xref: /petsc/src/mat/impls/aij/seq/seqcusparse/aijcusparse.cu (revision f4f49eeac7efa77fffa46b7ff95a3ed169f659ed)

/*
  Defines the basic matrix operations for the AIJ (compressed row)
  matrix storage format using the CUSPARSE library,
*/
#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>
#include <thrust/adjacent_difference.h>
#if PETSC_CPP_VERSION >= 14
  #define PETSC_HAVE_THRUST_ASYNC 1
  // thrust::for_each(thrust::cuda::par.on()) requires C++14
  #include <thrust/async/for_each.h>
#endif
#include <thrust/iterator/constant_iterator.h>
#include <thrust/remove.h>
#include <thrust/sort.h>
#include <thrust/unique.h>

const char *const MatCUSPARSEStorageFormats[] = {"CSR", "ELL", "HYB", "MatCUSPARSEStorageFormat", "MAT_CUSPARSE_", 0};
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
/* The following are copied from cusparse.h in CUDA-11.0. In MatCUSPARSESpMVAlgorithms[] etc, we copy them in
    0-based integer value order, since we want to use PetscOptionsEnum() to parse user command line options for them.

  typedef enum {
      CUSPARSE_MV_ALG_DEFAULT = 0,
      CUSPARSE_COOMV_ALG      = 1,
      CUSPARSE_CSRMV_ALG1     = 2,
      CUSPARSE_CSRMV_ALG2     = 3
  } cusparseSpMVAlg_t;

  typedef enum {
      CUSPARSE_MM_ALG_DEFAULT     CUSPARSE_DEPRECATED_ENUM(CUSPARSE_SPMM_ALG_DEFAULT) = 0,
      CUSPARSE_COOMM_ALG1         CUSPARSE_DEPRECATED_ENUM(CUSPARSE_SPMM_COO_ALG1)    = 1,
      CUSPARSE_COOMM_ALG2         CUSPARSE_DEPRECATED_ENUM(CUSPARSE_SPMM_COO_ALG2)    = 2,
      CUSPARSE_COOMM_ALG3         CUSPARSE_DEPRECATED_ENUM(CUSPARSE_SPMM_COO_ALG3)    = 3,
      CUSPARSE_CSRMM_ALG1         CUSPARSE_DEPRECATED_ENUM(CUSPARSE_SPMM_CSR_ALG1)    = 4,
      CUSPARSE_SPMM_ALG_DEFAULT = 0,
      CUSPARSE_SPMM_COO_ALG1    = 1,
      CUSPARSE_SPMM_COO_ALG2    = 2,
      CUSPARSE_SPMM_COO_ALG3    = 3,
      CUSPARSE_SPMM_COO_ALG4    = 5,
      CUSPARSE_SPMM_CSR_ALG1    = 4,
      CUSPARSE_SPMM_CSR_ALG2    = 6,
  } cusparseSpMMAlg_t;

  typedef enum {
      CUSPARSE_CSR2CSC_ALG1 = 1, // faster than V2 (in general), deterministic
      CUSPARSE_CSR2CSC_ALG2 = 2  // low memory requirement, non-deterministic
  } cusparseCsr2CscAlg_t;
  */
const char *const MatCUSPARSESpMVAlgorithms[]    = {"MV_ALG_DEFAULT", "COOMV_ALG", "CSRMV_ALG1", "CSRMV_ALG2", "cusparseSpMVAlg_t", "CUSPARSE_", 0};
const char *const MatCUSPARSESpMMAlgorithms[]    = {"ALG_DEFAULT", "COO_ALG1", "COO_ALG2", "COO_ALG3", "CSR_ALG1", "COO_ALG4", "CSR_ALG2", "cusparseSpMMAlg_t", "CUSPARSE_SPMM_", 0};
const char *const MatCUSPARSECsr2CscAlgorithms[] = {"INVALID" /*cusparse does not have enum 0! We created one*/, "ALG1", "ALG2", "cusparseCsr2CscAlg_t", "CUSPARSE_CSR2CSC_", 0};
#endif

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 *);
#if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
static PetscErrorCode MatSolve_SeqAIJCUSPARSE(Mat, Vec, Vec);
static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE(Mat, Vec, Vec);
static PetscErrorCode MatSolve_SeqAIJCUSPARSE_NaturalOrdering(Mat, Vec, Vec);
static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering(Mat, Vec, Vec);
static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct **);
#endif
static PetscErrorCode MatSetFromOptions_SeqAIJCUSPARSE(Mat, PetscOptionItems *PetscOptionsObject);
static PetscErrorCode MatAXPY_SeqAIJCUSPARSE(Mat, PetscScalar, Mat, MatStructure);
static PetscErrorCode MatScale_SeqAIJCUSPARSE(Mat, PetscScalar);
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_SeqAIJCUSPARSEMultStruct **, MatCUSPARSEStorageFormat);
static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors **);
static PetscErrorCode MatSeqAIJCUSPARSE_Destroy(Mat);

static PetscErrorCode MatSeqAIJCUSPARSECopyFromGPU(Mat);
static PetscErrorCode MatSeqAIJCUSPARSEInvalidateTranspose(Mat, PetscBool);

static PetscErrorCode MatSeqAIJCopySubArray_SeqAIJCUSPARSE(Mat, PetscInt, const PetscInt[], PetscScalar[]);
static PetscErrorCode MatSetPreallocationCOO_SeqAIJCUSPARSE(Mat, PetscCount, PetscInt[], PetscInt[]);
static PetscErrorCode MatSetValuesCOO_SeqAIJCUSPARSE(Mat, const PetscScalar[], InsertMode);

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:
    SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "unsupported operation %d for MatCUSPARSEFormatOperation. MAT_CUSPARSE_MULT and MAT_CUSPARSE_ALL are currently supported.", op);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatCUSPARSESetFormat - Sets the storage format of `MATSEQCUSPARSE` matrices for a particular
  operation. Only the `MatMult()` operation can use different GPU storage formats

  Not Collective

  Input Parameters:
+ A      - Matrix of type `MATSEQAIJCUSPARSE`
. op     - `MatCUSPARSEFormatOperation`. `MATSEQAIJCUSPARSE` matrices support `MAT_CUSPARSE_MULT` and `MAT_CUSPARSE_ALL`.
        `MATMPIAIJCUSPARSE` 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`.)

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MATSEQAIJCUSPARSE`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
@*/
PetscErrorCode MatCUSPARSESetFormat(Mat A, MatCUSPARSEFormatOperation op, MatCUSPARSEStorageFormat format)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscTryMethod(A, "MatCUSPARSESetFormat_C", (Mat, MatCUSPARSEFormatOperation, MatCUSPARSEStorageFormat), (A, op, format));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatCUSPARSESetUseCPUSolve_SeqAIJCUSPARSE(Mat A, PetscBool use_cpu)
{
  Mat_SeqAIJCUSPARSE *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;

  PetscFunctionBegin;
  cusparsestruct->use_cpu_solve = use_cpu;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatCUSPARSESetUseCPUSolve - Sets to use CPU `MatSolve()`.

  Input Parameters:
+ A       - Matrix of type `MATSEQAIJCUSPARSE`
- use_cpu - set flag for using the built-in CPU `MatSolve()`

  Level: intermediate

  Note:
  The cuSparse LU solver currently computes the factors with the built-in CPU method
  and moves the factors to the GPU for the solve. We have observed better performance keeping the data on the CPU and computing the solve there.
  This method to specify if the solve is done on the CPU or GPU (GPU is the default).

.seealso: [](ch_matrices), `Mat`, `MatSolve()`, `MATSEQAIJCUSPARSE`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
@*/
PetscErrorCode MatCUSPARSESetUseCPUSolve(Mat A, PetscBool use_cpu)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscTryMethod(A, "MatCUSPARSESetUseCPUSolve_C", (Mat, PetscBool), (A, use_cpu));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetOption_SeqAIJCUSPARSE(Mat A, MatOption op, PetscBool flg)
{
  PetscFunctionBegin;
  switch (op) {
  case MAT_FORM_EXPLICIT_TRANSPOSE:
    /* need to destroy the transpose matrix if present to prevent from logic errors if flg is set to true later */
    if (A->form_explicit_transpose && !flg) PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_TRUE));
    A->form_explicit_transpose = flg;
    break;
  default:
    PetscCall(MatSetOption_SeqAIJ(A, op, flg));
    break;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "SeqAIJCUSPARSE options");
  if (A->factortype == MAT_FACTOR_NONE) {
    PetscCall(PetscOptionsEnum("-mat_cusparse_mult_storage_format", "sets storage format of (seq)aijcusparse gpu matrices for SpMV", "MatCUSPARSESetFormat", MatCUSPARSEStorageFormats, (PetscEnum)cusparsestruct->format, (PetscEnum *)&format, &flg));
    if (flg) PetscCall(MatCUSPARSESetFormat(A, MAT_CUSPARSE_MULT, format));

    PetscCall(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));
    if (flg) PetscCall(MatCUSPARSESetFormat(A, MAT_CUSPARSE_ALL, format));
    PetscCall(PetscOptionsBool("-mat_cusparse_use_cpu_solve", "Use CPU (I)LU solve", "MatCUSPARSESetUseCPUSolve", cusparsestruct->use_cpu_solve, &cusparsestruct->use_cpu_solve, &flg));
    if (flg) PetscCall(MatCUSPARSESetUseCPUSolve(A, cusparsestruct->use_cpu_solve));
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
    PetscCall(PetscOptionsEnum("-mat_cusparse_spmv_alg", "sets cuSPARSE algorithm used in sparse-mat dense-vector multiplication (SpMV)", "cusparseSpMVAlg_t", MatCUSPARSESpMVAlgorithms, (PetscEnum)cusparsestruct->spmvAlg, (PetscEnum *)&cusparsestruct->spmvAlg, &flg));
    /* If user did use this option, check its consistency with cuSPARSE, since PetscOptionsEnum() sets enum values based on their position in MatCUSPARSESpMVAlgorithms[] */
  #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
    PetscCheck(!flg || CUSPARSE_SPMV_CSR_ALG1 == 2, PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSPARSE enum cusparseSpMVAlg_t has been changed but PETSc has not been updated accordingly");
  #else
    PetscCheck(!flg || CUSPARSE_CSRMV_ALG1 == 2, PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSPARSE enum cusparseSpMVAlg_t has been changed but PETSc has not been updated accordingly");
  #endif
    PetscCall(PetscOptionsEnum("-mat_cusparse_spmm_alg", "sets cuSPARSE algorithm used in sparse-mat dense-mat multiplication (SpMM)", "cusparseSpMMAlg_t", MatCUSPARSESpMMAlgorithms, (PetscEnum)cusparsestruct->spmmAlg, (PetscEnum *)&cusparsestruct->spmmAlg, &flg));
    PetscCheck(!flg || CUSPARSE_SPMM_CSR_ALG1 == 4, PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSPARSE enum cusparseSpMMAlg_t has been changed but PETSc has not been updated accordingly");

    PetscCall(
      PetscOptionsEnum("-mat_cusparse_csr2csc_alg", "sets cuSPARSE algorithm used in converting CSR matrices to CSC matrices", "cusparseCsr2CscAlg_t", MatCUSPARSECsr2CscAlgorithms, (PetscEnum)cusparsestruct->csr2cscAlg, (PetscEnum *)&cusparsestruct->csr2cscAlg, &flg));
    PetscCheck(!flg || CUSPARSE_CSR2CSC_ALG1 == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSPARSE enum cusparseCsr2CscAlg_t has been changed but PETSc has not been updated accordingly");
#endif
  }
  PetscOptionsHeadEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
static PetscErrorCode MatSeqAIJCUSPARSEBuildFactoredMatrix_LU(Mat A)
{
  Mat_SeqAIJ                   *a  = static_cast<Mat_SeqAIJ *>(A->data);
  PetscInt                      m  = A->rmap->n;
  Mat_SeqAIJCUSPARSETriFactors *fs = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
  const PetscInt               *Ai = a->i, *Aj = a->j, *Adiag = a->diag;
  const MatScalar              *Aa = a->a;
  PetscInt                     *Mi, *Mj, Mnz;
  PetscScalar                  *Ma;

  PetscFunctionBegin;
  if (A->offloadmask == PETSC_OFFLOAD_CPU) { // A's latest factors are on CPU
    if (!fs->csrRowPtr) {                    // Is't the first time to do the setup? Use csrRowPtr since it is not null even when m=0
      // Re-arrange the (skewed) factored matrix and put the result into M, a regular csr matrix on host
      Mnz = (Ai[m] - Ai[0]) + (Adiag[0] - Adiag[m]); // Lnz (without the unit diagonal) + Unz (with the non-unit diagonal)
      PetscCall(PetscMalloc1(m + 1, &Mi));
      PetscCall(PetscMalloc1(Mnz, &Mj)); // Mj is temp
      PetscCall(PetscMalloc1(Mnz, &Ma));
      Mi[0] = 0;
      for (PetscInt i = 0; i < m; i++) {
        PetscInt llen = Ai[i + 1] - Ai[i];
        PetscInt ulen = Adiag[i] - Adiag[i + 1];
        PetscCall(PetscArraycpy(Mj + Mi[i], Aj + Ai[i], llen));                           // entries of L
        Mj[Mi[i] + llen] = i;                                                             // diagonal entry
        PetscCall(PetscArraycpy(Mj + Mi[i] + llen + 1, Aj + Adiag[i + 1] + 1, ulen - 1)); // entries of U on the right of the diagonal
        Mi[i + 1] = Mi[i] + llen + ulen;
      }
      // Copy M (L,U) from host to device
      PetscCallCUDA(cudaMalloc(&fs->csrRowPtr, sizeof(*fs->csrRowPtr) * (m + 1)));
      PetscCallCUDA(cudaMalloc(&fs->csrColIdx, sizeof(*fs->csrColIdx) * Mnz));
      PetscCallCUDA(cudaMalloc(&fs->csrVal, sizeof(*fs->csrVal) * Mnz));
      PetscCallCUDA(cudaMemcpy(fs->csrRowPtr, Mi, sizeof(*fs->csrRowPtr) * (m + 1), cudaMemcpyHostToDevice));
      PetscCallCUDA(cudaMemcpy(fs->csrColIdx, Mj, sizeof(*fs->csrColIdx) * Mnz, cudaMemcpyHostToDevice));

      // Create descriptors for L, U. See https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
      // cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
      // assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
      // all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
      // assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
      cusparseFillMode_t        fillMode  = CUSPARSE_FILL_MODE_LOWER;
      cusparseDiagType_t        diagType  = CUSPARSE_DIAG_TYPE_UNIT;
      const cusparseIndexType_t indexType = PetscDefined(USE_64BIT_INDICES) ? CUSPARSE_INDEX_64I : CUSPARSE_INDEX_32I;

      PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_L, m, m, Mnz, fs->csrRowPtr, fs->csrColIdx, fs->csrVal, indexType, indexType, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
      PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
      PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));

      fillMode = CUSPARSE_FILL_MODE_UPPER;
      diagType = CUSPARSE_DIAG_TYPE_NON_UNIT;
      PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_U, m, m, Mnz, fs->csrRowPtr, fs->csrColIdx, fs->csrVal, indexType, indexType, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
      PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
      PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));

      // Allocate work vectors in SpSv
      PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(*fs->X) * m));
      PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(*fs->Y) * m));

      PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
      PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));

      // Query buffer sizes for SpSV and then allocate buffers, temporarily assuming opA = CUSPARSE_OPERATION_NON_TRANSPOSE
      PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_L));
      PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, &fs->spsvBufferSize_L));
      PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_U));
      PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, &fs->spsvBufferSize_U));
      PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_U, fs->spsvBufferSize_U));
      PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_L, fs->spsvBufferSize_L));

      // Record for reuse
      fs->csrRowPtr_h = Mi;
      fs->csrVal_h    = Ma;
      PetscCall(PetscFree(Mj));
    }
    // Copy the value
    Mi  = fs->csrRowPtr_h;
    Ma  = fs->csrVal_h;
    Mnz = Mi[m];
    for (PetscInt i = 0; i < m; i++) {
      PetscInt llen = Ai[i + 1] - Ai[i];
      PetscInt ulen = Adiag[i] - Adiag[i + 1];
      PetscCall(PetscArraycpy(Ma + Mi[i], Aa + Ai[i], llen));                           // entries of L
      Ma[Mi[i] + llen] = (MatScalar)1.0 / Aa[Adiag[i]];                                 // recover the diagonal entry
      PetscCall(PetscArraycpy(Ma + Mi[i] + llen + 1, Aa + Adiag[i + 1] + 1, ulen - 1)); // entries of U on the right of the diagonal
    }
    PetscCallCUDA(cudaMemcpy(fs->csrVal, Ma, sizeof(*Ma) * Mnz, cudaMemcpyHostToDevice));

    // Do cusparseSpSV_analysis(), which is numeric and requires valid and up-to-date matrix values
    PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, fs->spsvBuffer_L));

    PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, fs->spsvBuffer_U));

    // L, U values have changed, reset the flag to indicate we need to redo cusparseSpSV_analysis() for transpose solve
    fs->updatedTransposeSpSVAnalysis = PETSC_FALSE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
#else
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;
  const PetscInt                    *ai = a->i, *aj = a->j, *vi;
  const MatScalar                   *aa = a->a, *v;
  PetscInt                          *AiLo, *AjLo;
  PetscInt                           i, nz, nzLower, offset, rowOffset;

  PetscFunctionBegin;
  if (!n) PetscFunctionReturn(PETSC_SUCCESS);
  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];
      if (!loTriFactor) {
        PetscScalar *AALo;

        PetscCallCUDA(cudaMallocHost((void **)&AALo, nzLower * sizeof(PetscScalar)));

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

        /* 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;

          PetscCall(PetscArraycpy(&AjLo[offset], vi, nz));
          PetscCall(PetscArraycpy(&AALo[offset], v, nz));

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

          v += nz;
          vi += nz;
        }

        /* allocate space for the triangular factor information */
        PetscCall(PetscNew(&loTriFactor));
        loTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
        /* Create the matrix description */
        PetscCallCUSPARSE(cusparseCreateMatDescr(&loTriFactor->descr));
        PetscCallCUSPARSE(cusparseSetMatIndexBase(loTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
  #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
        PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
  #else
        PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
  #endif
        PetscCallCUSPARSE(cusparseSetMatFillMode(loTriFactor->descr, CUSPARSE_FILL_MODE_LOWER));
        PetscCallCUSPARSE(cusparseSetMatDiagType(loTriFactor->descr, CUSPARSE_DIAG_TYPE_UNIT));

        /* 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);

        /* Create the solve analysis information */
        PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
        PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&loTriFactor->solveInfo));
  #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
        PetscCallCUSPARSE(cusparseXcsrsv_buffsize(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, &loTriFactor->solveBufferSize));
        PetscCallCUDA(cudaMalloc(&loTriFactor->solveBuffer, loTriFactor->solveBufferSize));
  #endif

        /* perform the solve analysis */
        PetscCallCUSPARSE(cusparseXcsrsv_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, loTriFactor->solvePolicy, loTriFactor->solveBuffer));
        PetscCallCUDA(WaitForCUDA());
        PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));

        /* assign the pointer */
        ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->loTriFactorPtr = loTriFactor;
        loTriFactor->AA_h                                          = AALo;
        PetscCallCUDA(cudaFreeHost(AiLo));
        PetscCallCUDA(cudaFreeHost(AjLo));
        PetscCall(PetscLogCpuToGpu((n + 1 + nzLower) * sizeof(int) + nzLower * sizeof(PetscScalar)));
      } else { /* update values only */
        if (!loTriFactor->AA_h) PetscCallCUDA(cudaMallocHost((void **)&loTriFactor->AA_h, nzLower * sizeof(PetscScalar)));
        /* Fill the lower triangular matrix */
        loTriFactor->AA_h[0] = 1.0;
        v                    = aa;
        vi                   = aj;
        offset               = 1;
        for (i = 1; i < n; i++) {
          nz = ai[i + 1] - ai[i];
          PetscCall(PetscArraycpy(&loTriFactor->AA_h[offset], v, nz));
          offset += nz;
          loTriFactor->AA_h[offset] = 1.0;
          offset += 1;
          v += nz;
        }
        loTriFactor->csrMat->values->assign(loTriFactor->AA_h, loTriFactor->AA_h + nzLower);
        PetscCall(PetscLogCpuToGpu(nzLower * sizeof(PetscScalar)));
      }
    } catch (char *ex) {
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

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;
  const PetscInt                    *aj = a->j, *adiag = a->diag, *vi;
  const MatScalar                   *aa = a->a, *v;
  PetscInt                          *AiUp, *AjUp;
  PetscInt                           i, nz, nzUpper, offset;

  PetscFunctionBegin;
  if (!n) PetscFunctionReturn(PETSC_SUCCESS);
  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];
      if (!upTriFactor) {
        PetscScalar *AAUp;

        PetscCallCUDA(cudaMallocHost((void **)&AAUp, nzUpper * sizeof(PetscScalar)));

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

        /* 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);

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

        /* allocate space for the triangular factor information */
        PetscCall(PetscNew(&upTriFactor));
        upTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;

        /* Create the matrix description */
        PetscCallCUSPARSE(cusparseCreateMatDescr(&upTriFactor->descr));
        PetscCallCUSPARSE(cusparseSetMatIndexBase(upTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
  #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
        PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
  #else
        PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
  #endif
        PetscCallCUSPARSE(cusparseSetMatFillMode(upTriFactor->descr, CUSPARSE_FILL_MODE_UPPER));
        PetscCallCUSPARSE(cusparseSetMatDiagType(upTriFactor->descr, CUSPARSE_DIAG_TYPE_NON_UNIT));

        /* 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);

        /* Create the solve analysis information */
        PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
        PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&upTriFactor->solveInfo));
  #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
        PetscCallCUSPARSE(cusparseXcsrsv_buffsize(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, &upTriFactor->solveBufferSize));
        PetscCallCUDA(cudaMalloc(&upTriFactor->solveBuffer, upTriFactor->solveBufferSize));
  #endif

        /* perform the solve analysis */
        PetscCallCUSPARSE(cusparseXcsrsv_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, upTriFactor->solvePolicy, upTriFactor->solveBuffer));

        PetscCallCUDA(WaitForCUDA());
        PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));

        /* assign the pointer */
        ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->upTriFactorPtr = upTriFactor;
        upTriFactor->AA_h                                          = AAUp;
        PetscCallCUDA(cudaFreeHost(AiUp));
        PetscCallCUDA(cudaFreeHost(AjUp));
        PetscCall(PetscLogCpuToGpu((n + 1 + nzUpper) * sizeof(int) + nzUpper * sizeof(PetscScalar)));
      } else {
        if (!upTriFactor->AA_h) PetscCallCUDA(cudaMallocHost((void **)&upTriFactor->AA_h, nzUpper * sizeof(PetscScalar)));
        /* Fill the upper triangular matrix */
        offset = nzUpper;
        for (i = n - 1; i >= 0; i--) {
          v = aa + 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 */
          upTriFactor->AA_h[offset] = 1. / v[nz];
          PetscCall(PetscArraycpy(&upTriFactor->AA_h[offset + 1], v, nz));
        }
        upTriFactor->csrMat->values->assign(upTriFactor->AA_h, upTriFactor->AA_h + nzUpper);
        PetscCall(PetscLogCpuToGpu(nzUpper * sizeof(PetscScalar)));
      }
    } catch (char *ex) {
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

static PetscErrorCode MatSeqAIJCUSPARSEILUAnalysisAndCopyToGPU(Mat A)
{
  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;
  PetscInt                      n = A->rmap->n;

