/*
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   SLEPc - Scalable Library for Eigenvalue Problem Computations
   Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

   This file is part of SLEPc.
   SLEPc is distributed under a 2-clause BSD license (see LICENSE).
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/

#include <slepc/private/dsimpl.h>       /*I "slepcds.h" I*/
#include <slepcblaslapack.h>

typedef struct {
  PetscInt  m;             /* number of columns */
  PetscInt  t;             /* number of rows of V after truncating */
  PetscBool reorth;        /* reorthogonalize left vectors */
} DS_HSVD;

static PetscErrorCode DSAllocate_HSVD(DS ds,PetscInt ld)
{
  PetscFunctionBegin;
  if (!ds->compact) PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
  PetscCall(DSAllocateMat_Private(ds,DS_MAT_U));
  PetscCall(DSAllocateMat_Private(ds,DS_MAT_V));
  PetscCall(DSAllocateMat_Private(ds,DS_MAT_T));
  PetscCall(DSAllocateMat_Private(ds,DS_MAT_D));
  PetscCall(PetscFree(ds->perm));
  PetscCall(PetscMalloc1(ld,&ds->perm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*   0       l           k                 m-1
    -----------------------------------------
    |*       .           .                  |
    |  *     .           .                  |
    |    *   .           .                  |
    |      * .           .                  |
    |        o           o                  |
    |          o         o                  |
    |            o       o                  |
    |              o     o                  |
    |                o   o                  |
    |                  o o                  |
    |                    o x                |
    |                      x x              |
    |                        x x            |
    |                          x x          |
    |                            x x        |
    |                              x x      |
    |                                x x    |
    |                                  x x  |
    |                                    x x|
n-1 |                                      x|
    -----------------------------------------
*/

static PetscErrorCode DSView_HSVD(DS ds,PetscViewer viewer)
{
  DS_HSVD           *ctx = (DS_HSVD*)ds->data;
  PetscViewerFormat format;
  PetscInt          i,j,r,c,m=ctx->m,rows,cols;
  PetscReal         *T,*S,value;
  const char        *methodname[] = {
                     "Cross product A'*Omega*A"
  };
  const int         nmeth=PETSC_STATIC_ARRAY_LENGTH(methodname);

  PetscFunctionBegin;
  PetscCall(PetscViewerGetFormat(viewer,&format));
  if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscCall(PetscViewerASCIIPrintf(viewer,"number of columns: %" PetscInt_FMT "\n",m));
    if (ds->method<nmeth) PetscCall(PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]));
    if (ctx->reorth) PetscCall(PetscViewerASCIIPrintf(viewer,"reorthogonalizing left vectors\n"));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCheck(m,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"You should set the number of columns with DSHSVDSetDimensions()");
  if (ds->compact) {
    PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
    PetscCall(DSGetArrayReal(ds,DS_MAT_D,&S));
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_FALSE));
    rows = ds->n;
    cols = ds->extrarow? m+1: m;
    if (format == PETSC_VIEWER_ASCII_MATLAB) {
      PetscCall(PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",rows,cols));
      PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",3);\n",2*ds->n));
      PetscCall(PetscViewerASCIIPrintf(viewer,"zzz = [\n"));
      for (i=0;i<PetscMin(ds->n,m);i++) PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",i+1,i+1,(double)T[i]));
      for (i=0;i<cols-1;i++) {
        c = PetscMax(i+2,ds->k+1);
        r = i+1;
        value = i<ds->l? 0.0: T[i+ds->ld];
        PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",r,c,(double)value));
      }
      PetscCall(PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_T]));
      PetscCall(PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT "\n",ds->n,ds->n));
      PetscCall(PetscViewerASCIIPrintf(viewer,"omega = zeros(%" PetscInt_FMT ",3);\n",3*ds->n));
      PetscCall(PetscViewerASCIIPrintf(viewer,"omega = [\n"));
      for (i=0;i<ds->n;i++) PetscCall(PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",i+1,i+1,(double)S[i]));
      PetscCall(PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_D]));
    } else {
      PetscCall(PetscViewerASCIIPrintf(viewer,"T\n"));
      for (i=0;i<rows;i++) {
        for (j=0;j<cols;j++) {
          if (i==j) value = T[i];
          else if (i<ds->l) value = 0.0;
          else if (i<ds->k && j==ds->k) value = T[PetscMin(i,j)+ds->ld];
          else if (i+1==j && i>=ds->k) value = T[i+ds->ld];
          else value = 0.0;
          PetscCall(PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value));
        }
        PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
      }
      PetscCall(PetscViewerASCIIPrintf(viewer,"omega\n"));
      for (i=0;i<ds->n;i++) {
        for (j=0;j<ds->n;j++) {
          if (i==j) value = S[i];
          else value = 0.0;
          PetscCall(PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value));
        }
        PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
      }
    }
    PetscCall(PetscViewerASCIIUseTabs(viewer,PETSC_TRUE));
    PetscCall(PetscViewerFlush(viewer));
    PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
    PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&S));
  } else {
    PetscCall(DSViewMat(ds,viewer,DS_MAT_A));
    PetscCall(DSViewMat(ds,viewer,DS_MAT_D));
  }
  if (ds->state>DS_STATE_INTERMEDIATE) {
    PetscCall(DSViewMat(ds,viewer,DS_MAT_U));
    PetscCall(DSViewMat(ds,viewer,DS_MAT_V));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSVectors_HSVD(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
{
  PetscFunctionBegin;
  switch (mat) {
    case DS_MAT_U:
    case DS_MAT_V:
      if (rnorm) *rnorm = 0.0;
      break;
    default:
      SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSSort_HSVD(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
{
  DS_HSVD        *ctx = (DS_HSVD*)ds->data;
  PetscInt       n,l,i,*perm,ld=ds->ld;
  PetscScalar    *A;
  PetscReal      *d,*s;

