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/*                      

   SLEPc singular value solver: "trlanczos"

   Method: Golub-Kahan-Lanczos bidiagonalization with thick-restart

   Last update: Jun 2007

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

      SLEPc - Scalable Library for Eigenvalue Problem Computations

      Copyright (c) 2002-2007, Universidad Politecnica de Valencia, Spain

      This file is part of SLEPc. See the README file for conditions of use

      and additional information.

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

*/

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

#include "private/ipimpl.h"

#include "slepcblaslapack.h"

typedef struct {

  PetscTruth oneside;

} SVD_TRLANCZOS;

#undef __FUNCT__  

#define __FUNCT__ "SVDSetUp_TRLANCZOS"

PetscErrorCode SVDSetUp_TRLANCZOS(SVD svd)

{

  PetscErrorCode  ierr;

  PetscInt        i,N,nloc;

  PetscScalar     *pU;

  PetscFunctionBegin;

  ierr = SVDMatGetSize(svd,PETSC_NULL,&N);CHKERRQ(ierr);

  if (svd->ncv) { /* ncv set */

    if (svd->ncv<svd->nsv) SETERRQ(1,"The value of ncv must be at least nsv");

  }

  else if (svd->mpd) { /* mpd set */

    svd->ncv = PetscMin(N,svd->nsv+svd->mpd);

  }

  else { /* neither set: defaults depend on nsv being small or large */

    if (svd->nsv<500) svd->ncv = PetscMin(N,PetscMax(2*svd->nsv,10));

    else { svd->mpd = 500; svd->ncv = PetscMin(N,svd->nsv+svd->mpd); }

  }

  if (!svd->mpd) svd->mpd = svd->ncv;

  if (svd->ncv>svd->nsv+svd->mpd) SETERRQ(1,"The value of ncv must not be larger than nev+mpd");

  if (!svd->max_it)

    svd->max_it = PetscMax(N/svd->ncv,100);

  if (svd->ncv!=svd->n) {  

    if (svd->U) {

      ierr = VecGetArray(svd->U[0],&pU);CHKERRQ(ierr);

      for (i=0;i<svd->n;i++) { ierr = VecDestroy(svd->U[i]); CHKERRQ(ierr); }

      ierr = PetscFree(pU);CHKERRQ(ierr);

      ierr = PetscFree(svd->U);CHKERRQ(ierr);

    }

    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 (i=0;i<svd->ncv;i++) {

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

    }

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDOneSideTRLanczosMGS"

static PetscErrorCode SVDOneSideTRLanczosMGS(SVD svd,PetscReal *alpha,PetscReal *beta,PetscScalar* bb,Vec *V,Vec v,Vec* U,PetscInt nconv,PetscInt l,PetscInt n,PetscScalar* work,Vec wv,Vec wu)

{

  PetscErrorCode ierr;

  PetscReal      a,b;

  PetscInt       i,k=nconv+l;

  PetscFunctionBegin;

  ierr = SVDMatMult(svd,PETSC_FALSE,V[k],U[k]);CHKERRQ(ierr);

  if (l>0) {

    ierr = VecSet(wu,0.0);CHKERRQ(ierr);

    ierr = VecMAXPY(wu,l,bb,U+nconv);CHKERRQ(ierr);

    ierr = VecAXPY(U[k],-1.0,wu);CHKERRQ(ierr);