  PetscFunctionBegin;
  PetscCheck(cusparseTriFactors, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
  PetscCall(MatSeqAIJCUSPARSEBuildFactoredMatrix_LU(A));
#else
  PetscCall(MatSeqAIJCUSPARSEBuildILULowerTriMatrix(A));
  PetscCall(MatSeqAIJCUSPARSEBuildILUUpperTriMatrix(A));
  if (!cusparseTriFactors->workVector) cusparseTriFactors->workVector = new THRUSTARRAY(n);
#endif

  cusparseTriFactors->nnz = a->nz;

  A->offloadmask = PETSC_OFFLOAD_BOTH; // factored matrix is sync'ed to GPU
  /* lower triangular indices */
  PetscCall(ISIdentity(isrow, &row_identity));
  if (!row_identity && !cusparseTriFactors->rpermIndices) {
    const PetscInt *r;

    PetscCall(ISGetIndices(isrow, &r));
    cusparseTriFactors->rpermIndices = new THRUSTINTARRAY(n);
    cusparseTriFactors->rpermIndices->assign(r, r + n);
    PetscCall(ISRestoreIndices(isrow, &r));
    PetscCall(PetscLogCpuToGpu(n * sizeof(PetscInt)));
  }

  /* upper triangular indices */
  PetscCall(ISIdentity(iscol, &col_identity));
  if (!col_identity && !cusparseTriFactors->cpermIndices) {
    const PetscInt *c;

    PetscCall(ISGetIndices(iscol, &c));
    cusparseTriFactors->cpermIndices = new THRUSTINTARRAY(n);
    cusparseTriFactors->cpermIndices->assign(c, c + n);
    PetscCall(ISRestoreIndices(iscol, &c));
    PetscCall(PetscLogCpuToGpu(n * sizeof(PetscInt)));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
static PetscErrorCode MatSeqAIJCUSPARSEBuildFactoredMatrix_Cheolesky(Mat A)
{
  Mat_SeqAIJ                   *a  = static_cast<Mat_SeqAIJ *>(A->data);
  PetscInt                      m  = A->rmap->n;
  Mat_SeqAIJCUSPARSETriFactors *fs = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
  const PetscInt               *Ai = a->i, *Aj = a->j, *Adiag = a->diag;
  const MatScalar              *Aa = a->a;
  PetscInt                     *Mj, Mnz;
  PetscScalar                  *Ma, *D;

  PetscFunctionBegin;
  if (A->offloadmask == PETSC_OFFLOAD_CPU) { // A's latest factors are on CPU
    if (!fs->csrRowPtr) {                    // Is't the first time to do the setup? Use csrRowPtr since it is not null even m=0
      // Re-arrange the (skewed) factored matrix and put the result into M, a regular csr matrix on host.
      // See comments at MatICCFactorSymbolic_SeqAIJ() on the layout of the factored matrix (U) on host.
      Mnz = Ai[m]; // Unz (with the unit diagonal)
      PetscCall(PetscMalloc1(Mnz, &Ma));
      PetscCall(PetscMalloc1(Mnz, &Mj)); // Mj[] is temp
      PetscCall(PetscMalloc1(m, &D));    // the diagonal
      for (PetscInt i = 0; i < m; i++) {
        PetscInt ulen = Ai[i + 1] - Ai[i];
        Mj[Ai[i]]     = i;                                              // diagonal entry
        PetscCall(PetscArraycpy(Mj + Ai[i] + 1, Aj + Ai[i], ulen - 1)); // entries of U on the right of the diagonal
      }
      // Copy M (U) from host to device
      PetscCallCUDA(cudaMalloc(&fs->csrRowPtr, sizeof(*fs->csrRowPtr) * (m + 1)));
      PetscCallCUDA(cudaMalloc(&fs->csrColIdx, sizeof(*fs->csrColIdx) * Mnz));
      PetscCallCUDA(cudaMalloc(&fs->csrVal, sizeof(*fs->csrVal) * Mnz));
      PetscCallCUDA(cudaMalloc(&fs->diag, sizeof(*fs->diag) * m));
      PetscCallCUDA(cudaMemcpy(fs->csrRowPtr, Ai, sizeof(*Ai) * (m + 1), cudaMemcpyHostToDevice));
      PetscCallCUDA(cudaMemcpy(fs->csrColIdx, Mj, sizeof(*Mj) * Mnz, cudaMemcpyHostToDevice));

      // Create descriptors for L, U. See https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
      // cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
      // assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
      // all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
      // assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
      cusparseFillMode_t        fillMode  = CUSPARSE_FILL_MODE_UPPER;
      cusparseDiagType_t        diagType  = CUSPARSE_DIAG_TYPE_UNIT; // U is unit diagonal
      const cusparseIndexType_t indexType = PetscDefined(USE_64BIT_INDICES) ? CUSPARSE_INDEX_64I : CUSPARSE_INDEX_32I;

      PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_U, m, m, Mnz, fs->csrRowPtr, fs->csrColIdx, fs->csrVal, indexType, indexType, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
      PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
      PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));

      // Allocate work vectors in SpSv
      PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(*fs->X) * m));
      PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(*fs->Y) * m));

      PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
      PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));

      // Query buffer sizes for SpSV and then allocate buffers
      PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_U));
      PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, &fs->spsvBufferSize_U));
      PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_U, fs->spsvBufferSize_U));

      PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Ut)); // Ut solve uses the same matrix (spMatDescr_U), but different descr and buffer
      PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Ut, &fs->spsvBufferSize_Ut));
      PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Ut, fs->spsvBufferSize_Ut));

      // Record for reuse
      fs->csrVal_h = Ma;
      fs->diag_h   = D;
      PetscCall(PetscFree(Mj));
    }
    // Copy the value
    Ma  = fs->csrVal_h;
    D   = fs->diag_h;
    Mnz = Ai[m];
    for (PetscInt i = 0; i < m; i++) {
      D[i]      = Aa[Adiag[i]];   // actually Aa[Adiag[i]] is the inverse of the diagonal
      Ma[Ai[i]] = (MatScalar)1.0; // set the unit diagonal, which is cosmetic since cusparse does not really read it given CUSPARSE_DIAG_TYPE_UNIT
      for (PetscInt k = 0; k < Ai[i + 1] - Ai[i] - 1; k++) Ma[Ai[i] + 1 + k] = -Aa[Ai[i] + k];
    }
    PetscCallCUDA(cudaMemcpy(fs->csrVal, Ma, sizeof(*Ma) * Mnz, cudaMemcpyHostToDevice));
    PetscCallCUDA(cudaMemcpy(fs->diag, D, sizeof(*D) * m, cudaMemcpyHostToDevice));

    // Do cusparseSpSV_analysis(), which is numeric and requires valid and up-to-date matrix values
    PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, fs->spsvBuffer_U));
    PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Ut, fs->spsvBuffer_Ut));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

// Solve Ut D U x = b
static PetscErrorCode MatSolve_SeqAIJCUSPARSE_Cholesky(Mat A, Vec b, Vec x)
{
  Mat_SeqAIJCUSPARSETriFactors         *fs  = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
  Mat_SeqAIJ                           *aij = static_cast<Mat_SeqAIJ *>(A->data);
  const PetscScalar                    *barray;
  PetscScalar                          *xarray;
  thrust::device_ptr<const PetscScalar> bGPU;
  thrust::device_ptr<PetscScalar>       xGPU;
  const cusparseSpSVAlg_t               alg = CUSPARSE_SPSV_ALG_DEFAULT;
  PetscInt                              m   = A->rmap->n;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(VecCUDAGetArrayWrite(x, &xarray));
  PetscCall(VecCUDAGetArrayRead(b, &barray));
  xGPU = thrust::device_pointer_cast(xarray);
  bGPU = thrust::device_pointer_cast(barray);

  // Reorder b with the row permutation if needed, and wrap the result in fs->X
  if (fs->rpermIndices) {
    PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->end()), thrust::device_pointer_cast(fs->X)));
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
  } else {
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
  }

  // Solve Ut Y = X
  PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
  PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Ut));

  // Solve diag(D) Z = Y. Actually just do Y = Y*D since D is already inverted in MatCholeskyFactorNumeric_SeqAIJ().
  // It is basically a vector element-wise multiplication, but cublas does not have it!
  PetscCallThrust(thrust::transform(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::device_pointer_cast(fs->Y), thrust::device_pointer_cast(fs->Y + m), thrust::device_pointer_cast(fs->diag), thrust::device_pointer_cast(fs->Y), thrust::multiplies<PetscScalar>()));

  // Solve U X = Y
  if (fs->cpermIndices) { // if need to permute, we need to use the intermediate buffer X
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
  } else {
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
  }
  PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, alg, fs->spsvDescr_U));

  // Reorder X with the column permutation if needed, and put the result back to x
  if (fs->cpermIndices) {
    PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X), fs->cpermIndices->begin()),
                                 thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X + m), fs->cpermIndices->end()), xGPU));
  }

  PetscCall(VecCUDARestoreArrayRead(b, &barray));
  PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogGpuFlops(4.0 * aij->nz - A->rmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}
#else
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;
  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(PETSC_SUCCESS);
  if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
    try {
      PetscCallCUDA(cudaMallocHost((void **)&AAUp, nzUpper * sizeof(PetscScalar)));
      PetscCallCUDA(cudaMallocHost((void **)&AALo, nzUpper * sizeof(PetscScalar)));
      if (!upTriFactor && !loTriFactor) {
        /* Allocate Space for the upper triangular matrix */
        PetscCallCUDA(cudaMallocHost((void **)&AiUp, (n + 1) * sizeof(PetscInt)));
        PetscCallCUDA(cudaMallocHost((void **)&AjUp, nzUpper * sizeof(PetscInt)));

        /* 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) {
            PetscCall(PetscArraycpy(&AjUp[offset], vj, nz));
            PetscCall(PetscArraycpy(&AAUp[offset], v, nz));
            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 */
        PetscCall(PetscNew(&upTriFactor));
        upTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;

        /* Create the matrix description */
        PetscCallCUSPARSE(cusparseCreateMatDescr(&upTriFactor->descr));
        PetscCallCUSPARSE(cusparseSetMatIndexBase(upTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
  #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
        PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
  #else
        PetscCallCUSPARSE(cusparseSetMatType(upTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
  #endif
        PetscCallCUSPARSE(cusparseSetMatFillMode(upTriFactor->descr, CUSPARSE_FILL_MODE_UPPER));
        PetscCallCUSPARSE(cusparseSetMatDiagType(upTriFactor->descr, CUSPARSE_DIAG_TYPE_UNIT));

        /* 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);

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

        /* Create the solve analysis information */
        PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
        PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&upTriFactor->solveInfo));
  #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
        PetscCallCUSPARSE(cusparseXcsrsv_buffsize(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, &upTriFactor->solveBufferSize));
        PetscCallCUDA(cudaMalloc(&upTriFactor->solveBuffer, upTriFactor->solveBufferSize));
  #endif

        /* perform the solve analysis */
        PetscCallCUSPARSE(cusparseXcsrsv_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, upTriFactor->solvePolicy, upTriFactor->solveBuffer));

        PetscCallCUDA(WaitForCUDA());
        PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));

        /* assign the pointer */
        ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->upTriFactorPtr = upTriFactor;

        /* allocate space for the triangular factor information */
        PetscCall(PetscNew(&loTriFactor));
        loTriFactor->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;

        /* Create the matrix description */
        PetscCallCUSPARSE(cusparseCreateMatDescr(&loTriFactor->descr));
        PetscCallCUSPARSE(cusparseSetMatIndexBase(loTriFactor->descr, CUSPARSE_INDEX_BASE_ZERO));
  #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
        PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
  #else
        PetscCallCUSPARSE(cusparseSetMatType(loTriFactor->descr, CUSPARSE_MATRIX_TYPE_TRIANGULAR));
  #endif
        PetscCallCUSPARSE(cusparseSetMatFillMode(loTriFactor->descr, CUSPARSE_FILL_MODE_UPPER));
        PetscCallCUSPARSE(cusparseSetMatDiagType(loTriFactor->descr, CUSPARSE_DIAG_TYPE_NON_UNIT));

        /* 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);

        /* Create the solve analysis information */
        PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
        PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&loTriFactor->solveInfo));
  #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
        PetscCallCUSPARSE(cusparseXcsrsv_buffsize(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, &loTriFactor->solveBufferSize));
        PetscCallCUDA(cudaMalloc(&loTriFactor->solveBuffer, loTriFactor->solveBufferSize));
  #endif

        /* perform the solve analysis */
        PetscCallCUSPARSE(cusparseXcsrsv_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, loTriFactor->solvePolicy, loTriFactor->solveBuffer));

        PetscCallCUDA(WaitForCUDA());
        PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));

        /* assign the pointer */
        ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->loTriFactorPtr = loTriFactor;

        PetscCall(PetscLogCpuToGpu(2 * (((A->rmap->n + 1) + (a->nz)) * sizeof(int) + (a->nz) * sizeof(PetscScalar))));
        PetscCallCUDA(cudaFreeHost(AiUp));
        PetscCallCUDA(cudaFreeHost(AjUp));
      } else {
        /* Fill the upper triangular matrix */
        offset = 0;
        for (i = 0; i < n; i++) {
          /* set the pointers */
          v  = aa + ai[i];
          nz = ai[i + 1] - ai[i] - 1; /* exclude diag[i] */

          /* first, set the diagonal elements */
          AAUp[offset] = 1.0 / v[nz];
          AALo[offset] = 1.0 / v[nz];

          offset += 1;
          if (nz > 0) {
            PetscCall(PetscArraycpy(&AAUp[offset], v, nz));
            for (j = offset; j < offset + nz; j++) {
              AAUp[j] = -AAUp[j];
              AALo[j] = AAUp[j] / v[nz];
            }
            offset += nz;
          }
        }
        PetscCheck(upTriFactor, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
        PetscCheck(loTriFactor, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");
        upTriFactor->csrMat->values->assign(AAUp, AAUp + a->nz);
        loTriFactor->csrMat->values->assign(AALo, AALo + a->nz);
        PetscCall(PetscLogCpuToGpu(2 * (a->nz) * sizeof(PetscScalar)));
      }
      PetscCallCUDA(cudaFreeHost(AAUp));
      PetscCallCUDA(cudaFreeHost(AALo));
    } catch (char *ex) {
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

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

  PetscFunctionBegin;
  PetscCheck(cusparseTriFactors, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing cusparseTriFactors");

#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
  PetscCall(MatSeqAIJCUSPARSEBuildFactoredMatrix_Cheolesky(A));
#else
  PetscCall(MatSeqAIJCUSPARSEBuildICCTriMatrices(A));
  if (!cusparseTriFactors->workVector) cusparseTriFactors->workVector = new THRUSTARRAY(n);
#endif
  cusparseTriFactors->nnz = (a->nz - n) * 2 + n;

  A->offloadmask = PETSC_OFFLOAD_BOTH;

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

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

static PetscErrorCode MatCholeskyFactorNumeric_SeqAIJCUSPARSE(Mat B, Mat A, const MatFactorInfo *info)
{
  PetscFunctionBegin;
  PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
  PetscCall(MatCholeskyFactorNumeric_SeqAIJ(B, A, info));
  B->offloadmask = PETSC_OFFLOAD_CPU;

#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
  B->ops->solve          = MatSolve_SeqAIJCUSPARSE_Cholesky;
  B->ops->solvetranspose = MatSolve_SeqAIJCUSPARSE_Cholesky;
#else
  /* determine which version of MatSolve needs to be used. */
  Mat_SeqAIJ *b  = (Mat_SeqAIJ *)B->data;
  IS          ip = b->row;
  PetscBool   perm_identity;

  PetscCall(ISIdentity(ip, &perm_identity));
  if (perm_identity) {
    B->ops->solve          = MatSolve_SeqAIJCUSPARSE_NaturalOrdering;
    B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering;
  } else {
    B->ops->solve          = MatSolve_SeqAIJCUSPARSE;
    B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE;
  }
#endif
  B->ops->matsolve          = NULL;
  B->ops->matsolvetranspose = NULL;

  /* get the triangular factors */
  PetscCall(MatSeqAIJCUSPARSEICCAnalysisAndCopyToGPU(B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

#if PETSC_PKG_CUDA_VERSION_LT(11, 4, 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 *upTriFactorT;
  cusparseIndexBase_t                indexBase;
  cusparseMatrixType_t               matrixType;
  cusparseFillMode_t                 fillMode;
  cusparseDiagType_t                 diagType;

  PetscFunctionBegin;
  /* allocate space for the transpose of the lower triangular factor */
  PetscCall(PetscNew(&loTriFactorT));
  loTriFactorT->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;

  /* 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 */
  PetscCallCUSPARSE(cusparseCreateMatDescr(&loTriFactorT->descr));
  PetscCallCUSPARSE(cusparseSetMatIndexBase(loTriFactorT->descr, indexBase));
  PetscCallCUSPARSE(cusparseSetMatType(loTriFactorT->descr, matrixType));
  PetscCallCUSPARSE(cusparseSetMatFillMode(loTriFactorT->descr, fillMode));
  PetscCallCUSPARSE(cusparseSetMatDiagType(loTriFactorT->descr, diagType));

  /* 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_cols;
  loTriFactorT->csrMat->num_cols       = loTriFactor->csrMat->num_rows;
  loTriFactorT->csrMat->num_entries    = loTriFactor->csrMat->num_entries;
  loTriFactorT->csrMat->row_offsets    = new THRUSTINTARRAY32(loTriFactorT->csrMat->num_rows + 1);
  loTriFactorT->csrMat->column_indices = new THRUSTINTARRAY32(loTriFactorT->csrMat->num_entries);
  loTriFactorT->csrMat->values         = new THRUSTARRAY(loTriFactorT->csrMat->num_entries);

  /* compute the transpose of the lower triangular factor, i.e. the CSC */
  #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  PetscCallCUSPARSE(cusparseCsr2cscEx2_bufferSize(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->row_offsets->data().get(),
                                                  loTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, &loTriFactor->csr2cscBufferSize));
  PetscCallCUDA(cudaMalloc(&loTriFactor->csr2cscBuffer, loTriFactor->csr2cscBufferSize));
  #endif

  PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
  {
    // there is no clean way to have PetscCallCUSPARSE wrapping this function...
    auto 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(),
  #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
                                 loTriFactorT->csrMat->row_offsets->data().get(), loTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, loTriFactor->csr2cscBuffer);
  #else
                                 loTriFactorT->csrMat->column_indices->data().get(), loTriFactorT->csrMat->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
  #endif
    PetscCallCUSPARSE(stat);
  }

  PetscCallCUDA(WaitForCUDA());
  PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));

  /* Create the solve analysis information */
  PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
  PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&loTriFactorT->solveInfo));
  #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
  PetscCallCUSPARSE(cusparseXcsrsv_buffsize(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, &loTriFactorT->solveBufferSize));
  PetscCallCUDA(cudaMalloc(&loTriFactorT->solveBuffer, loTriFactorT->solveBufferSize));
  #endif

  /* perform the solve analysis */
  PetscCallCUSPARSE(cusparseXcsrsv_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, loTriFactorT->solvePolicy, loTriFactorT->solveBuffer));

  PetscCallCUDA(WaitForCUDA());
  PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));

  /* assign the pointer */
  ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->loTriFactorPtrTranspose = loTriFactorT;

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

  /* allocate space for the transpose of the upper triangular factor */
  PetscCall(PetscNew(&upTriFactorT));
  upTriFactorT->solvePolicy = CUSPARSE_SOLVE_POLICY_USE_LEVEL;

  /* 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 */
  PetscCallCUSPARSE(cusparseCreateMatDescr(&upTriFactorT->descr));
  PetscCallCUSPARSE(cusparseSetMatIndexBase(upTriFactorT->descr, indexBase));
  PetscCallCUSPARSE(cusparseSetMatType(upTriFactorT->descr, matrixType));
  PetscCallCUSPARSE(cusparseSetMatFillMode(upTriFactorT->descr, fillMode));
  PetscCallCUSPARSE(cusparseSetMatDiagType(upTriFactorT->descr, diagType));

  /* 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_cols;
  upTriFactorT->csrMat->num_cols       = upTriFactor->csrMat->num_rows;
  upTriFactorT->csrMat->num_entries    = upTriFactor->csrMat->num_entries;
  upTriFactorT->csrMat->row_offsets    = new THRUSTINTARRAY32(upTriFactorT->csrMat->num_rows + 1);
  upTriFactorT->csrMat->column_indices = new THRUSTINTARRAY32(upTriFactorT->csrMat->num_entries);
  upTriFactorT->csrMat->values         = new THRUSTARRAY(upTriFactorT->csrMat->num_entries);

  /* compute the transpose of the upper triangular factor, i.e. the CSC */
  #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  PetscCallCUSPARSE(cusparseCsr2cscEx2_bufferSize(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->row_offsets->data().get(),
                                                  upTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, &upTriFactor->csr2cscBufferSize));
  PetscCallCUDA(cudaMalloc(&upTriFactor->csr2cscBuffer, upTriFactor->csr2cscBufferSize));
  #endif

  PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
  {
    // there is no clean way to have PetscCallCUSPARSE wrapping this function...
    auto 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(),
  #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
                                 upTriFactorT->csrMat->row_offsets->data().get(), upTriFactorT->csrMat->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, CUSPARSE_CSR2CSC_ALG1, upTriFactor->csr2cscBuffer);
  #else
                                 upTriFactorT->csrMat->column_indices->data().get(), upTriFactorT->csrMat->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
  #endif
    PetscCallCUSPARSE(stat);
  }

  PetscCallCUDA(WaitForCUDA());
  PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));

  /* Create the solve analysis information */
  PetscCall(PetscLogEventBegin(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));
  PetscCallCUSPARSE(cusparseCreateCsrsvInfo(&upTriFactorT->solveInfo));
  #if PETSC_PKG_CUDA_VERSION_GE(9, 0, 0)
  PetscCallCUSPARSE(cusparseXcsrsv_buffsize(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, &upTriFactorT->solveBufferSize));
  PetscCallCUDA(cudaMalloc(&upTriFactorT->solveBuffer, upTriFactorT->solveBufferSize));
  #endif

  /* perform the solve analysis */
  /* christ, would it have killed you to put this stuff in a function????????? */
  PetscCallCUSPARSE(cusparseXcsrsv_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, upTriFactorT->solvePolicy, upTriFactorT->solveBuffer));

  PetscCallCUDA(WaitForCUDA());
  PetscCall(PetscLogEventEnd(MAT_CUSPARSESolveAnalysis, A, 0, 0, 0));