  PetscFunctionBegin;
  if (!ds->sc) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCheck(ctx->m,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"You should set the number of columns with DSHSVDSetDimensions()");
  l = ds->l;
  n = PetscMin(ds->n,ctx->m);
  PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
  PetscCall(DSGetArrayReal(ds,DS_MAT_D,&s));
  PetscCall(DSAllocateWork_Private(ds,0,ds->ld,0));
  perm = ds->perm;
  if (!rr) PetscCall(DSSortEigenvaluesReal_Private(ds,d,perm));
  else PetscCall(DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE));
  PetscCall(PetscArraycpy(ds->rwork,s,n));
  for (i=l;i<n;i++) s[i]  = ds->rwork[perm[i]];
  for (i=l;i<n;i++) wr[i] = d[perm[i]];
  PetscCall(DSPermuteBoth_Private(ds,l,n,ds->n,ctx->m,DS_MAT_U,DS_MAT_V,perm));
  for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
  if (!ds->compact) {
    PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
    for (i=l;i<n;i++) A[i+i*ld] = wr[i];
    PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
  }
  PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
  PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&s));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSUpdateExtraRow_HSVD(DS ds)
{
  DS_HSVD           *ctx = (DS_HSVD*)ds->data;
  PetscInt          i;
  PetscBLASInt      n=0,m=0,ld,l;
  const PetscScalar *U;
  PetscReal         *T,*e,*Omega,beta;

  PetscFunctionBegin;
  PetscCheck(ctx->m,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"You should set the number of columns with DSHSVDSetDimensions()");
  PetscCall(PetscBLASIntCast(ds->n,&n));
  PetscCall(PetscBLASIntCast(ctx->m,&m));
  PetscCall(PetscBLASIntCast(ds->ld,&ld));
  PetscCall(PetscBLASIntCast(ds->l,&l));
  PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_U],&U));
  PetscCall(DSGetArrayReal(ds,DS_MAT_D,&Omega));
  PetscCheck(ds->compact,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for non-compact storage");
  PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
  e = T+ld;
  beta = PetscAbs(e[m-1]);   /* in compact, we assume all entries are zero except the last one */
  for (i=0;i<n;i++) e[i] = PetscRealPart(beta*U[n-1+i*ld]*Omega[i]);
  ds->k = m;
  PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
  PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_U],&U));
  PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&Omega));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSTruncate_HSVD(DS ds,PetscInt n,PetscBool trim)
{
  PetscInt    i,ld=ds->ld,l=ds->l;
  PetscScalar *A;
  DS_HSVD     *ctx = (DS_HSVD*)ds->data;

