xref: /petsc/src/snes/mf/snesmfj.c (revision 7e9d52098864e914818e1858ada8132a0690855c)

/*$Id: snesmfj.c,v 1.124 2001/07/10 15:01:10 bsmith Exp bsmith $*/

#include "src/snes/snesimpl.h"
#include "src/snes/mf/snesmfj.h"   /*I  "petscsnes.h"   I*/
#include "src/mat/matimpl.h"

PetscFList      MatSNESMPetscFList              = 0;
PetscTruth MatSNESMFRegisterAllCalled = PETSC_FALSE;

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFSetType"
/*@C
    MatSNESMFSetType - Sets the method that is used to compute the
    differencing parameter for finite differene matrix-free formulations.

    Input Parameters:
+   mat - the "matrix-free" matrix created via MatCreateSNESMF(), or MatCreateMF()
          or MatSetType(mat,MATMFFD);
-   ftype - the type requested

    Level: advanced

    Notes:
    For example, such routines can compute h for use in
    Jacobian-vector products of the form

                        F(x+ha) - F(x)
          F'(u)a  ~=  ----------------
                              h

.seealso: MatCreateSNESMF(), MatSNESMFRegisterDynamic)
@*/
int MatSNESMFSetType(Mat mat,MatSNESMFType ftype)
{
  int          ierr,(*r)(MatSNESMFCtx);
  MatSNESMFCtx ctx = (MatSNESMFCtx)mat->data;
  PetscTruth   match;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_COOKIE);
  PetscValidCharPointer(ftype);

  /* already set, so just return */
  ierr = PetscTypeCompare((PetscObject)ctx,ftype,&match);CHKERRQ(ierr);
  if (match) PetscFunctionReturn(0);

  /* destroy the old one if it exists */
  if (ctx->ops->destroy) {
    ierr = (*ctx->ops->destroy)(ctx);CHKERRQ(ierr);
  }

  /* Get the function pointers for the requrested method */
  if (!MatSNESMFRegisterAllCalled) {ierr = MatSNESMFRegisterAll(PETSC_NULL);CHKERRQ(ierr);}

  ierr =  PetscFListFind(ctx->comm,MatSNESMPetscFList,ftype,(void (**)(void)) &r);CHKERRQ(ierr);

  if (!r) SETERRQ(1,"Unknown MatSNESMF type given");

  ierr = (*r)(ctx);CHKERRQ(ierr);

  ierr = PetscObjectChangeTypeName((PetscObject)ctx,ftype);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

/*MC
   MatSNESMFRegisterDynamic - Adds a method to the MatSNESMF registry.

   Synopsis:
   int MatSNESMFRegisterDynamic(char *name_solver,char *path,char *name_create,int (*routine_create)(MatSNESMF))

   Not Collective

   Input Parameters:
+  name_solver - name of a new user-defined compute-h module
.  path - path (either absolute or relative) the library containing this solver
.  name_create - name of routine to create method context
-  routine_create - routine to create method context

   Level: developer

   Notes:
   MatSNESMFRegisterDynamic) may be called multiple times to add several user-defined solvers.

   If dynamic libraries are used, then the fourth input argument (routine_create)
   is ignored.

   Sample usage:
.vb
   MatSNESMFRegisterDynamic"my_h",/home/username/my_lib/lib/libO/solaris/mylib.a,
               "MyHCreate",MyHCreate);
.ve

   Then, your solver can be chosen with the procedural interface via
$     MatSNESMFSetType(mfctx,"my_h")
   or at runtime via the option
$     -snes_mf_type my_h

.keywords: MatSNESMF, register

.seealso: MatSNESMFRegisterAll(), MatSNESMFRegisterDestroy()
M*/

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFRegister"
int MatSNESMFRegister(char *sname,char *path,char *name,int (*function)(MatSNESMFCtx))
{
  int ierr;
  char fullname[256];

  PetscFunctionBegin;
  ierr = PetscFListConcat(path,name,fullname);CHKERRQ(ierr);
  ierr = PetscFListAdd(&MatSNESMPetscFList,sname,fullname,(void (*)())function);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatSNESMFRegisterDestroy"
/*@C
   MatSNESMFRegisterDestroy - Frees the list of MatSNESMF methods that were
   registered by MatSNESMFRegisterDynamic).

