#ifdef PETSC_RCS_HEADER
static char vcid[] = "$Id: snesmfj.c,v 1.59 1997/12/01 01:56:46 bsmith Exp bsmith $";
#endif

#include "src/snes/snesimpl.h"   /*I  "snes.h"   I*/
#include "pinclude/pviewer.h"
#include <math.h>

typedef struct {  /* default context for matrix-free SNES */
  SNES        snes;      /* SNES context */
  Vec         w;         /* work vector */
  PCNullSpace sp;        /* null space context */
  double      error_rel; /* square root of relative error in computing function */
  double      umin;      /* minimum allowable u'a value relative to |u|_1 */
} MFCtx_Private;

#undef __FUNC__  
#define __FUNC__ "SNESMatrixFreeDestroy_Private"
int SNESMatrixFreeDestroy_Private(PetscObject obj)
{
  int           ierr;
  Mat           mat = (Mat) obj;
  MFCtx_Private *ctx;

  PetscFunctionBegin;
  ierr = MatShellGetContext(mat,(void **)&ctx);
  ierr = VecDestroy(ctx->w); CHKERRQ(ierr);
  if (ctx->sp) {ierr = PCNullSpaceDestroy(ctx->sp); CHKERRQ(ierr);}
  PetscFree(ctx);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "SNESMatrixFreeView_Private"
/*
   SNESMatrixFreeView_Private - Views matrix-free parameters.
 */
int SNESMatrixFreeView_Private(Mat J,Viewer viewer)
{
  int           ierr;
  MFCtx_Private *ctx;
  MPI_Comm      comm;
  FILE          *fd;
  ViewerType    vtype;

  PetscFunctionBegin;
  PetscObjectGetComm((PetscObject)J,&comm);
  ierr = MatShellGetContext(J,(void **)&ctx); CHKERRQ(ierr);
  ierr = ViewerGetType(viewer,&vtype); CHKERRQ(ierr);
  ierr = ViewerASCIIGetPointer(viewer,&fd); CHKERRQ(ierr);
  if (vtype == ASCII_FILE_VIEWER || vtype == ASCII_FILES_VIEWER) {
     PetscFPrintf(comm,fd,"  SNES matrix-free approximation:\n");
     PetscFPrintf(comm,fd,"    err=%g (relative error in function evaluation)\n",ctx->error_rel);
     PetscFPrintf(comm,fd,"    umin=%g (minimum iterate parameter)\n",ctx->umin);
  }
  PetscFunctionReturn(0);
}

extern int VecDot_Seq(Vec,Vec,Scalar *);
extern int VecNorm_Seq(Vec,NormType,double *);

#undef __FUNC__  
#define __FUNC__ "SNESMatrixFreeMult_Private"
/*
  SNESMatrixFreeMult_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 SNESMatrixFreeMult_Private(Mat mat,Vec a,Vec y)
{
  MFCtx_Private *ctx;
  SNES          snes;
  double        ovalues[3],values[3],norm, sum, umin;
  Scalar        h, dot, mone = -1.0;
  Vec           w,U,F;
  int           ierr, (*eval_fct)(SNES,Vec,Vec);
  MPI_Comm      comm;

  PetscFunctionBegin;
  PLogEventBegin(MAT_MatrixFreeMult,a,y,0,0);

  PetscObjectGetComm((PetscObject)mat,&comm);
  ierr = MatShellGetContext(mat,(void **)&ctx); CHKERRQ(ierr);
  snes = ctx->snes;
  w    = ctx->w;
  umin = ctx->umin;

  /* 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 = SNESGetSolution(snes,&U); CHKERRQ(ierr);
  if (snes->method_class == SNES_NONLINEAR_EQUATIONS) {
    eval_fct = SNESComputeFunction;
    ierr = SNESGetFunction(snes,&F); CHKERRQ(ierr);
  }
  else if (snes->method_class == SNES_UNCONSTRAINED_MINIMIZATION) {
    eval_fct = SNESComputeGradient;
    ierr = SNESGetGradient(snes,&F); CHKERRQ(ierr);
  }
  else SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,0,"Invalid method class");

  /* Determine a "good" step size, h */

  /*
    ierr = VecDot(U,a,&dot); CHKERRQ(ierr);
    ierr = VecNorm(a,NORM_1,&sum); CHKERRQ(ierr);
    ierr = VecNorm(a,NORM_2,&norm); CHKERRQ(ierr);
  */

  /*
     Call the Seq Vector routines and then do a single reduction 
     to reduce the number of communications required
  */

