error - Monitor error graphically, requires use to have provided TSSetSolutionFunction()
.  -ts_monitor_solution [ascii binary draw][:filename][:viewerformat] - monitors the solution at each timestep
.  -ts_monitor_solution_vtk <filename.vts,filename.vtu> - Save each time step to a binary file, use filename-%%03D.vts (filename-%%03D.vtu)
.  -ts_monitor_envelope - determine maximum and minimum value of each component of the solution over the solution time
.  -ts_adjoint_monitor - print information at each adjoint time step
-  -ts_adjoint_monitor_draw_sensi - monitor the sensitivity of the first cost function wrt initial conditions (lambda[0]) graphically

   Developer Note: We should unify all the -ts_monitor options in the way that -xxx_view has been unified

   Level: beginner

.keywords: TS, timestep, set, options, database

.seealso: TSGetType()
@*/
PetscErrorCode  TSSetFromOptions(TS ts)
{
  PetscBool              opt,flg,tflg;
  PetscErrorCode         ierr;
  char                   monfilename[PETSC_MAX_PATH_LEN];
  PetscReal              time_step;
  TSExactFinalTimeOption eftopt;
  char                   dir[16];
  TSIFunction            ifun;
  const char             *defaultType;
  char                   typeName[256];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);

  ierr = TSRegisterAll();CHKERRQ(ierr);
  ierr = TSGetIFunction(ts,NULL,&ifun,NULL);CHKERRQ(ierr);

  ierr = PetscObjectOptionsBegin((PetscObject)ts);CHKERRQ(ierr);
  if (((PetscObject)ts)->type_name)
    defaultType = ((PetscObject)ts)->type_name;
  else
    defaultType = ifun ? TSBEULER : TSEULER;
  ierr = PetscOptionsFList("-ts_type","TS method","TSSetType",TSList,defaultType,typeName,256,&opt);CHKERRQ(ierr);
  if (opt) {
    ierr = TSSetType(ts,typeName);CHKERRQ(ierr);
  } else {
    ierr = TSSetType(ts,defaultType);CHKERRQ(ierr);
  }

  /* Handle generic TS options */
  ierr = PetscOptionsReal("-ts_max_time","Maximum time to run to","TSSetMaxTime",ts->max_time,&ts->max_time,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsInt("-ts_max_steps","Maximum number of time steps","TSSetMaxSteps",ts->max_steps,&ts->max_steps,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ts_init_time","Initial time","TSSetTime",ts->ptime,&ts->ptime,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ts_final_time","Final time to run to","TSSetMaxTime",ts->max_time,&ts->max_time,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ts_dt","Initial time step","TSSetTimeStep",ts->time_step,&time_step,&flg);CHKERRQ(ierr);
  if (flg) {ierr = TSSetTimeStep(ts,time_step);CHKERRQ(ierr);}
  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);
  if (flg) {ierr = TSSetExactFinalTime(ts,eftopt);CHKERRQ(ierr);}
  ierr = PetscOptionsInt("-ts_max_snes_failures","Maximum number of nonlinear solve failures","TSSetMaxSNESFailures",ts->max_snes_failures,&ts->max_snes_failures,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsInt("-ts_max_reject","Maximum number of step rejections before step fails","TSSetMaxStepRejections",ts->max_reject,&ts->max_reject,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-ts_error_if_step_fails","Error if no step succeeds","TSSetErrorIfStepFails",ts->errorifstepfailed,&ts->errorifstepfailed,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ts_rtol","Relative tolerance for local truncation error","TSSetTolerances",ts->rtol,&ts->rtol,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-ts_atol","Absolute tolerance for local truncation error","TSSetTolerances",ts->atol,&ts->atol,NULL);CHKERRQ(ierr);

#if defined(PETSC_HAVE_SAWS)
  {
  PetscBool set;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsBool("-ts_saws_block","Block for SAWs memory snooper at end of TSSolve","PetscObjectSAWsBlock",((PetscObject)ts)->amspublishblock,&flg,&set);CHKERRQ(ierr);
  if (set) {
    ierr = PetscObjectSAWsSetBlock((PetscObject)ts,flg);CHKERRQ(ierr);
  }
  }
#endif

  /* Monitor options */
  ierr = TSMonitorSetFromOptions(ts,"-ts_monitor","Monitor time and timestep size","TSMonitorDefault",TSMonitorDefault,NULL);CHKERRQ(ierr);
  ierr = TSMonitorSetFromOptions(ts,"-ts_monitor_solution","View the solution at each timestep","TSMonitorSolution",TSMonitorSolution,NULL);CHKERRQ(ierr);
  ierr = TSAdjointMonitorSetFromOptions(ts,"-ts_adjoint_monitor","Monitor adjoint timestep size","TSAdjointMonitorDefault",TSAdjointMonitorDefault,NULL);CHKERRQ(ierr);
  ierr = TSAdjointMonitorSetFromOptions(ts,"-ts_adjoint_monitor_sensi","Monitor sensitivity in the adjoint computation","TSAdjointMonitorSensi",TSAdjointMonitorSensi,NULL);CHKERRQ(ierr);

  ierr = PetscOptionsString("-ts_monitor_python","Use Python function","TSMonitorSet",0,monfilename,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
  if (flg) {ierr = PetscPythonMonitorSet((PetscObject)ts,monfilename);CHKERRQ(ierr);}

  ierr = PetscOptionsName("-ts_monitor_lg_solution","Monitor solution graphically","TSMonitorLGSolution",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorLGCtx ctx;
    PetscInt       howoften = 1;

    ierr = PetscOptionsInt("-ts_monitor_lg_solution","Monitor solution graphically","TSMonitorLGSolution",howoften,&howoften,NULL);CHKERRQ(ierr);
    ierr = TSMonitorLGCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorLGSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
  }

  ierr = PetscOptionsName("-ts_monitor_lg_error","Monitor error graphically","TSMonitorLGError",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorLGCtx ctx;
    PetscInt       howoften = 1;

    ierr = PetscOptionsInt("-ts_monitor_lg_error","Monitor error graphically","TSMonitorLGError",howoften,&howoften,NULL);CHKERRQ(ierr);
    ierr = TSMonitorLGCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorLGError,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
  }

  ierr = PetscOptionsName("-ts_monitor_lg_timestep","Monitor timestep size graphically","TSMonitorLGTimeStep",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorLGCtx ctx;
    PetscInt       howoften = 1;

    ierr = PetscOptionsInt("-ts_monitor_lg_timestep","Monitor timestep size graphically","TSMonitorLGTimeStep",howoften,&howoften,NULL);CHKERRQ(ierr);
    ierr = TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorLGTimeStep,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
  }
  ierr = PetscOptionsName("-ts_monitor_lg_timestep_log","Monitor log timestep size graphically","TSMonitorLGTimeStep",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorLGCtx ctx;
    PetscInt       howoften = 1;

    ierr = PetscOptionsInt("-ts_monitor_lg_timestep_log","Monitor log timestep size graphically","TSMonitorLGTimeStep",howoften,&howoften,NULL);CHKERRQ(ierr);
    ierr = TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorLGTimeStep,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
    ctx->semilogy = PETSC_TRUE;
  }

  ierr = PetscOptionsName("-ts_monitor_lg_snes_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGSNESIterations",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorLGCtx ctx;
    PetscInt       howoften = 1;

    ierr = PetscOptionsInt("-ts_monitor_lg_snes_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGSNESIterations",howoften,&howoften,NULL);CHKERRQ(ierr);
    ierr = TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorLGSNESIterations,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
  }
  ierr = PetscOptionsName("-ts_monitor_lg_ksp_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGKSPIterations",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorLGCtx ctx;
    PetscInt       howoften = 1;

    ierr = PetscOptionsInt("-ts_monitor_lg_ksp_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGKSPIterations",howoften,&howoften,NULL);CHKERRQ(ierr);
    ierr = TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorLGKSPIterations,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);CHKERRQ(ierr);
  }
  ierr = PetscOptionsName("-ts_monitor_sp_eig","Monitor eigenvalues of linearized operator graphically","TSMonitorSPEig",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorSPEigCtx ctx;
    PetscInt          howoften = 1;

    ierr = PetscOptionsInt("-ts_monitor_sp_eig","Monitor eigenvalues of linearized operator graphically","TSMonitorSPEig",howoften,&howoften,NULL);CHKERRQ(ierr);
    ierr = TSMonitorSPEigCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorSPEig,ctx,(PetscErrorCode (*)(void**))TSMonitorSPEigCtxDestroy);CHKERRQ(ierr);
  }
  opt  = PETSC_FALSE;
  ierr = PetscOptionsName("-ts_monitor_draw_solution","Monitor solution graphically","TSMonitorDrawSolution",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorDrawCtx ctx;
    PetscInt         howoften = 1;

    ierr = PetscOptionsInt("-ts_monitor_draw_solution","Monitor solution graphically","TSMonitorDrawSolution",howoften,&howoften,NULL);CHKERRQ(ierr);
    ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorDrawSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
  }
  opt  = PETSC_FALSE;
  ierr = PetscOptionsName("-ts_adjoint_monitor_draw_sensi","Monitor adjoint sensitivities (lambda only) graphically","TSAdjointMonitorDrawSensi",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorDrawCtx ctx;
    PetscInt         howoften = 1;

    ierr = PetscOptionsInt("-ts_adjoint_monitor_draw_sensi","Monitor adjoint sensitivities (lambda only) graphically","TSAdjointMonitorDrawSensi",howoften,&howoften,NULL);CHKERRQ(ierr);
    ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
    ierr = TSAdjointMonitorSet(ts,TSAdjointMonitorDrawSensi,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
  }
  opt  = PETSC_FALSE;
  ierr = PetscOptionsName("-ts_monitor_draw_solution_phase","Monitor solution graphically","TSMonitorDrawSolutionPhase",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorDrawCtx ctx;
    PetscReal        bounds[4];
    PetscInt         n = 4;
    PetscDraw        draw;
    PetscDrawAxis    axis;

    ierr = PetscOptionsRealArray("-ts_monitor_draw_solution_phase","Monitor solution graphically","TSMonitorDrawSolutionPhase",bounds,&n,NULL);CHKERRQ(ierr);
    if (n != 4) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Must provide bounding box of phase field");
    ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,1,&ctx);CHKERRQ(ierr);
    ierr = PetscViewerDrawGetDraw(ctx->viewer,0,&draw);CHKERRQ(ierr);
    ierr = PetscViewerDrawGetDrawAxis(ctx->viewer,0,&axis);CHKERRQ(ierr);
    ierr = PetscDrawAxisSetLimits(axis,bounds[0],bounds[2],bounds[1],bounds[3]);CHKERRQ(ierr);
    ierr = PetscDrawAxisSetLabels(axis,"Phase Diagram","Variable 1","Variable 2");CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorDrawSolutionPhase,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
  }
  opt  = PETSC_FALSE;
  ierr = PetscOptionsName("-ts_monitor_draw_error","Monitor error graphically","TSMonitorDrawError",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorDrawCtx ctx;
    PetscInt         howoften = 1;

    ierr = PetscOptionsInt("-ts_monitor_draw_error","Monitor error graphically","TSMonitorDrawError",howoften,&howoften,NULL);CHKERRQ(ierr);
    ierr = TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),0,0,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorDrawError,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);CHKERRQ(ierr);
  }

  opt  = PETSC_FALSE;
  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);
  if (flg) {
    const char *ptr,*ptr2;
    char       *filetemplate;
    if (!monfilename[0]) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"-ts_monitor_solution_vtk requires a file template, e.g. filename-%%03D.vts");
    /* Do some cursory validation of the input. */
    ierr = PetscStrstr(monfilename,"%",(char**)&ptr);CHKERRQ(ierr);
    if (!ptr) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"-ts_monitor_solution_vtk requires a file template, e.g. filename-%%03D.vts");
    for (ptr++; ptr && *ptr; ptr++) {
      ierr = PetscStrchr("DdiouxX",*ptr,(char**)&ptr2);CHKERRQ(ierr);
      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");
      if (ptr2) break;
    }
    ierr = PetscStrallocpy(monfilename,&filetemplate);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorSolutionVTK,filetemplate,(PetscErrorCode (*)(void**))TSMonitorSolutionVTKDestroy);CHKERRQ(ierr);
  }

  ierr = PetscOptionsString("-ts_monitor_dmda_ray","Display a ray of the solution","None","y=0",dir,16,&flg);CHKERRQ(ierr);
  if (flg) {
    TSMonitorDMDARayCtx *rayctx;
    int                  ray = 0;
    DMDADirection        ddir;
    DM                   da;
    PetscMPIInt          rank;

    if (dir[1] != '=') SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Unknown ray %s",dir);
    if (dir[0] == 'x') ddir = DMDA_X;
    else if (dir[0] == 'y') ddir = DMDA_Y;
    else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Unknown ray %s",dir);
    sscanf(dir+2,"%d",&ray);

    ierr = PetscInfo2(((PetscObject)ts),"Displaying DMDA ray %c = %D\n",dir[0],ray);CHKERRQ(ierr);
    ierr = PetscNew(&rayctx);CHKERRQ(ierr);
    ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
    ierr = DMDAGetRay(da,ddir,ray,&rayctx->ray,&rayctx->scatter);CHKERRQ(ierr);
    ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)ts),&rank);CHKERRQ(ierr);
    if (!rank) {
      ierr = PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,0,0,600,300,&rayctx->viewer);CHKERRQ(ierr);
    }
    rayctx->lgctx = NULL;
    ierr = TSMonitorSet(ts,TSMonitorDMDARay,rayctx,TSMonitorDMDARayDestroy);CHKERRQ(ierr);
  }
  ierr = PetscOptionsString("-ts_monitor_lg_dmda_ray","Display a ray of the solution","None","x=0",dir,16,&flg);CHKERRQ(ierr);
  if (flg) {
    TSMonitorDMDARayCtx *rayctx;
    int                 ray = 0;
    DMDADirection       ddir;
    DM                  da;
    PetscInt            howoften = 1;

    if (dir[1] != '=') SETERRQ1(PetscObjectComm((PetscObject) ts), PETSC_ERR_ARG_WRONG, "Malformed ray %s", dir);
    if      (dir[0] == 'x') ddir = DMDA_X;
    else if (dir[0] == 'y') ddir = DMDA_Y;
    else SETERRQ1(PetscObjectComm((PetscObject) ts), PETSC_ERR_ARG_WRONG, "Unknown ray direction %s", dir);
    sscanf(dir+2, "%d", &ray);

    ierr = PetscInfo2(((PetscObject) ts),"Displaying LG DMDA ray %c = %D\n", dir[0], ray);CHKERRQ(ierr);
    ierr = PetscNew(&rayctx);CHKERRQ(ierr);
    ierr = TSGetDM(ts, &da);CHKERRQ(ierr);
    ierr = DMDAGetRay(da, ddir, ray, &rayctx->ray, &rayctx->scatter);CHKERRQ(ierr);
    ierr = TSMonitorLGCtxCreate(PETSC_COMM_SELF,0,0,PETSC_DECIDE,PETSC_DECIDE,600,400,howoften,&rayctx->lgctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts, TSMonitorLGDMDARay, rayctx, TSMonitorDMDARayDestroy);CHKERRQ(ierr);
  }

  ierr = PetscOptionsName("-ts_monitor_envelope","Monitor maximum and minimum value of each component of the solution","TSMonitorEnvelope",&opt);CHKERRQ(ierr);
  if (opt) {
    TSMonitorEnvelopeCtx ctx;

    ierr = TSMonitorEnvelopeCtxCreate(ts,&ctx);CHKERRQ(ierr);
    ierr = TSMonitorSet(ts,TSMonitorEnvelope,ctx,(PetscErrorCode (*)(void**))TSMonitorEnvelopeCtxDestroy);CHKERRQ(ierr);
  }

  flg  = PETSC_FALSE;
  ierr = PetscOptionsBool("-ts_fd_color", "Use finite differences with coloring to compute IJacobian", "TSComputeJacobianDefaultColor", flg, &flg, NULL);CHKERRQ(ierr);
  if (flg) {
    DM   dm;
    DMTS tdm;

    ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
    ierr = DMGetDMTS(dm, &tdm);CHKERRQ(ierr);
    tdm->ijacobianctx = NULL;
    ierr = TSSetIJacobian(ts, NULL, NULL, TSComputeIJacobianDefaultColor, 0);CHKERRQ(ierr);
    ierr = PetscInfo(ts, "Setting default finite difference coloring Jacobian matrix\n");CHKERRQ(ierr);
  }

  /* Handle specific TS options */
  if (ts->ops->setfromoptions) {
    ierr = (*ts->ops->setfromoptions)(PetscOptionsObject,ts);CHKERRQ(ierr);
  }

  /* Handle TSAdapt options */
  ierr = TSGetAdapt(ts,&ts->adapt);CHKERRQ(ierr);
  ierr = TSAdaptSetDefaultType(ts->adapt,ts->default_adapt_type);CHKERRQ(ierr);
  ierr = TSAdaptSetFromOptions(PetscOptionsObject,ts->adapt);CHKERRQ(ierr);

  /* TS trajectory must be set after TS, since it may use some TS options above */
  tflg = ts->trajectory ? PETSC_TRUE : PETSC_FALSE;
  ierr = PetscOptionsBool("-ts_save_trajectory","Save the solution at each timestep","TSSetSaveTrajectory",tflg,&tflg,NULL);CHKERRQ(ierr);
  if (tflg) {
    ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
  }
  tflg = ts->adjoint_solve ? PETSC_TRUE : PETSC_FALSE;
  ierr = PetscOptionsBool("-ts_adjoint_solve","Solve the adjoint problem immediately after solving the forward problem","",tflg,&tflg,&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
    ts->adjoint_solve = tflg;
  }

  /* process any options handlers added with PetscObjectAddOptionsHandler() */
  ierr = PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject)ts);CHKERRQ(ierr);
  ierr = PetscOptionsEnd();CHKERRQ(ierr);

  if (ts->trajectory) {
    ierr = TSTrajectorySetFromOptions(ts->trajectory,ts);CHKERRQ(ierr);
  }

  ierr = TSGetSNES(ts,&ts->snes);CHKERRQ(ierr);
  if (ts->problem_type == TS_LINEAR) {ierr = SNESSetType(ts->snes,SNESKSPONLY);CHKERRQ(ierr);}
  ierr = SNESSetFromOptions(ts->snes);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSGetTrajectory - Gets the trajectory from a TS if it exists

   Collective on TS

   Input Parameters:
.  ts - the TS context obtained from TSCreate()

   Output Parameters;
.  tr - the TSTrajectory object, if it exists

   Note: This routine should be called after all TS options have been set

   Level: advanced

.seealso: TSGetTrajectory(), TSAdjointSolve(), TSTrajectory, TSTrajectoryCreate()

.keywords: TS, set, checkpoint,
@*/
PetscErrorCode  TSGetTrajectory(TS ts,TSTrajectory *tr)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  *tr = ts->trajectory;
  PetscFunctionReturn(0);
}

/*@
   TSSetSaveTrajectory - Causes the TS to save its solutions as it iterates forward in time in a TSTrajectory object

   Collective on TS

   Input Parameters:
.  ts - the TS context obtained from TSCreate()

   Options Database:
+  -ts_save_trajectory - saves the trajectory to a file
-  -ts_trajectory_type type

Note: This routine should be called after all TS options have been set

    The TSTRAJECTORYVISUALIZATION files can be loaded into Python with $PETSC_DIR/bin/PetscBinaryIOTrajectory.py and
   MATLAB with $PETSC_DIR/share/petsc/matlab/PetscReadBinaryTrajectory.m

   Level: intermediate

.seealso: TSGetTrajectory(), TSAdjointSolve(), TSTrajectoryType, TSSetTrajectoryType()

.keywords: TS, set, checkpoint,
@*/
PetscErrorCode  TSSetSaveTrajectory(TS ts)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (!ts->trajectory) {
    ierr = TSTrajectoryCreate(PetscObjectComm((PetscObject)ts),&ts->trajectory);CHKERRQ(ierr);
    ierr = TSTrajectorySetFromOptions(ts->trajectory,ts);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@
   TSComputeRHSJacobian - Computes the Jacobian matrix that has been
      set with TSSetRHSJacobian().

   Collective on TS and Vec

   Input Parameters:
+  ts - the TS context
.  t - current timestep
-  U - input vector

   Output Parameters:
+  A - Jacobian matrix
.  B - optional preconditioning matrix
-  flag - flag indicating matrix structure

   Notes:
   Most users should not need to explicitly call this routine, as it
   is used internally within the nonlinear solvers.

   See KSPSetOperators() for important information about setting the
   flag parameter.

   Level: developer

.keywords: SNES, compute, Jacobian, matrix

.seealso:  TSSetRHSJacobian(), KSPSetOperators()
@*/
PetscErrorCode  TSComputeRHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B)
{
  PetscErrorCode   ierr;
  PetscObjectState Ustate;
  PetscObjectId    Uid;
  DM               dm;
  DMTS             tsdm;
  TSRHSJacobian    rhsjacobianfunc;
  void             *ctx;
  TSIJacobian      ijacobianfunc;
  TSRHSFunction    rhsfunction;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  PetscCheckSameComm(ts,1,U,3);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMGetDMTS(dm,&tsdm);CHKERRQ(ierr);
  ierr = DMTSGetRHSJacobian(dm,&rhsjacobianfunc,&ctx);CHKERRQ(ierr);
  ierr = DMTSGetIJacobian(dm,&ijacobianfunc,NULL);CHKERRQ(ierr);
  ierr = DMTSGetRHSFunction(dm,&rhsfunction,&ctx);CHKERRQ(ierr);
  ierr = PetscObjectStateGet((PetscObject)U,&Ustate);CHKERRQ(ierr);
  ierr = PetscObjectGetId((PetscObject)U,&Uid);CHKERRQ(ierr);
  if (ts->rhsjacobian.time == t && (ts->problem_type == TS_LINEAR || (ts->rhsjacobian.Xid == Uid && ts->rhsjacobian.Xstate == Ustate)) && (rhsfunction != TSComputeRHSFunctionLinear)) {
    PetscFunctionReturn(0);
  }

  if (!rhsjacobianfunc && !ijacobianfunc) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSJacobian() and / or TSSetIJacobian()");

  if (ts->rhsjacobian.reuse) {
    ierr = MatShift(A,-ts->rhsjacobian.shift);CHKERRQ(ierr);
    ierr = MatScale(A,1./ts->rhsjacobian.scale);CHKERRQ(ierr);
    if (A != B) {
      ierr = MatShift(B,-ts->rhsjacobian.shift);CHKERRQ(ierr);
      ierr = MatScale(B,1./ts->rhsjacobian.scale);CHKERRQ(ierr);
    }
    ts->rhsjacobian.shift = 0;
    ts->rhsjacobian.scale = 1.;
  }

  if (rhsjacobianfunc) {
    PetscBool missing;
    ierr = PetscLogEventBegin(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
    PetscStackPush("TS user Jacobian function");
    ierr = (*rhsjacobianfunc)(ts,t,U,A,B,ctx);CHKERRQ(ierr);
    PetscStackPop;
    ierr = PetscLogEventEnd(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
    if (A) {
      ierr = MatMissingDiagonal(A,&missing,NULL);CHKERRQ(ierr);
      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");
    }
    if (B && B != A) {
      ierr = MatMissingDiagonal(B,&missing,NULL);CHKERRQ(ierr);
      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");
    }
  } else {
    ierr = MatZeroEntries(A);CHKERRQ(ierr);
    if (A != B) {ierr = MatZeroEntries(B);CHKERRQ(ierr);}
  }
  ts->rhsjacobian.time       = t;
  ierr                       = PetscObjectGetId((PetscObject)U,&ts->rhsjacobian.Xid);CHKERRQ(ierr);
  ierr                       = PetscObjectStateGet((PetscObject)U,&ts->rhsjacobian.Xstate);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSComputeRHSFunction - Evaluates the right-hand-side function.

   Collective on TS and Vec

   Input Parameters:
+  ts - the TS context
.  t - current time
-  U - state vector

   Output Parameter:
.  y - right hand side

   Note:
   Most users should not need to explicitly call this routine, as it
   is used internally within the nonlinear solvers.

   Level: developer

.keywords: TS, compute

.seealso: TSSetRHSFunction(), TSComputeIFunction()
@*/
PetscErrorCode TSComputeRHSFunction(TS ts,PetscReal t,Vec U,Vec y)
{
  PetscErrorCode ierr;
  TSRHSFunction  rhsfunction;
  TSIFunction    ifunction;
  void           *ctx;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  PetscValidHeaderSpecific(y,VEC_CLASSID,4);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetRHSFunction(dm,&rhsfunction,&ctx);CHKERRQ(ierr);
  ierr = DMTSGetIFunction(dm,&ifunction,NULL);CHKERRQ(ierr);

  if (!rhsfunction && !ifunction) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSFunction() and / or TSSetIFunction()");

  ierr = PetscLogEventBegin(TS_FunctionEval,ts,U,y,0);CHKERRQ(ierr);
  if (rhsfunction) {
    PetscStackPush("TS user right-hand-side function");
    ierr = (*rhsfunction)(ts,t,U,y,ctx);CHKERRQ(ierr);
    PetscStackPop;
  } else {
    ierr = VecZeroEntries(y);CHKERRQ(ierr);
  }

  ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,y,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSComputeSolutionFunction - Evaluates the solution function.

   Collective on TS and Vec

   Input Parameters:
+  ts - the TS context
-  t - current time

   Output Parameter:
.  U - the solution

   Note:
   Most users should not need to explicitly call this routine, as it
   is used internally within the nonlinear solvers.

   Level: developer

.keywords: TS, compute

.seealso: TSSetSolutionFunction(), TSSetRHSFunction(), TSComputeIFunction()
@*/
PetscErrorCode TSComputeSolutionFunction(TS ts,PetscReal t,Vec U)
{
  PetscErrorCode     ierr;
  TSSolutionFunction solutionfunction;
  void               *ctx;
  DM                 dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetSolutionFunction(dm,&solutionfunction,&ctx);CHKERRQ(ierr);

  if (solutionfunction) {
    PetscStackPush("TS user solution function");
    ierr = (*solutionfunction)(ts,t,U,ctx);CHKERRQ(ierr);
    PetscStackPop;
  }
  PetscFunctionReturn(0);
}
/*@
   TSComputeForcingFunction - Evaluates the forcing function.

   Collective on TS and Vec

   Input Parameters:
+  ts - the TS context
-  t - current time

   Output Parameter:
.  U - the function value

   Note:
   Most users should not need to explicitly call this routine, as it
   is used internally within the nonlinear solvers.

   Level: developer

.keywords: TS, compute

.seealso: TSSetSolutionFunction(), TSSetRHSFunction(), TSComputeIFunction()
@*/
PetscErrorCode TSComputeForcingFunction(TS ts,PetscReal t,Vec U)
{
  PetscErrorCode     ierr, (*forcing)(TS,PetscReal,Vec,void*);
  void               *ctx;
  DM                 dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetForcingFunction(dm,&forcing,&ctx);CHKERRQ(ierr);

  if (forcing) {
    PetscStackPush("TS user forcing function");
    ierr = (*forcing)(ts,t,U,ctx);CHKERRQ(ierr);
    PetscStackPop;
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode TSGetRHSVec_Private(TS ts,Vec *Frhs)
{
  Vec            F;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  *Frhs = NULL;
  ierr  = TSGetIFunction(ts,&F,NULL,NULL);CHKERRQ(ierr);
  if (!ts->Frhs) {
    ierr = VecDuplicate(F,&ts->Frhs);CHKERRQ(ierr);
  }
  *Frhs = ts->Frhs;
  PetscFunctionReturn(0);
}

static PetscErrorCode TSGetRHSMats_Private(TS ts,Mat *Arhs,Mat *Brhs)
{
  Mat            A,B;
  PetscErrorCode ierr;
  TSIJacobian    ijacobian;

  PetscFunctionBegin;
  if (Arhs) *Arhs = NULL;
  if (Brhs) *Brhs = NULL;
  ierr = TSGetIJacobian(ts,&A,&B,&ijacobian,NULL);CHKERRQ(ierr);
  if (Arhs) {
    if (!ts->Arhs) {
      if (ijacobian) {
        ierr = MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&ts->Arhs);CHKERRQ(ierr);
      } else {
        ts->Arhs = A;
        ierr = PetscObjectReference((PetscObject)A);CHKERRQ(ierr);
      }
    } else {
      PetscBool flg;
      ierr = SNESGetUseMatrixFree(ts->snes,NULL,&flg);CHKERRQ(ierr);
      /* Handle case where user provided only RHSJacobian and used -snes_mf_operator */
      if (flg && !ijacobian && ts->Arhs == ts->Brhs){
        ierr = PetscObjectDereference((PetscObject)ts->Arhs);CHKERRQ(ierr);
        ts->Arhs = A;
        ierr = PetscObjectReference((PetscObject)A);CHKERRQ(ierr);
      }
    }
    *Arhs = ts->Arhs;
  }
  if (Brhs) {
    if (!ts->Brhs) {
      if (A != B) {
        if (ijacobian) {
          ierr = MatDuplicate(B,MAT_DO_NOT_COPY_VALUES,&ts->Brhs);CHKERRQ(ierr);
        } else {
          ts->Brhs = B;
          ierr = PetscObjectReference((PetscObject)B);CHKERRQ(ierr);
        }
      } else {
        ierr = PetscObjectReference((PetscObject)ts->Arhs);CHKERRQ(ierr);
        ts->Brhs = ts->Arhs;
      }
    }
    *Brhs = ts->Brhs;
  }
  PetscFunctionReturn(0);
}

/*@
   TSComputeIFunction - Evaluates the DAE residual written in implicit form F(t,U,Udot)=0

   Collective on TS and Vec

   Input Parameters:
+  ts - the TS context
.  t - current time
.  U - state vector
.  Udot - time derivative of state vector
-  imex - flag indicates if the method is IMEX so that the RHSFunction should be kept separate

   Output Parameter:
.  Y - right hand side

   Note:
   Most users should not need to explicitly call this routine, as it
   is used internally within the nonlinear solvers.

   If the user did did not write their equations in implicit form, this
   function recasts them in implicit form.