  }

  ierr = IPNorm(svd->ip,U[k],&a);CHKERRQ(ierr);

  ierr = VecScale(U[k],1.0/a);CHKERRQ(ierr);

  alpha[0] = a;

  for (i=k+1;i<n;i++) {

    ierr = SVDMatMult(svd,PETSC_TRUE,U[i-1],V[i]);CHKERRQ(ierr);

    ierr = IPOrthogonalize(svd->ip,i,PETSC_NULL,V,V[i],work,&b,PETSC_NULL,wv,PETSC_NULL);CHKERRQ(ierr);  

    ierr = VecScale(V[i],1.0/b);CHKERRQ(ierr);

    beta[i-k-1] = b;

    ierr = SVDMatMult(svd,PETSC_FALSE,V[i],U[i]);CHKERRQ(ierr);

    ierr = VecAXPY(U[i],-b,U[i-1]);CHKERRQ(ierr);

    ierr = IPNorm(svd->ip,U[i],&a);CHKERRQ(ierr);

    ierr = VecScale(U[i],1.0/a);CHKERRQ(ierr);

    alpha[i-k] = a;

  }

  ierr = SVDMatMult(svd,PETSC_TRUE,U[n-1],v);CHKERRQ(ierr);

  ierr = IPOrthogonalize(svd->ip,n,PETSC_NULL,V,v,work,&b,PETSC_NULL,wv,PETSC_NULL);CHKERRQ(ierr);      

  beta[n-k-1] = b;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDOneSideTRLanczosCGS"

static PetscErrorCode SVDOneSideTRLanczosCGS(SVD svd,PetscReal *alpha,PetscReal *beta,PetscScalar* bb,Vec *V,Vec v,Vec* U,PetscInt nconv,PetscInt l,PetscInt n,PetscScalar* work,Vec wv,Vec wu)

{

  PetscErrorCode ierr;

  PetscReal      a,b,sum,onorm;

  PetscScalar    dot;

  PetscInt       i,j,k=nconv+l;

  PetscFunctionBegin;

  ierr = SVDMatMult(svd,PETSC_FALSE,V[k],U[k]);CHKERRQ(ierr);

  if (l>0) {

    ierr = VecSet(wu,0.0);CHKERRQ(ierr);

    ierr = VecMAXPY(wu,l,bb,U+nconv);CHKERRQ(ierr);

    ierr = VecAXPY(U[k],-1.0,wu);CHKERRQ(ierr);

  }

  for (i=k+1;i<n;i++) {

    ierr = SVDMatMult(svd,PETSC_TRUE,U[i-1],V[i]);CHKERRQ(ierr);

    ierr = IPNormBegin(svd->ip,U[i-1],&a);CHKERRQ(ierr);

    if (svd->ip->orthog_ref == IP_ORTH_REFINE_IFNEEDED) {

      ierr = IPInnerProductBegin(svd->ip,V[i],V[i],&dot);CHKERRQ(ierr);

    }

    ierr = IPMInnerProductBegin(svd->ip,V[i],i,V,work);CHKERRQ(ierr);

    ierr = IPNormEnd(svd->ip,U[i-1],&a);CHKERRQ(ierr);

    if (svd->ip->orthog_ref == IP_ORTH_REFINE_IFNEEDED) {

      ierr = IPInnerProductEnd(svd->ip,V[i],V[i],&dot);CHKERRQ(ierr);

    }

    ierr = IPMInnerProductEnd(svd->ip,V[i],i,V,work);CHKERRQ(ierr);

    ierr = VecScale(U[i-1],1.0/a);CHKERRQ(ierr);

    ierr = VecScale(V[i],1.0/a);CHKERRQ(ierr);

    for (j=0;j<i;j++) work[j] = - work[j] / a;

    ierr = VecMAXPY(V[i],i,work,V);CHKERRQ(ierr);

    switch (svd->ip->orthog_ref) {

    case IP_ORTH_REFINE_NEVER:

      ierr = IPNorm(svd->ip,V[i],&b);CHKERRQ(ierr);

      break;      

    case IP_ORTH_REFINE_ALWAYS:

      ierr = IPOrthogonalizeCGS(svd->ip,i,PETSC_NULL,V,V[i],work,PETSC_NULL,&b,wv);CHKERRQ(ierr);

      break;

    case IP_ORTH_REFINE_IFNEEDED:

      onorm = sqrt(PetscRealPart(dot)) / a;

      sum = 0.0;

      for (j=0;j<i;j++) {

        sum += PetscRealPart(work[j] * PetscConj(work[j]));