  PetscFunctionBegin;
  if (!ds->compact && ds->extrarow) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
  if (trim) {
    if (!ds->compact && ds->extrarow) {   /* clean extra column */
      for (i=l;i<ds->n;i++) A[i+ctx->m*ld] = 0.0;
    }
    ds->l  = 0;
    ds->k  = 0;
    ds->n  = n;
    ctx->m = n;
    ds->t  = ds->n;   /* truncated length equal to the new dimension */
    ctx->t = ctx->m;  /* must also keep the previous dimension of V */
  } else {
    if (!ds->compact && ds->extrarow && ds->k==ds->n) {
      /* copy entries of extra column to the new position, then clean last row */
      for (i=l;i<n;i++) A[i+n*ld] = A[i+ctx->m*ld];
      for (i=l;i<ds->n;i++) A[i+ctx->m*ld] = 0.0;
    }
    ds->k  = (ds->extrarow)? n: 0;
    ds->t  = ds->n;   /* truncated length equal to previous dimension */
    ctx->t = ctx->m;  /* must also keep the previous dimension of V */
    ds->n  = n;
    ctx->m = n;
  }
  if (!ds->compact && ds->extrarow) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSSolve_HSVD_CROSS(DS ds,PetscScalar *wr,PetscScalar *wi)
{
  DS_HSVD        *ctx = (DS_HSVD*)ds->data;
  PetscInt       i,j,k=ds->k,rwu=0,iwu=0,swu=0,nv;
  PetscBLASInt   n1,n2,info,l=0,n=0,m=0,ld,off,one=1,*perm,*cmplx,incx=1,lwork;
  PetscScalar    *A,*U,*V,scal,*R,sone=1.0,szero=0.0;
  PetscReal      *d,*e,*dd,*ee,*Omega;

  PetscFunctionBegin;
  PetscCheck(ctx->m,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"You should set the number of columns with DSHSVDSetDimensions()");
  PetscCall(PetscBLASIntCast(ds->n,&n));
  PetscCall(PetscBLASIntCast(ctx->m,&m));
  PetscCheck(!ds->compact || n==m,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for non-square matrices in compact storage");
  PetscCheck(ds->compact || n>=m,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented for the case of more columns than rows");
  PetscCall(PetscBLASIntCast(ds->l,&l));
  PetscCall(PetscBLASIntCast(ds->ld,&ld));
  PetscCall(PetscBLASIntCast(PetscMax(0,ds->k-ds->l+1),&n2));
  n1 = n-l;     /* n1 = size of leading block, excl. locked + size of trailing block */
  off = l+l*ld;
  if (!ds->compact) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
  PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_U],&U));
  PetscCall(MatDenseGetArrayWrite(ds->omat[DS_MAT_V],&V));
  PetscCall(DSGetArrayReal(ds,DS_MAT_T,&d));
  e = d+ld;
  PetscCall(DSGetArrayReal(ds,DS_MAT_D,&Omega));
  PetscCall(PetscArrayzero(U,ld*ld));
  for (i=0;i<l;i++) U[i+i*ld] = 1.0;
  PetscCall(PetscArrayzero(V,ld*ld));
  for (i=0;i<n;i++) V[i+i*ld] = 1.0;
  for (i=0;i<l;i++) wr[i] = d[i];
  if (wi) for (i=0;i<l;i++) wi[i] = 0.0;

  if (ds->compact) {
    /* Form the arrow tridiagonal cross product T=A'*Omega*A, where A is the arrow
       bidiagonal matrix formed by d, e. T is stored in dd, ee */
    PetscCall(DSAllocateWork_Private(ds,(n+6)*ld,4*ld,2*ld));
    R = ds->work+swu;
    swu += n*ld;
    perm = ds->iwork+iwu;
    iwu += n;
    cmplx = ds->iwork+iwu;
    dd = ds->rwork+rwu;
    rwu += ld;
    ee = ds->rwork+rwu;
    rwu += ld;
    for (i=0;i<l;i++) {dd[i] = d[i]*d[i]*Omega[i]; ee[i] = 0.0;}
    for (i=l;i<=ds->k;i++) {
      dd[i] = Omega[i]*d[i]*d[i];
      ee[i] = Omega[i]*d[i]*e[i];
    }
    for (i=l;i<k;i++) dd[k] += Omega[i]*e[i]*e[i];
    for (i=k+1;i<n;i++) {
      dd[i] = Omega[i]*d[i]*d[i]+Omega[i-1]*e[i-1]*e[i-1];
      ee[i] = Omega[i]*d[i]*e[i];
    }

    /* Reduce T to tridiagonal form */
    PetscCall(DSArrowTridiag(n2,dd+l,ee+l,V+off,ld));

