xref: /petsc/src/mat/impls/aij/seq/seqcusparse/aijcusparse.cu (revision 2c7c0729d89b910088ee906aed2239ea927d033e)

/*
  Defines the basic matrix operations for the AIJ (compressed row)
  matrix storage format using the CUSPARSE library,
*/
#define PETSC_SKIP_SPINLOCK
#define PETSC_SKIP_CXX_COMPLEX_FIX
#define PETSC_SKIP_IMMINTRIN_H_CUDAWORKAROUND 1

#include <petscconf.h>
#include <../src/mat/impls/aij/seq/aij.h>          /*I "petscmat.h" I*/
#include <../src/mat/impls/sbaij/seq/sbaij.h>
#include <../src/vec/vec/impls/dvecimpl.h>
#include <petsc/private/vecimpl.h>
#undef VecType
#include <../src/mat/impls/aij/seq/seqcusparse/cusparsematimpl.h>

const char *const MatCUSPARSEStorageFormats[] = {"CSR","ELL","HYB","MatCUSPARSEStorageFormat","MAT_CUSPARSE_",0};

static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE(Mat,Mat,IS,const MatFactorInfo*);
static PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJCUSPARSE(Mat,Mat,IS,const MatFactorInfo*);
static PetscErrorCode MatCholeskyFactorNumeric_SeqAIJCUSPARSE(Mat,Mat,const MatFactorInfo*);

static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE(Mat,Mat,IS,IS,const MatFactorInfo*);
static PetscErrorCode MatLUFactorSymbolic_SeqAIJCUSPARSE(Mat,Mat,IS,IS,const MatFactorInfo*);
static PetscErrorCode MatLUFactorNumeric_SeqAIJCUSPARSE(Mat,Mat,const MatFactorInfo*);

static PetscErrorCode MatSolve_SeqAIJCUSPARSE(Mat,Vec,Vec);
static PetscErrorCode MatSolve_SeqAIJCUSPARSE_NaturalOrdering(Mat,Vec,Vec);
static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE(Mat,Vec,Vec);
static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering(Mat,Vec,Vec);
static PetscErrorCode MatSetFromOptions_SeqAIJCUSPARSE(PetscOptionItems *PetscOptionsObject,Mat);
static PetscErrorCode MatMult_SeqAIJCUSPARSE(Mat,Vec,Vec);
static PetscErrorCode MatMultAdd_SeqAIJCUSPARSE(Mat,Vec,Vec,Vec);
static PetscErrorCode MatMultTranspose_SeqAIJCUSPARSE(Mat,Vec,Vec);
static PetscErrorCode MatMultTransposeAdd_SeqAIJCUSPARSE(Mat,Vec,Vec,Vec);
static PetscErrorCode MatMultHermitianTranspose_SeqAIJCUSPARSE(Mat,Vec,Vec);
static PetscErrorCode MatMultHermitianTransposeAdd_SeqAIJCUSPARSE(Mat,Vec,Vec,Vec);
static PetscErrorCode MatMultAddKernel_SeqAIJCUSPARSE(Mat,Vec,Vec,Vec,PetscBool,PetscBool);

static PetscErrorCode CsrMatrix_Destroy(CsrMatrix**);
static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct**);
static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSEMultStruct**,MatCUSPARSEStorageFormat);
static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Reset(Mat_SeqAIJCUSPARSETriFactors**);
static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors**);
static PetscErrorCode MatSeqAIJCUSPARSE_Destroy(Mat_SeqAIJCUSPARSE**);

PetscErrorCode MatCUSPARSESetStream(Mat A,const cudaStream_t stream)
{
  cusparseStatus_t   stat;
  Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;

  PetscFunctionBegin;
  cusparsestruct->stream = stream;
  stat = cusparseSetStream(cusparsestruct->handle,cusparsestruct->stream);CHKERRCUSPARSE(stat);
  PetscFunctionReturn(0);
}

PetscErrorCode MatCUSPARSESetHandle(Mat A,const cusparseHandle_t handle)
{
  cusparseStatus_t   stat;
  Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;

  PetscFunctionBegin;
  if (cusparsestruct->handle != handle) {
    if (cusparsestruct->handle) {
      stat = cusparseDestroy(cusparsestruct->handle);CHKERRCUSPARSE(stat);
    }
    cusparsestruct->handle = handle;
  }
  stat = cusparseSetPointerMode(cusparsestruct->handle, CUSPARSE_POINTER_MODE_DEVICE);CHKERRCUSPARSE(stat);
  PetscFunctionReturn(0);
}

PetscErrorCode MatCUSPARSEClearHandle(Mat A)
{
  Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;

  PetscFunctionBegin;
  if (cusparsestruct->handle) cusparsestruct->handle = 0;
  PetscFunctionReturn(0);
}

PetscErrorCode MatFactorGetSolverType_seqaij_cusparse(Mat A,MatSolverType *type)
{
  PetscFunctionBegin;
  *type = MATSOLVERCUSPARSE;
  PetscFunctionReturn(0);
}

/*MC
  MATSOLVERCUSPARSE = "cusparse" - A matrix type providing triangular solvers for seq matrices
  on a single GPU of type, seqaijcusparse, aijcusparse, or seqaijcusp, aijcusp. Currently supported
  algorithms are ILU(k) and ICC(k). Typically, deeper factorizations (larger k) results in poorer
  performance in the triangular solves. Full LU, and Cholesky decompositions can be solved through the
  CUSPARSE triangular solve algorithm. However, the performance can be quite poor and thus these
  algorithms are not recommended. This class does NOT support direct solver operations.

  Level: beginner

.seealso: PCFactorSetMatSolverType(), MatSolverType, MatCreateSeqAIJCUSPARSE(), MATAIJCUSPARSE, MatCreateAIJCUSPARSE(), MatCUSPARSESetFormat(), MatCUSPARSEStorageFormat, MatCUSPARSEFormatOperation
M*/

PETSC_EXTERN PetscErrorCode MatGetFactor_seqaijcusparse_cusparse(Mat A,MatFactorType ftype,Mat *B)
{
  PetscErrorCode ierr;
  PetscInt       n = A->rmap->n;

  PetscFunctionBegin;
  ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
  ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
  (*B)->factortype = ftype;
  (*B)->useordering = PETSC_TRUE;
  ierr = MatSetType(*B,MATSEQAIJCUSPARSE);CHKERRQ(ierr);

  if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
    ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
    (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJCUSPARSE;
    (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJCUSPARSE;
  } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
    (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJCUSPARSE;
    (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJCUSPARSE;
  } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported for CUSPARSE Matrix Types");

  ierr = MatSeqAIJSetPreallocation(*B,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)(*B),"MatFactorGetSolverType_C",MatFactorGetSolverType_seqaij_cusparse);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatCUSPARSESetFormat_SeqAIJCUSPARSE(Mat A,MatCUSPARSEFormatOperation op,MatCUSPARSEStorageFormat format)
{
  Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;

  PetscFunctionBegin;
  switch (op) {
  case MAT_CUSPARSE_MULT:
    cusparsestruct->format = format;
    break;
  case MAT_CUSPARSE_ALL:
    cusparsestruct->format = format;
    break;
  default:
    SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unsupported operation %d for MatCUSPARSEFormatOperation. MAT_CUSPARSE_MULT and MAT_CUSPARSE_ALL are currently supported.",op);
  }
  PetscFunctionReturn(0);
}

/*@
   MatCUSPARSESetFormat - Sets the storage format of CUSPARSE matrices for a particular
   operation. Only the MatMult operation can use different GPU storage formats
   for MPIAIJCUSPARSE matrices.
   Not Collective

   Input Parameters:
+  A - Matrix of type SEQAIJCUSPARSE
.  op - MatCUSPARSEFormatOperation. SEQAIJCUSPARSE matrices support MAT_CUSPARSE_MULT and MAT_CUSPARSE_ALL. MPIAIJCUSPARSE matrices support MAT_CUSPARSE_MULT_DIAG, MAT_CUSPARSE_MULT_OFFDIAG, and MAT_CUSPARSE_ALL.
-  format - MatCUSPARSEStorageFormat (one of MAT_CUSPARSE_CSR, MAT_CUSPARSE_ELL, MAT_CUSPARSE_HYB. The latter two require CUDA 4.2)

   Output Parameter:

   Level: intermediate

.seealso: MatCUSPARSEStorageFormat, MatCUSPARSEFormatOperation
@*/
PetscErrorCode MatCUSPARSESetFormat(Mat A,MatCUSPARSEFormatOperation op,MatCUSPARSEStorageFormat format)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID,1);
  ierr = PetscTryMethod(A,"MatCUSPARSESetFormat_C",(Mat,MatCUSPARSEFormatOperation,MatCUSPARSEStorageFormat),(A,op,format));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   MatSeqAIJCUSPARSESetGenerateTranspose - Sets the flag to explicitly generate the tranpose matrix before calling MatMultTranspose

   Collective on mat

   Input Parameters:
+  A - Matrix of type SEQAIJCUSPARSE
-  transgen - the boolean flag

   Level: intermediate

.seealso: MATSEQAIJCUSPARSE
@*/
PetscErrorCode MatSeqAIJCUSPARSESetGenerateTranspose(Mat A,PetscBool transgen)
{
  PetscErrorCode ierr;
  PetscBool      flg;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  ierr = PetscObjectTypeCompare(((PetscObject)A),MATSEQAIJCUSPARSE,&flg);CHKERRQ(ierr);
  if (flg) {
    Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE*)A->spptr;

    if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    cusp->transgen = transgen;
    if (!transgen) { /* need to destroy the transpose matrix if present to prevent from logic errors if transgen is set to true later */
      ierr = MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->matTranspose,cusp->format);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSetFromOptions_SeqAIJCUSPARSE(PetscOptionItems *PetscOptionsObject,Mat A)
{
  PetscErrorCode           ierr;
  MatCUSPARSEStorageFormat format;
  PetscBool                flg;
  Mat_SeqAIJCUSPARSE       *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;

  PetscFunctionBegin;
  ierr = PetscOptionsHead(PetscOptionsObject,"SeqAIJCUSPARSE options");CHKERRQ(ierr);
  if (A->factortype == MAT_FACTOR_NONE) {
    PetscBool transgen = cusparsestruct->transgen;

    ierr = PetscOptionsBool("-mat_cusparse_transgen","Generate explicit transpose for MatMultTranspose","MatSeqAIJCUSPARSESetGenerateTranspose",transgen,&transgen,&flg);CHKERRQ(ierr);
    if (flg) {
      ierr = MatSeqAIJCUSPARSESetGenerateTranspose(A,transgen);CHKERRQ(ierr);
    }
    ierr = PetscOptionsEnum("-mat_cusparse_mult_storage_format","sets storage format of (seq)aijcusparse gpu matrices for SpMV",
                            "MatCUSPARSESetFormat",MatCUSPARSEStorageFormats,(PetscEnum)cusparsestruct->format,(PetscEnum*)&format,&flg);CHKERRQ(ierr);
    if (flg) {
      ierr = MatCUSPARSESetFormat(A,MAT_CUSPARSE_MULT,format);CHKERRQ(ierr);
    }
  }
  ierr = PetscOptionsEnum("-mat_cusparse_storage_format","sets storage format of (seq)aijcusparse gpu matrices for SpMV and TriSolve",
                          "MatCUSPARSESetFormat",MatCUSPARSEStorageFormats,(PetscEnum)cusparsestruct->format,(PetscEnum*)&format,&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = MatCUSPARSESetFormat(A,MAT_CUSPARSE_ALL,format);CHKERRQ(ierr);
  }
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatILUFactorSymbolic_SeqAIJ(B,A,isrow,iscol,info);CHKERRQ(ierr);
  B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJCUSPARSE;
  PetscFunctionReturn(0);
}

static PetscErrorCode MatLUFactorSymbolic_SeqAIJCUSPARSE(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatLUFactorSymbolic_SeqAIJ(B,A,isrow,iscol,info);CHKERRQ(ierr);
  B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJCUSPARSE;
  PetscFunctionReturn(0);
}

static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE(Mat B,Mat A,IS perm,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatICCFactorSymbolic_SeqAIJ(B,A,perm,info);CHKERRQ(ierr);
  B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJCUSPARSE;
  PetscFunctionReturn(0);
}

static PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJCUSPARSE(Mat B,Mat A,IS perm,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatCholeskyFactorSymbolic_SeqAIJ(B,A,perm,info);CHKERRQ(ierr);
  B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJCUSPARSE;
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSEBuildILULowerTriMatrix(Mat A)
{
  Mat_SeqAIJ                        *a = (Mat_SeqAIJ*)A->data;
  PetscInt                          n = A->rmap->n;
  Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
  Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtr;
  cusparseStatus_t                  stat;
  const PetscInt                    *ai = a->i,*aj = a->j,*vi;
  const MatScalar                   *aa = a->a,*v;
  PetscInt                          *AiLo, *AjLo;
  PetscScalar                       *AALo;
  PetscInt                          i,nz, nzLower, offset, rowOffset;
  PetscErrorCode                    ierr;
  cudaError_t                       cerr;