  /* assign the pointer */
  ((Mat_SeqAIJCUSPARSETriFactors *)A->spptr)->upTriFactorPtrTranspose = upTriFactorT;
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

struct PetscScalarToPetscInt {
  __host__ __device__ PetscInt operator()(PetscScalar s) { return (PetscInt)PetscRealPart(s); }
};

static PetscErrorCode MatSeqAIJCUSPARSEFormExplicitTranspose(Mat A)
{
  Mat_SeqAIJCUSPARSE           *cusparsestruct = (Mat_SeqAIJCUSPARSE *)A->spptr;
  Mat_SeqAIJCUSPARSEMultStruct *matstruct, *matstructT;
  Mat_SeqAIJ                   *a = (Mat_SeqAIJ *)A->data;
  cusparseStatus_t              stat;
  cusparseIndexBase_t           indexBase;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
  PetscCheck(matstruct, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing mat struct");
  matstructT = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->matTranspose;
  PetscCheck(!A->transupdated || matstructT, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing matTranspose struct");
  if (A->transupdated) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscLogEventBegin(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
  PetscCall(PetscLogGpuTimeBegin());
  if (cusparsestruct->format != MAT_CUSPARSE_CSR) PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_TRUE));
  if (!cusparsestruct->matTranspose) { /* create cusparse matrix */
    matstructT = new Mat_SeqAIJCUSPARSEMultStruct;
    PetscCallCUSPARSE(cusparseCreateMatDescr(&matstructT->descr));
    indexBase = cusparseGetMatIndexBase(matstruct->descr);
    PetscCallCUSPARSE(cusparseSetMatIndexBase(matstructT->descr, indexBase));
    PetscCallCUSPARSE(cusparseSetMatType(matstructT->descr, CUSPARSE_MATRIX_TYPE_GENERAL));

    /* set alpha and beta */
    PetscCallCUDA(cudaMalloc((void **)&matstructT->alpha_one, sizeof(PetscScalar)));
    PetscCallCUDA(cudaMalloc((void **)&matstructT->beta_zero, sizeof(PetscScalar)));
    PetscCallCUDA(cudaMalloc((void **)&matstructT->beta_one, sizeof(PetscScalar)));
    PetscCallCUDA(cudaMemcpy(matstructT->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
    PetscCallCUDA(cudaMemcpy(matstructT->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
    PetscCallCUDA(cudaMemcpy(matstructT->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));

    if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
      CsrMatrix *matrixT      = new CsrMatrix;
      matstructT->mat         = matrixT;
      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);

      if (!cusparsestruct->rowoffsets_gpu) cusparsestruct->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
      cusparsestruct->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);

#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  #if PETSC_PKG_CUDA_VERSION_GE(11, 2, 1)
      stat = cusparseCreateCsr(&matstructT->matDescr, matrixT->num_rows, matrixT->num_cols, matrixT->num_entries, matrixT->row_offsets->data().get(), matrixT->column_indices->data().get(), matrixT->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, /* row offset, col idx type due to THRUSTINTARRAY32 */
                               indexBase, cusparse_scalartype);
      PetscCallCUSPARSE(stat);
  #else
      /* cusparse-11.x returns errors with zero-sized matrices until 11.2.1,
           see https://docs.nvidia.com/cuda/cuda-toolkit-release-notes/index.html#cusparse-11.2.1

           I don't know what a proper value should be for matstructT->matDescr with empty matrices, so I just set
           it to NULL to blow it up if one relies on it. Per https://docs.nvidia.com/cuda/cusparse/index.html#csr2cscEx2,
           when nnz = 0, matrixT->row_offsets[] should be filled with indexBase. So I also set it accordingly.
        */
      if (matrixT->num_entries) {
        stat = cusparseCreateCsr(&matstructT->matDescr, matrixT->num_rows, matrixT->num_cols, matrixT->num_entries, matrixT->row_offsets->data().get(), matrixT->column_indices->data().get(), matrixT->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, indexBase, cusparse_scalartype);
        PetscCallCUSPARSE(stat);

      } else {
        matstructT->matDescr = NULL;
        matrixT->row_offsets->assign(matrixT->row_offsets->size(), indexBase);
      }
  #endif
#endif
    } else if (cusparsestruct->format == MAT_CUSPARSE_ELL || cusparsestruct->format == MAT_CUSPARSE_HYB) {
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
#else
      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());
      PetscCallCUSPARSE(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);
      PetscCallCUSPARSE(stat);

      /* Last, convert CSC to HYB */
      cusparseHybMat_t hybMat;
      PetscCallCUSPARSE(cusparseCreateHybMat(&hybMat));
      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);
      PetscCallCUSPARSE(stat);

      /* assign the pointer */
      matstructT->mat = hybMat;
      A->transupdated = PETSC_TRUE;
      /* 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;
      }
#endif
    }
  }
  if (cusparsestruct->format == MAT_CUSPARSE_CSR) { /* transpose mat struct may be already present, update data */
    CsrMatrix *matrix  = (CsrMatrix *)matstruct->mat;
    CsrMatrix *matrixT = (CsrMatrix *)matstructT->mat;
    PetscCheck(matrix, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix");
    PetscCheck(matrix->row_offsets, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix rows");
    PetscCheck(matrix->column_indices, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix cols");
    PetscCheck(matrix->values, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrix values");
    PetscCheck(matrixT, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT");
    PetscCheck(matrixT->row_offsets, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT rows");
    PetscCheck(matrixT->column_indices, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT cols");
    PetscCheck(matrixT->values, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CsrMatrixT values");
    if (!cusparsestruct->rowoffsets_gpu) { /* this may be absent when we did not construct the transpose with csr2csc */
      cusparsestruct->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
      cusparsestruct->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
      PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
    }
    if (!cusparsestruct->csr2csc_i) {
      THRUSTARRAY csr2csc_a(matrix->num_entries);
      PetscCallThrust(thrust::sequence(thrust::device, csr2csc_a.begin(), csr2csc_a.end(), 0.0));

      indexBase = cusparseGetMatIndexBase(matstruct->descr);
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
      void  *csr2cscBuffer;
      size_t csr2cscBufferSize;
      stat = cusparseCsr2cscEx2_bufferSize(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->row_offsets->data().get(), matrixT->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, cusparsestruct->csr2cscAlg, &csr2cscBufferSize);
      PetscCallCUSPARSE(stat);
      PetscCallCUDA(cudaMalloc(&csr2cscBuffer, csr2cscBufferSize));
#endif

      if (matrix->num_entries) {
        /* When there are no nonzeros, this routine mistakenly returns CUSPARSE_STATUS_INVALID_VALUE in
           mat_tests-ex62_15_mpiaijcusparse on ranks 0 and 2 with CUDA-11. But CUDA-10 is OK.
           I checked every parameters and they were just fine. I have no clue why cusparse complains.

           Per https://docs.nvidia.com/cuda/cusparse/index.html#csr2cscEx2, when nnz = 0, matrixT->row_offsets[]
           should be filled with indexBase. So I just take a shortcut here.
        */
        stat = cusparse_csr2csc(cusparsestruct->handle, A->rmap->n, A->cmap->n, matrix->num_entries, csr2csc_a.data().get(), cusparsestruct->rowoffsets_gpu->data().get(), matrix->column_indices->data().get(), matrixT->values->data().get(),
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
                                matrixT->row_offsets->data().get(), matrixT->column_indices->data().get(), cusparse_scalartype, CUSPARSE_ACTION_NUMERIC, indexBase, cusparsestruct->csr2cscAlg, csr2cscBuffer);
        PetscCallCUSPARSE(stat);
#else
                                matrixT->column_indices->data().get(), matrixT->row_offsets->data().get(), CUSPARSE_ACTION_NUMERIC, indexBase);
        PetscCallCUSPARSE(stat);
#endif
      } else {
        matrixT->row_offsets->assign(matrixT->row_offsets->size(), indexBase);
      }

      cusparsestruct->csr2csc_i = new THRUSTINTARRAY(matrix->num_entries);
      PetscCallThrust(thrust::transform(thrust::device, matrixT->values->begin(), matrixT->values->end(), cusparsestruct->csr2csc_i->begin(), PetscScalarToPetscInt()));
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
      PetscCallCUDA(cudaFree(csr2cscBuffer));
#endif
    }
    PetscCallThrust(
      thrust::copy(thrust::device, thrust::make_permutation_iterator(matrix->values->begin(), cusparsestruct->csr2csc_i->begin()), thrust::make_permutation_iterator(matrix->values->begin(), cusparsestruct->csr2csc_i->end()), matrixT->values->begin()));
  }
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogEventEnd(MAT_CUSPARSEGenerateTranspose, A, 0, 0, 0));
  /* the compressed row indices is not used for matTranspose */
  matstructT->cprowIndices = NULL;
  /* assign the pointer */
  ((Mat_SeqAIJCUSPARSE *)A->spptr)->matTranspose = matstructT;
  A->transupdated                                = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
static PetscErrorCode MatSolve_SeqAIJCUSPARSE_LU(Mat A, Vec b, Vec x)
{
  const PetscScalar                    *barray;
  PetscScalar                          *xarray;
  thrust::device_ptr<const PetscScalar> bGPU;
  thrust::device_ptr<PetscScalar>       xGPU;
  Mat_SeqAIJCUSPARSETriFactors         *fs  = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
  const Mat_SeqAIJ                     *aij = static_cast<Mat_SeqAIJ *>(A->data);
  const cusparseOperation_t             op  = CUSPARSE_OPERATION_NON_TRANSPOSE;
  const cusparseSpSVAlg_t               alg = CUSPARSE_SPSV_ALG_DEFAULT;
  PetscInt                              m   = A->rmap->n;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(VecCUDAGetArrayWrite(x, &xarray));
  PetscCall(VecCUDAGetArrayRead(b, &barray));
  xGPU = thrust::device_pointer_cast(xarray);
  bGPU = thrust::device_pointer_cast(barray);

  // Reorder b with the row permutation if needed, and wrap the result in fs->X
  if (fs->rpermIndices) {
    PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->end()), thrust::device_pointer_cast(fs->X)));
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
  } else {
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
  }

  // Solve L Y = X
  PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
  // Note that cusparseSpSV_solve() secretly uses the external buffer used in cusparseSpSV_analysis()!
  PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, op, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_L));

  // Solve U X = Y
  if (fs->cpermIndices) {
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
  } else {
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
  }
  PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, op, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, alg, fs->spsvDescr_U));

  // Reorder X with the column permutation if needed, and put the result back to x
  if (fs->cpermIndices) {
    PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X), fs->cpermIndices->begin()),
                                 thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X + m), fs->cpermIndices->end()), xGPU));
  }
  PetscCall(VecCUDARestoreArrayRead(b, &barray));
  PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogGpuFlops(2.0 * aij->nz - m));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_LU(Mat A, Vec b, Vec x)
{
  Mat_SeqAIJCUSPARSETriFactors         *fs  = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(A->spptr);
  Mat_SeqAIJ                           *aij = static_cast<Mat_SeqAIJ *>(A->data);
  const PetscScalar                    *barray;
  PetscScalar                          *xarray;
  thrust::device_ptr<const PetscScalar> bGPU;
  thrust::device_ptr<PetscScalar>       xGPU;
  const cusparseOperation_t             opA = CUSPARSE_OPERATION_TRANSPOSE;
  const cusparseSpSVAlg_t               alg = CUSPARSE_SPSV_ALG_DEFAULT;
  PetscInt                              m   = A->rmap->n;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  if (!fs->createdTransposeSpSVDescr) { // Call MatSolveTranspose() for the first time
    PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Lt));
    PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, /* The matrix is still L. We only do transpose solve with it */
                                              fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Lt, &fs->spsvBufferSize_Lt));

    PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Ut));
    PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Ut, &fs->spsvBufferSize_Ut));
    PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Lt, fs->spsvBufferSize_Lt));
    PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Ut, fs->spsvBufferSize_Ut));
    fs->createdTransposeSpSVDescr = PETSC_TRUE;
  }

  if (!fs->updatedTransposeSpSVAnalysis) {
    PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Lt, fs->spsvBuffer_Lt));

    PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Ut, fs->spsvBuffer_Ut));
    fs->updatedTransposeSpSVAnalysis = PETSC_TRUE;
  }

  PetscCall(VecCUDAGetArrayWrite(x, &xarray));
  PetscCall(VecCUDAGetArrayRead(b, &barray));
  xGPU = thrust::device_pointer_cast(xarray);
  bGPU = thrust::device_pointer_cast(barray);

  // Reorder b with the row permutation if needed, and wrap the result in fs->X
  if (fs->rpermIndices) {
    PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU, fs->rpermIndices->end()), thrust::device_pointer_cast(fs->X)));
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
  } else {
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
  }

  // Solve Ut Y = X
  PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
  PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, alg, fs->spsvDescr_Ut));

  // Solve Lt X = Y
  if (fs->cpermIndices) { // if need to permute, we need to use the intermediate buffer X
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, fs->X));
  } else {
    PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
  }
  PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, opA, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, alg, fs->spsvDescr_Lt));

  // Reorder X with the column permutation if needed, and put the result back to x
  if (fs->cpermIndices) {
    PetscCallThrust(thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X), fs->cpermIndices->begin()),
                                 thrust::make_permutation_iterator(thrust::device_pointer_cast(fs->X + m), fs->cpermIndices->end()), xGPU));
  }

  PetscCall(VecCUDARestoreArrayRead(b, &barray));
  PetscCall(VecCUDARestoreArrayWrite(x, &xarray));
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogGpuFlops(2.0 * aij->nz - A->rmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}
#else
/* Why do we need to analyze the transposed 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;
  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;

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

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

  PetscCall(PetscLogGpuTimeBegin());
  /* First, reorder with the row permutation */
  thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU + n, cusparseTriFactors->rpermIndices->end()), xGPU);

  /* First, solve U */
  PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, upTriFactorT->solveOp, upTriFactorT->csrMat->num_rows, upTriFactorT->csrMat->num_entries, &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(), upTriFactorT->solvePolicy, upTriFactorT->solveBuffer));

  /* Then, solve L */
  PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, loTriFactorT->solveOp, loTriFactorT->csrMat->num_rows, loTriFactorT->csrMat->num_entries, &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, loTriFactorT->solvePolicy, loTriFactorT->solveBuffer));

  /* Last, copy the solution, xGPU, into a temporary with the column permutation ... can't be done in place. */
  thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), 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(thrust::cuda::par.on(PetscDefaultCudaStream), tempGPU->begin(), tempGPU->end(), xGPU);

  /* restore */
  PetscCall(VecCUDARestoreArrayRead(bb, &barray));
  PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering(Mat A, Vec bb, Vec xx)
{
  const PetscScalar                 *barray;
  PetscScalar                       *xarray;
  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;

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

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

  PetscCall(PetscLogGpuTimeBegin());
  /* First, solve U */
  PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, upTriFactorT->solveOp, upTriFactorT->csrMat->num_rows, upTriFactorT->csrMat->num_entries, &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(), upTriFactorT->solvePolicy, upTriFactorT->solveBuffer));

  /* Then, solve L */
  PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, loTriFactorT->solveOp, loTriFactorT->csrMat->num_rows, loTriFactorT->csrMat->num_entries, &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, loTriFactorT->solvePolicy, loTriFactorT->solveBuffer));

  /* restore */
  PetscCall(VecCUDARestoreArrayRead(bb, &barray));
  PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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;
  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;

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

  PetscCall(PetscLogGpuTimeBegin());
  /* First, reorder with the row permutation */
  thrust::copy(thrust::cuda::par.on(PetscDefaultCudaStream), thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->begin()), thrust::make_permutation_iterator(bGPU, cusparseTriFactors->rpermIndices->end()), tempGPU->begin());

  /* Next, solve L */
  PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, &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, loTriFactor->solvePolicy, loTriFactor->solveBuffer));

  /* Then, solve U */
  PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, &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(), upTriFactor->solvePolicy, upTriFactor->solveBuffer));

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

  PetscCall(VecCUDARestoreArrayRead(bb, &barray));
  PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSolve_SeqAIJCUSPARSE_NaturalOrdering(Mat A, Vec bb, Vec xx)
{
  const PetscScalar                 *barray;
  PetscScalar                       *xarray;
  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;

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

  PetscCall(PetscLogGpuTimeBegin());
  /* First, solve L */
  PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, loTriFactor->solveOp, loTriFactor->csrMat->num_rows, loTriFactor->csrMat->num_entries, &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(), loTriFactor->solvePolicy, loTriFactor->solveBuffer));

  /* Next, solve U */
  PetscCallCUSPARSE(cusparseXcsrsv_solve(cusparseTriFactors->handle, upTriFactor->solveOp, upTriFactor->csrMat->num_rows, upTriFactor->csrMat->num_entries, &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, upTriFactor->solvePolicy, upTriFactor->solveBuffer));

  PetscCall(VecCUDARestoreArrayRead(bb, &barray));
  PetscCall(VecCUDARestoreArrayWrite(xx, &xarray));
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogGpuFlops(2.0 * cusparseTriFactors->nnz - A->cmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
static PetscErrorCode MatILUFactorNumeric_SeqAIJCUSPARSE_ILU0(Mat fact, Mat A, const MatFactorInfo *)
{
  Mat_SeqAIJCUSPARSETriFactors *fs    = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
  Mat_SeqAIJ                   *aij   = (Mat_SeqAIJ *)fact->data;
  Mat_SeqAIJCUSPARSE           *Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
  CsrMatrix                    *Acsr;
  PetscInt                      m, nz;
  PetscBool                     flg;

  PetscFunctionBegin;
  if (PetscDefined(USE_DEBUG)) {
    PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
    PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
  }

  /* Copy A's value to fact */
  m  = fact->rmap->n;
  nz = aij->nz;
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  Acsr = (CsrMatrix *)Acusp->mat->mat;
  PetscCallCUDA(cudaMemcpyAsync(fs->csrVal, Acsr->values->data().get(), sizeof(PetscScalar) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));

  /* Factorize fact inplace */
  if (m)
    PetscCallCUSPARSE(cusparseXcsrilu02(fs->handle, m, nz, /* cusparseXcsrilu02 errors out with empty matrices (m=0) */
                                        fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ilu0Info_M, fs->policy_M, fs->factBuffer_M));
  if (PetscDefined(USE_DEBUG)) {
    int              numerical_zero;
    cusparseStatus_t status;
    status = cusparseXcsrilu02_zeroPivot(fs->handle, fs->ilu0Info_M, &numerical_zero);
    PetscAssert(CUSPARSE_STATUS_ZERO_PIVOT != status, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "Numerical zero pivot detected in csrilu02: A(%d,%d) is zero", numerical_zero, numerical_zero);
  }

  /* cusparseSpSV_analysis() is numeric, i.e., it requires valid matrix values, therefore, we do it after cusparseXcsrilu02()
     See discussion at https://github.com/NVIDIA/CUDALibrarySamples/issues/78
  */
  PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, fs->spsvBuffer_L));

  PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, fs->spsvBuffer_U));

  /* L, U values have changed, reset the flag to indicate we need to redo cusparseSpSV_analysis() for transpose solve */
  fs->updatedTransposeSpSVAnalysis = PETSC_FALSE;

  fact->offloadmask            = PETSC_OFFLOAD_GPU;
  fact->ops->solve             = MatSolve_SeqAIJCUSPARSE_LU; // spMatDescr_L/U uses 32-bit indices, but cusparseSpSV_solve() supports both 32 and 64. The info is encoded in cusparseSpMatDescr_t.
  fact->ops->solvetranspose    = MatSolveTranspose_SeqAIJCUSPARSE_LU;
  fact->ops->matsolve          = NULL;
  fact->ops->matsolvetranspose = NULL;
  PetscCall(PetscLogGpuFlops(fs->numericFactFlops));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE_ILU0(Mat fact, Mat A, IS, IS, const MatFactorInfo *info)
{
  Mat_SeqAIJCUSPARSETriFactors *fs  = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
  Mat_SeqAIJ                   *aij = (Mat_SeqAIJ *)fact->data;
  PetscInt                      m, nz;

  PetscFunctionBegin;
  if (PetscDefined(USE_DEBUG)) {
    PetscInt  i;
    PetscBool flg, missing;

    PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
    PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
    PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Must be square matrix, rows %" PetscInt_FMT " columns %" PetscInt_FMT, A->rmap->n, A->cmap->n);
    PetscCall(MatMissingDiagonal(A, &missing, &i));
    PetscCheck(!missing, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is missing diagonal entry %" PetscInt_FMT, i);
  }

  /* Free the old stale stuff */
  PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&fs));

  /* Copy over A's meta data to fact. Note that we also allocated fact's i,j,a on host,
     but they will not be used. Allocate them just for easy debugging.
   */
  PetscCall(MatDuplicateNoCreate_SeqAIJ(fact, A, MAT_DO_NOT_COPY_VALUES, PETSC_TRUE /*malloc*/));

  fact->offloadmask            = PETSC_OFFLOAD_BOTH;
  fact->factortype             = MAT_FACTOR_ILU;
  fact->info.factor_mallocs    = 0;
  fact->info.fill_ratio_given  = info->fill;
  fact->info.fill_ratio_needed = 1.0;

  aij->row = NULL;
  aij->col = NULL;

  /* ====================================================================== */
  /* Copy A's i, j to fact and also allocate the value array of fact.       */
  /* We'll do in-place factorization on fact                                */
  /* ====================================================================== */
  const int *Ai, *Aj;

  m  = fact->rmap->n;
  nz = aij->nz;

  PetscCallCUDA(cudaMalloc((void **)&fs->csrRowPtr32, sizeof(*fs->csrRowPtr32) * (m + 1)));
  PetscCallCUDA(cudaMalloc((void **)&fs->csrColIdx32, sizeof(*fs->csrColIdx32) * nz));
  PetscCallCUDA(cudaMalloc((void **)&fs->csrVal, sizeof(*fs->csrVal) * nz));
  PetscCall(MatSeqAIJCUSPARSEGetIJ(A, PETSC_FALSE, &Ai, &Aj)); /* Do not use compressed Ai.  The returned Ai, Aj are 32-bit */
  PetscCallCUDA(cudaMemcpyAsync(fs->csrRowPtr32, Ai, sizeof(*Ai) * (m + 1), cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
  PetscCallCUDA(cudaMemcpyAsync(fs->csrColIdx32, Aj, sizeof(*Aj) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));

  /* ====================================================================== */
  /* Create descriptors for M, L, U                                         */
  /* ====================================================================== */
  cusparseFillMode_t fillMode;
  cusparseDiagType_t diagType;

  PetscCallCUSPARSE(cusparseCreateMatDescr(&fs->matDescr_M));
  PetscCallCUSPARSE(cusparseSetMatIndexBase(fs->matDescr_M, CUSPARSE_INDEX_BASE_ZERO));
  PetscCallCUSPARSE(cusparseSetMatType(fs->matDescr_M, CUSPARSE_MATRIX_TYPE_GENERAL));