   Not Collective

   Level: developer

.keywords: MatSNESMF, register, destroy

.seealso: MatSNESMFRegisterDynamic), MatSNESMFRegisterAll()
@*/
int MatSNESMFRegisterDestroy(void)
{
  int ierr;

  PetscFunctionBegin;
  if (MatSNESMPetscFList) {
    ierr = PetscFListDestroy(&MatSNESMPetscFList);CHKERRQ(ierr);
    MatSNESMPetscFList = 0;
  }
  MatSNESMFRegisterAllCalled = PETSC_FALSE;
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "MatSNESMFDestroy_Private"
int MatSNESMFDestroy_Private(Mat mat)
{
  int          ierr;
  MatSNESMFCtx ctx = (MatSNESMFCtx)mat->data;

  PetscFunctionBegin;
  ierr = VecDestroy(ctx->w);CHKERRQ(ierr);
  if (ctx->ops->destroy) {ierr = (*ctx->ops->destroy)(ctx);CHKERRQ(ierr);}
  if (ctx->sp) {ierr = MatNullSpaceDestroy(ctx->sp);CHKERRQ(ierr);}
  PetscHeaderDestroy(ctx);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFView_Private"
/*
   MatSNESMFView_Private - Views matrix-free parameters.

*/
int MatSNESMFView_Private(Mat J,PetscViewer viewer)
{
  int          ierr;
  MatSNESMFCtx ctx = (MatSNESMFCtx)J->data;
  PetscTruth   isascii;

  PetscFunctionBegin;
  ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&isascii);CHKERRQ(ierr);
  if (isascii) {
     ierr = PetscViewerASCIIPrintf(viewer,"  SNES matrix-free approximation:\n");CHKERRQ(ierr);
     ierr = PetscViewerASCIIPrintf(viewer,"    err=%g (relative error in function evaluation)\n",ctx->error_rel);CHKERRQ(ierr);
     if (!ctx->type_name) {
       ierr = PetscViewerASCIIPrintf(viewer,"    The compute h routine has not yet been set\n");CHKERRQ(ierr);
     } else {
       ierr = PetscViewerASCIIPrintf(viewer,"    Using %s compute h routine\n",ctx->type_name);CHKERRQ(ierr);
     }
     if (ctx->ops->view) {
       ierr = (*ctx->ops->view)(ctx,viewer);CHKERRQ(ierr);
     }
  } else {
    SETERRQ1(1,"Viewer type %s not supported for SNES matrix free matrix",((PetscObject)viewer)->type_name);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFAssemblyEnd_Private"
/*
   MatSNESMFAssemblyEnd_Private - Resets the ctx->ncurrenth to zero. This
   allows the user to indicate the beginning of a new linear solve by calling
   MatAssemblyXXX() on the matrix free matrix. This then allows the
   MatSNESMFCreate_WP() to properly compute ||U|| only the first time
   in the linear solver rather than every time.
*/
int MatSNESMFAssemblyEnd_Private(Mat J,MatAssemblyType mt)
{
  int          ierr;
  MatSNESMFCtx j = (MatSNESMFCtx)J->data;

  PetscFunctionBegin;
  ierr = MatSNESMFResetHHistory(J);CHKERRQ(ierr);
  if (j->usesnes) {
    ierr = SNESGetSolution(j->snes,&j->current_u);CHKERRQ(ierr);
    if (j->snes->method_class == SNES_NONLINEAR_EQUATIONS) {
      ierr = SNESGetFunction(j->snes,&j->current_f,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
    } else if (j->snes->method_class == SNES_UNCONSTRAINED_MINIMIZATION) {
      ierr = SNESGetGradient(j->snes,&j->current_f,PETSC_NULL);CHKERRQ(ierr);
    } else SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Invalid method class");
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFMult_Private"
/*
  MatSNESMFMult_Private - Default matrix-free form for Jacobian-vector
  product, y = F'(u)*a:

        y ~= (F(u + ha) - F(u))/h,
  where F = nonlinear function, as set by SNESSetFunction()
        u = current iterate
        h = difference interval
*/
int MatSNESMFMult_Private(Mat mat,Vec a,Vec y)
{
  MatSNESMFCtx ctx = (MatSNESMFCtx)mat->data;
  SNES         snes;
  Scalar       h,mone = -1.0;
  Vec          w,U,F;
  int          ierr,(*eval_fct)(SNES,Vec,Vec)=0;

  PetscFunctionBegin;
  /* We log matrix-free matrix-vector products separately, so that we can
     separate the performance monitoring from the cases that use conventional
     storage.  We may eventually modify event logging to associate events
     with particular objects, hence alleviating the more general problem. */
  ierr = PetscLogEventBegin(MAT_MatrixFreeMult,a,y,0,0);CHKERRQ(ierr);

  snes = ctx->snes;
  w    = ctx->w;
  U    = ctx->current_u;

  /*
      Compute differencing parameter
  */
  if (!ctx->ops->compute) {
    ierr = MatSNESMFSetType(mat,MATSNESMF_DEFAULT);CHKERRQ(ierr);
    ierr = MatSNESMFSetFromOptions(mat);CHKERRQ(ierr);
  }
  ierr = (*ctx->ops->compute)(ctx,U,a,&h);CHKERRQ(ierr);