  PetscFunctionBegin;
  if (!n) PetscFunctionReturn(0);
  if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
    try {
      /* first figure out the number of nonzeros in the lower triangular matrix including 1's on the diagonal. */
      nzLower=n+ai[n]-ai[1];

      /* Allocate Space for the lower triangular matrix */
      cerr = cudaMallocHost((void**) &AiLo, (n+1)*sizeof(PetscInt));CHKERRCUDA(cerr);
      cerr = cudaMallocHost((void**) &AjLo, nzLower*sizeof(PetscInt));CHKERRCUDA(cerr);
      cerr = cudaMallocHost((void**) &AALo, nzLower*sizeof(PetscScalar));CHKERRCUDA(cerr);

      /* Fill the lower triangular matrix */
      AiLo[0]  = (PetscInt) 0;
      AiLo[n]  = nzLower;
      AjLo[0]  = (PetscInt) 0;
      AALo[0]  = (MatScalar) 1.0;
      v        = aa;
      vi       = aj;
      offset   = 1;
      rowOffset= 1;
      for (i=1; i<n; i++) {
        nz = ai[i+1] - ai[i];
        /* additional 1 for the term on the diagonal */
        AiLo[i]    = rowOffset;
        rowOffset += nz+1;

        ierr = PetscArraycpy(&(AjLo[offset]), vi, nz);CHKERRQ(ierr);
        ierr = PetscArraycpy(&(AALo[offset]), v, nz);CHKERRQ(ierr);

        offset      += nz;
        AjLo[offset] = (PetscInt) i;
        AALo[offset] = (MatScalar) 1.0;
        offset      += 1;

        v  += nz;
        vi += nz;
      }

      /* allocate space for the triangular factor information */
      loTriFactor = new Mat_SeqAIJCUSPARSETriFactorStruct;

      /* Create the matrix description */
      stat = cusparseCreateMatDescr(&loTriFactor->descr);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatIndexBase(loTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatFillMode(loTriFactor->descr, CUSPARSE_FILL_MODE_LOWER);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatDiagType(loTriFactor->descr, CUSPARSE_DIAG_TYPE_UNIT);CHKERRCUSPARSE(stat);

      /* Create the solve analysis information */
      stat = cusparseCreateSolveAnalysisInfo(&loTriFactor->solveInfo);CHKERRCUSPARSE(stat);

      /* set the operation */
      loTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;

      /* set the matrix */
      loTriFactor->csrMat = new CsrMatrix;
      loTriFactor->csrMat->num_rows = n;
      loTriFactor->csrMat->num_cols = n;
      loTriFactor->csrMat->num_entries = nzLower;

      loTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(n+1);
      loTriFactor->csrMat->row_offsets->assign(AiLo, AiLo+n+1);

      loTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(nzLower);
      loTriFactor->csrMat->column_indices->assign(AjLo, AjLo+nzLower);

      loTriFactor->csrMat->values = new THRUSTARRAY(nzLower);
      loTriFactor->csrMat->values->assign(AALo, AALo+nzLower);

      /* perform the solve analysis */
      stat = cusparse_analysis(cusparseTriFactors->handle, loTriFactor->solveOp,
                               loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr,
                               loTriFactor->csrMat->values->data().get(), loTriFactor->csrMat->row_offsets->data().get(),
                               loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo);CHKERRCUSPARSE(stat);

      /* assign the pointer. Is this really necessary? */
      ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->loTriFactorPtr = loTriFactor;

      cerr = cudaFreeHost(AiLo);CHKERRCUDA(cerr);
      cerr = cudaFreeHost(AjLo);CHKERRCUDA(cerr);
      cerr = cudaFreeHost(AALo);CHKERRCUDA(cerr);
      ierr = PetscLogCpuToGpu((n+1+nzLower)*sizeof(int)+nzLower*sizeof(PetscScalar));CHKERRQ(ierr);
    } catch(char *ex) {
      SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
    }
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSEBuildILUUpperTriMatrix(Mat A)
{
  Mat_SeqAIJ                        *a = (Mat_SeqAIJ*)A->data;
  PetscInt                          n = A->rmap->n;
  Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
  Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtr;
  cusparseStatus_t                  stat;
  const PetscInt                    *aj = a->j,*adiag = a->diag,*vi;
  const MatScalar                   *aa = a->a,*v;
  PetscInt                          *AiUp, *AjUp;
  PetscScalar                       *AAUp;
  PetscInt                          i,nz, nzUpper, offset;
  PetscErrorCode                    ierr;
  cudaError_t                       cerr;

  PetscFunctionBegin;
  if (!n) PetscFunctionReturn(0);
  if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
    try {
      /* next, figure out the number of nonzeros in the upper triangular matrix. */
      nzUpper = adiag[0]-adiag[n];

      /* Allocate Space for the upper triangular matrix */
      cerr = cudaMallocHost((void**) &AiUp, (n+1)*sizeof(PetscInt));CHKERRCUDA(cerr);
      cerr = cudaMallocHost((void**) &AjUp, nzUpper*sizeof(PetscInt));CHKERRCUDA(cerr);
      cerr = cudaMallocHost((void**) &AAUp, nzUpper*sizeof(PetscScalar));CHKERRCUDA(cerr);

      /* Fill the upper triangular matrix */
      AiUp[0]=(PetscInt) 0;
      AiUp[n]=nzUpper;
      offset = nzUpper;
      for (i=n-1; i>=0; i--) {
        v  = aa + adiag[i+1] + 1;
        vi = aj + adiag[i+1] + 1;

        /* number of elements NOT on the diagonal */
        nz = adiag[i] - adiag[i+1]-1;

        /* decrement the offset */
        offset -= (nz+1);

        /* first, set the diagonal elements */
        AjUp[offset] = (PetscInt) i;
        AAUp[offset] = (MatScalar)1./v[nz];
        AiUp[i]      = AiUp[i+1] - (nz+1);

        ierr = PetscArraycpy(&(AjUp[offset+1]), vi, nz);CHKERRQ(ierr);
        ierr = PetscArraycpy(&(AAUp[offset+1]), v, nz);CHKERRQ(ierr);
      }

      /* allocate space for the triangular factor information */
      upTriFactor = new Mat_SeqAIJCUSPARSETriFactorStruct;

      /* Create the matrix description */
      stat = cusparseCreateMatDescr(&upTriFactor->descr);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatIndexBase(upTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatFillMode(upTriFactor->descr, CUSPARSE_FILL_MODE_UPPER);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatDiagType(upTriFactor->descr, CUSPARSE_DIAG_TYPE_NON_UNIT);CHKERRCUSPARSE(stat);

      /* Create the solve analysis information */
      stat = cusparseCreateSolveAnalysisInfo(&upTriFactor->solveInfo);CHKERRCUSPARSE(stat);

      /* set the operation */
      upTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;

      /* set the matrix */
      upTriFactor->csrMat = new CsrMatrix;
      upTriFactor->csrMat->num_rows = n;
      upTriFactor->csrMat->num_cols = n;
      upTriFactor->csrMat->num_entries = nzUpper;

      upTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(n+1);
      upTriFactor->csrMat->row_offsets->assign(AiUp, AiUp+n+1);

      upTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(nzUpper);
      upTriFactor->csrMat->column_indices->assign(AjUp, AjUp+nzUpper);

      upTriFactor->csrMat->values = new THRUSTARRAY(nzUpper);
      upTriFactor->csrMat->values->assign(AAUp, AAUp+nzUpper);

      /* perform the solve analysis */
      stat = cusparse_analysis(cusparseTriFactors->handle, upTriFactor->solveOp,
                               upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr,
                               upTriFactor->csrMat->values->data().get(), upTriFactor->csrMat->row_offsets->data().get(),
                               upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo);CHKERRCUSPARSE(stat);

      /* assign the pointer. Is this really necessary? */
      ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->upTriFactorPtr = upTriFactor;

      cerr = cudaFreeHost(AiUp);CHKERRCUDA(cerr);
      cerr = cudaFreeHost(AjUp);CHKERRCUDA(cerr);
      cerr = cudaFreeHost(AAUp);CHKERRCUDA(cerr);
      ierr = PetscLogCpuToGpu((n+1+nzUpper)*sizeof(int)+nzUpper*sizeof(PetscScalar));CHKERRQ(ierr);
    } catch(char *ex) {
      SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
    }
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSEILUAnalysisAndCopyToGPU(Mat A)
{
  PetscErrorCode               ierr;
  Mat_SeqAIJ                   *a                  = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
  IS                           isrow = a->row,iscol = a->icol;
  PetscBool                    row_identity,col_identity;
  const PetscInt               *r,*c;
  PetscInt                     n = A->rmap->n;

  PetscFunctionBegin;
  ierr = MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors);CHKERRQ(ierr);
  ierr = MatSeqAIJCUSPARSEBuildILULowerTriMatrix(A);CHKERRQ(ierr);
  ierr = MatSeqAIJCUSPARSEBuildILUUpperTriMatrix(A);CHKERRQ(ierr);

  cusparseTriFactors->workVector = new THRUSTARRAY(n);
  cusparseTriFactors->nnz=a->nz;

  A->offloadmask = PETSC_OFFLOAD_BOTH;
  /* lower triangular indices */
  ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
  ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
  if (!row_identity) {
    cusparseTriFactors->rpermIndices = new THRUSTINTARRAY(n);
    cusparseTriFactors->rpermIndices->assign(r, r+n);
  }
  ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);

  /* upper triangular indices */
  ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr);
  ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
  if (!col_identity) {
    cusparseTriFactors->cpermIndices = new THRUSTINTARRAY(n);
    cusparseTriFactors->cpermIndices->assign(c, c+n);
  }

  if (!row_identity && !col_identity) {
    ierr = PetscLogCpuToGpu(2*n*sizeof(PetscInt));CHKERRQ(ierr);
  } else if(!row_identity) {
    ierr = PetscLogCpuToGpu(n*sizeof(PetscInt));CHKERRQ(ierr);
  } else if(!col_identity) {
    ierr = PetscLogCpuToGpu(n*sizeof(PetscInt));CHKERRQ(ierr);
  }

  ierr = ISRestoreIndices(iscol,&c);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSEBuildICCTriMatrices(Mat A)
{
  Mat_SeqAIJ                        *a = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
  Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtr;
  Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtr;
  cusparseStatus_t                  stat;
  PetscErrorCode                    ierr;
  cudaError_t                       cerr;
  PetscInt                          *AiUp, *AjUp;
  PetscScalar                       *AAUp;
  PetscScalar                       *AALo;
  PetscInt                          nzUpper = a->nz,n = A->rmap->n,i,offset,nz,j;
  Mat_SeqSBAIJ                      *b = (Mat_SeqSBAIJ*)A->data;
  const PetscInt                    *ai = b->i,*aj = b->j,*vj;
  const MatScalar                   *aa = b->a,*v;

  PetscFunctionBegin;
  if (!n) PetscFunctionReturn(0);
  if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
    try {
      /* Allocate Space for the upper triangular matrix */
      cerr = cudaMallocHost((void**) &AiUp, (n+1)*sizeof(PetscInt));CHKERRCUDA(cerr);
      cerr = cudaMallocHost((void**) &AjUp, nzUpper*sizeof(PetscInt));CHKERRCUDA(cerr);
      cerr = cudaMallocHost((void**) &AAUp, nzUpper*sizeof(PetscScalar));CHKERRCUDA(cerr);
      cerr = cudaMallocHost((void**) &AALo, nzUpper*sizeof(PetscScalar));CHKERRCUDA(cerr);

      /* Fill the upper triangular matrix */
      AiUp[0]=(PetscInt) 0;
      AiUp[n]=nzUpper;
      offset = 0;
      for (i=0; i<n; i++) {
        /* set the pointers */
        v  = aa + ai[i];
        vj = aj + ai[i];
        nz = ai[i+1] - ai[i] - 1; /* exclude diag[i] */

        /* first, set the diagonal elements */
        AjUp[offset] = (PetscInt) i;
        AAUp[offset] = (MatScalar)1.0/v[nz];
        AiUp[i]      = offset;
        AALo[offset] = (MatScalar)1.0/v[nz];

        offset+=1;
        if (nz>0) {
          ierr = PetscArraycpy(&(AjUp[offset]), vj, nz);CHKERRQ(ierr);
          ierr = PetscArraycpy(&(AAUp[offset]), v, nz);CHKERRQ(ierr);
          for (j=offset; j<offset+nz; j++) {
            AAUp[j] = -AAUp[j];
            AALo[j] = AAUp[j]/v[nz];
          }
          offset+=nz;
        }
      }

      /* allocate space for the triangular factor information */
      upTriFactor = new Mat_SeqAIJCUSPARSETriFactorStruct;

      /* Create the matrix description */
      stat = cusparseCreateMatDescr(&upTriFactor->descr);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatIndexBase(upTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatFillMode(upTriFactor->descr, CUSPARSE_FILL_MODE_UPPER);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatDiagType(upTriFactor->descr, CUSPARSE_DIAG_TYPE_UNIT);CHKERRCUSPARSE(stat);

      /* Create the solve analysis information */
      stat = cusparseCreateSolveAnalysisInfo(&upTriFactor->solveInfo);CHKERRCUSPARSE(stat);