   Level: developer

.keywords: TS, compute

.seealso: TSSetIFunction(), TSComputeRHSFunction()
@*/
PetscErrorCode TSComputeIFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec Y,PetscBool imex)
{
  PetscErrorCode ierr;
  TSIFunction    ifunction;
  TSRHSFunction  rhsfunction;
  void           *ctx;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  PetscValidHeaderSpecific(Udot,VEC_CLASSID,4);
  PetscValidHeaderSpecific(Y,VEC_CLASSID,5);

  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetIFunction(dm,&ifunction,&ctx);CHKERRQ(ierr);
  ierr = DMTSGetRHSFunction(dm,&rhsfunction,NULL);CHKERRQ(ierr);

  if (!rhsfunction && !ifunction) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSFunction() and / or TSSetIFunction()");

  ierr = PetscLogEventBegin(TS_FunctionEval,ts,U,Udot,Y);CHKERRQ(ierr);
  if (ifunction) {
    PetscStackPush("TS user implicit function");
    ierr = (*ifunction)(ts,t,U,Udot,Y,ctx);CHKERRQ(ierr);
    PetscStackPop;
  }
  if (imex) {
    if (!ifunction) {
      ierr = VecCopy(Udot,Y);CHKERRQ(ierr);
    }
  } else if (rhsfunction) {
    if (ifunction) {
      Vec Frhs;
      ierr = TSGetRHSVec_Private(ts,&Frhs);CHKERRQ(ierr);
      ierr = TSComputeRHSFunction(ts,t,U,Frhs);CHKERRQ(ierr);
      ierr = VecAXPY(Y,-1,Frhs);CHKERRQ(ierr);
    } else {
      ierr = TSComputeRHSFunction(ts,t,U,Y);CHKERRQ(ierr);
      ierr = VecAYPX(Y,-1,Udot);CHKERRQ(ierr);
    }
  }
  ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,Udot,Y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSComputeIJacobian - Evaluates the Jacobian of the DAE

   Collective on TS and Vec

   Input
      Input Parameters:
+  ts - the TS context
.  t - current timestep
.  U - state vector
.  Udot - time derivative of state vector
.  shift - shift to apply, see note below
-  imex - flag indicates if the method is IMEX so that the RHSJacobian should be kept separate

   Output Parameters:
+  A - Jacobian matrix
-  B - matrix from which the preconditioner is constructed; often the same as A

   Notes:
   If F(t,U,Udot)=0 is the DAE, the required Jacobian is

   dF/dU + shift*dF/dUdot

   Most users should not need to explicitly call this routine, as it
   is used internally within the nonlinear solvers.

   Level: developer

.keywords: TS, compute, Jacobian, matrix

.seealso:  TSSetIJacobian()
@*/
PetscErrorCode TSComputeIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat A,Mat B,PetscBool imex)
{
  PetscErrorCode ierr;
  TSIJacobian    ijacobian;
  TSRHSJacobian  rhsjacobian;
  DM             dm;
  void           *ctx;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  PetscValidHeaderSpecific(Udot,VEC_CLASSID,4);
  PetscValidPointer(A,6);
  PetscValidHeaderSpecific(A,MAT_CLASSID,6);
  PetscValidPointer(B,7);
  PetscValidHeaderSpecific(B,MAT_CLASSID,7);

  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetIJacobian(dm,&ijacobian,&ctx);CHKERRQ(ierr);
  ierr = DMTSGetRHSJacobian(dm,&rhsjacobian,NULL);CHKERRQ(ierr);

  if (!rhsjacobian && !ijacobian) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSJacobian() and / or TSSetIJacobian()");

  ierr = PetscLogEventBegin(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
  if (ijacobian) {
    PetscBool missing;
    PetscStackPush("TS user implicit Jacobian");
    ierr = (*ijacobian)(ts,t,U,Udot,shift,A,B,ctx);CHKERRQ(ierr);
    PetscStackPop;
    ierr = MatMissingDiagonal(A,&missing,NULL);CHKERRQ(ierr);
    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");
    if (B != A) {
      ierr = MatMissingDiagonal(B,&missing,NULL);CHKERRQ(ierr);
      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");
    }
  }
  if (imex) {
    if (!ijacobian) {  /* system was written as Udot = G(t,U) */
      PetscBool assembled;
      ierr = MatZeroEntries(A);CHKERRQ(ierr);
      ierr = MatAssembled(A,&assembled);CHKERRQ(ierr);
      if (!assembled) {
        ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
        ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
      }
      ierr = MatShift(A,shift);CHKERRQ(ierr);
      if (A != B) {
        ierr = MatZeroEntries(B);CHKERRQ(ierr);
        ierr = MatAssembled(B,&assembled);CHKERRQ(ierr);
        if (!assembled) {
          ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
          ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
        }
        ierr = MatShift(B,shift);CHKERRQ(ierr);
      }
    }
  } else {
    Mat Arhs = NULL,Brhs = NULL;
    if (rhsjacobian) {
      ierr = TSGetRHSMats_Private(ts,&Arhs,&Brhs);CHKERRQ(ierr);
      ierr = TSComputeRHSJacobian(ts,t,U,Arhs,Brhs);CHKERRQ(ierr);
    }
    if (Arhs == A) {           /* No IJacobian, so we only have the RHS matrix */
      PetscBool flg;
      ts->rhsjacobian.scale = -1;
      ts->rhsjacobian.shift = shift;
      ierr = SNESGetUseMatrixFree(ts->snes,NULL,&flg);CHKERRQ(ierr);
      /* since -snes_mf_operator uses the full SNES function it does not need to be shifted or scaled here */
      if (!flg) {
        ierr = MatScale(A,-1);CHKERRQ(ierr);
        ierr = MatShift(A,shift);CHKERRQ(ierr);
      }
      if (A != B) {
        ierr = MatScale(B,-1);CHKERRQ(ierr);
        ierr = MatShift(B,shift);CHKERRQ(ierr);
      }
    } else if (Arhs) {          /* Both IJacobian and RHSJacobian */
      MatStructure axpy = DIFFERENT_NONZERO_PATTERN;
      if (!ijacobian) {         /* No IJacobian provided, but we have a separate RHS matrix */
        ierr = MatZeroEntries(A);CHKERRQ(ierr);
        ierr = MatShift(A,shift);CHKERRQ(ierr);
        if (A != B) {
          ierr = MatZeroEntries(B);CHKERRQ(ierr);
          ierr = MatShift(B,shift);CHKERRQ(ierr);
        }
      }
      ierr = MatAXPY(A,-1,Arhs,axpy);CHKERRQ(ierr);
      if (A != B) {
        ierr = MatAXPY(B,-1,Brhs,axpy);CHKERRQ(ierr);
      }
    }
  }
  ierr = PetscLogEventEnd(TS_JacobianEval,ts,U,A,B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
    TSSetRHSFunction - Sets the routine for evaluating the function,
    where U_t = G(t,u).

    Logically Collective on TS

    Input Parameters:
+   ts - the TS context obtained from TSCreate()
.   r - vector to put the computed right hand side (or NULL to have it created)
.   f - routine for evaluating the right-hand-side function
-   ctx - [optional] user-defined context for private data for the
          function evaluation routine (may be NULL)

    Calling sequence of func:
$     func (TS ts,PetscReal t,Vec u,Vec F,void *ctx);

+   t - current timestep
.   u - input vector
.   F - function vector
-   ctx - [optional] user-defined function context

    Level: beginner

    Notes: You must call this function or TSSetIFunction() to define your ODE. You cannot use this function when solving a DAE.

.keywords: TS, timestep, set, right-hand-side, function

.seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSSetIFunction()
@*/
PetscErrorCode  TSSetRHSFunction(TS ts,Vec r,PetscErrorCode (*f)(TS,PetscReal,Vec,Vec,void*),void *ctx)
{
  PetscErrorCode ierr;
  SNES           snes;
  Vec            ralloc = NULL;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (r) PetscValidHeaderSpecific(r,VEC_CLASSID,2);

  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSSetRHSFunction(dm,f,ctx);CHKERRQ(ierr);
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  if (!r && !ts->dm && ts->vec_sol) {
    ierr = VecDuplicate(ts->vec_sol,&ralloc);CHKERRQ(ierr);
    r = ralloc;
  }
  ierr = SNESSetFunction(snes,r,SNESTSFormFunction,ts);CHKERRQ(ierr);
  ierr = VecDestroy(&ralloc);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
    TSSetSolutionFunction - Provide a function that computes the solution of the ODE or DAE

    Logically Collective on TS

    Input Parameters:
+   ts - the TS context obtained from TSCreate()
.   f - routine for evaluating the solution
-   ctx - [optional] user-defined context for private data for the
          function evaluation routine (may be NULL)

    Calling sequence of func:
$     func (TS ts,PetscReal t,Vec u,void *ctx);

+   t - current timestep
.   u - output vector
-   ctx - [optional] user-defined function context

    Notes:
    This routine is used for testing accuracy of time integration schemes when you already know the solution.
    If analytic solutions are not known for your system, consider using the Method of Manufactured Solutions to
    create closed-form solutions with non-physical forcing terms.

    For low-dimensional problems solved in serial, such as small discrete systems, TSMonitorLGError() can be used to monitor the error history.

    Level: beginner

.keywords: TS, timestep, set, right-hand-side, function

.seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSComputeSolutionFunction(), TSSetForcingFunction()
@*/
PetscErrorCode  TSSetSolutionFunction(TS ts,PetscErrorCode (*f)(TS,PetscReal,Vec,void*),void *ctx)
{
  PetscErrorCode ierr;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSSetSolutionFunction(dm,f,ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
    TSSetForcingFunction - Provide a function that computes a forcing term for a ODE or PDE

    Logically Collective on TS

    Input Parameters:
+   ts - the TS context obtained from TSCreate()
.   func - routine for evaluating the forcing function
-   ctx - [optional] user-defined context for private data for the
          function evaluation routine (may be NULL)

    Calling sequence of func:
$     func (TS ts,PetscReal t,Vec f,void *ctx);

+   t - current timestep
.   f - output vector
-   ctx - [optional] user-defined function context

    Notes:
    This routine is useful for testing accuracy of time integration schemes when using the Method of Manufactured Solutions to
    create closed-form solutions with a non-physical forcing term. It allows you to use the Method of Manufactored Solution without directly editing the
    definition of the problem you are solving and hence possibly introducing bugs.

    This replaces the ODE F(u,u_t,t) = 0 the TS is solving with F(u,u_t,t) - func(t) = 0

    This forcing function does not depend on the solution to the equations, it can only depend on spatial location, time, and possibly parameters, the
    parameters can be passed in the ctx variable.

    For low-dimensional problems solved in serial, such as small discrete systems, TSMonitorLGError() can be used to monitor the error history.

    Level: beginner

.keywords: TS, timestep, set, right-hand-side, function

.seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSComputeSolutionFunction(), TSSetSolutionFunction()
@*/
PetscErrorCode  TSSetForcingFunction(TS ts,TSForcingFunction func,void *ctx)
{
  PetscErrorCode ierr;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSSetForcingFunction(dm,func,ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSSetRHSJacobian - Sets the function to compute the Jacobian of G,
   where U_t = G(U,t), as well as the location to store the matrix.

   Logically Collective on TS

   Input Parameters:
+  ts  - the TS context obtained from TSCreate()
.  Amat - (approximate) Jacobian matrix
.  Pmat - matrix from which preconditioner is to be constructed (usually the same as Amat)
.  f   - the Jacobian evaluation routine
-  ctx - [optional] user-defined context for private data for the
         Jacobian evaluation routine (may be NULL)

   Calling sequence of f:
$     func (TS ts,PetscReal t,Vec u,Mat A,Mat B,void *ctx);

+  t - current timestep
.  u - input vector
.  Amat - (approximate) Jacobian matrix
.  Pmat - matrix from which preconditioner is to be constructed (usually the same as Amat)
-  ctx - [optional] user-defined context for matrix evaluation routine

   Notes:
   You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value

   The TS solver may modify the nonzero structure and the entries of the matrices Amat and Pmat between the calls to f()
   You should not assume the values are the same in the next call to f() as you set them in the previous call.

   Level: beginner

.keywords: TS, timestep, set, right-hand-side, Jacobian

.seealso: SNESComputeJacobianDefaultColor(), TSSetRHSFunction(), TSRHSJacobianSetReuse(), TSSetIJacobian()

@*/
PetscErrorCode  TSSetRHSJacobian(TS ts,Mat Amat,Mat Pmat,TSRHSJacobian f,void *ctx)
{
  PetscErrorCode ierr;
  SNES           snes;
  DM             dm;
  TSIJacobian    ijacobian;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (Amat) PetscValidHeaderSpecific(Amat,MAT_CLASSID,2);
  if (Pmat) PetscValidHeaderSpecific(Pmat,MAT_CLASSID,3);
  if (Amat) PetscCheckSameComm(ts,1,Amat,2);
  if (Pmat) PetscCheckSameComm(ts,1,Pmat,3);

  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSSetRHSJacobian(dm,f,ctx);CHKERRQ(ierr);
  if (f == TSComputeRHSJacobianConstant) {
    /* Handle this case automatically for the user; otherwise user should call themselves. */
    ierr = TSRHSJacobianSetReuse(ts,PETSC_TRUE);CHKERRQ(ierr);
  }
  ierr = DMTSGetIJacobian(dm,&ijacobian,NULL);CHKERRQ(ierr);
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  if (!ijacobian) {
    ierr = SNESSetJacobian(snes,Amat,Pmat,SNESTSFormJacobian,ts);CHKERRQ(ierr);
  }
  if (Amat) {
    ierr = PetscObjectReference((PetscObject)Amat);CHKERRQ(ierr);
    ierr = MatDestroy(&ts->Arhs);CHKERRQ(ierr);
    ts->Arhs = Amat;
  }
  if (Pmat) {
    ierr = PetscObjectReference((PetscObject)Pmat);CHKERRQ(ierr);
    ierr = MatDestroy(&ts->Brhs);CHKERRQ(ierr);
    ts->Brhs = Pmat;
  }
  PetscFunctionReturn(0);
}

/*@C
   TSSetIFunction - Set the function to compute F(t,U,U_t) where F() = 0 is the DAE to be solved.

   Logically Collective on TS

   Input Parameters:
+  ts  - the TS context obtained from TSCreate()
.  r   - vector to hold the residual (or NULL to have it created internally)
.  f   - the function evaluation routine
-  ctx - user-defined context for private data for the function evaluation routine (may be NULL)

   Calling sequence of f:
$  f(TS ts,PetscReal t,Vec u,Vec u_t,Vec F,ctx);

+  t   - time at step/stage being solved
.  u   - state vector
.  u_t - time derivative of state vector
.  F   - function vector
-  ctx - [optional] user-defined context for matrix evaluation routine

   Important:
   The user MUST call either this routine or TSSetRHSFunction() to define the ODE.  When solving DAEs you must use this function.

   Level: beginner

.keywords: TS, timestep, set, DAE, Jacobian

.seealso: TSSetRHSJacobian(), TSSetRHSFunction(), TSSetIJacobian()
@*/
PetscErrorCode  TSSetIFunction(TS ts,Vec r,TSIFunction f,void *ctx)
{
  PetscErrorCode ierr;
  SNES           snes;
  Vec            ralloc = NULL;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (r) PetscValidHeaderSpecific(r,VEC_CLASSID,2);

  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSSetIFunction(dm,f,ctx);CHKERRQ(ierr);

  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  if (!r && !ts->dm && ts->vec_sol) {
    ierr = VecDuplicate(ts->vec_sol,&ralloc);CHKERRQ(ierr);
    r  = ralloc;
  }
  ierr = SNESSetFunction(snes,r,SNESTSFormFunction,ts);CHKERRQ(ierr);
  ierr = VecDestroy(&ralloc);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSGetIFunction - Returns the vector where the implicit residual is stored and the function/contex to compute it.

   Not Collective

   Input Parameter:
.  ts - the TS context

   Output Parameter:
+  r - vector to hold residual (or NULL)
.  func - the function to compute residual (or NULL)
-  ctx - the function context (or NULL)

   Level: advanced

.keywords: TS, nonlinear, get, function

.seealso: TSSetIFunction(), SNESGetFunction()
@*/
PetscErrorCode TSGetIFunction(TS ts,Vec *r,TSIFunction *func,void **ctx)
{
  PetscErrorCode ierr;
  SNES           snes;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESGetFunction(snes,r,NULL,NULL);CHKERRQ(ierr);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetIFunction(dm,func,ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSGetRHSFunction - Returns the vector where the right hand side is stored and the function/context to compute it.

   Not Collective

   Input Parameter:
.  ts - the TS context

   Output Parameter:
+  r - vector to hold computed right hand side (or NULL)
.  func - the function to compute right hand side (or NULL)
-  ctx - the function context (or NULL)

   Level: advanced

.keywords: TS, nonlinear, get, function

.seealso: TSSetRHSFunction(), SNESGetFunction()
@*/
PetscErrorCode TSGetRHSFunction(TS ts,Vec *r,TSRHSFunction *func,void **ctx)
{
  PetscErrorCode ierr;
  SNES           snes;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESGetFunction(snes,r,NULL,NULL);CHKERRQ(ierr);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetRHSFunction(dm,func,ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSSetIJacobian - Set the function to compute the matrix dF/dU + a*dF/dU_t where F(t,U,U_t) is the function
        provided with TSSetIFunction().

   Logically Collective on TS

   Input Parameters:
+  ts  - the TS context obtained from TSCreate()
.  Amat - (approximate) Jacobian matrix
.  Pmat - matrix used to compute preconditioner (usually the same as Amat)
.  f   - the Jacobian evaluation routine
-  ctx - user-defined context for private data for the Jacobian evaluation routine (may be NULL)

   Calling sequence of f:
$  f(TS ts,PetscReal t,Vec U,Vec U_t,PetscReal a,Mat Amat,Mat Pmat,void *ctx);

+  t    - time at step/stage being solved
.  U    - state vector
.  U_t  - time derivative of state vector
.  a    - shift
.  Amat - (approximate) Jacobian of F(t,U,W+a*U), equivalent to dF/dU + a*dF/dU_t
.  Pmat - matrix used for constructing preconditioner, usually the same as Amat
-  ctx  - [optional] user-defined context for matrix evaluation routine

   Notes:
   The matrices Amat and Pmat are exactly the matrices that are used by SNES for the nonlinear solve.

   If you know the operator Amat has a null space you can use MatSetNullSpace() and MatSetTransposeNullSpace() to supply the null
   space to Amat and the KSP solvers will automatically use that null space as needed during the solution process.

   The matrix dF/dU + a*dF/dU_t you provide turns out to be
   the Jacobian of F(t,U,W+a*U) where F(t,U,U_t) = 0 is the DAE to be solved.
   The time integrator internally approximates U_t by W+a*U where the positive "shift"
   a and vector W depend on the integration method, step size, and past states. For example with
   the backward Euler method a = 1/dt and W = -a*U(previous timestep) so
   W + a*U = a*(U - U(previous timestep)) = (U - U(previous timestep))/dt

   You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value

   The TS solver may modify the nonzero structure and the entries of the matrices Amat and Pmat between the calls to f()
   You should not assume the values are the same in the next call to f() as you set them in the previous call.

   Level: beginner

.keywords: TS, timestep, DAE, Jacobian

.seealso: TSSetIFunction(), TSSetRHSJacobian(), SNESComputeJacobianDefaultColor(), SNESComputeJacobianDefault(), TSSetRHSFunction()

@*/
PetscErrorCode  TSSetIJacobian(TS ts,Mat Amat,Mat Pmat,TSIJacobian f,void *ctx)
{
  PetscErrorCode ierr;
  SNES           snes;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (Amat) PetscValidHeaderSpecific(Amat,MAT_CLASSID,2);
  if (Pmat) PetscValidHeaderSpecific(Pmat,MAT_CLASSID,3);
  if (Amat) PetscCheckSameComm(ts,1,Amat,2);
  if (Pmat) PetscCheckSameComm(ts,1,Pmat,3);

  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSSetIJacobian(dm,f,ctx);CHKERRQ(ierr);

  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESSetJacobian(snes,Amat,Pmat,SNESTSFormJacobian,ts);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSRHSJacobianSetReuse - restore RHS Jacobian before re-evaluating.  Without this flag, TS will change the sign and
   shift the RHS Jacobian for a finite-time-step implicit solve, in which case the user function will need to recompute
   the entire Jacobian.  The reuse flag must be set if the evaluation function will assume that the matrix entries have
   not been changed by the TS.

   Logically Collective

   Input Arguments:
+  ts - TS context obtained from TSCreate()
-  reuse - PETSC_TRUE if the RHS Jacobian

   Level: intermediate

.seealso: TSSetRHSJacobian(), TSComputeRHSJacobianConstant()
@*/
PetscErrorCode TSRHSJacobianSetReuse(TS ts,PetscBool reuse)
{
  PetscFunctionBegin;
  ts->rhsjacobian.reuse = reuse;
  PetscFunctionReturn(0);
}

/*@C
   TSSetI2Function - Set the function to compute F(t,U,U_t,U_tt) where F = 0 is the DAE to be solved.

   Logically Collective on TS

   Input Parameters:
+  ts  - the TS context obtained from TSCreate()
.  F   - vector to hold the residual (or NULL to have it created internally)
.  fun - the function evaluation routine
-  ctx - user-defined context for private data for the function evaluation routine (may be NULL)

   Calling sequence of fun:
$  fun(TS ts,PetscReal t,Vec U,Vec U_t,Vec U_tt,Vec F,ctx);

+  t    - time at step/stage being solved
.  U    - state vector
.  U_t  - time derivative of state vector
.  U_tt - second time derivative of state vector
.  F    - function vector
-  ctx  - [optional] user-defined context for matrix evaluation routine (may be NULL)

   Level: beginner

.keywords: TS, timestep, set, ODE, DAE, Function

.seealso: TSSetI2Jacobian()
@*/
PetscErrorCode TSSetI2Function(TS ts,Vec F,TSI2Function fun,void *ctx)
{
  DM             dm;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (F) PetscValidHeaderSpecific(F,VEC_CLASSID,2);
  ierr = TSSetIFunction(ts,F,NULL,NULL);CHKERRQ(ierr);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSSetI2Function(dm,fun,ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  TSGetI2Function - Returns the vector where the implicit residual is stored and the function/contex to compute it.

  Not Collective

  Input Parameter:
. ts - the TS context

  Output Parameter:
+ r - vector to hold residual (or NULL)
. fun - the function to compute residual (or NULL)
- ctx - the function context (or NULL)

  Level: advanced

.keywords: TS, nonlinear, get, function

.seealso: TSSetI2Function(), SNESGetFunction()
@*/
PetscErrorCode TSGetI2Function(TS ts,Vec *r,TSI2Function *fun,void **ctx)
{
  PetscErrorCode ierr;
  SNES           snes;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESGetFunction(snes,r,NULL,NULL);CHKERRQ(ierr);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetI2Function(dm,fun,ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSSetI2Jacobian - Set the function to compute the matrix dF/dU + v*dF/dU_t  + a*dF/dU_tt
        where F(t,U,U_t,U_tt) is the function you provided with TSSetI2Function().

   Logically Collective on TS

   Input Parameters:
+  ts  - the TS context obtained from TSCreate()
.  J   - Jacobian matrix
.  P   - preconditioning matrix for J (may be same as J)
.  jac - the Jacobian evaluation routine
-  ctx - user-defined context for private data for the Jacobian evaluation routine (may be NULL)

   Calling sequence of jac:
$  jac(TS ts,PetscReal t,Vec U,Vec U_t,Vec U_tt,PetscReal v,PetscReal a,Mat J,Mat P,void *ctx);

+  t    - time at step/stage being solved
.  U    - state vector
.  U_t  - time derivative of state vector
.  U_tt - second time derivative of state vector
.  v    - shift for U_t
.  a    - shift for U_tt
.  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
.  P    - preconditioning matrix for J, may be same as J
-  ctx  - [optional] user-defined context for matrix evaluation routine

   Notes:
   The matrices J and P are exactly the matrices that are used by SNES for the nonlinear solve.

   The matrix dF/dU + v*dF/dU_t + a*dF/dU_tt you provide turns out to be
   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.
   The time integrator internally approximates U_t by W+v*U and U_tt by W'+a*U  where the positive "shift"
   parameters 'v' and 'a' and vectors W, W' depend on the integration method, step size, and past states.

   Level: beginner

.keywords: TS, timestep, set, ODE, DAE, Jacobian

.seealso: TSSetI2Function()
@*/
PetscErrorCode TSSetI2Jacobian(TS ts,Mat J,Mat P,TSI2Jacobian jac,void *ctx)
{
  DM             dm;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (J) PetscValidHeaderSpecific(J,MAT_CLASSID,2);
  if (P) PetscValidHeaderSpecific(P,MAT_CLASSID,3);
  ierr = TSSetIJacobian(ts,J,P,NULL,NULL);CHKERRQ(ierr);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSSetI2Jacobian(dm,jac,ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  TSGetI2Jacobian - Returns the implicit Jacobian at the present timestep.

  Not Collective, but parallel objects are returned if TS is parallel

  Input Parameter:
. ts  - The TS context obtained from TSCreate()

  Output Parameters:
+ J  - The (approximate) Jacobian of F(t,U,U_t,U_tt)
. P - The matrix from which the preconditioner is constructed, often the same as J
. jac - The function to compute the Jacobian matrices
- ctx - User-defined context for Jacobian evaluation routine

  Notes: You can pass in NULL for any return argument you do not need.

  Level: advanced

.seealso: TSGetTimeStep(), TSGetMatrices(), TSGetTime(), TSGetStepNumber()

.keywords: TS, timestep, get, matrix, Jacobian
@*/
PetscErrorCode  TSGetI2Jacobian(TS ts,Mat *J,Mat *P,TSI2Jacobian *jac,void **ctx)
{
  PetscErrorCode ierr;
  SNES           snes;
  DM             dm;

  PetscFunctionBegin;
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr);
  ierr = SNESGetJacobian(snes,J,P,NULL,NULL);CHKERRQ(ierr);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetI2Jacobian(dm,jac,ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  TSComputeI2Function - Evaluates the DAE residual written in implicit form F(t,U,U_t,U_tt) = 0

  Collective on TS and Vec

  Input Parameters:
+ ts - the TS context
. t - current time
. U - state vector
. V - time derivative of state vector (U_t)
- A - second time derivative of state vector (U_tt)

  Output Parameter:
. F - the residual vector

  Note:
  Most users should not need to explicitly call this routine, as it
  is used internally within the nonlinear solvers.

  Level: developer

.keywords: TS, compute, function, vector

.seealso: TSSetI2Function()
@*/
PetscErrorCode TSComputeI2Function(TS ts,PetscReal t,Vec U,Vec V,Vec A,Vec F)
{
  DM             dm;
  TSI2Function   I2Function;
  void           *ctx;
  TSRHSFunction  rhsfunction;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  PetscValidHeaderSpecific(V,VEC_CLASSID,4);
  PetscValidHeaderSpecific(A,VEC_CLASSID,5);
  PetscValidHeaderSpecific(F,VEC_CLASSID,6);

  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetI2Function(dm,&I2Function,&ctx);CHKERRQ(ierr);
  ierr = DMTSGetRHSFunction(dm,&rhsfunction,NULL);CHKERRQ(ierr);

  if (!I2Function) {
    ierr = TSComputeIFunction(ts,t,U,A,F,PETSC_FALSE);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  ierr = PetscLogEventBegin(TS_FunctionEval,ts,U,V,F);CHKERRQ(ierr);

  PetscStackPush("TS user implicit function");
  ierr = I2Function(ts,t,U,V,A,F,ctx);CHKERRQ(ierr);
  PetscStackPop;

  if (rhsfunction) {
    Vec Frhs;
    ierr = TSGetRHSVec_Private(ts,&Frhs);CHKERRQ(ierr);
    ierr = TSComputeRHSFunction(ts,t,U,Frhs);CHKERRQ(ierr);
    ierr = VecAXPY(F,-1,Frhs);CHKERRQ(ierr);
  }

  ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,V,F);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  TSComputeI2Jacobian - Evaluates the Jacobian of the DAE

  Collective on TS and Vec

  Input Parameters:
+ ts - the TS context
. t - current timestep
. U - state vector
. V - time derivative of state vector
. A - second time derivative of state vector
. shiftV - shift to apply, see note below
- shiftA - shift to apply, see note below

  Output Parameters:
+ J - Jacobian matrix
- P - optional preconditioning matrix

  Notes:
  If F(t,U,V,A)=0 is the DAE, the required Jacobian is

  dF/dU + shiftV*dF/dV + shiftA*dF/dA

  Most users should not need to explicitly call this routine, as it
  is used internally within the nonlinear solvers.

  Level: developer

.keywords: TS, compute, Jacobian, matrix

.seealso:  TSSetI2Jacobian()
@*/
PetscErrorCode TSComputeI2Jacobian(TS ts,PetscReal t,Vec U,Vec V,Vec A,PetscReal shiftV,PetscReal shiftA,Mat J,Mat P)
{
  DM             dm;
  TSI2Jacobian   I2Jacobian;
  void           *ctx;
  TSRHSJacobian  rhsjacobian;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  PetscValidHeaderSpecific(V,VEC_CLASSID,4);
  PetscValidHeaderSpecific(A,VEC_CLASSID,5);
  PetscValidHeaderSpecific(J,MAT_CLASSID,8);
  PetscValidHeaderSpecific(P,MAT_CLASSID,9);

  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetI2Jacobian(dm,&I2Jacobian,&ctx);CHKERRQ(ierr);
  ierr = DMTSGetRHSJacobian(dm,&rhsjacobian,NULL);CHKERRQ(ierr);

  if (!I2Jacobian) {
    ierr = TSComputeIJacobian(ts,t,U,A,shiftA,J,P,PETSC_FALSE);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  ierr = PetscLogEventBegin(TS_JacobianEval,ts,U,J,P);CHKERRQ(ierr);

  PetscStackPush("TS user implicit Jacobian");
  ierr = I2Jacobian(ts,t,U,V,A,shiftV,shiftA,J,P,ctx);CHKERRQ(ierr);
  PetscStackPop;

  if (rhsjacobian) {
    Mat Jrhs,Prhs; MatStructure axpy = DIFFERENT_NONZERO_PATTERN;
    ierr = TSGetRHSMats_Private(ts,&Jrhs,&Prhs);CHKERRQ(ierr);
    ierr = TSComputeRHSJacobian(ts,t,U,Jrhs,Prhs);CHKERRQ(ierr);
    ierr = MatAXPY(J,-1,Jrhs,axpy);CHKERRQ(ierr);
    if (P != J) {ierr = MatAXPY(P,-1,Prhs,axpy);CHKERRQ(ierr);}
  }

  ierr = PetscLogEventEnd(TS_JacobianEval,ts,U,J,P);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TS2SetSolution - Sets the initial solution and time derivative vectors
   for use by the TS routines handling second order equations.

   Logically Collective on TS and Vec

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
.  u - the solution vector
-  v - the time derivative vector

   Level: beginner

.keywords: TS, timestep, set, solution, initial conditions
@*/
PetscErrorCode  TS2SetSolution(TS ts,Vec u,Vec v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(u,VEC_CLASSID,2);
  PetscValidHeaderSpecific(v,VEC_CLASSID,3);
  ierr = TSSetSolution(ts,u);CHKERRQ(ierr);
  ierr = PetscObjectReference((PetscObject)v);CHKERRQ(ierr);
  ierr = VecDestroy(&ts->vec_dot);CHKERRQ(ierr);
  ts->vec_dot = v;
  PetscFunctionReturn(0);
}

/*@
   TS2GetSolution - Returns the solution and time derivative at the present timestep
   for second order equations. It is valid to call this routine inside the function
   that you are evaluating in order to move to the new timestep. This vector not
   changed until the solution at the next timestep has been calculated.

   Not Collective, but Vec returned is parallel if TS is parallel

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
+  u - the vector containing the solution
-  v - the vector containing the time derivative

   Level: intermediate

.seealso: TS2SetSolution(), TSGetTimeStep(), TSGetTime()

.keywords: TS, timestep, get, solution
@*/
PetscErrorCode  TS2GetSolution(TS ts,Vec *u,Vec *v)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (u) PetscValidPointer(u,2);
  if (v) PetscValidPointer(v,3);
  if (u) *u = ts->vec_sol;
  if (v) *v = ts->vec_dot;
  PetscFunctionReturn(0);
}

/*@C
  TSLoad - Loads a KSP that has been stored in binary  with KSPView().