  /* keep a record of the current differencing parameter h */
  ctx->currenth = h;
#if defined(PETSC_USE_COMPLEX)
  PetscLogInfo(mat,"MatSNESMFMult_Private:Current differencing parameter: %g + %g i\n",PetscRealPart(h),PetscImaginaryPart(h));
#else
  PetscLogInfo(mat,"MatSNESMFMult_Private:Current differencing parameter: %15.12e\n",h);
#endif
  if (ctx->historyh && ctx->ncurrenth < ctx->maxcurrenth) {
    ctx->historyh[ctx->ncurrenth] = h;
  }
  ctx->ncurrenth++;

  /* w = u + ha */
  ierr = VecWAXPY(&h,a,U,w);CHKERRQ(ierr);

  if (ctx->usesnes) {
    if (snes->method_class == SNES_NONLINEAR_EQUATIONS) {
      eval_fct = SNESComputeFunction;
    } else if (snes->method_class == SNES_UNCONSTRAINED_MINIMIZATION) {
      eval_fct = SNESComputeGradient;
    } else SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Invalid method class");
    F    = ctx->current_f;
    if (!F) SETERRQ(1,"You must call MatAssembly() even on matrix-free matrices");
    ierr = (*eval_fct)(snes,w,y);CHKERRQ(ierr);
  } else {
    F = ctx->funcvec;
    /* compute func(U) as base for differencing */
    if (ctx->ncurrenth == 1) {
      ierr = (*ctx->func)(snes,U,F,ctx->funcctx);CHKERRQ(ierr);
    }
    ierr = (*ctx->func)(snes,w,y,ctx->funcctx);CHKERRQ(ierr);
  }

  ierr = VecAXPY(&mone,F,y);CHKERRQ(ierr);
  h    = 1.0/h;
  ierr = VecScale(&h,y);CHKERRQ(ierr);
  if (ctx->sp) {ierr = MatNullSpaceRemove(ctx->sp,y,PETSC_NULL);CHKERRQ(ierr);}

  ierr = PetscLogEventEnd(MAT_MatrixFreeMult,a,y,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFGetDiagonal_Private"
/*
  MatSNESMFGetDiagonal_Private - Gets the diagonal for a matrix free matrix

        y ~= (F(u + ha) - F(u))/h,
  where F = nonlinear function, as set by SNESSetFunction()
        u = current iterate
        h = difference interval
*/
int MatSNESMFGetDiagonal_Private(Mat mat,Vec a)
{
  MatSNESMFCtx ctx = (MatSNESMFCtx)mat->data;
  Scalar       h,h1,mone = -1.0,*aa,*ww,v,epsilon = 1.e-8,umin = 1.e-6;
  Vec          w,U,F;
  int          i,ierr,rstart,rend;

  PetscFunctionBegin;
  if (!ctx->funci) {
    SETERRQ(1,"Requirers calling MatSNESMFSetFunctioni() first");
  }

  w    = ctx->w;
  U    = ctx->current_u;
  ierr = (*ctx->func)(0,U,a,ctx->funcctx);CHKERRQ(ierr);
  ierr = (*ctx->funcisetbase)(U,ctx->funcctx);CHKERRQ(ierr);
  ierr = VecCopy(U,w);CHKERRQ(ierr);

  ierr = VecGetOwnershipRange(a,&rstart,&rend);CHKERRQ(ierr);
  ierr = VecGetArray(a,&aa);CHKERRQ(ierr);
  for (i=rstart; i<rend; i++) {
    ierr = VecGetArray(w,&ww);CHKERRQ(ierr);
    h  = ww[i-rstart];
    if (h == 0.0) h = 1.0;
#if !defined(PETSC_USE_COMPLEX)
    if (h < umin && h >= 0.0)      h = umin;
    else if (h < 0.0 && h > -umin) h = -umin;
#else
    if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0)     h = umin;
    else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
#endif
    h     *= epsilon;

    ww[i-rstart] += h;
    ierr = VecRestoreArray(w,&ww);CHKERRQ(ierr);
    ierr          = (*ctx->funci)(i,w,&v,ctx->funcctx);CHKERRQ(ierr);
    aa[i-rstart]  = (v - aa[i-rstart])/h;
    ierr = VecGetArray(w,&ww);CHKERRQ(ierr);
    ww[i-rstart] -= h;
    ierr = VecRestoreArray(w,&ww);CHKERRQ(ierr);
  }
  ierr = VecRestoreArray(a,&aa);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCreateSNESMF"
/*@C
   MatCreateSNESMF - Creates a matrix-free matrix context for use with
   a SNES solver.  This matrix can be used as the Jacobian argument for
   the routine SNESSetJacobian().

   Collective on SNES and Vec

   Input Parameters:
+  snes - the SNES context
-  x - vector where SNES solution is to be stored.

