snes/interface/snesut.c

#include <petsc/private/snesimpl.h>       /*I   "petsc/private/snesimpl.h"   I*/
#include <petscdm.h>
#include <petscsection.h>
#include <petscblaslapack.h>

/*@C
   SNESMonitorSolution - Monitors progress of the SNES solvers by calling
   VecView() for the approximate solution at each iteration.

   Collective on SNES

   Input Parameters:
+  snes - the SNES context
.  its - iteration number
.  fgnorm - 2-norm of residual
-  dummy -  a viewer

   Options Database Keys:
.  -snes_monitor_solution [ascii binary draw][:filename][:viewer format] - plots solution at each iteration

   Level: intermediate

.seealso: SNESMonitorSet(), SNESMonitorDefault(), VecView()
@*/
PetscErrorCode  SNESMonitorSolution(SNES snes,PetscInt its,PetscReal fgnorm,PetscViewerAndFormat *vf)
{
  PetscErrorCode ierr;
  Vec            x;
  PetscViewer    viewer = vf->viewer;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
  ierr = SNESGetSolution(snes,&x);CHKERRQ(ierr);
  ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
  ierr = VecView(x,viewer);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   SNESMonitorResidual - Monitors progress of the SNES solvers by calling
   VecView() for the residual at each iteration.

   Collective on SNES

   Input Parameters:
+  snes - the SNES context
.  its - iteration number
.  fgnorm - 2-norm of residual
-  dummy -  a viewer

   Options Database Keys:
.  -snes_monitor_residual [ascii binary draw][:filename][:viewer format] - plots residual (not its norm) at each iteration

   Level: intermediate

.seealso: SNESMonitorSet(), SNESMonitorDefault(), VecView()
@*/
PetscErrorCode  SNESMonitorResidual(SNES snes,PetscInt its,PetscReal fgnorm,PetscViewerAndFormat *vf)
{
  PetscErrorCode ierr;
  Vec            x;
  PetscViewer    viewer = vf->viewer;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
  ierr = SNESGetFunction(snes,&x,0,0);CHKERRQ(ierr);
  ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
  ierr = VecView(x,viewer);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   SNESMonitorSolutionUpdate - Monitors progress of the SNES solvers by calling
   VecView() for the UPDATE to the solution at each iteration.

   Collective on SNES

   Input Parameters:
+  snes - the SNES context
.  its - iteration number
.  fgnorm - 2-norm of residual
-  dummy - a viewer

   Options Database Keys:
.  -snes_monitor_solution_update [ascii binary draw][:filename][:viewer format] - plots update to solution at each iteration

   Level: intermediate

.seealso: SNESMonitorSet(), SNESMonitorDefault(), VecView()
@*/
PetscErrorCode  SNESMonitorSolutionUpdate(SNES snes,PetscInt its,PetscReal fgnorm,PetscViewerAndFormat *vf)
{
  PetscErrorCode ierr;
  Vec            x;
  PetscViewer    viewer = vf->viewer;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
  ierr = SNESGetSolutionUpdate(snes,&x);CHKERRQ(ierr);
  ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
  ierr = VecView(x,viewer);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   KSPMonitorSNES - Print the residual norm of the nonlinear function at each iteration of the linear iterative solver.

   Collective on KSP

   Input Parameters:
+  ksp   - iterative context
.  n     - iteration number
.  rnorm - 2-norm (preconditioned) residual value (may be estimated).
-  dummy - unused monitor context

   Level: intermediate

.seealso: KSPMonitorSet(), KSPMonitorTrueResidualNorm(), KSPMonitorLGResidualNormCreate()
@*/
PetscErrorCode  KSPMonitorSNES(KSP ksp,PetscInt n,PetscReal rnorm,void *dummy)
{
  PetscErrorCode ierr;
  PetscViewer    viewer;
  SNES           snes = (SNES) dummy;
  Vec            snes_solution,work1,work2;
  PetscReal      snorm;