  Collective on PetscViewer

  Input Parameters:
+ newdm - the newly loaded TS, this needs to have been created with TSCreate() or
           some related function before a call to TSLoad().
- viewer - binary file viewer, obtained from PetscViewerBinaryOpen()

   Level: intermediate

  Notes:
   The type is determined by the data in the file, any type set into the TS before this call is ignored.

  Notes for advanced users:
  Most users should not need to know the details of the binary storage
  format, since TSLoad() and TSView() completely hide these details.
  But for anyone who's interested, the standard binary matrix storage
  format is
.vb
     has not yet been determined
.ve

.seealso: PetscViewerBinaryOpen(), TSView(), MatLoad(), VecLoad()
@*/
PetscErrorCode  TSLoad(TS ts, PetscViewer viewer)
{
  PetscErrorCode ierr;
  PetscBool      isbinary;
  PetscInt       classid;
  char           type[256];
  DMTS           sdm;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
  if (!isbinary) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid viewer; open viewer with PetscViewerBinaryOpen()");

  ierr = PetscViewerBinaryRead(viewer,&classid,1,NULL,PETSC_INT);CHKERRQ(ierr);
  if (classid != TS_FILE_CLASSID) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Not TS next in file");
  ierr = PetscViewerBinaryRead(viewer,type,256,NULL,PETSC_CHAR);CHKERRQ(ierr);
  ierr = TSSetType(ts, type);CHKERRQ(ierr);
  if (ts->ops->load) {
    ierr = (*ts->ops->load)(ts,viewer);CHKERRQ(ierr);
  }
  ierr = DMCreate(PetscObjectComm((PetscObject)ts),&dm);CHKERRQ(ierr);
  ierr = DMLoad(dm,viewer);CHKERRQ(ierr);
  ierr = TSSetDM(ts,dm);CHKERRQ(ierr);
  ierr = DMCreateGlobalVector(ts->dm,&ts->vec_sol);CHKERRQ(ierr);
  ierr = VecLoad(ts->vec_sol,viewer);CHKERRQ(ierr);
  ierr = DMGetDMTS(ts->dm,&sdm);CHKERRQ(ierr);
  ierr = DMTSLoad(sdm,viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#include <petscdraw.h>
#if defined(PETSC_HAVE_SAWS)
#include <petscviewersaws.h>
#endif
/*@C
    TSView - Prints the TS data structure.

    Collective on TS

    Input Parameters:
+   ts - the TS context obtained from TSCreate()
-   viewer - visualization context

    Options Database Key:
.   -ts_view - calls TSView() at end of TSStep()

    Notes:
    The available visualization contexts include
+     PETSC_VIEWER_STDOUT_SELF - standard output (default)
-     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
         output where only the first processor opens
         the file.  All other processors send their
         data to the first processor to print.

    The user can open an alternative visualization context with
    PetscViewerASCIIOpen() - output to a specified file.

    Level: beginner

.keywords: TS, timestep, view

.seealso: PetscViewerASCIIOpen()
@*/
PetscErrorCode  TSView(TS ts,PetscViewer viewer)
{
  PetscErrorCode ierr;
  TSType         type;
  PetscBool      iascii,isstring,isundials,isbinary,isdraw;
  DMTS           sdm;
#if defined(PETSC_HAVE_SAWS)
  PetscBool      issaws;
#endif

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (!viewer) {
    ierr = PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)ts),&viewer);CHKERRQ(ierr);
  }
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
  PetscCheckSameComm(ts,1,viewer,2);

  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
#if defined(PETSC_HAVE_SAWS)
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSAWS,&issaws);CHKERRQ(ierr);
#endif
  if (iascii) {
    ierr = PetscObjectPrintClassNamePrefixType((PetscObject)ts,viewer);CHKERRQ(ierr);
    if (ts->ops->view) {
      ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
      ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
    }
    if (ts->max_steps < PETSC_MAX_INT) {
      ierr = PetscViewerASCIIPrintf(viewer,"  maximum steps=%D\n",ts->max_steps);CHKERRQ(ierr);
    }
    if (ts->max_time < PETSC_MAX_REAL) {
      ierr = PetscViewerASCIIPrintf(viewer,"  maximum time=%g\n",(double)ts->max_time);CHKERRQ(ierr);
    }
    if (ts->usessnes) {
      PetscBool lin;
      if (ts->problem_type == TS_NONLINEAR) {
        ierr = PetscViewerASCIIPrintf(viewer,"  total number of nonlinear solver iterations=%D\n",ts->snes_its);CHKERRQ(ierr);
      }
      ierr = PetscViewerASCIIPrintf(viewer,"  total number of linear solver iterations=%D\n",ts->ksp_its);CHKERRQ(ierr);
      ierr = PetscObjectTypeCompare((PetscObject)ts->snes,SNESKSPONLY,&lin);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(viewer,"  total number of %slinear solve failures=%D\n",lin ? "" : "non",ts->num_snes_failures);CHKERRQ(ierr);
    }
    ierr = PetscViewerASCIIPrintf(viewer,"  total number of rejected steps=%D\n",ts->reject);CHKERRQ(ierr);
    if (ts->vrtol) {
      ierr = PetscViewerASCIIPrintf(viewer,"  using vector of relative error tolerances, ");CHKERRQ(ierr);
    } else {
      ierr = PetscViewerASCIIPrintf(viewer,"  using relative error tolerance of %g, ",(double)ts->rtol);CHKERRQ(ierr);
    }
    if (ts->vatol) {
      ierr = PetscViewerASCIIPrintf(viewer,"  using vector of absolute error tolerances\n");CHKERRQ(ierr);
    } else {
      ierr = PetscViewerASCIIPrintf(viewer,"  using absolute error tolerance of %g\n",(double)ts->atol);CHKERRQ(ierr);
    }
    ierr = TSAdaptView(ts->adapt,viewer);CHKERRQ(ierr);
    if (ts->snes && ts->usessnes)  {ierr = SNESView(ts->snes,viewer);CHKERRQ(ierr);}
    ierr = DMGetDMTS(ts->dm,&sdm);CHKERRQ(ierr);
    ierr = DMTSView(sdm,viewer);CHKERRQ(ierr);
  } else if (isstring) {
    ierr = TSGetType(ts,&type);CHKERRQ(ierr);
    ierr = PetscViewerStringSPrintf(viewer," %-7.7s",type);CHKERRQ(ierr);
  } else if (isbinary) {
    PetscInt    classid = TS_FILE_CLASSID;
    MPI_Comm    comm;
    PetscMPIInt rank;
    char        type[256];

    ierr = PetscObjectGetComm((PetscObject)ts,&comm);CHKERRQ(ierr);
    ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
    if (!rank) {
      ierr = PetscViewerBinaryWrite(viewer,&classid,1,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
      ierr = PetscStrncpy(type,((PetscObject)ts)->type_name,256);CHKERRQ(ierr);
      ierr = PetscViewerBinaryWrite(viewer,type,256,PETSC_CHAR,PETSC_FALSE);CHKERRQ(ierr);
    }
    if (ts->ops->view) {
      ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
    }
    if (ts->adapt) {ierr = TSAdaptView(ts->adapt,viewer);CHKERRQ(ierr);}
    ierr = DMView(ts->dm,viewer);CHKERRQ(ierr);
    ierr = VecView(ts->vec_sol,viewer);CHKERRQ(ierr);
    ierr = DMGetDMTS(ts->dm,&sdm);CHKERRQ(ierr);
    ierr = DMTSView(sdm,viewer);CHKERRQ(ierr);
  } else if (isdraw) {
    PetscDraw draw;
    char      str[36];
    PetscReal x,y,bottom,h;

    ierr   = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
    ierr   = PetscDrawGetCurrentPoint(draw,&x,&y);CHKERRQ(ierr);
    ierr   = PetscStrcpy(str,"TS: ");CHKERRQ(ierr);
    ierr   = PetscStrcat(str,((PetscObject)ts)->type_name);CHKERRQ(ierr);
    ierr   = PetscDrawStringBoxed(draw,x,y,PETSC_DRAW_BLACK,PETSC_DRAW_BLACK,str,NULL,&h);CHKERRQ(ierr);
    bottom = y - h;
    ierr   = PetscDrawPushCurrentPoint(draw,x,bottom);CHKERRQ(ierr);
    if (ts->ops->view) {
      ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
    }
    if (ts->adapt) {ierr = TSAdaptView(ts->adapt,viewer);CHKERRQ(ierr);}
    if (ts->snes)  {ierr = SNESView(ts->snes,viewer);CHKERRQ(ierr);}
    ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
#if defined(PETSC_HAVE_SAWS)
  } else if (issaws) {
    PetscMPIInt rank;
    const char  *name;

    ierr = PetscObjectGetName((PetscObject)ts,&name);CHKERRQ(ierr);
    ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
    if (!((PetscObject)ts)->amsmem && !rank) {
      char       dir[1024];

      ierr = PetscObjectViewSAWs((PetscObject)ts,viewer);CHKERRQ(ierr);
      ierr = PetscSNPrintf(dir,1024,"/PETSc/Objects/%s/time_step",name);CHKERRQ(ierr);
      PetscStackCallSAWs(SAWs_Register,(dir,&ts->steps,1,SAWs_READ,SAWs_INT));
      ierr = PetscSNPrintf(dir,1024,"/PETSc/Objects/%s/time",name);CHKERRQ(ierr);
      PetscStackCallSAWs(SAWs_Register,(dir,&ts->ptime,1,SAWs_READ,SAWs_DOUBLE));
    }
    if (ts->ops->view) {
      ierr = (*ts->ops->view)(ts,viewer);CHKERRQ(ierr);
    }
#endif
  }

  ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)ts,TSSUNDIALS,&isundials);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSSetApplicationContext - Sets an optional user-defined context for
   the timesteppers.

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
-  usrP - optional user context

   Fortran Notes: To use this from Fortran you must write a Fortran interface definition for this
    function that tells Fortran the Fortran derived data type that you are passing in as the ctx argument.

   Level: intermediate

.keywords: TS, timestep, set, application, context

.seealso: TSGetApplicationContext()
@*/
PetscErrorCode  TSSetApplicationContext(TS ts,void *usrP)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ts->user = usrP;
  PetscFunctionReturn(0);
}

/*@
    TSGetApplicationContext - Gets the user-defined context for the
    timestepper.

    Not Collective

    Input Parameter:
.   ts - the TS context obtained from TSCreate()

    Output Parameter:
.   usrP - user context

   Fortran Notes: To use this from Fortran you must write a Fortran interface definition for this
    function that tells Fortran the Fortran derived data type that you are passing in as the ctx argument.

    Level: intermediate

.keywords: TS, timestep, get, application, context

.seealso: TSSetApplicationContext()
@*/
PetscErrorCode  TSGetApplicationContext(TS ts,void *usrP)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  *(void**)usrP = ts->user;
  PetscFunctionReturn(0);
}

/*@
   TSGetStepNumber - Gets the number of steps completed.

   Not Collective

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
.  steps - number of steps completed so far

   Level: intermediate

.keywords: TS, timestep, get, iteration, number
.seealso: TSGetTime(), TSGetTimeStep(), TSSetPreStep(), TSSetPreStage(), TSSetPostStage(), TSSetPostStep()
@*/
PetscErrorCode TSGetStepNumber(TS ts,PetscInt *steps)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidIntPointer(steps,2);
  *steps = ts->steps;
  PetscFunctionReturn(0);
}

/*@
   TSSetStepNumber - Sets the number of steps completed.

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context
-  steps - number of steps completed so far

   Notes:
   For most uses of the TS solvers the user need not explicitly call
   TSSetStepNumber(), as the step counter is appropriately updated in
   TSSolve()/TSStep()/TSRollBack(). Power users may call this routine to
   reinitialize timestepping by setting the step counter to zero (and time
   to the initial time) to solve a similar problem with different initial
   conditions or parameters. Other possible use case is to continue
   timestepping from a previously interrupted run in such a way that TS
   monitors will be called with a initial nonzero step counter.

   Level: advanced

.keywords: TS, timestep, set, iteration, number
.seealso: TSGetStepNumber(), TSSetTime(), TSSetTimeStep(), TSSetSolution()
@*/
PetscErrorCode TSSetStepNumber(TS ts,PetscInt steps)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidLogicalCollectiveInt(ts,steps,2);
  if (steps < 0) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Step number must be non-negative");
  ts->steps = steps;
  PetscFunctionReturn(0);
}

/*@
   TSSetTimeStep - Allows one to reset the timestep at any time,
   useful for simple pseudo-timestepping codes.

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
-  time_step - the size of the timestep

   Level: intermediate

.seealso: TSGetTimeStep(), TSSetTime()

.keywords: TS, set, timestep
@*/
PetscErrorCode  TSSetTimeStep(TS ts,PetscReal time_step)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidLogicalCollectiveReal(ts,time_step,2);
  ts->time_step = time_step;
  PetscFunctionReturn(0);
}

/*@
   TSSetExactFinalTime - Determines whether to adapt the final time step to
     match the exact final time, interpolate solution to the exact final time,
     or just return at the final time TS computed.

  Logically Collective on TS

   Input Parameter:
+   ts - the time-step context
-   eftopt - exact final time option

$  TS_EXACTFINALTIME_STEPOVER    - Don't do anything if final time is exceeded
$  TS_EXACTFINALTIME_INTERPOLATE - Interpolate back to final time
$  TS_EXACTFINALTIME_MATCHSTEP - Adapt final time step to match the final time

   Options Database:
.   -ts_exact_final_time <stepover,interpolate,matchstep> - select the final step at runtime

   Warning: If you use the option TS_EXACTFINALTIME_STEPOVER the solution may be at a very different time
    then the final time you selected.

   Level: beginner

.seealso: TSExactFinalTimeOption, TSGetExactFinalTime()
@*/
PetscErrorCode TSSetExactFinalTime(TS ts,TSExactFinalTimeOption eftopt)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidLogicalCollectiveEnum(ts,eftopt,2);
  ts->exact_final_time = eftopt;
  PetscFunctionReturn(0);
}

/*@
   TSGetExactFinalTime - Gets the exact final time option.

   Not Collective

   Input Parameter:
.  ts - the TS context

   Output Parameter:
.  eftopt - exact final time option

   Level: beginner

.seealso: TSExactFinalTimeOption, TSSetExactFinalTime()
@*/
PetscErrorCode TSGetExactFinalTime(TS ts,TSExactFinalTimeOption *eftopt)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(eftopt,2);
  *eftopt = ts->exact_final_time;
  PetscFunctionReturn(0);
}

/*@
   TSGetTimeStep - Gets the current timestep size.

   Not Collective

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
.  dt - the current timestep size

   Level: intermediate

.seealso: TSSetTimeStep(), TSGetTime()

.keywords: TS, get, timestep
@*/
PetscErrorCode  TSGetTimeStep(TS ts,PetscReal *dt)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidRealPointer(dt,2);
  *dt = ts->time_step;
  PetscFunctionReturn(0);
}

/*@
   TSGetSolution - Returns the solution at the present timestep. It
   is valid to call this routine inside the function that you are evaluating
   in order to move to the new timestep. This vector not changed until
   the solution at the next timestep has been calculated.

   Not Collective, but Vec returned is parallel if TS is parallel

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
.  v - the vector containing the solution

   Note: If you used TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP); this does not return the solution at the requested
   final time. It returns the solution at the next timestep.

   Level: intermediate

.seealso: TSGetTimeStep(), TSGetTime(), TSGetSolveTime(), TSGetSolutionComponents()

.keywords: TS, timestep, get, solution
@*/
PetscErrorCode  TSGetSolution(TS ts,Vec *v)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(v,2);
  *v = ts->vec_sol;
  PetscFunctionReturn(0);
}

/*@
   TSGetSolutionComponents - Returns any solution components at the present
   timestep, if available for the time integration method being used.
   Solution components are quantities that share the same size and
   structure as the solution vector.

   Not Collective, but Vec returned is parallel if TS is parallel

   Parameters :
.  ts - the TS context obtained from TSCreate() (input parameter).
.  n - If v is PETSC_NULL, then the number of solution components is
       returned through n, else the n-th solution component is
       returned in v.
.  v - the vector containing the n-th solution component
       (may be PETSC_NULL to use this function to find out
        the number of solutions components).

   Level: advanced

.seealso: TSGetSolution()

.keywords: TS, timestep, get, solution
@*/
PetscErrorCode  TSGetSolutionComponents(TS ts,PetscInt *n,Vec *v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (!ts->ops->getsolutioncomponents) *n = 0;
  else {
    ierr = (*ts->ops->getsolutioncomponents)(ts,n,v);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@
   TSGetAuxSolution - Returns an auxiliary solution at the present
   timestep, if available for the time integration method being used.

   Not Collective, but Vec returned is parallel if TS is parallel

   Parameters :
.  ts - the TS context obtained from TSCreate() (input parameter).
.  v - the vector containing the auxiliary solution

   Level: intermediate

.seealso: TSGetSolution()

.keywords: TS, timestep, get, solution
@*/
PetscErrorCode  TSGetAuxSolution(TS ts,Vec *v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (ts->ops->getauxsolution) {
    ierr = (*ts->ops->getauxsolution)(ts,v);CHKERRQ(ierr);
  } else {
    ierr = VecZeroEntries(*v); CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@
   TSGetTimeError - Returns the estimated error vector, if the chosen
   TSType has an error estimation functionality.

   Not Collective, but Vec returned is parallel if TS is parallel

   Note: MUST call after TSSetUp()

   Parameters :
.  ts - the TS context obtained from TSCreate() (input parameter).
.  n - current estimate (n=0) or previous one (n=-1)
.  v - the vector containing the error (same size as the solution).

   Level: intermediate

.seealso: TSGetSolution(), TSSetTimeError()

.keywords: TS, timestep, get, error
@*/
PetscErrorCode  TSGetTimeError(TS ts,PetscInt n,Vec *v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (ts->ops->gettimeerror) {
    ierr = (*ts->ops->gettimeerror)(ts,n,v);CHKERRQ(ierr);
  } else {
    ierr = VecZeroEntries(*v);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@
   TSSetTimeError - Sets the estimated error vector, if the chosen
   TSType has an error estimation functionality. This can be used
   to restart such a time integrator with a given error vector.

   Not Collective, but Vec returned is parallel if TS is parallel

   Parameters :
.  ts - the TS context obtained from TSCreate() (input parameter).
.  v - the vector containing the error (same size as the solution).

   Level: intermediate

.seealso: TSSetSolution(), TSGetTimeError)

.keywords: TS, timestep, get, error
@*/
PetscErrorCode  TSSetTimeError(TS ts,Vec v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (!ts->setupcalled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetUp() first");
  if (ts->ops->settimeerror) {
    ierr = (*ts->ops->settimeerror)(ts,v);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@
   TSGetCostGradients - Returns the gradients from the TSAdjointSolve()

   Not Collective, but Vec returned is parallel if TS is parallel

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
+  lambda - vectors containing the gradients of the cost functions with respect to the ODE/DAE solution variables
-  mu - vectors containing the gradients of the cost functions with respect to the problem parameters

   Level: intermediate

.seealso: TSGetTimeStep()

.keywords: TS, timestep, get, sensitivity
@*/
PetscErrorCode  TSGetCostGradients(TS ts,PetscInt *numcost,Vec **lambda,Vec **mu)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (numcost) *numcost = ts->numcost;
  if (lambda)  *lambda  = ts->vecs_sensi;
  if (mu)      *mu      = ts->vecs_sensip;
  PetscFunctionReturn(0);
}

/* ----- Routines to initialize and destroy a timestepper ---- */
/*@
  TSSetProblemType - Sets the type of problem to be solved.

  Not collective

  Input Parameters:
+ ts   - The TS
- type - One of TS_LINEAR, TS_NONLINEAR where these types refer to problems of the forms
.vb
         U_t - A U = 0      (linear)
         U_t - A(t) U = 0   (linear)
         F(t,U,U_t) = 0     (nonlinear)
.ve

   Level: beginner

.keywords: TS, problem type
.seealso: TSSetUp(), TSProblemType, TS
@*/
PetscErrorCode  TSSetProblemType(TS ts, TSProblemType type)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  ts->problem_type = type;
  if (type == TS_LINEAR) {
    SNES snes;
    ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
    ierr = SNESSetType(snes,SNESKSPONLY);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@C
  TSGetProblemType - Gets the type of problem to be solved.

  Not collective

  Input Parameter:
. ts   - The TS

  Output Parameter:
. type - One of TS_LINEAR, TS_NONLINEAR where these types refer to problems of the forms
.vb
         M U_t = A U
         M(t) U_t = A(t) U
         F(t,U,U_t)
.ve

   Level: beginner

.keywords: TS, problem type
.seealso: TSSetUp(), TSProblemType, TS
@*/
PetscErrorCode  TSGetProblemType(TS ts, TSProblemType *type)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  PetscValidIntPointer(type,2);
  *type = ts->problem_type;
  PetscFunctionReturn(0);
}

/*@
   TSSetUp - Sets up the internal data structures for the later use
   of a timestepper.

   Collective on TS

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Notes:
   For basic use of the TS solvers the user need not explicitly call
   TSSetUp(), since these actions will automatically occur during
   the call to TSStep().  However, if one wishes to control this
   phase separately, TSSetUp() should be called after TSCreate()
   and optional routines of the form TSSetXXX(), but before TSStep().

   Level: advanced

.keywords: TS, timestep, setup

.seealso: TSCreate(), TSStep(), TSDestroy()
@*/
PetscErrorCode  TSSetUp(TS ts)
{
  PetscErrorCode ierr;
  DM             dm;
  PetscErrorCode (*func)(SNES,Vec,Vec,void*);
  PetscErrorCode (*jac)(SNES,Vec,Mat,Mat,void*);
  TSIFunction    ifun;
  TSIJacobian    ijac;
  TSI2Jacobian   i2jac;
  TSRHSJacobian  rhsjac;
  PetscBool      isnone;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (ts->setupcalled) PetscFunctionReturn(0);

  if (!((PetscObject)ts)->type_name) {
    ierr = TSGetIFunction(ts,NULL,&ifun,NULL);CHKERRQ(ierr);
    ierr = TSSetType(ts,ifun ? TSBEULER : TSEULER);CHKERRQ(ierr);
  }

  if (!ts->vec_sol) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetSolution() first");

  if (ts->rhsjacobian.reuse) {
    Mat Amat,Pmat;
    SNES snes;
    ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
    ierr = SNESGetJacobian(snes,&Amat,&Pmat,NULL,NULL);CHKERRQ(ierr);
    /* Matching matrices implies that an IJacobian is NOT set, because if it had been set, the IJacobian's matrix would
     * have displaced the RHS matrix */
    if (Amat == ts->Arhs) {
      /* we need to copy the values of the matrix because for the constant Jacobian case the user will never set the numerical values in this new location */
      ierr = MatDuplicate(ts->Arhs,MAT_COPY_VALUES,&Amat);CHKERRQ(ierr);
      ierr = SNESSetJacobian(snes,Amat,NULL,NULL,NULL);CHKERRQ(ierr);
      ierr = MatDestroy(&Amat);CHKERRQ(ierr);
    }
    if (Pmat == ts->Brhs) {
      ierr = MatDuplicate(ts->Brhs,MAT_COPY_VALUES,&Pmat);CHKERRQ(ierr);
      ierr = SNESSetJacobian(snes,NULL,Pmat,NULL,NULL);CHKERRQ(ierr);
      ierr = MatDestroy(&Pmat);CHKERRQ(ierr);
    }
  }

  ierr = TSGetAdapt(ts,&ts->adapt);CHKERRQ(ierr);
  ierr = TSAdaptSetDefaultType(ts->adapt,ts->default_adapt_type);CHKERRQ(ierr);

  if (ts->ops->setup) {
    ierr = (*ts->ops->setup)(ts);CHKERRQ(ierr);
  }

  /* Attempt to check/preset a default value for the exact final time option */
  ierr = PetscObjectTypeCompare((PetscObject)ts->adapt,TSADAPTNONE,&isnone);CHKERRQ(ierr);
  if (!isnone && ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED)
    ts->exact_final_time = TS_EXACTFINALTIME_MATCHSTEP;

  /* In the case where we've set a DMTSFunction or what have you, we need the default SNESFunction
     to be set right but can't do it elsewhere due to the overreliance on ctx=ts.
   */
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMSNESGetFunction(dm,&func,NULL);CHKERRQ(ierr);
  if (!func) {
    ierr = DMSNESSetFunction(dm,SNESTSFormFunction,ts);CHKERRQ(ierr);
  }
  /* If the SNES doesn't have a jacobian set and the TS has an ijacobian or rhsjacobian set, set the SNES to use it.
     Otherwise, the SNES will use coloring internally to form the Jacobian.
   */
  ierr = DMSNESGetJacobian(dm,&jac,NULL);CHKERRQ(ierr);
  ierr = DMTSGetIJacobian(dm,&ijac,NULL);CHKERRQ(ierr);
  ierr = DMTSGetI2Jacobian(dm,&i2jac,NULL);CHKERRQ(ierr);
  ierr = DMTSGetRHSJacobian(dm,&rhsjac,NULL);CHKERRQ(ierr);
  if (!jac && (ijac || i2jac || rhsjac)) {
    ierr = DMSNESSetJacobian(dm,SNESTSFormJacobian,ts);CHKERRQ(ierr);
  }

  /* if time integration scheme has a starting method, call it */
  if (ts->ops->startingmethod) {
    ierr = (*ts->ops->startingmethod)(ts);CHKERRQ(ierr);
  }

  ts->setupcalled = PETSC_TRUE;
  PetscFunctionReturn(0);
}

/*@
   TSAdjointSetUp - Sets up the internal data structures for the later use
   of an adjoint solver

   Collective on TS

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Level: advanced

.keywords: TS, timestep, setup

.seealso: TSCreate(), TSAdjointStep(), TSSetCostGradients()
@*/
PetscErrorCode  TSAdjointSetUp(TS ts)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (ts->adjointsetupcalled) PetscFunctionReturn(0);
  if (!ts->vecs_sensi) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetCostGradients() first");
  if (ts->vecs_sensip && !ts->Jacp) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"Must call TSAdjointSetRHSJacobian() first");

  if (ts->vec_costintegral) { /* if there is integral in the cost function */
    ierr = VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&ts->vecs_drdy);CHKERRQ(ierr);
    if (ts->vecs_sensip){
      ierr = VecDuplicateVecs(ts->vecs_sensip[0],ts->numcost,&ts->vecs_drdp);CHKERRQ(ierr);
    }
  }

  if (ts->ops->adjointsetup) {
    ierr = (*ts->ops->adjointsetup)(ts);CHKERRQ(ierr);
  }
  ts->adjointsetupcalled = PETSC_TRUE;
  PetscFunctionReturn(0);
}

/*@
   TSReset - Resets a TS context and removes any allocated Vecs and Mats.

   Collective on TS

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Level: beginner

.keywords: TS, timestep, reset

.seealso: TSCreate(), TSSetup(), TSDestroy()
@*/
PetscErrorCode  TSReset(TS ts)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);

  if (ts->ops->reset) {
    ierr = (*ts->ops->reset)(ts);CHKERRQ(ierr);
  }
  if (ts->snes) {ierr = SNESReset(ts->snes);CHKERRQ(ierr);}
  if (ts->adapt) {ierr = TSAdaptReset(ts->adapt);CHKERRQ(ierr);}

  ierr = MatDestroy(&ts->Arhs);CHKERRQ(ierr);
  ierr = MatDestroy(&ts->Brhs);CHKERRQ(ierr);
  ierr = VecDestroy(&ts->Frhs);CHKERRQ(ierr);
  ierr = VecDestroy(&ts->vec_sol);CHKERRQ(ierr);
  ierr = VecDestroy(&ts->vec_dot);CHKERRQ(ierr);
  ierr = VecDestroy(&ts->vatol);CHKERRQ(ierr);
  ierr = VecDestroy(&ts->vrtol);CHKERRQ(ierr);
  ierr = VecDestroyVecs(ts->nwork,&ts->work);CHKERRQ(ierr);

  ierr = VecDestroyVecs(ts->numcost,&ts->vecs_drdy);CHKERRQ(ierr);
  ierr = VecDestroyVecs(ts->numcost,&ts->vecs_drdp);CHKERRQ(ierr);

  ierr = MatDestroy(&ts->Jacp);CHKERRQ(ierr);
  ierr = VecDestroy(&ts->vec_costintegral);CHKERRQ(ierr);
  ierr = VecDestroy(&ts->vec_costintegrand);CHKERRQ(ierr);

  ierr = PetscFree(ts->vecs_fwdsensipacked);CHKERRQ(ierr);

  ts->setupcalled = PETSC_FALSE;
  PetscFunctionReturn(0);
}

/*@
   TSDestroy - Destroys the timestepper context that was created
   with TSCreate().

   Collective on TS

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Level: beginner

.keywords: TS, timestepper, destroy

.seealso: TSCreate(), TSSetUp(), TSSolve()
@*/
PetscErrorCode  TSDestroy(TS *ts)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!*ts) PetscFunctionReturn(0);
  PetscValidHeaderSpecific((*ts),TS_CLASSID,1);
  if (--((PetscObject)(*ts))->refct > 0) {*ts = 0; PetscFunctionReturn(0);}

  ierr = TSReset((*ts));CHKERRQ(ierr);

  /* if memory was published with SAWs then destroy it */
  ierr = PetscObjectSAWsViewOff((PetscObject)*ts);CHKERRQ(ierr);
  if ((*ts)->ops->destroy) {ierr = (*(*ts)->ops->destroy)((*ts));CHKERRQ(ierr);}

  ierr = TSTrajectoryDestroy(&(*ts)->trajectory);CHKERRQ(ierr);

  ierr = TSAdaptDestroy(&(*ts)->adapt);CHKERRQ(ierr);
  ierr = TSEventDestroy(&(*ts)->event);CHKERRQ(ierr);

  ierr = SNESDestroy(&(*ts)->snes);CHKERRQ(ierr);
  ierr = DMDestroy(&(*ts)->dm);CHKERRQ(ierr);
  ierr = TSMonitorCancel((*ts));CHKERRQ(ierr);
  ierr = TSAdjointMonitorCancel((*ts));CHKERRQ(ierr);

  ierr = PetscHeaderDestroy(ts);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSGetSNES - Returns the SNES (nonlinear solver) associated with
   a TS (timestepper) context. Valid only for nonlinear problems.

   Not Collective, but SNES is parallel if TS is parallel

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
.  snes - the nonlinear solver context

   Notes:
   The user can then directly manipulate the SNES context to set various
   options, etc.  Likewise, the user can then extract and manipulate the
   KSP, KSP, and PC contexts as well.

   TSGetSNES() does not work for integrators that do not use SNES; in
   this case TSGetSNES() returns NULL in snes.