    /* Solve the tridiagonal eigenproblem corresponding to T */
    PetscCallBLAS("LAPACKsteqr",LAPACKsteqr_("V",&n1,dd+l,ee+l,V+off,&ld,ds->rwork+rwu,&info));
    SlepcCheckLapackInfo("steqr",info);
    for (i=l;i<n;i++) wr[i] = PetscSqrtScalar(PetscAbs(dd[i]));

    /* Build left singular vectors: U=A*V*Sigma^-1 */
    PetscCall(PetscArrayzero(U+l*ld,n1*ld));
    for (i=l;i<n-1;i++) {
      scal = d[i];
      PetscCallBLAS("BLASaxpy",BLASaxpy_(&n1,&scal,V+l*ld+i,&ld,U+l*ld+i,&ld));
      j = (i<k)?k:i+1;
      scal = e[i];
      PetscCallBLAS("BLASaxpy",BLASaxpy_(&n1,&scal,V+l*ld+j,&ld,U+l*ld+i,&ld));
    }
    scal = d[n-1];
    PetscCallBLAS("BLASaxpy",BLASaxpy_(&n1,&scal,V+off+(n1-1),&ld,U+off+(n1-1),&ld));
    /* Multiply by Sigma^-1 */
    for (i=l;i<n;i++) {scal = 1.0/wr[i]; PetscCallBLAS("BLASscal",BLASscal_(&n1,&scal,U+i*ld+l,&one));}

  } else { /* non-compact */

    PetscCall(DSAllocateWork_Private(ds,(n+6)*ld,PetscDefined(USE_COMPLEX)?4*ld:ld,2*ld));
    R = ds->work+swu;
    swu += n*ld;
    perm = ds->iwork+iwu;
    iwu += n;
    cmplx = ds->iwork+iwu;
    dd = ds->rwork+rwu;
    for (j=l;j<m;j++) {
      for (i=0;i<n;i++) ds->work[i] = Omega[i]*A[i+j*ld];
      PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&m,&sone,A,&ld,ds->work,&incx,&szero,V+j*ld,&incx));
    }

    /* compute eigenvalues */
    lwork = (n+6)*ld;
#if defined(PETSC_USE_COMPLEX)
    rwu += ld;
    PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&m,V,&ld,dd,ds->work,&lwork,ds->rwork+rwu,&info));
#else
    PetscCallBLAS("LAPACKsyev",LAPACKsyev_("V","L",&m,V,&ld,dd,ds->work,&lwork,&info));
#endif
    SlepcCheckLapackInfo("syev",info);
    for (i=l;i<PetscMin(n,m);i++) d[i] = PetscSqrtReal(PetscAbsReal(dd[i]));

    /* Build left singular vectors: U=A*V*Sigma^-1 */
    for (j=l;j<PetscMin(n,m);j++) {
      scal = 1.0/d[j];
      PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&m,&scal,A,&ld,V+j*ld,&incx,&szero,U+j*ld,&incx));
    }
  }

  if (ctx->reorth) { /* Reinforce orthogonality */
    nv = n1;
    for (i=0;i<n;i++) cmplx[i] = 0;
    PetscCall(DSPseudoOrthog_HR(&nv,U+off,ld,Omega+l,R,ld,perm,cmplx,NULL,ds->work+swu));
  } else { /* Update Omega */
    for (i=l;i<PetscMin(n,m);i++) Omega[i] = PetscSign(dd[i]);
  }

  /* Update projected problem */
  if (ds->compact) {
    for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
    PetscCall(PetscArrayzero(e,n-1));
  } else {
    for (i=l;i<m;i++) PetscCall(PetscArrayzero(A+l+i*ld,n-l));
    for (i=l;i<n;i++) A[i+i*ld] = d[i];
  }
  for (i=l;i<PetscMin(n,m);i++) wr[i] = d[i];
  if (wi) for (i=l;i<PetscMin(n,m);i++) wi[i] = 0.0;

  if (ctx->reorth) { /* Update vectors V with R */
    scal = -1.0;
    for (i=0;i<nv;i++) {
      if (PetscRealPart(R[i+i*ld]) < 0.0) PetscCallBLAS("BLASscal",BLASscal_(&n1,&scal,V+(i+l)*ld+l,&one));
    }
  }

  if (!ds->compact) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
  PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_U],&U));
  PetscCall(MatDenseRestoreArrayWrite(ds->omat[DS_MAT_V],&V));
  PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&d));
  PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&Omega));
  PetscFunctionReturn(PETSC_SUCCESS);
}