  PetscFunctionBegin;
  ierr = SNESGetSolution(snes,&snes_solution);CHKERRQ(ierr);
  ierr = VecDuplicate(snes_solution,&work1);CHKERRQ(ierr);
  ierr = VecDuplicate(snes_solution,&work2);CHKERRQ(ierr);
  ierr = KSPBuildSolution(ksp,work1,NULL);CHKERRQ(ierr);
  ierr = VecAYPX(work1,-1.0,snes_solution);CHKERRQ(ierr);
  ierr = SNESComputeFunction(snes,work1,work2);CHKERRQ(ierr);
  ierr = VecNorm(work2,NORM_2,&snorm);CHKERRQ(ierr);
  ierr = VecDestroy(&work1);CHKERRQ(ierr);
  ierr = VecDestroy(&work2);CHKERRQ(ierr);

  ierr = PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)ksp),&viewer);CHKERRQ(ierr);
  ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)ksp)->tablevel);CHKERRQ(ierr);
  if (n == 0 && ((PetscObject)ksp)->prefix) {
    ierr = PetscViewerASCIIPrintf(viewer,"  Residual norms for %s solve.\n",((PetscObject)ksp)->prefix);CHKERRQ(ierr);
  }
  ierr = PetscViewerASCIIPrintf(viewer,"%3D SNES Residual norm %5.3e KSP Residual norm %5.3e \n",n,(double)snorm,(double)rnorm);CHKERRQ(ierr);
  ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)ksp)->tablevel);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#include <petscdraw.h>

/*@C
   KSPMonitorSNESLGResidualNormCreate - Creates a line graph context for use with
   KSP to monitor convergence of preconditioned residual norms.

   Collective on KSP

   Input Parameters:
+  comm - communicator context
.  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

   Output Parameter:
.  draw - the drawing context

   Options Database Key:
.  -ksp_monitor_lg_residualnorm - Sets line graph monitor

   Notes:
   Use KSPMonitorSNESLGResidualNormDestroy() to destroy this line graph; do not use PetscDrawLGDestroy().

   Level: intermediate

.seealso: KSPMonitorSNESLGResidualNormDestroy(), KSPMonitorSet(), KSPMonitorSNESLGTrueResidualCreate()
@*/
PetscErrorCode  KSPMonitorSNESLGResidualNormCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscObject **objs)
{
  PetscDraw      draw;
  PetscErrorCode ierr;
  PetscDrawAxis  axis;
  PetscDrawLG    lg;
  const char     *names[] = {"Linear residual","Nonlinear residual"};

  PetscFunctionBegin;
  ierr = PetscDrawCreate(comm,host,label,x,y,m,n,&draw);CHKERRQ(ierr);
  ierr = PetscDrawSetFromOptions(draw);CHKERRQ(ierr);
  ierr = PetscDrawLGCreate(draw,2,&lg);CHKERRQ(ierr);
  ierr = PetscDrawLGSetLegend(lg,names);CHKERRQ(ierr);
  ierr = PetscDrawLGSetFromOptions(lg);CHKERRQ(ierr);
  ierr = PetscDrawLGGetAxis(lg,&axis);CHKERRQ(ierr);
  ierr = PetscDrawAxisSetLabels(axis,"Convergence of Residual Norm","Iteration","Residual Norm");CHKERRQ(ierr);
  ierr = PetscDrawDestroy(&draw);CHKERRQ(ierr);

  ierr = PetscMalloc1(2,objs);CHKERRQ(ierr);
  (*objs)[1] = (PetscObject)lg;
  PetscFunctionReturn(0);
}

PetscErrorCode  KSPMonitorSNESLGResidualNorm(KSP ksp,PetscInt n,PetscReal rnorm,PetscObject *objs)
{
  SNES           snes = (SNES) objs[0];
  PetscDrawLG    lg   = (PetscDrawLG) objs[1];
  PetscErrorCode ierr;
  PetscReal      y[2];
  Vec            snes_solution,work1,work2;

  PetscFunctionBegin;
  if (rnorm > 0.0) y[0] = PetscLog10Real(rnorm);
  else y[0] = -15.0;

  ierr = SNESGetSolution(snes,&snes_solution);CHKERRQ(ierr);
  ierr = VecDuplicate(snes_solution,&work1);CHKERRQ(ierr);
  ierr = VecDuplicate(snes_solution,&work2);CHKERRQ(ierr);
  ierr = KSPBuildSolution(ksp,work1,NULL);CHKERRQ(ierr);
  ierr = VecAYPX(work1,-1.0,snes_solution);CHKERRQ(ierr);
  ierr = SNESComputeFunction(snes,work1,work2);CHKERRQ(ierr);
  ierr = VecNorm(work2,NORM_2,y+1);CHKERRQ(ierr);
  if (y[1] > 0.0) y[1] = PetscLog10Real(y[1]);
  else y[1] = -15.0;
  ierr = VecDestroy(&work1);CHKERRQ(ierr);
  ierr = VecDestroy(&work2);CHKERRQ(ierr);

  ierr = PetscDrawLGAddPoint(lg,NULL,y);CHKERRQ(ierr);
  if (n < 20 || !(n % 5) || snes->reason) {
    ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);
    ierr = PetscDrawLGSave(lg);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*@
   KSPMonitorSNESLGResidualNormDestroy - Destroys a line graph context that was created
   with KSPMonitorSNESLGResidualNormCreate().