      }

      b = PetscRealPart(dot)/(a*a) - sum;

      if (b>0.0) b = sqrt(b);

      else {

        ierr = IPNorm(svd->ip,V[i],&b);CHKERRQ(ierr);

      }

      if (b < svd->ip->orthog_eta * onorm) {

        ierr = IPOrthogonalizeCGS(svd->ip,i,PETSC_NULL,V,V[i],work,PETSC_NULL,&b,wv);CHKERRQ(ierr);

      }

      break;

    }

    ierr = VecScale(V[i],1.0/b);CHKERRQ(ierr);

    ierr = SVDMatMult(svd,PETSC_FALSE,V[i],U[i]);CHKERRQ(ierr);

    ierr = VecAXPY(U[i],-b,U[i-1]);CHKERRQ(ierr);

    alpha[i-k-1] = a;

    beta[i-k-1] = b;

  }

  ierr = SVDMatMult(svd,PETSC_TRUE,U[n-1],v);CHKERRQ(ierr);

  ierr = IPNormBegin(svd->ip,U[n-1],&a);CHKERRQ(ierr);

  if (svd->ip->orthog_ref == IP_ORTH_REFINE_IFNEEDED) {

    ierr = IPInnerProductBegin(svd->ip,v,v,&dot);CHKERRQ(ierr);

  }

  ierr = IPMInnerProductBegin(svd->ip,v,n,V,work);CHKERRQ(ierr);

  ierr = IPNormEnd(svd->ip,U[n-1],&a);CHKERRQ(ierr);

  if (svd->ip->orthog_ref == IP_ORTH_REFINE_IFNEEDED) {

    ierr = IPInnerProductEnd(svd->ip,v,v,&dot);CHKERRQ(ierr);

  }

  ierr = IPMInnerProductEnd(svd->ip,v,n,V,work);CHKERRQ(ierr);

  ierr = VecScale(U[n-1],1.0/a);CHKERRQ(ierr);

  ierr = VecScale(v,1.0/a);CHKERRQ(ierr);

  for (j=0;j<n;j++) work[j] = - work[j] / a;

  ierr = VecMAXPY(v,n,work,V);CHKERRQ(ierr);

  switch (svd->ip->orthog_ref) {

  case IP_ORTH_REFINE_NEVER:

    ierr = IPNorm(svd->ip,v,&b);CHKERRQ(ierr);

    break;      

  case IP_ORTH_REFINE_ALWAYS:

    ierr = IPOrthogonalizeCGS(svd->ip,n,PETSC_NULL,V,v,work,PETSC_NULL,&b,wv);CHKERRQ(ierr);

    break;

  case IP_ORTH_REFINE_IFNEEDED:

    onorm = sqrt(PetscRealPart(dot)) / a;

    sum = 0.0;

    for (j=0;j<i;j++) {

      sum += PetscRealPart(work[j] * PetscConj(work[j]));

    }

    b = PetscRealPart(dot)/(a*a) - sum;

    if (b>0.0) b = sqrt(b);

    else {

      ierr = IPNorm(svd->ip,v,&b);CHKERRQ(ierr);

    }

    if (b < svd->ip->orthog_eta * onorm) {

      ierr = IPOrthogonalizeCGS(svd->ip,n,PETSC_NULL,V,v,work,PETSC_NULL,&b,wv);CHKERRQ(ierr);

    }

    break;

  }

  alpha[n-k-1] = a;

  beta[n-k-1] = b;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDSolve_TRLANCZOS"

PetscErrorCode SVDSolve_TRLANCZOS(SVD svd)

{

  PetscErrorCode ierr;

  SVD_TRLANCZOS  *lanczos = (SVD_TRLANCZOS *)svd->data;

  PetscReal      *alpha,*beta,norm;