   Output Parameter:
.  J - the matrix-free matrix

   Level: advanced

   Notes:
   The matrix-free matrix context merely contains the function pointers
   and work space for performing finite difference approximations of
   Jacobian-vector products, F'(u)*a,

   The default code uses the following approach to compute h

.vb
     F'(u)*a = [F(u+h*a) - F(u)]/h where
     h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
       = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
 where
     error_rel = square root of relative error in function evaluation
     umin = minimum iterate parameter
.ve

   The user can set the error_rel via MatSNESMFSetFunctionError() and
   umin via MatSNESMFDefaultSetUmin(); see the nonlinear solvers chapter
   of the users manual for details.

   The user should call MatDestroy() when finished with the matrix-free
   matrix context.

   Options Database Keys:
+  -snes_mf_err <error_rel> - Sets error_rel
.  -snes_mf_unim <umin> - Sets umin (for default PETSc routine that computes h only)
-  -snes_mf_ksp_monitor - KSP monitor routine that prints differencing h

.keywords: SNES, default, matrix-free, create, matrix

.seealso: MatDestroy(), MatSNESMFSetFunctionError(), MatSNESMFDefaultSetUmin()
          MatSNESMFSetHHistory(), MatSNESMFResetHHistory(), MatCreateMF(),
          MatSNESMFGetH(),MatSNESMFKSPMonitor(), MatSNESMFRegisterDynamic), MatSNESMFComputeJacobian()

@*/
int MatCreateSNESMF(SNES snes,Vec x,Mat *J)
{
  MatSNESMFCtx mfctx;
  int          ierr;

  PetscFunctionBegin;
  ierr = MatCreateMF(x,J);CHKERRQ(ierr);

  mfctx          = (MatSNESMFCtx)(*J)->data;
  mfctx->snes    = snes;
  mfctx->usesnes = PETSC_TRUE;
  PetscLogObjectParent(snes,*J);
  PetscFunctionReturn(0);
}

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatSNESMFSetBase_FD"
int MatSNESMFSetBase_FD(Mat J,Vec U)
{
  int          ierr;
  MatSNESMFCtx ctx = (MatSNESMFCtx)J->data;

  PetscFunctionBegin;
  ierr = MatSNESMFResetHHistory(J);CHKERRQ(ierr);
  ctx->current_u = U;
  ctx->usesnes   = PETSC_FALSE;
  PetscFunctionReturn(0);
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFSetFromOptions"
/*@
   MatSNESMFSetFromOptions - Sets the MatSNESMF options from the command line
   parameter.

   Collective on Mat

   Input Parameters:
.  mat - the matrix obtained with MatCreateSNESMF()

   Options Database Keys:
+  -snes_mf_type - <default,wp>
-  -snes_mf_err - square root of estimated relative error in function evaluation
-  -snes_mf_period - how often h is recomputed, defaults to 1, everytime

   Level: advanced

.keywords: SNES, matrix-free, parameters

.seealso: MatCreateSNESMF(),MatSNESMFSetHHistory(),
          MatSNESMFResetHHistory(), MatSNESMFKSPMonitor()
@*/
int MatSNESMFSetFromOptions(Mat mat)
{
  MatSNESMFCtx mfctx = (MatSNESMFCtx)mat->data;
  int          ierr;
  PetscTruth   flg;
  char         ftype[256];

  PetscFunctionBegin;
  if (mfctx) {
    if (!MatSNESMFRegisterAllCalled) {ierr = MatSNESMFRegisterAll(PETSC_NULL);CHKERRQ(ierr);}

    ierr = PetscOptionsBegin(mfctx->comm,mfctx->prefix,"Set matrix free computation parameters","MatSNESMF");CHKERRQ(ierr);
      ierr = PetscOptionsList("-snes_mf_type","Matrix free type","MatSNESMFSetType",MatSNESMPetscFList,mfctx->type_name,ftype,256,&flg);CHKERRQ(ierr);
      if (flg) {
        ierr = MatSNESMFSetType(mat,ftype);CHKERRQ(ierr);
      }

      ierr = PetscOptionsDouble("-snes_mf_err","set sqrt relative error in function","MatSNESMFSetFunctionError",mfctx->error_rel,&mfctx->error_rel,0);CHKERRQ(ierr);
      ierr = PetscOptionsInt("-snes_mf_period","how often h is recomputed","MatSNESMFSetPeriod",mfctx->recomputeperiod,&mfctx->recomputeperiod,0);CHKERRQ(ierr);
      if (mfctx->snes) {
        ierr = PetscOptionsName("-snes_mf_ksp_monitor","Monitor matrix-free parameters","MatSNESMFKSPMonitor",&flg);CHKERRQ(ierr);
        if (flg) {
          SLES sles;
          KSP  ksp;
          ierr = SNESGetSLES(mfctx->snes,&sles);CHKERRQ(ierr);
          ierr = SLESGetKSP(sles,&ksp);CHKERRQ(ierr);
          ierr = KSPSetMonitor(ksp,MatSNESMFKSPMonitor,PETSC_NULL,0);CHKERRQ(ierr);
        }
      }
      if (mfctx->ops->setfromoptions) {
        ierr = (*mfctx->ops->setfromoptions)(mfctx);CHKERRQ(ierr);
      }
    ierr = PetscOptionsEnd();CHKERRQ(ierr);