   Collective on KSP

   Input Parameter:
.  draw - the drawing context

   Level: intermediate

.seealso: KSPMonitorSNESLGResidualNormCreate(), KSPMonitorSNESLGTrueResidualDestroy(), KSPMonitorSet()
@*/
PetscErrorCode  KSPMonitorSNESLGResidualNormDestroy(PetscObject **objs)
{
  PetscErrorCode ierr;
  PetscDrawLG    lg = (PetscDrawLG) (*objs)[1];

  PetscFunctionBegin;
  ierr = PetscDrawLGDestroy(&lg);CHKERRQ(ierr);
  ierr = PetscFree(*objs);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   SNESMonitorDefault - Monitors progress of the SNES solvers (default).

   Collective on SNES

   Input Parameters:
+  snes - the SNES context
.  its - iteration number
.  fgnorm - 2-norm of residual
-  vf - viewer and format structure

   Notes:
   This routine prints the residual norm at each iteration.

   Level: intermediate

.seealso: SNESMonitorSet(), SNESMonitorSolution()
@*/
PetscErrorCode  SNESMonitorDefault(SNES snes,PetscInt its,PetscReal fgnorm,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)snes)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"%3D SNES Function norm %14.12e \n",its,(double)fgnorm);CHKERRQ(ierr);
  ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   SNESMonitorScaling - Monitors the largest value in each row of the Jacobian.

   Collective on SNES

   Input Parameters:
+  snes - the SNES context
.  its - iteration number
.  fgnorm - 2-norm of residual
-  vf - viewer and format structure

   Notes:
   This routine prints the largest value in each row of the Jacobian

   Level: intermediate

.seealso: SNESMonitorSet(), SNESMonitorSolution()
@*/
PetscErrorCode  SNESMonitorScaling(SNES snes,PetscInt its,PetscReal fgnorm,PetscViewerAndFormat *vf)
{
  PetscErrorCode ierr;
  PetscViewer    viewer = vf->viewer;
  KSP            ksp;
  Mat            J;
  Vec            v;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
  ierr = SNESGetKSP(snes,&ksp);CHKERRQ(ierr);
  ierr = KSPGetOperators(ksp,&J,NULL);CHKERRQ(ierr);
  ierr = MatCreateVecs(J,&v,NULL);CHKERRQ(ierr);
  ierr = MatGetRowMaxAbs(J,v,NULL);CHKERRQ(ierr);
  ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
  ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"%3D SNES Jacobian maximum row entries \n");CHKERRQ(ierr);
  ierr = VecView(v,viewer);CHKERRQ(ierr);
  ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  ierr = VecDestroy(&v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode SNESMonitorJacUpdateSpectrum(SNES snes,PetscInt it,PetscReal fnorm,PetscViewerAndFormat *vf)
{
#if defined(PETSC_HAVE_ESSL)
  SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_SUP,"GEEV - No support for ESSL Lapack Routines");
#else
  Vec            X;
  Mat            J,dJ,dJdense;
  PetscErrorCode ierr;
  PetscErrorCode (*func)(SNES,Vec,Mat,Mat,void*);
  PetscInt       n,i;
  PetscBLASInt   nb,lwork;
  PetscReal      *eigr,*eigi;
  PetscScalar    *work;
  PetscScalar    *a;

  PetscFunctionBegin;
  if (it == 0) PetscFunctionReturn(0);
  /* create the difference between the current update and the current jacobian */
  ierr = SNESGetSolution(snes,&X);CHKERRQ(ierr);
  ierr = SNESGetJacobian(snes,NULL,&J,&func,NULL);CHKERRQ(ierr);
  ierr = MatDuplicate(J,MAT_COPY_VALUES,&dJ);CHKERRQ(ierr);
  ierr = SNESComputeJacobian(snes,X,dJ,dJ);CHKERRQ(ierr);
  ierr = MatAXPY(dJ,-1.0,J,SAME_NONZERO_PATTERN);CHKERRQ(ierr);