      /* set the operation */
      upTriFactor->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;

      /* set the matrix */
      upTriFactor->csrMat = new CsrMatrix;
      upTriFactor->csrMat->num_rows = A->rmap->n;
      upTriFactor->csrMat->num_cols = A->cmap->n;
      upTriFactor->csrMat->num_entries = a->nz;

      upTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(A->rmap->n+1);
      upTriFactor->csrMat->row_offsets->assign(AiUp, AiUp+A->rmap->n+1);

      upTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(a->nz);
      upTriFactor->csrMat->column_indices->assign(AjUp, AjUp+a->nz);

      upTriFactor->csrMat->values = new THRUSTARRAY(a->nz);
      upTriFactor->csrMat->values->assign(AAUp, AAUp+a->nz);

      /* perform the solve analysis */
      stat = cusparse_analysis(cusparseTriFactors->handle, upTriFactor->solveOp,
                               upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, upTriFactor->descr,
                               upTriFactor->csrMat->values->data().get(), upTriFactor->csrMat->row_offsets->data().get(),
                               upTriFactor->csrMat->column_indices->data().get(), upTriFactor->solveInfo);CHKERRCUSPARSE(stat);

      /* assign the pointer. Is this really necessary? */
      ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->upTriFactorPtr = upTriFactor;

      /* allocate space for the triangular factor information */
      loTriFactor = new Mat_SeqAIJCUSPARSETriFactorStruct;

      /* Create the matrix description */
      stat = cusparseCreateMatDescr(&loTriFactor->descr);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatIndexBase(loTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatFillMode(loTriFactor->descr, CUSPARSE_FILL_MODE_UPPER);CHKERRCUSPARSE(stat);
      stat = cusparseSetMatDiagType(loTriFactor->descr, CUSPARSE_DIAG_TYPE_NON_UNIT);CHKERRCUSPARSE(stat);

      /* Create the solve analysis information */
      stat = cusparseCreateSolveAnalysisInfo(&loTriFactor->solveInfo);CHKERRCUSPARSE(stat);

      /* set the operation */
      loTriFactor->solveOp = CUSPARSE_OPERATION_TRANSPOSE;

      /* set the matrix */
      loTriFactor->csrMat = new CsrMatrix;
      loTriFactor->csrMat->num_rows = A->rmap->n;
      loTriFactor->csrMat->num_cols = A->cmap->n;
      loTriFactor->csrMat->num_entries = a->nz;

      loTriFactor->csrMat->row_offsets = new THRUSTINTARRAY32(A->rmap->n+1);
      loTriFactor->csrMat->row_offsets->assign(AiUp, AiUp+A->rmap->n+1);

      loTriFactor->csrMat->column_indices = new THRUSTINTARRAY32(a->nz);
      loTriFactor->csrMat->column_indices->assign(AjUp, AjUp+a->nz);

      loTriFactor->csrMat->values = new THRUSTARRAY(a->nz);
      loTriFactor->csrMat->values->assign(AALo, AALo+a->nz);
      ierr = PetscLogCpuToGpu(2*(((A->rmap->n+1)+(a->nz))*sizeof(int)+(a->nz)*sizeof(PetscScalar)));CHKERRQ(ierr);

      /* perform the solve analysis */
      stat = cusparse_analysis(cusparseTriFactors->handle, loTriFactor->solveOp,
                               loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, loTriFactor->descr,
                               loTriFactor->csrMat->values->data().get(), loTriFactor->csrMat->row_offsets->data().get(),
                               loTriFactor->csrMat->column_indices->data().get(), loTriFactor->solveInfo);CHKERRCUSPARSE(stat);

      /* assign the pointer. Is this really necessary? */
      ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->loTriFactorPtr = loTriFactor;

      A->offloadmask = PETSC_OFFLOAD_BOTH;
      cerr = cudaFreeHost(AiUp);CHKERRCUDA(cerr);
      cerr = cudaFreeHost(AjUp);CHKERRCUDA(cerr);
      cerr = cudaFreeHost(AAUp);CHKERRCUDA(cerr);
      cerr = cudaFreeHost(AALo);CHKERRCUDA(cerr);
    } catch(char *ex) {
      SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
    }
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSEICCAnalysisAndCopyToGPU(Mat A)
{
  PetscErrorCode               ierr;
  Mat_SeqAIJ                   *a                  = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
  IS                           ip = a->row;
  const PetscInt               *rip;
  PetscBool                    perm_identity;
  PetscInt                     n = A->rmap->n;

  PetscFunctionBegin;
  ierr = MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors);CHKERRQ(ierr);
  ierr = MatSeqAIJCUSPARSEBuildICCTriMatrices(A);CHKERRQ(ierr);
  cusparseTriFactors->workVector = new THRUSTARRAY(n);
  cusparseTriFactors->nnz=(a->nz-n)*2 + n;

  /* lower triangular indices */
  ierr = ISGetIndices(ip,&rip);CHKERRQ(ierr);
  ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
  if (!perm_identity) {
    IS             iip;
    const PetscInt *irip;

    ierr = ISInvertPermutation(ip,PETSC_DECIDE,&iip);CHKERRQ(ierr);
    ierr = ISGetIndices(iip,&irip);CHKERRQ(ierr);
    cusparseTriFactors->rpermIndices = new THRUSTINTARRAY(n);
    cusparseTriFactors->rpermIndices->assign(rip, rip+n);
    cusparseTriFactors->cpermIndices = new THRUSTINTARRAY(n);
    cusparseTriFactors->cpermIndices->assign(irip, irip+n);
    ierr = ISRestoreIndices(iip,&irip);CHKERRQ(ierr);
    ierr = ISDestroy(&iip);CHKERRQ(ierr);
    ierr = PetscLogCpuToGpu(2*n*sizeof(PetscInt));CHKERRQ(ierr);
  }
  ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatLUFactorNumeric_SeqAIJCUSPARSE(Mat B,Mat A,const MatFactorInfo *info)
{
  Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
  IS             isrow = b->row,iscol = b->col;
  PetscBool      row_identity,col_identity;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatLUFactorNumeric_SeqAIJ(B,A,info);CHKERRQ(ierr);
  B->offloadmask = PETSC_OFFLOAD_CPU;
  /* determine which version of MatSolve needs to be used. */
  ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
  ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
  if (row_identity && col_identity) {
    B->ops->solve = MatSolve_SeqAIJCUSPARSE_NaturalOrdering;
    B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering;
    B->ops->matsolve = NULL;
    B->ops->matsolvetranspose = NULL;
  } else {
    B->ops->solve = MatSolve_SeqAIJCUSPARSE;
    B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE;
    B->ops->matsolve = NULL;
    B->ops->matsolvetranspose = NULL;
  }

  /* get the triangular factors */
  ierr = MatSeqAIJCUSPARSEILUAnalysisAndCopyToGPU(B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatCholeskyFactorNumeric_SeqAIJCUSPARSE(Mat B,Mat A,const MatFactorInfo *info)
{
  Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
  IS             ip = b->row;
  PetscBool      perm_identity;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatCholeskyFactorNumeric_SeqAIJ(B,A,info);CHKERRQ(ierr);
  B->offloadmask = PETSC_OFFLOAD_CPU;
  /* determine which version of MatSolve needs to be used. */
  ierr = ISIdentity(ip,&perm_identity);CHKERRQ(ierr);
  if (perm_identity) {
    B->ops->solve = MatSolve_SeqAIJCUSPARSE_NaturalOrdering;
    B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering;
    B->ops->matsolve = NULL;
    B->ops->matsolvetranspose = NULL;
  } else {
    B->ops->solve = MatSolve_SeqAIJCUSPARSE;
    B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE;
    B->ops->matsolve = NULL;
    B->ops->matsolvetranspose = NULL;
  }

  /* get the triangular factors */
  ierr = MatSeqAIJCUSPARSEICCAnalysisAndCopyToGPU(B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(Mat A)
{
  Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
  Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtr;
  Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtr;
  Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtrTranspose;
  Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtrTranspose;
  cusparseStatus_t                  stat;
  cusparseIndexBase_t               indexBase;
  cusparseMatrixType_t              matrixType;
  cusparseFillMode_t                fillMode;
  cusparseDiagType_t                diagType;

  PetscFunctionBegin;

  /*********************************************/
  /* Now the Transpose of the Lower Tri Factor */
  /*********************************************/

  /* allocate space for the transpose of the lower triangular factor */
  loTriFactorT = new Mat_SeqAIJCUSPARSETriFactorStruct;

  /* set the matrix descriptors of the lower triangular factor */
  matrixType = cusparseGetMatType(loTriFactor->descr);
  indexBase = cusparseGetMatIndexBase(loTriFactor->descr);
  fillMode = cusparseGetMatFillMode(loTriFactor->descr)==CUSPARSE_FILL_MODE_UPPER ?
    CUSPARSE_FILL_MODE_LOWER : CUSPARSE_FILL_MODE_UPPER;
  diagType = cusparseGetMatDiagType(loTriFactor->descr);

  /* Create the matrix description */
  stat = cusparseCreateMatDescr(&loTriFactorT->descr);CHKERRCUSPARSE(stat);
  stat = cusparseSetMatIndexBase(loTriFactorT->descr, indexBase);CHKERRCUSPARSE(stat);
  stat = cusparseSetMatType(loTriFactorT->descr, matrixType);CHKERRCUSPARSE(stat);
  stat = cusparseSetMatFillMode(loTriFactorT->descr, fillMode);CHKERRCUSPARSE(stat);
  stat = cusparseSetMatDiagType(loTriFactorT->descr, diagType);CHKERRCUSPARSE(stat);

  /* Create the solve analysis information */
  stat = cusparseCreateSolveAnalysisInfo(&loTriFactorT->solveInfo);CHKERRCUSPARSE(stat);

  /* set the operation */
  loTriFactorT->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;

  /* allocate GPU space for the CSC of the lower triangular factor*/
  loTriFactorT->csrMat = new CsrMatrix;
  loTriFactorT->csrMat->num_rows = loTriFactor->csrMat->num_rows;
  loTriFactorT->csrMat->num_cols = loTriFactor->csrMat->num_cols;
  loTriFactorT->csrMat->num_entries = loTriFactor->csrMat->num_entries;
  loTriFactorT->csrMat->row_offsets = new THRUSTINTARRAY32(loTriFactor->csrMat->num_rows+1);
  loTriFactorT->csrMat->column_indices = new THRUSTINTARRAY32(loTriFactor->csrMat->num_entries);
  loTriFactorT->csrMat->values = new THRUSTARRAY(loTriFactor->csrMat->num_entries);

  /* compute the transpose of the lower triangular factor, i.e. the CSC */
  stat = cusparse_csr2csc(cusparseTriFactors->handle, loTriFactor->csrMat->num_rows,
                          loTriFactor->csrMat->num_cols, loTriFactor->csrMat->num_entries,
                          loTriFactor->csrMat->values->data().get(),
                          loTriFactor->csrMat->row_offsets->data().get(),
                          loTriFactor->csrMat->column_indices->data().get(),
                          loTriFactorT->csrMat->values->data().get(),
                          loTriFactorT->csrMat->column_indices->data().get(),
                          loTriFactorT->csrMat->row_offsets->data().get(),
                          CUSPARSE_ACTION_NUMERIC, indexBase);CHKERRCUSPARSE(stat);

  /* perform the solve analysis on the transposed matrix */
  stat = cusparse_analysis(cusparseTriFactors->handle, loTriFactorT->solveOp,
                           loTriFactorT->csrMat->num_rows, loTriFactorT->csrMat->num_entries,
                           loTriFactorT->descr, loTriFactorT->csrMat->values->data().get(),
                           loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(),
                           loTriFactorT->solveInfo);CHKERRCUSPARSE(stat);

  /* assign the pointer. Is this really necessary? */
  ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->loTriFactorPtrTranspose = loTriFactorT;

  /*********************************************/
  /* Now the Transpose of the Upper Tri Factor */
  /*********************************************/

  /* allocate space for the transpose of the upper triangular factor */
  upTriFactorT = new Mat_SeqAIJCUSPARSETriFactorStruct;

  /* set the matrix descriptors of the upper triangular factor */
  matrixType = cusparseGetMatType(upTriFactor->descr);
  indexBase = cusparseGetMatIndexBase(upTriFactor->descr);
  fillMode = cusparseGetMatFillMode(upTriFactor->descr)==CUSPARSE_FILL_MODE_UPPER ?
    CUSPARSE_FILL_MODE_LOWER : CUSPARSE_FILL_MODE_UPPER;
  diagType = cusparseGetMatDiagType(upTriFactor->descr);

  /* Create the matrix description */
  stat = cusparseCreateMatDescr(&upTriFactorT->descr);CHKERRCUSPARSE(stat);
  stat = cusparseSetMatIndexBase(upTriFactorT->descr, indexBase);CHKERRCUSPARSE(stat);
  stat = cusparseSetMatType(upTriFactorT->descr, matrixType);CHKERRCUSPARSE(stat);
  stat = cusparseSetMatFillMode(upTriFactorT->descr, fillMode);CHKERRCUSPARSE(stat);
  stat = cusparseSetMatDiagType(upTriFactorT->descr, diagType);CHKERRCUSPARSE(stat);