#if !defined(USE_PETSC_COMPLEX)
  PLogEventBegin(VEC_Dot,U,a,0,0);
  ierr = VecDot_Seq(U,a,ovalues); CHKERRQ(ierr);
  PLogEventEnd(VEC_Dot,U,a,0,0);
  PLogEventBegin(VEC_Norm,a,0,0,0);
  ierr = VecNorm_Seq(a,NORM_1,ovalues+1); CHKERRQ(ierr);
  ierr = VecNorm_Seq(a,NORM_2,ovalues+2); CHKERRQ(ierr);
  ovalues[2] = ovalues[2]*ovalues[2];
  PLogEventBarrierBegin(VEC_NormBarrier,0,0,0,0,comm);
  ierr = MPI_Allreduce(ovalues,values,3,MPI_DOUBLE,MPI_SUM,comm );CHKERRQ(ierr);
  PLogEventBarrierEnd(VEC_NormBarrier,0,0,0,0,comm);
  dot = values[0]; sum = values[1]; norm = sqrt(values[2]);
  PLogEventEnd(VEC_Norm,a,0,0,0);
#else
  {
    Scalar cvalues[3],covalues[3];

    PLogEventBegin(VEC_Dot,U,a,0,0);
    ierr = VecDot_Seq(U,a,covalues); CHKERRQ(ierr);
    PLogEventEnd(VEC_Dot,U,a,0,0);
    PLogEventBegin(VEC_Norm,a,0,0,0);
    ierr = VecNorm_Seq(a,NORM_1,ovalues+1); CHKERRQ(ierr);
    ierr = VecNorm_Seq(a,NORM_2,ovalues+2); CHKERRQ(ierr);
    covalues[1] = ovalues[1];
    covalues[2] = ovalues[2]*ovalues[2];
    PLogEventBarrierBegin(VEC_NormBarrier,0,0,0,0,comm);
    ierr = MPI_Allreduce(covalues,cvalues,6,MPI_DOUBLE,MPI_SUM,comm);CHKERRQ(ierr);
    PLogEventBarrierBegin(VEC_NormBarrier,0,0,0,0,comm);
    dot = cvalues[0]; sum = PetscReal(cvalues[1]); norm = sqrt(PetscReal(cvalues[2]));
    PLogEventEnd(VEC_Norm,a,0,0,0);
  }
#endif


  /* Safeguard for step sizes too small */
  if (sum == 0.0) {dot = 1.0; norm = 1.0;}
#if defined(USE_PETSC_COMPLEX)
  else if (abs(dot) < umin*sum && real(dot) >= 0.0) dot = umin*sum;
  else if (abs(dot) < 0.0 && real(dot) > -umin*sum) dot = -umin*sum;
#else
  else if (dot < umin*sum && dot >= 0.0) dot = umin*sum;
  else if (dot < 0.0 && dot > -umin*sum) dot = -umin*sum;
#endif
  h = ctx->error_rel*dot/(norm*norm);
  
  /* Evaluate function at F(u + ha) */
  ierr = VecWAXPY(&h,a,U,w); CHKERRQ(ierr);
  ierr = eval_fct(snes,w,y); CHKERRQ(ierr);
  ierr = VecAXPY(&mone,F,y); CHKERRQ(ierr);
  h = 1.0/h;
  ierr = VecScale(&h,y); CHKERRQ(ierr);
  if (ctx->sp) {ierr = PCNullSpaceRemove(ctx->sp,y); CHKERRQ(ierr);}

  PLogEventEnd(MAT_MatrixFreeMult,a,y,0,0);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "SNESDefaultMatrixFreeMatCreate"
/*@C
   SNESDefaultMatrixFreeMatCreate - 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().

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

   Output Parameter:
.  J - the matrix-free matrix

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

$       J(u)*a = [J(u+h*a) - J(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

   The user can set these parameters via SNESSetMatrixFreeParameters().
   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>
$  -snes_mf_unim <umin>

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

.seealso: MatDestroy(), SNESSetMatrixFreeParameters()
@*/
int SNESDefaultMatrixFreeMatCreate(SNES snes,Vec x, Mat *J)
{
  MPI_Comm      comm;
  MFCtx_Private *mfctx;
  int           n, nloc, ierr, flg;
  char          p[64];

