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/*

      SVD routines related to the solution process.

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

   SLEPc - Scalable Library for Eigenvalue Problem Computations

   Copyright (c) 2002-2009, Universidad Politecnica de Valencia, Spain

   This file is part of SLEPc.

   SLEPc is free software: you can redistribute it and/or modify it under  the

   terms of version 3 of the GNU Lesser General Public License as published by

   the Free Software Foundation.

   SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY

   WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS

   FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for

   more details.

   You  should have received a copy of the GNU Lesser General  Public  License

   along with SLEPc. If not, see <http://www.gnu.org/licenses/>.

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*/

#include "private/svdimpl.h"   /*I "slepcsvd.h" I*/

#undef __FUNCT__  

#define __FUNCT__ "SVDSolve"

/*@

   SVDSolve - Solves the singular value problem.

   Collective on SVD

   Input Parameter:

.  svd - singular value solver context obtained from SVDCreate()

   Options Database:

.   -svd_view - print information about the solver used

   Level: beginner

.seealso: SVDCreate(), SVDSetUp(), SVDDestroy()

@*/

PetscErrorCode SVDSolve(SVD svd)

{

  PetscErrorCode ierr;

  PetscTruth     flg;

  PetscInt       i,*workperm;

  char           filename[PETSC_MAX_PATH_LEN];

  PetscViewer    viewer;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(svd,SVD_COOKIE,1);

  if (!svd->setupcalled) { ierr = SVDSetUp(svd);CHKERRQ(ierr); }

  svd->its = 0;

  svd->matvecs = 0;

  svd->nconv = 0;

  svd->reason = SVD_CONVERGED_ITERATING;

  ierr = IPResetOperationCounters(svd->ip);CHKERRQ(ierr);

  for (i=0;i<svd->ncv;i++) svd->sigma[i]=svd->errest[i]=0.0;

  SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,svd->ncv);

  ierr = PetscLogEventBegin(SVD_Solve,svd,0,0,0);CHKERRQ(ierr);

  ierr = (*svd->ops->solve)(svd);CHKERRQ(ierr);

  ierr = PetscLogEventEnd(SVD_Solve,svd,0,0,0);CHKERRQ(ierr);

  /* sort singular triplets */

  if (svd->which == SVD_SMALLEST) {

    for (i=0;i<svd->nconv;i++) svd->perm[i] = i;

    ierr = PetscSortRealWithPermutation(svd->nconv,svd->sigma,svd->perm);CHKERRQ(ierr);

  } else {

    ierr = PetscMalloc(sizeof(PetscInt)*svd->nconv,&workperm);CHKERRQ(ierr);

    for (i=0;i<svd->nconv;i++) workperm[i] = i;

    ierr = PetscSortRealWithPermutation(svd->nconv,svd->sigma,workperm);CHKERRQ(ierr);

    for (i=0;i<svd->nconv;i++) svd->perm[i] = workperm[svd->nconv-i-1];

    ierr = PetscFree(workperm);CHKERRQ(ierr);

  }

  ierr = PetscOptionsGetString(((PetscObject)svd)->prefix,"-svd_view",filename,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);

  if (flg && !PetscPreLoadingOn) {

    ierr = PetscViewerASCIIOpen(((PetscObject)svd)->comm,filename,&viewer);CHKERRQ(ierr);

    ierr = SVDView(svd,viewer);CHKERRQ(ierr);

    ierr = PetscViewerDestroy(viewer);CHKERRQ(ierr);

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDGetIterationNumber"

/*@

   SVDGetIterationNumber - Gets the current iteration number. If the

   call to SVDSolve() is complete, then it returns the number of iterations

   carried out by the solution method.

   Not Collective

   Input Parameter:

.  svd - the singular value solver context

   Output Parameter:

.  its - number of iterations

   Level: intermediate

   Notes:

      During the i-th iteration this call returns i-1. If SVDSolve() is

      complete, then parameter "its" contains either the iteration number at

      which convergence was successfully reached, or failure was detected.  

      Call SVDGetConvergedReason() to determine if the solver converged or

      failed and why.

@*/

PetscErrorCode SVDGetIterationNumber(SVD svd,PetscInt *its)

{

  PetscFunctionBegin;

  PetscValidHeaderSpecific(svd,SVD_COOKIE,1);

  PetscValidIntPointer(its,2);

  *its = svd->its;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDGetConvergedReason"

/*@C

   SVDGetConvergedReason - Gets the reason why the SVDSolve() iteration was

   stopped.