  /* compute the spectrum directly */
  ierr  = MatConvert(dJ,MATSEQDENSE,MAT_INITIAL_MATRIX,&dJdense);CHKERRQ(ierr);
  ierr  = MatGetSize(dJ,&n,NULL);CHKERRQ(ierr);
  ierr  = PetscBLASIntCast(n,&nb);CHKERRQ(ierr);
  lwork = 3*nb;
  ierr  = PetscMalloc1(n,&eigr);CHKERRQ(ierr);
  ierr  = PetscMalloc1(n,&eigi);CHKERRQ(ierr);
  ierr  = PetscMalloc1(lwork,&work);CHKERRQ(ierr);
  ierr  = MatDenseGetArray(dJdense,&a);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
  {
    PetscBLASInt lierr;
    ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
    PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","N",&nb,a,&nb,eigr,eigi,NULL,&nb,NULL,&nb,work,&lwork,&lierr));
    if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"geev() error %d",lierr);
    ierr = PetscFPTrapPop();CHKERRQ(ierr);
  }
#else
  SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not coded for complex");
#endif
  ierr = PetscPrintf(PetscObjectComm((PetscObject)snes),"Eigenvalues of J_%d - J_%d:\n",it,it-1);CHKERRQ(ierr);
  for (i=0;i<n;i++) {
    ierr = PetscPrintf(PetscObjectComm((PetscObject)snes),"%5d: %20.5g + %20.5gi\n",i,(double)eigr[i],(double)eigi[i]);CHKERRQ(ierr);
  }
  ierr = MatDenseRestoreArray(dJdense,&a);CHKERRQ(ierr);
  ierr = MatDestroy(&dJ);CHKERRQ(ierr);
  ierr = MatDestroy(&dJdense);CHKERRQ(ierr);
  ierr = PetscFree(eigr);CHKERRQ(ierr);
  ierr = PetscFree(eigi);CHKERRQ(ierr);
  ierr = PetscFree(work);CHKERRQ(ierr);
  PetscFunctionReturn(0);
#endif
}

PETSC_INTERN PetscErrorCode  SNESMonitorRange_Private(SNES,PetscInt,PetscReal*);

PetscErrorCode  SNESMonitorRange_Private(SNES snes,PetscInt it,PetscReal *per)
{
  PetscErrorCode ierr;
  Vec            resid;
  PetscReal      rmax,pwork;
  PetscInt       i,n,N;
  PetscScalar    *r;

  PetscFunctionBegin;
  ierr  = SNESGetFunction(snes,&resid,0,0);CHKERRQ(ierr);
  ierr  = VecNorm(resid,NORM_INFINITY,&rmax);CHKERRQ(ierr);
  ierr  = VecGetLocalSize(resid,&n);CHKERRQ(ierr);
  ierr  = VecGetSize(resid,&N);CHKERRQ(ierr);
  ierr  = VecGetArray(resid,&r);CHKERRQ(ierr);
  pwork = 0.0;
  for (i=0; i<n; i++) {
    pwork += (PetscAbsScalar(r[i]) > .20*rmax);
  }
  ierr = MPIU_Allreduce(&pwork,per,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)snes));CHKERRQ(ierr);
  ierr = VecRestoreArray(resid,&r);CHKERRQ(ierr);
  *per = *per/N;
  PetscFunctionReturn(0);
}

/*@C
   SNESMonitorRange - Prints the percentage of residual elements that are more then 10 percent of the maximum value.

   Collective on SNES

   Input Parameters:
+  snes   - iterative context
.  it    - iteration number
.  rnorm - 2-norm (preconditioned) residual value (may be estimated).
-  dummy - unused monitor context

   Options Database Key:
.  -snes_monitor_range - Activates SNESMonitorRange()