   Level: beginner

.keywords: timestep, get, SNES
@*/
PetscErrorCode  TSGetSNES(TS ts,SNES *snes)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(snes,2);
  if (!ts->snes) {
    ierr = SNESCreate(PetscObjectComm((PetscObject)ts),&ts->snes);CHKERRQ(ierr);
    ierr = SNESSetFunction(ts->snes,NULL,SNESTSFormFunction,ts);CHKERRQ(ierr);
    ierr = PetscLogObjectParent((PetscObject)ts,(PetscObject)ts->snes);CHKERRQ(ierr);
    ierr = PetscObjectIncrementTabLevel((PetscObject)ts->snes,(PetscObject)ts,1);CHKERRQ(ierr);
    if (ts->dm) {ierr = SNESSetDM(ts->snes,ts->dm);CHKERRQ(ierr);}
    if (ts->problem_type == TS_LINEAR) {
      ierr = SNESSetType(ts->snes,SNESKSPONLY);CHKERRQ(ierr);
    }
  }
  *snes = ts->snes;
  PetscFunctionReturn(0);
}

/*@
   TSSetSNES - Set the SNES (nonlinear solver) to be used by the timestepping context

   Collective

   Input Parameter:
+  ts - the TS context obtained from TSCreate()
-  snes - the nonlinear solver context

   Notes:
   Most users should have the TS created by calling TSGetSNES()

   Level: developer

.keywords: timestep, set, SNES
@*/
PetscErrorCode TSSetSNES(TS ts,SNES snes)
{
  PetscErrorCode ierr;
  PetscErrorCode (*func)(SNES,Vec,Mat,Mat,void*);

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(snes,SNES_CLASSID,2);
  ierr = PetscObjectReference((PetscObject)snes);CHKERRQ(ierr);
  ierr = SNESDestroy(&ts->snes);CHKERRQ(ierr);

  ts->snes = snes;

  ierr = SNESSetFunction(ts->snes,NULL,SNESTSFormFunction,ts);CHKERRQ(ierr);
  ierr = SNESGetJacobian(ts->snes,NULL,NULL,&func,NULL);CHKERRQ(ierr);
  if (func == SNESTSFormJacobian) {
    ierr = SNESSetJacobian(ts->snes,NULL,NULL,SNESTSFormJacobian,ts);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@
   TSGetKSP - Returns the KSP (linear solver) associated with
   a TS (timestepper) context.

   Not Collective, but KSP is parallel if TS is parallel

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
.  ksp - the nonlinear solver context

   Notes:
   The user can then directly manipulate the KSP context to set various
   options, etc.  Likewise, the user can then extract and manipulate the
   KSP and PC contexts as well.

   TSGetKSP() does not work for integrators that do not use KSP;
   in this case TSGetKSP() returns NULL in ksp.

   Level: beginner

.keywords: timestep, get, KSP
@*/
PetscErrorCode  TSGetKSP(TS ts,KSP *ksp)
{
  PetscErrorCode ierr;
  SNES           snes;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(ksp,2);
  if (!((PetscObject)ts)->type_name) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"KSP is not created yet. Call TSSetType() first");
  if (ts->problem_type != TS_LINEAR) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Linear only; use TSGetSNES()");
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESGetKSP(snes,ksp);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ----------- Routines to set solver parameters ---------- */

/*@
   TSSetMaxSteps - Sets the maximum number of steps to use.

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
-  maxsteps - maximum number of steps to use

   Options Database Keys:
.  -ts_max_steps <maxsteps> - Sets maxsteps

   Notes:
   The default maximum number of steps is 5000

   Level: intermediate

.keywords: TS, timestep, set, maximum, steps

.seealso: TSGetMaxSteps(), TSSetMaxTime(), TSSetExactFinalTime()
@*/
PetscErrorCode TSSetMaxSteps(TS ts,PetscInt maxsteps)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidLogicalCollectiveInt(ts,maxsteps,2);
  if (maxsteps < 0 ) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Maximum number of steps must be non-negative");
  ts->max_steps = maxsteps;
  PetscFunctionReturn(0);
}

/*@
   TSGetMaxSteps - Gets the maximum number of steps to use.

   Not Collective

   Input Parameters:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
.  maxsteps - maximum number of steps to use

   Level: advanced

.keywords: TS, timestep, get, maximum, steps

.seealso: TSSetMaxSteps(), TSGetMaxTime(), TSSetMaxTime()
@*/
PetscErrorCode TSGetMaxSteps(TS ts,PetscInt *maxsteps)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidIntPointer(maxsteps,2);
  *maxsteps = ts->max_steps;
  PetscFunctionReturn(0);
}

/*@
   TSSetMaxTime - Sets the maximum (or final) time for timestepping.

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
-  maxtime - final time to step to

   Options Database Keys:
.  -ts_max_time <maxtime> - Sets maxtime

   Notes:
   The default maximum time is 5.0

   Level: intermediate

.keywords: TS, timestep, set, maximum, time

.seealso: TSGetMaxTime(), TSSetMaxSteps(), TSSetExactFinalTime()
@*/
PetscErrorCode TSSetMaxTime(TS ts,PetscReal maxtime)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidLogicalCollectiveReal(ts,maxtime,2);
  ts->max_time = maxtime;
  PetscFunctionReturn(0);
}

/*@
   TSGetMaxTime - Gets the maximum (or final) time for timestepping.

   Not Collective

   Input Parameters:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
.  maxtime - final time to step to

   Level: advanced

.keywords: TS, timestep, get, maximum, time

.seealso: TSSetMaxTime(), TSGetMaxSteps(), TSSetMaxSteps()
@*/
PetscErrorCode TSGetMaxTime(TS ts,PetscReal *maxtime)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidRealPointer(maxtime,2);
  *maxtime = ts->max_time;
  PetscFunctionReturn(0);
}

/*@
   TSSetInitialTimeStep - Deprecated, use TSSetTime() and TSSetTimeStep().
@*/
PetscErrorCode  TSSetInitialTimeStep(TS ts,PetscReal initial_time,PetscReal time_step)
{
  PetscErrorCode ierr;
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = TSSetTime(ts,initial_time);CHKERRQ(ierr);
  ierr = TSSetTimeStep(ts,time_step);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSGetDuration - Deprecated, use TSGetMaxSteps() and TSGetMaxTime().
@*/
PetscErrorCode TSGetDuration(TS ts, PetscInt *maxsteps, PetscReal *maxtime)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  if (maxsteps) {
    PetscValidIntPointer(maxsteps,2);
    *maxsteps = ts->max_steps;
  }
  if (maxtime) {
    PetscValidScalarPointer(maxtime,3);
    *maxtime = ts->max_time;
  }
  PetscFunctionReturn(0);
}

/*@
   TSSetDuration - Deprecated, use TSSetMaxSteps() and TSSetMaxTime().
@*/
PetscErrorCode TSSetDuration(TS ts,PetscInt maxsteps,PetscReal maxtime)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidLogicalCollectiveInt(ts,maxsteps,2);
  PetscValidLogicalCollectiveReal(ts,maxtime,2);
  if (maxsteps >= 0) ts->max_steps = maxsteps;
  if (maxtime != PETSC_DEFAULT) ts->max_time = maxtime;
  PetscFunctionReturn(0);
}

/*@
   TSGetTimeStepNumber - Deprecated, use TSGetStepNumber().
@*/
PetscErrorCode TSGetTimeStepNumber(TS ts,PetscInt *steps) { return TSGetStepNumber(ts,steps); }

/*@
   TSGetTotalSteps - Deprecated, use TSGetStepNumber().
@*/
PetscErrorCode TSGetTotalSteps(TS ts,PetscInt *steps) { return TSGetStepNumber(ts,steps); }

/*@
   TSSetSolution - Sets the initial solution vector
   for use by the TS routines.

   Logically Collective on TS and Vec

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
-  u - the solution vector

   Level: beginner

.keywords: TS, timestep, set, solution, initial values
@*/
PetscErrorCode  TSSetSolution(TS ts,Vec u)
{
  PetscErrorCode ierr;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(u,VEC_CLASSID,2);
  ierr = PetscObjectReference((PetscObject)u);CHKERRQ(ierr);
  ierr = VecDestroy(&ts->vec_sol);CHKERRQ(ierr);
  ts->vec_sol = u;

  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMShellSetGlobalVector(dm,u);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSAdjointSetSteps - Sets the number of steps the adjoint solver should take backward in time

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
.  steps - number of steps to use

   Level: intermediate

   Notes: Normally one does not call this and TSAdjointSolve() integrates back to the original timestep. One can call this
          so as to integrate back to less than the original timestep

.keywords: TS, timestep, set, maximum, iterations

.seealso: TSSetExactFinalTime()
@*/
PetscErrorCode  TSAdjointSetSteps(TS ts,PetscInt steps)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidLogicalCollectiveInt(ts,steps,2);
  if (steps < 0) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Cannot step back a negative number of steps");
  if (steps > ts->steps) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Cannot step back more than the total number of forward steps");
  ts->adjoint_max_steps = steps;
  PetscFunctionReturn(0);
}

/*@
   TSSetCostGradients - Sets the initial value of the gradients of the cost function w.r.t. initial values and w.r.t. the problem parameters
      for use by the TSAdjoint routines.

   Logically Collective on TS and Vec

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
.  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
-  mu - gradients with respect to the parameters, the number of entries in these vectors is the same as the number of parameters

   Level: beginner

   Notes: the entries in these vectors must be correctly initialized with the values lamda_i = df/dy|finaltime  mu_i = df/dp|finaltime

.keywords: TS, timestep, set, sensitivity, initial values
@*/
PetscErrorCode  TSSetCostGradients(TS ts,PetscInt numcost,Vec *lambda,Vec *mu)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(lambda,2);
  ts->vecs_sensi  = lambda;
  ts->vecs_sensip = mu;
  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");
  ts->numcost  = numcost;
  PetscFunctionReturn(0);
}

/*@C
  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.

  Logically Collective on TS

  Input Parameters:
+ ts   - The TS context obtained from TSCreate()
- func - The function

  Calling sequence of func:
$ func (TS ts,PetscReal t,Vec y,Mat A,void *ctx);
+   t - current timestep
.   y - input vector (current ODE solution)
.   A - output matrix
-   ctx - [optional] user-defined function context

  Level: intermediate

  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

.keywords: TS, sensitivity
.seealso:
@*/
PetscErrorCode  TSAdjointSetRHSJacobian(TS ts,Mat Amat,PetscErrorCode (*func)(TS,PetscReal,Vec,Mat,void*),void *ctx)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  PetscValidHeaderSpecific(Amat,MAT_CLASSID,2);

  ts->rhsjacobianp    = func;
  ts->rhsjacobianpctx = ctx;
  if(Amat) {
    ierr = PetscObjectReference((PetscObject)Amat);CHKERRQ(ierr);
    ierr = MatDestroy(&ts->Jacp);CHKERRQ(ierr);
    ts->Jacp = Amat;
  }
  PetscFunctionReturn(0);
}

/*@C
  TSAdjointComputeRHSJacobian - Runs the user-defined Jacobian function.

  Collective on TS

  Input Parameters:
. ts   - The TS context obtained from TSCreate()

  Level: developer

.keywords: TS, sensitivity
.seealso: TSAdjointSetRHSJacobian()
@*/
PetscErrorCode  TSAdjointComputeRHSJacobian(TS ts,PetscReal t,Vec X,Mat Amat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(X,VEC_CLASSID,3);
  PetscValidPointer(Amat,4);

  PetscStackPush("TS user JacobianP function for sensitivity analysis");
  ierr = (*ts->rhsjacobianp)(ts,t,X,Amat,ts->rhsjacobianpctx); CHKERRQ(ierr);
  PetscStackPop;
  PetscFunctionReturn(0);
}

/*@C
    TSSetCostIntegrand - Sets the routine for evaluating the integral term in one or more cost functions

    Logically Collective on TS

    Input Parameters:
+   ts - the TS context obtained from TSCreate()
.   numcost - number of gradients to be computed, this is the number of cost functions
.   costintegral - vector that stores the integral values
.   rf - routine for evaluating the integrand function
.   drdyf - function that computes the gradients of the r's with respect to y,NULL if not a function y
.   drdpf - function that computes the gradients of the r's with respect to p, NULL if not a function of p
.   fwd - flag indicating whether to evaluate cost integral in the forward run or the adjoint run
-   ctx - [optional] user-defined context for private data for the function evaluation routine (may be NULL)

    Calling sequence of rf:
$   PetscErrorCode rf(TS ts,PetscReal t,Vec y,Vec f,void *ctx);

    Calling sequence of drdyf:
$   PetscErroCode drdyf(TS ts,PetscReal t,Vec y,Vec *drdy,void *ctx);

    Calling sequence of drdpf:
$   PetscErroCode drdpf(TS ts,PetscReal t,Vec y,Vec *drdp,void *ctx);

    Level: intermediate

    Notes: For optimization there is usually a single cost function (numcost = 1). For sensitivities there may be multiple cost functions

.keywords: TS, sensitivity analysis, timestep, set, quadrature, function

.seealso: TSAdjointSetRHSJacobian(),TSGetCostGradients(), TSSetCostGradients()
@*/
PetscErrorCode  TSSetCostIntegrand(TS ts,PetscInt numcost,Vec costintegral,PetscErrorCode (*rf)(TS,PetscReal,Vec,Vec,void*),
                                                          PetscErrorCode (*drdyf)(TS,PetscReal,Vec,Vec*,void*),
                                                          PetscErrorCode (*drdpf)(TS,PetscReal,Vec,Vec*,void*),
                                                          PetscBool fwd,void *ctx)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (costintegral) PetscValidHeaderSpecific(costintegral,VEC_CLASSID,3);
  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() or TSForwardSetIntegralGradients()");
  if (!ts->numcost) ts->numcost=numcost;

  if (costintegral) {
    ierr = PetscObjectReference((PetscObject)costintegral);CHKERRQ(ierr);
    ierr = VecDestroy(&ts->vec_costintegral);CHKERRQ(ierr);
    ts->vec_costintegral = costintegral;
  } else {
    if (!ts->vec_costintegral) { /* Create a seq vec if user does not provide one */
      ierr = VecCreateSeq(PETSC_COMM_SELF,numcost,&ts->vec_costintegral);CHKERRQ(ierr);
    } else {
      ierr = VecSet(ts->vec_costintegral,0.0);CHKERRQ(ierr);
    }
  }
  if (!ts->vec_costintegrand) {
    ierr = VecDuplicate(ts->vec_costintegral,&ts->vec_costintegrand);CHKERRQ(ierr);
  } else {
    ierr = VecSet(ts->vec_costintegrand,0.0);CHKERRQ(ierr);
  }
  ts->costintegralfwd  = fwd; /* Evaluate the cost integral in forward run if fwd is true */
  ts->costintegrand    = rf;
  ts->costintegrandctx = ctx;
  ts->drdyfunction     = drdyf;
  ts->drdpfunction     = drdpf;
  PetscFunctionReturn(0);
}

/*@
   TSGetCostIntegral - Returns the values of the integral term in the cost functions.
   It is valid to call the routine after a backward run.

   Not Collective

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
.  v - the vector containing the integrals for each cost function

   Level: intermediate

.seealso: TSSetCostIntegrand()

.keywords: TS, sensitivity analysis
@*/
PetscErrorCode  TSGetCostIntegral(TS ts,Vec *v)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(v,2);
  *v = ts->vec_costintegral;
  PetscFunctionReturn(0);
}

/*@
   TSComputeCostIntegrand - Evaluates the integral function in the cost functions.

   Input Parameters:
+  ts - the TS context
.  t - current time
-  y - state vector, i.e. current solution

   Output Parameter:
.  q - vector of size numcost to hold the outputs

   Note:
   Most users should not need to explicitly call this routine, as it
   is used internally within the sensitivity analysis context.

   Level: developer

.keywords: TS, compute

.seealso: TSSetCostIntegrand()
@*/
PetscErrorCode TSComputeCostIntegrand(TS ts,PetscReal t,Vec y,Vec q)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);
  PetscValidHeaderSpecific(q,VEC_CLASSID,4);

  ierr = PetscLogEventBegin(TS_FunctionEval,ts,y,q,0);CHKERRQ(ierr);
  if (ts->costintegrand) {
    PetscStackPush("TS user integrand in the cost function");
    ierr = (*ts->costintegrand)(ts,t,y,q,ts->costintegrandctx);CHKERRQ(ierr);
    PetscStackPop;
  } else {
    ierr = VecZeroEntries(q);CHKERRQ(ierr);
  }

  ierr = PetscLogEventEnd(TS_FunctionEval,ts,y,q,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  TSAdjointComputeDRDYFunction - Runs the user-defined DRDY function.

  Collective on TS

  Input Parameters:
. ts   - The TS context obtained from TSCreate()

  Notes:
  TSAdjointComputeDRDYFunction() is typically used for sensitivity implementation,
  so most users would not generally call this routine themselves.

  Level: developer

.keywords: TS, sensitivity
.seealso: TSAdjointComputeDRDYFunction()
@*/
PetscErrorCode  TSAdjointComputeDRDYFunction(TS ts,PetscReal t,Vec y,Vec *drdy)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);

  PetscStackPush("TS user DRDY function for sensitivity analysis");
  ierr = (*ts->drdyfunction)(ts,t,y,drdy,ts->costintegrandctx); CHKERRQ(ierr);
  PetscStackPop;
  PetscFunctionReturn(0);
}

/*@
  TSAdjointComputeDRDPFunction - Runs the user-defined DRDP function.

  Collective on TS

  Input Parameters:
. ts   - The TS context obtained from TSCreate()

  Notes:
  TSDRDPFunction() is typically used for sensitivity implementation,
  so most users would not generally call this routine themselves.

  Level: developer

.keywords: TS, sensitivity
.seealso: TSAdjointSetDRDPFunction()
@*/
PetscErrorCode  TSAdjointComputeDRDPFunction(TS ts,PetscReal t,Vec y,Vec *drdp)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);

  PetscStackPush("TS user DRDP function for sensitivity analysis");
  ierr = (*ts->drdpfunction)(ts,t,y,drdp,ts->costintegrandctx); CHKERRQ(ierr);
  PetscStackPop;
  PetscFunctionReturn(0);
}

/*@C
  TSSetPreStep - Sets the general-purpose function
  called once at the beginning of each time step.

  Logically Collective on TS

  Input Parameters:
+ ts   - The TS context obtained from TSCreate()
- func - The function

  Calling sequence of func:
. func (TS ts);

  Level: intermediate

.keywords: TS, timestep
.seealso: TSSetPreStage(), TSSetPostStage(), TSSetPostStep(), TSStep()
@*/
PetscErrorCode  TSSetPreStep(TS ts, PetscErrorCode (*func)(TS))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  ts->prestep = func;
  PetscFunctionReturn(0);
}

/*@
  TSPreStep - Runs the user-defined pre-step function.

  Collective on TS

  Input Parameters:
. ts   - The TS context obtained from TSCreate()

  Notes:
  TSPreStep() is typically used within time stepping implementations,
  so most users would not generally call this routine themselves.

  Level: developer

.keywords: TS, timestep
.seealso: TSSetPreStep(), TSPreStage(), TSPostStage(), TSPostStep()
@*/
PetscErrorCode  TSPreStep(TS ts)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (ts->prestep) {
    Vec              U;
    PetscObjectState sprev,spost;

    ierr = TSGetSolution(ts,&U);CHKERRQ(ierr);
    ierr = PetscObjectStateGet((PetscObject)U,&sprev);CHKERRQ(ierr);
    PetscStackCallStandard((*ts->prestep),(ts));
    ierr = PetscObjectStateGet((PetscObject)U,&spost);CHKERRQ(ierr);
    if (sprev != spost) ts->steprestart = PETSC_TRUE;
  }
  PetscFunctionReturn(0);
}

/*@C
  TSSetPreStage - Sets the general-purpose function
  called once at the beginning of each stage.

  Logically Collective on TS

  Input Parameters:
+ ts   - The TS context obtained from TSCreate()
- func - The function

  Calling sequence of func:
. PetscErrorCode func(TS ts, PetscReal stagetime);

  Level: intermediate

  Note:
  There may be several stages per time step. If the solve for a given stage fails, the step may be rejected and retried.
  The time step number being computed can be queried using TSGetStepNumber() and the total size of the step being
  attempted can be obtained using TSGetTimeStep(). The time at the start of the step is available via TSGetTime().

.keywords: TS, timestep
.seealso: TSSetPostStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
@*/
PetscErrorCode  TSSetPreStage(TS ts, PetscErrorCode (*func)(TS,PetscReal))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  ts->prestage = func;
  PetscFunctionReturn(0);
}

/*@C
  TSSetPostStage - Sets the general-purpose function
  called once at the end of each stage.

  Logically Collective on TS

  Input Parameters:
+ ts   - The TS context obtained from TSCreate()
- func - The function

  Calling sequence of func:
. PetscErrorCode func(TS ts, PetscReal stagetime, PetscInt stageindex, Vec* Y);

  Level: intermediate

  Note:
  There may be several stages per time step. If the solve for a given stage fails, the step may be rejected and retried.
  The time step number being computed can be queried using TSGetStepNumber() and the total size of the step being
  attempted can be obtained using TSGetTimeStep(). The time at the start of the step is available via TSGetTime().

.keywords: TS, timestep
.seealso: TSSetPreStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
@*/
PetscErrorCode  TSSetPostStage(TS ts, PetscErrorCode (*func)(TS,PetscReal,PetscInt,Vec*))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  ts->poststage = func;
  PetscFunctionReturn(0);
}

/*@C
  TSSetPostEvaluate - Sets the general-purpose function
  called once at the end of each step evaluation.

  Logically Collective on TS

  Input Parameters:
+ ts   - The TS context obtained from TSCreate()
- func - The function

  Calling sequence of func:
. PetscErrorCode func(TS ts);

  Level: intermediate

  Note:
  Semantically, TSSetPostEvaluate() differs from TSSetPostStep() since the function it sets is called before event-handling
  thus guaranteeing the same solution (computed by the time-stepper) will be passed to it. On the other hand, TSPostStep()
  may be passed a different solution, possibly changed by the event handler. TSPostEvaluate() is called after the next step
  solution is evaluated allowing to modify it, if need be. The solution can be obtained with TSGetSolution(), the time step
  with TSGetTimeStep(), and the time at the start of the step is available via TSGetTime()

.keywords: TS, timestep
.seealso: TSSetPreStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
@*/
PetscErrorCode  TSSetPostEvaluate(TS ts, PetscErrorCode (*func)(TS))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  ts->postevaluate = func;
  PetscFunctionReturn(0);
}

/*@
  TSPreStage - Runs the user-defined pre-stage function set using TSSetPreStage()

  Collective on TS

  Input Parameters:
. ts          - The TS context obtained from TSCreate()
  stagetime   - The absolute time of the current stage

  Notes:
  TSPreStage() is typically used within time stepping implementations,
  most users would not generally call this routine themselves.

  Level: developer

.keywords: TS, timestep
.seealso: TSPostStage(), TSSetPreStep(), TSPreStep(), TSPostStep()
@*/
PetscErrorCode  TSPreStage(TS ts, PetscReal stagetime)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (ts->prestage) {
    PetscStackCallStandard((*ts->prestage),(ts,stagetime));
  }
  PetscFunctionReturn(0);
}

/*@
  TSPostStage - Runs the user-defined post-stage function set using TSSetPostStage()

  Collective on TS

  Input Parameters:
. ts          - The TS context obtained from TSCreate()
  stagetime   - The absolute time of the current stage
  stageindex  - Stage number
  Y           - Array of vectors (of size = total number
                of stages) with the stage solutions

  Notes:
  TSPostStage() is typically used within time stepping implementations,
  most users would not generally call this routine themselves.

  Level: developer

.keywords: TS, timestep
.seealso: TSPreStage(), TSSetPreStep(), TSPreStep(), TSPostStep()
@*/
PetscErrorCode  TSPostStage(TS ts, PetscReal stagetime, PetscInt stageindex, Vec *Y)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (ts->poststage) {
    PetscStackCallStandard((*ts->poststage),(ts,stagetime,stageindex,Y));
  }
  PetscFunctionReturn(0);
}

/*@
  TSPostEvaluate - Runs the user-defined post-evaluate function set using TSSetPostEvaluate()

  Collective on TS

  Input Parameters:
. ts          - The TS context obtained from TSCreate()

  Notes:
  TSPostEvaluate() is typically used within time stepping implementations,
  most users would not generally call this routine themselves.

  Level: developer

.keywords: TS, timestep
.seealso: TSSetPostEvaluate(), TSSetPreStep(), TSPreStep(), TSPostStep()
@*/
PetscErrorCode  TSPostEvaluate(TS ts)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (ts->postevaluate) {
    PetscStackCallStandard((*ts->postevaluate),(ts));
  }
  PetscFunctionReturn(0);
}

/*@C
  TSSetPostStep - Sets the general-purpose function
  called once at the end of each time step.

  Logically Collective on TS

  Input Parameters:
+ ts   - The TS context obtained from TSCreate()
- func - The function

  Calling sequence of func:
$ func (TS ts);

  Notes:
  The function set by TSSetPostStep() is called after each successful step. The solution vector X
  obtained by TSGetSolution() may be different than that computed at the step end if the event handler
  locates an event and TSPostEvent() modifies it. Use TSSetPostEvaluate() if an unmodified solution is needed instead.

  Level: intermediate

.keywords: TS, timestep
.seealso: TSSetPreStep(), TSSetPreStage(), TSSetPostEvaluate(), TSGetTimeStep(), TSGetStepNumber(), TSGetTime()
@*/
PetscErrorCode  TSSetPostStep(TS ts, PetscErrorCode (*func)(TS))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  ts->poststep = func;
  PetscFunctionReturn(0);
}

/*@
  TSPostStep - Runs the user-defined post-step function.

  Collective on TS

  Input Parameters:
. ts   - The TS context obtained from TSCreate()

  Notes:
  TSPostStep() is typically used within time stepping implementations,
  so most users would not generally call this routine themselves.

  Level: developer

.keywords: TS, timestep
@*/
PetscErrorCode  TSPostStep(TS ts)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (ts->poststep) {
    Vec              U;
    PetscObjectState sprev,spost;

    ierr = TSGetSolution(ts,&U);CHKERRQ(ierr);
    ierr = PetscObjectStateGet((PetscObject)U,&sprev);CHKERRQ(ierr);
    PetscStackCallStandard((*ts->poststep),(ts));
    ierr = PetscObjectStateGet((PetscObject)U,&spost);CHKERRQ(ierr);
    if (sprev != spost) ts->steprestart = PETSC_TRUE;
  }
  PetscFunctionReturn(0);
}

/* ------------ Routines to set performance monitoring options ----------- */

/*@C
   TSMonitorSet - Sets an ADDITIONAL function that is to be used at every
   timestep to display the iteration's  progress.

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
.  monitor - monitoring routine
.  mctx - [optional] user-defined context for private data for the
             monitor routine (use NULL if no context is desired)
-  monitordestroy - [optional] routine that frees monitor context
          (may be NULL)

   Calling sequence of monitor:
$    int monitor(TS ts,PetscInt steps,PetscReal time,Vec u,void *mctx)

+    ts - the TS context
.    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)
.    time - current time
.    u - current iterate
-    mctx - [optional] monitoring context

   Notes:
   This routine adds an additional monitor to the list of monitors that
   already has been loaded.

   Fortran notes: Only a single monitor function can be set for each TS object

   Level: intermediate

.keywords: TS, timestep, set, monitor

.seealso: TSMonitorDefault(), TSMonitorCancel()
@*/
PetscErrorCode  TSMonitorSet(TS ts,PetscErrorCode (*monitor)(TS,PetscInt,PetscReal,Vec,void*),void *mctx,PetscErrorCode (*mdestroy)(void**))
{
  PetscErrorCode ierr;
  PetscInt       i;
  PetscBool      identical;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  for (i=0; i<ts->numbermonitors;i++) {
    ierr = PetscMonitorCompare((PetscErrorCode (*)(void))monitor,mctx,mdestroy,(PetscErrorCode (*)(void))ts->monitor[i],ts->monitorcontext[i],ts->monitordestroy[i],&identical);CHKERRQ(ierr);
    if (identical) PetscFunctionReturn(0);
  }
  if (ts->numbermonitors >= MAXTSMONITORS) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many monitors set");
  ts->monitor[ts->numbermonitors]          = monitor;
  ts->monitordestroy[ts->numbermonitors]   = mdestroy;
  ts->monitorcontext[ts->numbermonitors++] = (void*)mctx;
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorCancel - Clears all the monitors that have been set on a time-step object.

   Logically Collective on TS

   Input Parameters:
.  ts - the TS context obtained from TSCreate()

   Notes:
   There is no way to remove a single, specific monitor.

   Level: intermediate

.keywords: TS, timestep, set, monitor

.seealso: TSMonitorDefault(), TSMonitorSet()
@*/
PetscErrorCode  TSMonitorCancel(TS ts)
{
  PetscErrorCode ierr;
  PetscInt       i;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  for (i=0; i<ts->numbermonitors; i++) {
    if (ts->monitordestroy[i]) {
      ierr = (*ts->monitordestroy[i])(&ts->monitorcontext[i]);CHKERRQ(ierr);
    }
  }
  ts->numbermonitors = 0;
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorDefault - The Default monitor, prints the timestep and time for each step

   Level: intermediate

.keywords: TS, set, monitor

.seealso:  TSMonitorSet()
@*/
PetscErrorCode TSMonitorDefault(TS ts,PetscInt step,PetscReal ptime,Vec v,PetscViewerAndFormat *vf)
{
  PetscErrorCode ierr;
  PetscViewer    viewer =  vf->viewer;
  PetscBool      iascii,ibinary;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&ibinary);CHKERRQ(ierr);
  ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
  if (iascii) {
    ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
    if (step == -1){ /* this indicates it is an interpolated solution */
      ierr = PetscViewerASCIIPrintf(viewer,"Interpolated solution at time %g between steps %D and %D\n",(double)ptime,ts->steps-1,ts->steps);CHKERRQ(ierr);
    } else {
      ierr = PetscViewerASCIIPrintf(viewer,"%D TS dt %g time %g%s",step,(double)ts->time_step,(double)ptime,ts->steprollback ? " (r)\n" : "\n");CHKERRQ(ierr);
    }
    ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
  } else if (ibinary) {
    PetscMPIInt rank;
    ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)viewer),&rank);CHKERRQ(ierr);
    if (!rank) {
      PetscBool skipHeader;
      PetscInt  classid = REAL_FILE_CLASSID;

      ierr = PetscViewerBinaryGetSkipHeader(viewer,&skipHeader);CHKERRQ(ierr);
      if (!skipHeader) {
         ierr = PetscViewerBinaryWrite(viewer,&classid,1,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
       }
      ierr = PetscRealView(1,&ptime,viewer);CHKERRQ(ierr);
    } else {
      ierr = PetscRealView(0,&ptime,viewer);CHKERRQ(ierr);
    }
  }
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSAdjointMonitorSet - Sets an ADDITIONAL function that is to be used at every
   timestep to display the iteration's  progress.

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
.  adjointmonitor - monitoring routine
.  adjointmctx - [optional] user-defined context for private data for the
             monitor routine (use NULL if no context is desired)
-  adjointmonitordestroy - [optional] routine that frees monitor context
          (may be NULL)

   Calling sequence of monitor:
$    int adjointmonitor(TS ts,PetscInt steps,PetscReal time,Vec u,PetscInt numcost,Vec *lambda, Vec *mu,void *adjointmctx)

+    ts - the TS context
.    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
                               been interpolated to)
.    time - current time
.    u - current iterate
.    numcost - number of cost functionos
.    lambda - sensitivities to initial conditions
.    mu - sensitivities to parameters
-    adjointmctx - [optional] adjoint monitoring context

   Notes:
   This routine adds an additional monitor to the list of monitors that
   already has been loaded.