  PetscScalar    *b,*Q,*PT,*swork;

  PetscInt       i,j,k,l,m,n,nv;

  Vec            v,wv,wu;

  PetscTruth     conv;

  IPOrthogonalizationType orthog;

  PetscFunctionBegin;

  /* allocate working space */

  ierr = PetscMalloc(sizeof(PetscReal)*svd->n,&alpha);CHKERRQ(ierr);

  ierr = PetscMalloc(sizeof(PetscReal)*svd->n,&beta);CHKERRQ(ierr);

  ierr = PetscMalloc(sizeof(PetscScalar)*svd->n,&b);CHKERRQ(ierr);

  ierr = PetscMalloc(sizeof(PetscScalar)*svd->n*svd->n,&Q);CHKERRQ(ierr);

  ierr = PetscMalloc(sizeof(PetscScalar)*svd->n*svd->n,&PT);CHKERRQ(ierr);

#if !defined(PETSC_USE_COMPLEX)

  if (svd->which == SVD_SMALLEST) {

#endif

    ierr = PetscMalloc(sizeof(PetscScalar)*svd->n*svd->n,&swork);CHKERRQ(ierr);

#if !defined(PETSC_USE_COMPLEX)

  } else {

    ierr = PetscMalloc(sizeof(PetscScalar)*svd->n,&swork);CHKERRQ(ierr);

  }

#endif

  ierr = VecDuplicate(svd->V[0],&v);CHKERRQ(ierr);

  ierr = VecDuplicate(svd->V[0],&wv);CHKERRQ(ierr);

  ierr = VecDuplicate(svd->U[0],&wu);CHKERRQ(ierr);

  ierr = IPGetOrthogonalization(svd->ip,&orthog,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

  /* normalize start vector */

  ierr = VecCopy(svd->vec_initial,svd->V[0]);CHKERRQ(ierr);

  ierr = VecNormalize(svd->V[0],&norm);CHKERRQ(ierr);

  l = 0;

  while (svd->reason == SVD_CONVERGED_ITERATING) {

    svd->its++;

    /* inner loop */

    nv = PetscMin(svd->nconv+svd->mpd,svd->n);

    if (lanczos->oneside) {

      if (orthog == IP_MGS_ORTH) {

        ierr = SVDOneSideTRLanczosMGS(svd,alpha,beta,b+svd->nconv,svd->V,v,svd->U,svd->nconv,l,nv,swork,wv,wu);CHKERRQ(ierr);

      } else {

        ierr = SVDOneSideTRLanczosCGS(svd,alpha,beta,b+svd->nconv,svd->V,v,svd->U,svd->nconv,l,nv,swork,wv,wu);CHKERRQ(ierr);

      }

    } else {

      ierr = SVDTwoSideLanczos(svd,alpha,beta,svd->V,v,svd->U,svd->nconv+l,nv,swork,wv,wu);CHKERRQ(ierr);

    }

    ierr = VecScale(v,1.0/beta[nv-svd->nconv-l-1]);CHKERRQ(ierr);

    /* compute SVD of general matrix */

    n = nv - svd->nconv;

    /* first l columns */

    for (j=0;j<l;j++) {

      for (i=0;i<j;i++) Q[j*n+i] = 0.0;    

      Q[j*n+j] = svd->sigma[svd->nconv+j];

      for (i=j+1;i<n;i++) Q[j*n+i] = 0.0;

    }

    /* l+1 column */

    for (i=0;i<l;i++) Q[l*n+i] = b[i+svd->nconv];

    Q[l*n+l] = alpha[0];

    for (i=l+1;i<n;i++) Q[l*n+i] = 0.0;

    /* rest of matrix */

    for (j=l+1;j<n;j++) {

      for (i=0;i<j-1;i++) Q[j*n+i] = 0.0;

      Q[j*n+j-1] = beta[j-l-1];