  /* https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
    cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
    assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
    all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
    assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
  */
  fillMode = CUSPARSE_FILL_MODE_LOWER;
  diagType = CUSPARSE_DIAG_TYPE_UNIT;
  PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_L, m, m, nz, fs->csrRowPtr32, fs->csrColIdx32, fs->csrVal, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
  PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
  PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));

  fillMode = CUSPARSE_FILL_MODE_UPPER;
  diagType = CUSPARSE_DIAG_TYPE_NON_UNIT;
  PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_U, m, m, nz, fs->csrRowPtr32, fs->csrColIdx32, fs->csrVal, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
  PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
  PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_U, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));

  /* ========================================================================= */
  /* Query buffer sizes for csrilu0, SpSV and allocate buffers                 */
  /* ========================================================================= */
  PetscCallCUSPARSE(cusparseCreateCsrilu02Info(&fs->ilu0Info_M));
  if (m)
    PetscCallCUSPARSE(cusparseXcsrilu02_bufferSize(fs->handle, m, nz, /* cusparseXcsrilu02 errors out with empty matrices (m=0) */
                                                   fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ilu0Info_M, &fs->factBufferSize_M));

  PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(PetscScalar) * m));
  PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(PetscScalar) * m));

  PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
  PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));

  PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_L));
  PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, &fs->spsvBufferSize_L));

  PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_U));
  PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_U, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_U, &fs->spsvBufferSize_U));

  /* From my experiment with the example at https://github.com/NVIDIA/CUDALibrarySamples/tree/master/cuSPARSE/bicgstab,
     and discussion at https://github.com/NVIDIA/CUDALibrarySamples/issues/77,
     spsvBuffer_L/U can not be shared (i.e., the same) for our case, but factBuffer_M can share with either of spsvBuffer_L/U.
     To save memory, we make factBuffer_M share with the bigger of spsvBuffer_L/U.
   */
  if (fs->spsvBufferSize_L > fs->spsvBufferSize_U) {
    PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_L, (size_t)fs->factBufferSize_M)));
    fs->spsvBuffer_L = fs->factBuffer_M;
    PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_U, fs->spsvBufferSize_U));
  } else {
    PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_U, (size_t)fs->factBufferSize_M)));
    fs->spsvBuffer_U = fs->factBuffer_M;
    PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_L, fs->spsvBufferSize_L));
  }

  /* ========================================================================== */
  /* Perform analysis of ilu0 on M, SpSv on L and U                             */
  /* The lower(upper) triangular part of M has the same sparsity pattern as L(U)*/
  /* ========================================================================== */
  int              structural_zero;
  cusparseStatus_t status;

  fs->policy_M = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
  if (m)
    PetscCallCUSPARSE(cusparseXcsrilu02_analysis(fs->handle, m, nz, /* cusparseXcsrilu02 errors out with empty matrices (m=0) */
                                                 fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ilu0Info_M, fs->policy_M, fs->factBuffer_M));
  if (PetscDefined(USE_DEBUG)) {
    /* Function cusparseXcsrilu02_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done. */
    status = cusparseXcsrilu02_zeroPivot(fs->handle, fs->ilu0Info_M, &structural_zero);
    PetscCheck(CUSPARSE_STATUS_ZERO_PIVOT != status, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "Structural zero pivot detected in csrilu02: A(%d,%d) is missing", structural_zero, structural_zero);
  }

  /* Estimate FLOPs of the numeric factorization */
  {
    Mat_SeqAIJ    *Aseq = (Mat_SeqAIJ *)A->data;
    PetscInt      *Ai, *Adiag, nzRow, nzLeft;
    PetscLogDouble flops = 0.0;

    PetscCall(MatMarkDiagonal_SeqAIJ(A));
    Ai    = Aseq->i;
    Adiag = Aseq->diag;
    for (PetscInt i = 0; i < m; i++) {
      if (Ai[i] < Adiag[i] && Adiag[i] < Ai[i + 1]) { /* There are nonzeros left to the diagonal of row i */
        nzRow  = Ai[i + 1] - Ai[i];
        nzLeft = Adiag[i] - Ai[i];
        /* We want to eliminate nonzeros left to the diagonal one by one. Assume each time, nonzeros right
          and include the eliminated one will be updated, which incurs a multiplication and an addition.
        */
        nzLeft = (nzRow - 1) / 2;
        flops += nzLeft * (2.0 * nzRow - nzLeft + 1);
      }
    }
    fs->numericFactFlops = flops;
  }
  fact->ops->lufactornumeric = MatILUFactorNumeric_SeqAIJCUSPARSE_ILU0;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSolve_SeqAIJCUSPARSE_ICC0(Mat fact, Vec b, Vec x)
{
  Mat_SeqAIJCUSPARSETriFactors *fs  = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
  Mat_SeqAIJ                   *aij = (Mat_SeqAIJ *)fact->data;
  const PetscScalar            *barray;
  PetscScalar                  *xarray;

  PetscFunctionBegin;
  PetscCall(VecCUDAGetArrayWrite(x, &xarray));
  PetscCall(VecCUDAGetArrayRead(b, &barray));
  PetscCall(PetscLogGpuTimeBegin());

  /* Solve L*y = b */
  PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, (void *)barray));
  PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_Y, fs->Y));
  PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, /* L Y = X */
                                       fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L));

  /* Solve Lt*x = y */
  PetscCallCUSPARSE(cusparseDnVecSetValues(fs->dnVecDescr_X, xarray));
  PetscCallCUSPARSE(cusparseSpSV_solve(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, /* Lt X = Y */
                                       fs->dnVecDescr_Y, fs->dnVecDescr_X, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Lt));

  PetscCall(VecCUDARestoreArrayRead(b, &barray));
  PetscCall(VecCUDARestoreArrayWrite(x, &xarray));

  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogGpuFlops(2.0 * aij->nz - fact->rmap->n));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatICCFactorNumeric_SeqAIJCUSPARSE_ICC0(Mat fact, Mat A, const MatFactorInfo *)
{
  Mat_SeqAIJCUSPARSETriFactors *fs    = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
  Mat_SeqAIJ                   *aij   = (Mat_SeqAIJ *)fact->data;
  Mat_SeqAIJCUSPARSE           *Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
  CsrMatrix                    *Acsr;
  PetscInt                      m, nz;
  PetscBool                     flg;

  PetscFunctionBegin;
  if (PetscDefined(USE_DEBUG)) {
    PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
    PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
  }

  /* Copy A's value to fact */
  m  = fact->rmap->n;
  nz = aij->nz;
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  Acsr = (CsrMatrix *)Acusp->mat->mat;
  PetscCallCUDA(cudaMemcpyAsync(fs->csrVal, Acsr->values->data().get(), sizeof(PetscScalar) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));

  /* Factorize fact inplace */
  /* https://docs.nvidia.com/cuda/cusparse/index.html#csric02_solve
     Function csric02() only takes the lower triangular part of matrix A to perform factorization.
     The matrix type must be CUSPARSE_MATRIX_TYPE_GENERAL, the fill mode and diagonal type are ignored,
     and the strictly upper triangular part is ignored and never touched. It does not matter if A is Hermitian or not.
     In other words, from the point of view of csric02() A is Hermitian and only the lower triangular part is provided.
   */
  if (m) PetscCallCUSPARSE(cusparseXcsric02(fs->handle, m, nz, fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ic0Info_M, fs->policy_M, fs->factBuffer_M));
  if (PetscDefined(USE_DEBUG)) {
    int              numerical_zero;
    cusparseStatus_t status;
    status = cusparseXcsric02_zeroPivot(fs->handle, fs->ic0Info_M, &numerical_zero);
    PetscAssert(CUSPARSE_STATUS_ZERO_PIVOT != status, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "Numerical zero pivot detected in csric02: A(%d,%d) is zero", numerical_zero, numerical_zero);
  }

  PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, fs->spsvBuffer_L));

  /* Note that cusparse reports this error if we use double and CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE
    ** On entry to cusparseSpSV_analysis(): conjugate transpose (opA) is not supported for matA data type, current -> CUDA_R_64F
  */
  PetscCallCUSPARSE(cusparseSpSV_analysis(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Lt, fs->spsvBuffer_Lt));

  fact->offloadmask            = PETSC_OFFLOAD_GPU;
  fact->ops->solve             = MatSolve_SeqAIJCUSPARSE_ICC0;
  fact->ops->solvetranspose    = MatSolve_SeqAIJCUSPARSE_ICC0;
  fact->ops->matsolve          = NULL;
  fact->ops->matsolvetranspose = NULL;
  PetscCall(PetscLogGpuFlops(fs->numericFactFlops));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE_ICC0(Mat fact, Mat A, IS, const MatFactorInfo *info)
{
  Mat_SeqAIJCUSPARSETriFactors *fs  = (Mat_SeqAIJCUSPARSETriFactors *)fact->spptr;
  Mat_SeqAIJ                   *aij = (Mat_SeqAIJ *)fact->data;
  PetscInt                      m, nz;

  PetscFunctionBegin;
  if (PetscDefined(USE_DEBUG)) {
    PetscInt  i;
    PetscBool flg, missing;

    PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
    PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Expected MATSEQAIJCUSPARSE, but input is %s", ((PetscObject)A)->type_name);
    PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Must be square matrix, rows %" PetscInt_FMT " columns %" PetscInt_FMT, A->rmap->n, A->cmap->n);
    PetscCall(MatMissingDiagonal(A, &missing, &i));
    PetscCheck(!missing, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is missing diagonal entry %" PetscInt_FMT, i);
  }

  /* Free the old stale stuff */
  PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&fs));

  /* Copy over A's meta data to fact. Note that we also allocated fact's i,j,a on host,
     but they will not be used. Allocate them just for easy debugging.
   */
  PetscCall(MatDuplicateNoCreate_SeqAIJ(fact, A, MAT_DO_NOT_COPY_VALUES, PETSC_TRUE /*malloc*/));

  fact->offloadmask            = PETSC_OFFLOAD_BOTH;
  fact->factortype             = MAT_FACTOR_ICC;
  fact->info.factor_mallocs    = 0;
  fact->info.fill_ratio_given  = info->fill;
  fact->info.fill_ratio_needed = 1.0;

  aij->row = NULL;
  aij->col = NULL;

  /* ====================================================================== */
  /* Copy A's i, j to fact and also allocate the value array of fact.       */
  /* We'll do in-place factorization on fact                                */
  /* ====================================================================== */
  const int *Ai, *Aj;

  m  = fact->rmap->n;
  nz = aij->nz;

  PetscCallCUDA(cudaMalloc((void **)&fs->csrRowPtr32, sizeof(*fs->csrRowPtr32) * (m + 1)));
  PetscCallCUDA(cudaMalloc((void **)&fs->csrColIdx32, sizeof(*fs->csrColIdx32) * nz));
  PetscCallCUDA(cudaMalloc((void **)&fs->csrVal, sizeof(PetscScalar) * nz));
  PetscCall(MatSeqAIJCUSPARSEGetIJ(A, PETSC_FALSE, &Ai, &Aj)); /* Do not use compressed Ai */
  PetscCallCUDA(cudaMemcpyAsync(fs->csrRowPtr32, Ai, sizeof(*Ai) * (m + 1), cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));
  PetscCallCUDA(cudaMemcpyAsync(fs->csrColIdx32, Aj, sizeof(*Aj) * nz, cudaMemcpyDeviceToDevice, PetscDefaultCudaStream));

  /* ====================================================================== */
  /* Create mat descriptors for M, L                                        */
  /* ====================================================================== */
  cusparseFillMode_t fillMode;
  cusparseDiagType_t diagType;

  PetscCallCUSPARSE(cusparseCreateMatDescr(&fs->matDescr_M));
  PetscCallCUSPARSE(cusparseSetMatIndexBase(fs->matDescr_M, CUSPARSE_INDEX_BASE_ZERO));
  PetscCallCUSPARSE(cusparseSetMatType(fs->matDescr_M, CUSPARSE_MATRIX_TYPE_GENERAL));

  /* https://docs.nvidia.com/cuda/cusparse/index.html#cusparseDiagType_t
    cusparseDiagType_t: This type indicates if the matrix diagonal entries are unity. The diagonal elements are always
    assumed to be present, but if CUSPARSE_DIAG_TYPE_UNIT is passed to an API routine, then the routine assumes that
    all diagonal entries are unity and will not read or modify those entries. Note that in this case the routine
    assumes the diagonal entries are equal to one, regardless of what those entries are actually set to in memory.
  */
  fillMode = CUSPARSE_FILL_MODE_LOWER;
  diagType = CUSPARSE_DIAG_TYPE_NON_UNIT;
  PetscCallCUSPARSE(cusparseCreateCsr(&fs->spMatDescr_L, m, m, nz, fs->csrRowPtr32, fs->csrColIdx32, fs->csrVal, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype));
  PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_FILL_MODE, &fillMode, sizeof(fillMode)));
  PetscCallCUSPARSE(cusparseSpMatSetAttribute(fs->spMatDescr_L, CUSPARSE_SPMAT_DIAG_TYPE, &diagType, sizeof(diagType)));

  /* ========================================================================= */
  /* Query buffer sizes for csric0, SpSV of L and Lt, and allocate buffers     */
  /* ========================================================================= */
  PetscCallCUSPARSE(cusparseCreateCsric02Info(&fs->ic0Info_M));
  if (m) PetscCallCUSPARSE(cusparseXcsric02_bufferSize(fs->handle, m, nz, fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ic0Info_M, &fs->factBufferSize_M));

  PetscCallCUDA(cudaMalloc((void **)&fs->X, sizeof(PetscScalar) * m));
  PetscCallCUDA(cudaMalloc((void **)&fs->Y, sizeof(PetscScalar) * m));

  PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_X, m, fs->X, cusparse_scalartype));
  PetscCallCUSPARSE(cusparseCreateDnVec(&fs->dnVecDescr_Y, m, fs->Y, cusparse_scalartype));

  PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_L));
  PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_L, &fs->spsvBufferSize_L));

  PetscCallCUSPARSE(cusparseSpSV_createDescr(&fs->spsvDescr_Lt));
  PetscCallCUSPARSE(cusparseSpSV_bufferSize(fs->handle, CUSPARSE_OPERATION_TRANSPOSE, &PETSC_CUSPARSE_ONE, fs->spMatDescr_L, fs->dnVecDescr_X, fs->dnVecDescr_Y, cusparse_scalartype, CUSPARSE_SPSV_ALG_DEFAULT, fs->spsvDescr_Lt, &fs->spsvBufferSize_Lt));

  /* To save device memory, we make the factorization buffer share with one of the solver buffer.
     See also comments in MatILUFactorSymbolic_SeqAIJCUSPARSE_ILU0().
   */
  if (fs->spsvBufferSize_L > fs->spsvBufferSize_Lt) {
    PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_L, (size_t)fs->factBufferSize_M)));
    fs->spsvBuffer_L = fs->factBuffer_M;
    PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_Lt, fs->spsvBufferSize_Lt));
  } else {
    PetscCallCUDA(cudaMalloc((void **)&fs->factBuffer_M, PetscMax(fs->spsvBufferSize_Lt, (size_t)fs->factBufferSize_M)));
    fs->spsvBuffer_Lt = fs->factBuffer_M;
    PetscCallCUDA(cudaMalloc((void **)&fs->spsvBuffer_L, fs->spsvBufferSize_L));
  }

  /* ========================================================================== */
  /* Perform analysis of ic0 on M                                               */
  /* The lower triangular part of M has the same sparsity pattern as L          */
  /* ========================================================================== */
  int              structural_zero;
  cusparseStatus_t status;

  fs->policy_M = CUSPARSE_SOLVE_POLICY_USE_LEVEL;
  if (m) PetscCallCUSPARSE(cusparseXcsric02_analysis(fs->handle, m, nz, fs->matDescr_M, fs->csrVal, fs->csrRowPtr32, fs->csrColIdx32, fs->ic0Info_M, fs->policy_M, fs->factBuffer_M));
  if (PetscDefined(USE_DEBUG)) {
    /* Function cusparseXcsric02_zeroPivot() is a blocking call. It calls cudaDeviceSynchronize() to make sure all previous kernels are done. */
    status = cusparseXcsric02_zeroPivot(fs->handle, fs->ic0Info_M, &structural_zero);
    PetscCheck(CUSPARSE_STATUS_ZERO_PIVOT != status, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "Structural zero pivot detected in csric02: A(%d,%d) is missing", structural_zero, structural_zero);
  }

  /* Estimate FLOPs of the numeric factorization */
  {
    Mat_SeqAIJ    *Aseq = (Mat_SeqAIJ *)A->data;
    PetscInt      *Ai, nzRow, nzLeft;
    PetscLogDouble flops = 0.0;

    Ai = Aseq->i;
    for (PetscInt i = 0; i < m; i++) {
      nzRow = Ai[i + 1] - Ai[i];
      if (nzRow > 1) {
        /* We want to eliminate nonzeros left to the diagonal one by one. Assume each time, nonzeros right
          and include the eliminated one will be updated, which incurs a multiplication and an addition.
        */
        nzLeft = (nzRow - 1) / 2;
        flops += nzLeft * (2.0 * nzRow - nzLeft + 1);
      }
    }
    fs->numericFactFlops = flops;
  }
  fact->ops->choleskyfactornumeric = MatICCFactorNumeric_SeqAIJCUSPARSE_ICC0;
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

static PetscErrorCode MatLUFactorNumeric_SeqAIJCUSPARSE(Mat B, Mat A, const MatFactorInfo *info)
{
  // use_cpu_solve is a field in Mat_SeqAIJCUSPARSE. B, a factored matrix, uses Mat_SeqAIJCUSPARSETriFactors.
  Mat_SeqAIJCUSPARSE *cusparsestruct = static_cast<Mat_SeqAIJCUSPARSE *>(A->spptr);

  PetscFunctionBegin;
  PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
  PetscCall(MatLUFactorNumeric_SeqAIJ(B, A, info));
  B->offloadmask = PETSC_OFFLOAD_CPU;

  if (!cusparsestruct->use_cpu_solve) {
#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
    B->ops->solve          = MatSolve_SeqAIJCUSPARSE_LU;
    B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_LU;
#else
    /* determine which version of MatSolve needs to be used. */
    Mat_SeqAIJ *b     = (Mat_SeqAIJ *)B->data;
    IS          isrow = b->row, iscol = b->col;
    PetscBool   row_identity, col_identity;

    PetscCall(ISIdentity(isrow, &row_identity));
    PetscCall(ISIdentity(iscol, &col_identity));
    if (row_identity && col_identity) {
      B->ops->solve          = MatSolve_SeqAIJCUSPARSE_NaturalOrdering;
      B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE_NaturalOrdering;
    } else {
      B->ops->solve          = MatSolve_SeqAIJCUSPARSE;
      B->ops->solvetranspose = MatSolveTranspose_SeqAIJCUSPARSE;
    }
#endif
  }
  B->ops->matsolve          = NULL;
  B->ops->matsolvetranspose = NULL;

  /* get the triangular factors */
  if (!cusparsestruct->use_cpu_solve) PetscCall(MatSeqAIJCUSPARSEILUAnalysisAndCopyToGPU(B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatLUFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
{
  Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = static_cast<Mat_SeqAIJCUSPARSETriFactors *>(B->spptr);

  PetscFunctionBegin;
  PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
  PetscCall(MatLUFactorSymbolic_SeqAIJ(B, A, isrow, iscol, info));
  B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJCUSPARSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatILUFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
{
  Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)B->spptr;

  PetscFunctionBegin;
#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
  PetscBool row_identity = PETSC_FALSE, col_identity = PETSC_FALSE;
  if (cusparseTriFactors->factorizeOnDevice) {
    PetscCall(ISIdentity(isrow, &row_identity));
    PetscCall(ISIdentity(iscol, &col_identity));
  }
  if (!info->levels && row_identity && col_identity) {
    PetscCall(MatILUFactorSymbolic_SeqAIJCUSPARSE_ILU0(B, A, isrow, iscol, info));
  } else
#endif
  {
    PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
    PetscCall(MatILUFactorSymbolic_SeqAIJ(B, A, isrow, iscol, info));
    B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJCUSPARSE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatICCFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS perm, const MatFactorInfo *info)
{
  Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)B->spptr;

  PetscFunctionBegin;
#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
  PetscBool perm_identity = PETSC_FALSE;
  if (cusparseTriFactors->factorizeOnDevice) PetscCall(ISIdentity(perm, &perm_identity));
  if (!info->levels && perm_identity) {
    PetscCall(MatICCFactorSymbolic_SeqAIJCUSPARSE_ICC0(B, A, perm, info));
  } else
#endif
  {
    PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
    PetscCall(MatICCFactorSymbolic_SeqAIJ(B, A, perm, info));
    B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJCUSPARSE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJCUSPARSE(Mat B, Mat A, IS perm, const MatFactorInfo *info)
{
  Mat_SeqAIJCUSPARSETriFactors *cusparseTriFactors = (Mat_SeqAIJCUSPARSETriFactors *)B->spptr;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(&cusparseTriFactors));
  PetscCall(MatCholeskyFactorSymbolic_SeqAIJ(B, A, perm, info));
  B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJCUSPARSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

/*MC
  MATSOLVERCUSPARSE = "cusparse" - A matrix type providing triangular solvers for seq matrices
  on a single GPU of type, `MATSEQAIJCUSPARSE`. 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: [](ch_matrices), `Mat`, `MATSEQAIJCUSPARSE`, `PCFactorSetMatSolverType()`, `MatSolverType`, `MatCreateSeqAIJCUSPARSE()`,
          `MATAIJCUSPARSE`, `MatCreateAIJCUSPARSE()`, `MatCUSPARSESetFormat()`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
M*/

PETSC_EXTERN PetscErrorCode MatGetFactor_seqaijcusparse_cusparse(Mat A, MatFactorType ftype, Mat *B)
{
  PetscInt  n = A->rmap->n;
  PetscBool factOnDevice, factOnHost;
  char     *prefix;
  char      factPlace[32] = "device"; /* the default */