   Fortran notes: Only a single monitor function can be set for each TS object

   Level: intermediate

.keywords: TS, timestep, set, adjoint, monitor

.seealso: TSAdjointMonitorCancel()
@*/
PetscErrorCode  TSAdjointMonitorSet(TS ts,PetscErrorCode (*adjointmonitor)(TS,PetscInt,PetscReal,Vec,PetscInt,Vec*,Vec*,void*),void *adjointmctx,PetscErrorCode (*adjointmdestroy)(void**))
{
  PetscErrorCode ierr;
  PetscInt       i;
  PetscBool      identical;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  for (i=0; i<ts->numbermonitors;i++) {
    ierr = PetscMonitorCompare((PetscErrorCode (*)(void))adjointmonitor,adjointmctx,adjointmdestroy,(PetscErrorCode (*)(void))ts->adjointmonitor[i],ts->adjointmonitorcontext[i],ts->adjointmonitordestroy[i],&identical);CHKERRQ(ierr);
    if (identical) PetscFunctionReturn(0);
  }
  if (ts->numberadjointmonitors >= MAXTSMONITORS) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many adjoint monitors set");
  ts->adjointmonitor[ts->numberadjointmonitors]          = adjointmonitor;
  ts->adjointmonitordestroy[ts->numberadjointmonitors]   = adjointmdestroy;
  ts->adjointmonitorcontext[ts->numberadjointmonitors++] = (void*)adjointmctx;
  PetscFunctionReturn(0);
}

/*@C
   TSAdjointMonitorCancel - Clears all the adjoint monitors that have been set on a time-step object.

   Logically Collective on TS

   Input Parameters:
.  ts - the TS context obtained from TSCreate()

   Notes:
   There is no way to remove a single, specific monitor.

   Level: intermediate

.keywords: TS, timestep, set, adjoint, monitor

.seealso: TSAdjointMonitorSet()
@*/
PetscErrorCode  TSAdjointMonitorCancel(TS ts)
{
  PetscErrorCode ierr;
  PetscInt       i;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  for (i=0; i<ts->numberadjointmonitors; i++) {
    if (ts->adjointmonitordestroy[i]) {
      ierr = (*ts->adjointmonitordestroy[i])(&ts->adjointmonitorcontext[i]);CHKERRQ(ierr);
    }
  }
  ts->numberadjointmonitors = 0;
  PetscFunctionReturn(0);
}

/*@C
   TSAdjointMonitorDefault - the default monitor of adjoint computations

   Level: intermediate

.keywords: TS, set, monitor

.seealso: TSAdjointMonitorSet()
@*/
PetscErrorCode TSAdjointMonitorDefault(TS ts,PetscInt step,PetscReal ptime,Vec v,PetscInt numcost,Vec *lambda,Vec *mu,PetscViewerAndFormat *vf)
{
  PetscErrorCode ierr;
  PetscViewer    viewer = vf->viewer;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
  ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
  ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"%D TS dt %g time %g%s",step,(double)ts->time_step,(double)ptime,ts->steprollback ? " (r)\n" : "\n");CHKERRQ(ierr);
  ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)ts)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSInterpolate - Interpolate the solution computed during the previous step to an arbitrary location in the interval

   Collective on TS

   Input Argument:
+  ts - time stepping context
-  t - time to interpolate to

   Output Argument:
.  U - state at given time

   Level: intermediate

   Developer Notes:
   TSInterpolate() and the storing of previous steps/stages should be generalized to support delay differential equations and continuous adjoints.

.keywords: TS, set

.seealso: TSSetExactFinalTime(), TSSolve()
@*/
PetscErrorCode TSInterpolate(TS ts,PetscReal t,Vec U)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  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);
  if (!ts->ops->interpolate) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"%s does not provide interpolation",((PetscObject)ts)->type_name);
  ierr = (*ts->ops->interpolate)(ts,t,U);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSStep - Steps one time step

   Collective on TS

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Level: developer

   Notes:
   The public interface for the ODE/DAE solvers is TSSolve(), you should almost for sure be using that routine and not this routine.

   The hook set using TSSetPreStep() is called before each attempt to take the step. In general, the time step size may
   be changed due to adaptive error controller or solve failures. Note that steps may contain multiple stages.

   This may over-step the final time provided in TSSetMaxTime() depending on the time-step used. TSSolve() interpolates to exactly the
   time provided in TSSetMaxTime(). One can use TSInterpolate() to determine an interpolated solution within the final timestep.

.keywords: TS, timestep, solve

.seealso: TSCreate(), TSSetUp(), TSDestroy(), TSSolve(), TSSetPreStep(), TSSetPreStage(), TSSetPostStage(), TSInterpolate()
@*/
PetscErrorCode  TSStep(TS ts)
{
  PetscErrorCode   ierr;
  static PetscBool cite = PETSC_FALSE;
  PetscReal        ptime;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = PetscCitationsRegister("@techreport{tspaper,\n"
                                "  title       = {{PETSc/TS}: A Modern Scalable {DAE/ODE} Solver Library},\n"
                                "  author      = {Shrirang Abhyankar and Jed Brown and Emil Constantinescu and Debojyoti Ghosh and Barry F. Smith},\n"
                                "  type        = {Preprint},\n"
                                "  number      = {ANL/MCS-P5061-0114},\n"
                                "  institution = {Argonne National Laboratory},\n"
                                "  year        = {2014}\n}\n",&cite);CHKERRQ(ierr);

  ierr = TSSetUp(ts);CHKERRQ(ierr);
  ierr = TSTrajectorySetUp(ts->trajectory,ts);CHKERRQ(ierr);

  if (ts->max_time >= PETSC_MAX_REAL && ts->max_steps == PETSC_MAX_INT) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"You must call TSSetMaxTime() or TSSetMaxSteps(), or use -ts_max_time <time> or -ts_max_steps <steps>");
  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()");
  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");

  if (!ts->steps) ts->ptime_prev = ts->ptime;
  ptime = ts->ptime; ts->ptime_prev_rollback = ts->ptime_prev;
  ts->reason = TS_CONVERGED_ITERATING;
  if (!ts->ops->step) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSStep not implemented for type '%s'",((PetscObject)ts)->type_name);
  ierr = PetscLogEventBegin(TS_Step,ts,0,0,0);CHKERRQ(ierr);
  ierr = (*ts->ops->step)(ts);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(TS_Step,ts,0,0,0);CHKERRQ(ierr);
  ts->ptime_prev = ptime;
  ts->steps++;
  ts->steprollback = PETSC_FALSE;
  ts->steprestart  = PETSC_FALSE;

  if (ts->reason < 0) {
    if (ts->errorifstepfailed) {
      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]);
      else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s",TSConvergedReasons[ts->reason]);
    }
  } else if (!ts->reason) {
    if (ts->steps >= ts->max_steps) ts->reason = TS_CONVERGED_ITS;
    else if (ts->ptime >= ts->max_time) ts->reason = TS_CONVERGED_TIME;
  }
  PetscFunctionReturn(0);
}

/*@
   TSAdjointStep - Steps one time step backward in the adjoint run

   Collective on TS

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Level: intermediate

.keywords: TS, adjoint, step

.seealso: TSAdjointSetUp(), TSAdjointSolve()
@*/
PetscErrorCode  TSAdjointStep(TS ts)
{
  DM               dm;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = TSAdjointSetUp(ts);CHKERRQ(ierr);

  ierr = VecViewFromOptions(ts->vec_sol,(PetscObject)ts,"-ts_view_solution");CHKERRQ(ierr);

  ts->reason = TS_CONVERGED_ITERATING;
  ts->ptime_prev = ts->ptime;
  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);
  ierr = PetscLogEventBegin(TS_AdjointStep,ts,0,0,0);CHKERRQ(ierr);
  ierr = (*ts->ops->adjointstep)(ts);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(TS_AdjointStep,ts,0,0,0);CHKERRQ(ierr);
  ts->adjoint_steps++; ts->steps--;

  if (ts->reason < 0) {
    if (ts->errorifstepfailed) {
      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]);
      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]);
      else SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_NOT_CONVERGED,"TSStep has failed due to %s",TSConvergedReasons[ts->reason]);
    }
  } else if (!ts->reason) {
    if (ts->adjoint_steps >= ts->adjoint_max_steps) ts->reason = TS_CONVERGED_ITS;
  }
  PetscFunctionReturn(0);
}

/*@
   TSEvaluateWLTE - Evaluate the weighted local truncation error norm
   at the end of a time step with a given order of accuracy.

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  wnormtype - norm type, either NORM_2 or NORM_INFINITY
-  order - optional, desired order for the error evaluation or PETSC_DECIDE

   Output Arguments:
+  order - optional, the actual order of the error evaluation
-  wlte - the weighted local truncation error norm

   Level: advanced

   Notes:
   If the timestepper cannot evaluate the error in a particular step
   (eg. in the first step or restart steps after event handling),
   this routine returns wlte=-1.0 .

.seealso: TSStep(), TSAdapt, TSErrorWeightedNorm()
@*/
PetscErrorCode TSEvaluateWLTE(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidType(ts,1);
  PetscValidLogicalCollectiveEnum(ts,wnormtype,4);
  if (order) PetscValidIntPointer(order,3);
  if (order) PetscValidLogicalCollectiveInt(ts,*order,3);
  PetscValidRealPointer(wlte,4);
  if (wnormtype != NORM_2 && wnormtype != NORM_INFINITY) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
  if (!ts->ops->evaluatewlte) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSEvaluateWLTE not implemented for type '%s'",((PetscObject)ts)->type_name);
  ierr = (*ts->ops->evaluatewlte)(ts,wnormtype,order,wlte);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSEvaluateStep - Evaluate the solution at the end of a time step with a given order of accuracy.

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  order - desired order of accuracy
-  done - whether the step was evaluated at this order (pass NULL to generate an error if not available)

   Output Arguments:
.  U - state at the end of the current step

   Level: advanced

   Notes:
   This function cannot be called until all stages have been evaluated.
   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.

.seealso: TSStep(), TSAdapt
@*/
PetscErrorCode TSEvaluateStep(TS ts,PetscInt order,Vec U,PetscBool *done)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidType(ts,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  if (!ts->ops->evaluatestep) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSEvaluateStep not implemented for type '%s'",((PetscObject)ts)->type_name);
  ierr = (*ts->ops->evaluatestep)(ts,order,U,done);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSForwardCostIntegral - Evaluate the cost integral in the forward run.

   Collective on TS

   Input Arguments:
.  ts - time stepping context

   Level: advanced

   Notes:
   This function cannot be called until TSStep() has been completed.

.seealso: TSSolve(), TSAdjointCostIntegral()
@*/
PetscErrorCode TSForwardCostIntegral(TS ts)
{
  PetscErrorCode ierr;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  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);
  ierr = (*ts->ops->forwardintegral)(ts);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSSolve - Steps the requested number of timesteps.

   Collective on TS

   Input Parameter:
+  ts - the TS context obtained from TSCreate()
-  u - the solution vector  (can be null if TSSetSolution() was used and TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP) was not used,
                             otherwise must contain the initial conditions and will contain the solution at the final requested time

   Level: beginner

   Notes:
   The final time returned by this function may be different from the time of the internally
   held state accessible by TSGetSolution() and TSGetTime() because the method may have
   stepped over the final time.

.keywords: TS, timestep, solve

.seealso: TSCreate(), TSSetSolution(), TSStep(), TSGetTime(), TSGetSolveTime()
@*/
PetscErrorCode TSSolve(TS ts,Vec u)
{
  Vec               solution;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (u) PetscValidHeaderSpecific(u,VEC_CLASSID,2);

  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 */
    PetscValidHeaderSpecific(u,VEC_CLASSID,2);
    if (!ts->vec_sol || u == ts->vec_sol) {
      ierr = VecDuplicate(u,&solution);CHKERRQ(ierr);
      ierr = TSSetSolution(ts,solution);CHKERRQ(ierr);
      ierr = VecDestroy(&solution);CHKERRQ(ierr); /* grant ownership */
    }
    ierr = VecCopy(u,ts->vec_sol);CHKERRQ(ierr);
    if (ts->forward_solve) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Sensitivity analysis does not support the mode TS_EXACTFINALTIME_INTERPOLATE");
  } else if (u) {
    ierr = TSSetSolution(ts,u);CHKERRQ(ierr);
  }
  ierr = TSSetUp(ts);CHKERRQ(ierr);
  ierr = TSTrajectorySetUp(ts->trajectory,ts);CHKERRQ(ierr);

  if (ts->max_time >= PETSC_MAX_REAL && ts->max_steps == PETSC_MAX_INT) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"You must call TSSetMaxTime() or TSSetMaxSteps(), or use -ts_max_time <time> or -ts_max_steps <steps>");
  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()");
  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");

  if (ts->forward_solve) {
    ierr = TSForwardSetUp(ts);CHKERRQ(ierr);
  }

  /* reset number of steps only when the step is not restarted. ARKIMEX
     restarts the step after an event. Resetting these counters in such case causes
     TSTrajectory to incorrectly save the output files
  */
  /* reset time step and iteration counters */

  if (!ts->steps) {
    ts->ksp_its           = 0;
    ts->snes_its          = 0;
    ts->num_snes_failures = 0;
    ts->reject            = 0;
    ts->steprestart       = PETSC_TRUE;
    ts->steprollback      = PETSC_FALSE;
  }
  ts->reason = TS_CONVERGED_ITERATING;

  ierr = TSViewFromOptions(ts,NULL,"-ts_view_pre");CHKERRQ(ierr);

  if (ts->ops->solve) { /* This private interface is transitional and should be removed when all implementations are updated. */
    ierr = (*ts->ops->solve)(ts);CHKERRQ(ierr);
    if (u) {ierr = VecCopy(ts->vec_sol,u);CHKERRQ(ierr);}
    ts->solvetime = ts->ptime;
    solution = ts->vec_sol;
  } else { /* Step the requested number of timesteps. */
    if (ts->steps >= ts->max_steps) ts->reason = TS_CONVERGED_ITS;
    else if (ts->ptime >= ts->max_time) ts->reason = TS_CONVERGED_TIME;

    if (!ts->steps) {
      ierr = TSTrajectorySet(ts->trajectory,ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
      ierr = TSEventInitialize(ts->event,ts,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
    }

    while (!ts->reason) {
      ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
      if (!ts->steprollback) {
        ierr = TSPreStep(ts);CHKERRQ(ierr);
      }
      ierr = TSStep(ts);CHKERRQ(ierr);
      if (ts->vec_costintegral && ts->costintegralfwd) { /* Must evaluate the cost integral before event is handled. The cost integral value can also be rolled back. */
        ierr = TSForwardCostIntegral(ts);CHKERRQ(ierr);
      }
      if (!ts->steprollback && ts->forward_solve) { /* compute forward sensitivities before event handling because postevent() may change RHS and jump conditions may have to be applied */
        ierr = TSForwardStep(ts);CHKERRQ(ierr);
      }
      ierr = TSPostEvaluate(ts);CHKERRQ(ierr);
      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. */
      if (!ts->steprollback) {
        ierr = TSTrajectorySet(ts->trajectory,ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);
        ierr = TSPostStep(ts);CHKERRQ(ierr);
      }
    }
    ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr);

    if (ts->exact_final_time == TS_EXACTFINALTIME_INTERPOLATE && ts->ptime > ts->max_time) {
      ierr = TSInterpolate(ts,ts->max_time,u);CHKERRQ(ierr);
      ts->solvetime = ts->max_time;
      solution = u;
      ierr = TSMonitor(ts,-1,ts->solvetime,solution);CHKERRQ(ierr);
    } else {
      if (u) {ierr = VecCopy(ts->vec_sol,u);CHKERRQ(ierr);}
      ts->solvetime = ts->ptime;
      solution = ts->vec_sol;
    }
  }

  ierr = TSViewFromOptions(ts,NULL,"-ts_view");CHKERRQ(ierr);
  ierr = VecViewFromOptions(solution,NULL,"-ts_view_solution");CHKERRQ(ierr);
  ierr = PetscObjectSAWsBlock((PetscObject)ts);CHKERRQ(ierr);
  if (ts->adjoint_solve) {
    ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@
 TSAdjointCostIntegral - Evaluate the cost integral in the adjoint run.

 Collective on TS

 Input Arguments:
 .  ts - time stepping context

 Level: advanced

 Notes:
 This function cannot be called until TSAdjointStep() has been completed.

 .seealso: TSAdjointSolve(), TSAdjointStep
 @*/
PetscErrorCode TSAdjointCostIntegral(TS ts)
{
    PetscErrorCode ierr;
    PetscValidHeaderSpecific(ts,TS_CLASSID,1);
    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);
    ierr = (*ts->ops->adjointintegral)(ts);CHKERRQ(ierr);
    PetscFunctionReturn(0);
}

/*@
   TSAdjointSolve - Solves the discrete ajoint problem for an ODE/DAE

   Collective on TS

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Options Database:
. -ts_adjoint_view_solution <viewerinfo> - views the first gradient with respect to the initial values

   Level: intermediate

   Notes:
   This must be called after a call to TSSolve() that solves the forward problem

   By default this will integrate back to the initial time, one can use TSAdjointSetSteps() to step back to a later time

.keywords: TS, timestep, solve

.seealso: TSCreate(), TSSetCostGradients(), TSSetSolution(), TSAdjointStep()
@*/
PetscErrorCode TSAdjointSolve(TS ts)
{
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = TSAdjointSetUp(ts);CHKERRQ(ierr);

  /* reset time step and iteration counters */
  ts->adjoint_steps     = 0;
  ts->ksp_its           = 0;
  ts->snes_its          = 0;
  ts->num_snes_failures = 0;
  ts->reject            = 0;
  ts->reason            = TS_CONVERGED_ITERATING;

  if (!ts->adjoint_max_steps) ts->adjoint_max_steps = ts->steps;
  if (ts->adjoint_steps >= ts->adjoint_max_steps) ts->reason = TS_CONVERGED_ITS;

  while (!ts->reason) {
    ierr = TSTrajectoryGet(ts->trajectory,ts,ts->steps,&ts->ptime);CHKERRQ(ierr);
    ierr = TSAdjointMonitor(ts,ts->steps,ts->ptime,ts->vec_sol,ts->numcost,ts->vecs_sensi,ts->vecs_sensip);CHKERRQ(ierr);
    ierr = TSAdjointEventHandler(ts);CHKERRQ(ierr);
    ierr = TSAdjointStep(ts);CHKERRQ(ierr);
    if (ts->vec_costintegral && !ts->costintegralfwd) {
      ierr = TSAdjointCostIntegral(ts);CHKERRQ(ierr);
    }
  }
  ierr = TSTrajectoryGet(ts->trajectory,ts,ts->steps,&ts->ptime);CHKERRQ(ierr);
  ierr = TSAdjointMonitor(ts,ts->steps,ts->ptime,ts->vec_sol,ts->numcost,ts->vecs_sensi,ts->vecs_sensip);CHKERRQ(ierr);
  ts->solvetime = ts->ptime;
  ierr = TSTrajectoryViewFromOptions(ts->trajectory,NULL,"-ts_trajectory_view");CHKERRQ(ierr);
  ierr = VecViewFromOptions(ts->vecs_sensi[0],(PetscObject) ts, "-ts_adjoint_view_solution");CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSMonitor - Runs all user-provided monitor routines set using TSMonitorSet()

   Collective on TS

   Input Parameters:
+  ts - time stepping context obtained from TSCreate()
.  step - step number that has just completed
.  ptime - model time of the state
-  u - state at the current model time

   Notes:
   TSMonitor() is typically used automatically within the time stepping implementations.
   Users would almost never call this routine directly.

   A step of -1 indicates that the monitor is being called on a solution obtained by interpolating from computed solutions

   Level: developer

.keywords: TS, timestep
@*/
PetscErrorCode TSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec u)
{
  DM             dm;
  PetscInt       i,n = ts->numbermonitors;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(u,VEC_CLASSID,4);

  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMSetOutputSequenceNumber(dm,step,ptime);CHKERRQ(ierr);

  ierr = VecLockPush(u);CHKERRQ(ierr);
  for (i=0; i<n; i++) {
    ierr = (*ts->monitor[i])(ts,step,ptime,u,ts->monitorcontext[i]);CHKERRQ(ierr);
  }
  ierr = VecLockPop(u);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSAdjointMonitor - Runs all user-provided adjoint monitor routines set using TSAdjointMonitorSet()

   Collective on TS

   Input Parameters:
+  ts - time stepping context obtained from TSCreate()
.  step - step number that has just completed
.  ptime - model time of the state
.  u - state at the current model time
.  numcost - number of cost functions (dimension of lambda  or mu)
.  lambda - vectors containing the gradients of the cost functions with respect to the ODE/DAE solution variables
-  mu - vectors containing the gradients of the cost functions with respect to the problem parameters

   Notes:
   TSAdjointMonitor() is typically used automatically within the time stepping implementations.
   Users would almost never call this routine directly.

   Level: developer

.keywords: TS, timestep
@*/
PetscErrorCode TSAdjointMonitor(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscInt numcost,Vec *lambda, Vec *mu)
{
  PetscErrorCode ierr;
  PetscInt       i,n = ts->numberadjointmonitors;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(u,VEC_CLASSID,4);
  ierr = VecLockPush(u);CHKERRQ(ierr);
  for (i=0; i<n; i++) {
    ierr = (*ts->adjointmonitor[i])(ts,step,ptime,u,numcost,lambda,mu,ts->adjointmonitorcontext[i]);CHKERRQ(ierr);
  }
  ierr = VecLockPop(u);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------------*/
/*@C
   TSMonitorLGCtxCreate - Creates a TSMonitorLGCtx context for use with
   TS to monitor the solution process graphically in various ways

   Collective on TS

   Input Parameters:
+  host - the X display to open, or null for the local machine
.  label - the title to put in the title bar
.  x, y - the screen coordinates of the upper left coordinate of the window
.  m, n - the screen width and height in pixels
-  howoften - if positive then determines the frequency of the plotting, if -1 then only at the final time

   Output Parameter:
.  ctx - the context

   Options Database Key:
+  -ts_monitor_lg_timestep - automatically sets line graph monitor
+  -ts_monitor_lg_timestep_log - automatically sets line graph monitor
.  -ts_monitor_lg_solution - monitor the solution (or certain values of the solution by calling TSMonitorLGSetDisplayVariables() or TSMonitorLGCtxSetDisplayVariables())
.  -ts_monitor_lg_error -  monitor the error
.  -ts_monitor_lg_ksp_iterations - monitor the number of KSP iterations needed for each timestep
.  -ts_monitor_lg_snes_iterations - monitor the number of SNES iterations needed for each timestep
-  -lg_use_markers <true,false> - mark the data points (at each time step) on the plot; default is true

   Notes:
   Use TSMonitorLGCtxDestroy() to destroy.

   One can provide a function that transforms the solution before plotting it with TSMonitorLGCtxSetTransform() or TSMonitorLGSetTransform()

   Many of the functions that control the monitoring have two forms: TSMonitorLGSet/GetXXXX() and TSMonitorLGCtxSet/GetXXXX() the first take a TS object as the
   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
   as the first argument.

   One can control the names displayed for each solution or error variable with TSMonitorLGCtxSetVariableNames() or TSMonitorLGSetVariableNames()

   Level: intermediate

.keywords: TS, monitor, line graph, residual

.seealso: TSMonitorLGTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError(), TSMonitorDefault(), VecView(),
           TSMonitorLGCtxCreate(), TSMonitorLGCtxSetVariableNames(), TSMonitorLGCtxGetVariableNames(),
           TSMonitorLGSetVariableNames(), TSMonitorLGGetVariableNames(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetDisplayVariables(),
           TSMonitorLGCtxSetTransform(), TSMonitorLGSetTransform(), TSMonitorLGError(), TSMonitorLGSNESIterations(), TSMonitorLGKSPIterations(),
           TSMonitorEnvelopeCtxCreate(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxDestroy(), TSMonitorEnvelop()

@*/
PetscErrorCode  TSMonitorLGCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorLGCtx *ctx)
{
  PetscDraw      draw;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscNew(ctx);CHKERRQ(ierr);
  ierr = PetscDrawCreate(comm,host,label,x,y,m,n,&draw);CHKERRQ(ierr);
  ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
  ierr = PetscDrawLGCreate(draw,1,&(*ctx)->lg);CHKERRQ(ierr);
  ierr = PetscDrawLGSetFromOptions((*ctx)->lg);CHKERRQ(ierr);
  ierr = PetscDrawDestroy(&draw);CHKERRQ(ierr);
  (*ctx)->howoften = howoften;
  PetscFunctionReturn(0);
}

PetscErrorCode TSMonitorLGTimeStep(TS ts,PetscInt step,PetscReal ptime,Vec v,void *monctx)
{
  TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
  PetscReal      x   = ptime,y;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (step < 0) PetscFunctionReturn(0); /* -1 indicates an interpolated solution */
  if (!step) {
    PetscDrawAxis axis;
    const char *ylabel = ctx->semilogy ? "Log Time Step" : "Time Step";
    ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
    ierr = PetscDrawAxisSetLabels(axis,"Timestep as function of time","Time",ylabel);CHKERRQ(ierr);
    ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
  }
  ierr = TSGetTimeStep(ts,&y);CHKERRQ(ierr);
  if (ctx->semilogy) y = PetscLog10Real(y);
  ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
  if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
    ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
    ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorLGCtxDestroy - Destroys a line graph context that was created
   with TSMonitorLGCtxCreate().

   Collective on TSMonitorLGCtx

   Input Parameter:
.  ctx - the monitor context

   Level: intermediate

.keywords: TS, monitor, line graph, destroy

.seealso: TSMonitorLGCtxCreate(),  TSMonitorSet(), TSMonitorLGTimeStep();
@*/
PetscErrorCode  TSMonitorLGCtxDestroy(TSMonitorLGCtx *ctx)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if ((*ctx)->transformdestroy) {
    ierr = ((*ctx)->transformdestroy)((*ctx)->transformctx);CHKERRQ(ierr);
  }
  ierr = PetscDrawLGDestroy(&(*ctx)->lg);CHKERRQ(ierr);
  ierr = PetscStrArrayDestroy(&(*ctx)->names);CHKERRQ(ierr);
  ierr = PetscStrArrayDestroy(&(*ctx)->displaynames);CHKERRQ(ierr);
  ierr = PetscFree((*ctx)->displayvariables);CHKERRQ(ierr);
  ierr = PetscFree((*ctx)->displayvalues);CHKERRQ(ierr);
  ierr = PetscFree(*ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSGetTime - Gets the time of the most recently completed step.

   Not Collective

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
.  t  - the current time. This time may not corresponds to the final time set with TSSetMaxTime(), use TSGetSolveTime().

   Level: beginner

   Note:
   When called during time step evaluation (e.g. during residual evaluation or via hooks set using TSSetPreStep(),
   TSSetPreStage(), TSSetPostStage(), or TSSetPostStep()), the time is the time at the start of the step being evaluated.

.seealso:  TSGetSolveTime(), TSSetTime(), TSGetTimeStep()

.keywords: TS, get, time
@*/
PetscErrorCode  TSGetTime(TS ts,PetscReal *t)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidRealPointer(t,2);
  *t = ts->ptime;
  PetscFunctionReturn(0);
}

/*@
   TSGetPrevTime - Gets the starting time of the previously completed step.

   Not Collective

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Output Parameter:
.  t  - the previous time

   Level: beginner

.seealso: TSGetTime(), TSGetSolveTime(), TSGetTimeStep()

.keywords: TS, get, time
@*/
PetscErrorCode  TSGetPrevTime(TS ts,PetscReal *t)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidRealPointer(t,2);
  *t = ts->ptime_prev;
  PetscFunctionReturn(0);
}

/*@
   TSSetTime - Allows one to reset the time.

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context obtained from TSCreate()
-  time - the time

   Level: intermediate

.seealso: TSGetTime(), TSSetMaxSteps()

.keywords: TS, set, time
@*/
PetscErrorCode  TSSetTime(TS ts, PetscReal t)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidLogicalCollectiveReal(ts,t,2);
  ts->ptime = t;
  PetscFunctionReturn(0);
}

/*@C
   TSSetOptionsPrefix - Sets the prefix used for searching for all
   TS options in the database.

   Logically Collective on TS

   Input Parameter:
+  ts     - The TS context
-  prefix - The prefix to prepend to all option names

   Notes:
   A hyphen (-) must NOT be given at the beginning of the prefix name.
   The first character of all runtime options is AUTOMATICALLY the
   hyphen.

   Level: advanced

.keywords: TS, set, options, prefix, database

.seealso: TSSetFromOptions()

@*/
PetscErrorCode  TSSetOptionsPrefix(TS ts,const char prefix[])
{
  PetscErrorCode ierr;
  SNES           snes;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = PetscObjectSetOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESSetOptionsPrefix(snes,prefix);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSAppendOptionsPrefix - Appends to the prefix used for searching for all
   TS options in the database.

   Logically Collective on TS

   Input Parameter:
+  ts     - The TS context
-  prefix - The prefix to prepend to all option names

   Notes:
   A hyphen (-) must NOT be given at the beginning of the prefix name.
   The first character of all runtime options is AUTOMATICALLY the
   hyphen.

   Level: advanced

.keywords: TS, append, options, prefix, database

.seealso: TSGetOptionsPrefix()

@*/
PetscErrorCode  TSAppendOptionsPrefix(TS ts,const char prefix[])
{
  PetscErrorCode ierr;
  SNES           snes;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ierr = PetscObjectAppendOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESAppendOptionsPrefix(snes,prefix);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSGetOptionsPrefix - Sets the prefix used for searching for all
   TS options in the database.

   Not Collective

   Input Parameter:
.  ts - The TS context

   Output Parameter:
.  prefix - A pointer to the prefix string used

   Notes: On the fortran side, the user should pass in a string 'prifix' of
   sufficient length to hold the prefix.

   Level: intermediate

.keywords: TS, get, options, prefix, database

.seealso: TSAppendOptionsPrefix()
@*/
PetscErrorCode  TSGetOptionsPrefix(TS ts,const char *prefix[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(prefix,2);
  ierr = PetscObjectGetOptionsPrefix((PetscObject)ts,prefix);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSGetRHSJacobian - Returns the Jacobian J at the present timestep.

   Not Collective, but parallel objects are returned if TS is parallel

   Input Parameter:
.  ts  - The TS context obtained from TSCreate()

   Output Parameters:
+  Amat - The (approximate) Jacobian J of G, where U_t = G(U,t)  (or NULL)
.  Pmat - The matrix from which the preconditioner is constructed, usually the same as Amat  (or NULL)
.  func - Function to compute the Jacobian of the RHS  (or NULL)
-  ctx - User-defined context for Jacobian evaluation routine  (or NULL)

   Notes: You can pass in NULL for any return argument you do not need.