      Q[j*n+j] = alpha[j-l];

      for (i=j+1;i<n;i++) Q[j*n+i] = 0.0;

    }

    ierr = SVDDense(n,n,Q,alpha,PETSC_NULL,PT);CHKERRQ(ierr);

    /* compute error estimates */

    k = 0;

    conv = PETSC_TRUE;

    for (i=svd->nconv;i<svd->n;i++) {

      if (svd->which == SVD_SMALLEST) j = n-i+svd->nconv-1;

      else j = i-svd->nconv;

      svd->sigma[i] = alpha[j];

      b[i] = Q[j*n+n-1]*beta[n-l-1];

      svd->errest[i] = PetscAbsScalar(b[i]);

      if (alpha[j] > svd->tol) svd->errest[i] /= alpha[j];

      if (conv) {

        if (svd->errest[i] < svd->tol) k++;

        else conv = PETSC_FALSE;

      }

    }

    /* check convergence and update l */

    if (svd->its >= svd->max_it) svd->reason = SVD_DIVERGED_ITS;

    if (svd->nconv+k >= svd->nsv) svd->reason = SVD_CONVERGED_TOL;

    if (svd->reason != SVD_CONVERGED_ITERATING) l = 0;

    else l = PetscMax((nv - svd->nconv - k) / 2,1);

    /* compute converged singular vectors and restart vectors*/

#if !defined(PETSC_USE_COMPLEX)

    if (svd->which == SVD_SMALLEST) {

#endif

    for (i=0;i<k+l;i++) {

      if (svd->which == SVD_SMALLEST) j = n-i-1;

      else j = i;

      for (m=0;m<n;m++) swork[j*n+m] = PT[m*n+j];

    }

    ierr = SlepcUpdateVectors(n,svd->V+svd->nconv,0,k+l,swork,n,PETSC_FALSE);CHKERRQ(ierr);

    for (i=0;i<k+l;i++) {

      if (svd->which == SVD_SMALLEST) j = n-i-1;

      else j = i;

      for (m=0;m<n;m++) swork[j*n+m] = Q[j*n+m];

    }

    ierr = SlepcUpdateVectors(n,svd->U+svd->nconv,0,k+l,swork,n,PETSC_FALSE);CHKERRQ(ierr);

#if !defined(PETSC_USE_COMPLEX)

    } else {

      ierr = SlepcUpdateVectors(n,svd->V+svd->nconv,0,k+l,PT,n,PETSC_TRUE);CHKERRQ(ierr);

      ierr = SlepcUpdateVectors(n,svd->U+svd->nconv,0,k+l,Q,n,PETSC_FALSE);CHKERRQ(ierr);

    }

#endif

    /* copy the last vector to be the next initial vector */

    if (svd->reason == SVD_CONVERGED_ITERATING) {

      ierr = VecCopy(v,svd->V[svd->nconv+k+l]);CHKERRQ(ierr);

    }

    svd->nconv += k;

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

  }

  /* orthonormalize U columns in one side method */

  if (lanczos->oneside) {

    for (i=0;i<svd->nconv;i++) {

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

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

    }

  }

  /* free working space */

  ierr = VecDestroy(v);CHKERRQ(ierr);

  ierr = VecDestroy(wv);CHKERRQ(ierr);

  ierr = VecDestroy(wu);CHKERRQ(ierr);

  ierr = PetscFree(alpha);CHKERRQ(ierr);

  ierr = PetscFree(beta);CHKERRQ(ierr);

  ierr = PetscFree(b);CHKERRQ(ierr);

  ierr = PetscFree(Q);CHKERRQ(ierr);

  ierr = PetscFree(PT);CHKERRQ(ierr);

  ierr = PetscFree(swork);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDSetFromOptions_TRLANCZOS"

PetscErrorCode SVDSetFromOptions_TRLANCZOS(SVD svd)

{

  PetscErrorCode ierr;

  SVD_TRLANCZOS  *lanczos = (SVD_TRLANCZOS *)svd->data;