  PetscFunctionBegin;
  PetscCall(MatCreate(PetscObjectComm((PetscObject)A), B));
  PetscCall(MatSetSizes(*B, n, n, n, n));
  (*B)->factortype = ftype; // factortype makes MatSetType() allocate spptr of type Mat_SeqAIJCUSPARSETriFactors
  PetscCall(MatSetType(*B, MATSEQAIJCUSPARSE));

  prefix = (*B)->factorprefix ? (*B)->factorprefix : ((PetscObject)A)->prefix;
  PetscOptionsBegin(PetscObjectComm((PetscObject)*B), prefix, "MatGetFactor", "Mat");
  PetscCall(PetscOptionsString("-mat_factor_bind_factorization", "Do matrix factorization on host or device when possible", "MatGetFactor", NULL, factPlace, sizeof(factPlace), NULL));
  PetscOptionsEnd();
  PetscCall(PetscStrcasecmp("device", factPlace, &factOnDevice));
  PetscCall(PetscStrcasecmp("host", factPlace, &factOnHost));
  PetscCheck(factOnDevice || factOnHost, PetscObjectComm((PetscObject)*B), PETSC_ERR_ARG_OUTOFRANGE, "Wrong option %s to -mat_factor_bind_factorization <string>. Only host and device are allowed", factPlace);
  ((Mat_SeqAIJCUSPARSETriFactors *)(*B)->spptr)->factorizeOnDevice = factOnDevice;

  if (A->boundtocpu && A->bindingpropagates) PetscCall(MatBindToCPU(*B, PETSC_TRUE));
  if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
    PetscCall(MatSetBlockSizesFromMats(*B, A, A));
    if (!A->boundtocpu) {
      (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJCUSPARSE;
      (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJCUSPARSE;
    } else {
      (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
      (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqAIJ;
    }
    PetscCall(PetscStrallocpy(MATORDERINGND, (char **)&(*B)->preferredordering[MAT_FACTOR_LU]));
    PetscCall(PetscStrallocpy(MATORDERINGNATURAL, (char **)&(*B)->preferredordering[MAT_FACTOR_ILU]));
    PetscCall(PetscStrallocpy(MATORDERINGNATURAL, (char **)&(*B)->preferredordering[MAT_FACTOR_ILUDT]));
  } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
    if (!A->boundtocpu) {
      (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJCUSPARSE;
      (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJCUSPARSE;
    } else {
      (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqAIJ;
      (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
    }
    PetscCall(PetscStrallocpy(MATORDERINGND, (char **)&(*B)->preferredordering[MAT_FACTOR_CHOLESKY]));
    PetscCall(PetscStrallocpy(MATORDERINGNATURAL, (char **)&(*B)->preferredordering[MAT_FACTOR_ICC]));
  } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor type not supported for CUSPARSE Matrix Types");

  PetscCall(MatSeqAIJSetPreallocation(*B, MAT_SKIP_ALLOCATION, NULL));
  (*B)->canuseordering = PETSC_TRUE;
  PetscCall(PetscObjectComposeFunction((PetscObject)*B, "MatFactorGetSolverType_C", MatFactorGetSolverType_seqaij_cusparse));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJCUSPARSECopyFromGPU(Mat A)
{
  Mat_SeqAIJ         *a    = (Mat_SeqAIJ *)A->data;
  Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
  Mat_SeqAIJCUSPARSETriFactors *fs = (Mat_SeqAIJCUSPARSETriFactors *)A->spptr;
#endif

  PetscFunctionBegin;
  if (A->offloadmask == PETSC_OFFLOAD_GPU) {
    PetscCall(PetscLogEventBegin(MAT_CUSPARSECopyFromGPU, A, 0, 0, 0));
    if (A->factortype == MAT_FACTOR_NONE) {
      CsrMatrix *matrix = (CsrMatrix *)cusp->mat->mat;
      PetscCallCUDA(cudaMemcpy(a->a, matrix->values->data().get(), a->nz * sizeof(PetscScalar), cudaMemcpyDeviceToHost));
    }
#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
    else if (fs->csrVal) {
      /* We have a factorized matrix on device and are able to copy it to host */
      PetscCallCUDA(cudaMemcpy(a->a, fs->csrVal, a->nz * sizeof(PetscScalar), cudaMemcpyDeviceToHost));
    }
#endif
    else
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for copying this type of factorized matrix from device to host");
    PetscCall(PetscLogGpuToCpu(a->nz * sizeof(PetscScalar)));
    PetscCall(PetscLogEventEnd(MAT_CUSPARSECopyFromGPU, A, 0, 0, 0));
    A->offloadmask = PETSC_OFFLOAD_BOTH;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJGetArray_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
{
  PetscFunctionBegin;
  PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
  *array = ((Mat_SeqAIJ *)A->data)->a;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJRestoreArray_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
{
  PetscFunctionBegin;
  A->offloadmask = PETSC_OFFLOAD_CPU;
  *array         = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJGetArrayRead_SeqAIJCUSPARSE(Mat A, const PetscScalar *array[])
{
  PetscFunctionBegin;
  PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));
  *array = ((Mat_SeqAIJ *)A->data)->a;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJRestoreArrayRead_SeqAIJCUSPARSE(Mat, const PetscScalar *array[])
{
  PetscFunctionBegin;
  *array = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJGetArrayWrite_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
{
  PetscFunctionBegin;
  *array = ((Mat_SeqAIJ *)A->data)->a;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJRestoreArrayWrite_SeqAIJCUSPARSE(Mat A, PetscScalar *array[])
{
  PetscFunctionBegin;
  A->offloadmask = PETSC_OFFLOAD_CPU;
  *array         = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJGetCSRAndMemType_SeqAIJCUSPARSE(Mat A, const PetscInt **i, const PetscInt **j, PetscScalar **a, PetscMemType *mtype)
{
  Mat_SeqAIJCUSPARSE *cusp;
  CsrMatrix          *matrix;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  PetscCheck(A->factortype == MAT_FACTOR_NONE, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
  cusp = static_cast<Mat_SeqAIJCUSPARSE *>(A->spptr);
  PetscCheck(cusp != NULL, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "cusp is NULL");
  matrix = (CsrMatrix *)cusp->mat->mat;

  if (i) {
#if !defined(PETSC_USE_64BIT_INDICES)
    *i = matrix->row_offsets->data().get();
#else
    SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSparse does not supported 64-bit indices");
#endif
  }
  if (j) {
#if !defined(PETSC_USE_64BIT_INDICES)
    *j = matrix->column_indices->data().get();
#else
    SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSparse does not supported 64-bit indices");
#endif
  }
  if (a) *a = matrix->values->data().get();
  if (mtype) *mtype = PETSC_MEMTYPE_CUDA;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN 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;
  cusparseStatus_t              stat;
  PetscBool                     both = PETSC_TRUE;

  PetscFunctionBegin;
  PetscCheck(!A->boundtocpu, PETSC_COMM_SELF, PETSC_ERR_GPU, "Cannot copy to GPU");
  if (A->offloadmask == PETSC_OFFLOAD_UNALLOCATED || A->offloadmask == PETSC_OFFLOAD_CPU) {
    if (A->nonzerostate == cusparsestruct->nonzerostate && cusparsestruct->format == MAT_CUSPARSE_CSR) { /* Copy values only */
      CsrMatrix *matrix;
      matrix = (CsrMatrix *)cusparsestruct->mat->mat;

      PetscCheck(!a->nz || a->a, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CSR values");
      PetscCall(PetscLogEventBegin(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
      matrix->values->assign(a->a, a->a + a->nz);
      PetscCallCUDA(WaitForCUDA());
      PetscCall(PetscLogCpuToGpu(a->nz * sizeof(PetscScalar)));
      PetscCall(PetscLogEventEnd(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
      PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
    } else {
      PetscInt nnz;
      PetscCall(PetscLogEventBegin(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
      PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusparsestruct->mat, cusparsestruct->format));
      PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_TRUE));
      delete cusparsestruct->workVector;
      delete cusparsestruct->rowoffsets_gpu;
      cusparsestruct->workVector     = NULL;
      cusparsestruct->rowoffsets_gpu = NULL;
      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;
        }
        PetscCheck(ii, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CSR row data");
        if (!a->a) {
          nnz  = ii[m];
          both = PETSC_FALSE;
        } else nnz = a->nz;
        PetscCheck(!nnz || a->j, PETSC_COMM_SELF, PETSC_ERR_GPU, "Missing CSR column data");

        /* create cusparse matrix */
        cusparsestruct->nrows = m;
        matstruct             = new Mat_SeqAIJCUSPARSEMultStruct;
        PetscCallCUSPARSE(cusparseCreateMatDescr(&matstruct->descr));
        PetscCallCUSPARSE(cusparseSetMatIndexBase(matstruct->descr, CUSPARSE_INDEX_BASE_ZERO));
        PetscCallCUSPARSE(cusparseSetMatType(matstruct->descr, CUSPARSE_MATRIX_TYPE_GENERAL));

        PetscCallCUDA(cudaMalloc((void **)&matstruct->alpha_one, sizeof(PetscScalar)));
        PetscCallCUDA(cudaMalloc((void **)&matstruct->beta_zero, sizeof(PetscScalar)));
        PetscCallCUDA(cudaMalloc((void **)&matstruct->beta_one, sizeof(PetscScalar)));
        PetscCallCUDA(cudaMemcpy(matstruct->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
        PetscCallCUDA(cudaMemcpy(matstruct->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
        PetscCallCUDA(cudaMemcpy(matstruct->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
        PetscCallCUSPARSE(cusparseSetPointerMode(cusparsestruct->handle, CUSPARSE_POINTER_MODE_DEVICE));

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

          mat->column_indices = new THRUSTINTARRAY32(nnz);
          mat->column_indices->assign(a->j, a->j + nnz);

          mat->values = new THRUSTARRAY(nnz);
          if (a->a) mat->values->assign(a->a, a->a + nnz);

          /* assign the pointer */
          matstruct->mat = mat;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
          if (mat->num_rows) { /* cusparse errors on empty matrices! */
            stat = cusparseCreateCsr(&matstruct->matDescr, mat->num_rows, mat->num_cols, mat->num_entries, mat->row_offsets->data().get(), mat->column_indices->data().get(), mat->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, /* row offset, col idx types due to THRUSTINTARRAY32 */
                                     CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
            PetscCallCUSPARSE(stat);
          }
#endif
        } else if (cusparsestruct->format == MAT_CUSPARSE_ELL || cusparsestruct->format == MAT_CUSPARSE_HYB) {
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
          SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
#else
          CsrMatrix *mat   = new CsrMatrix;
          mat->num_rows    = m;
          mat->num_cols    = A->cmap->n;
          mat->num_entries = nnz;
          mat->row_offsets = new THRUSTINTARRAY32(m + 1);
          mat->row_offsets->assign(ii, ii + m + 1);

          mat->column_indices = new THRUSTINTARRAY32(nnz);
          mat->column_indices->assign(a->j, a->j + nnz);

          mat->values = new THRUSTARRAY(nnz);
          if (a->a) mat->values->assign(a->a, a->a + nnz);

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

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

        /* 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;
        }
        PetscCall(PetscLogCpuToGpu(((m + 1) + (a->nz)) * sizeof(int) + tmp * sizeof(PetscInt) + (3 + (a->nz)) * sizeof(PetscScalar)));

        /* assign the pointer */
        cusparsestruct->mat = matstruct;
      } catch (char *ex) {
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
      }
      PetscCallCUDA(WaitForCUDA());
      PetscCall(PetscLogEventEnd(MAT_CUSPARSECopyToGPU, A, 0, 0, 0));
      cusparsestruct->nonzerostate = A->nonzerostate;
    }
    if (both) A->offloadmask = PETSC_OFFLOAD_BOTH;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

struct VecCUDAEquals {
  template <typename Tuple>
  __host__ __device__ void operator()(Tuple 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);
  }
};

struct MatMatCusparse {
  PetscBool      cisdense;
  PetscScalar   *Bt;
  Mat            X;
  PetscBool      reusesym; /* Cusparse does not have split symbolic and numeric phases for sparse matmat operations */
  PetscLogDouble flops;
  CsrMatrix     *Bcsr;

#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  cusparseSpMatDescr_t matSpBDescr;
  PetscBool            initialized; /* C = alpha op(A) op(B) + beta C */
  cusparseDnMatDescr_t matBDescr;
  cusparseDnMatDescr_t matCDescr;
  PetscInt             Blda, Clda; /* Record leading dimensions of B and C here to detect changes*/
  #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
  void *dBuffer4;
  void *dBuffer5;
  #endif
  size_t                mmBufferSize;
  void                 *mmBuffer;
  void                 *mmBuffer2; /* SpGEMM WorkEstimation buffer */
  cusparseSpGEMMDescr_t spgemmDesc;
#endif
};

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

  PetscFunctionBegin;
  PetscCallCUDA(cudaFree(mmdata->Bt));
  delete mmdata->Bcsr;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  if (mmdata->matSpBDescr) PetscCallCUSPARSE(cusparseDestroySpMat(mmdata->matSpBDescr));
  if (mmdata->matBDescr) PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matBDescr));
  if (mmdata->matCDescr) PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matCDescr));
  if (mmdata->spgemmDesc) PetscCallCUSPARSE(cusparseSpGEMM_destroyDescr(mmdata->spgemmDesc));
  #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
  if (mmdata->dBuffer4) PetscCallCUDA(cudaFree(mmdata->dBuffer4));
  if (mmdata->dBuffer5) PetscCallCUDA(cudaFree(mmdata->dBuffer5));
  #endif
  if (mmdata->mmBuffer) PetscCallCUDA(cudaFree(mmdata->mmBuffer));
  if (mmdata->mmBuffer2) PetscCallCUDA(cudaFree(mmdata->mmBuffer2));
#endif
  PetscCall(MatDestroy(&mmdata->X));
  PetscCall(PetscFree(data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

#include <../src/mat/impls/dense/seq/dense.h> // MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Internal()

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

  PetscFunctionBegin;
  MatCheckProduct(C, 1);
  PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data empty");
  mmdata = (MatMatCusparse *)product->data;
  A      = product->A;
  B      = product->B;
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "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 */
  PetscCheck(!A->boundtocpu, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Cannot bind to CPU a CUSPARSE matrix between MatProductSymbolic and MatProductNumeric phases");
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  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;
    n   = B->cmap->n;
    break;
  case MATPRODUCT_AtB:
    if (!A->form_explicit_transpose) {
      mat = cusp->mat;
      opA = CUSPARSE_OPERATION_TRANSPOSE;
    } else {
      PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
      mat = cusp->matTranspose;
      opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
    }
    m = A->cmap->n;
    n = B->cmap->n;
    break;
  case MATPRODUCT_ABt:
  case MATPRODUCT_RARt:
    mat = cusp->mat;
    opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
    m   = A->rmap->n;
    n   = B->rmap->n;
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
  }
  PetscCheck(mat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing Mat_SeqAIJCUSPARSEMultStruct");
  csrmat = (CsrMatrix *)mat->mat;
  /* if the user passed a CPU matrix, copy the data to the GPU */
  PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQDENSECUDA, &biscuda));
  if (!biscuda) PetscCall(MatConvert(B, MATSEQDENSECUDA, MAT_INPLACE_MATRIX, &B));
  PetscCall(MatDenseGetArrayReadAndMemType(B, &barray, nullptr));

  PetscCall(MatDenseGetLDA(B, &blda));
  if (product->type == MATPRODUCT_RARt || product->type == MATPRODUCT_PtAP) {
    PetscCall(MatDenseGetArrayWriteAndMemType(mmdata->X, &carray, nullptr));
    PetscCall(MatDenseGetLDA(mmdata->X, &clda));
  } else {
    PetscCall(MatDenseGetArrayWriteAndMemType(C, &carray, nullptr));
    PetscCall(MatDenseGetLDA(C, &clda));
  }

  PetscCall(PetscLogGpuTimeBegin());
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  cusparseOperation_t opB = (product->type == MATPRODUCT_ABt || product->type == MATPRODUCT_RARt) ? CUSPARSE_OPERATION_TRANSPOSE : CUSPARSE_OPERATION_NON_TRANSPOSE;
  /* (re)allocate mmBuffer if not initialized or LDAs are different */
  if (!mmdata->initialized || mmdata->Blda != blda || mmdata->Clda != clda) {
    size_t mmBufferSize;
    if (mmdata->initialized && mmdata->Blda != blda) {
      PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matBDescr));
      mmdata->matBDescr = NULL;
    }
    if (!mmdata->matBDescr) {
      PetscCallCUSPARSE(cusparseCreateDnMat(&mmdata->matBDescr, B->rmap->n, B->cmap->n, blda, (void *)barray, cusparse_scalartype, CUSPARSE_ORDER_COL));
      mmdata->Blda = blda;
    }

    if (mmdata->initialized && mmdata->Clda != clda) {
      PetscCallCUSPARSE(cusparseDestroyDnMat(mmdata->matCDescr));
      mmdata->matCDescr = NULL;
    }
    if (!mmdata->matCDescr) { /* matCDescr is for C or mmdata->X */
      PetscCallCUSPARSE(cusparseCreateDnMat(&mmdata->matCDescr, m, n, clda, (void *)carray, cusparse_scalartype, CUSPARSE_ORDER_COL));
      mmdata->Clda = clda;
    }

    if (!mat->matDescr) {
      stat = cusparseCreateCsr(&mat->matDescr, csrmat->num_rows, csrmat->num_cols, csrmat->num_entries, csrmat->row_offsets->data().get(), csrmat->column_indices->data().get(), csrmat->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, /* row offset, col idx types due to THRUSTINTARRAY32 */
                               CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
      PetscCallCUSPARSE(stat);
    }
    stat = cusparseSpMM_bufferSize(cusp->handle, opA, opB, mat->alpha_one, mat->matDescr, mmdata->matBDescr, mat->beta_zero, mmdata->matCDescr, cusparse_scalartype, cusp->spmmAlg, &mmBufferSize);
    PetscCallCUSPARSE(stat);
    if ((mmdata->mmBuffer && mmdata->mmBufferSize < mmBufferSize) || !mmdata->mmBuffer) {
      PetscCallCUDA(cudaFree(mmdata->mmBuffer));
      PetscCallCUDA(cudaMalloc(&mmdata->mmBuffer, mmBufferSize));
      mmdata->mmBufferSize = mmBufferSize;
    }
    mmdata->initialized = PETSC_TRUE;
  } else {
    /* to be safe, always update pointers of the mats */
    PetscCallCUSPARSE(cusparseSpMatSetValues(mat->matDescr, csrmat->values->data().get()));
    PetscCallCUSPARSE(cusparseDnMatSetValues(mmdata->matBDescr, (void *)barray));
    PetscCallCUSPARSE(cusparseDnMatSetValues(mmdata->matCDescr, (void *)carray));
  }

  /* do cusparseSpMM, which supports transpose on B */
  stat = cusparseSpMM(cusp->handle, opA, opB, mat->alpha_one, mat->matDescr, mmdata->matBDescr, mat->beta_zero, mmdata->matCDescr, cusparse_scalartype, cusp->spmmAlg, mmdata->mmBuffer);
  PetscCallCUSPARSE(stat);
#else
  PetscInt k;
  /* cusparseXcsrmm does not support transpose on B */
  if (product->type == MATPRODUCT_ABt || product->type == MATPRODUCT_RARt) {
    cublasHandle_t cublasv2handle;
    cublasStatus_t cerr;

    PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
    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);
    PetscCallCUBLAS(cerr);
    blda = B->cmap->n;
    k    = B->cmap->n;
  } else {
    k = B->rmap->n;
  }

  /* perform the MatMat operation, op(A) is m x k, op(B) is k x n */
  stat = cusparse_csr_spmm(cusp->handle, opA, m, n, k, csrmat->num_entries, mat->alpha_one, mat->descr, 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);
  PetscCallCUSPARSE(stat);
#endif
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogGpuFlops(n * 2.0 * csrmat->num_entries));
  PetscCall(MatDenseRestoreArrayReadAndMemType(B, &barray));
  if (product->type == MATPRODUCT_RARt) {
    PetscCall(MatDenseRestoreArrayWriteAndMemType(mmdata->X, &carray));
    PetscCall(MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Internal(B, mmdata->X, C, PETSC_FALSE, PETSC_FALSE));
  } else if (product->type == MATPRODUCT_PtAP) {
    PetscCall(MatDenseRestoreArrayWriteAndMemType(mmdata->X, &carray));
    PetscCall(MatMatMultNumeric_SeqDenseCUDA_SeqDenseCUDA_Internal(B, mmdata->X, C, PETSC_TRUE, PETSC_FALSE));
  } else {
    PetscCall(MatDenseRestoreArrayWriteAndMemType(C, &carray));
  }
  if (mmdata->cisdense) PetscCall(MatConvert(C, MATSEQDENSE, MAT_INPLACE_MATRIX, &C));
  if (!biscuda) PetscCall(MatConvert(B, MATSEQDENSE, MAT_INPLACE_MATRIX, &B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBegin;
  MatCheckProduct(C, 1);
  PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data not empty");
  A = product->A;
  B = product->B;
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
  cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
  PetscCheck(cusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "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:
    SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
  }
  PetscCall(MatSetSizes(C, m, n, m, n));
  /* if C is of type MATSEQDENSE (CPU), perform the operation on the GPU and then copy on the CPU */
  PetscCall(PetscObjectTypeCompare((PetscObject)C, MATSEQDENSE, &cisdense));
  PetscCall(MatSetType(C, MATSEQDENSECUDA));

  /* product data */
  PetscCall(PetscNew(&mmdata));
  mmdata->cisdense = cisdense;
#if PETSC_PKG_CUDA_VERSION_LT(11, 0, 0)
  /* cusparseXcsrmm does not support transpose on B, so we allocate buffer to store B^T */
  if (product->type == MATPRODUCT_ABt || product->type == MATPRODUCT_RARt) PetscCallCUDA(cudaMalloc((void **)&mmdata->Bt, (size_t)B->rmap->n * (size_t)B->cmap->n * sizeof(PetscScalar)));
#endif
  /* for these products we need intermediate storage */
  if (product->type == MATPRODUCT_RARt || product->type == MATPRODUCT_PtAP) {
    PetscCall(MatCreate(PetscObjectComm((PetscObject)C), &mmdata->X));
    PetscCall(MatSetType(mmdata->X, MATSEQDENSECUDA));
    if (product->type == MATPRODUCT_RARt) { /* do not preallocate, since the first call to MatDenseCUDAGetArray will preallocate on the GPU for us */
      PetscCall(MatSetSizes(mmdata->X, A->rmap->n, B->rmap->n, A->rmap->n, B->rmap->n));
    } else {
      PetscCall(MatSetSizes(mmdata->X, A->rmap->n, B->cmap->n, A->rmap->n, B->cmap->n));
    }
  }
  C->product->data    = mmdata;
  C->product->destroy = MatDestroy_MatMatCusparse;

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

static PetscErrorCode MatProductNumeric_SeqAIJCUSPARSE_SeqAIJCUSPARSE(Mat C)
{
  Mat_Product                  *product = C->product;
  Mat                           A, B;
  Mat_SeqAIJCUSPARSE           *Acusp, *Bcusp, *Ccusp;
  Mat_SeqAIJ                   *c = (Mat_SeqAIJ *)C->data;
  Mat_SeqAIJCUSPARSEMultStruct *Amat, *Bmat, *Cmat;
  CsrMatrix                    *Acsr, *Bcsr, *Ccsr;
  PetscBool                     flg;
  cusparseStatus_t              stat;
  MatProductType                ptype;
  MatMatCusparse               *mmdata;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  cusparseSpMatDescr_t BmatSpDescr;
#endif
  cusparseOperation_t opA = CUSPARSE_OPERATION_NON_TRANSPOSE, opB = CUSPARSE_OPERATION_NON_TRANSPOSE; /* cuSPARSE spgemm doesn't support transpose yet */