   Level: intermediate

.seealso: TSGetTimeStep(), TSGetMatrices(), TSGetTime(), TSGetStepNumber()

.keywords: TS, timestep, get, matrix, Jacobian
@*/
PetscErrorCode  TSGetRHSJacobian(TS ts,Mat *Amat,Mat *Pmat,TSRHSJacobian *func,void **ctx)
{
  PetscErrorCode ierr;
  DM             dm;

  PetscFunctionBegin;
  if (Amat || Pmat) {
    SNES snes;
    ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
    ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr);
    ierr = SNESGetJacobian(snes,Amat,Pmat,NULL,NULL);CHKERRQ(ierr);
  }
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetRHSJacobian(dm,func,ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSGetIJacobian - Returns the implicit Jacobian at the present timestep.

   Not Collective, but parallel objects are returned if TS is parallel

   Input Parameter:
.  ts  - The TS context obtained from TSCreate()

   Output Parameters:
+  Amat  - The (approximate) Jacobian of F(t,U,U_t)
.  Pmat - The matrix from which the preconditioner is constructed, often the same as Amat
.  f   - The function to compute the matrices
- ctx - User-defined context for Jacobian evaluation routine

   Notes: You can pass in NULL for any return argument you do not need.

   Level: advanced

.seealso: TSGetTimeStep(), TSGetRHSJacobian(), TSGetMatrices(), TSGetTime(), TSGetStepNumber()

.keywords: TS, timestep, get, matrix, Jacobian
@*/
PetscErrorCode  TSGetIJacobian(TS ts,Mat *Amat,Mat *Pmat,TSIJacobian *f,void **ctx)
{
  PetscErrorCode ierr;
  DM             dm;

  PetscFunctionBegin;
  if (Amat || Pmat) {
    SNES snes;
    ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
    ierr = SNESSetUpMatrices(snes);CHKERRQ(ierr);
    ierr = SNESGetJacobian(snes,Amat,Pmat,NULL,NULL);CHKERRQ(ierr);
  }
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetIJacobian(dm,f,ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorDrawSolution - Monitors progress of the TS solvers by calling
   VecView() for the solution at each timestep

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  step - current time-step
.  ptime - current time
-  dummy - either a viewer or NULL

   Options Database:
.   -ts_monitor_draw_solution_initial - show initial solution as well as current solution

   Notes: the initial solution and current solution are not display with a common axis scaling so generally the option -ts_monitor_draw_solution_initial
       will look bad

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
@*/
PetscErrorCode  TSMonitorDrawSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
{
  PetscErrorCode   ierr;
  TSMonitorDrawCtx ictx = (TSMonitorDrawCtx)dummy;
  PetscDraw        draw;

  PetscFunctionBegin;
  if (!step && ictx->showinitial) {
    if (!ictx->initialsolution) {
      ierr = VecDuplicate(u,&ictx->initialsolution);CHKERRQ(ierr);
    }
    ierr = VecCopy(u,ictx->initialsolution);CHKERRQ(ierr);
  }
  if (!(((ictx->howoften > 0) && (!(step % ictx->howoften))) || ((ictx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);

  if (ictx->showinitial) {
    PetscReal pause;
    ierr = PetscViewerDrawGetPause(ictx->viewer,&pause);CHKERRQ(ierr);
    ierr = PetscViewerDrawSetPause(ictx->viewer,0.0);CHKERRQ(ierr);
    ierr = VecView(ictx->initialsolution,ictx->viewer);CHKERRQ(ierr);
    ierr = PetscViewerDrawSetPause(ictx->viewer,pause);CHKERRQ(ierr);
    ierr = PetscViewerDrawSetHold(ictx->viewer,PETSC_TRUE);CHKERRQ(ierr);
  }
  ierr = VecView(u,ictx->viewer);CHKERRQ(ierr);
  if (ictx->showtimestepandtime) {
    PetscReal xl,yl,xr,yr,h;
    char      time[32];

    ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
    ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
    ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
    h    = yl + .95*(yr - yl);
    ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
    ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
  }

  if (ictx->showinitial) {
    ierr = PetscViewerDrawSetHold(ictx->viewer,PETSC_FALSE);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@C
   TSAdjointMonitorDrawSensi - Monitors progress of the adjoint TS solvers by calling
   VecView() for the sensitivities to initial states at each timestep

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  step - current time-step
.  ptime - current time
.  u - current state
.  numcost - number of cost functions
.  lambda - sensitivities to initial conditions
.  mu - sensitivities to parameters
-  dummy - either a viewer or NULL

   Level: intermediate

.keywords: TS,  vector, adjoint, monitor, view

.seealso: TSAdjointMonitorSet(), TSAdjointMonitorDefault(), VecView()
@*/
PetscErrorCode  TSAdjointMonitorDrawSensi(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscInt numcost,Vec *lambda,Vec *mu,void *dummy)
{
  PetscErrorCode   ierr;
  TSMonitorDrawCtx ictx = (TSMonitorDrawCtx)dummy;
  PetscDraw        draw;
  PetscReal        xl,yl,xr,yr,h;
  char             time[32];

  PetscFunctionBegin;
  if (!(((ictx->howoften > 0) && (!(step % ictx->howoften))) || ((ictx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);

  ierr = VecView(lambda[0],ictx->viewer);CHKERRQ(ierr);
  ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
  ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
  ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
  h    = yl + .95*(yr - yl);
  ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
  ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorDrawSolutionPhase - Monitors progress of the TS solvers by plotting the solution as a phase diagram

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  step - current time-step
.  ptime - current time
-  dummy - either a viewer or NULL

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
@*/
PetscErrorCode  TSMonitorDrawSolutionPhase(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
{
  PetscErrorCode    ierr;
  TSMonitorDrawCtx  ictx = (TSMonitorDrawCtx)dummy;
  PetscDraw         draw;
  PetscDrawAxis     axis;
  PetscInt          n;
  PetscMPIInt       size;
  PetscReal         U0,U1,xl,yl,xr,yr,h;
  char              time[32];
  const PetscScalar *U;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject)ts),&size);CHKERRQ(ierr);
  if (size != 1) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Only allowed for sequential runs");
  ierr = VecGetSize(u,&n);CHKERRQ(ierr);
  if (n != 2) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Only for ODEs with two unknowns");

  ierr = PetscViewerDrawGetDraw(ictx->viewer,0,&draw);CHKERRQ(ierr);
  ierr = PetscViewerDrawGetDrawAxis(ictx->viewer,0,&axis);CHKERRQ(ierr);
  ierr = PetscDrawAxisGetLimits(axis,&xl,&xr,&yl,&yr);CHKERRQ(ierr);
  if (!step) {
    ierr = PetscDrawClear(draw);CHKERRQ(ierr);
    ierr = PetscDrawAxisDraw(axis);CHKERRQ(ierr);
  }

  ierr = VecGetArrayRead(u,&U);CHKERRQ(ierr);
  U0 = PetscRealPart(U[0]);
  U1 = PetscRealPart(U[1]);
  ierr = VecRestoreArrayRead(u,&U);CHKERRQ(ierr);
  if ((U0 < xl) || (U1 < yl) || (U0 > xr) || (U1 > yr)) PetscFunctionReturn(0);

  ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
  ierr = PetscDrawPoint(draw,U0,U1,PETSC_DRAW_BLACK);CHKERRQ(ierr);
  if (ictx->showtimestepandtime) {
    ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
    ierr = PetscSNPrintf(time,32,"Timestep %d Time %g",(int)step,(double)ptime);CHKERRQ(ierr);
    h    = yl + .95*(yr - yl);
    ierr = PetscDrawStringCentered(draw,.5*(xl+xr),h,PETSC_DRAW_BLACK,time);CHKERRQ(ierr);
  }
  ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
  ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
  ierr = PetscDrawPause(draw);CHKERRQ(ierr);
  ierr = PetscDrawSave(draw);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorDrawCtxDestroy - Destroys the monitor context for TSMonitorDrawSolution()

   Collective on TS

   Input Parameters:
.    ctx - the monitor context

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorDrawSolution(), TSMonitorDrawError()
@*/
PetscErrorCode  TSMonitorDrawCtxDestroy(TSMonitorDrawCtx *ictx)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscViewerDestroy(&(*ictx)->viewer);CHKERRQ(ierr);
  ierr = VecDestroy(&(*ictx)->initialsolution);CHKERRQ(ierr);
  ierr = PetscFree(*ictx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorDrawCtxCreate - Creates the monitor context for TSMonitorDrawCtx

   Collective on TS

   Input Parameter:
.    ts - time-step context

   Output Patameter:
.    ctx - the monitor context

   Options Database:
.   -ts_monitor_draw_solution_initial - show initial solution as well as current solution

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorDrawCtx()
@*/
PetscErrorCode  TSMonitorDrawCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorDrawCtx *ctx)
{
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = PetscNew(ctx);CHKERRQ(ierr);
  ierr = PetscViewerDrawOpen(comm,host,label,x,y,m,n,&(*ctx)->viewer);CHKERRQ(ierr);
  ierr = PetscViewerSetFromOptions((*ctx)->viewer);CHKERRQ(ierr);

  (*ctx)->howoften    = howoften;
  (*ctx)->showinitial = PETSC_FALSE;
  ierr = PetscOptionsGetBool(NULL,NULL,"-ts_monitor_draw_solution_initial",&(*ctx)->showinitial,NULL);CHKERRQ(ierr);

  (*ctx)->showtimestepandtime = PETSC_FALSE;
  ierr = PetscOptionsGetBool(NULL,NULL,"-ts_monitor_draw_solution_show_time",&(*ctx)->showtimestepandtime,NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorDrawError - Monitors progress of the TS solvers by calling
   VecView() for the error at each timestep

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  step - current time-step
.  ptime - current time
-  dummy - either a viewer or NULL

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
@*/
PetscErrorCode  TSMonitorDrawError(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
{
  PetscErrorCode   ierr;
  TSMonitorDrawCtx ctx    = (TSMonitorDrawCtx)dummy;
  PetscViewer      viewer = ctx->viewer;
  Vec              work;

  PetscFunctionBegin;
  if (!(((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason))) PetscFunctionReturn(0);
  ierr = VecDuplicate(u,&work);CHKERRQ(ierr);
  ierr = TSComputeSolutionFunction(ts,ptime,work);CHKERRQ(ierr);
  ierr = VecAXPY(work,-1.0,u);CHKERRQ(ierr);
  ierr = VecView(work,viewer);CHKERRQ(ierr);
  ierr = VecDestroy(&work);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#include <petsc/private/dmimpl.h>
/*@
   TSSetDM - Sets the DM that may be used by some nonlinear solvers or preconditioners under the TS

   Logically Collective on TS and DM

   Input Parameters:
+  ts - the ODE integrator object
-  dm - the dm, cannot be NULL

   Level: intermediate

.seealso: TSGetDM(), SNESSetDM(), SNESGetDM()
@*/
PetscErrorCode  TSSetDM(TS ts,DM dm)
{
  PetscErrorCode ierr;
  SNES           snes;
  DMTS           tsdm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(dm,DM_CLASSID,2);
  ierr = PetscObjectReference((PetscObject)dm);CHKERRQ(ierr);
  if (ts->dm) {               /* Move the DMTS context over to the new DM unless the new DM already has one */
    if (ts->dm->dmts && !dm->dmts) {
      ierr = DMCopyDMTS(ts->dm,dm);CHKERRQ(ierr);
      ierr = DMGetDMTS(ts->dm,&tsdm);CHKERRQ(ierr);
      if (tsdm->originaldm == ts->dm) { /* Grant write privileges to the replacement DM */
        tsdm->originaldm = dm;
      }
    }
    ierr = DMDestroy(&ts->dm);CHKERRQ(ierr);
  }
  ts->dm = dm;

  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESSetDM(snes,dm);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSGetDM - Gets the DM that may be used by some preconditioners

   Not Collective

   Input Parameter:
. ts - the preconditioner context

   Output Parameter:
.  dm - the dm

   Level: intermediate

.seealso: TSSetDM(), SNESSetDM(), SNESGetDM()
@*/
PetscErrorCode  TSGetDM(TS ts,DM *dm)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (!ts->dm) {
    ierr = DMShellCreate(PetscObjectComm((PetscObject)ts),&ts->dm);CHKERRQ(ierr);
    if (ts->snes) {ierr = SNESSetDM(ts->snes,ts->dm);CHKERRQ(ierr);}
  }
  *dm = ts->dm;
  PetscFunctionReturn(0);
}

/*@
   SNESTSFormFunction - Function to evaluate nonlinear residual

   Logically Collective on SNES

   Input Parameter:
+ snes - nonlinear solver
. U - the current state at which to evaluate the residual
- ctx - user context, must be a TS

   Output Parameter:
. F - the nonlinear residual

   Notes:
   This function is not normally called by users and is automatically registered with the SNES used by TS.
   It is most frequently passed to MatFDColoringSetFunction().

   Level: advanced

.seealso: SNESSetFunction(), MatFDColoringSetFunction()
@*/
PetscErrorCode  SNESTSFormFunction(SNES snes,Vec U,Vec F,void *ctx)
{
  TS             ts = (TS)ctx;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,2);
  PetscValidHeaderSpecific(F,VEC_CLASSID,3);
  PetscValidHeaderSpecific(ts,TS_CLASSID,4);
  ierr = (ts->ops->snesfunction)(snes,U,F,ts);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   SNESTSFormJacobian - Function to evaluate the Jacobian

   Collective on SNES

   Input Parameter:
+ snes - nonlinear solver
. U - the current state at which to evaluate the residual
- ctx - user context, must be a TS

   Output Parameter:
+ A - the Jacobian
. B - the preconditioning matrix (may be the same as A)
- flag - indicates any structure change in the matrix

   Notes:
   This function is not normally called by users and is automatically registered with the SNES used by TS.

   Level: developer

.seealso: SNESSetJacobian()
@*/
PetscErrorCode  SNESTSFormJacobian(SNES snes,Vec U,Mat A,Mat B,void *ctx)
{
  TS             ts = (TS)ctx;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,2);
  PetscValidPointer(A,3);
  PetscValidHeaderSpecific(A,MAT_CLASSID,3);
  PetscValidPointer(B,4);
  PetscValidHeaderSpecific(B,MAT_CLASSID,4);
  PetscValidHeaderSpecific(ts,TS_CLASSID,6);
  ierr = (ts->ops->snesjacobian)(snes,U,A,B,ts);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSComputeRHSFunctionLinear - Evaluate the right hand side via the user-provided Jacobian, for linear problems Udot = A U only

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  t - time at which to evaluate
.  U - state at which to evaluate
-  ctx - context

   Output Arguments:
.  F - right hand side

   Level: intermediate

   Notes:
   This function is intended to be passed to TSSetRHSFunction() to evaluate the right hand side for linear problems.
   The matrix (and optionally the evaluation context) should be passed to TSSetRHSJacobian().

.seealso: TSSetRHSFunction(), TSSetRHSJacobian(), TSComputeRHSJacobianConstant()
@*/
PetscErrorCode TSComputeRHSFunctionLinear(TS ts,PetscReal t,Vec U,Vec F,void *ctx)
{
  PetscErrorCode ierr;
  Mat            Arhs,Brhs;

  PetscFunctionBegin;
  ierr = TSGetRHSMats_Private(ts,&Arhs,&Brhs);CHKERRQ(ierr);
  ierr = TSComputeRHSJacobian(ts,t,U,Arhs,Brhs);CHKERRQ(ierr);
  ierr = MatMult(Arhs,U,F);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSComputeRHSJacobianConstant - Reuses a Jacobian that is time-independent.

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  t - time at which to evaluate
.  U - state at which to evaluate
-  ctx - context

   Output Arguments:
+  A - pointer to operator
.  B - pointer to preconditioning matrix
-  flg - matrix structure flag

   Level: intermediate

   Notes:
   This function is intended to be passed to TSSetRHSJacobian() to evaluate the Jacobian for linear time-independent problems.

.seealso: TSSetRHSFunction(), TSSetRHSJacobian(), TSComputeRHSFunctionLinear()
@*/
PetscErrorCode TSComputeRHSJacobianConstant(TS ts,PetscReal t,Vec U,Mat A,Mat B,void *ctx)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

/*@C
   TSComputeIFunctionLinear - Evaluate the left hand side via the user-provided Jacobian, for linear problems only

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  t - time at which to evaluate
.  U - state at which to evaluate
.  Udot - time derivative of state vector
-  ctx - context

   Output Arguments:
.  F - left hand side

   Level: intermediate

   Notes:
   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
   user is required to write their own TSComputeIFunction.
   This function is intended to be passed to TSSetIFunction() to evaluate the left hand side for linear problems.
   The matrix (and optionally the evaluation context) should be passed to TSSetIJacobian().

   Note that using this function is NOT equivalent to using TSComputeRHSFunctionLinear() since that solves Udot = A U

.seealso: TSSetIFunction(), TSSetIJacobian(), TSComputeIJacobianConstant(), TSComputeRHSFunctionLinear()
@*/
PetscErrorCode TSComputeIFunctionLinear(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
{
  PetscErrorCode ierr;
  Mat            A,B;

  PetscFunctionBegin;
  ierr = TSGetIJacobian(ts,&A,&B,NULL,NULL);CHKERRQ(ierr);
  ierr = TSComputeIJacobian(ts,t,U,Udot,1.0,A,B,PETSC_TRUE);CHKERRQ(ierr);
  ierr = MatMult(A,Udot,F);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSComputeIJacobianConstant - Reuses a time-independent for a semi-implicit DAE or ODE

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  t - time at which to evaluate
.  U - state at which to evaluate
.  Udot - time derivative of state vector
.  shift - shift to apply
-  ctx - context

   Output Arguments:
+  A - pointer to operator
.  B - pointer to preconditioning matrix
-  flg - matrix structure flag

   Level: advanced

   Notes:
   This function is intended to be passed to TSSetIJacobian() to evaluate the Jacobian for linear time-independent problems.

   It is only appropriate for problems of the form

$     M Udot = F(U,t)

  where M is constant and F is non-stiff.  The user must pass M to TSSetIJacobian().  The current implementation only
  works with IMEX time integration methods such as TSROSW and TSARKIMEX, since there is no support for de-constructing
  an implicit operator of the form

$    shift*M + J

  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
  a copy of M or reassemble it when requested.

.seealso: TSSetIFunction(), TSSetIJacobian(), TSComputeIFunctionLinear()
@*/
PetscErrorCode TSComputeIJacobianConstant(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat A,Mat B,void *ctx)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatScale(A, shift / ts->ijacobian.shift);CHKERRQ(ierr);
  ts->ijacobian.shift = shift;
  PetscFunctionReturn(0);
}

/*@
   TSGetEquationType - Gets the type of the equation that TS is solving.

   Not Collective

   Input Parameter:
.  ts - the TS context

   Output Parameter:
.  equation_type - see TSEquationType

   Level: beginner

.keywords: TS, equation type

.seealso: TSSetEquationType(), TSEquationType
@*/
PetscErrorCode  TSGetEquationType(TS ts,TSEquationType *equation_type)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(equation_type,2);
  *equation_type = ts->equation_type;
  PetscFunctionReturn(0);
}

/*@
   TSSetEquationType - Sets the type of the equation that TS is solving.

   Not Collective

   Input Parameter:
+  ts - the TS context
-  equation_type - see TSEquationType

   Level: advanced

.keywords: TS, equation type

.seealso: TSGetEquationType(), TSEquationType
@*/
PetscErrorCode  TSSetEquationType(TS ts,TSEquationType equation_type)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ts->equation_type = equation_type;
  PetscFunctionReturn(0);
}

/*@
   TSGetConvergedReason - Gets the reason the TS iteration was stopped.

   Not Collective

   Input Parameter:
.  ts - the TS context

   Output Parameter:
.  reason - negative value indicates diverged, positive value converged, see TSConvergedReason or the
            manual pages for the individual convergence tests for complete lists

   Level: beginner

   Notes:
   Can only be called after the call to TSSolve() is complete.

.keywords: TS, nonlinear, set, convergence, test

.seealso: TSSetConvergenceTest(), TSConvergedReason
@*/
PetscErrorCode  TSGetConvergedReason(TS ts,TSConvergedReason *reason)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(reason,2);
  *reason = ts->reason;
  PetscFunctionReturn(0);
}

/*@
   TSSetConvergedReason - Sets the reason for handling the convergence of TSSolve.

   Not Collective

   Input Parameter:
+  ts - the TS context
.  reason - negative value indicates diverged, positive value converged, see TSConvergedReason or the
            manual pages for the individual convergence tests for complete lists

   Level: advanced

   Notes:
   Can only be called during TSSolve() is active.

.keywords: TS, nonlinear, set, convergence, test

.seealso: TSConvergedReason
@*/
PetscErrorCode  TSSetConvergedReason(TS ts,TSConvergedReason reason)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ts->reason = reason;
  PetscFunctionReturn(0);
}

/*@
   TSGetSolveTime - Gets the time after a call to TSSolve()

   Not Collective

   Input Parameter:
.  ts - the TS context

   Output Parameter:
.  ftime - the final time. This time corresponds to the final time set with TSSetMaxTime()

   Level: beginner

   Notes:
   Can only be called after the call to TSSolve() is complete.

.keywords: TS, nonlinear, set, convergence, test

.seealso: TSSetConvergenceTest(), TSConvergedReason
@*/
PetscErrorCode  TSGetSolveTime(TS ts,PetscReal *ftime)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(ftime,2);
  *ftime = ts->solvetime;
  PetscFunctionReturn(0);
}

/*@
   TSGetSNESIterations - Gets the total number of nonlinear iterations
   used by the time integrator.

   Not Collective

   Input Parameter:
.  ts - TS context

   Output Parameter:
.  nits - number of nonlinear iterations

   Notes:
   This counter is reset to zero for each successive call to TSSolve().

   Level: intermediate

.keywords: TS, get, number, nonlinear, iterations

.seealso:  TSGetKSPIterations()
@*/
PetscErrorCode TSGetSNESIterations(TS ts,PetscInt *nits)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidIntPointer(nits,2);
  *nits = ts->snes_its;
  PetscFunctionReturn(0);
}

/*@
   TSGetKSPIterations - Gets the total number of linear iterations
   used by the time integrator.

   Not Collective

   Input Parameter:
.  ts - TS context

   Output Parameter:
.  lits - number of linear iterations

   Notes:
   This counter is reset to zero for each successive call to TSSolve().

   Level: intermediate

.keywords: TS, get, number, linear, iterations

.seealso:  TSGetSNESIterations(), SNESGetKSPIterations()
@*/
PetscErrorCode TSGetKSPIterations(TS ts,PetscInt *lits)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidIntPointer(lits,2);
  *lits = ts->ksp_its;
  PetscFunctionReturn(0);
}

/*@
   TSGetStepRejections - Gets the total number of rejected steps.

   Not Collective

   Input Parameter:
.  ts - TS context

   Output Parameter:
.  rejects - number of steps rejected

   Notes:
   This counter is reset to zero for each successive call to TSSolve().

   Level: intermediate

.keywords: TS, get, number

.seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetSNESFailures(), TSSetMaxSNESFailures(), TSSetErrorIfStepFails()
@*/
PetscErrorCode TSGetStepRejections(TS ts,PetscInt *rejects)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidIntPointer(rejects,2);
  *rejects = ts->reject;
  PetscFunctionReturn(0);
}

/*@
   TSGetSNESFailures - Gets the total number of failed SNES solves

   Not Collective

   Input Parameter:
.  ts - TS context

   Output Parameter:
.  fails - number of failed nonlinear solves

   Notes:
   This counter is reset to zero for each successive call to TSSolve().

   Level: intermediate

.keywords: TS, get, number

.seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSSetMaxSNESFailures()
@*/
PetscErrorCode TSGetSNESFailures(TS ts,PetscInt *fails)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidIntPointer(fails,2);
  *fails = ts->num_snes_failures;
  PetscFunctionReturn(0);
}

/*@
   TSSetMaxStepRejections - Sets the maximum number of step rejections before a step fails

   Not Collective

   Input Parameter:
+  ts - TS context
-  rejects - maximum number of rejected steps, pass -1 for unlimited

   Notes:
   The counter is reset to zero for each step

   Options Database Key:
 .  -ts_max_reject - Maximum number of step rejections before a step fails

   Level: intermediate

.keywords: TS, set, maximum, number

.seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxSNESFailures(), TSGetStepRejections(), TSGetSNESFailures(), TSSetErrorIfStepFails(), TSGetConvergedReason()
@*/
PetscErrorCode TSSetMaxStepRejections(TS ts,PetscInt rejects)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ts->max_reject = rejects;
  PetscFunctionReturn(0);
}

/*@
   TSSetMaxSNESFailures - Sets the maximum number of failed SNES solves

   Not Collective

   Input Parameter:
+  ts - TS context
-  fails - maximum number of failed nonlinear solves, pass -1 for unlimited

   Notes:
   The counter is reset to zero for each successive call to TSSolve().

   Options Database Key:
 .  -ts_max_snes_failures - Maximum number of nonlinear solve failures

   Level: intermediate

.keywords: TS, set, maximum, number

.seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSGetSNESFailures(), SNESGetConvergedReason(), TSGetConvergedReason()
@*/
PetscErrorCode TSSetMaxSNESFailures(TS ts,PetscInt fails)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ts->max_snes_failures = fails;
  PetscFunctionReturn(0);
}

/*@
   TSSetErrorIfStepFails - Error if no step succeeds

   Not Collective

   Input Parameter:
+  ts - TS context
-  err - PETSC_TRUE to error if no step succeeds, PETSC_FALSE to return without failure

   Options Database Key:
 .  -ts_error_if_step_fails - Error if no step succeeds

   Level: intermediate

.keywords: TS, set, error

.seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSGetSNESFailures(), TSSetErrorIfStepFails(), TSGetConvergedReason()
@*/
PetscErrorCode TSSetErrorIfStepFails(TS ts,PetscBool err)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ts->errorifstepfailed = err;
  PetscFunctionReturn(0);
}

/*@C
   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

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  step - current time-step
.  ptime - current time
.  u - current state
-  vf - viewer and its format

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
@*/
PetscErrorCode  TSMonitorSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,PetscViewerAndFormat *vf)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscViewerPushFormat(vf->viewer,vf->format);CHKERRQ(ierr);
  ierr = VecView(u,vf->viewer);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(vf->viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorSolutionVTK - Monitors progress of the TS solvers by VecView() for the solution at each timestep.

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  step - current time-step
.  ptime - current time
.  u - current state
-  filenametemplate - string containing a format specifier for the integer time step (e.g. %03D)

   Level: intermediate

   Notes:
   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.
   These are named according to the file name template.

   This function is normally passed as an argument to TSMonitorSet() along with TSMonitorSolutionVTKDestroy().

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView()
@*/
PetscErrorCode TSMonitorSolutionVTK(TS ts,PetscInt step,PetscReal ptime,Vec u,void *filenametemplate)
{
  PetscErrorCode ierr;
  char           filename[PETSC_MAX_PATH_LEN];
  PetscViewer    viewer;

  PetscFunctionBegin;
  if (step < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
  ierr = PetscSNPrintf(filename,sizeof(filename),(const char*)filenametemplate,step);CHKERRQ(ierr);
  ierr = PetscViewerVTKOpen(PetscObjectComm((PetscObject)ts),filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
  ierr = VecView(u,viewer);CHKERRQ(ierr);
  ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorSolutionVTKDestroy - Destroy context for monitoring

   Collective on TS

   Input Parameters:
.  filenametemplate - string containing a format specifier for the integer time step (e.g. %03D)

   Level: intermediate

   Note:
   This function is normally passed to TSMonitorSet() along with TSMonitorSolutionVTK().

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorSolutionVTK()
@*/
PetscErrorCode TSMonitorSolutionVTKDestroy(void *filenametemplate)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscFree(*(char**)filenametemplate);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSGetAdapt - Get the adaptive controller context for the current method

   Collective on TS if controller has not been created yet

   Input Arguments:
.  ts - time stepping context

   Output Arguments:
.  adapt - adaptive controller

   Level: intermediate

.seealso: TSAdapt, TSAdaptSetType(), TSAdaptChoose()
@*/
PetscErrorCode TSGetAdapt(TS ts,TSAdapt *adapt)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidPointer(adapt,2);
  if (!ts->adapt) {
    ierr = TSAdaptCreate(PetscObjectComm((PetscObject)ts),&ts->adapt);CHKERRQ(ierr);
    ierr = PetscLogObjectParent((PetscObject)ts,(PetscObject)ts->adapt);CHKERRQ(ierr);
    ierr = PetscObjectIncrementTabLevel((PetscObject)ts->adapt,(PetscObject)ts,1);CHKERRQ(ierr);
  }
  *adapt = ts->adapt;
  PetscFunctionReturn(0);
}

/*@
   TSSetTolerances - Set tolerances for local truncation error when using adaptive controller

   Logically Collective

   Input Arguments:
+  ts - time integration context
.  atol - scalar absolute tolerances, PETSC_DECIDE to leave current value
.  vatol - vector of absolute tolerances or NULL, used in preference to atol if present
.  rtol - scalar relative tolerances, PETSC_DECIDE to leave current value
-  vrtol - vector of relative tolerances or NULL, used in preference to atol if present

   Options Database keys:
+  -ts_rtol <rtol> - relative tolerance for local truncation error
-  -ts_atol <atol> Absolute tolerance for local truncation error

   Notes:
   With PETSc's implicit schemes for DAE problems, the calculation of the local truncation error
   (LTE) includes both the differential and the algebraic variables. If one wants the LTE to be
   computed only for the differential or the algebraic part then this can be done using the vector of
   tolerances vatol. For example, by setting the tolerance vector with the desired tolerance for the
   differential part and infinity for the algebraic part, the LTE calculation will include only the
   differential variables.