  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCreate_MFFD"
EXTERN_C_BEGIN
int MatCreate_MFFD(Mat A)
{
  PetscFunctionBegin;
  MPI_Comm     comm;
  MatSNESMFCtx mfctx;
  int          n,nloc,ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)x,&comm);CHKERRQ(ierr);
  PetscHeaderCreate(mfctx,_p_MatSNESMFCtx,struct _MFOps,MATSNESMFCTX_COOKIE,0,"SNESMF",comm,MatSNESMFDestroy_Private,MatSNESMFView_Private);
  PetscLogObjectCreate(mfctx);
  mfctx->sp              = 0;
  mfctx->snes            = 0;
  mfctx->error_rel       = 1.e-8; /* assumes PetscReal precision */
  mfctx->recomputeperiod = 1;
  mfctx->count           = 0;
  mfctx->currenth        = 0.0;
  mfctx->historyh        = PETSC_NULL;
  mfctx->ncurrenth       = 0;
  mfctx->maxcurrenth     = 0;
  mfctx->type_name       = 0;
  mfctx->usesnes         = PETSC_FALSE;

  /*
     Create the empty data structure to contain compute-h routines.
     These will be filled in below from the command line options or
     a later call with MatSNESMFSetType() or if that is not called
     then it will default in the first use of MatSNESMFMult_private()
  */
  mfctx->ops->compute        = 0;
  mfctx->ops->destroy        = 0;
  mfctx->ops->view           = 0;
  mfctx->ops->setfromoptions = 0;
  mfctx->hctx                = 0;

  mfctx->func                = 0;
  mfctx->funcctx             = 0;
  mfctx->funcvec             = 0;

  ierr = VecDuplicate(x,&mfctx->w);CHKERRQ(ierr);
  ierr = VecGetSize(mfctx->w,&n);CHKERRQ(ierr);
  ierr = VecGetLocalSize(mfctx->w,&nloc);CHKERRQ(ierr);
  ierr = MatCreate(comm,nloc,nloc,n,n,J);CHKERRQ(ierr);
  (*J)->data = mfctx;

  (*J)->ops->mult           = MatSNESMFMult_Private;
  (*J)->ops->destroy        = MatSNESMFDestroy_Private;
  (*J)->ops->view           = MatSNESMFView_Private;
  (*J)->ops->assemblyend    = MatSNESMFAssemblyEnd_Private;
  (*J)->ops->getdiagonal    = MatSNESMFGetDiagonal_Private;
  (*J)->ops->setfromoptions = MatSNESMFSetFromOptions;

  ierr = PetscObjectChangeTypeName((PetscObject)*J,MATMFFD);CHKERRQ(ierr);

  ierr = PetscObjectComposeFunctionDynamic((PetscObject)*J,"MatSNESMFSetBase_C","MatSNESMFSetBase_FD",MatSNESMFSetBase_FD);CHKERRQ(ierr);
  PetscLogObjectParent(*J,mfctx->w);

  PetscFunctionReturn(0);
}

EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "MatCreateMF"
/*@C
   MatCreateMF - Creates a matrix-free matrix. See also MatCreateSNESMF()

   Collective on Vec

   Input Parameters:
.  x - vector that defines layout of the vectors and matrices

   Output Parameter:
.  J - the matrix-free matrix

   Level: advanced

   Notes:
   The matrix-free matrix context merely contains the function pointers
   and work space for performing finite difference approximations of
   Jacobian-vector products, F'(u)*a,

   The default code uses the following approach to compute h

.vb
     F'(u)*a = [F(u+h*a) - F(u)]/h where
     h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
       = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   otherwise
 where
     error_rel = square root of relative error in function evaluation
     umin = minimum iterate parameter
.ve

   The user can set the error_rel via MatSNESMFSetFunctionError() and
   umin via MatSNESMFDefaultSetUmin(); see the nonlinear solvers chapter
   of the users manual for details.

   The user should call MatDestroy() when finished with the matrix-free
   matrix context.