  PetscFunctionBegin;

  ierr = PetscOptionsBegin(((PetscObject)svd)->comm,((PetscObject)svd)->prefix,"TRLANCZOS Singular Value Solver Options","SVD");CHKERRQ(ierr);

  ierr = PetscOptionsTruth("-svd_trlanczos_oneside","Lanczos one-side reorthogonalization","SVDTRLanczosSetOneSide",PETSC_FALSE,&lanczos->oneside,PETSC_NULL);CHKERRQ(ierr);

  ierr = PetscOptionsEnd();CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "SVDTRLanczosSetOneSide_TRLANCZOS"

PetscErrorCode SVDTRLanczosSetOneSide_TRLANCZOS(SVD svd,PetscTruth oneside)

{

  SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS *)svd->data;

  PetscFunctionBegin;

  lanczos->oneside = oneside;

  PetscFunctionReturn(0);

}

EXTERN_C_END

#undef __FUNCT__

#define __FUNCT__ "SVDTRLanczosSetOneSide"

/*@

   SVDTRLanczosSetOneSide - Indicate if the variant of the Lanczos method

   to be used is one-sided or two-sided.

   Collective on SVD

   Input Parameters:

+  svd     - singular value solver

-  oneside - boolean flag indicating if the method is one-sided or not

   Options Database Key:

.  -svd_trlanczos_oneside <boolean> - Indicates the boolean flag

   Note:

   By default, a two-sided variant is selected, which is sometimes slightly

   more robust. However, the one-sided variant is faster because it avoids

   the orthogonalization associated to left singular vectors.

   Level: advanced

.seealso: SVDLanczosSetOneSide()

@*/

PetscErrorCode SVDTRLanczosSetOneSide(SVD svd,PetscTruth oneside)

{

  PetscErrorCode ierr, (*f)(SVD,PetscTruth);

  PetscFunctionBegin;

  PetscValidHeaderSpecific(svd,SVD_COOKIE,1);

  ierr = PetscObjectQueryFunction((PetscObject)svd,"SVDTRLanczosSetOneSide_C",(void (**)())&f);CHKERRQ(ierr);

  if (f) {

    ierr = (*f)(svd,oneside);CHKERRQ(ierr);

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDView_TRLANCZOS"

PetscErrorCode SVDView_TRLANCZOS(SVD svd,PetscViewer viewer)

{

  PetscErrorCode ierr;

  SVD_TRLANCZOS  *lanczos = (SVD_TRLANCZOS *)svd->data;

  PetscFunctionBegin;

  ierr = PetscViewerASCIIPrintf(viewer,"Lanczos reorthogonalization: %s\n",lanczos->oneside ? "one-side" : "two-side");CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "SVDCreate_TRLANCZOS"

PetscErrorCode SVDCreate_TRLANCZOS(SVD svd)

{

  PetscErrorCode ierr;

  SVD_TRLANCZOS  *lanczos;

  PetscFunctionBegin;

  ierr = PetscNew(SVD_TRLANCZOS,&lanczos);CHKERRQ(ierr);

  PetscLogObjectMemory(svd,sizeof(SVD_TRLANCZOS));

  svd->data                = (void *)lanczos;

  svd->ops->setup          = SVDSetUp_TRLANCZOS;

  svd->ops->solve          = SVDSolve_TRLANCZOS;

  svd->ops->destroy        = SVDDestroy_Default;

  svd->ops->setfromoptions = SVDSetFromOptions_TRLANCZOS;

  svd->ops->view           = SVDView_TRLANCZOS;

  lanczos->oneside         = PETSC_FALSE;

  ierr = PetscObjectComposeFunctionDynamic((PetscObject)svd,"SVDTRLanczosSetOneSide_C","SVDTRLanczosSetOneSide_TRLANCZOS",SVDTRLanczosSetOneSide_TRLANCZOS);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_END