   Not Collective

   Input Parameter:

.  svd - the singular value solver context

   Output Parameter:

.  reason - negative value indicates diverged, positive value converged

   (see SVDConvergedReason)

   Possible values for reason:

+  SVD_CONVERGED_TOL - converged up to tolerance

.  SVD_DIVERGED_ITS - required more than its to reach convergence

-  SVD_DIVERGED_BREAKDOWN - generic breakdown in method

   Level: intermediate

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

.seealso: SVDSetTolerances(), SVDSolve(), SVDConvergedReason

@*/

PetscErrorCode SVDGetConvergedReason(SVD svd,SVDConvergedReason *reason)

{

  PetscFunctionBegin;

  PetscValidHeaderSpecific(svd,SVD_COOKIE,1);

  PetscValidIntPointer(reason,2);

  *reason = svd->reason;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDGetConverged"

/*@

   SVDGetConverged - Gets the number of converged singular values.

   Not Collective

   Input Parameter:

.  svd - the singular value solver context

   Output Parameter:

.  nconv - number of converged singular values

   Note:

   This function should be called after SVDSolve() has finished.

   Level: beginner

@*/

PetscErrorCode SVDGetConverged(SVD svd,PetscInt *nconv)

{

  PetscFunctionBegin;

  PetscValidHeaderSpecific(svd,SVD_COOKIE,1);

  PetscValidIntPointer(nconv,2);

  if (svd->reason == SVD_CONVERGED_ITERATING) {

    SETERRQ(PETSC_ERR_ARG_WRONGSTATE, "SVDSolve must be called first");

  }

  *nconv = svd->nconv;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDGetSingularTriplet" 

/*@

   SVDGetSingularTriplet - Gets the i-th triplet of the singular value decomposition

   as computed by SVDSolve(). The solution consists in the singular value and its left

   and right singular vectors.

   Not Collective

   Input Parameters:

+  svd - singular value solver context

-  i   - index of the solution

   Output Parameters:

+  sigma - singular value

.  u     - left singular vector

-  v     - right singular vector

   Note:

   The index i should be a value between 0 and nconv-1 (see SVDGetConverged()).

   Both U or V can be PETSC_NULL if singular vectors are not required.

   Level: beginner

.seealso: SVDSolve(),  SVDGetConverged()

@*/

PetscErrorCode SVDGetSingularTriplet(SVD svd, PetscInt i, PetscReal *sigma, Vec u, Vec v)

{

  PetscErrorCode ierr;

  PetscReal      norm;

  PetscInt       j,nloc,M,N;

  PetscScalar    *pU;

  Vec            w;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(svd,SVD_COOKIE,1);

  PetscValidPointer(sigma,3);

  if (svd->reason == SVD_CONVERGED_ITERATING) {

    SETERRQ(PETSC_ERR_ARG_WRONGSTATE, "SVDSolve must be called first");

  }

  if (i<0 || i>=svd->nconv) {

    SETERRQ(PETSC_ERR_ARG_OUTOFRANGE, "Argument 2 out of range");

  }

  *sigma = svd->sigma[svd->perm[i]];

  ierr = MatGetSize(svd->OP,&M,&N);CHKERRQ(ierr);

  if (M<N) { w = u; u = v; v = w; }

  if (u) {

    PetscValidHeaderSpecific(u,VEC_COOKIE,4);

    if (!svd->U) {

      ierr = PetscMalloc(sizeof(Vec)*svd->ncv,&svd->U);CHKERRQ(ierr);

      ierr = SVDMatGetLocalSize(svd,&nloc,PETSC_NULL);CHKERRQ(ierr);

      ierr = PetscMalloc(svd->ncv*nloc*sizeof(PetscScalar),&pU);CHKERRQ(ierr);

      for (j=0;j<svd->ncv;j++) {

        ierr = VecCreateMPIWithArray(((PetscObject)svd)->comm,nloc,PETSC_DECIDE,pU+j*nloc,&svd->U[j]);CHKERRQ(ierr);

      }

      for (j=0;j<svd->nconv;j++) {

        ierr = SVDMatMult(svd,PETSC_FALSE,svd->V[j],svd->U[j]);CHKERRQ(ierr);

        ierr = IPOrthogonalize(svd->ip,0,PETSC_NULL,j,PETSC_NULL,svd->U,svd->U[j],PETSC_NULL,&norm,PETSC_NULL);CHKERRQ(ierr);

        ierr = VecScale(svd->U[j],1.0/norm);CHKERRQ(ierr);

      }

    }

    ierr = VecCopy(svd->U[svd->perm[i]],u);CHKERRQ(ierr);

  }

  if (v) {

    PetscValidHeaderSpecific(v,VEC_COOKIE,5);  

    ierr = VecCopy(svd->V[svd->perm[i]],v);CHKERRQ(ierr);

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDComputeResidualNorms"

/*@

   SVDComputeResidualNorms - Computes the norms of the residual vectors associated with

   the i-th computed singular triplet.

   Collective on SVD

   Input Parameters:

+  svd  - the singular value solver context

-  i    - the solution index

   Output Parameters:

+  norm1 - the norm ||A*v-sigma*u||_2 where sigma is the

           singular value, u and v are the left and right singular vectors.