#if !defined(PETSC_HAVE_MPIUNI)
static PetscErrorCode DSSynchronize_HSVD(DS ds,PetscScalar eigr[],PetscScalar eigi[])
{
  PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
  PetscMPIInt    n,rank,off=0,size,ldn,ld3,ld_;
  PetscScalar    *A,*U,*V;
  PetscReal      *T,*D;

  PetscFunctionBegin;
  if (ds->compact) kr = 3*ld;
  else k = (ds->n-l)*ld;
  kr += ld;
  if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
  if (eigr) k += ds->n-l;
  PetscCall(DSAllocateWork_Private(ds,k+kr,0,0));
  PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size));
  PetscCall(PetscMPIIntCast(ds->n-l,&n));
  PetscCall(PetscMPIIntCast(ld*(ds->n-l),&ldn));
  PetscCall(PetscMPIIntCast(3*ld,&ld3));
  PetscCall(PetscMPIIntCast(ld,&ld_));
  if (ds->compact) PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
  else PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
  PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
  if (ds->state>DS_STATE_RAW) {
    PetscCall(MatDenseGetArray(ds->omat[DS_MAT_U],&U));
    PetscCall(MatDenseGetArray(ds->omat[DS_MAT_V],&V));
  }
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
  if (!rank) {
    if (ds->compact) PetscCallMPI(MPI_Pack(T,ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    else PetscCallMPI(MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    PetscCallMPI(MPI_Pack(D,ld_,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    if (ds->state>DS_STATE_RAW) {
      PetscCallMPI(MPI_Pack(U+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
      PetscCallMPI(MPI_Pack(V+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    }
    if (eigr) PetscCallMPI(MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
  }
  PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
  if (rank) {
    if (ds->compact) PetscCallMPI(MPI_Unpack(ds->work,size,&off,T,ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds)));
    else PetscCallMPI(MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    PetscCallMPI(MPI_Unpack(ds->work,size,&off,D,ld_,MPIU_REAL,PetscObjectComm((PetscObject)ds)));
    if (ds->state>DS_STATE_RAW) {
      PetscCallMPI(MPI_Unpack(ds->work,size,&off,U+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
      PetscCallMPI(MPI_Unpack(ds->work,size,&off,V+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    }
    if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
  }
  if (ds->compact) PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
  else PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
  PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
  if (ds->state>DS_STATE_RAW) {
    PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_U],&U));
    PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_V],&V));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

static PetscErrorCode DSMatGetSize_HSVD(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
{
  DS_HSVD *ctx = (DS_HSVD*)ds->data;

  PetscFunctionBegin;
  PetscCheck(ctx->m,PetscObjectComm((PetscObject)ds),PETSC_ERR_ORDER,"You should set the number of columns with DSHSVDSetDimensions()");
  switch (t) {
    case DS_MAT_A:
      *rows = ds->n;
      *cols = ds->extrarow? ctx->m+1: ctx->m;
      break;
    case DS_MAT_T:
      *rows = ds->n;
      *cols = PetscDefined(USE_COMPLEX)? 2: 3;
      break;
    case DS_MAT_D:
      *rows = ds->n;
      *cols = 1;
      break;
    case DS_MAT_U:
      *rows = ds->state==DS_STATE_TRUNCATED? ds->t: ds->n;
      *cols = ds->n;
      break;
    case DS_MAT_V:
      *rows = ds->state==DS_STATE_TRUNCATED? ctx->t: ctx->m;
      *cols = ctx->m;
      break;
    default:
      SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid t parameter");
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSHSVDSetDimensions_HSVD(DS ds,PetscInt m)
{
  DS_HSVD *ctx = (DS_HSVD*)ds->data;

  PetscFunctionBegin;
  DSCheckAlloc(ds,1);
  if (m==PETSC_DECIDE || m==PETSC_DEFAULT) {
    ctx->m = ds->ld;
  } else {
    PetscCheck(m>0 && m<=ds->ld,PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of m. Must be between 1 and ld");
    ctx->m = m;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   DSHSVDSetDimensions - Sets the number of columns for a `DSHSVD`.

   Logically Collective

   Input Parameters:
+  ds - the direct solver context
-  m  - the number of columns

   Notes:
   This call is complementary to `DSSetDimensions()`, to provide a dimension
   that is specific to this `DS` type.