  /* Create the solve analysis information */
  stat = cusparseCreateSolveAnalysisInfo(&upTriFactorT->solveInfo);CHKERRCUSPARSE(stat);

  /* set the operation */
  upTriFactorT->solveOp = CUSPARSE_OPERATION_NON_TRANSPOSE;

  /* allocate GPU space for the CSC of the upper triangular factor*/
  upTriFactorT->csrMat = new CsrMatrix;
  upTriFactorT->csrMat->num_rows = upTriFactor->csrMat->num_rows;
  upTriFactorT->csrMat->num_cols = upTriFactor->csrMat->num_cols;
  upTriFactorT->csrMat->num_entries = upTriFactor->csrMat->num_entries;
  upTriFactorT->csrMat->row_offsets = new THRUSTINTARRAY32(upTriFactor->csrMat->num_rows+1);
  upTriFactorT->csrMat->column_indices = new THRUSTINTARRAY32(upTriFactor->csrMat->num_entries);
  upTriFactorT->csrMat->values = new THRUSTARRAY(upTriFactor->csrMat->num_entries);

  /* compute the transpose of the upper triangular factor, i.e. the CSC */
  stat = cusparse_csr2csc(cusparseTriFactors->handle, upTriFactor->csrMat->num_rows,
                          upTriFactor->csrMat->num_cols, upTriFactor->csrMat->num_entries,
                          upTriFactor->csrMat->values->data().get(),
                          upTriFactor->csrMat->row_offsets->data().get(),
                          upTriFactor->csrMat->column_indices->data().get(),
                          upTriFactorT->csrMat->values->data().get(),
                          upTriFactorT->csrMat->column_indices->data().get(),
                          upTriFactorT->csrMat->row_offsets->data().get(),
                          CUSPARSE_ACTION_NUMERIC, indexBase);CHKERRCUSPARSE(stat);

  /* perform the solve analysis on the transposed matrix */
  stat = cusparse_analysis(cusparseTriFactors->handle, upTriFactorT->solveOp,
                           upTriFactorT->csrMat->num_rows, upTriFactorT->csrMat->num_entries,
                           upTriFactorT->descr, upTriFactorT->csrMat->values->data().get(),
                           upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(),
                           upTriFactorT->solveInfo);CHKERRCUSPARSE(stat);

  /* assign the pointer. Is this really necessary? */
  ((Mat_SeqAIJCUSPARSETriFactors*)A->spptr)->upTriFactorPtrTranspose = upTriFactorT;
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSEGenerateTransposeForMult(Mat A)
{
  Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
  Mat_SeqAIJCUSPARSEMultStruct *matstruct = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->mat;
  Mat_SeqAIJCUSPARSEMultStruct *matstructT = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->matTranspose;
  Mat_SeqAIJ                   *a = (Mat_SeqAIJ*)A->data;
  cusparseStatus_t             stat;
  cusparseIndexBase_t          indexBase;
  cudaError_t                  err;
  PetscErrorCode               ierr;

  PetscFunctionBegin;
  if (!cusparsestruct->transgen || cusparsestruct->matTranspose) PetscFunctionReturn(0);
  ierr = PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose,A,0,0,0);CHKERRQ(ierr);
  ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);
  /* create cusparse matrix */
  matstructT = new Mat_SeqAIJCUSPARSEMultStruct;
  stat = cusparseCreateMatDescr(&matstructT->descr);CHKERRCUSPARSE(stat);
  indexBase = cusparseGetMatIndexBase(matstruct->descr);
  stat = cusparseSetMatIndexBase(matstructT->descr, indexBase);CHKERRCUSPARSE(stat);
  stat = cusparseSetMatType(matstructT->descr, CUSPARSE_MATRIX_TYPE_GENERAL);CHKERRCUSPARSE(stat);

  /* set alpha and beta */
  err = cudaMalloc((void **)&(matstructT->alpha),    sizeof(PetscScalar));CHKERRCUDA(err);
  err = cudaMalloc((void **)&(matstructT->beta_zero),sizeof(PetscScalar));CHKERRCUDA(err);
  err = cudaMalloc((void **)&(matstructT->beta_one), sizeof(PetscScalar));CHKERRCUDA(err);
  err = cudaMemcpy(matstructT->alpha,    &PETSC_CUSPARSE_ONE, sizeof(PetscScalar),cudaMemcpyHostToDevice);CHKERRCUDA(err);
  err = cudaMemcpy(matstructT->beta_zero,&PETSC_CUSPARSE_ZERO,sizeof(PetscScalar),cudaMemcpyHostToDevice);CHKERRCUDA(err);
  err = cudaMemcpy(matstructT->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar),cudaMemcpyHostToDevice);CHKERRCUDA(err);
  stat = cusparseSetPointerMode(cusparsestruct->handle, CUSPARSE_POINTER_MODE_DEVICE);CHKERRCUSPARSE(stat);

  if (cusparsestruct->format==MAT_CUSPARSE_CSR) {
    CsrMatrix *matrix = (CsrMatrix*)matstruct->mat;
    CsrMatrix *matrixT= new CsrMatrix;
    matrixT->num_rows = A->cmap->n;
    matrixT->num_cols = A->rmap->n;
    matrixT->num_entries = a->nz;
    matrixT->row_offsets = new THRUSTINTARRAY32(matrixT->num_rows+1);
    matrixT->column_indices = new THRUSTINTARRAY32(a->nz);
    matrixT->values = new THRUSTARRAY(a->nz);

    cusparsestruct->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n+1);
    cusparsestruct->rowoffsets_gpu->assign(a->i,a->i+A->rmap->n+1);
    /* compute the transpose, i.e. the CSC */
    indexBase = cusparseGetMatIndexBase(matstruct->descr);
    stat = cusparse_csr2csc(cusparsestruct->handle, A->rmap->n,
                            A->cmap->n, matrix->num_entries,
                            matrix->values->data().get(),
                            cusparsestruct->rowoffsets_gpu->data().get(),
                            matrix->column_indices->data().get(),
                            matrixT->values->data().get(),
                            matrixT->column_indices->data().get(),
                            matrixT->row_offsets->data().get(),
                            CUSPARSE_ACTION_NUMERIC, indexBase);CHKERRCUSPARSE(stat);
    matstructT->mat = matrixT;
  } else if (cusparsestruct->format==MAT_CUSPARSE_ELL || cusparsestruct->format==MAT_CUSPARSE_HYB) {
    CsrMatrix *temp = new CsrMatrix;
    CsrMatrix *tempT = new CsrMatrix;

    /* First convert HYB to CSR */
    temp->num_rows = A->rmap->n;
    temp->num_cols = A->cmap->n;
    temp->num_entries = a->nz;
    temp->row_offsets = new THRUSTINTARRAY32(A->rmap->n+1);
    temp->column_indices = new THRUSTINTARRAY32(a->nz);
    temp->values = new THRUSTARRAY(a->nz);

    stat = cusparse_hyb2csr(cusparsestruct->handle,
                            matstruct->descr, (cusparseHybMat_t)matstruct->mat,
                            temp->values->data().get(),
                            temp->row_offsets->data().get(),
                            temp->column_indices->data().get());CHKERRCUSPARSE(stat);

    /* Next, convert CSR to CSC (i.e. the matrix transpose) */
    tempT->num_rows = A->rmap->n;
    tempT->num_cols = A->cmap->n;
    tempT->num_entries = a->nz;
    tempT->row_offsets = new THRUSTINTARRAY32(A->rmap->n+1);
    tempT->column_indices = new THRUSTINTARRAY32(a->nz);
    tempT->values = new THRUSTARRAY(a->nz);

    stat = cusparse_csr2csc(cusparsestruct->handle, temp->num_rows,
                            temp->num_cols, temp->num_entries,
                            temp->values->data().get(),
                            temp->row_offsets->data().get(),
                            temp->column_indices->data().get(),
                            tempT->values->data().get(),
                            tempT->column_indices->data().get(),
                            tempT->row_offsets->data().get(),
                            CUSPARSE_ACTION_NUMERIC, indexBase);CHKERRCUSPARSE(stat);

    /* Last, convert CSC to HYB */
    cusparseHybMat_t hybMat;
    stat = cusparseCreateHybMat(&hybMat);CHKERRCUSPARSE(stat);
    cusparseHybPartition_t partition = cusparsestruct->format==MAT_CUSPARSE_ELL ?
      CUSPARSE_HYB_PARTITION_MAX : CUSPARSE_HYB_PARTITION_AUTO;
    stat = cusparse_csr2hyb(cusparsestruct->handle, A->rmap->n, A->cmap->n,
                            matstructT->descr, tempT->values->data().get(),
                            tempT->row_offsets->data().get(),
                            tempT->column_indices->data().get(),
                            hybMat, 0, partition);CHKERRCUSPARSE(stat);

    /* assign the pointer */
    matstructT->mat = hybMat;
    /* delete temporaries */
    if (tempT) {
      if (tempT->values) delete (THRUSTARRAY*) tempT->values;
      if (tempT->column_indices) delete (THRUSTINTARRAY32*) tempT->column_indices;
      if (tempT->row_offsets) delete (THRUSTINTARRAY32*) tempT->row_offsets;
      delete (CsrMatrix*) tempT;
    }
    if (temp) {
      if (temp->values) delete (THRUSTARRAY*) temp->values;
      if (temp->column_indices) delete (THRUSTINTARRAY32*) temp->column_indices;
      if (temp->row_offsets) delete (THRUSTINTARRAY32*) temp->row_offsets;
      delete (CsrMatrix*) temp;
    }
  }
  err  = WaitForGPU();CHKERRCUDA(err);
  ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_CUSPARSEGenerateTranspose,A,0,0,0);CHKERRQ(ierr);
  /* the compressed row indices is not used for matTranspose */
  matstructT->cprowIndices = NULL;
  /* assign the pointer */
  ((Mat_SeqAIJCUSPARSE*)A->spptr)->matTranspose = matstructT;
  PetscFunctionReturn(0);
}

/* Why do we need to analyze the tranposed matrix again? Can't we just use op(A) = CUSPARSE_OPERATION_TRANSPOSE in MatSolve_SeqAIJCUSPARSE? */
static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE(Mat A,Vec bb,Vec xx)
{
  PetscInt                              n = xx->map->n;
  const PetscScalar                     *barray;
  PetscScalar                           *xarray;
  thrust::device_ptr<const PetscScalar> bGPU;
  thrust::device_ptr<PetscScalar>       xGPU;
  cusparseStatus_t                      stat;
  Mat_SeqAIJCUSPARSETriFactors          *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
  Mat_SeqAIJCUSPARSETriFactorStruct     *loTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtrTranspose;
  Mat_SeqAIJCUSPARSETriFactorStruct     *upTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtrTranspose;
  THRUSTARRAY                           *tempGPU = (THRUSTARRAY*)cusparseTriFactors->workVector;
  PetscErrorCode                        ierr;
  cudaError_t                           cerr;

  PetscFunctionBegin;
  /* Analyze the matrix and create the transpose ... on the fly */
  if (!loTriFactorT && !upTriFactorT) {
    ierr = MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(A);CHKERRQ(ierr);
    loTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtrTranspose;
    upTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtrTranspose;
  }

  /* Get the GPU pointers */
  ierr = VecCUDAGetArrayWrite(xx,&xarray);CHKERRQ(ierr);
  ierr = VecCUDAGetArrayRead(bb,&barray);CHKERRQ(ierr);
  xGPU = thrust::device_pointer_cast(xarray);
  bGPU = thrust::device_pointer_cast(barray);

  ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);
  /* First, reorder with the row permutation */
  thrust::copy(thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->begin()),
               thrust::make_permutation_iterator(bGPU+n, cusparseTriFactors->rpermIndices->end()),
               xGPU);

  /* First, solve U */
  stat = cusparse_solve(cusparseTriFactors->handle, upTriFactorT->solveOp,
                        upTriFactorT->csrMat->num_rows, &PETSC_CUSPARSE_ONE, upTriFactorT->descr,
                        upTriFactorT->csrMat->values->data().get(),
                        upTriFactorT->csrMat->row_offsets->data().get(),
                        upTriFactorT->csrMat->column_indices->data().get(),
                        upTriFactorT->solveInfo,
                        xarray, tempGPU->data().get());CHKERRCUSPARSE(stat);

  /* Then, solve L */
  stat = cusparse_solve(cusparseTriFactors->handle, loTriFactorT->solveOp,
                        loTriFactorT->csrMat->num_rows, &PETSC_CUSPARSE_ONE, loTriFactorT->descr,
                        loTriFactorT->csrMat->values->data().get(),
                        loTriFactorT->csrMat->row_offsets->data().get(),
                        loTriFactorT->csrMat->column_indices->data().get(),
                        loTriFactorT->solveInfo,
                        tempGPU->data().get(), xarray);CHKERRCUSPARSE(stat);