   Level: intermediate

.seealso: SNESMonitorSet(), SNESMonitorDefault(), SNESMonitorLGCreate()
@*/
PetscErrorCode  SNESMonitorRange(SNES snes,PetscInt it,PetscReal rnorm,PetscViewerAndFormat *vf)
{
  PetscErrorCode ierr;
  PetscReal      perc,rel;
  PetscViewer    viewer = vf->viewer;
  /* should be in a MonitorRangeContext */
  static PetscReal prev;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
  if (!it) prev = rnorm;
  ierr = SNESMonitorRange_Private(snes,it,&perc);CHKERRQ(ierr);

  rel  = (prev - rnorm)/prev;
  prev = rnorm;
  ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
  ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"%3D SNES preconditioned resid norm %14.12e Percent values above 20 percent of maximum %5.2f relative decrease %5.2e ratio %5.2e \n",it,(double)rnorm,(double)(100.0*perc),(double)rel,(double)(rel/perc));CHKERRQ(ierr);
  ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   SNESMonitorRatio - Monitors progress of the SNES solvers by printing the ratio
   of residual norm at each iteration to the previous.

   Collective on SNES

   Input Parameters:
+  snes - the SNES context
.  its - iteration number
.  fgnorm - 2-norm of residual (or gradient)
-  dummy -  context of monitor

   Level: intermediate

   Notes:
    Insure that SNESMonitorRatio() is called when you set this monitor
.seealso: SNESMonitorSet(), SNESMonitorSolution(), SNESMonitorRatio()
@*/
PetscErrorCode  SNESMonitorRatio(SNES snes,PetscInt its,PetscReal fgnorm,PetscViewerAndFormat *vf)
{
  PetscErrorCode          ierr;
  PetscInt                len;
  PetscReal               *history;
  PetscViewer             viewer = vf->viewer;

  PetscFunctionBegin;
  ierr = SNESGetConvergenceHistory(snes,&history,NULL,&len);CHKERRQ(ierr);
  ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
  ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  if (!its || !history || its > len) {
    ierr = PetscViewerASCIIPrintf(viewer,"%3D SNES Function norm %14.12e \n",its,(double)fgnorm);CHKERRQ(ierr);
  } else {
    PetscReal ratio = fgnorm/history[its-1];
    ierr = PetscViewerASCIIPrintf(viewer,"%3D SNES Function norm %14.12e %14.12e \n",its,(double)fgnorm,(double)ratio);CHKERRQ(ierr);
  }
  ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
   SNESMonitorRatioSetUp - Insures the SNES object is saving its history since this monitor needs access to it

   Collective on SNES

   Input Parameters:
+   snes - the SNES context
-   viewer - the PetscViewer object (ignored)

   Level: intermediate

.seealso: SNESMonitorSet(), SNESMonitorSolution(), SNESMonitorDefault(), SNESMonitorRatio()
@*/
PetscErrorCode  SNESMonitorRatioSetUp(SNES snes,PetscViewerAndFormat *vf)
{
  PetscErrorCode          ierr;
  PetscReal               *history;

  PetscFunctionBegin;
  ierr = SNESGetConvergenceHistory(snes,&history,NULL,NULL);CHKERRQ(ierr);
  if (!history) {
    ierr = SNESSetConvergenceHistory(snes,NULL,NULL,100,PETSC_TRUE);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/* ---------------------------------------------------------------- */
/*
     Default (short) SNES Monitor, same as SNESMonitorDefault() except
  it prints fewer digits of the residual as the residual gets smaller.
  This is because the later digits are meaningless and are often
  different on different machines; by using this routine different
  machines will usually generate the same output.

  Deprecated: Intentionally has no manual page
*/
PetscErrorCode  SNESMonitorDefaultShort(SNES snes,PetscInt its,PetscReal fgnorm,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)snes)->tablevel);CHKERRQ(ierr);
  if (fgnorm > 1.e-9) {
    ierr = PetscViewerASCIIPrintf(viewer,"%3D SNES Function norm %g \n",its,(double)fgnorm);CHKERRQ(ierr);
  } else if (fgnorm > 1.e-11) {
    ierr = PetscViewerASCIIPrintf(viewer,"%3D SNES Function norm %5.3e \n",its,(double)fgnorm);CHKERRQ(ierr);
  } else {
    ierr = PetscViewerASCIIPrintf(viewer,"%3D SNES Function norm < 1.e-11\n",its);CHKERRQ(ierr);
  }
  ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)snes)->tablevel);CHKERRQ(ierr);
  ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  SNESMonitorDefaultField - Monitors progress of the SNES solvers, separated into fields.