   Level: intermediate

.seealso: [](sec:ds), `DSHSVD`, `DSHSVDGetDimensions()`, `DSSetDimensions()`
@*/
PetscErrorCode DSHSVDSetDimensions(DS ds,PetscInt m)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds,DS_CLASSID,1);
  PetscValidLogicalCollectiveInt(ds,m,2);
  PetscTryMethod(ds,"DSHSVDSetDimensions_C",(DS,PetscInt),(ds,m));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSHSVDGetDimensions_HSVD(DS ds,PetscInt *m)
{
  DS_HSVD *ctx = (DS_HSVD*)ds->data;

  PetscFunctionBegin;
  *m = ctx->m;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   DSHSVDGetDimensions - Returns the number of columns for a `DSHSVD`.

   Not Collective

   Input Parameter:
.  ds - the direct solver context

   Output Parameter:
.  m - the number of columns

   Level: intermediate

.seealso: [](sec:ds), `DSHSVD`, `DSHSVDSetDimensions()`
@*/
PetscErrorCode DSHSVDGetDimensions(DS ds,PetscInt *m)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds,DS_CLASSID,1);
  PetscAssertPointer(m,2);
  PetscUseMethod(ds,"DSHSVDGetDimensions_C",(DS,PetscInt*),(ds,m));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSHSVDSetReorthogonalize_HSVD(DS ds,PetscBool reorth)
{
  DS_HSVD *ctx = (DS_HSVD*)ds->data;

  PetscFunctionBegin;
  ctx->reorth = reorth;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   DSHSVDSetReorthogonalize - Sets the reorthogonalization of the left vectors in a `DSHSVD`.

   Logically Collective

   Input Parameters:
+  ds     - the direct solver context
-  reorth - the reorthogonalization flag

   Options Database Key:
.  -ds_hsvd_reorthog (true|false) - sets the reorthogonalization flag

   Note:
   The computed left vectors (`U`) should be orthogonal with respect to the signature (`D`).
   But it may be necessary to enforce this with a final reorthogonalization step (omitted
   by default).

   Level: intermediate

.seealso: [](sec:ds), `DSHSVD`, `DSHSVDGetReorthogonalize()`
@*/
PetscErrorCode DSHSVDSetReorthogonalize(DS ds,PetscBool reorth)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds,DS_CLASSID,1);
  PetscValidLogicalCollectiveBool(ds,reorth,2);
  PetscTryMethod(ds,"DSHSVDSetReorthogonalize_C",(DS,PetscBool),(ds,reorth));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSHSVDGetReorthogonalize_HSVD(DS ds,PetscBool *reorth)
{
  DS_HSVD *ctx = (DS_HSVD*)ds->data;

  PetscFunctionBegin;
  *reorth = ctx->reorth;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   DSHSVDGetReorthogonalize - Returns the reorthogonalization flag of a `DSHSVD`.

   Not Collective

   Input Parameter:
.  ds - the direct solver context

   Output Parameter:
.  reorth - the reorthogonalization flag

   Level: intermediate

.seealso: [](sec:ds), `DSHSVD`, `DSHSVDSetReorthogonalize()`
@*/
PetscErrorCode DSHSVDGetReorthogonalize(DS ds,PetscBool *reorth)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ds,DS_CLASSID,1);
  PetscAssertPointer(reorth,2);
  PetscUseMethod(ds,"DSHSVDGetReorthogonalize_C",(DS,PetscBool*),(ds,reorth));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSSetFromOptions_HSVD(DS ds,PetscOptionItems PetscOptionsObject)
{
  PetscBool      flg,reorth;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject,"DS HSVD Options");

    PetscCall(PetscOptionsBool("-ds_hsvd_reorthog","Reorthogonalize U vectors","DSHSVDSetReorthogonalize",PETSC_FALSE,&reorth,&flg));
    if (flg) PetscCall(DSHSVDSetReorthogonalize(ds,reorth));

  PetscOptionsHeadEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSDestroy_HSVD(DS ds)
{
  PetscFunctionBegin;
  PetscCall(PetscFree(ds->data));
  PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDSetDimensions_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDGetDimensions_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDSetReorthogonalize_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDGetReorthogonalize_C",NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSSetCompact_HSVD(DS ds,PetscBool comp)
{
  PetscFunctionBegin;
  if (!comp) PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DSReallocate_HSVD(DS ds,PetscInt ld)
{
  PetscInt i,*perm=ds->perm;