   Options Database Keys:
+  -snes_mf_err <error_rel> - Sets error_rel
.  -snes_mf_unim <umin> - Sets umin (for default PETSc routine that computes h only)
-  -snes_mf_ksp_monitor - KSP monitor routine that prints differencing h

.keywords: default, matrix-free, create, matrix

.seealso: MatDestroy(), MatSNESMFSetFunctionError(), MatSNESMFDefaultSetUmin()
          MatSNESMFSetHHistory(), MatSNESMFResetHHistory(), MatCreateSNESMF(),
          MatSNESMFGetH(),MatSNESMFKSPMonitor(), MatSNESMFRegisterDynamic),, MatSNESMFComputeJacobian()

@*/
int MatCreateMF(Vec x,Mat *J)
{
  MPI_Comm     comm;
  MatSNESMFCtx mfctx;
  int          n,nloc,ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)x,&comm);CHKERRQ(ierr);
  PetscHeaderCreate(mfctx,_p_MatSNESMFCtx,struct _MFOps,MATSNESMFCTX_COOKIE,0,"SNESMF",comm,MatSNESMFDestroy_Private,MatSNESMFView_Private);
  PetscLogObjectCreate(mfctx);
  mfctx->sp              = 0;
  mfctx->snes            = 0;
  mfctx->error_rel       = 1.e-8; /* assumes PetscReal precision */
  mfctx->recomputeperiod = 1;
  mfctx->count           = 0;
  mfctx->currenth        = 0.0;
  mfctx->historyh        = PETSC_NULL;
  mfctx->ncurrenth       = 0;
  mfctx->maxcurrenth     = 0;
  mfctx->type_name       = 0;
  mfctx->usesnes         = PETSC_FALSE;

  /*
     Create the empty data structure to contain compute-h routines.
     These will be filled in below from the command line options or
     a later call with MatSNESMFSetType() or if that is not called
     then it will default in the first use of MatSNESMFMult_private()
  */
  mfctx->ops->compute        = 0;
  mfctx->ops->destroy        = 0;
  mfctx->ops->view           = 0;
  mfctx->ops->setfromoptions = 0;
  mfctx->hctx                = 0;

  mfctx->func                = 0;
  mfctx->funcctx             = 0;
  mfctx->funcvec             = 0;

  ierr = VecDuplicate(x,&mfctx->w);CHKERRQ(ierr);
  ierr = VecGetSize(mfctx->w,&n);CHKERRQ(ierr);
  ierr = VecGetLocalSize(mfctx->w,&nloc);CHKERRQ(ierr);
  ierr = MatCreate(comm,nloc,nloc,n,n,J);CHKERRQ(ierr);
  (*J)->data = mfctx;

  (*J)->ops->mult           = MatSNESMFMult_Private;
  (*J)->ops->destroy        = MatSNESMFDestroy_Private;
  (*J)->ops->view           = MatSNESMFView_Private;
  (*J)->ops->assemblyend    = MatSNESMFAssemblyEnd_Private;
  (*J)->ops->getdiagonal    = MatSNESMFGetDiagonal_Private;
  (*J)->ops->setfromoptions = MatSNESMFSetFromOptions;

  ierr = PetscObjectChangeTypeName((PetscObject)*J,MATMFFD);CHKERRQ(ierr);

  ierr = PetscObjectComposeFunctionDynamic((PetscObject)*J,"MatSNESMFSetBase_C","MatSNESMFSetBase_FD",MatSNESMFSetBase_FD);CHKERRQ(ierr);
  PetscLogObjectParent(*J,mfctx->w);

  mfctx->mat = *J;
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatSNESMFGetH"
/*@
   MatSNESMFGetH - Gets the last value that was used as the differencing
   parameter.

   Not Collective

   Input Parameters:
.  mat - the matrix obtained with MatCreateSNESMF()

   Output Paramter:
.  h - the differencing step size

   Level: advanced

.keywords: SNES, matrix-free, parameters

.seealso: MatCreateSNESMF(),MatSNESMFSetHHistory(),
          MatSNESMFResetHHistory(),MatSNESMFKSPMonitor()
@*/
int MatSNESMFGetH(Mat mat,Scalar *h)
{
  MatSNESMFCtx ctx = (MatSNESMFCtx)mat->data;
  int          ierr;

  PetscFunctionBegin;
  *h = ctx->currenth;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFKSPMonitor"
/*
   MatSNESMFKSPMonitor - A KSP monitor for use with the default PETSc
   SNES matrix free routines. Prints the differencing parameter used at
   each step.
*/
int MatSNESMFKSPMonitor(KSP ksp,int n,PetscReal rnorm,void *dummy)
{
  PC             pc;
  MatSNESMFCtx   ctx;
  int            ierr;
  Mat            mat;
  MPI_Comm       comm;
  PetscTruth     nonzeroinitialguess;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)ksp,&comm);CHKERRQ(ierr);
  ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
  ierr = KSPGetInitialGuessNonzero(ksp,&nonzeroinitialguess);CHKERRQ(ierr);
  ierr = PCGetOperators(pc,&mat,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
  ctx  = (MatSNESMFCtx)mat->data;