  Collective on SNES

  Input Parameters:
+ snes   - the SNES context
. its    - iteration number
. fgnorm - 2-norm of residual
- ctx    - the PetscViewer

  Notes:
  This routine uses the DM attached to the residual vector

  Level: intermediate

.seealso: SNESMonitorSet(), SNESMonitorSolution(), SNESMonitorDefault()
@*/
PetscErrorCode SNESMonitorDefaultField(SNES snes, PetscInt its, PetscReal fgnorm, PetscViewerAndFormat *vf)
{
  PetscViewer    viewer = vf->viewer;
  Vec            r;
  DM             dm;
  PetscReal      res[256];
  PetscInt       tablevel;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
  ierr = SNESGetFunction(snes, &r, NULL, NULL);CHKERRQ(ierr);
  ierr = VecGetDM(r, &dm);CHKERRQ(ierr);
  if (!dm) {ierr = SNESMonitorDefault(snes, its, fgnorm, vf);CHKERRQ(ierr);}
  else {
    PetscSection s, gs;
    PetscInt     Nf, f;

    ierr = DMGetLocalSection(dm, &s);CHKERRQ(ierr);
    ierr = DMGetGlobalSection(dm, &gs);CHKERRQ(ierr);
    if (!s || !gs) {ierr = SNESMonitorDefault(snes, its, fgnorm, vf);CHKERRQ(ierr);}
    ierr = PetscSectionGetNumFields(s, &Nf);CHKERRQ(ierr);
    if (Nf > 256) SETERRQ1(PetscObjectComm((PetscObject) snes), PETSC_ERR_SUP, "Do not support %d fields > 256", Nf);
    ierr = PetscSectionVecNorm(s, gs, r, NORM_2, res);CHKERRQ(ierr);
    ierr = PetscObjectGetTabLevel((PetscObject) snes, &tablevel);CHKERRQ(ierr);
    ierr = PetscViewerPushFormat(viewer,vf->format);CHKERRQ(ierr);
    ierr = PetscViewerASCIIAddTab(viewer, tablevel);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "%3D SNES Function norm %14.12e [", its, (double) fgnorm);CHKERRQ(ierr);
    for (f = 0; f < Nf; ++f) {
      if (f) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
      ierr = PetscViewerASCIIPrintf(viewer, "%14.12e", res[f]);CHKERRQ(ierr);
    }
    ierr = PetscViewerASCIIPrintf(viewer, "] \n");CHKERRQ(ierr);
    ierr = PetscViewerASCIISubtractTab(viewer, tablevel);CHKERRQ(ierr);
    ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}
/* ---------------------------------------------------------------- */
/*@C
   SNESConvergedDefault - Convergence test of the solvers for
   systems of nonlinear equations (default).

   Collective on SNES

   Input Parameters:
+  snes - the SNES context
.  it - the iteration (0 indicates before any Newton steps)
.  xnorm - 2-norm of current iterate
.  snorm - 2-norm of current step
.  fnorm - 2-norm of function at current iterate
-  dummy - unused context

   Output Parameter:
.   reason  - one of
$  SNES_CONVERGED_FNORM_ABS       - (fnorm < abstol),
$  SNES_CONVERGED_SNORM_RELATIVE  - (snorm < stol*xnorm),
$  SNES_CONVERGED_FNORM_RELATIVE  - (fnorm < rtol*fnorm0),
$  SNES_DIVERGED_FUNCTION_COUNT   - (nfct > maxf),
$  SNES_DIVERGED_FNORM_NAN        - (fnorm == NaN),
$  SNES_CONVERGED_ITERATING       - (otherwise),

   where
+    maxf - maximum number of function evaluations,
            set with SNESSetTolerances()
.    nfct - number of function evaluations,
.    abstol - absolute function norm tolerance,
            set with SNESSetTolerances()
-    rtol - relative function norm tolerance, set with SNESSetTolerances()

   Level: intermediate

.seealso: SNESSetConvergenceTest()
@*/
PetscErrorCode  SNESConvergedDefault(SNES snes,PetscInt it,PetscReal xnorm,PetscReal snorm,PetscReal fnorm,SNESConvergedReason *reason,void *dummy)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
  PetscValidPointer(reason,6);