  PetscFunctionBegin;
  for (i=0;i<DS_NUM_MAT;i++) {
    if (!ds->compact && i==DS_MAT_A) continue;
    if (i!=DS_MAT_U && i!=DS_MAT_V && i!=DS_MAT_T && i!=DS_MAT_D) PetscCall(MatDestroy(&ds->omat[i]));
  }

  if (!ds->compact) PetscCall(DSReallocateMat_Private(ds,DS_MAT_A,ld));
  PetscCall(DSReallocateMat_Private(ds,DS_MAT_U,ld));
  PetscCall(DSReallocateMat_Private(ds,DS_MAT_V,ld));
  PetscCall(DSReallocateMat_Private(ds,DS_MAT_T,ld));
  PetscCall(DSReallocateMat_Private(ds,DS_MAT_D,ld));

  PetscCall(PetscMalloc1(ld,&ds->perm));
  PetscCall(PetscArraycpy(ds->perm,perm,ds->ld));
  PetscCall(PetscFree(perm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
   DSHSVD - Dense Hyperbolic Singular Value Decomposition.

   Notes:
   The problem is expressed as $A = U\Sigma V^*$, where $A$ is rectangular in
   general, with $n$ rows and $m$ columns. $U$ is orthogonal with respect to a
   signature matrix $\Omega$, stored in $D$, $V$ is orthogonal, $\Sigma$ is a diagonal
   matrix whose diagonal elements are the arguments of `DSSolve()`. After
   solve, $A$ is overwritten with $\Sigma$, $D$ is overwritten with the new signature.

   The matrices of left and right singular vectors, $U$ and $V$, have size $n$ and $m$,
   respectively. The number of columns m must be specified via `DSHSVDSetDimensions()`.

   If the `DS` object is in the intermediate state, $A$ is assumed to be in upper
   bidiagonal form (possibly with an arrow) and is stored in compact format
   on matrix $T$. The compact storage is implemented for the square case
   only, $m=n$. The extra row should be interpreted in this case as an extra column.

   Used DS matrices:
+  `DS_MAT_A` - problem matrix (used only if `compact=PETSC_FALSE`)
.  `DS_MAT_T` - upper bidiagonal matrix
.  `DS_MAT_D` - diagonal matrix (signature)
.  `DS_MAT_U` - left singular vectors
-  `DS_MAT_V` - right singular vectors

   Implemented methods:
.  0 - Cross product $A^*\Omega A$

   Level: beginner

.seealso: [](sec:ds), `DSCreate()`, `DSSetType()`, `DSType`, `DSHSVDSetDimensions()`, `DSSetCompact()`
M*/
SLEPC_EXTERN PetscErrorCode DSCreate_HSVD(DS ds)
{
  DS_HSVD         *ctx;

  PetscFunctionBegin;
  PetscCall(PetscNew(&ctx));
  ds->data = (void*)ctx;

  ds->ops->allocate       = DSAllocate_HSVD;
  ds->ops->setfromoptions = DSSetFromOptions_HSVD;
  ds->ops->view           = DSView_HSVD;
  ds->ops->vectors        = DSVectors_HSVD;
  ds->ops->solve[0]       = DSSolve_HSVD_CROSS;
  ds->ops->sort           = DSSort_HSVD;
  ds->ops->truncate       = DSTruncate_HSVD;
  ds->ops->update         = DSUpdateExtraRow_HSVD;
  ds->ops->destroy        = DSDestroy_HSVD;
  ds->ops->matgetsize     = DSMatGetSize_HSVD;
#if !defined(PETSC_HAVE_MPIUNI)
  ds->ops->synchronize    = DSSynchronize_HSVD;
#endif
  ds->ops->setcompact     = DSSetCompact_HSVD;
  ds->ops->reallocate     = DSReallocate_HSVD;
  PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDSetDimensions_C",DSHSVDSetDimensions_HSVD));
  PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDGetDimensions_C",DSHSVDGetDimensions_HSVD));
  PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDSetReorthogonalize_C",DSHSVDSetReorthogonalize_HSVD));
  PetscCall(PetscObjectComposeFunction((PetscObject)ds,"DSHSVDGetReorthogonalize_C",DSHSVDGetReorthogonalize_HSVD));
  PetscFunctionReturn(PETSC_SUCCESS);
}
