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/*                      

   SLEPc singular value solver: "trlanczos"

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

   Last update: Mar 2007

*/

#include "src/svd/svdimpl.h"                /*I "slepcsvd.h" I*/

#include "slepcblaslapack.h"

typedef struct {

  PetscTruth oneside;

} SVD_TRLANCZOS;

#undef __FUNCT__  

#define __FUNCT__ "SVDSetUp_TRLANCZOS"

PetscErrorCode SVDSetUp_TRLANCZOS(SVD svd)

{

  PetscErrorCode  ierr;

  PetscInt        N;

  int             i;

  PetscFunctionBegin;

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

  if (svd->ncv == PETSC_DECIDE)

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

  if (svd->max_it == PETSC_DECIDE)

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

  if (svd->ncv!=svd->n) {  

    if (svd->U) {

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

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

    }

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

    for (i=0;i<svd->ncv;i++) { ierr = SVDMatGetVecs(svd,PETSC_NULL,svd->U+i);CHKERRQ(ierr); }

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SVDOneSideTRLanczos"

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

{

  PetscErrorCode ierr;

  PetscReal      a,b;

  int            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);

    svd->dots += i;

    ierr = VecNormBegin(U[i-1],NORM_2,&a);CHKERRQ(ierr);

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

    ierr = VecNormEnd(U[i-1],NORM_2,&a);CHKERRQ(ierr);

    ierr = VecMDotEnd(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);

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

    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);

  svd->dots += i;

  ierr = VecNormBegin(U[n-1],NORM_2,&a);CHKERRQ(ierr);

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

  ierr = VecNormEnd(U[n-1],NORM_2,&a);CHKERRQ(ierr);

  ierr = VecMDotEnd(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);

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

  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;

  PetscInt       *perm;

  int            i,j,k,l,m,n,nwork=0;

  Vec            v,wv,wu,*workV,*workU,*permV,*permU;

  PetscTruth     conv;

  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);

  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 = PetscMalloc(sizeof(Vec)*svd->n,&workV);CHKERRQ(ierr);

  ierr = PetscMalloc(sizeof(Vec)*svd->n,&workU);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 */

    if (lanczos->oneside) {

      ierr = SVDOneSideTRLanczos(svd,alpha,beta,b+svd->nconv,svd->V,v,svd->U,svd->nconv,l,svd->n,PT,wv,wu);CHKERRQ(ierr);

    } else {

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

    }

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

    /* compute SVD of general matrix */

    n = svd->n - 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((svd->n - svd->nconv - k) / 2,1);

    /* allocate work space for converged singular and restart vectors */

    if (nwork<k+l) {

      for (i=nwork;i<k+l;i++) {

        ierr = SVDMatGetVecs(svd,workV+i,workU+i);CHKERRQ(ierr);

      }

      nwork = k+l;

    }

    /* compute converged singular vectors and restart vectors*/

    for (i=0;i<k+l;i++) {

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

      else j = i;

      ierr = VecSet(workV[i],0.0);CHKERRQ(ierr);

      for (m=0;m<n;m++) {

        ierr = VecAXPY(workV[i],PT[m*n+j],svd->V[m+svd->nconv]);CHKERRQ(ierr);

      }      

      ierr = VecSet(workU[i],0.0);CHKERRQ(ierr);

      ierr = VecMAXPY(workU[i],n,Q+j*n,svd->U+svd->nconv);CHKERRQ(ierr);

    }

    /* 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);

    }

    /* copy converged singular vectors and restart vectors from temporary space */

    for (i=0;i<k+l;i++) {

      ierr = VecCopy(workV[i],svd->V[i+svd->nconv]);CHKERRQ(ierr);

      ierr = VecCopy(workU[i],svd->U[i+svd->nconv]);CHKERRQ(ierr);

    }

    svd->nconv += k;

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

  }

  /* sort singular triplets */

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

  ierr = PetscMalloc(sizeof(Vec)*svd->nconv,&permV);CHKERRQ(ierr);

  ierr = PetscMalloc(sizeof(Vec)*svd->nconv,&permU);CHKERRQ(ierr);

  for (i=0;i<svd->nconv;i++) {

    alpha[i] = svd->sigma[i];

    beta[i] = svd->errest[i];

    permV[i] = svd->V[i];

    permU[i] = svd->U[i];

    perm[i] = i;

  }

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

  for (i=0;i<svd->nconv;i++) {

    if (svd->which == SVD_SMALLEST) j = perm[i];

    else j = perm[svd->nconv-i-1];

    svd->sigma[i] = alpha[j];

    svd->errest[i] = beta[j];

    svd->V[i] = permV[j];

    svd->U[i] = permU[j];

  }

  /* free working space */

  ierr = VecDestroy(v);CHKERRQ(ierr);

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

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

  for (i=0;i<nwork;i++) { ierr = VecDestroy(workV[i]);CHKERRQ(ierr); }

  ierr = PetscFree(workV);CHKERRQ(ierr);

  for (i=0;i<nwork;i++) { ierr = VecDestroy(workU[i]);CHKERRQ(ierr); }

  ierr = PetscFree(workU);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(perm);CHKERRQ(ierr);

  ierr = PetscFree(permV);CHKERRQ(ierr);

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

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

  ierr = PetscOptionsEnd();CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "SVDTRLanczosSetOneSideReorthogonalization_TRLANCZOS"

PetscErrorCode SVDTRLanczosSetOneSideReorthogonalization_TRLANCZOS(SVD svd,PetscTruth oneside)

{

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

  PetscFunctionBegin;

  lanczos->oneside = oneside;

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__

#define __FUNCT__ "SVDTRLanczosSetOneSideReorthogonalization"

PetscErrorCode SVDTRLanczosSetOneSideReorthogonalization(SVD svd,PetscTruth oneside)

{

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

  PetscFunctionBegin;

  PetscValidHeaderSpecific(svd,SVD_COOKIE,1);

  ierr = PetscObjectQueryFunction((PetscObject)svd,"SVDTRLanczosSetOneSideReorthogonalization_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->setfromoptions = SVDSetFromOptions_TRLANCZOS;

  svd->ops->view           = SVDView_TRLANCZOS;

  lanczos->oneside         = PETSC_FALSE;

  ierr = PetscObjectComposeFunctionDynamic((PetscObject)svd,"SVDTRLanczosSetOneSideReorthogonalization_C","SVDTRLanczosSetOneSideReorthogonalization_TRLANCZOS",SVDTRLanczosSetOneSideReorthogonalization_TRLANCZOS);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_END