  /* Last, copy the solution, xGPU, into a temporary with the column permutation ... can't be done in place. */
  thrust::copy(thrust::make_permutation_iterator(xGPU, cusparseTriFactors->cpermIndices->begin()),
               thrust::make_permutation_iterator(xGPU+n, cusparseTriFactors->cpermIndices->end()),
               tempGPU->begin());

  /* Copy the temporary to the full solution. */
  thrust::copy(tempGPU->begin(), tempGPU->end(), xGPU);

  /* restore */
  ierr = VecCUDARestoreArrayRead(bb,&barray);CHKERRQ(ierr);
  ierr = VecCUDARestoreArrayWrite(xx,&xarray);CHKERRQ(ierr);
  cerr = WaitForGPU();CHKERRCUDA(cerr);
  ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);
  ierr = PetscLogGpuFlops(2.0*cusparseTriFactors->nnz - A->cmap->n);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  const PetscScalar                 *barray;
  PetscScalar                       *xarray;
  cusparseStatus_t                  stat;
  Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
  Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtrTranspose;
  Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactorT = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtrTranspose;
  THRUSTARRAY                       *tempGPU = (THRUSTARRAY*)cusparseTriFactors->workVector;
  PetscErrorCode                    ierr;
  cudaError_t                       cerr;

  PetscFunctionBegin;
  /* Analyze the matrix and create the transpose ... on the fly */
  if (!loTriFactorT && !upTriFactorT) {
    ierr = MatSeqAIJCUSPARSEAnalyzeTransposeForSolve(A);CHKERRQ(ierr);
    loTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtrTranspose;
    upTriFactorT       = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtrTranspose;
  }

  /* Get the GPU pointers */
  ierr = VecCUDAGetArrayWrite(xx,&xarray);CHKERRQ(ierr);
  ierr = VecCUDAGetArrayRead(bb,&barray);CHKERRQ(ierr);

  ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);
  /* First, solve U */
  stat = cusparse_solve(cusparseTriFactors->handle, upTriFactorT->solveOp,
                        upTriFactorT->csrMat->num_rows, &PETSC_CUSPARSE_ONE, upTriFactorT->descr,
                        upTriFactorT->csrMat->values->data().get(),
                        upTriFactorT->csrMat->row_offsets->data().get(),
                        upTriFactorT->csrMat->column_indices->data().get(),
                        upTriFactorT->solveInfo,
                        barray, tempGPU->data().get());CHKERRCUSPARSE(stat);

  /* Then, solve L */
  stat = cusparse_solve(cusparseTriFactors->handle, loTriFactorT->solveOp,
                        loTriFactorT->csrMat->num_rows, &PETSC_CUSPARSE_ONE, loTriFactorT->descr,
                        loTriFactorT->csrMat->values->data().get(),
                        loTriFactorT->csrMat->row_offsets->data().get(),
                        loTriFactorT->csrMat->column_indices->data().get(),
                        loTriFactorT->solveInfo,
                        tempGPU->data().get(), xarray);CHKERRCUSPARSE(stat);

  /* restore */
  ierr = VecCUDARestoreArrayRead(bb,&barray);CHKERRQ(ierr);
  ierr = VecCUDARestoreArrayWrite(xx,&xarray);CHKERRQ(ierr);
  cerr = WaitForGPU();CHKERRCUDA(cerr);
  ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);
  ierr = PetscLogGpuFlops(2.0*cusparseTriFactors->nnz - A->cmap->n);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSolve_SeqAIJCUSPARSE(Mat A,Vec bb,Vec xx)
{
  const PetscScalar                     *barray;
  PetscScalar                           *xarray;
  thrust::device_ptr<const PetscScalar> bGPU;
  thrust::device_ptr<PetscScalar>       xGPU;
  cusparseStatus_t                      stat;
  Mat_SeqAIJCUSPARSETriFactors          *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
  Mat_SeqAIJCUSPARSETriFactorStruct     *loTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtr;
  Mat_SeqAIJCUSPARSETriFactorStruct     *upTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtr;
  THRUSTARRAY                           *tempGPU = (THRUSTARRAY*)cusparseTriFactors->workVector;
  PetscErrorCode                        ierr;
  cudaError_t                           cerr;

  PetscFunctionBegin;

  /* Get the GPU pointers */
  ierr = VecCUDAGetArrayWrite(xx,&xarray);CHKERRQ(ierr);
  ierr = VecCUDAGetArrayRead(bb,&barray);CHKERRQ(ierr);
  xGPU = thrust::device_pointer_cast(xarray);
  bGPU = thrust::device_pointer_cast(barray);

  ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);
  /* First, reorder with the row permutation */
  thrust::copy(thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->begin()),
               thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->end()),
               tempGPU->begin());

  /* Next, solve L */
  stat = cusparse_solve(cusparseTriFactors->handle, loTriFactor->solveOp,
                        loTriFactor->csrMat->num_rows, &PETSC_CUSPARSE_ONE, loTriFactor->descr,
                        loTriFactor->csrMat->values->data().get(),
                        loTriFactor->csrMat->row_offsets->data().get(),
                        loTriFactor->csrMat->column_indices->data().get(),
                        loTriFactor->solveInfo,
                        tempGPU->data().get(), xarray);CHKERRCUSPARSE(stat);

  /* Then, solve U */
  stat = cusparse_solve(cusparseTriFactors->handle, upTriFactor->solveOp,
                        upTriFactor->csrMat->num_rows, &PETSC_CUSPARSE_ONE, upTriFactor->descr,
                        upTriFactor->csrMat->values->data().get(),
                        upTriFactor->csrMat->row_offsets->data().get(),
                        upTriFactor->csrMat->column_indices->data().get(),
                        upTriFactor->solveInfo,
                        xarray, tempGPU->data().get());CHKERRCUSPARSE(stat);

  /* Last, reorder with the column permutation */
  thrust::copy(thrust::make_permutation_iterator(tempGPU->begin(), cusparseTriFactors->cpermIndices->begin()),
               thrust::make_permutation_iterator(tempGPU->begin(), cusparseTriFactors->cpermIndices->end()),
               xGPU);

  ierr = VecCUDARestoreArrayRead(bb,&barray);CHKERRQ(ierr);
  ierr = VecCUDARestoreArrayWrite(xx,&xarray);CHKERRQ(ierr);
  cerr = WaitForGPU();CHKERRCUDA(cerr);
  ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);
  ierr = PetscLogGpuFlops(2.0*cusparseTriFactors->nnz - A->cmap->n);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSolve_SeqAIJCUSPARSE_NaturalOrdering(Mat A,Vec bb,Vec xx)
{
  const PetscScalar                 *barray;
  PetscScalar                       *xarray;
  cusparseStatus_t                  stat;
  Mat_SeqAIJCUSPARSETriFactors      *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors*)A->spptr;
  Mat_SeqAIJCUSPARSETriFactorStruct *loTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->loTriFactorPtr;
  Mat_SeqAIJCUSPARSETriFactorStruct *upTriFactor = (Mat_SeqAIJCUSPARSETriFactorStruct*)cusparseTriFactors->upTriFactorPtr;
  THRUSTARRAY                       *tempGPU = (THRUSTARRAY*)cusparseTriFactors->workVector;
  PetscErrorCode                    ierr;
  cudaError_t                       cerr;

  PetscFunctionBegin;
  /* Get the GPU pointers */
  ierr = VecCUDAGetArrayWrite(xx,&xarray);CHKERRQ(ierr);
  ierr = VecCUDAGetArrayRead(bb,&barray);CHKERRQ(ierr);

  ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);
  /* First, solve L */
  stat = cusparse_solve(cusparseTriFactors->handle, loTriFactor->solveOp,
                        loTriFactor->csrMat->num_rows, &PETSC_CUSPARSE_ONE, loTriFactor->descr,
                        loTriFactor->csrMat->values->data().get(),
                        loTriFactor->csrMat->row_offsets->data().get(),
                        loTriFactor->csrMat->column_indices->data().get(),
                        loTriFactor->solveInfo,
                        barray, tempGPU->data().get());CHKERRCUSPARSE(stat);

  /* Next, solve U */
  stat = cusparse_solve(cusparseTriFactors->handle, upTriFactor->solveOp,
                        upTriFactor->csrMat->num_rows, &PETSC_CUSPARSE_ONE, upTriFactor->descr,
                        upTriFactor->csrMat->values->data().get(),
                        upTriFactor->csrMat->row_offsets->data().get(),
                        upTriFactor->csrMat->column_indices->data().get(),
                        upTriFactor->solveInfo,
                        tempGPU->data().get(), xarray);CHKERRCUSPARSE(stat);

  ierr = VecCUDARestoreArrayRead(bb,&barray);CHKERRQ(ierr);
  ierr = VecCUDARestoreArrayWrite(xx,&xarray);CHKERRQ(ierr);
  cerr = WaitForGPU();CHKERRCUDA(cerr);
  ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);
  ierr = PetscLogGpuFlops(2.0*cusparseTriFactors->nnz - A->cmap->n);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSECopyToGPU(Mat A)
{
  Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
  Mat_SeqAIJCUSPARSEMultStruct *matstruct = cusparsestruct->mat;
  Mat_SeqAIJ                   *a = (Mat_SeqAIJ*)A->data;
  PetscInt                     m = A->rmap->n,*ii,*ridx,tmp;
  PetscErrorCode               ierr;
  cusparseStatus_t             stat;
  cudaError_t                  err;

  PetscFunctionBegin;
  if (A->boundtocpu) PetscFunctionReturn(0);
  if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
    if (A->was_assembled && A->nonzerostate == cusparsestruct->nonzerostate && cusparsestruct->format == MAT_CUSPARSE_CSR) {
      /* Copy values only */
      CsrMatrix *mat,*matT;
      mat  = (CsrMatrix*)cusparsestruct->mat->mat;

      ierr = PetscLogEventBegin(MAT_CUSPARSECopyToGPU,A,0,0,0);CHKERRQ(ierr);
      ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);
      mat->values->assign(a->a, a->a+a->nz);
      err  = WaitForGPU();CHKERRCUDA(err);
      ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);
      ierr = PetscLogCpuToGpu((a->nz)*sizeof(PetscScalar));CHKERRQ(ierr);
      ierr = PetscLogEventEnd(MAT_CUSPARSECopyToGPU,A,0,0,0);CHKERRQ(ierr);

      /* Update matT when it was built before */
      if (cusparsestruct->matTranspose) {
        cusparseIndexBase_t indexBase = cusparseGetMatIndexBase(cusparsestruct->mat->descr);
        matT = (CsrMatrix*)cusparsestruct->matTranspose->mat;
        ierr = PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose,A,0,0,0);CHKERRQ(ierr);
        ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);
        stat = cusparse_csr2csc(cusparsestruct->handle, A->rmap->n,
                                 A->cmap->n, mat->num_entries,
                                 mat->values->data().get(),
                                 cusparsestruct->rowoffsets_gpu->data().get(),
                                 mat->column_indices->data().get(),
                                 matT->values->data().get(),
                                 matT->column_indices->data().get(),
                                 matT->row_offsets->data().get(),
                                 CUSPARSE_ACTION_NUMERIC,indexBase);CHKERRCUSPARSE(stat);
        err  = WaitForGPU();CHKERRCUDA(err);
        ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);
        ierr = PetscLogEventEnd(MAT_CUSPARSEGenerateTranspose,A,0,0,0);CHKERRQ(ierr);
      }
    } else {
      ierr = PetscLogEventBegin(MAT_CUSPARSECopyToGPU,A,0,0,0);CHKERRQ(ierr);
      ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);
      ierr = MatSeqAIJCUSPARSEMultStruct_Destroy(&cusparsestruct->mat,cusparsestruct->format);CHKERRQ(ierr);
      ierr = MatSeqAIJCUSPARSEMultStruct_Destroy(&cusparsestruct->matTranspose,cusparsestruct->format);CHKERRQ(ierr);
      delete cusparsestruct->workVector;
      delete cusparsestruct->rowoffsets_gpu;
      try {
        if (a->compressedrow.use) {
          m    = a->compressedrow.nrows;
          ii   = a->compressedrow.i;
          ridx = a->compressedrow.rindex;
        } else {
          m    = A->rmap->n;
          ii   = a->i;
          ridx = NULL;
        }
        cusparsestruct->nrows = m;

        /* create cusparse matrix */
        matstruct = new Mat_SeqAIJCUSPARSEMultStruct;
        stat = cusparseCreateMatDescr(&matstruct->descr);CHKERRCUSPARSE(stat);
        stat = cusparseSetMatIndexBase(matstruct->descr, CUSPARSE_INDEX_BASE_ZERO);CHKERRCUSPARSE(stat);
        stat = cusparseSetMatType(matstruct->descr, CUSPARSE_MATRIX_TYPE_GENERAL);CHKERRCUSPARSE(stat);

        err = cudaMalloc((void **)&(matstruct->alpha),    sizeof(PetscScalar));CHKERRCUDA(err);
        err = cudaMalloc((void **)&(matstruct->beta_zero),sizeof(PetscScalar));CHKERRCUDA(err);
        err = cudaMalloc((void **)&(matstruct->beta_one), sizeof(PetscScalar));CHKERRCUDA(err);
        err = cudaMemcpy(matstruct->alpha,    &PETSC_CUSPARSE_ONE, sizeof(PetscScalar),cudaMemcpyHostToDevice);CHKERRCUDA(err);
        err = cudaMemcpy(matstruct->beta_zero,&PETSC_CUSPARSE_ZERO,sizeof(PetscScalar),cudaMemcpyHostToDevice);CHKERRCUDA(err);
        err = cudaMemcpy(matstruct->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar),cudaMemcpyHostToDevice);CHKERRCUDA(err);
        stat = cusparseSetPointerMode(cusparsestruct->handle, CUSPARSE_POINTER_MODE_DEVICE);CHKERRCUSPARSE(stat);