  if (n > 0 || nonzeroinitialguess) {
#if defined(PETSC_USE_COMPLEX)
    ierr = PetscPrintf(comm,"%d KSP Residual norm %14.12e h %g + %g i\n",n,rnorm,
                PetscRealPart(ctx->currenth),PetscImaginaryPart(ctx->currenth));CHKERRQ(ierr);
#else
    ierr = PetscPrintf(comm,"%d KSP Residual norm %14.12e h %g \n",n,rnorm,ctx->currenth);CHKERRQ(ierr);
#endif
  } else {
    ierr = PetscPrintf(comm,"%d KSP Residual norm %14.12e\n",n,rnorm);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFSetFunction"
/*@C
   MatSNESMFSetFunction - Sets the function used in applying the matrix free.

   Collective on Mat

   Input Parameters:
+  mat - the matrix free matrix created via MatCreateSNESMF()
.  v   - workspace vector
.  func - the function to use
-  funcctx - optional function context passed to function

   Level: advanced

   Notes:
    If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
    matrix inside your compute Jacobian routine

    If this is not set then it will use the function set with SNESSetFunction()

.keywords: SNES, matrix-free, function

.seealso: MatCreateSNESMF(),MatSNESMFGetH(),
          MatSNESMFSetHHistory(), MatSNESMFResetHHistory(),
          MatSNESMFKSPMonitor(), SNESetFunction()
@*/
int MatSNESMFSetFunction(Mat mat,Vec v,int (*func)(SNES,Vec,Vec,void *),void *funcctx)
{
  MatSNESMFCtx ctx = (MatSNESMFCtx)mat->data;
  int          ierr;

  PetscFunctionBegin;
  ctx->func    = func;
  ctx->funcctx = funcctx;
  ctx->funcvec = v;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFSetFunctioni"
/*@C
   MatSNESMFSetFunctioni - Sets the function for a single component

   Collective on Mat

   Input Parameters:
+  mat - the matrix free matrix created via MatCreateSNESMF()
-  funci - the function to use

   Level: advanced

   Notes:
    If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
    matrix inside your compute Jacobian routine


.keywords: SNES, matrix-free, function

.seealso: MatCreateSNESMF(),MatSNESMFGetH(),
          MatSNESMFSetHHistory(), MatSNESMFResetHHistory(),
          MatSNESMFKSPMonitor(), SNESetFunction()
@*/
int MatSNESMFSetFunctioni(Mat mat,int (*funci)(int,Vec,Scalar*,void *))
{
  MatSNESMFCtx ctx = (MatSNESMFCtx)mat->data;
  int          ierr;

  PetscFunctionBegin;
  ctx->funci   = funci;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFSetFunctioniBase"
/*@C
   MatSNESMFSetFunctioniBase - Sets the base vector for a single component function evaluation

   Collective on Mat

   Input Parameters:
+  mat - the matrix free matrix created via MatCreateSNESMF()
-  func - the function to use

   Level: advanced

   Notes:
    If you use this you MUST call MatAssemblyBegin()/MatAssemblyEnd() on the matrix free
    matrix inside your compute Jacobian routine


.keywords: SNES, matrix-free, function

.seealso: MatCreateSNESMF(),MatSNESMFGetH(),
          MatSNESMFSetHHistory(), MatSNESMFResetHHistory(),
          MatSNESMFKSPMonitor(), SNESetFunction()
@*/
int MatSNESMFSetFunctioniBase(Mat mat,int (*func)(Vec,void *))
{
  MatSNESMFCtx ctx = (MatSNESMFCtx)mat->data;
  int          ierr;

  PetscFunctionBegin;
  ctx->funcisetbase   = func;
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatSNESMFSetPeriod"
/*@
   MatSNESMFSetPeriod - Sets how often h is recomputed, by default it is everytime

   Collective on Mat

   Input Parameters:
+  mat - the matrix free matrix created via MatCreateSNESMF()
-  period - 1 for everytime, 2 for every second etc

   Options Database Keys:
+  -snes_mf_period <period>

   Level: advanced


.keywords: SNES, matrix-free, parameters

.seealso: MatCreateSNESMF(),MatSNESMFGetH(),
          MatSNESMFSetHHistory(), MatSNESMFResetHHistory(),
          MatSNESMFKSPMonitor()
@*/
int MatSNESMFSetPeriod(Mat mat,int period)
{
  MatSNESMFCtx ctx = (MatSNESMFCtx)mat->data;
  int          ierr;

  PetscFunctionBegin;
  ctx->recomputeperiod = period;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFSetFunctionError"
/*@
   MatSNESMFSetFunctionError - Sets the error_rel for the approximation of
   matrix-vector products using finite differences.