   Level: beginner

.seealso: TS, TSAdapt, TSVecNormWRMS(), TSGetTolerances()
@*/
PetscErrorCode TSSetTolerances(TS ts,PetscReal atol,Vec vatol,PetscReal rtol,Vec vrtol)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (atol != PETSC_DECIDE && atol != PETSC_DEFAULT) ts->atol = atol;
  if (vatol) {
    ierr = PetscObjectReference((PetscObject)vatol);CHKERRQ(ierr);
    ierr = VecDestroy(&ts->vatol);CHKERRQ(ierr);
    ts->vatol = vatol;
  }
  if (rtol != PETSC_DECIDE && rtol != PETSC_DEFAULT) ts->rtol = rtol;
  if (vrtol) {
    ierr = PetscObjectReference((PetscObject)vrtol);CHKERRQ(ierr);
    ierr = VecDestroy(&ts->vrtol);CHKERRQ(ierr);
    ts->vrtol = vrtol;
  }
  PetscFunctionReturn(0);
}

/*@
   TSGetTolerances - Get tolerances for local truncation error when using adaptive controller

   Logically Collective

   Input Arguments:
.  ts - time integration context

   Output Arguments:
+  atol - scalar absolute tolerances, NULL to ignore
.  vatol - vector of absolute tolerances, NULL to ignore
.  rtol - scalar relative tolerances, NULL to ignore
-  vrtol - vector of relative tolerances, NULL to ignore

   Level: beginner

.seealso: TS, TSAdapt, TSVecNormWRMS(), TSSetTolerances()
@*/
PetscErrorCode TSGetTolerances(TS ts,PetscReal *atol,Vec *vatol,PetscReal *rtol,Vec *vrtol)
{
  PetscFunctionBegin;
  if (atol)  *atol  = ts->atol;
  if (vatol) *vatol = ts->vatol;
  if (rtol)  *rtol  = ts->rtol;
  if (vrtol) *vrtol = ts->vrtol;
  PetscFunctionReturn(0);
}

/*@
   TSErrorWeightedNorm2 - compute a weighted 2-norm of the difference between two state vectors

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  U - state vector, usually ts->vec_sol
-  Y - state vector to be compared to U

   Output Arguments:
.  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
.  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
.  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances

   Level: developer

.seealso: TSErrorWeightedNorm(), TSErrorWeightedNormInfinity()
@*/
PetscErrorCode TSErrorWeightedNorm2(TS ts,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
{
  PetscErrorCode    ierr;
  PetscInt          i,n,N,rstart;
  PetscInt          n_loc,na_loc,nr_loc;
  PetscReal         n_glb,na_glb,nr_glb;
  const PetscScalar *u,*y;
  PetscReal         sum,suma,sumr,gsum,gsuma,gsumr,diff;
  PetscReal         tol,tola,tolr;
  PetscReal         err_loc[6],err_glb[6];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,2);
  PetscValidHeaderSpecific(Y,VEC_CLASSID,3);
  PetscValidType(U,2);
  PetscValidType(Y,3);
  PetscCheckSameComm(U,2,Y,3);
  PetscValidPointer(norm,4);
  PetscValidPointer(norma,5);
  PetscValidPointer(normr,6);
  if (U == Y) SETERRQ(PetscObjectComm((PetscObject)U),PETSC_ERR_ARG_IDN,"U and Y cannot be the same vector");

  ierr = VecGetSize(U,&N);CHKERRQ(ierr);
  ierr = VecGetLocalSize(U,&n);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(U,&rstart,NULL);CHKERRQ(ierr);
  ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
  ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
  sum  = 0.; n_loc  = 0;
  suma = 0.; na_loc = 0;
  sumr = 0.; nr_loc = 0;
  if (ts->vatol && ts->vrtol) {
    const PetscScalar *atol,*rtol;
    ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      diff = PetscAbsScalar(y[i] - u[i]);
      tola = PetscRealPart(atol[i]);
      if(tola>0.){
        suma  += PetscSqr(diff/tola);
        na_loc++;
      }
      tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      if(tolr>0.){
        sumr  += PetscSqr(diff/tolr);
        nr_loc++;
      }
      tol=tola+tolr;
      if(tol>0.){
        sum  += PetscSqr(diff/tol);
        n_loc++;
      }
    }
    ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
  } else if (ts->vatol) {       /* vector atol, scalar rtol */
    const PetscScalar *atol;
    ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      diff = PetscAbsScalar(y[i] - u[i]);
      tola = PetscRealPart(atol[i]);
      if(tola>0.){
        suma  += PetscSqr(diff/tola);
        na_loc++;
      }
      tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      if(tolr>0.){
        sumr  += PetscSqr(diff/tolr);
        nr_loc++;
      }
      tol=tola+tolr;
      if(tol>0.){
        sum  += PetscSqr(diff/tol);
        n_loc++;
      }
    }
    ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
  } else if (ts->vrtol) {       /* scalar atol, vector rtol */
    const PetscScalar *rtol;
    ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      diff = PetscAbsScalar(y[i] - u[i]);
      tola = ts->atol;
      if(tola>0.){
        suma  += PetscSqr(diff/tola);
        na_loc++;
      }
      tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      if(tolr>0.){
        sumr  += PetscSqr(diff/tolr);
        nr_loc++;
      }
      tol=tola+tolr;
      if(tol>0.){
        sum  += PetscSqr(diff/tol);
        n_loc++;
      }
    }
    ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
  } else {                      /* scalar atol, scalar rtol */
    for (i=0; i<n; i++) {
      diff = PetscAbsScalar(y[i] - u[i]);
     tola = ts->atol;
      if(tola>0.){
        suma  += PetscSqr(diff/tola);
        na_loc++;
      }
      tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      if(tolr>0.){
        sumr  += PetscSqr(diff/tolr);
        nr_loc++;
      }
      tol=tola+tolr;
      if(tol>0.){
        sum  += PetscSqr(diff/tol);
        n_loc++;
      }
    }
  }
  ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);

  err_loc[0] = sum;
  err_loc[1] = suma;
  err_loc[2] = sumr;
  err_loc[3] = (PetscReal)n_loc;
  err_loc[4] = (PetscReal)na_loc;
  err_loc[5] = (PetscReal)nr_loc;

  ierr = MPIU_Allreduce(err_loc,err_glb,6,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);

  gsum   = err_glb[0];
  gsuma  = err_glb[1];
  gsumr  = err_glb[2];
  n_glb  = err_glb[3];
  na_glb = err_glb[4];
  nr_glb = err_glb[5];

  *norm  = 0.;
  if(n_glb>0. ){*norm  = PetscSqrtReal(gsum  / n_glb );}
  *norma = 0.;
  if(na_glb>0.){*norma = PetscSqrtReal(gsuma / na_glb);}
  *normr = 0.;
  if(nr_glb>0.){*normr = PetscSqrtReal(gsumr / nr_glb);}

  if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
  if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
  if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
  PetscFunctionReturn(0);
}

/*@
   TSErrorWeightedNormInfinity - compute a weighted infinity-norm of the difference between two state vectors

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  U - state vector, usually ts->vec_sol
-  Y - state vector to be compared to U

   Output Arguments:
.  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
.  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
.  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances

   Level: developer

.seealso: TSErrorWeightedNorm(), TSErrorWeightedNorm2()
@*/
PetscErrorCode TSErrorWeightedNormInfinity(TS ts,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
{
  PetscErrorCode    ierr;
  PetscInt          i,n,N,rstart;
  const PetscScalar *u,*y;
  PetscReal         max,gmax,maxa,gmaxa,maxr,gmaxr;
  PetscReal         tol,tola,tolr,diff;
  PetscReal         err_loc[3],err_glb[3];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,2);
  PetscValidHeaderSpecific(Y,VEC_CLASSID,3);
  PetscValidType(U,2);
  PetscValidType(Y,3);
  PetscCheckSameComm(U,2,Y,3);
  PetscValidPointer(norm,4);
  PetscValidPointer(norma,5);
  PetscValidPointer(normr,6);
  if (U == Y) SETERRQ(PetscObjectComm((PetscObject)U),PETSC_ERR_ARG_IDN,"U and Y cannot be the same vector");

  ierr = VecGetSize(U,&N);CHKERRQ(ierr);
  ierr = VecGetLocalSize(U,&n);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(U,&rstart,NULL);CHKERRQ(ierr);
  ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
  ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);

  max=0.;
  maxa=0.;
  maxr=0.;

  if (ts->vatol && ts->vrtol) {     /* vector atol, vector rtol */
    const PetscScalar *atol,*rtol;
    ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);

    for (i=0; i<n; i++) {
      diff = PetscAbsScalar(y[i] - u[i]);
      tola = PetscRealPart(atol[i]);
      tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      tol  = tola+tolr;
      if(tola>0.){
        maxa = PetscMax(maxa,diff / tola);
      }
      if(tolr>0.){
        maxr = PetscMax(maxr,diff / tolr);
      }
      if(tol>0.){
        max = PetscMax(max,diff / tol);
      }
    }
    ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
  } else if (ts->vatol) {       /* vector atol, scalar rtol */
    const PetscScalar *atol;
    ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      diff = PetscAbsScalar(y[i] - u[i]);
      tola = PetscRealPart(atol[i]);
      tolr = ts->rtol  * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      tol  = tola+tolr;
      if(tola>0.){
        maxa = PetscMax(maxa,diff / tola);
      }
      if(tolr>0.){
        maxr = PetscMax(maxr,diff / tolr);
      }
      if(tol>0.){
        max = PetscMax(max,diff / tol);
      }
    }
    ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
  } else if (ts->vrtol) {       /* scalar atol, vector rtol */
    const PetscScalar *rtol;
    ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);

    for (i=0; i<n; i++) {
      diff = PetscAbsScalar(y[i] - u[i]);
      tola = ts->atol;
      tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      tol  = tola+tolr;
      if(tola>0.){
        maxa = PetscMax(maxa,diff / tola);
      }
      if(tolr>0.){
        maxr = PetscMax(maxr,diff / tolr);
      }
      if(tol>0.){
        max = PetscMax(max,diff / tol);
      }
    }
    ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
  } else {                      /* scalar atol, scalar rtol */

    for (i=0; i<n; i++) {
      diff = PetscAbsScalar(y[i] - u[i]);
      tola = ts->atol;
      tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      tol  = tola+tolr;
      if(tola>0.){
        maxa = PetscMax(maxa,diff / tola);
      }
      if(tolr>0.){
        maxr = PetscMax(maxr,diff / tolr);
      }
      if(tol>0.){
        max = PetscMax(max,diff / tol);
      }
    }
  }
  ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
  err_loc[0] = max;
  err_loc[1] = maxa;
  err_loc[2] = maxr;
  ierr  = MPIU_Allreduce(err_loc,err_glb,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
  gmax   = err_glb[0];
  gmaxa  = err_glb[1];
  gmaxr  = err_glb[2];

  *norm = gmax;
  *norma = gmaxa;
  *normr = gmaxr;
  if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
    if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
    if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
  PetscFunctionReturn(0);
}

/*@
   TSErrorWeightedNorm - compute a weighted norm of the difference between two state vectors based on supplied absolute and relative tolerances

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  U - state vector, usually ts->vec_sol
.  Y - state vector to be compared to U
-  wnormtype - norm type, either NORM_2 or NORM_INFINITY

   Output Arguments:
.  norm  - weighted norm, a value of 1.0 achieves a balance between absolute and relative tolerances
.  norma - weighted norm, a value of 1.0 means that the error meets the absolute tolerance set by the user
.  normr - weighted norm, a value of 1.0 means that the error meets the relative tolerance set by the user

   Options Database Keys:
.  -ts_adapt_wnormtype <wnormtype> - 2, INFINITY

   Level: developer

.seealso: TSErrorWeightedNormInfinity(), TSErrorWeightedNorm2(), TSErrorWeightedENorm
@*/
PetscErrorCode TSErrorWeightedNorm(TS ts,Vec U,Vec Y,NormType wnormtype,PetscReal *norm,PetscReal *norma,PetscReal *normr)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (wnormtype == NORM_2) {
    ierr = TSErrorWeightedNorm2(ts,U,Y,norm,norma,normr);CHKERRQ(ierr);
  } else if(wnormtype == NORM_INFINITY) {
    ierr = TSErrorWeightedNormInfinity(ts,U,Y,norm,norma,normr);CHKERRQ(ierr);
  } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
  PetscFunctionReturn(0);
}


/*@
   TSErrorWeightedENorm2 - compute a weighted 2 error norm based on supplied absolute and relative tolerances

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  E - error vector
.  U - state vector, usually ts->vec_sol
-  Y - state vector, previous time step

   Output Arguments:
.  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
.  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
.  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances

   Level: developer

.seealso: TSErrorWeightedENorm(), TSErrorWeightedENormInfinity()
@*/
PetscErrorCode TSErrorWeightedENorm2(TS ts,Vec E,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
{
  PetscErrorCode    ierr;
  PetscInt          i,n,N,rstart;
  PetscInt          n_loc,na_loc,nr_loc;
  PetscReal         n_glb,na_glb,nr_glb;
  const PetscScalar *e,*u,*y;
  PetscReal         err,sum,suma,sumr,gsum,gsuma,gsumr;
  PetscReal         tol,tola,tolr;
  PetscReal         err_loc[6],err_glb[6];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(E,VEC_CLASSID,2);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  PetscValidHeaderSpecific(Y,VEC_CLASSID,4);
  PetscValidType(E,2);
  PetscValidType(U,3);
  PetscValidType(Y,4);
  PetscCheckSameComm(E,2,U,3);
  PetscCheckSameComm(U,2,Y,3);
  PetscValidPointer(norm,5);
  PetscValidPointer(norma,6);
  PetscValidPointer(normr,7);

  ierr = VecGetSize(E,&N);CHKERRQ(ierr);
  ierr = VecGetLocalSize(E,&n);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(E,&rstart,NULL);CHKERRQ(ierr);
  ierr = VecGetArrayRead(E,&e);CHKERRQ(ierr);
  ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
  ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
  sum  = 0.; n_loc  = 0;
  suma = 0.; na_loc = 0;
  sumr = 0.; nr_loc = 0;
  if (ts->vatol && ts->vrtol) {
    const PetscScalar *atol,*rtol;
    ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      err = PetscAbsScalar(e[i]);
      tola = PetscRealPart(atol[i]);
      if(tola>0.){
        suma  += PetscSqr(err/tola);
        na_loc++;
      }
      tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      if(tolr>0.){
        sumr  += PetscSqr(err/tolr);
        nr_loc++;
      }
      tol=tola+tolr;
      if(tol>0.){
        sum  += PetscSqr(err/tol);
        n_loc++;
      }
    }
    ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
  } else if (ts->vatol) {       /* vector atol, scalar rtol */
    const PetscScalar *atol;
    ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      err = PetscAbsScalar(e[i]);
      tola = PetscRealPart(atol[i]);
      if(tola>0.){
        suma  += PetscSqr(err/tola);
        na_loc++;
      }
      tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      if(tolr>0.){
        sumr  += PetscSqr(err/tolr);
        nr_loc++;
      }
      tol=tola+tolr;
      if(tol>0.){
        sum  += PetscSqr(err/tol);
        n_loc++;
      }
    }
    ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
  } else if (ts->vrtol) {       /* scalar atol, vector rtol */
    const PetscScalar *rtol;
    ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      err = PetscAbsScalar(e[i]);
      tola = ts->atol;
      if(tola>0.){
        suma  += PetscSqr(err/tola);
        na_loc++;
      }
      tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      if(tolr>0.){
        sumr  += PetscSqr(err/tolr);
        nr_loc++;
      }
      tol=tola+tolr;
      if(tol>0.){
        sum  += PetscSqr(err/tol);
        n_loc++;
      }
    }
    ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
  } else {                      /* scalar atol, scalar rtol */
    for (i=0; i<n; i++) {
      err = PetscAbsScalar(e[i]);
     tola = ts->atol;
      if(tola>0.){
        suma  += PetscSqr(err/tola);
        na_loc++;
      }
      tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      if(tolr>0.){
        sumr  += PetscSqr(err/tolr);
        nr_loc++;
      }
      tol=tola+tolr;
      if(tol>0.){
        sum  += PetscSqr(err/tol);
        n_loc++;
      }
    }
  }
  ierr = VecRestoreArrayRead(E,&e);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);

  err_loc[0] = sum;
  err_loc[1] = suma;
  err_loc[2] = sumr;
  err_loc[3] = (PetscReal)n_loc;
  err_loc[4] = (PetscReal)na_loc;
  err_loc[5] = (PetscReal)nr_loc;

  ierr = MPIU_Allreduce(err_loc,err_glb,6,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);

  gsum   = err_glb[0];
  gsuma  = err_glb[1];
  gsumr  = err_glb[2];
  n_glb  = err_glb[3];
  na_glb = err_glb[4];
  nr_glb = err_glb[5];

  *norm  = 0.;
  if(n_glb>0. ){*norm  = PetscSqrtReal(gsum  / n_glb );}
  *norma = 0.;
  if(na_glb>0.){*norma = PetscSqrtReal(gsuma / na_glb);}
  *normr = 0.;
  if(nr_glb>0.){*normr = PetscSqrtReal(gsumr / nr_glb);}

  if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
  if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
  if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
  PetscFunctionReturn(0);
}

/*@
   TSErrorWeightedENormInfinity - compute a weighted infinity error norm based on supplied absolute and relative tolerances
   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  E - error vector
.  U - state vector, usually ts->vec_sol
-  Y - state vector, previous time step

   Output Arguments:
.  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
.  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
.  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances

   Level: developer

.seealso: TSErrorWeightedENorm(), TSErrorWeightedENorm2()
@*/
PetscErrorCode TSErrorWeightedENormInfinity(TS ts,Vec E,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
{
  PetscErrorCode    ierr;
  PetscInt          i,n,N,rstart;
  const PetscScalar *e,*u,*y;
  PetscReal         err,max,gmax,maxa,gmaxa,maxr,gmaxr;
  PetscReal         tol,tola,tolr;
  PetscReal         err_loc[3],err_glb[3];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(E,VEC_CLASSID,2);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  PetscValidHeaderSpecific(Y,VEC_CLASSID,4);
  PetscValidType(E,2);
  PetscValidType(U,3);
  PetscValidType(Y,4);
  PetscCheckSameComm(E,2,U,3);
  PetscCheckSameComm(U,2,Y,3);
  PetscValidPointer(norm,5);
  PetscValidPointer(norma,6);
  PetscValidPointer(normr,7);

  ierr = VecGetSize(E,&N);CHKERRQ(ierr);
  ierr = VecGetLocalSize(E,&n);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(E,&rstart,NULL);CHKERRQ(ierr);
  ierr = VecGetArrayRead(E,&e);CHKERRQ(ierr);
  ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
  ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);

  max=0.;
  maxa=0.;
  maxr=0.;

  if (ts->vatol && ts->vrtol) {     /* vector atol, vector rtol */
    const PetscScalar *atol,*rtol;
    ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);

    for (i=0; i<n; i++) {
      err = PetscAbsScalar(e[i]);
      tola = PetscRealPart(atol[i]);
      tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      tol  = tola+tolr;
      if(tola>0.){
        maxa = PetscMax(maxa,err / tola);
      }
      if(tolr>0.){
        maxr = PetscMax(maxr,err / tolr);
      }
      if(tol>0.){
        max = PetscMax(max,err / tol);
      }
    }
    ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
  } else if (ts->vatol) {       /* vector atol, scalar rtol */
    const PetscScalar *atol;
    ierr = VecGetArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      err = PetscAbsScalar(e[i]);
      tola = PetscRealPart(atol[i]);
      tolr = ts->rtol  * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      tol  = tola+tolr;
      if(tola>0.){
        maxa = PetscMax(maxa,err / tola);
      }
      if(tolr>0.){
        maxr = PetscMax(maxr,err / tolr);
      }
      if(tol>0.){
        max = PetscMax(max,err / tol);
      }
    }
    ierr = VecRestoreArrayRead(ts->vatol,&atol);CHKERRQ(ierr);
  } else if (ts->vrtol) {       /* scalar atol, vector rtol */
    const PetscScalar *rtol;
    ierr = VecGetArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);

    for (i=0; i<n; i++) {
      err = PetscAbsScalar(e[i]);
      tola = ts->atol;
      tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      tol  = tola+tolr;
      if(tola>0.){
        maxa = PetscMax(maxa,err / tola);
      }
      if(tolr>0.){
        maxr = PetscMax(maxr,err / tolr);
      }
      if(tol>0.){
        max = PetscMax(max,err / tol);
      }
    }
    ierr = VecRestoreArrayRead(ts->vrtol,&rtol);CHKERRQ(ierr);
  } else {                      /* scalar atol, scalar rtol */

    for (i=0; i<n; i++) {
      err = PetscAbsScalar(e[i]);
      tola = ts->atol;
      tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
      tol  = tola+tolr;
      if(tola>0.){
        maxa = PetscMax(maxa,err / tola);
      }
      if(tolr>0.){
        maxr = PetscMax(maxr,err / tolr);
      }
      if(tol>0.){
        max = PetscMax(max,err / tol);
      }
    }
  }
  ierr = VecRestoreArrayRead(E,&e);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
  err_loc[0] = max;
  err_loc[1] = maxa;
  err_loc[2] = maxr;
  ierr  = MPIU_Allreduce(err_loc,err_glb,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
  gmax   = err_glb[0];
  gmaxa  = err_glb[1];
  gmaxr  = err_glb[2];

  *norm = gmax;
  *norma = gmaxa;
  *normr = gmaxr;
  if (PetscIsInfOrNanScalar(*norm)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norm");
    if (PetscIsInfOrNanScalar(*norma)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in norma");
    if (PetscIsInfOrNanScalar(*normr)) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_FP,"Infinite or not-a-number generated in normr");
  PetscFunctionReturn(0);
}

/*@
   TSErrorWeightedENorm - compute a weighted error norm based on supplied absolute and relative tolerances

   Collective on TS

   Input Arguments:
+  ts - time stepping context
.  E - error vector
.  U - state vector, usually ts->vec_sol
.  Y - state vector, previous time step
-  wnormtype - norm type, either NORM_2 or NORM_INFINITY

   Output Arguments:
.  norm  - weighted norm, a value of 1.0 achieves a balance between absolute and relative tolerances
.  norma - weighted norm, a value of 1.0 means that the error meets the absolute tolerance set by the user
.  normr - weighted norm, a value of 1.0 means that the error meets the relative tolerance set by the user

   Options Database Keys:
.  -ts_adapt_wnormtype <wnormtype> - 2, INFINITY

   Level: developer

.seealso: TSErrorWeightedENormInfinity(), TSErrorWeightedENorm2(), TSErrorWeightedNormInfinity(), TSErrorWeightedNorm2()
@*/
PetscErrorCode TSErrorWeightedENorm(TS ts,Vec E,Vec U,Vec Y,NormType wnormtype,PetscReal *norm,PetscReal *norma,PetscReal *normr)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (wnormtype == NORM_2) {
    ierr = TSErrorWeightedENorm2(ts,E,U,Y,norm,norma,normr);CHKERRQ(ierr);
  } else if(wnormtype == NORM_INFINITY) {
    ierr = TSErrorWeightedENormInfinity(ts,E,U,Y,norm,norma,normr);CHKERRQ(ierr);
  } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
  PetscFunctionReturn(0);
}


/*@
   TSSetCFLTimeLocal - Set the local CFL constraint relative to forward Euler

   Logically Collective on TS

   Input Arguments:
+  ts - time stepping context
-  cfltime - maximum stable time step if using forward Euler (value can be different on each process)

   Note:
   After calling this function, the global CFL time can be obtained by calling TSGetCFLTime()

   Level: intermediate

.seealso: TSGetCFLTime(), TSADAPTCFL
@*/
PetscErrorCode TSSetCFLTimeLocal(TS ts,PetscReal cfltime)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  ts->cfltime_local = cfltime;
  ts->cfltime       = -1.;
  PetscFunctionReturn(0);
}

/*@
   TSGetCFLTime - Get the maximum stable time step according to CFL criteria applied to forward Euler

   Collective on TS

   Input Arguments:
.  ts - time stepping context

   Output Arguments:
.  cfltime - maximum stable time step for forward Euler

   Level: advanced

.seealso: TSSetCFLTimeLocal()
@*/
PetscErrorCode TSGetCFLTime(TS ts,PetscReal *cfltime)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (ts->cfltime < 0) {
    ierr = MPIU_Allreduce(&ts->cfltime_local,&ts->cfltime,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));CHKERRQ(ierr);
  }
  *cfltime = ts->cfltime;
  PetscFunctionReturn(0);
}

/*@
   TSVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu

   Input Parameters:
.  ts   - the TS context.
.  xl   - lower bound.
.  xu   - upper bound.

   Notes:
   If this routine is not called then the lower and upper bounds are set to
   PETSC_NINFINITY and PETSC_INFINITY respectively during SNESSetUp().

   Level: advanced

@*/
PetscErrorCode TSVISetVariableBounds(TS ts, Vec xl, Vec xu)
{
  PetscErrorCode ierr;
  SNES           snes;

  PetscFunctionBegin;
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESVISetVariableBounds(snes,xl,xu);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#if defined(PETSC_HAVE_MATLAB_ENGINE)
#include <mex.h>

typedef struct {char *funcname; mxArray *ctx;} TSMatlabContext;

/*
   TSComputeFunction_Matlab - Calls the function that has been set with
                         TSSetFunctionMatlab().

   Collective on TS

   Input Parameters:
+  snes - the TS context
-  u - input vector

   Output Parameter:
.  y - function vector, as set by TSSetFunction()

   Notes:
   TSComputeFunction() is typically used within nonlinear solvers
   implementations, so most users would not generally call this routine
   themselves.

   Level: developer

.keywords: TS, nonlinear, compute, function

.seealso: TSSetFunction(), TSGetFunction()
*/
PetscErrorCode  TSComputeFunction_Matlab(TS snes,PetscReal time,Vec u,Vec udot,Vec y, void *ctx)
{
  PetscErrorCode  ierr;
  TSMatlabContext *sctx = (TSMatlabContext*)ctx;
  int             nlhs  = 1,nrhs = 7;
  mxArray         *plhs[1],*prhs[7];
  long long int   lx = 0,lxdot = 0,ly = 0,ls = 0;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(snes,TS_CLASSID,1);
  PetscValidHeaderSpecific(u,VEC_CLASSID,3);
  PetscValidHeaderSpecific(udot,VEC_CLASSID,4);
  PetscValidHeaderSpecific(y,VEC_CLASSID,5);
  PetscCheckSameComm(snes,1,u,3);
  PetscCheckSameComm(snes,1,y,5);

  ierr = PetscMemcpy(&ls,&snes,sizeof(snes));CHKERRQ(ierr);
  ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
  ierr = PetscMemcpy(&lxdot,&udot,sizeof(udot));CHKERRQ(ierr);
  ierr = PetscMemcpy(&ly,&y,sizeof(u));CHKERRQ(ierr);

  prhs[0] =  mxCreateDoubleScalar((double)ls);
  prhs[1] =  mxCreateDoubleScalar(time);
  prhs[2] =  mxCreateDoubleScalar((double)lx);
  prhs[3] =  mxCreateDoubleScalar((double)lxdot);
  prhs[4] =  mxCreateDoubleScalar((double)ly);
  prhs[5] =  mxCreateString(sctx->funcname);
  prhs[6] =  sctx->ctx;
  ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSComputeFunctionInternal");CHKERRQ(ierr);
  ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
  mxDestroyArray(prhs[0]);
  mxDestroyArray(prhs[1]);
  mxDestroyArray(prhs[2]);
  mxDestroyArray(prhs[3]);
  mxDestroyArray(prhs[4]);
  mxDestroyArray(prhs[5]);
  mxDestroyArray(plhs[0]);
  PetscFunctionReturn(0);
}

/*
   TSSetFunctionMatlab - Sets the function evaluation routine and function
   vector for use by the TS routines in solving ODEs
   equations from MATLAB. Here the function is a string containing the name of a MATLAB function

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context
-  func - function evaluation routine

   Calling sequence of func:
$    func (TS ts,PetscReal time,Vec u,Vec udot,Vec f,void *ctx);

   Level: beginner

.keywords: TS, nonlinear, set, function

.seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
*/
PetscErrorCode  TSSetFunctionMatlab(TS ts,const char *func,mxArray *ctx)
{
  PetscErrorCode  ierr;
  TSMatlabContext *sctx;

  PetscFunctionBegin;
  /* currently sctx is memory bleed */
  ierr = PetscNew(&sctx);CHKERRQ(ierr);
  ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
  /*
     This should work, but it doesn't
  sctx->ctx = ctx;
  mexMakeArrayPersistent(sctx->ctx);
  */
  sctx->ctx = mxDuplicateArray(ctx);

  ierr = TSSetIFunction(ts,NULL,TSComputeFunction_Matlab,sctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
   TSComputeJacobian_Matlab - Calls the function that has been set with
                         TSSetJacobianMatlab().

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  u - input vector
.  A, B - the matrices
-  ctx - user context

   Level: developer

.keywords: TS, nonlinear, compute, function

.seealso: TSSetFunction(), TSGetFunction()
@*/
PetscErrorCode  TSComputeJacobian_Matlab(TS ts,PetscReal time,Vec u,Vec udot,PetscReal shift,Mat A,Mat B,void *ctx)
{
  PetscErrorCode  ierr;
  TSMatlabContext *sctx = (TSMatlabContext*)ctx;
  int             nlhs  = 2,nrhs = 9;
  mxArray         *plhs[2],*prhs[9];
  long long int   lx = 0,lxdot = 0,lA = 0,ls = 0, lB = 0;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(u,VEC_CLASSID,3);

  /* call Matlab function in ctx with arguments u and y */

  ierr = PetscMemcpy(&ls,&ts,sizeof(ts));CHKERRQ(ierr);
  ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);
  ierr = PetscMemcpy(&lxdot,&udot,sizeof(u));CHKERRQ(ierr);
  ierr = PetscMemcpy(&lA,A,sizeof(u));CHKERRQ(ierr);
  ierr = PetscMemcpy(&lB,B,sizeof(u));CHKERRQ(ierr);

  prhs[0] =  mxCreateDoubleScalar((double)ls);
  prhs[1] =  mxCreateDoubleScalar((double)time);
  prhs[2] =  mxCreateDoubleScalar((double)lx);
  prhs[3] =  mxCreateDoubleScalar((double)lxdot);
  prhs[4] =  mxCreateDoubleScalar((double)shift);
  prhs[5] =  mxCreateDoubleScalar((double)lA);
  prhs[6] =  mxCreateDoubleScalar((double)lB);
  prhs[7] =  mxCreateString(sctx->funcname);
  prhs[8] =  sctx->ctx;
  ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSComputeJacobianInternal");CHKERRQ(ierr);
  ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
  mxDestroyArray(prhs[0]);
  mxDestroyArray(prhs[1]);
  mxDestroyArray(prhs[2]);
  mxDestroyArray(prhs[3]);
  mxDestroyArray(prhs[4]);
  mxDestroyArray(prhs[5]);
  mxDestroyArray(prhs[6]);
  mxDestroyArray(prhs[7]);
  mxDestroyArray(plhs[0]);
  mxDestroyArray(plhs[1]);
  PetscFunctionReturn(0);
}

/*
   TSSetJacobianMatlab - Sets the Jacobian function evaluation routine and two empty Jacobian matrices
   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

   Logically Collective on TS

   Input Parameters:
+  ts - the TS context
.  A,B - Jacobian matrices
.  func - function evaluation routine
-  ctx - user context

   Calling sequence of func:
$    flag = func (TS ts,PetscReal time,Vec u,Vec udot,Mat A,Mat B,void *ctx);

   Level: developer

.keywords: TS, nonlinear, set, function

.seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
*/
PetscErrorCode  TSSetJacobianMatlab(TS ts,Mat A,Mat B,const char *func,mxArray *ctx)
{
  PetscErrorCode  ierr;
  TSMatlabContext *sctx;

  PetscFunctionBegin;
  /* currently sctx is memory bleed */
  ierr = PetscNew(&sctx);CHKERRQ(ierr);
  ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
  /*
     This should work, but it doesn't
  sctx->ctx = ctx;
  mexMakeArrayPersistent(sctx->ctx);
  */
  sctx->ctx = mxDuplicateArray(ctx);

  ierr = TSSetIJacobian(ts,A,B,TSComputeJacobian_Matlab,sctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
   TSMonitor_Matlab - Calls the function that has been set with TSMonitorSetMatlab().