-  norm2 - the norm ||A^T*u-sigma*v||_2 with the same sigma, u and v

   Note:

   The index i should be a value between 0 and nconv-1 (see SVDGetConverged()).

   Both output parameters can be PETSC_NULL on input if not needed.

   Level: beginner

.seealso: SVDSolve(), SVDGetConverged(), SVDComputeRelativeError()

@*/

PetscErrorCode SVDComputeResidualNorms(SVD svd, PetscInt i, PetscReal *norm1, PetscReal *norm2)

{

  PetscErrorCode ierr;

  Vec            u,v,x = PETSC_NULL,y = PETSC_NULL;

  PetscReal      sigma;

  PetscInt       M,N;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(svd,SVD_COOKIE,1);

  if (svd->reason == SVD_CONVERGED_ITERATING) {

    SETERRQ(PETSC_ERR_ARG_WRONGSTATE, "SVDSolve must be called first");

  }

  if (i<0 || i>=svd->nconv) {

    SETERRQ(PETSC_ERR_ARG_OUTOFRANGE, "Argument 2 out of range");

  }

  ierr = MatGetVecs(svd->OP,&v,&u);CHKERRQ(ierr);

  ierr = SVDGetSingularTriplet(svd,i,&sigma,u,v);CHKERRQ(ierr);

  if (norm1) {

    ierr = VecDuplicate(u,&x);CHKERRQ(ierr);

    ierr = MatMult(svd->OP,v,x);CHKERRQ(ierr);

    ierr = VecAXPY(x,-sigma,u);CHKERRQ(ierr);

    ierr = VecNorm(x,NORM_2,norm1);CHKERRQ(ierr);

  }

  if (norm2) {

    ierr = VecDuplicate(v,&y);CHKERRQ(ierr);

    if (svd->A && svd->AT) {

      ierr = MatGetSize(svd->OP,&M,&N);CHKERRQ(ierr);

      if (M<N) {

        ierr = MatMult(svd->A,u,y);CHKERRQ(ierr);

      } else {

        ierr = MatMult(svd->AT,u,y);CHKERRQ(ierr);

      }

    } else {

      ierr = MatMultTranspose(svd->OP,u,y);CHKERRQ(ierr);

    }

    ierr = VecAXPY(y,-sigma,v);CHKERRQ(ierr);

    ierr = VecNorm(y,NORM_2,norm2);CHKERRQ(ierr);

  }

  ierr = VecDestroy(v);CHKERRQ(ierr);

  ierr = VecDestroy(u);CHKERRQ(ierr);

  if (x) { ierr = VecDestroy(x);CHKERRQ(ierr); }

  if (y) { ierr = VecDestroy(y);CHKERRQ(ierr); }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDComputeRelativeError"

/*@

   SVDComputeRelativeError - Computes the relative error bound associated

   with the i-th singular triplet.

   Collective on SVD

   Input Parameter:

+  svd - the singular value solver context

-  i   - the solution index

   Output Parameter:

.  error - the relative error bound, computed as sqrt(n1^2+n2^2)/sigma

   where n1 = ||A*v-sigma*u||_2 , n2 = ||A^T*u-sigma*v||_2 , sigma is the singular value,

   u and v are the left and right singular vectors.

   If sigma is too small the relative error is computed as sqrt(n1^2+n2^2).

   Level: beginner

.seealso: SVDSolve(), SVDComputeResidualNorms()

@*/

PetscErrorCode SVDComputeRelativeError(SVD svd,PetscInt i,PetscReal *error)

{

  PetscErrorCode ierr;

  PetscReal      sigma,norm1,norm2;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(svd,SVD_COOKIE,1);

  PetscValidPointer(error,2);

  ierr = SVDGetSingularTriplet(svd,i,&sigma,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

  ierr = SVDComputeResidualNorms(svd,i,&norm1,&norm2);CHKERRQ(ierr);

  *error = sqrt(norm1*norm1+norm2*norm2);

  if (sigma>*error) *error /= sigma;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDGetOperationCounters"

/*@

   SVDGetOperationCounters - Gets the total number of matrix vector and dot

   products used by the SVD object during the last SVDSolve() call.

   Not Collective

   Input Parameter:

.  svd - SVD context

   Output Parameter:

+  matvecs - number of matrix vector product operations

-  dots    - number of dot product operations

   Notes:

   These counters are reset to zero at each successive call to SVDSolve().

   Level: intermediate

@*/

PetscErrorCode SVDGetOperationCounters(SVD svd,PetscInt* matvecs,PetscInt* dots)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(svd,SVD_COOKIE,1);

  if (matvecs) *matvecs = svd->matvecs;

  if (dots) {

    ierr = IPGetOperationCounters(svd->ip,dots);CHKERRQ(ierr);

  }

  PetscFunctionReturn(0);

}