        /* Build a hybrid/ellpack matrix if this option is chosen for the storage */
        if (cusparsestruct->format==MAT_CUSPARSE_CSR) {
          /* set the matrix */
          CsrMatrix *matrix= new CsrMatrix;
          matrix->num_rows = m;
          matrix->num_cols = A->cmap->n;
          matrix->num_entries = a->nz;
          matrix->row_offsets = new THRUSTINTARRAY32(m+1);
          matrix->row_offsets->assign(ii, ii + m+1);

          matrix->column_indices = new THRUSTINTARRAY32(a->nz);
          matrix->column_indices->assign(a->j, a->j+a->nz);

          matrix->values = new THRUSTARRAY(a->nz);
          matrix->values->assign(a->a, a->a+a->nz);

          /* assign the pointer */
          matstruct->mat = matrix;

        } else if (cusparsestruct->format==MAT_CUSPARSE_ELL || cusparsestruct->format==MAT_CUSPARSE_HYB) {
          CsrMatrix *matrix= new CsrMatrix;
          matrix->num_rows = m;
          matrix->num_cols = A->cmap->n;
          matrix->num_entries = a->nz;
          matrix->row_offsets = new THRUSTINTARRAY32(m+1);
          matrix->row_offsets->assign(ii, ii + m+1);

          matrix->column_indices = new THRUSTINTARRAY32(a->nz);
          matrix->column_indices->assign(a->j, a->j+a->nz);

          matrix->values = new THRUSTARRAY(a->nz);
          matrix->values->assign(a->a, a->a+a->nz);

          cusparseHybMat_t hybMat;
          stat = cusparseCreateHybMat(&hybMat);CHKERRCUSPARSE(stat);
          cusparseHybPartition_t partition = cusparsestruct->format==MAT_CUSPARSE_ELL ?
            CUSPARSE_HYB_PARTITION_MAX : CUSPARSE_HYB_PARTITION_AUTO;
          stat = cusparse_csr2hyb(cusparsestruct->handle, matrix->num_rows, matrix->num_cols,
              matstruct->descr, matrix->values->data().get(),
              matrix->row_offsets->data().get(),
              matrix->column_indices->data().get(),
              hybMat, 0, partition);CHKERRCUSPARSE(stat);
          /* assign the pointer */
          matstruct->mat = hybMat;

          if (matrix) {
            if (matrix->values) delete (THRUSTARRAY*)matrix->values;
            if (matrix->column_indices) delete (THRUSTINTARRAY32*)matrix->column_indices;
            if (matrix->row_offsets) delete (THRUSTINTARRAY32*)matrix->row_offsets;
            delete (CsrMatrix*)matrix;
          }
        }

        /* assign the compressed row indices */
        if (a->compressedrow.use) {
          cusparsestruct->workVector = new THRUSTARRAY(m);
          matstruct->cprowIndices    = new THRUSTINTARRAY(m);
          matstruct->cprowIndices->assign(ridx,ridx+m);
          tmp = m;
        } else {
          cusparsestruct->workVector = NULL;
          matstruct->cprowIndices    = NULL;
          tmp = 0;
        }
        ierr = PetscLogCpuToGpu(((m+1)+(a->nz))*sizeof(int)+tmp*sizeof(PetscInt)+(3+(a->nz))*sizeof(PetscScalar));CHKERRQ(ierr);

        /* assign the pointer */
        cusparsestruct->mat = matstruct;
      } catch(char *ex) {
        SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
      }
      err  = WaitForGPU();CHKERRCUDA(err);
      ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);
      ierr = PetscLogEventEnd(MAT_CUSPARSECopyToGPU,A,0,0,0);CHKERRQ(ierr);
      cusparsestruct->nonzerostate = A->nonzerostate;
    }
    A->offloadmask = PETSC_OFFLOAD_BOTH;
  }
  PetscFunctionReturn(0);
}

struct VecCUDAPlusEquals
{
  template <typename Tuple>
  __host__ __device__
  void operator()(Tuple t)
  {
    thrust::get<1>(t) = thrust::get<1>(t) + thrust::get<0>(t);
  }
};

struct VecCUDAEqualsReverse
{
  template <typename Tuple>
  __host__ __device__
  void operator()(Tuple t)
  {
    thrust::get<0>(t) = thrust::get<1>(t);
  }
};

typedef struct {
  PetscBool   cisdense;
  PetscScalar *Bt;
  Mat         X;
} MatMatCusparse;

static PetscErrorCode MatDestroy_MatMatCusparse(void *data)
{
  PetscErrorCode ierr;
  MatMatCusparse *mmdata = (MatMatCusparse *)data;
  cudaError_t    cerr;

  PetscFunctionBegin;
  cerr = cudaFree(mmdata->Bt);CHKERRCUDA(cerr);
  ierr = MatDestroy(&mmdata->X);CHKERRQ(ierr);
  ierr = PetscFree(data);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Private(Mat,Mat,Mat,PetscBool,PetscBool);

static PetscErrorCode MatProductNumeric_SeqAIJCUSPARSE_SeqDENSECUDA(Mat C)
{
  Mat_Product                  *product = C->product;
  Mat                          A,B;
  PetscInt                     m,n,k,blda,clda;
  PetscBool                    flg,biscuda;
  Mat_SeqAIJCUSPARSE           *cusp;
  cusparseStatus_t             stat;
  cusparseOperation_t          opA;
  cusparseMatDescr_t           matA;
  const PetscScalar            *barray;
  PetscScalar                  *carray;
  PetscErrorCode               ierr;
  MatMatCusparse               *mmdata;
  Mat_SeqAIJCUSPARSEMultStruct *mat;
  CsrMatrix                    *csrmat;
  cudaError_t                  cuer;

  PetscFunctionBegin;
  MatCheckProduct(C,1);
  if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
  mmdata = (MatMatCusparse*)product->data;
  A    = product->A;
  B    = product->B;
  ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJCUSPARSE,&flg);CHKERRQ(ierr);
  if (!flg) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_PLIB,"Not for type %s",((PetscObject)A)->type_name);
  /* currently CopyToGpu does not copy if the matrix is bound to CPU
     Instead of silently accepting the wrong answer, I prefer to raise the error */
  if (A->boundtocpu) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Cannot bind to CPU a CUSPARSE matrix between MatProductSymbolic and MatProductNumeric phases");
  ierr = MatSeqAIJCUSPARSECopyToGPU(A);CHKERRQ(ierr);
  cusp = (Mat_SeqAIJCUSPARSE*)A->spptr;
  switch (product->type) {
  case MATPRODUCT_AB:
  case MATPRODUCT_PtAP:
    mat = cusp->mat;
    opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
    m   = A->rmap->n;
    k   = A->cmap->n;
    n   = B->cmap->n;
    break;
  case MATPRODUCT_AtB:
    if (!cusp->transgen) {
      mat = cusp->mat;
      opA = CUSPARSE_OPERATION_TRANSPOSE;
    } else {
      ierr = MatSeqAIJCUSPARSEGenerateTransposeForMult(A);CHKERRQ(ierr);
      mat  = cusp->matTranspose;
      opA  = CUSPARSE_OPERATION_NON_TRANSPOSE;
    }
    m = A->cmap->n;
    k = A->rmap->n;
    n = B->cmap->n;
    break;
  case MATPRODUCT_ABt:
  case MATPRODUCT_RARt:
    mat = cusp->mat;
    opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
    m   = A->rmap->n;
    k   = B->cmap->n;
    n   = B->rmap->n;
    break;
  default:
    SETERRQ1(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Unsupported product type %s",MatProductTypes[product->type]);
  }
  if (!mat) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Missing Mat_SeqAIJCUSPARSEMultStruct");
  matA   = mat->descr;
  csrmat = (CsrMatrix*)mat->mat;
  /* if the user passed a CPU matrix, copy the data to the GPU */
  ierr = PetscObjectTypeCompare((PetscObject)B,MATSEQDENSECUDA,&biscuda);CHKERRQ(ierr);
  if (!biscuda) {
    ierr = MatConvert(B,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&B);CHKERRQ(ierr);
  }
  ierr = MatDenseCUDAGetArrayRead(B,&barray);CHKERRQ(ierr);
  ierr = MatDenseGetLDA(B,&blda);CHKERRQ(ierr);
  if (product->type == MATPRODUCT_RARt || product->type == MATPRODUCT_PtAP) {
    ierr = MatDenseCUDAGetArrayWrite(mmdata->X,&carray);CHKERRQ(ierr);
    ierr = MatDenseGetLDA(mmdata->X,&clda);CHKERRQ(ierr);
  } else {
    ierr = MatDenseCUDAGetArrayWrite(C,&carray);CHKERRQ(ierr);
    ierr = MatDenseGetLDA(C,&clda);CHKERRQ(ierr);
  }

  ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);

  /* cusparse spmm does not support transpose on B */
  if (product->type == MATPRODUCT_ABt || product->type == MATPRODUCT_RARt) {
    cublasHandle_t cublasv2handle;
    cublasStatus_t cerr;

    ierr = PetscCUBLASGetHandle(&cublasv2handle);CHKERRQ(ierr);
    cerr = cublasXgeam(cublasv2handle,CUBLAS_OP_T,CUBLAS_OP_T,
                       B->cmap->n,B->rmap->n,
                       &PETSC_CUSPARSE_ONE ,barray,blda,
                       &PETSC_CUSPARSE_ZERO,barray,blda,
                       mmdata->Bt,B->cmap->n);CHKERRCUBLAS(cerr);
    blda = B->cmap->n;
  }

  /* perform the MatMat operation */
  stat = cusparse_csr_spmm(cusp->handle,opA,m,n,k,
                           csrmat->num_entries,mat->alpha,matA,
                           csrmat->values->data().get(),
                           csrmat->row_offsets->data().get(),
                           csrmat->column_indices->data().get(),
                           mmdata->Bt ? mmdata->Bt : barray,blda,mat->beta_zero,
                           carray,clda);CHKERRCUSPARSE(stat);
  cuer = WaitForGPU();CHKERRCUDA(cuer);
  ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);
  ierr = PetscLogGpuFlops(n*2.0*csrmat->num_entries);CHKERRQ(ierr);
  ierr = MatDenseCUDARestoreArrayRead(B,&barray);CHKERRQ(ierr);
  if (product->type == MATPRODUCT_RARt) {
    ierr = MatDenseCUDARestoreArrayWrite(mmdata->X,&carray);CHKERRQ(ierr);
    ierr = MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Private(B,mmdata->X,C,PETSC_FALSE,PETSC_FALSE);CHKERRQ(ierr);
  } else if (product->type == MATPRODUCT_PtAP) {
    ierr = MatDenseCUDARestoreArrayWrite(mmdata->X,&carray);CHKERRQ(ierr);
    ierr = MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Private(B,mmdata->X,C,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
  } else {
    ierr = MatDenseCUDARestoreArrayWrite(C,&carray);CHKERRQ(ierr);
  }
  if (mmdata->cisdense) {
    ierr = MatConvert(C,MATSEQDENSE,MAT_INPLACE_MATRIX,&C);CHKERRQ(ierr);
  }
  if (!biscuda) {
    ierr = MatConvert(B,MATSEQDENSE,MAT_INPLACE_MATRIX,&B);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatProductSymbolic_SeqAIJCUSPARSE_SeqDENSECUDA(Mat C)
{
  Mat_Product        *product = C->product;
  Mat                A,B;
  PetscInt           m,n;
  PetscBool          cisdense,flg;
  PetscErrorCode     ierr;
  MatMatCusparse     *mmdata;
  Mat_SeqAIJCUSPARSE *cusp;

  PetscFunctionBegin;
  MatCheckProduct(C,1);
  if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
  A    = product->A;
  B    = product->B;
  ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJCUSPARSE,&flg);CHKERRQ(ierr);
  if (!flg) SETERRQ1(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Not for type %s",((PetscObject)A)->type_name);
  cusp = (Mat_SeqAIJCUSPARSE*)A->spptr;
  if (cusp->format != MAT_CUSPARSE_CSR) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Only for MAT_CUSPARSE_CSR format");
  switch (product->type) {
  case MATPRODUCT_AB:
    m = A->rmap->n;
    n = B->cmap->n;
    break;
  case MATPRODUCT_AtB:
    m = A->cmap->n;
    n = B->cmap->n;
    break;
  case MATPRODUCT_ABt:
    m = A->rmap->n;
    n = B->rmap->n;
    break;
  case MATPRODUCT_PtAP:
    m = B->cmap->n;
    n = B->cmap->n;
    break;
  case MATPRODUCT_RARt:
    m = B->rmap->n;
    n = B->rmap->n;
    break;
  default:
    SETERRQ1(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Unsupported product type %s",MatProductTypes[product->type]);
  }
  ierr = MatSetSizes(C,m,n,m,n);CHKERRQ(ierr);
  /* if C is of type MATSEQDENSE (CPU), perform the operation on the GPU and then copy on the CPU */
  ierr = PetscObjectTypeCompare((PetscObject)C,MATSEQDENSE,&cisdense);CHKERRQ(ierr);
  ierr = MatSetType(C,MATSEQDENSECUDA);CHKERRQ(ierr);