  PetscFunctionBegin;
  MatCheckProduct(C, 1);
  PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data empty");
  PetscCall(PetscObjectTypeCompare((PetscObject)C, MATSEQAIJCUSPARSE, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for C of type %s", ((PetscObject)C)->type_name);
  mmdata = (MatMatCusparse *)C->product->data;
  A      = product->A;
  B      = product->B;
  if (mmdata->reusesym) { /* this happens when api_user is true, meaning that the matrix values have been already computed in the MatProductSymbolic phase */
    mmdata->reusesym = PETSC_FALSE;
    Ccusp            = (Mat_SeqAIJCUSPARSE *)C->spptr;
    PetscCheck(Ccusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
    Cmat = Ccusp->mat;
    PetscCheck(Cmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C mult struct for product type %s", MatProductTypes[C->product->type]);
    Ccsr = (CsrMatrix *)Cmat->mat;
    PetscCheck(Ccsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C CSR struct");
    goto finalize;
  }
  if (!c->nz) goto finalize;
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
  PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQAIJCUSPARSE, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for B of type %s", ((PetscObject)B)->type_name);
  PetscCheck(!A->boundtocpu, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONG, "Cannot bind to CPU a CUSPARSE matrix between MatProductSymbolic and MatProductNumeric phases");
  PetscCheck(!B->boundtocpu, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONG, "Cannot bind to CPU a CUSPARSE matrix between MatProductSymbolic and MatProductNumeric phases");
  Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
  Bcusp = (Mat_SeqAIJCUSPARSE *)B->spptr;
  Ccusp = (Mat_SeqAIJCUSPARSE *)C->spptr;
  PetscCheck(Acusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
  PetscCheck(Bcusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
  PetscCheck(Ccusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));

  ptype = product->type;
  if (A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
    ptype = MATPRODUCT_AB;
    PetscCheck(product->symbolic_used_the_fact_A_is_symmetric, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Symbolic should have been built using the fact that A is symmetric");
  }
  if (B->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_ABt) {
    ptype = MATPRODUCT_AB;
    PetscCheck(product->symbolic_used_the_fact_B_is_symmetric, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Symbolic should have been built using the fact that B is symmetric");
  }
  switch (ptype) {
  case MATPRODUCT_AB:
    Amat = Acusp->mat;
    Bmat = Bcusp->mat;
    break;
  case MATPRODUCT_AtB:
    Amat = Acusp->matTranspose;
    Bmat = Bcusp->mat;
    break;
  case MATPRODUCT_ABt:
    Amat = Acusp->mat;
    Bmat = Bcusp->matTranspose;
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
  }
  Cmat = Ccusp->mat;
  PetscCheck(Amat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A mult struct for product type %s", MatProductTypes[ptype]);
  PetscCheck(Bmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B mult struct for product type %s", MatProductTypes[ptype]);
  PetscCheck(Cmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C mult struct for product type %s", MatProductTypes[ptype]);
  Acsr = (CsrMatrix *)Amat->mat;
  Bcsr = mmdata->Bcsr ? mmdata->Bcsr : (CsrMatrix *)Bmat->mat; /* B may be in compressed row storage */
  Ccsr = (CsrMatrix *)Cmat->mat;
  PetscCheck(Acsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A CSR struct");
  PetscCheck(Bcsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B CSR struct");
  PetscCheck(Ccsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing C CSR struct");
  PetscCall(PetscLogGpuTimeBegin());
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  BmatSpDescr = mmdata->Bcsr ? mmdata->matSpBDescr : Bmat->matDescr; /* B may be in compressed row storage */
  PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_DEVICE));
  #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
  stat = cusparseSpGEMMreuse_compute(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc);
  PetscCallCUSPARSE(stat);
  #else
  stat = cusparseSpGEMM_compute(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &mmdata->mmBufferSize, mmdata->mmBuffer);
  PetscCallCUSPARSE(stat);
  stat = cusparseSpGEMM_copy(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc);
  PetscCallCUSPARSE(stat);
  #endif
#else
  stat = cusparse_csr_spgemm(Ccusp->handle, opA, opB, Acsr->num_rows, Bcsr->num_cols, Acsr->num_cols, Amat->descr, Acsr->num_entries, Acsr->values->data().get(), Acsr->row_offsets->data().get(), Acsr->column_indices->data().get(), Bmat->descr, Bcsr->num_entries,
                             Bcsr->values->data().get(), Bcsr->row_offsets->data().get(), Bcsr->column_indices->data().get(), Cmat->descr, Ccsr->values->data().get(), Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get());
  PetscCallCUSPARSE(stat);
#endif
  PetscCall(PetscLogGpuFlops(mmdata->flops));
  PetscCallCUDA(WaitForCUDA());
  PetscCall(PetscLogGpuTimeEnd());
  C->offloadmask = PETSC_OFFLOAD_GPU;
finalize:
  /* shorter version of MatAssemblyEnd_SeqAIJ */
  PetscCall(PetscInfo(C, "Matrix size: %" PetscInt_FMT " X %" PetscInt_FMT "; storage space: 0 unneeded,%" PetscInt_FMT " used\n", C->rmap->n, C->cmap->n, c->nz));
  PetscCall(PetscInfo(C, "Number of mallocs during MatSetValues() is 0\n"));
  PetscCall(PetscInfo(C, "Maximum nonzeros in any row is %" PetscInt_FMT "\n", c->rmax));
  c->reallocs = 0;
  C->info.mallocs += 0;
  C->info.nz_unneeded = 0;
  C->assembled = C->was_assembled = PETSC_TRUE;
  C->num_ass++;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatProductSymbolic_SeqAIJCUSPARSE_SeqAIJCUSPARSE(Mat C)
{
  Mat_Product                  *product = C->product;
  Mat                           A, B;
  Mat_SeqAIJCUSPARSE           *Acusp, *Bcusp, *Ccusp;
  Mat_SeqAIJ                   *a, *b, *c;
  Mat_SeqAIJCUSPARSEMultStruct *Amat, *Bmat, *Cmat;
  CsrMatrix                    *Acsr, *Bcsr, *Ccsr;
  PetscInt                      i, j, m, n, k;
  PetscBool                     flg;
  cusparseStatus_t              stat;
  MatProductType                ptype;
  MatMatCusparse               *mmdata;
  PetscLogDouble                flops;
  PetscBool                     biscompressed, ciscompressed;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  int64_t              C_num_rows1, C_num_cols1, C_nnz1;
  cusparseSpMatDescr_t BmatSpDescr;
#else
  int cnz;
#endif
  cusparseOperation_t opA = CUSPARSE_OPERATION_NON_TRANSPOSE, opB = CUSPARSE_OPERATION_NON_TRANSPOSE; /* cuSPARSE spgemm doesn't support transpose yet */

  PetscFunctionBegin;
  MatCheckProduct(C, 1);
  PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Product data not empty");
  A = product->A;
  B = product->B;
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJCUSPARSE, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for type %s", ((PetscObject)A)->type_name);
  PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQAIJCUSPARSE, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Not for B of type %s", ((PetscObject)B)->type_name);
  a = (Mat_SeqAIJ *)A->data;
  b = (Mat_SeqAIJ *)B->data;
  /* product data */
  PetscCall(PetscNew(&mmdata));
  C->product->data    = mmdata;
  C->product->destroy = MatDestroy_MatMatCusparse;

  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
  Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr; /* Access spptr after MatSeqAIJCUSPARSECopyToGPU, not before */
  Bcusp = (Mat_SeqAIJCUSPARSE *)B->spptr;
  PetscCheck(Acusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");
  PetscCheck(Bcusp->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Only for MAT_CUSPARSE_CSR format");

  ptype = product->type;
  if (A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
    ptype                                          = MATPRODUCT_AB;
    product->symbolic_used_the_fact_A_is_symmetric = PETSC_TRUE;
  }
  if (B->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_ABt) {
    ptype                                          = MATPRODUCT_AB;
    product->symbolic_used_the_fact_B_is_symmetric = PETSC_TRUE;
  }
  biscompressed = PETSC_FALSE;
  ciscompressed = PETSC_FALSE;
  switch (ptype) {
  case MATPRODUCT_AB:
    m    = A->rmap->n;
    n    = B->cmap->n;
    k    = A->cmap->n;
    Amat = Acusp->mat;
    Bmat = Bcusp->mat;
    if (a->compressedrow.use) ciscompressed = PETSC_TRUE;
    if (b->compressedrow.use) biscompressed = PETSC_TRUE;
    break;
  case MATPRODUCT_AtB:
    m = A->cmap->n;
    n = B->cmap->n;
    k = A->rmap->n;
    PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
    Amat = Acusp->matTranspose;
    Bmat = Bcusp->mat;
    if (b->compressedrow.use) biscompressed = PETSC_TRUE;
    break;
  case MATPRODUCT_ABt:
    m = A->rmap->n;
    n = B->rmap->n;
    k = A->cmap->n;
    PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(B));
    Amat = Acusp->mat;
    Bmat = Bcusp->matTranspose;
    if (a->compressedrow.use) ciscompressed = PETSC_TRUE;
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Unsupported product type %s", MatProductTypes[product->type]);
  }

  /* create cusparse matrix */
  PetscCall(MatSetSizes(C, m, n, m, n));
  PetscCall(MatSetType(C, MATSEQAIJCUSPARSE));
  c     = (Mat_SeqAIJ *)C->data;
  Ccusp = (Mat_SeqAIJCUSPARSE *)C->spptr;
  Cmat  = new Mat_SeqAIJCUSPARSEMultStruct;
  Ccsr  = new CsrMatrix;

  c->compressedrow.use = ciscompressed;
  if (c->compressedrow.use) { /* if a is in compressed row, than c will be in compressed row format */
    c->compressedrow.nrows = a->compressedrow.nrows;
    PetscCall(PetscMalloc2(c->compressedrow.nrows + 1, &c->compressedrow.i, c->compressedrow.nrows, &c->compressedrow.rindex));
    PetscCall(PetscArraycpy(c->compressedrow.rindex, a->compressedrow.rindex, c->compressedrow.nrows));
    Ccusp->workVector  = new THRUSTARRAY(c->compressedrow.nrows);
    Cmat->cprowIndices = new THRUSTINTARRAY(c->compressedrow.nrows);
    Cmat->cprowIndices->assign(c->compressedrow.rindex, c->compressedrow.rindex + c->compressedrow.nrows);
  } else {
    c->compressedrow.nrows  = 0;
    c->compressedrow.i      = NULL;
    c->compressedrow.rindex = NULL;
    Ccusp->workVector       = NULL;
    Cmat->cprowIndices      = NULL;
  }
  Ccusp->nrows      = ciscompressed ? c->compressedrow.nrows : m;
  Ccusp->mat        = Cmat;
  Ccusp->mat->mat   = Ccsr;
  Ccsr->num_rows    = Ccusp->nrows;
  Ccsr->num_cols    = n;
  Ccsr->row_offsets = new THRUSTINTARRAY32(Ccusp->nrows + 1);
  PetscCallCUSPARSE(cusparseCreateMatDescr(&Cmat->descr));
  PetscCallCUSPARSE(cusparseSetMatIndexBase(Cmat->descr, CUSPARSE_INDEX_BASE_ZERO));
  PetscCallCUSPARSE(cusparseSetMatType(Cmat->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
  PetscCallCUDA(cudaMalloc((void **)&Cmat->alpha_one, sizeof(PetscScalar)));
  PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_zero, sizeof(PetscScalar)));
  PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_one, sizeof(PetscScalar)));
  PetscCallCUDA(cudaMemcpy(Cmat->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
  PetscCallCUDA(cudaMemcpy(Cmat->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
  PetscCallCUDA(cudaMemcpy(Cmat->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
  if (!Ccsr->num_rows || !Ccsr->num_cols || !a->nz || !b->nz) { /* cusparse raise errors in different calls when matrices have zero rows/columns! */
    PetscCallThrust(thrust::fill(thrust::device, Ccsr->row_offsets->begin(), Ccsr->row_offsets->end(), 0));
    c->nz                = 0;
    Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
    Ccsr->values         = new THRUSTARRAY(c->nz);
    goto finalizesym;
  }

  PetscCheck(Amat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A mult struct for product type %s", MatProductTypes[ptype]);
  PetscCheck(Bmat, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B mult struct for product type %s", MatProductTypes[ptype]);
  Acsr = (CsrMatrix *)Amat->mat;
  if (!biscompressed) {
    Bcsr = (CsrMatrix *)Bmat->mat;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
    BmatSpDescr = Bmat->matDescr;
#endif
  } else { /* we need to use row offsets for the full matrix */
    CsrMatrix *cBcsr     = (CsrMatrix *)Bmat->mat;
    Bcsr                 = new CsrMatrix;
    Bcsr->num_rows       = B->rmap->n;
    Bcsr->num_cols       = cBcsr->num_cols;
    Bcsr->num_entries    = cBcsr->num_entries;
    Bcsr->column_indices = cBcsr->column_indices;
    Bcsr->values         = cBcsr->values;
    if (!Bcusp->rowoffsets_gpu) {
      Bcusp->rowoffsets_gpu = new THRUSTINTARRAY32(B->rmap->n + 1);
      Bcusp->rowoffsets_gpu->assign(b->i, b->i + B->rmap->n + 1);
      PetscCall(PetscLogCpuToGpu((B->rmap->n + 1) * sizeof(PetscInt)));
    }
    Bcsr->row_offsets = Bcusp->rowoffsets_gpu;
    mmdata->Bcsr      = Bcsr;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
    if (Bcsr->num_rows && Bcsr->num_cols) {
      stat = cusparseCreateCsr(&mmdata->matSpBDescr, Bcsr->num_rows, Bcsr->num_cols, Bcsr->num_entries, Bcsr->row_offsets->data().get(), Bcsr->column_indices->data().get(), Bcsr->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
      PetscCallCUSPARSE(stat);
    }
    BmatSpDescr = mmdata->matSpBDescr;
#endif
  }
  PetscCheck(Acsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing A CSR struct");
  PetscCheck(Bcsr, PetscObjectComm((PetscObject)C), PETSC_ERR_GPU, "Missing B CSR struct");
  /* precompute flops count */
  if (ptype == MATPRODUCT_AB) {
    for (i = 0, flops = 0; i < A->rmap->n; i++) {
      const PetscInt st = a->i[i];
      const PetscInt en = a->i[i + 1];
      for (j = st; j < en; j++) {
        const PetscInt brow = a->j[j];
        flops += 2. * (b->i[brow + 1] - b->i[brow]);
      }
    }
  } else if (ptype == MATPRODUCT_AtB) {
    for (i = 0, flops = 0; i < A->rmap->n; i++) {
      const PetscInt anzi = a->i[i + 1] - a->i[i];
      const PetscInt bnzi = b->i[i + 1] - b->i[i];
      flops += (2. * anzi) * bnzi;
    }
  } else { /* TODO */
    flops = 0.;
  }

  mmdata->flops = flops;
  PetscCall(PetscLogGpuTimeBegin());

#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_DEVICE));
  // cuda-12.2 requires non-null csrRowOffsets
  stat = cusparseCreateCsr(&Cmat->matDescr, Ccsr->num_rows, Ccsr->num_cols, 0, Ccsr->row_offsets->data().get(), NULL, NULL, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
  PetscCallCUSPARSE(stat);
  PetscCallCUSPARSE(cusparseSpGEMM_createDescr(&mmdata->spgemmDesc));
  #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
  {
    /* cusparseSpGEMMreuse has more reasonable APIs than cusparseSpGEMM, so we prefer to use it.
     We follow the sample code at https://github.com/NVIDIA/CUDALibrarySamples/blob/master/cuSPARSE/spgemm_reuse
  */
    void *dBuffer1 = NULL;
    void *dBuffer2 = NULL;
    void *dBuffer3 = NULL;
    /* dBuffer4, dBuffer5 are needed by cusparseSpGEMMreuse_compute, and therefore are stored in mmdata */
    size_t bufferSize1 = 0;
    size_t bufferSize2 = 0;
    size_t bufferSize3 = 0;
    size_t bufferSize4 = 0;
    size_t bufferSize5 = 0;

    /* ask bufferSize1 bytes for external memory */
    stat = cusparseSpGEMMreuse_workEstimation(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize1, NULL);
    PetscCallCUSPARSE(stat);
    PetscCallCUDA(cudaMalloc((void **)&dBuffer1, bufferSize1));
    /* inspect the matrices A and B to understand the memory requirement for the next step */
    stat = cusparseSpGEMMreuse_workEstimation(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize1, dBuffer1);
    PetscCallCUSPARSE(stat);

    stat = cusparseSpGEMMreuse_nnz(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize2, NULL, &bufferSize3, NULL, &bufferSize4, NULL);
    PetscCallCUSPARSE(stat);
    PetscCallCUDA(cudaMalloc((void **)&dBuffer2, bufferSize2));
    PetscCallCUDA(cudaMalloc((void **)&dBuffer3, bufferSize3));
    PetscCallCUDA(cudaMalloc((void **)&mmdata->dBuffer4, bufferSize4));
    stat = cusparseSpGEMMreuse_nnz(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize2, dBuffer2, &bufferSize3, dBuffer3, &bufferSize4, mmdata->dBuffer4);
    PetscCallCUSPARSE(stat);
    PetscCallCUDA(cudaFree(dBuffer1));
    PetscCallCUDA(cudaFree(dBuffer2));

    /* get matrix C non-zero entries C_nnz1 */
    PetscCallCUSPARSE(cusparseSpMatGetSize(Cmat->matDescr, &C_num_rows1, &C_num_cols1, &C_nnz1));
    c->nz = (PetscInt)C_nnz1;
    /* allocate matrix C */
    Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
    PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
    Ccsr->values = new THRUSTARRAY(c->nz);
    PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
    /* update matC with the new pointers */
    stat = cusparseCsrSetPointers(Cmat->matDescr, Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get(), Ccsr->values->data().get());
    PetscCallCUSPARSE(stat);

    stat = cusparseSpGEMMreuse_copy(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize5, NULL);
    PetscCallCUSPARSE(stat);
    PetscCallCUDA(cudaMalloc((void **)&mmdata->dBuffer5, bufferSize5));
    stat = cusparseSpGEMMreuse_copy(Ccusp->handle, opA, opB, Amat->matDescr, BmatSpDescr, Cmat->matDescr, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufferSize5, mmdata->dBuffer5);
    PetscCallCUSPARSE(stat);
    PetscCallCUDA(cudaFree(dBuffer3));
    stat = cusparseSpGEMMreuse_compute(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc);
    PetscCallCUSPARSE(stat);
    PetscCall(PetscInfo(C, "Buffer sizes for type %s, result %" PetscInt_FMT " x %" PetscInt_FMT " (k %" PetscInt_FMT ", nzA %" PetscInt_FMT ", nzB %" PetscInt_FMT ", nzC %" PetscInt_FMT ") are: %ldKB %ldKB\n", MatProductTypes[ptype], m, n, k, a->nz, b->nz, c->nz, bufferSize4 / 1024, bufferSize5 / 1024));
  }
  #else
  size_t bufSize2;
  /* ask bufferSize bytes for external memory */
  stat = cusparseSpGEMM_workEstimation(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufSize2, NULL);
  PetscCallCUSPARSE(stat);
  PetscCallCUDA(cudaMalloc((void **)&mmdata->mmBuffer2, bufSize2));
  /* inspect the matrices A and B to understand the memory requirement for the next step */
  stat = cusparseSpGEMM_workEstimation(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &bufSize2, mmdata->mmBuffer2);
  PetscCallCUSPARSE(stat);
  /* ask bufferSize again bytes for external memory */
  stat = cusparseSpGEMM_compute(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &mmdata->mmBufferSize, NULL);
  PetscCallCUSPARSE(stat);
  /* The CUSPARSE documentation is not clear, nor the API
     We need both buffers to perform the operations properly!
     mmdata->mmBuffer2 does not appear anywhere in the compute/copy API
     it only appears for the workEstimation stuff, but it seems it is needed in compute, so probably the address
     is stored in the descriptor! What a messy API... */
  PetscCallCUDA(cudaMalloc((void **)&mmdata->mmBuffer, mmdata->mmBufferSize));
  /* compute the intermediate product of A * B */
  stat = cusparseSpGEMM_compute(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc, &mmdata->mmBufferSize, mmdata->mmBuffer);
  PetscCallCUSPARSE(stat);
  /* get matrix C non-zero entries C_nnz1 */
  PetscCallCUSPARSE(cusparseSpMatGetSize(Cmat->matDescr, &C_num_rows1, &C_num_cols1, &C_nnz1));
  c->nz = (PetscInt)C_nnz1;
  PetscCall(PetscInfo(C, "Buffer sizes for type %s, result %" PetscInt_FMT " x %" PetscInt_FMT " (k %" PetscInt_FMT ", nzA %" PetscInt_FMT ", nzB %" PetscInt_FMT ", nzC %" PetscInt_FMT ") are: %ldKB %ldKB\n", MatProductTypes[ptype], m, n, k, a->nz, b->nz, c->nz, bufSize2 / 1024,
                      mmdata->mmBufferSize / 1024));
  Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
  PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
  Ccsr->values = new THRUSTARRAY(c->nz);
  PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
  stat = cusparseCsrSetPointers(Cmat->matDescr, Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get(), Ccsr->values->data().get());
  PetscCallCUSPARSE(stat);
  stat = cusparseSpGEMM_copy(Ccusp->handle, opA, opB, Cmat->alpha_one, Amat->matDescr, BmatSpDescr, Cmat->beta_zero, Cmat->matDescr, cusparse_scalartype, CUSPARSE_SPGEMM_DEFAULT, mmdata->spgemmDesc);
  PetscCallCUSPARSE(stat);
  #endif // PETSC_PKG_CUDA_VERSION_GE(11,4,0)
#else
  PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_HOST));
  stat = cusparseXcsrgemmNnz(Ccusp->handle, opA, opB, Acsr->num_rows, Bcsr->num_cols, Acsr->num_cols, Amat->descr, Acsr->num_entries, Acsr->row_offsets->data().get(), Acsr->column_indices->data().get(), Bmat->descr, Bcsr->num_entries,
                             Bcsr->row_offsets->data().get(), Bcsr->column_indices->data().get(), Cmat->descr, Ccsr->row_offsets->data().get(), &cnz);
  PetscCallCUSPARSE(stat);
  c->nz                = cnz;
  Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
  PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */
  Ccsr->values = new THRUSTARRAY(c->nz);
  PetscCallCUDA(cudaPeekAtLastError()); /* catch out of memory errors */