   Collective on TS

.seealso: TSSetFunction(), TSGetFunction()
@*/
PetscErrorCode  TSMonitor_Matlab(TS ts,PetscInt it, PetscReal time,Vec u, void *ctx)
{
  PetscErrorCode  ierr;
  TSMatlabContext *sctx = (TSMatlabContext*)ctx;
  int             nlhs  = 1,nrhs = 6;
  mxArray         *plhs[1],*prhs[6];
  long long int   lx = 0,ls = 0;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(u,VEC_CLASSID,4);

  ierr = PetscMemcpy(&ls,&ts,sizeof(ts));CHKERRQ(ierr);
  ierr = PetscMemcpy(&lx,&u,sizeof(u));CHKERRQ(ierr);

  prhs[0] =  mxCreateDoubleScalar((double)ls);
  prhs[1] =  mxCreateDoubleScalar((double)it);
  prhs[2] =  mxCreateDoubleScalar((double)time);
  prhs[3] =  mxCreateDoubleScalar((double)lx);
  prhs[4] =  mxCreateString(sctx->funcname);
  prhs[5] =  sctx->ctx;
  ierr    =  mexCallMATLAB(nlhs,plhs,nrhs,prhs,"PetscTSMonitorInternal");CHKERRQ(ierr);
  ierr    =  mxGetScalar(plhs[0]);CHKERRQ(ierr);
  mxDestroyArray(prhs[0]);
  mxDestroyArray(prhs[1]);
  mxDestroyArray(prhs[2]);
  mxDestroyArray(prhs[3]);
  mxDestroyArray(prhs[4]);
  mxDestroyArray(plhs[0]);
  PetscFunctionReturn(0);
}

/*
   TSMonitorSetMatlab - Sets the monitor function from Matlab

   Level: developer

.keywords: TS, nonlinear, set, function

.seealso: TSGetFunction(), TSComputeFunction(), TSSetJacobian(), TSSetFunction()
*/
PetscErrorCode  TSMonitorSetMatlab(TS ts,const char *func,mxArray *ctx)
{
  PetscErrorCode  ierr;
  TSMatlabContext *sctx;

  PetscFunctionBegin;
  /* currently sctx is memory bleed */
  ierr = PetscNew(&sctx);CHKERRQ(ierr);
  ierr = PetscStrallocpy(func,&sctx->funcname);CHKERRQ(ierr);
  /*
     This should work, but it doesn't
  sctx->ctx = ctx;
  mexMakeArrayPersistent(sctx->ctx);
  */
  sctx->ctx = mxDuplicateArray(ctx);

  ierr = TSMonitorSet(ts,TSMonitor_Matlab,sctx,NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
#endif

/*@C
   TSMonitorLGSolution - Monitors progress of the TS solvers by plotting each component of the solution vector
       in a time based line graph

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  step - current time-step
.  ptime - current time
.  u - current solution
-  dctx - the TSMonitorLGCtx object that contains all the options for the monitoring, this is created with TSMonitorLGCtxCreate()

   Options Database:
.   -ts_monitor_lg_solution_variables

   Level: intermediate

   Notes: Each process in a parallel run displays its component solutions in a separate window

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGCtxCreate(), TSMonitorLGCtxSetVariableNames(), TSMonitorLGCtxGetVariableNames(),
           TSMonitorLGSetVariableNames(), TSMonitorLGGetVariableNames(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetDisplayVariables(),
           TSMonitorLGCtxSetTransform(), TSMonitorLGSetTransform(), TSMonitorLGError(), TSMonitorLGSNESIterations(), TSMonitorLGKSPIterations(),
           TSMonitorEnvelopeCtxCreate(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxDestroy(), TSMonitorEnvelop()
@*/
PetscErrorCode  TSMonitorLGSolution(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dctx)
{
  PetscErrorCode    ierr;
  TSMonitorLGCtx    ctx = (TSMonitorLGCtx)dctx;
  const PetscScalar *yy;
  Vec               v;

  PetscFunctionBegin;
  if (step < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
  if (!step) {
    PetscDrawAxis axis;
    PetscInt      dim;
    ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
    ierr = PetscDrawAxisSetLabels(axis,"Solution as function of time","Time","Solution");CHKERRQ(ierr);
    if (!ctx->names) {
      PetscBool flg;
      /* user provides names of variables to plot but no names has been set so assume names are integer values */
      ierr = PetscOptionsHasName(((PetscObject)ts)->options,((PetscObject)ts)->prefix,"-ts_monitor_lg_solution_variables",&flg);CHKERRQ(ierr);
      if (flg) {
        PetscInt i,n;
        char     **names;
        ierr = VecGetSize(u,&n);CHKERRQ(ierr);
        ierr = PetscMalloc1(n+1,&names);CHKERRQ(ierr);
        for (i=0; i<n; i++) {
          ierr = PetscMalloc1(5,&names[i]);CHKERRQ(ierr);
          ierr = PetscSNPrintf(names[i],5,"%D",i);CHKERRQ(ierr);
        }
        names[n] = NULL;
        ctx->names = names;
      }
    }
    if (ctx->names && !ctx->displaynames) {
      char      **displaynames;
      PetscBool flg;
      ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
      ierr = PetscMalloc1(dim+1,&displaynames);CHKERRQ(ierr);
      ierr = PetscMemzero(displaynames,(dim+1)*sizeof(char*));CHKERRQ(ierr);
      ierr = PetscOptionsGetStringArray(((PetscObject)ts)->options,((PetscObject)ts)->prefix,"-ts_monitor_lg_solution_variables",displaynames,&dim,&flg);CHKERRQ(ierr);
      if (flg) {
        ierr = TSMonitorLGCtxSetDisplayVariables(ctx,(const char *const *)displaynames);CHKERRQ(ierr);
      }
      ierr = PetscStrArrayDestroy(&displaynames);CHKERRQ(ierr);
    }
    if (ctx->displaynames) {
      ierr = PetscDrawLGSetDimension(ctx->lg,ctx->ndisplayvariables);CHKERRQ(ierr);
      ierr = PetscDrawLGSetLegend(ctx->lg,(const char *const *)ctx->displaynames);CHKERRQ(ierr);
    } else if (ctx->names) {
      ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
      ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
      ierr = PetscDrawLGSetLegend(ctx->lg,(const char *const *)ctx->names);CHKERRQ(ierr);
    } else {
      ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
      ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
    }
    ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
  }

  if (!ctx->transform) v = u;
  else {ierr = (*ctx->transform)(ctx->transformctx,u,&v);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(v,&yy);CHKERRQ(ierr);
  if (ctx->displaynames) {
    PetscInt i;
    for (i=0; i<ctx->ndisplayvariables; i++)
      ctx->displayvalues[i] = PetscRealPart(yy[ctx->displayvariables[i]]);
    ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,ctx->displayvalues);CHKERRQ(ierr);
  } else {
#if defined(PETSC_USE_COMPLEX)
    PetscInt  i,n;
    PetscReal *yreal;
    ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
    ierr = PetscMalloc1(n,&yreal);CHKERRQ(ierr);
    for (i=0; i<n; i++) yreal[i] = PetscRealPart(yy[i]);
    ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yreal);CHKERRQ(ierr);
    ierr = PetscFree(yreal);CHKERRQ(ierr);
#else
    ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yy);CHKERRQ(ierr);
#endif
  }
  ierr = VecRestoreArrayRead(v,&yy);CHKERRQ(ierr);
  if (ctx->transform) {ierr = VecDestroy(&v);CHKERRQ(ierr);}

  if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
    ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
    ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorLGSetVariableNames - Sets the name of each component in the solution vector so that it may be displayed in the plot

   Collective on TS

   Input Parameters:
+  ts - the TS context
-  names - the names of the components, final string must be NULL

   Level: intermediate

   Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables(), TSMonitorLGCtxSetVariableNames()
@*/
PetscErrorCode  TSMonitorLGSetVariableNames(TS ts,const char * const *names)
{
  PetscErrorCode    ierr;
  PetscInt          i;

  PetscFunctionBegin;
  for (i=0; i<ts->numbermonitors; i++) {
    if (ts->monitor[i] == TSMonitorLGSolution) {
      ierr = TSMonitorLGCtxSetVariableNames((TSMonitorLGCtx)ts->monitorcontext[i],names);CHKERRQ(ierr);
      break;
    }
  }
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorLGCtxSetVariableNames - Sets the name of each component in the solution vector so that it may be displayed in the plot

   Collective on TS

   Input Parameters:
+  ts - the TS context
-  names - the names of the components, final string must be NULL

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables(), TSMonitorLGSetVariableNames()
@*/
PetscErrorCode  TSMonitorLGCtxSetVariableNames(TSMonitorLGCtx ctx,const char * const *names)
{
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = PetscStrArrayDestroy(&ctx->names);CHKERRQ(ierr);
  ierr = PetscStrArrayallocpy(names,&ctx->names);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorLGGetVariableNames - Gets the name of each component in the solution vector so that it may be displayed in the plot

   Collective on TS

   Input Parameter:
.  ts - the TS context

   Output Parameter:
.  names - the names of the components, final string must be NULL

   Level: intermediate

   Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables()
@*/
PetscErrorCode  TSMonitorLGGetVariableNames(TS ts,const char *const **names)
{
  PetscInt       i;

  PetscFunctionBegin;
  *names = NULL;
  for (i=0; i<ts->numbermonitors; i++) {
    if (ts->monitor[i] == TSMonitorLGSolution) {
      TSMonitorLGCtx  ctx = (TSMonitorLGCtx) ts->monitorcontext[i];
      *names = (const char *const *)ctx->names;
      break;
    }
  }
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorLGCtxSetDisplayVariables - Sets the variables that are to be display in the monitor

   Collective on TS

   Input Parameters:
+  ctx - the TSMonitorLG context
.  displaynames - the names of the components, final string must be NULL

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames()
@*/
PetscErrorCode  TSMonitorLGCtxSetDisplayVariables(TSMonitorLGCtx ctx,const char * const *displaynames)
{
  PetscInt          j = 0,k;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  if (!ctx->names) PetscFunctionReturn(0);
  ierr = PetscStrArrayDestroy(&ctx->displaynames);CHKERRQ(ierr);
  ierr = PetscStrArrayallocpy(displaynames,&ctx->displaynames);CHKERRQ(ierr);
  while (displaynames[j]) j++;
  ctx->ndisplayvariables = j;
  ierr = PetscMalloc1(ctx->ndisplayvariables,&ctx->displayvariables);CHKERRQ(ierr);
  ierr = PetscMalloc1(ctx->ndisplayvariables,&ctx->displayvalues);CHKERRQ(ierr);
  j = 0;
  while (displaynames[j]) {
    k = 0;
    while (ctx->names[k]) {
      PetscBool flg;
      ierr = PetscStrcmp(displaynames[j],ctx->names[k],&flg);CHKERRQ(ierr);
      if (flg) {
        ctx->displayvariables[j] = k;
        break;
      }
      k++;
    }
    j++;
  }
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorLGSetDisplayVariables - Sets the variables that are to be display in the monitor

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  displaynames - the names of the components, final string must be NULL

   Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames()
@*/
PetscErrorCode  TSMonitorLGSetDisplayVariables(TS ts,const char * const *displaynames)
{
  PetscInt          i;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  for (i=0; i<ts->numbermonitors; i++) {
    if (ts->monitor[i] == TSMonitorLGSolution) {
      ierr = TSMonitorLGCtxSetDisplayVariables((TSMonitorLGCtx)ts->monitorcontext[i],displaynames);CHKERRQ(ierr);
      break;
    }
  }
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorLGSetTransform - Solution vector will be transformed by provided function before being displayed

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  transform - the transform function
.  destroy - function to destroy the optional context
-  ctx - optional context used by transform function

   Notes: If the TS object does not have a TSMonitorLGCtx associated with it then this function is ignored

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames(), TSMonitorLGCtxSetTransform()
@*/
PetscErrorCode  TSMonitorLGSetTransform(TS ts,PetscErrorCode (*transform)(void*,Vec,Vec*),PetscErrorCode (*destroy)(void*),void *tctx)
{
  PetscInt          i;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  for (i=0; i<ts->numbermonitors; i++) {
    if (ts->monitor[i] == TSMonitorLGSolution) {
      ierr = TSMonitorLGCtxSetTransform((TSMonitorLGCtx)ts->monitorcontext[i],transform,destroy,tctx);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorLGCtxSetTransform - Solution vector will be transformed by provided function before being displayed

   Collective on TSLGCtx

   Input Parameters:
+  ts - the TS context
.  transform - the transform function
.  destroy - function to destroy the optional context
-  ctx - optional context used by transform function

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetVariableNames(), TSMonitorLGSetTransform()
@*/
PetscErrorCode  TSMonitorLGCtxSetTransform(TSMonitorLGCtx ctx,PetscErrorCode (*transform)(void*,Vec,Vec*),PetscErrorCode (*destroy)(void*),void *tctx)
{
  PetscFunctionBegin;
  ctx->transform    = transform;
  ctx->transformdestroy = destroy;
  ctx->transformctx = tctx;
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorLGError - Monitors progress of the TS solvers by plotting each component of the error
       in a time based line graph

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  step - current time-step
.  ptime - current time
.  u - current solution
-  dctx - TSMonitorLGCtx object created with TSMonitorLGCtxCreate()

   Level: intermediate

   Notes: Each process in a parallel run displays its component errors in a separate window

   The user must provide the solution using TSSetSolutionFunction() to use this monitor.

   Options Database Keys:
.  -ts_monitor_lg_error - create a graphical monitor of error history

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSSetSolutionFunction()
@*/
PetscErrorCode  TSMonitorLGError(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dummy)
{
  PetscErrorCode    ierr;
  TSMonitorLGCtx    ctx = (TSMonitorLGCtx)dummy;
  const PetscScalar *yy;
  Vec               y;

  PetscFunctionBegin;
  if (!step) {
    PetscDrawAxis axis;
    PetscInt      dim;
    ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
    ierr = PetscDrawAxisSetLabels(axis,"Error in solution as function of time","Time","Error");CHKERRQ(ierr);
    ierr = VecGetLocalSize(u,&dim);CHKERRQ(ierr);
    ierr = PetscDrawLGSetDimension(ctx->lg,dim);CHKERRQ(ierr);
    ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
  }
  ierr = VecDuplicate(u,&y);CHKERRQ(ierr);
  ierr = TSComputeSolutionFunction(ts,ptime,y);CHKERRQ(ierr);
  ierr = VecAXPY(y,-1.0,u);CHKERRQ(ierr);
  ierr = VecGetArrayRead(y,&yy);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
  {
    PetscReal *yreal;
    PetscInt  i,n;
    ierr = VecGetLocalSize(y,&n);CHKERRQ(ierr);
    ierr = PetscMalloc1(n,&yreal);CHKERRQ(ierr);
    for (i=0; i<n; i++) yreal[i] = PetscRealPart(yy[i]);
    ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yreal);CHKERRQ(ierr);
    ierr = PetscFree(yreal);CHKERRQ(ierr);
  }
#else
  ierr = PetscDrawLGAddCommonPoint(ctx->lg,ptime,yy);CHKERRQ(ierr);
#endif
  ierr = VecRestoreArrayRead(y,&yy);CHKERRQ(ierr);
  ierr = VecDestroy(&y);CHKERRQ(ierr);
  if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
    ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
    ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

PetscErrorCode TSMonitorLGSNESIterations(TS ts,PetscInt n,PetscReal ptime,Vec v,void *monctx)
{
  TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
  PetscReal      x   = ptime,y;
  PetscErrorCode ierr;
  PetscInt       its;

  PetscFunctionBegin;
  if (n < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
  if (!n) {
    PetscDrawAxis axis;
    ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
    ierr = PetscDrawAxisSetLabels(axis,"Nonlinear iterations as function of time","Time","SNES Iterations");CHKERRQ(ierr);
    ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
    ctx->snes_its = 0;
  }
  ierr = TSGetSNESIterations(ts,&its);CHKERRQ(ierr);
  y    = its - ctx->snes_its;
  ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
  if (((ctx->howoften > 0) && (!(n % ctx->howoften)) && (n > -1)) || ((ctx->howoften == -1) && (n == -1))) {
    ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
    ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
  }
  ctx->snes_its = its;
  PetscFunctionReturn(0);
}

PetscErrorCode TSMonitorLGKSPIterations(TS ts,PetscInt n,PetscReal ptime,Vec v,void *monctx)
{
  TSMonitorLGCtx ctx = (TSMonitorLGCtx) monctx;
  PetscReal      x   = ptime,y;
  PetscErrorCode ierr;
  PetscInt       its;

  PetscFunctionBegin;
  if (n < 0) PetscFunctionReturn(0); /* -1 indicates interpolated solution */
  if (!n) {
    PetscDrawAxis axis;
    ierr = PetscDrawLGGetAxis(ctx->lg,&axis);CHKERRQ(ierr);
    ierr = PetscDrawAxisSetLabels(axis,"Linear iterations as function of time","Time","KSP Iterations");CHKERRQ(ierr);
    ierr = PetscDrawLGReset(ctx->lg);CHKERRQ(ierr);
    ctx->ksp_its = 0;
  }
  ierr = TSGetKSPIterations(ts,&its);CHKERRQ(ierr);
  y    = its - ctx->ksp_its;
  ierr = PetscDrawLGAddPoint(ctx->lg,&x,&y);CHKERRQ(ierr);
  if (((ctx->howoften > 0) && (!(n % ctx->howoften)) && (n > -1)) || ((ctx->howoften == -1) && (n == -1))) {
    ierr = PetscDrawLGDraw(ctx->lg);CHKERRQ(ierr);
    ierr = PetscDrawLGSave(ctx->lg);CHKERRQ(ierr);
  }
  ctx->ksp_its = its;
  PetscFunctionReturn(0);
}

/*@
   TSComputeLinearStability - computes the linear stability function at a point

   Collective on TS and Vec

   Input Parameters:
+  ts - the TS context
-  xr,xi - real and imaginary part of input arguments

   Output Parameters:
.  yr,yi - real and imaginary part of function value

   Level: developer

.keywords: TS, compute

.seealso: TSSetRHSFunction(), TSComputeIFunction()
@*/
PetscErrorCode TSComputeLinearStability(TS ts,PetscReal xr,PetscReal xi,PetscReal *yr,PetscReal *yi)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  if (!ts->ops->linearstability) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Linearized stability function not provided for this method");
  ierr = (*ts->ops->linearstability)(ts,xr,xi,yr,yi);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------------*/
/*@C
   TSMonitorEnvelopeCtxCreate - Creates a context for use with TSMonitorEnvelope()

   Collective on TS

   Input Parameters:
.  ts  - the ODE solver object

   Output Parameter:
.  ctx - the context

   Level: intermediate

.keywords: TS, monitor, line graph, residual, seealso

.seealso: TSMonitorLGTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError()

@*/
PetscErrorCode  TSMonitorEnvelopeCtxCreate(TS ts,TSMonitorEnvelopeCtx *ctx)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscNew(ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorEnvelope - Monitors the maximum and minimum value of each component of the solution

   Collective on TS

   Input Parameters:
+  ts - the TS context
.  step - current time-step
.  ptime - current time
.  u  - current solution
-  dctx - the envelope context

   Options Database:
.  -ts_monitor_envelope

   Level: intermediate

   Notes: after a solve you can use TSMonitorEnvelopeGetBounds() to access the envelope

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorEnvelopeGetBounds(), TSMonitorEnvelopeCtxCreate()
@*/
PetscErrorCode  TSMonitorEnvelope(TS ts,PetscInt step,PetscReal ptime,Vec u,void *dctx)
{
  PetscErrorCode       ierr;
  TSMonitorEnvelopeCtx ctx = (TSMonitorEnvelopeCtx)dctx;

  PetscFunctionBegin;
  if (!ctx->max) {
    ierr = VecDuplicate(u,&ctx->max);CHKERRQ(ierr);
    ierr = VecDuplicate(u,&ctx->min);CHKERRQ(ierr);
    ierr = VecCopy(u,ctx->max);CHKERRQ(ierr);
    ierr = VecCopy(u,ctx->min);CHKERRQ(ierr);
  } else {
    ierr = VecPointwiseMax(ctx->max,u,ctx->max);CHKERRQ(ierr);
    ierr = VecPointwiseMin(ctx->min,u,ctx->min);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorEnvelopeGetBounds - Gets the bounds for the components of the solution

   Collective on TS

   Input Parameter:
.  ts - the TS context

   Output Parameter:
+  max - the maximum values
-  min - the minimum values

   Notes: If the TS does not have a TSMonitorEnvelopeCtx associated with it then this function is ignored

   Level: intermediate

.keywords: TS,  vector, monitor, view

.seealso: TSMonitorSet(), TSMonitorDefault(), VecView(), TSMonitorLGSetDisplayVariables()
@*/
PetscErrorCode  TSMonitorEnvelopeGetBounds(TS ts,Vec *max,Vec *min)
{
  PetscInt i;

  PetscFunctionBegin;
  if (max) *max = NULL;
  if (min) *min = NULL;
  for (i=0; i<ts->numbermonitors; i++) {
    if (ts->monitor[i] == TSMonitorEnvelope) {
      TSMonitorEnvelopeCtx  ctx = (TSMonitorEnvelopeCtx) ts->monitorcontext[i];
      if (max) *max = ctx->max;
      if (min) *min = ctx->min;
      break;
    }
  }
  PetscFunctionReturn(0);
}

/*@C
   TSMonitorEnvelopeCtxDestroy - Destroys a context that was created  with TSMonitorEnvelopeCtxCreate().

   Collective on TSMonitorEnvelopeCtx

   Input Parameter:
.  ctx - the monitor context

   Level: intermediate

.keywords: TS, monitor, line graph, destroy

.seealso: TSMonitorLGCtxCreate(),  TSMonitorSet(), TSMonitorLGTimeStep()
@*/
PetscErrorCode  TSMonitorEnvelopeCtxDestroy(TSMonitorEnvelopeCtx *ctx)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecDestroy(&(*ctx)->min);CHKERRQ(ierr);
  ierr = VecDestroy(&(*ctx)->max);CHKERRQ(ierr);
  ierr = PetscFree(*ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   TSRollBack - Rolls back one time step

   Collective on TS

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Level: advanced

.keywords: TS, timestep, rollback

.seealso: TSCreate(), TSSetUp(), TSDestroy(), TSSolve(), TSSetPreStep(), TSSetPreStage(), TSInterpolate()
@*/
PetscErrorCode  TSRollBack(TS ts)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  if (ts->steprollback) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONGSTATE,"TSRollBack already called");
  if (!ts->ops->rollback) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRollBack not implemented for type '%s'",((PetscObject)ts)->type_name);
  ierr = (*ts->ops->rollback)(ts);CHKERRQ(ierr);
  ts->time_step = ts->ptime - ts->ptime_prev;
  ts->ptime = ts->ptime_prev;
  ts->ptime_prev = ts->ptime_prev_rollback;
  ts->steps--;
  ierr = TSPostEvaluate(ts);CHKERRQ(ierr);
  ts->steprollback = PETSC_TRUE;
  PetscFunctionReturn(0);
}

/*@
   TSGetStages - Get the number of stages and stage values

   Input Parameter:
.  ts - the TS context obtained from TSCreate()

   Level: advanced

.keywords: TS, getstages

.seealso: TSCreate()
@*/
PetscErrorCode  TSGetStages(TS ts,PetscInt *ns,Vec **Y)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  PetscValidPointer(ns,2);

  if (!ts->ops->getstages) *ns=0;
  else {
    ierr = (*ts->ops->getstages)(ts,ns,Y);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@C
  TSComputeIJacobianDefaultColor - Computes the Jacobian using finite differences and coloring to exploit matrix sparsity.

  Collective on SNES

  Input Parameters:
+ ts - the TS context
. t - current timestep
. U - state vector
. Udot - time derivative of state vector
. shift - shift to apply, see note below
- ctx - an optional user context

  Output Parameters:
+ J - Jacobian matrix (not altered in this routine)
- B - newly computed Jacobian matrix to use with preconditioner (generally the same as J)

  Level: intermediate

  Notes:
  If F(t,U,Udot)=0 is the DAE, the required Jacobian is

  dF/dU + shift*dF/dUdot

  Most users should not need to explicitly call this routine, as it
  is used internally within the nonlinear solvers.

  This will first try to get the coloring from the DM.  If the DM type has no coloring
  routine, then it will try to get the coloring from the matrix.  This requires that the
  matrix have nonzero entries precomputed.

.keywords: TS, finite differences, Jacobian, coloring, sparse
.seealso: TSSetIJacobian(), MatFDColoringCreate(), MatFDColoringSetFunction()
@*/
PetscErrorCode TSComputeIJacobianDefaultColor(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat J,Mat B,void *ctx)
{
  SNES           snes;
  MatFDColoring  color;
  PetscBool      hascolor, matcolor = PETSC_FALSE;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscOptionsGetBool(((PetscObject)ts)->options,((PetscObject) ts)->prefix, "-ts_fd_color_use_mat", &matcolor, NULL);CHKERRQ(ierr);
  ierr = PetscObjectQuery((PetscObject) B, "TSMatFDColoring", (PetscObject *) &color);CHKERRQ(ierr);
  if (!color) {
    DM         dm;
    ISColoring iscoloring;

    ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
    ierr = DMHasColoring(dm, &hascolor);CHKERRQ(ierr);
    if (hascolor && !matcolor) {
      ierr = DMCreateColoring(dm, IS_COLORING_GLOBAL, &iscoloring);CHKERRQ(ierr);
      ierr = MatFDColoringCreate(B, iscoloring, &color);CHKERRQ(ierr);
      ierr = MatFDColoringSetFunction(color, (PetscErrorCode (*)(void)) SNESTSFormFunction, (void *) ts);CHKERRQ(ierr);
      ierr = MatFDColoringSetFromOptions(color);CHKERRQ(ierr);
      ierr = MatFDColoringSetUp(B, iscoloring, color);CHKERRQ(ierr);
      ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
    } else {
      MatColoring mc;

      ierr = MatColoringCreate(B, &mc);CHKERRQ(ierr);
      ierr = MatColoringSetDistance(mc, 2);CHKERRQ(ierr);
      ierr = MatColoringSetType(mc, MATCOLORINGSL);CHKERRQ(ierr);
      ierr = MatColoringSetFromOptions(mc);CHKERRQ(ierr);
      ierr = MatColoringApply(mc, &iscoloring);CHKERRQ(ierr);
      ierr = MatColoringDestroy(&mc);CHKERRQ(ierr);
      ierr = MatFDColoringCreate(B, iscoloring, &color);CHKERRQ(ierr);
      ierr = MatFDColoringSetFunction(color, (PetscErrorCode (*)(void)) SNESTSFormFunction, (void *) ts);CHKERRQ(ierr);
      ierr = MatFDColoringSetFromOptions(color);CHKERRQ(ierr);
      ierr = MatFDColoringSetUp(B, iscoloring, color);CHKERRQ(ierr);
      ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
    }
    ierr = PetscObjectCompose((PetscObject) B, "TSMatFDColoring", (PetscObject) color);CHKERRQ(ierr);
    ierr = PetscObjectDereference((PetscObject) color);CHKERRQ(ierr);
  }
  ierr = TSGetSNES(ts, &snes);CHKERRQ(ierr);
  ierr = MatFDColoringApply(B, color, U, snes);CHKERRQ(ierr);
  if (J != B) {
    ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@
    TSSetFunctionDomainError - Set the function testing if the current state vector is valid

    Input Parameters:
    ts - the TS context
    func - function called within TSFunctionDomainError

    Level: intermediate

.keywords: TS, state, domain
.seealso: TSAdaptCheckStage(), TSFunctionDomainError()
@*/

PetscErrorCode TSSetFunctionDomainError(TS ts, PetscErrorCode (*func)(TS,PetscReal,Vec,PetscBool*))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID,1);
  ts->functiondomainerror = func;
  PetscFunctionReturn(0);
}

/*@
    TSFunctionDomainError - Check if the current state is valid

    Input Parameters:
    ts - the TS context
    stagetime - time of the simulation
    Y - state vector to check.

    Output Parameter:
    accept - Set to PETSC_FALSE if the current state vector is valid.

    Note:
    This function should be used to ensure the state is in a valid part of the space.
    For example, one can ensure here all values are positive.

    Level: advanced
@*/
PetscErrorCode TSFunctionDomainError(TS ts,PetscReal stagetime,Vec Y,PetscBool* accept)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  *accept = PETSC_TRUE;
  if (ts->functiondomainerror) {
    PetscStackCallStandard((*ts->functiondomainerror),(ts,stagetime,Y,accept));
  }
  PetscFunctionReturn(0);
}

/*@C
  TSClone - This function clones a time step object.

  Collective on MPI_Comm

  Input Parameter:
. tsin    - The input TS

  Output Parameter:
. tsout   - The output TS (cloned)

  Notes:
  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.

  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);

  Level: developer

.keywords: TS, clone
.seealso: TSCreate(), TSSetType(), TSSetUp(), TSDestroy(), TSSetProblemType()
@*/
PetscErrorCode  TSClone(TS tsin, TS *tsout)
{
  TS             t;
  PetscErrorCode ierr;
  SNES           snes_start;
  DM             dm;
  TSType         type;

  PetscFunctionBegin;
  PetscValidPointer(tsin,1);
  *tsout = NULL;

  ierr = PetscHeaderCreate(t, TS_CLASSID, "TS", "Time stepping", "TS", PetscObjectComm((PetscObject)tsin), TSDestroy, TSView);CHKERRQ(ierr);

  /* General TS description */
  t->numbermonitors    = 0;
  t->setupcalled       = 0;
  t->ksp_its           = 0;
  t->snes_its          = 0;
  t->nwork             = 0;
  t->rhsjacobian.time  = -1e20;
  t->rhsjacobian.scale = 1.;
  t->ijacobian.shift   = 1.;

  ierr = TSGetSNES(tsin,&snes_start);CHKERRQ(ierr);
  ierr = TSSetSNES(t,snes_start);CHKERRQ(ierr);

  ierr = TSGetDM(tsin,&dm);CHKERRQ(ierr);
  ierr = TSSetDM(t,dm);CHKERRQ(ierr);

  t->adapt = tsin->adapt;
  ierr = PetscObjectReference((PetscObject)t->adapt);CHKERRQ(ierr);

  t->trajectory = tsin->trajectory;
  ierr = PetscObjectReference((PetscObject)t->trajectory);CHKERRQ(ierr);

  t->event = tsin->event;
  if (t->event) t->event->refct++;

  t->problem_type      = tsin->problem_type;
  t->ptime             = tsin->ptime;
  t->ptime_prev        = tsin->ptime_prev;
  t->time_step         = tsin->time_step;
  t->max_time          = tsin->max_time;
  t->steps             = tsin->steps;
  t->max_steps         = tsin->max_steps;
  t->equation_type     = tsin->equation_type;
  t->atol              = tsin->atol;
  t->rtol              = tsin->rtol;
  t->max_snes_failures = tsin->max_snes_failures;
  t->max_reject        = tsin->max_reject;
  t->errorifstepfailed = tsin->errorifstepfailed;

  ierr = TSGetType(tsin,&type);CHKERRQ(ierr);
  ierr = TSSetType(t,type);CHKERRQ(ierr);

  t->vec_sol           = NULL;

  t->cfltime          = tsin->cfltime;
  t->cfltime_local    = tsin->cfltime_local;
  t->exact_final_time = tsin->exact_final_time;

  ierr = PetscMemcpy(t->ops,tsin->ops,sizeof(struct _TSOps));CHKERRQ(ierr);

  if (((PetscObject)tsin)->fortran_func_pointers) {
    PetscInt i;
    ierr = PetscMalloc((10)*sizeof(void(*)(void)),&((PetscObject)t)->fortran_func_pointers);CHKERRQ(ierr);
    for (i=0; i<10; i++) {
      ((PetscObject)t)->fortran_func_pointers[i] = ((PetscObject)tsin)->fortran_func_pointers[i];
    }
  }
  *tsout = t;
  PetscFunctionReturn(0);
}