   Collective on Mat

   Input Parameters:
+  mat - the matrix free matrix created via MatCreateSNESMF()
-  error_rel - relative error (should be set to the square root of
               the relative error in the function evaluations)

   Options Database Keys:
+  -snes_mf_err <error_rel> - Sets error_rel

   Level: advanced

   Notes:
   The default matrix-free matrix-vector product routine computes
.vb
     F'(u)*a = [F(u+h*a) - F(u)]/h where
     h = error_rel*u'a/||a||^2                        if  |u'a| > umin*||a||_{1}
       = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2   else
.ve

.keywords: SNES, matrix-free, parameters

.seealso: MatCreateSNESMF(),MatSNESMFGetH(),
          MatSNESMFSetHHistory(), MatSNESMFResetHHistory(),
          MatSNESMFKSPMonitor()
@*/
int MatSNESMFSetFunctionError(Mat mat,PetscReal error)
{
  MatSNESMFCtx ctx = (MatSNESMFCtx)mat->data;
  int          ierr;

  PetscFunctionBegin;
  if (error != PETSC_DEFAULT) ctx->error_rel = error;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFAddNullSpace"
/*@
   MatSNESMFAddNullSpace - Provides a null space that an operator is
   supposed to have.  Since roundoff will create a small component in
   the null space, if you know the null space you may have it
   automatically removed.

   Collective on Mat

   Input Parameters:
+  J - the matrix-free matrix context
-  nullsp - object created with MatNullSpaceCreate()

   Level: advanced

.keywords: SNES, matrix-free, null space

.seealso: MatNullSpaceCreate(), MatSNESMFGetH(), MatCreateSNESMF(),
          MatSNESMFSetHHistory(), MatSNESMFResetHHistory(),
          MatSNESMFKSPMonitor(), MatSNESMFErrorRel()
@*/
int MatSNESMFAddNullSpace(Mat J,MatNullSpace nullsp)
{
  int          ierr;
  MatSNESMFCtx ctx = (MatSNESMFCtx)J->data;
  MPI_Comm     comm;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)J,&comm);CHKERRQ(ierr);

  ctx->sp = nullsp;
  ierr    = PetscObjectReference((PetscObject)nullsp);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFSetHHistory"
/*@
   MatSNESMFSetHHistory - Sets an array to collect a history of the
   differencing values (h) computed for the matrix-free product.

   Collective on Mat

   Input Parameters:
+  J - the matrix-free matrix context
.  histroy - space to hold the history
-  nhistory - number of entries in history, if more entries are generated than
              nhistory, then the later ones are discarded

   Level: advanced

   Notes:
   Use MatSNESMFResetHHistory() to reset the history counter and collect
   a new batch of differencing parameters, h.

.keywords: SNES, matrix-free, h history, differencing history

.seealso: MatSNESMFGetH(), MatCreateSNESMF(),
          MatSNESMFResetHHistory(),
          MatSNESMFKSPMonitor(), MatSNESMFSetFunctionError()

@*/
int MatSNESMFSetHHistory(Mat J,Scalar *history,int nhistory)
{
  int          ierr;
  MatSNESMFCtx ctx = (MatSNESMFCtx)J->data;

  PetscFunctionBegin;
  ctx->historyh    = history;
  ctx->maxcurrenth = nhistory;
  ctx->currenth    = 0;

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFResetHHistory"
/*@
   MatSNESMFResetHHistory - Resets the counter to zero to begin
   collecting a new set of differencing histories.

   Collective on Mat

   Input Parameters:
.  J - the matrix-free matrix context

   Level: advanced

   Notes:
   Use MatSNESMFSetHHistory() to create the original history counter.

.keywords: SNES, matrix-free, h history, differencing history

.seealso: MatSNESMFGetH(), MatCreateSNESMF(),
          MatSNESMFSetHHistory(),
          MatSNESMFKSPMonitor(), MatSNESMFSetFunctionError()

@*/
int MatSNESMFResetHHistory(Mat J)
{
  int          ierr;
  MatSNESMFCtx ctx = (MatSNESMFCtx)J->data;

  PetscFunctionBegin;
  ctx->ncurrenth    = 0;

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFComputeJacobian"
int MatSNESMFComputeJacobian(SNES snes,Vec x,Mat *jac,Mat *B,MatStructure *flag,void *dummy)
{
  int ierr;
  PetscFunctionBegin;
  ierr = MatAssemblyBegin(*jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(*jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSNESMFSetBase"
int MatSNESMFSetBase(Mat J,Vec U)
{
  int  ierr,(*f)(Mat,Vec);

  PetscFunctionBegin;
  PetscValidHeaderSpecific(J,MAT_COOKIE);
  PetscValidHeaderSpecific(U,VEC_COOKIE);
  ierr = PetscObjectQueryFunction((PetscObject)J,"MatSNESMFSetBase_C",(void (**)())&f);CHKERRQ(ierr);
  if (f) {
    ierr = (*f)(J,U);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}