  /* product data */
  ierr = PetscNew(&mmdata);CHKERRQ(ierr);
  mmdata->cisdense = cisdense;
  /* cusparse spmm does not support transpose on B */
  if (product->type == MATPRODUCT_ABt || product->type == MATPRODUCT_RARt) {
    cudaError_t cerr;

    cerr = cudaMalloc((void**)&mmdata->Bt,(size_t)B->rmap->n*(size_t)B->cmap->n*sizeof(PetscScalar));CHKERRCUDA(cerr);
  }
  /* for these products we need intermediate storage */
  if (product->type == MATPRODUCT_RARt || product->type == MATPRODUCT_PtAP) {
    ierr = MatCreate(PetscObjectComm((PetscObject)C),&mmdata->X);CHKERRQ(ierr);
    ierr = MatSetType(mmdata->X,MATSEQDENSECUDA);CHKERRQ(ierr);
    if (product->type == MATPRODUCT_RARt) { /* do not preallocate, since the first call to MatDenseCUDAGetArray will preallocate on the GPU for us */
      ierr = MatSetSizes(mmdata->X,A->rmap->n,B->rmap->n,A->rmap->n,B->rmap->n);CHKERRQ(ierr);
    } else {
      ierr = MatSetSizes(mmdata->X,A->rmap->n,B->cmap->n,A->rmap->n,B->cmap->n);CHKERRQ(ierr);
    }
  }
  C->product->data    = mmdata;
  C->product->destroy = MatDestroy_MatMatCusparse;

  C->ops->productnumeric = MatProductNumeric_SeqAIJCUSPARSE_SeqDENSECUDA;
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense(Mat);

/* handles dense B */
static PetscErrorCode MatProductSetFromOptions_SeqAIJCUSPARSE(Mat C)
{
  Mat_Product    *product = C->product;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  MatCheckProduct(C,1);
  if (!product->A) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing A");
  if (product->A->boundtocpu) {
    ierr = MatProductSetFromOptions_SeqAIJ_SeqDense(C);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  switch (product->type) {
  case MATPRODUCT_AB:
  case MATPRODUCT_AtB:
  case MATPRODUCT_ABt:
  case MATPRODUCT_PtAP:
  case MATPRODUCT_RARt:
    C->ops->productsymbolic = MatProductSymbolic_SeqAIJCUSPARSE_SeqDENSECUDA;
  default:
    break;
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatMult_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatMultAddKernel_SeqAIJCUSPARSE(A,xx,NULL,yy,PETSC_FALSE,PETSC_FALSE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatMultAdd_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy, Vec zz)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatMultAddKernel_SeqAIJCUSPARSE(A,xx,yy,zz,PETSC_FALSE,PETSC_FALSE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatMultHermitianTranspose_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatMultAddKernel_SeqAIJCUSPARSE(A,xx,NULL,yy,PETSC_TRUE,PETSC_TRUE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatMultHermitianTransposeAdd_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy,Vec zz)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatMultAddKernel_SeqAIJCUSPARSE(A,xx,yy,zz,PETSC_TRUE,PETSC_TRUE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatMultTranspose_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatMultAddKernel_SeqAIJCUSPARSE(A,xx,NULL,yy,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatMultAddKernel_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy,Vec zz,PetscBool trans,PetscBool herm)
{
  Mat_SeqAIJ                   *a = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE*)A->spptr;
  Mat_SeqAIJCUSPARSEMultStruct *matstruct;
  PetscScalar                  *xarray,*zarray,*dptr,*beta,*xptr;
  PetscErrorCode               ierr;
  cudaError_t                  cerr;
  cusparseStatus_t             stat;
  cusparseOperation_t          opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
  PetscBool                    compressed;

  PetscFunctionBegin;
  if (herm && !trans) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_PLIB,"Hermitian and not transpose not supported");
  if (!a->nonzerorowcnt) {
    if (!yy) {
      ierr = VecSet_SeqCUDA(zz,0);CHKERRQ(ierr);
    }
    PetscFunctionReturn(0);
  }
  /* The line below is necessary due to the operations that modify the matrix on the CPU (axpy, scale, etc) */
  ierr = MatSeqAIJCUSPARSECopyToGPU(A);CHKERRQ(ierr);
  if (!trans) {
    matstruct = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->mat;
  } else {
    if (herm || !cusparsestruct->transgen) {
      opA = herm ? CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE : CUSPARSE_OPERATION_TRANSPOSE;
      matstruct = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->mat;
    } else {
      matstruct = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->matTranspose;
      if (!matstruct) {
        ierr = MatSeqAIJCUSPARSEGenerateTransposeForMult(A);CHKERRQ(ierr);
        matstruct = (Mat_SeqAIJCUSPARSEMultStruct*)cusparsestruct->matTranspose;
      }
    }
  }
  /* Does the matrix use compressed rows (i.e., drop zero rows)? */
  compressed = matstruct->cprowIndices ? PETSC_TRUE : PETSC_FALSE;

  try {
    ierr = VecCUDAGetArrayRead(xx,(const PetscScalar**)&xarray);CHKERRQ(ierr);
    if (yy == zz) {ierr = VecCUDAGetArray(zz,&zarray);CHKERRQ(ierr);} /* read & write zz, so need to get uptodate zarray on GPU */
    else {ierr = VecCUDAGetArrayWrite(zz,&zarray);CHKERRQ(ierr);} /* write zz, so no need to init zarray on GPU */
    ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);
    if (opA == CUSPARSE_OPERATION_NON_TRANSPOSE) {
      xptr = xarray;
      dptr = compressed ? cusparsestruct->workVector->data().get() : zarray; /* Use a work vector for SpMv output if compressed */
      beta = (yy == zz && !compressed) ? matstruct->beta_one : matstruct->beta_zero;
    } else {
      xptr = compressed ? cusparsestruct->workVector->data().get() : xarray; /* Use a work vector for SpMv input if compressed */
      dptr = zarray;
      beta = yy ? matstruct->beta_one : matstruct->beta_zero;

      if (compressed) {
        thrust::device_ptr<PetscScalar> xarr = thrust::device_pointer_cast(xarray);

        thrust::for_each(thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(xarr, matstruct->cprowIndices->begin()))),
                         thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(xarr, matstruct->cprowIndices->begin()))) + matstruct->cprowIndices->size(),
                         VecCUDAEqualsReverse());
      }
    }

    /* csr_spmv does y = alpha*Ax + beta*y */
    if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
      CsrMatrix *mat = (CsrMatrix*)matstruct->mat;
      stat = cusparse_csr_spmv(cusparsestruct->handle, opA,
                               mat->num_rows, mat->num_cols,
                               mat->num_entries, matstruct->alpha, matstruct->descr,
                               mat->values->data().get(), mat->row_offsets->data().get(),
                               mat->column_indices->data().get(), xptr, beta,
                               dptr);CHKERRCUSPARSE(stat);
    } else {
      if (cusparsestruct->nrows) {
        cusparseHybMat_t hybMat = (cusparseHybMat_t)matstruct->mat;
        stat = cusparse_hyb_spmv(cusparsestruct->handle, opA,
                                 matstruct->alpha, matstruct->descr, hybMat,
                                 xptr, beta,
                                 dptr);CHKERRCUSPARSE(stat);
      }
    }
    cerr = WaitForGPU();CHKERRCUDA(cerr);
    ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);

    if (opA == CUSPARSE_OPERATION_NON_TRANSPOSE) {
      if (yy) { /* MatMultAdd: zz = A*xx + yy */
        if (compressed) { /* A is compressed. We first copy yy to zz, then ScatterAdd the work vector to zz */
          ierr = VecCopy_SeqCUDA(yy,zz);CHKERRQ(ierr); /* zz = yy */
        } else if (zz != yy) { /* A is not compressed. zz already contains A*xx, and we just need to add yy */
          ierr = VecAXPY_SeqCUDA(zz,1.0,yy);CHKERRQ(ierr); /* zz += yy */
        }
      } else if (compressed) { /* MatMult: zz = A*xx. A is compressed, so we zero zz first, then ScatterAdd the work vector to zz */
        ierr = VecSet_SeqCUDA(zz,0);CHKERRQ(ierr);
      }

      /* ScatterAdd the result from work vector into the full vector when A is compressed */
      if (compressed) {
        thrust::device_ptr<PetscScalar> zptr = thrust::device_pointer_cast(zarray);

        ierr = PetscLogGpuTimeBegin();CHKERRQ(ierr);
        thrust::for_each(thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(zptr, matstruct->cprowIndices->begin()))),
                         thrust::make_zip_iterator(thrust::make_tuple(cusparsestruct->workVector->begin(), thrust::make_permutation_iterator(zptr, matstruct->cprowIndices->begin()))) + matstruct->cprowIndices->size(),
                         VecCUDAPlusEquals());
        cerr = WaitForGPU();CHKERRCUDA(cerr);
        ierr = PetscLogGpuTimeEnd();CHKERRQ(ierr);
      }
    } else {
      if (yy && yy != zz) {
        ierr = VecAXPY_SeqCUDA(zz,1.0,yy);CHKERRQ(ierr); /* zz += yy */
      }
    }
    ierr = VecCUDARestoreArrayRead(xx,(const PetscScalar**)&xarray);CHKERRQ(ierr);
    if (yy == zz) {ierr = VecCUDARestoreArray(zz,&zarray);CHKERRQ(ierr);}
    else {ierr = VecCUDARestoreArrayWrite(zz,&zarray);CHKERRQ(ierr);}
  } catch(char *ex) {
    SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"CUSPARSE error: %s", ex);
  }
  if (yy) {
    ierr = PetscLogGpuFlops(2.0*a->nz);CHKERRQ(ierr);
  } else {
    ierr = PetscLogGpuFlops(2.0*a->nz-a->nonzerorowcnt);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatMultTransposeAdd_SeqAIJCUSPARSE(Mat A,Vec xx,Vec yy,Vec zz)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatMultAddKernel_SeqAIJCUSPARSE(A,xx,yy,zz,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatAssemblyEnd_SeqAIJCUSPARSE(Mat A,MatAssemblyType mode)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatAssemblyEnd_SeqAIJ(A,mode);CHKERRQ(ierr);
  if (mode == MAT_FLUSH_ASSEMBLY || A->boundtocpu) PetscFunctionReturn(0);
  if (A->factortype == MAT_FACTOR_NONE) {
    ierr = MatSeqAIJCUSPARSECopyToGPU(A);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/* --------------------------------------------------------------------------------*/
/*@
   MatCreateSeqAIJCUSPARSE - Creates a sparse matrix in AIJ (compressed row) format
   (the default parallel PETSc format). This matrix will ultimately pushed down
   to NVidia GPUs and use the CUSPARSE library for calculations. For good matrix
   assembly performance the user should preallocate the matrix storage by setting
   the parameter nz (or the array nnz).  By setting these parameters accurately,
   performance during matrix assembly can be increased by more than a factor of 50.

   Collective

   Input Parameters:
+  comm - MPI communicator, set to PETSC_COMM_SELF
.  m - number of rows
.  n - number of columns
.  nz - number of nonzeros per row (same for all rows)
-  nnz - array containing the number of nonzeros in the various rows
         (possibly different for each row) or NULL

   Output Parameter:
.  A - the matrix

   It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
   MatXXXXSetPreallocation() paradgm instead of this routine directly.
   [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]

   Notes:
   If nnz is given then nz is ignored

   The AIJ format (also called the Yale sparse matrix format or
   compressed row storage), is fully compatible with standard Fortran 77
   storage.  That is, the stored row and column indices can begin at
   either one (as in Fortran) or zero.  See the users' manual for details.

   Specify the preallocated storage with either nz or nnz (not both).
   Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
   allocation.  For large problems you MUST preallocate memory or you
   will get TERRIBLE performance, see the users' manual chapter on matrices.

   By default, this format uses inodes (identical nodes) when possible, to
   improve numerical efficiency of matrix-vector products and solves. We
   search for consecutive rows with the same nonzero structure, thereby
   reusing matrix information to achieve increased efficiency.