  PetscCallCUSPARSE(cusparseSetPointerMode(Ccusp->handle, CUSPARSE_POINTER_MODE_DEVICE));
  /* with the old gemm interface (removed from 11.0 on) we cannot compute the symbolic factorization only.
     I have tried using the gemm2 interface (alpha * A * B + beta * D), which allows to do symbolic by passing NULL for values, but it seems quite buggy when
     D is NULL, despite the fact that CUSPARSE documentation claims it is supported! */
  stat = cusparse_csr_spgemm(Ccusp->handle, opA, opB, Acsr->num_rows, Bcsr->num_cols, Acsr->num_cols, Amat->descr, Acsr->num_entries, Acsr->values->data().get(), Acsr->row_offsets->data().get(), Acsr->column_indices->data().get(), Bmat->descr, Bcsr->num_entries,
                             Bcsr->values->data().get(), Bcsr->row_offsets->data().get(), Bcsr->column_indices->data().get(), Cmat->descr, Ccsr->values->data().get(), Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get());
  PetscCallCUSPARSE(stat);
#endif
  PetscCall(PetscLogGpuFlops(mmdata->flops));
  PetscCall(PetscLogGpuTimeEnd());
finalizesym:
  c->singlemalloc = PETSC_FALSE;
  c->free_a       = PETSC_TRUE;
  c->free_ij      = PETSC_TRUE;
  PetscCall(PetscMalloc1(m + 1, &c->i));
  PetscCall(PetscMalloc1(c->nz, &c->j));
  if (PetscDefined(USE_64BIT_INDICES)) { /* 32 to 64-bit conversion on the GPU and then copy to host (lazy) */
    PetscInt      *d_i = c->i;
    THRUSTINTARRAY ii(Ccsr->row_offsets->size());
    THRUSTINTARRAY jj(Ccsr->column_indices->size());
    ii = *Ccsr->row_offsets;
    jj = *Ccsr->column_indices;
    if (ciscompressed) d_i = c->compressedrow.i;
    PetscCallCUDA(cudaMemcpy(d_i, ii.data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(c->j, jj.data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
  } else {
    PetscInt *d_i = c->i;
    if (ciscompressed) d_i = c->compressedrow.i;
    PetscCallCUDA(cudaMemcpy(d_i, Ccsr->row_offsets->data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(c->j, Ccsr->column_indices->data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
  }
  if (ciscompressed) { /* need to expand host row offsets */
    PetscInt r = 0;
    c->i[0]    = 0;
    for (k = 0; k < c->compressedrow.nrows; k++) {
      const PetscInt next = c->compressedrow.rindex[k];
      const PetscInt old  = c->compressedrow.i[k];
      for (; r < next; r++) c->i[r + 1] = old;
    }
    for (; r < m; r++) c->i[r + 1] = c->compressedrow.i[c->compressedrow.nrows];
  }
  PetscCall(PetscLogGpuToCpu((Ccsr->column_indices->size() + Ccsr->row_offsets->size()) * sizeof(PetscInt)));
  PetscCall(PetscMalloc1(m, &c->ilen));
  PetscCall(PetscMalloc1(m, &c->imax));
  c->maxnz         = c->nz;
  c->nonzerorowcnt = 0;
  c->rmax          = 0;
  for (k = 0; k < m; k++) {
    const PetscInt nn = c->i[k + 1] - c->i[k];
    c->ilen[k] = c->imax[k] = nn;
    c->nonzerorowcnt += (PetscInt) !!nn;
    c->rmax = PetscMax(c->rmax, nn);
  }
  PetscCall(MatMarkDiagonal_SeqAIJ(C));
  PetscCall(PetscMalloc1(c->nz, &c->a));
  Ccsr->num_entries = c->nz;

  C->nonzerostate++;
  PetscCall(PetscLayoutSetUp(C->rmap));
  PetscCall(PetscLayoutSetUp(C->cmap));
  Ccusp->nonzerostate = C->nonzerostate;
  C->offloadmask      = PETSC_OFFLOAD_UNALLOCATED;
  C->preallocated     = PETSC_TRUE;
  C->assembled        = PETSC_FALSE;
  C->was_assembled    = PETSC_FALSE;
  if (product->api_user && A->offloadmask == PETSC_OFFLOAD_BOTH && B->offloadmask == PETSC_OFFLOAD_BOTH) { /* flag the matrix C values as computed, so that the numeric phase will only call MatAssembly */
    mmdata->reusesym = PETSC_TRUE;
    C->offloadmask   = PETSC_OFFLOAD_GPU;
  }
  C->ops->productnumeric = MatProductNumeric_SeqAIJCUSPARSE_SeqAIJCUSPARSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense(Mat);

/* handles sparse or dense B */
static PetscErrorCode MatProductSetFromOptions_SeqAIJCUSPARSE(Mat mat)
{
  Mat_Product *product = mat->product;
  PetscBool    isdense = PETSC_FALSE, Biscusp = PETSC_FALSE, Ciscusp = PETSC_TRUE;

  PetscFunctionBegin;
  MatCheckProduct(mat, 1);
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)product->B, MATSEQDENSE, &isdense));
  if (!product->A->boundtocpu && !product->B->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->B, MATSEQAIJCUSPARSE, &Biscusp));
  if (product->type == MATPRODUCT_ABC) {
    Ciscusp = PETSC_FALSE;
    if (!product->C->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->C, MATSEQAIJCUSPARSE, &Ciscusp));
  }
  if (Biscusp && Ciscusp) { /* we can always select the CPU backend */
    PetscBool usecpu = PETSC_FALSE;
    switch (product->type) {
    case MATPRODUCT_AB:
      if (product->api_user) {
        PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMult", "Mat");
        PetscCall(PetscOptionsBool("-matmatmult_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
        PetscOptionsEnd();
      } else {
        PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AB", "Mat");
        PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
        PetscOptionsEnd();
      }
      break;
    case MATPRODUCT_AtB:
      if (product->api_user) {
        PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatTransposeMatMult", "Mat");
        PetscCall(PetscOptionsBool("-mattransposematmult_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
        PetscOptionsEnd();
      } else {
        PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AtB", "Mat");
        PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
        PetscOptionsEnd();
      }
      break;
    case MATPRODUCT_PtAP:
      if (product->api_user) {
        PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatPtAP", "Mat");
        PetscCall(PetscOptionsBool("-matptap_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
        PetscOptionsEnd();
      } else {
        PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_PtAP", "Mat");
        PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
        PetscOptionsEnd();
      }
      break;
    case MATPRODUCT_RARt:
      if (product->api_user) {
        PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatRARt", "Mat");
        PetscCall(PetscOptionsBool("-matrart_backend_cpu", "Use CPU code", "MatRARt", usecpu, &usecpu, NULL));
        PetscOptionsEnd();
      } else {
        PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_RARt", "Mat");
        PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatRARt", usecpu, &usecpu, NULL));
        PetscOptionsEnd();
      }
      break;
    case MATPRODUCT_ABC:
      if (product->api_user) {
        PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMatMult", "Mat");
        PetscCall(PetscOptionsBool("-matmatmatmult_backend_cpu", "Use CPU code", "MatMatMatMult", usecpu, &usecpu, NULL));
        PetscOptionsEnd();
      } else {
        PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_ABC", "Mat");
        PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMatMult", usecpu, &usecpu, NULL));
        PetscOptionsEnd();
      }
      break;
    default:
      break;
    }
    if (usecpu) Biscusp = Ciscusp = PETSC_FALSE;
  }
  /* dispatch */
  if (isdense) {
    switch (product->type) {
    case MATPRODUCT_AB:
    case MATPRODUCT_AtB:
    case MATPRODUCT_ABt:
    case MATPRODUCT_PtAP:
    case MATPRODUCT_RARt:
      if (product->A->boundtocpu) {
        PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense(mat));
      } else {
        mat->ops->productsymbolic = MatProductSymbolic_SeqAIJCUSPARSE_SeqDENSECUDA;
      }
      break;
    case MATPRODUCT_ABC:
      mat->ops->productsymbolic = MatProductSymbolic_ABC_Basic;
      break;
    default:
      break;
    }
  } else if (Biscusp && Ciscusp) {
    switch (product->type) {
    case MATPRODUCT_AB:
    case MATPRODUCT_AtB:
    case MATPRODUCT_ABt:
      mat->ops->productsymbolic = MatProductSymbolic_SeqAIJCUSPARSE_SeqAIJCUSPARSE;
      break;
    case MATPRODUCT_PtAP:
    case MATPRODUCT_RARt:
    case MATPRODUCT_ABC:
      mat->ops->productsymbolic = MatProductSymbolic_ABC_Basic;
      break;
    default:
      break;
    }
  } else { /* fallback for AIJ */
    PetscCall(MatProductSetFromOptions_SeqAIJ(mat));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMult_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
{
  PetscFunctionBegin;
  PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_FALSE, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
{
  PetscFunctionBegin;
  PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_FALSE, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultHermitianTranspose_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
{
  PetscFunctionBegin;
  PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_TRUE, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultHermitianTransposeAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
{
  PetscFunctionBegin;
  PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_TRUE, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultTranspose_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy)
{
  PetscFunctionBegin;
  PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, NULL, yy, PETSC_TRUE, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

__global__ static void ScatterAdd(PetscInt n, PetscInt *idx, const PetscScalar *x, PetscScalar *y)
{
  int i = blockIdx.x * blockDim.x + threadIdx.x;
  if (i < n) y[idx[i]] += x[i];
}

/* z = op(A) x + y. If trans & !herm, op = ^T; if trans & herm, op = ^H; if !trans, op = no-op */
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;
  cusparseOperation_t           opA = CUSPARSE_OPERATION_NON_TRANSPOSE;
  PetscBool                     compressed;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  PetscInt nx, ny;
#endif

  PetscFunctionBegin;
  PetscCheck(!herm || trans, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "Hermitian and not transpose not supported");
  if (!a->nz) {
    if (yy) PetscCall(VecSeq_CUDA::Copy(yy, zz));
    else PetscCall(VecSeq_CUDA::Set(zz, 0));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  /* The line below is necessary due to the operations that modify the matrix on the CPU (axpy, scale, etc) */
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  if (!trans) {
    matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
    PetscCheck(matstruct, PetscObjectComm((PetscObject)A), PETSC_ERR_GPU, "SeqAIJCUSPARSE does not have a 'mat' (need to fix)");
  } else {
    if (herm || !A->form_explicit_transpose) {
      opA       = herm ? CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE : CUSPARSE_OPERATION_TRANSPOSE;
      matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->mat;
    } else {
      if (!cusparsestruct->matTranspose) PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
      matstruct = (Mat_SeqAIJCUSPARSEMultStruct *)cusparsestruct->matTranspose;
    }
  }
  /* Does the matrix use compressed rows (i.e., drop zero rows)? */
  compressed = matstruct->cprowIndices ? PETSC_TRUE : PETSC_FALSE;

  try {
    PetscCall(VecCUDAGetArrayRead(xx, (const PetscScalar **)&xarray));
    if (yy == zz) PetscCall(VecCUDAGetArray(zz, &zarray)); /* read & write zz, so need to get up-to-date zarray on GPU */
    else PetscCall(VecCUDAGetArrayWrite(zz, &zarray));     /* write zz, so no need to init zarray on GPU */

    PetscCall(PetscLogGpuTimeBegin());
    if (opA == CUSPARSE_OPERATION_NON_TRANSPOSE) {
      /* z = A x + beta y.
         If A is compressed (with less rows), then Ax is shorter than the full z, so we need a work vector to store Ax.
         When A is non-compressed, and z = y, we can set beta=1 to compute y = Ax + y in one call.
      */
      xptr = xarray;
      dptr = compressed ? cusparsestruct->workVector->data().get() : zarray;
      beta = (yy == zz && !compressed) ? matstruct->beta_one : matstruct->beta_zero;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
      /* Get length of x, y for y=Ax. ny might be shorter than the work vector's allocated length, since the work vector is
          allocated to accommodate different uses. So we get the length info directly from mat.
       */
      if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
        CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
        nx             = mat->num_cols;
        ny             = mat->num_rows;
      }
#endif
    } else {
      /* z = A^T x + beta y
         If A is compressed, then we need a work vector as the shorter version of x to compute A^T x.
         Note A^Tx is of full length, so we set beta to 1.0 if y exists.
       */
      xptr = compressed ? cusparsestruct->workVector->data().get() : xarray;
      dptr = zarray;
      beta = yy ? matstruct->beta_one : matstruct->beta_zero;
      if (compressed) { /* Scatter x to work vector */
        thrust::device_ptr<PetscScalar> xarr = thrust::device_pointer_cast(xarray);

        thrust::for_each(
#if PetscDefined(HAVE_THRUST_ASYNC)
          thrust::cuda::par.on(PetscDefaultCudaStream),
#endif
          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());
      }
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
      if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
        CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
        nx             = mat->num_rows;
        ny             = mat->num_cols;
      }
#endif
    }

    /* csr_spmv does y = alpha op(A) x + beta y */
    if (cusparsestruct->format == MAT_CUSPARSE_CSR) {
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
      PetscCheck(opA >= 0 && opA <= 2, PETSC_COMM_SELF, PETSC_ERR_SUP, "cuSPARSE ABI on cusparseOperation_t has changed and PETSc has not been updated accordingly");
      if (!matstruct->cuSpMV[opA].initialized) { /* built on demand */
        PetscCallCUSPARSE(cusparseCreateDnVec(&matstruct->cuSpMV[opA].vecXDescr, nx, xptr, cusparse_scalartype));
        PetscCallCUSPARSE(cusparseCreateDnVec(&matstruct->cuSpMV[opA].vecYDescr, ny, dptr, cusparse_scalartype));
        PetscCallCUSPARSE(
          cusparseSpMV_bufferSize(cusparsestruct->handle, opA, matstruct->alpha_one, matstruct->matDescr, matstruct->cuSpMV[opA].vecXDescr, beta, matstruct->cuSpMV[opA].vecYDescr, cusparse_scalartype, cusparsestruct->spmvAlg, &matstruct->cuSpMV[opA].spmvBufferSize));
        PetscCallCUDA(cudaMalloc(&matstruct->cuSpMV[opA].spmvBuffer, matstruct->cuSpMV[opA].spmvBufferSize));

        matstruct->cuSpMV[opA].initialized = PETSC_TRUE;
      } else {
        /* x, y's value pointers might change between calls, but their shape is kept, so we just update pointers */
        PetscCallCUSPARSE(cusparseDnVecSetValues(matstruct->cuSpMV[opA].vecXDescr, xptr));
        PetscCallCUSPARSE(cusparseDnVecSetValues(matstruct->cuSpMV[opA].vecYDescr, dptr));
      }

      PetscCallCUSPARSE(cusparseSpMV(cusparsestruct->handle, opA, matstruct->alpha_one, matstruct->matDescr, /* built in MatSeqAIJCUSPARSECopyToGPU() or MatSeqAIJCUSPARSEFormExplicitTranspose() */
                                     matstruct->cuSpMV[opA].vecXDescr, beta, matstruct->cuSpMV[opA].vecYDescr, cusparse_scalartype, cusparsestruct->spmvAlg, matstruct->cuSpMV[opA].spmvBuffer));
#else
      CsrMatrix *mat = (CsrMatrix *)matstruct->mat;
      PetscCallCUSPARSE(cusparse_csr_spmv(cusparsestruct->handle, opA, mat->num_rows, mat->num_cols, mat->num_entries, matstruct->alpha_one, matstruct->descr, mat->values->data().get(), mat->row_offsets->data().get(), mat->column_indices->data().get(), xptr, beta, dptr));
#endif
    } else {
      if (cusparsestruct->nrows) {
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
#else
        cusparseHybMat_t hybMat = (cusparseHybMat_t)matstruct->mat;
        PetscCallCUSPARSE(cusparse_hyb_spmv(cusparsestruct->handle, opA, matstruct->alpha_one, matstruct->descr, hybMat, xptr, beta, dptr));
#endif
      }
    }
    PetscCall(PetscLogGpuTimeEnd());

    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 */
          PetscCall(VecSeq_CUDA::Copy(yy, zz));      /* zz = yy */
        } else if (zz != yy) {                       /* A is not compressed. zz already contains A*xx, and we just need to add yy */
          PetscCall(VecSeq_CUDA::AXPY(zz, 1.0, yy)); /* zz += yy */
        }
      } else if (compressed) { /* MatMult: zz = A*xx. A is compressed, so we zero zz first, then ScatterAdd the work vector to zz */
        PetscCall(VecSeq_CUDA::Set(zz, 0));
      }

      /* ScatterAdd the result from work vector into the full vector when A is compressed */
      if (compressed) {
        PetscCall(PetscLogGpuTimeBegin());
        /* I wanted to make this for_each asynchronous but failed. thrust::async::for_each() returns an event (internally registered)
           and in the destructor of the scope, it will call cudaStreamSynchronize() on this stream. One has to store all events to
           prevent that. So I just add a ScatterAdd kernel.
         */
#if 0
        thrust::device_ptr<PetscScalar> zptr = thrust::device_pointer_cast(zarray);
        thrust::async::for_each(thrust::cuda::par.on(cusparsestruct->stream),
                         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());
#else
        PetscInt n = matstruct->cprowIndices->size();
        ScatterAdd<<<(n + 255) / 256, 256, 0, PetscDefaultCudaStream>>>(n, matstruct->cprowIndices->data().get(), cusparsestruct->workVector->data().get(), zarray);
#endif
        PetscCall(PetscLogGpuTimeEnd());
      }
    } else {
      if (yy && yy != zz) PetscCall(VecSeq_CUDA::AXPY(zz, 1.0, yy)); /* zz += yy */
    }
    PetscCall(VecCUDARestoreArrayRead(xx, (const PetscScalar **)&xarray));
    if (yy == zz) PetscCall(VecCUDARestoreArray(zz, &zarray));
    else PetscCall(VecCUDARestoreArrayWrite(zz, &zarray));
  } catch (char *ex) {
    SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "CUSPARSE error: %s", ex);
  }
  if (yy) {
    PetscCall(PetscLogGpuFlops(2.0 * a->nz));
  } else {
    PetscCall(PetscLogGpuFlops(2.0 * a->nz - a->nonzerorowcnt));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultTransposeAdd_SeqAIJCUSPARSE(Mat A, Vec xx, Vec yy, Vec zz)
{
  PetscFunctionBegin;
  PetscCall(MatMultAddKernel_SeqAIJCUSPARSE(A, xx, yy, zz, PETSC_TRUE, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAssemblyEnd_SeqAIJCUSPARSE(Mat A, MatAssemblyType mode)
{
  PetscFunctionBegin;
  PetscCall(MatAssemblyEnd_SeqAIJ(A, mode));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatCreateSeqAIJCUSPARSE - Creates a sparse matrix in `MATAIJCUSPARSE` (compressed row) format
  (the default parallel PETSc format).

  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), ignored if `nnz` is provide
- nnz  - array containing the number of nonzeros in the various rows (possibly different for each row) or `NULL`

  Output Parameter:
. A - the matrix

  Level: intermediate

  Notes:
  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`).

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

  The AIJ format, also called
  compressed row storage, is fully compatible with standard Fortran
  storage.  That is, the stored row and column indices can begin at
  either one (as in Fortran) or zero.

  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.

.seealso: [](ch_matrices), `Mat`, `MATSEQAIJCUSPARSE`, `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`, `MATAIJCUSPARSE`
@*/
PetscErrorCode MatCreateSeqAIJCUSPARSE(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt nz, const PetscInt nnz[], Mat *A)
{
  PetscFunctionBegin;
  PetscCall(MatCreate(comm, A));
  PetscCall(MatSetSizes(*A, m, n, m, n));
  PetscCall(MatSetType(*A, MATSEQAIJCUSPARSE));
  PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*A, nz, (PetscInt *)nnz));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDestroy_SeqAIJCUSPARSE(Mat A)
{
  PetscFunctionBegin;
  if (A->factortype == MAT_FACTOR_NONE) {
    PetscCall(MatSeqAIJCUSPARSE_Destroy(A));
  } else {
    PetscCall(MatSeqAIJCUSPARSETriFactors_Destroy((Mat_SeqAIJCUSPARSETriFactors **)&A->spptr));
  }
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatCUSPARSESetFormat_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatCUSPARSESetUseCPUSolve_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaijcusparse_hypre_C", NULL));
  PetscCall(MatDestroy_SeqAIJ(A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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)
{
  PetscFunctionBegin;
  PetscCall(MatDuplicate_SeqAIJ(A, cpvalues, B));
  PetscCall(MatConvert_SeqAIJ_SeqAIJCUSPARSE(*B, MATSEQAIJCUSPARSE, MAT_INPLACE_MATRIX, B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAXPY_SeqAIJCUSPARSE(Mat Y, PetscScalar a, Mat X, MatStructure str)
{
  Mat_SeqAIJ         *x = (Mat_SeqAIJ *)X->data, *y = (Mat_SeqAIJ *)Y->data;
  Mat_SeqAIJCUSPARSE *cy;
  Mat_SeqAIJCUSPARSE *cx;
  PetscScalar        *ay;
  const PetscScalar  *ax;
  CsrMatrix          *csry, *csrx;

  PetscFunctionBegin;
  cy = (Mat_SeqAIJCUSPARSE *)Y->spptr;
  cx = (Mat_SeqAIJCUSPARSE *)X->spptr;
  if (X->ops->axpy != Y->ops->axpy) {
    PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(Y, PETSC_FALSE));
    PetscCall(MatAXPY_SeqAIJ(Y, a, X, str));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  /* if we are here, it means both matrices are bound to GPU */
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(Y));
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(X));
  PetscCheck(cy->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)Y), PETSC_ERR_GPU, "only MAT_CUSPARSE_CSR supported");
  PetscCheck(cx->format == MAT_CUSPARSE_CSR, PetscObjectComm((PetscObject)X), PETSC_ERR_GPU, "only MAT_CUSPARSE_CSR supported");
  csry = (CsrMatrix *)cy->mat->mat;
  csrx = (CsrMatrix *)cx->mat->mat;
  /* see if we can turn this into a cublas axpy */
  if (str != SAME_NONZERO_PATTERN && x->nz == y->nz && !x->compressedrow.use && !y->compressedrow.use) {
    bool eq = thrust::equal(thrust::device, csry->row_offsets->begin(), csry->row_offsets->end(), csrx->row_offsets->begin());
    if (eq) eq = thrust::equal(thrust::device, csry->column_indices->begin(), csry->column_indices->end(), csrx->column_indices->begin());
    if (eq) str = SAME_NONZERO_PATTERN;
  }
  /* spgeam is buggy with one column */
  if (Y->cmap->n == 1 && str != SAME_NONZERO_PATTERN) str = DIFFERENT_NONZERO_PATTERN;

  if (str == SUBSET_NONZERO_PATTERN) {
    PetscScalar b = 1.0;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
    size_t bufferSize;
    void  *buffer;
#endif