  PetscFunctionBegin;
  mfctx = (MFCtx_Private *) PetscMalloc(sizeof(MFCtx_Private)); CHKPTRQ(mfctx);
  PLogObjectMemory(snes,sizeof(MFCtx_Private));
  mfctx->sp   = 0;
  mfctx->snes = snes;
  mfctx->error_rel = 1.e-8; /* assumes double precision */
  mfctx->umin      = 1.e-6;
  ierr = OptionsGetDouble(snes->prefix,"-snes_mf_err",&mfctx->error_rel,&flg); CHKERRQ(ierr);
  ierr = OptionsGetDouble(snes->prefix,"-snes_mf_umin",&mfctx->umin,&flg); CHKERRQ(ierr);
  ierr = OptionsHasName(PETSC_NULL,"-help",&flg); CHKERRQ(ierr);
  PetscStrcpy(p,"-");
  if (snes->prefix) PetscStrcat(p,snes->prefix);
  if (flg) {
    (*PetscHelpPrintf)(snes->comm,"   %ssnes_mf_err <err>: set sqrt rel error in function (default %g)\n",p,mfctx->error_rel);
    (*PetscHelpPrintf)(snes->comm,"   %ssnes_mf_umin <umin> see users manual (default %g)\n",p,mfctx->umin);
  }
  ierr = VecDuplicate(x,&mfctx->w); CHKERRQ(ierr);
  ierr = PetscObjectGetComm((PetscObject)x,&comm); CHKERRQ(ierr);
  ierr = VecGetSize(x,&n); CHKERRQ(ierr);
  ierr = VecGetLocalSize(x,&nloc); CHKERRQ(ierr);
  ierr = MatCreateShell(comm,nloc,n,n,n,mfctx,J); CHKERRQ(ierr);
  ierr = MatShellSetOperation(*J,MATOP_MULT,(void*)SNESMatrixFreeMult_Private);CHKERRQ(ierr);
  ierr = MatShellSetOperation(*J,MATOP_DESTROY,(void *)SNESMatrixFreeDestroy_Private);CHKERRQ(ierr);
  ierr = MatShellSetOperation(*J,MATOP_VIEW,(void *)SNESMatrixFreeView_Private); CHKERRQ(ierr);
  PLogObjectParent(*J,mfctx->w);
  PLogObjectParent(snes,*J);
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "SNESSetMatrixFreeParameters"
/*@
   SNESSetMatrixFreeParameters - Sets the parameters for the approximation of
   matrix-vector products using finite differences.

$       J(u)*a = [J(u+h*a) - J(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
$
   Input Parameters:
.  snes - the SNES context
.  error_rel - relative error (should be set to the square root of
     the relative error in the function evaluations)
.  umin - minimum allowable u-value

.keywords: SNES, matrix-free, parameters

.seealso: SNESDefaultMatrixFreeMatCreate()
@*/
int SNESSetMatrixFreeParameters(SNES snes,double error,double umin)
{
  MFCtx_Private *ctx;
  int           ierr;
  Mat           mat;

  PetscFunctionBegin;
  ierr = SNESGetJacobian(snes,&mat,PETSC_NULL,PETSC_NULL); CHKERRQ(ierr);
  ierr = MatShellGetContext(mat,(void **)&ctx); CHKERRQ(ierr);
  if (ctx) {
    if (error != PETSC_DEFAULT) ctx->error_rel = error;
    if (umin != PETSC_DEFAULT)  ctx->umin = umin;
  }
  PetscFunctionReturn(0);
}

#undef __FUNC__  
#define __FUNC__ "SNESDefaultMatrixFreeMatAddNullSpace"
/*@
   SNESDefaultMatrixFreeMatAddNullSpace - 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.

   Input Parameters:
.  J - the matrix-free matrix context
.  has_cnst - PETSC_TRUE or PETSC_FALSE, indicating if null space has constants
.  n - number of vectors (excluding constant vector) in null space
.  vecs - the vectors that span the null space (excluding the constant vector);
.         these vectors must be orthonormal

.keywords: SNES, matrix-free, null space
@*/
int SNESDefaultMatrixFreeMatAddNullSpace(Mat J,int has_cnst,int n,Vec *vecs)
{
  int           ierr;
  MFCtx_Private *ctx;
  MPI_Comm      comm;

  PetscFunctionBegin;
  PetscObjectGetComm((PetscObject)J,&comm);

  ierr = MatShellGetContext(J,(void **)&ctx); CHKERRQ(ierr);
  /* no context indicates that it is not the "matrix free" matrix type */
  if (!ctx) PetscFunctionReturn(0);
  ierr = PCNullSpaceCreate(comm,has_cnst,n,vecs,&ctx->sp); CHKERRQ(ierr);
  PetscFunctionReturn(0);
}