  *reason = SNES_CONVERGED_ITERATING;

  if (!it) {
    /* set parameter for default relative tolerance convergence test */
    snes->ttol   = fnorm*snes->rtol;
    snes->rnorm0 = fnorm;
  }
  if (PetscIsInfOrNanReal(fnorm)) {
    ierr    = PetscInfo(snes,"Failed to converged, function norm is NaN\n");CHKERRQ(ierr);
    *reason = SNES_DIVERGED_FNORM_NAN;
  } else if (fnorm < snes->abstol && (it || !snes->forceiteration)) {
    ierr    = PetscInfo2(snes,"Converged due to function norm %14.12e < %14.12e\n",(double)fnorm,(double)snes->abstol);CHKERRQ(ierr);
    *reason = SNES_CONVERGED_FNORM_ABS;
  } else if (snes->nfuncs >= snes->max_funcs && snes->max_funcs >= 0) {
    ierr    = PetscInfo2(snes,"Exceeded maximum number of function evaluations: %D > %D\n",snes->nfuncs,snes->max_funcs);CHKERRQ(ierr);
    *reason = SNES_DIVERGED_FUNCTION_COUNT;
  }

  if (it && !*reason) {
    if (fnorm <= snes->ttol) {
      ierr    = PetscInfo2(snes,"Converged due to function norm %14.12e < %14.12e (relative tolerance)\n",(double)fnorm,(double)snes->ttol);CHKERRQ(ierr);
      *reason = SNES_CONVERGED_FNORM_RELATIVE;
    } else if (snorm < snes->stol*xnorm) {
      ierr    = PetscInfo3(snes,"Converged due to small update length: %14.12e < %14.12e * %14.12e\n",(double)snorm,(double)snes->stol,(double)xnorm);CHKERRQ(ierr);
      *reason = SNES_CONVERGED_SNORM_RELATIVE;
    } else if (snes->divtol > 0 && (fnorm > snes->divtol*snes->rnorm0)) {
      ierr    = PetscInfo3(snes,"Diverged due to increase in function norm: %14.12e > %14.12e * %14.12e\n",(double)fnorm,(double)snes->divtol,(double)snes->rnorm0);CHKERRQ(ierr);
      *reason = SNES_DIVERGED_DTOL;
    }

  }
  PetscFunctionReturn(0);
}

/*@C
   SNESConvergedSkip - Convergence test for SNES that NEVER returns as
   converged, UNLESS the maximum number of iteration have been reached.

   Logically Collective on SNES

   Input Parameters:
+  snes - the SNES context
.  it - the iteration (0 indicates before any Newton steps)
.  xnorm - 2-norm of current iterate
.  snorm - 2-norm of current step
.  fnorm - 2-norm of function at current iterate
-  dummy - unused context

   Output Parameter:
.   reason  - SNES_CONVERGED_ITERATING, SNES_CONVERGED_ITS, or SNES_DIVERGED_FNORM_NAN

   Notes:
   Convergence is then declared after a fixed number of iterations have been used.

   Level: advanced

.seealso: SNESSetConvergenceTest()
@*/
PetscErrorCode  SNESConvergedSkip(SNES snes,PetscInt it,PetscReal xnorm,PetscReal snorm,PetscReal fnorm,SNESConvergedReason *reason,void *dummy)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(snes,SNES_CLASSID,1);
  PetscValidPointer(reason,6);

  *reason = SNES_CONVERGED_ITERATING;

  if (fnorm != fnorm) {
    ierr    = PetscInfo(snes,"Failed to converged, function norm is NaN\n");CHKERRQ(ierr);
    *reason = SNES_DIVERGED_FNORM_NAN;
  } else if (it == snes->max_its) {
    *reason = SNES_CONVERGED_ITS;
  }
  PetscFunctionReturn(0);
}

/*@C
  SNESSetWorkVecs - Gets a number of work vectors.

  Input Parameters:
+ snes  - the SNES context
- nw - number of work vectors to allocate

  Level: developer

@*/
PetscErrorCode SNESSetWorkVecs(SNES snes,PetscInt nw)
{
  DM             dm;
  Vec            v;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (snes->work) {ierr = VecDestroyVecs(snes->nwork,&snes->work);CHKERRQ(ierr);}
  snes->nwork = nw;

  ierr = SNESGetDM(snes, &dm);CHKERRQ(ierr);
  ierr = DMGetGlobalVector(dm, &v);CHKERRQ(ierr);
  ierr = VecDuplicateVecs(v,snes->nwork,&snes->work);CHKERRQ(ierr);
  ierr = DMRestoreGlobalVector(dm, &v);CHKERRQ(ierr);
  ierr = PetscLogObjectParents(snes,nw,snes->work);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}