   Level: intermediate

.seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatCreateAIJ(), MATSEQAIJCUSPARSE, MATAIJCUSPARSE
@*/
PetscErrorCode  MatCreateSeqAIJCUSPARSE(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatCreate(comm,A);CHKERRQ(ierr);
  ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
  ierr = MatSetType(*A,MATSEQAIJCUSPARSE);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,(PetscInt*)nnz);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatDestroy_SeqAIJCUSPARSE(Mat A)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (A->factortype == MAT_FACTOR_NONE) {
    ierr = MatSeqAIJCUSPARSE_Destroy((Mat_SeqAIJCUSPARSE**)&A->spptr);CHKERRQ(ierr);
  } else {
    ierr = MatSeqAIJCUSPARSETriFactors_Destroy((Mat_SeqAIJCUSPARSETriFactors**)&A->spptr);CHKERRQ(ierr);
  }
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatCUSPARSESetFormat_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaijcusparse_seqdense_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatFactorGetSolverType_C",NULL);CHKERRQ(ierr);
  ierr = MatDestroy_SeqAIJ(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat,MatType,MatReuse,Mat*);
static PetscErrorCode MatBindToCPU_SeqAIJCUSPARSE(Mat,PetscBool);
static PetscErrorCode MatDuplicate_SeqAIJCUSPARSE(Mat A,MatDuplicateOption cpvalues,Mat *B)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatDuplicate_SeqAIJ(A,cpvalues,B);CHKERRQ(ierr);
  ierr = MatConvert_SeqAIJ_SeqAIJCUSPARSE(*B,MATSEQAIJCUSPARSE,MAT_INPLACE_MATRIX,B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatBindToCPU_SeqAIJCUSPARSE(Mat A,PetscBool flg)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (A->factortype != MAT_FACTOR_NONE) PetscFunctionReturn(0);
  /* Currently, there is no case in which an AIJCUSPARSE matrix ever has its offloadmask set to PETS_OFFLOAD_GPU.
     If this changes, we need to implement a routine to update the CPU (host) version of the matrix from the GPU one.
     Right now, for safety we simply check for PETSC_OFFLOAD_GPU and have MatBindToCPU() error in this case.
     TODO: Add MatAIJCUSPARSECopyFromGPU() and make MatBindToCPU() functional for AIJCUSPARSE matries;
           can follow the example of MatBindToCPU_SeqAIJViennaCL(). */
  if (flg && A->offloadmask == PETSC_OFFLOAD_GPU) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_PLIB,"PETSC_OFFLOAD_GPU should not happen. Please report your use case to petsc-dev@mcs.anl.gov");
  /* TODO: add support for this? */
  if (flg) {
    A->ops->mult                      = MatMult_SeqAIJ;
    A->ops->multadd                   = MatMultAdd_SeqAIJ;
    A->ops->multtranspose             = MatMultTranspose_SeqAIJ;
    A->ops->multtransposeadd          = MatMultTransposeAdd_SeqAIJ;
    A->ops->multhermitiantranspose    = NULL;
    A->ops->multhermitiantransposeadd = NULL;
    ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C",NULL);CHKERRQ(ierr);
    ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaijcusparse_seqdense_C",NULL);CHKERRQ(ierr);
  } else {
    A->ops->mult                      = MatMult_SeqAIJCUSPARSE;
    A->ops->multadd                   = MatMultAdd_SeqAIJCUSPARSE;
    A->ops->multtranspose             = MatMultTranspose_SeqAIJCUSPARSE;
    A->ops->multtransposeadd          = MatMultTransposeAdd_SeqAIJCUSPARSE;
    A->ops->multhermitiantranspose    = MatMultHermitianTranspose_SeqAIJCUSPARSE;
    A->ops->multhermitiantransposeadd = MatMultHermitianTransposeAdd_SeqAIJCUSPARSE;
    ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C",MatProductSetFromOptions_SeqAIJCUSPARSE);CHKERRQ(ierr);
    ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaijcusparse_seqdense_C",MatProductSetFromOptions_SeqAIJCUSPARSE);CHKERRQ(ierr);
  }
  A->boundtocpu = flg;
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat A, MatType mtype, MatReuse reuse, Mat* newmat)
{
  PetscErrorCode   ierr;
  cusparseStatus_t stat;
  Mat              B;

  PetscFunctionBegin;
  if (reuse == MAT_INITIAL_MATRIX) {
    ierr = MatDuplicate(A,MAT_COPY_VALUES,newmat);CHKERRQ(ierr);
  } else if (reuse == MAT_REUSE_MATRIX) {
    ierr = MatCopy(A,*newmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
  }
  B = *newmat;

  ierr = PetscFree(B->defaultvectype);CHKERRQ(ierr);
  ierr = PetscStrallocpy(VECCUDA,&B->defaultvectype);CHKERRQ(ierr);

  if (reuse != MAT_REUSE_MATRIX && !B->spptr) {
    if (B->factortype == MAT_FACTOR_NONE) {
      Mat_SeqAIJCUSPARSE *spptr;

      ierr = PetscNew(&spptr);CHKERRQ(ierr);
      spptr->format = MAT_CUSPARSE_CSR;
      stat = cusparseCreate(&spptr->handle);CHKERRCUSPARSE(stat);
      B->spptr = spptr;
    } else {
      Mat_SeqAIJCUSPARSETriFactors *spptr;

      ierr = PetscNew(&spptr);CHKERRQ(ierr);
      stat = cusparseCreate(&spptr->handle);CHKERRCUSPARSE(stat);
      B->spptr = spptr;
    }
    B->offloadmask = PETSC_OFFLOAD_UNALLOCATED;
  }
  B->ops->assemblyend    = MatAssemblyEnd_SeqAIJCUSPARSE;
  B->ops->destroy        = MatDestroy_SeqAIJCUSPARSE;
  B->ops->setfromoptions = MatSetFromOptions_SeqAIJCUSPARSE;
  B->ops->bindtocpu      = MatBindToCPU_SeqAIJCUSPARSE;
  B->ops->duplicate      = MatDuplicate_SeqAIJCUSPARSE;

  ierr = MatBindToCPU_SeqAIJCUSPARSE(B,PETSC_FALSE);CHKERRQ(ierr);
  ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJCUSPARSE);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatCUSPARSESetFormat_C",MatCUSPARSESetFormat_SeqAIJCUSPARSE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJCUSPARSE(Mat B)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatCreate_SeqAIJ(B);CHKERRQ(ierr);
  ierr = MatConvert_SeqAIJ_SeqAIJCUSPARSE(B,MATSEQAIJCUSPARSE,MAT_INPLACE_MATRIX,&B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*MC
   MATSEQAIJCUSPARSE - MATAIJCUSPARSE = "(seq)aijcusparse" - A matrix type to be used for sparse matrices.

   A matrix type type whose data resides on Nvidia GPUs. These matrices can be in either
   CSR, ELL, or Hybrid format. The ELL and HYB formats require CUDA 4.2 or later.
   All matrix calculations are performed on Nvidia GPUs using the CUSPARSE library.

   Options Database Keys:
+  -mat_type aijcusparse - sets the matrix type to "seqaijcusparse" during a call to MatSetFromOptions()
.  -mat_cusparse_storage_format csr - sets the storage format of matrices (for MatMult and factors in MatSolve) during a call to MatSetFromOptions(). Other options include ell (ellpack) or hyb (hybrid).
-  -mat_cusparse_mult_storage_format csr - sets the storage format of matrices (for MatMult) during a call to MatSetFromOptions(). Other options include ell (ellpack) or hyb (hybrid).

  Level: beginner

.seealso: MatCreateSeqAIJCUSPARSE(), MATAIJCUSPARSE, MatCreateAIJCUSPARSE(), MatCUSPARSESetFormat(), MatCUSPARSEStorageFormat, MatCUSPARSEFormatOperation
M*/

PETSC_EXTERN PetscErrorCode MatGetFactor_seqaijcusparse_cusparse(Mat,MatFactorType,Mat*);


PETSC_EXTERN PetscErrorCode MatSolverTypeRegister_CUSPARSE(void)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatSolverTypeRegister(MATSOLVERCUSPARSE,MATSEQAIJCUSPARSE,MAT_FACTOR_LU,MatGetFactor_seqaijcusparse_cusparse);CHKERRQ(ierr);
  ierr = MatSolverTypeRegister(MATSOLVERCUSPARSE,MATSEQAIJCUSPARSE,MAT_FACTOR_CHOLESKY,MatGetFactor_seqaijcusparse_cusparse);CHKERRQ(ierr);
  ierr = MatSolverTypeRegister(MATSOLVERCUSPARSE,MATSEQAIJCUSPARSE,MAT_FACTOR_ILU,MatGetFactor_seqaijcusparse_cusparse);CHKERRQ(ierr);
  ierr = MatSolverTypeRegister(MATSOLVERCUSPARSE,MATSEQAIJCUSPARSE,MAT_FACTOR_ICC,MatGetFactor_seqaijcusparse_cusparse);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSE_Destroy(Mat_SeqAIJCUSPARSE **cusparsestruct)
{
  PetscErrorCode   ierr;
  cusparseStatus_t stat;
  cusparseHandle_t handle;

  PetscFunctionBegin;
  if (*cusparsestruct) {
    ierr = MatSeqAIJCUSPARSEMultStruct_Destroy(&(*cusparsestruct)->mat,(*cusparsestruct)->format);CHKERRQ(ierr);
    ierr = MatSeqAIJCUSPARSEMultStruct_Destroy(&(*cusparsestruct)->matTranspose,(*cusparsestruct)->format);CHKERRQ(ierr);
    delete (*cusparsestruct)->workVector;
    delete (*cusparsestruct)->rowoffsets_gpu;
    if (handle = (*cusparsestruct)->handle) {
      stat = cusparseDestroy(handle);CHKERRCUSPARSE(stat);
    }
    ierr = PetscFree(*cusparsestruct);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode CsrMatrix_Destroy(CsrMatrix **mat)
{
  PetscFunctionBegin;
  if (*mat) {
    delete (*mat)->values;
    delete (*mat)->column_indices;
    delete (*mat)->row_offsets;
    delete *mat;
    *mat = 0;
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct **trifactor)
{
  cusparseStatus_t stat;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  if (*trifactor) {
    if ((*trifactor)->descr) { stat = cusparseDestroyMatDescr((*trifactor)->descr);CHKERRCUSPARSE(stat); }
    if ((*trifactor)->solveInfo) { stat = cusparseDestroySolveAnalysisInfo((*trifactor)->solveInfo);CHKERRCUSPARSE(stat); }
    ierr = CsrMatrix_Destroy(&(*trifactor)->csrMat);CHKERRQ(ierr);
    delete *trifactor;
    *trifactor = 0;
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSEMultStruct **matstruct,MatCUSPARSEStorageFormat format)
{
  CsrMatrix        *mat;
  cusparseStatus_t stat;
  cudaError_t      err;

  PetscFunctionBegin;
  if (*matstruct) {
    if ((*matstruct)->mat) {
      if (format==MAT_CUSPARSE_ELL || format==MAT_CUSPARSE_HYB) {
        cusparseHybMat_t hybMat = (cusparseHybMat_t)(*matstruct)->mat;
        stat = cusparseDestroyHybMat(hybMat);CHKERRCUSPARSE(stat);
      } else {
        mat = (CsrMatrix*)(*matstruct)->mat;
        CsrMatrix_Destroy(&mat);
      }
    }
    if ((*matstruct)->descr) { stat = cusparseDestroyMatDescr((*matstruct)->descr);CHKERRCUSPARSE(stat); }
    delete (*matstruct)->cprowIndices;
    if ((*matstruct)->alpha)     { err=cudaFree((*matstruct)->alpha);CHKERRCUDA(err); }
    if ((*matstruct)->beta_zero) { err=cudaFree((*matstruct)->beta_zero);CHKERRCUDA(err); }
    if ((*matstruct)->beta_one)  { err=cudaFree((*matstruct)->beta_one);CHKERRCUDA(err); }
    delete *matstruct;
    *matstruct = 0;
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Reset(Mat_SeqAIJCUSPARSETriFactors** trifactors)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (*trifactors) {
    ierr = MatSeqAIJCUSPARSEMultStruct_Destroy(&(*trifactors)->loTriFactorPtr);CHKERRQ(ierr);
    ierr = MatSeqAIJCUSPARSEMultStruct_Destroy(&(*trifactors)->upTriFactorPtr);CHKERRQ(ierr);
    ierr = MatSeqAIJCUSPARSEMultStruct_Destroy(&(*trifactors)->loTriFactorPtrTranspose);CHKERRQ(ierr);
    ierr = MatSeqAIJCUSPARSEMultStruct_Destroy(&(*trifactors)->upTriFactorPtrTranspose);CHKERRQ(ierr);
    delete (*trifactors)->rpermIndices;
    delete (*trifactors)->cpermIndices;
    delete (*trifactors)->workVector;
    (*trifactors)->rpermIndices = 0;
    (*trifactors)->cpermIndices = 0;
    (*trifactors)->workVector = 0;
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors** trifactors)
{
  PetscErrorCode   ierr;
  cusparseHandle_t handle;
  cusparseStatus_t stat;

  PetscFunctionBegin;
  if (*trifactors) {
    ierr = MatSeqAIJCUSPARSETriFactors_Reset(trifactors);CHKERRQ(ierr);
    if (handle = (*trifactors)->handle) {
      stat = cusparseDestroy(handle);CHKERRCUSPARSE(stat);
    }
    ierr = PetscFree(*trifactors);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}