    PetscCall(MatSeqAIJCUSPARSEGetArrayRead(X, &ax));
    PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
    PetscCallCUSPARSE(cusparseSetPointerMode(cy->handle, CUSPARSE_POINTER_MODE_HOST));
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
    PetscCallCUSPARSE(cusparse_csr_spgeam_bufferSize(cy->handle, Y->rmap->n, Y->cmap->n, &a, cx->mat->descr, x->nz, ax, csrx->row_offsets->data().get(), csrx->column_indices->data().get(), &b, cy->mat->descr, y->nz, ay, csry->row_offsets->data().get(),
                                                     csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get(), &bufferSize));
    PetscCallCUDA(cudaMalloc(&buffer, bufferSize));
    PetscCall(PetscLogGpuTimeBegin());
    PetscCallCUSPARSE(cusparse_csr_spgeam(cy->handle, Y->rmap->n, Y->cmap->n, &a, cx->mat->descr, x->nz, ax, csrx->row_offsets->data().get(), csrx->column_indices->data().get(), &b, cy->mat->descr, y->nz, ay, csry->row_offsets->data().get(),
                                          csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get(), buffer));
    PetscCall(PetscLogGpuFlops(x->nz + y->nz));
    PetscCall(PetscLogGpuTimeEnd());
    PetscCallCUDA(cudaFree(buffer));
#else
    PetscCall(PetscLogGpuTimeBegin());
    PetscCallCUSPARSE(cusparse_csr_spgeam(cy->handle, Y->rmap->n, Y->cmap->n, &a, cx->mat->descr, x->nz, ax, csrx->row_offsets->data().get(), csrx->column_indices->data().get(), &b, cy->mat->descr, y->nz, ay, csry->row_offsets->data().get(),
                                          csry->column_indices->data().get(), cy->mat->descr, ay, csry->row_offsets->data().get(), csry->column_indices->data().get()));
    PetscCall(PetscLogGpuFlops(x->nz + y->nz));
    PetscCall(PetscLogGpuTimeEnd());
#endif
    PetscCallCUSPARSE(cusparseSetPointerMode(cy->handle, CUSPARSE_POINTER_MODE_DEVICE));
    PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(X, &ax));
    PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
    PetscCall(MatSeqAIJInvalidateDiagonal(Y));
  } else if (str == SAME_NONZERO_PATTERN) {
    cublasHandle_t cublasv2handle;
    PetscBLASInt   one = 1, bnz = 1;

    PetscCall(MatSeqAIJCUSPARSEGetArrayRead(X, &ax));
    PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
    PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
    PetscCall(PetscBLASIntCast(x->nz, &bnz));
    PetscCall(PetscLogGpuTimeBegin());
    PetscCallCUBLAS(cublasXaxpy(cublasv2handle, bnz, &a, ax, one, ay, one));
    PetscCall(PetscLogGpuFlops(2.0 * bnz));
    PetscCall(PetscLogGpuTimeEnd());
    PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(X, &ax));
    PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
    PetscCall(MatSeqAIJInvalidateDiagonal(Y));
  } else {
    PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(Y, PETSC_FALSE));
    PetscCall(MatAXPY_SeqAIJ(Y, a, X, str));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatScale_SeqAIJCUSPARSE(Mat Y, PetscScalar a)
{
  Mat_SeqAIJ    *y = (Mat_SeqAIJ *)Y->data;
  PetscScalar   *ay;
  cublasHandle_t cublasv2handle;
  PetscBLASInt   one = 1, bnz = 1;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJCUSPARSEGetArray(Y, &ay));
  PetscCall(PetscCUBLASGetHandle(&cublasv2handle));
  PetscCall(PetscBLASIntCast(y->nz, &bnz));
  PetscCall(PetscLogGpuTimeBegin());
  PetscCallCUBLAS(cublasXscal(cublasv2handle, bnz, &a, ay, one));
  PetscCall(PetscLogGpuFlops(bnz));
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(MatSeqAIJCUSPARSERestoreArray(Y, &ay));
  PetscCall(MatSeqAIJInvalidateDiagonal(Y));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroEntries_SeqAIJCUSPARSE(Mat A)
{
  PetscBool   both = PETSC_FALSE;
  Mat_SeqAIJ *a    = (Mat_SeqAIJ *)A->data;

  PetscFunctionBegin;
  if (A->factortype == MAT_FACTOR_NONE) {
    Mat_SeqAIJCUSPARSE *spptr = (Mat_SeqAIJCUSPARSE *)A->spptr;
    if (spptr->mat) {
      CsrMatrix *matrix = (CsrMatrix *)spptr->mat->mat;
      if (matrix->values) {
        both = PETSC_TRUE;
        thrust::fill(thrust::device, matrix->values->begin(), matrix->values->end(), 0.);
      }
    }
    if (spptr->matTranspose) {
      CsrMatrix *matrix = (CsrMatrix *)spptr->matTranspose->mat;
      if (matrix->values) thrust::fill(thrust::device, matrix->values->begin(), matrix->values->end(), 0.);
    }
  }
  PetscCall(PetscArrayzero(a->a, a->i[A->rmap->n]));
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  if (both) A->offloadmask = PETSC_OFFLOAD_BOTH;
  else A->offloadmask = PETSC_OFFLOAD_CPU;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatBindToCPU_SeqAIJCUSPARSE(Mat A, PetscBool flg)
{
  Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;

  PetscFunctionBegin;
  if (A->factortype != MAT_FACTOR_NONE) {
    A->boundtocpu = flg;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  if (flg) {
    PetscCall(MatSeqAIJCUSPARSECopyFromGPU(A));

    A->ops->scale                     = MatScale_SeqAIJ;
    A->ops->axpy                      = MatAXPY_SeqAIJ;
    A->ops->zeroentries               = MatZeroEntries_SeqAIJ;
    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;
    A->ops->productsetfromoptions     = MatProductSetFromOptions_SeqAIJ;
    PetscCall(PetscMemzero(a->ops, sizeof(Mat_SeqAIJOps)));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", NULL));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", NULL));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", NULL));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", NULL));
  } else {
    A->ops->scale                     = MatScale_SeqAIJCUSPARSE;
    A->ops->axpy                      = MatAXPY_SeqAIJCUSPARSE;
    A->ops->zeroentries               = MatZeroEntries_SeqAIJCUSPARSE;
    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;
    A->ops->productsetfromoptions     = MatProductSetFromOptions_SeqAIJCUSPARSE;
    a->ops->getarray                  = MatSeqAIJGetArray_SeqAIJCUSPARSE;
    a->ops->restorearray              = MatSeqAIJRestoreArray_SeqAIJCUSPARSE;
    a->ops->getarrayread              = MatSeqAIJGetArrayRead_SeqAIJCUSPARSE;
    a->ops->restorearrayread          = MatSeqAIJRestoreArrayRead_SeqAIJCUSPARSE;
    a->ops->getarraywrite             = MatSeqAIJGetArrayWrite_SeqAIJCUSPARSE;
    a->ops->restorearraywrite         = MatSeqAIJRestoreArrayWrite_SeqAIJCUSPARSE;
    a->ops->getcsrandmemtype          = MatSeqAIJGetCSRAndMemType_SeqAIJCUSPARSE;

    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", MatSeqAIJCopySubArray_SeqAIJCUSPARSE));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdensecuda_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqdense_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_SeqAIJCUSPARSE));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", MatSetValuesCOO_SeqAIJCUSPARSE));
    PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaijcusparse_C", MatProductSetFromOptions_SeqAIJCUSPARSE));
  }
  A->boundtocpu = flg;
  if (flg && a->inode.size) {
    a->inode.use = PETSC_TRUE;
  } else {
    a->inode.use = PETSC_FALSE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBegin;
  PetscCall(PetscDeviceInitialize(PETSC_DEVICE_CUDA)); /* first use of CUSPARSE may be via MatConvert */
  if (reuse == MAT_INITIAL_MATRIX) {
    PetscCall(MatDuplicate(A, MAT_COPY_VALUES, newmat));
  } else if (reuse == MAT_REUSE_MATRIX) {
    PetscCall(MatCopy(A, *newmat, SAME_NONZERO_PATTERN));
  }
  B = *newmat;

  PetscCall(PetscFree(B->defaultvectype));
  PetscCall(PetscStrallocpy(VECCUDA, &B->defaultvectype));

  if (reuse != MAT_REUSE_MATRIX && !B->spptr) {
    if (B->factortype == MAT_FACTOR_NONE) {
      Mat_SeqAIJCUSPARSE *spptr;
      PetscCall(PetscNew(&spptr));
      PetscCallCUSPARSE(cusparseCreate(&spptr->handle));
      PetscCallCUSPARSE(cusparseSetStream(spptr->handle, PetscDefaultCudaStream));
      spptr->format = MAT_CUSPARSE_CSR;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
  #if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
      spptr->spmvAlg = CUSPARSE_SPMV_CSR_ALG1; /* default, since we only support csr */
  #else
      spptr->spmvAlg = CUSPARSE_CSRMV_ALG1; /* default, since we only support csr */
  #endif
      spptr->spmmAlg    = CUSPARSE_SPMM_CSR_ALG1; /* default, only support column-major dense matrix B */
      spptr->csr2cscAlg = CUSPARSE_CSR2CSC_ALG1;
#endif
      B->spptr = spptr;
    } else {
      Mat_SeqAIJCUSPARSETriFactors *spptr;

      PetscCall(PetscNew(&spptr));
      PetscCallCUSPARSE(cusparseCreate(&spptr->handle));
      PetscCallCUSPARSE(cusparseSetStream(spptr->handle, PetscDefaultCudaStream));
      B->spptr = spptr;
    }
    B->offloadmask = PETSC_OFFLOAD_UNALLOCATED;
  }
  B->ops->assemblyend    = MatAssemblyEnd_SeqAIJCUSPARSE;
  B->ops->destroy        = MatDestroy_SeqAIJCUSPARSE;
  B->ops->setoption      = MatSetOption_SeqAIJCUSPARSE;
  B->ops->setfromoptions = MatSetFromOptions_SeqAIJCUSPARSE;
  B->ops->bindtocpu      = MatBindToCPU_SeqAIJCUSPARSE;
  B->ops->duplicate      = MatDuplicate_SeqAIJCUSPARSE;

  PetscCall(MatBindToCPU_SeqAIJCUSPARSE(B, PETSC_FALSE));
  PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJCUSPARSE));
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatCUSPARSESetFormat_C", MatCUSPARSESetFormat_SeqAIJCUSPARSE));
#if defined(PETSC_HAVE_HYPRE)
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaijcusparse_hypre_C", MatConvert_AIJ_HYPRE));
#endif
  PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatCUSPARSESetUseCPUSolve_C", MatCUSPARSESetUseCPUSolve_SeqAIJCUSPARSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJCUSPARSE(Mat B)
{
  PetscFunctionBegin;
  PetscCall(MatCreate_SeqAIJ(B));
  PetscCall(MatConvert_SeqAIJ_SeqAIJCUSPARSE(B, MATSEQAIJCUSPARSE, MAT_INPLACE_MATRIX, &B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

   A matrix type whose data resides on NVIDIA GPUs. These matrices can be in either
   CSR, ELL, or Hybrid format.
   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()`).
                                      Other options include ell (ellpack) or hyb (hybrid).
.  -mat_cusparse_mult_storage_format csr - sets the storage format of matrices (for `MatMult()`). Other options include ell (ellpack) or hyb (hybrid).
-  -mat_cusparse_use_cpu_solve - Do `MatSolve()` on CPU

  Level: beginner

.seealso: [](ch_matrices), `Mat`, `MatCreateSeqAIJCUSPARSE()`, `MatCUSPARSESetUseCPUSolve()`, `MATAIJCUSPARSE`, `MatCreateAIJCUSPARSE()`, `MatCUSPARSESetFormat()`, `MatCUSPARSEStorageFormat`, `MatCUSPARSEFormatOperation`
M*/

PETSC_EXTERN PetscErrorCode MatSolverTypeRegister_CUSPARSE(void)
{
  PetscFunctionBegin;
  PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_LU, MatGetFactor_seqaijcusparse_cusparse));
  PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_CHOLESKY, MatGetFactor_seqaijcusparse_cusparse));
  PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_ILU, MatGetFactor_seqaijcusparse_cusparse));
  PetscCall(MatSolverTypeRegister(MATSOLVERCUSPARSE, MATSEQAIJCUSPARSE, MAT_FACTOR_ICC, MatGetFactor_seqaijcusparse_cusparse));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJCUSPARSE_Destroy(Mat mat)
{
  Mat_SeqAIJCUSPARSE *cusp = static_cast<Mat_SeqAIJCUSPARSE *>(mat->spptr);

  PetscFunctionBegin;
  if (cusp) {
    PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->mat, cusp->format));
    PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->matTranspose, cusp->format));
    delete cusp->workVector;
    delete cusp->rowoffsets_gpu;
    delete cusp->csr2csc_i;
    delete cusp->coords;
    if (cusp->handle) PetscCallCUSPARSE(cusparseDestroy(cusp->handle));
    PetscCall(PetscFree(mat->spptr));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

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(PETSC_SUCCESS);
}

#if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSETriFactorStruct **trifactor)
{
  PetscFunctionBegin;
  if (*trifactor) {
    if ((*trifactor)->descr) PetscCallCUSPARSE(cusparseDestroyMatDescr((*trifactor)->descr));
    if ((*trifactor)->solveInfo) PetscCallCUSPARSE(cusparseDestroyCsrsvInfo((*trifactor)->solveInfo));
    PetscCall(CsrMatrix_Destroy(&(*trifactor)->csrMat));
    if ((*trifactor)->solveBuffer) PetscCallCUDA(cudaFree((*trifactor)->solveBuffer));
    if ((*trifactor)->AA_h) PetscCallCUDA(cudaFreeHost((*trifactor)->AA_h));
  #if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
    if ((*trifactor)->csr2cscBuffer) PetscCallCUDA(cudaFree((*trifactor)->csr2cscBuffer));
  #endif
    PetscCall(PetscFree(*trifactor));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif

static PetscErrorCode MatSeqAIJCUSPARSEMultStruct_Destroy(Mat_SeqAIJCUSPARSEMultStruct **matstruct, MatCUSPARSEStorageFormat format)
{
  CsrMatrix *mat;

  PetscFunctionBegin;
  if (*matstruct) {
    if ((*matstruct)->mat) {
      if (format == MAT_CUSPARSE_ELL || format == MAT_CUSPARSE_HYB) {
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_CUSPARSE_ELL and MAT_CUSPARSE_HYB are not supported since CUDA-11.0");
#else
        cusparseHybMat_t hybMat = (cusparseHybMat_t)(*matstruct)->mat;
        PetscCallCUSPARSE(cusparseDestroyHybMat(hybMat));
#endif
      } else {
        mat = (CsrMatrix *)(*matstruct)->mat;
        PetscCall(CsrMatrix_Destroy(&mat));
      }
    }
    if ((*matstruct)->descr) PetscCallCUSPARSE(cusparseDestroyMatDescr((*matstruct)->descr));
    delete (*matstruct)->cprowIndices;
    if ((*matstruct)->alpha_one) PetscCallCUDA(cudaFree((*matstruct)->alpha_one));
    if ((*matstruct)->beta_zero) PetscCallCUDA(cudaFree((*matstruct)->beta_zero));
    if ((*matstruct)->beta_one) PetscCallCUDA(cudaFree((*matstruct)->beta_one));

#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
    Mat_SeqAIJCUSPARSEMultStruct *mdata = *matstruct;
    if (mdata->matDescr) PetscCallCUSPARSE(cusparseDestroySpMat(mdata->matDescr));
    for (int i = 0; i < 3; i++) {
      if (mdata->cuSpMV[i].initialized) {
        PetscCallCUDA(cudaFree(mdata->cuSpMV[i].spmvBuffer));
        PetscCallCUSPARSE(cusparseDestroyDnVec(mdata->cuSpMV[i].vecXDescr));
        PetscCallCUSPARSE(cusparseDestroyDnVec(mdata->cuSpMV[i].vecYDescr));
      }
    }
#endif
    delete *matstruct;
    *matstruct = NULL;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSeqAIJCUSPARSETriFactors_Reset(Mat_SeqAIJCUSPARSETriFactors_p *trifactors)
{
  Mat_SeqAIJCUSPARSETriFactors *fs = *trifactors;

  PetscFunctionBegin;
  if (fs) {
#if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
    PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->loTriFactorPtr));
    PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->upTriFactorPtr));
    PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->loTriFactorPtrTranspose));
    PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&fs->upTriFactorPtrTranspose));
    delete fs->workVector;
    fs->workVector = NULL;
#endif
    delete fs->rpermIndices;
    delete fs->cpermIndices;
    fs->rpermIndices  = NULL;
    fs->cpermIndices  = NULL;
    fs->init_dev_prop = PETSC_FALSE;
#if PETSC_PKG_CUDA_VERSION_GE(11, 4, 0)
    PetscCallCUDA(cudaFree(fs->csrRowPtr));
    PetscCallCUDA(cudaFree(fs->csrColIdx));
    PetscCallCUDA(cudaFree(fs->csrRowPtr32));
    PetscCallCUDA(cudaFree(fs->csrColIdx32));
    PetscCallCUDA(cudaFree(fs->csrVal));
    PetscCallCUDA(cudaFree(fs->diag));
    PetscCallCUDA(cudaFree(fs->X));
    PetscCallCUDA(cudaFree(fs->Y));
    // PetscCallCUDA(cudaFree(fs->factBuffer_M)); /* No needed since factBuffer_M shares with one of spsvBuffer_L/U */
    PetscCallCUDA(cudaFree(fs->spsvBuffer_L));
    PetscCallCUDA(cudaFree(fs->spsvBuffer_U));
    PetscCallCUDA(cudaFree(fs->spsvBuffer_Lt));
    PetscCallCUDA(cudaFree(fs->spsvBuffer_Ut));
    PetscCallCUSPARSE(cusparseDestroyMatDescr(fs->matDescr_M));
    PetscCallCUSPARSE(cusparseDestroySpMat(fs->spMatDescr_L));
    PetscCallCUSPARSE(cusparseDestroySpMat(fs->spMatDescr_U));
    PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_L));
    PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_Lt));
    PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_U));
    PetscCallCUSPARSE(cusparseSpSV_destroyDescr(fs->spsvDescr_Ut));
    PetscCallCUSPARSE(cusparseDestroyDnVec(fs->dnVecDescr_X));
    PetscCallCUSPARSE(cusparseDestroyDnVec(fs->dnVecDescr_Y));
    PetscCallCUSPARSE(cusparseDestroyCsrilu02Info(fs->ilu0Info_M));
    PetscCallCUSPARSE(cusparseDestroyCsric02Info(fs->ic0Info_M));
    PetscCall(PetscFree(fs->csrRowPtr_h));
    PetscCall(PetscFree(fs->csrVal_h));
    PetscCall(PetscFree(fs->diag_h));
    fs->createdTransposeSpSVDescr    = PETSC_FALSE;
    fs->updatedTransposeSpSVAnalysis = PETSC_FALSE;
#endif
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJCUSPARSETriFactors_Destroy(Mat_SeqAIJCUSPARSETriFactors **trifactors)
{
  PetscFunctionBegin;
  if (*trifactors) {
    PetscCall(MatSeqAIJCUSPARSETriFactors_Reset(trifactors));
    PetscCallCUSPARSE(cusparseDestroy((*trifactors)->handle));
    PetscCall(PetscFree(*trifactors));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

struct IJCompare {
  __host__ __device__ inline bool operator()(const thrust::tuple<PetscInt, PetscInt> &t1, const thrust::tuple<PetscInt, PetscInt> &t2)
  {
    if (t1.get<0>() < t2.get<0>()) return true;
    if (t1.get<0>() == t2.get<0>()) return t1.get<1>() < t2.get<1>();
    return false;
  }
};

static PetscErrorCode MatSeqAIJCUSPARSEInvalidateTranspose(Mat A, PetscBool destroy)
{
  Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;

  PetscFunctionBegin;
  PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
  if (!cusp) PetscFunctionReturn(PETSC_SUCCESS);
  if (destroy) {
    PetscCall(MatSeqAIJCUSPARSEMultStruct_Destroy(&cusp->matTranspose, cusp->format));
    delete cusp->csr2csc_i;
    cusp->csr2csc_i = NULL;
  }
  A->transupdated = PETSC_FALSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCOOStructDestroy_SeqAIJCUSPARSE(void *data)
{
  MatCOOStruct_SeqAIJ *coo = (MatCOOStruct_SeqAIJ *)data;

  PetscFunctionBegin;
  PetscCallCUDA(cudaFree(coo->perm));
  PetscCallCUDA(cudaFree(coo->jmap));
  PetscCall(PetscFree(coo));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetPreallocationCOO_SeqAIJCUSPARSE(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
{
  PetscBool            dev_ij = PETSC_FALSE;
  PetscMemType         mtype  = PETSC_MEMTYPE_HOST;
  PetscInt            *i, *j;
  PetscContainer       container_h, container_d;
  MatCOOStruct_SeqAIJ *coo_h, *coo_d;

  PetscFunctionBegin;
  // The two MatResetPreallocationCOO_* must be done in order. The former relies on values that might be destroyed by the latter
  PetscCall(PetscGetMemType(coo_i, &mtype));
  if (PetscMemTypeDevice(mtype)) {
    dev_ij = PETSC_TRUE;
    PetscCall(PetscMalloc2(coo_n, &i, coo_n, &j));
    PetscCallCUDA(cudaMemcpy(i, coo_i, coo_n * sizeof(PetscInt), cudaMemcpyDeviceToHost));
    PetscCallCUDA(cudaMemcpy(j, coo_j, coo_n * sizeof(PetscInt), cudaMemcpyDeviceToHost));
  } else {
    i = coo_i;
    j = coo_j;
  }

  PetscCall(MatSetPreallocationCOO_SeqAIJ(mat, coo_n, i, j));
  if (dev_ij) PetscCall(PetscFree2(i, j));
  mat->offloadmask = PETSC_OFFLOAD_CPU;
  // Create the GPU memory
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(mat));

  // Copy the COO struct to device
  PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject *)&container_h));
  PetscCall(PetscContainerGetPointer(container_h, (void **)&coo_h));
  PetscCall(PetscMalloc1(1, &coo_d));
  *coo_d = *coo_h; // do a shallow copy and then amend some fields that need to be different
  PetscCallCUDA(cudaMalloc((void **)&coo_d->jmap, (coo_h->nz + 1) * sizeof(PetscCount)));
  PetscCallCUDA(cudaMemcpy(coo_d->jmap, coo_h->jmap, (coo_h->nz + 1) * sizeof(PetscCount), cudaMemcpyHostToDevice));
  PetscCallCUDA(cudaMalloc((void **)&coo_d->perm, coo_h->Atot * sizeof(PetscCount)));
  PetscCallCUDA(cudaMemcpy(coo_d->perm, coo_h->perm, coo_h->Atot * sizeof(PetscCount), cudaMemcpyHostToDevice));

  // Put the COO struct in a container and then attach that to the matrix
  PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container_d));
  PetscCall(PetscContainerSetPointer(container_d, coo_d));
  PetscCall(PetscContainerSetUserDestroy(container_d, MatCOOStructDestroy_SeqAIJCUSPARSE));
  PetscCall(PetscObjectCompose((PetscObject)mat, "__PETSc_MatCOOStruct_Device", (PetscObject)container_d));
  PetscCall(PetscContainerDestroy(&container_d));
  PetscFunctionReturn(PETSC_SUCCESS);
}

__global__ static void MatAddCOOValues(const PetscScalar kv[], PetscCount nnz, const PetscCount jmap[], const PetscCount perm[], InsertMode imode, PetscScalar a[])
{
  PetscCount       i         = blockIdx.x * blockDim.x + threadIdx.x;
  const PetscCount grid_size = gridDim.x * blockDim.x;
  for (; i < nnz; i += grid_size) {
    PetscScalar sum = 0.0;
    for (PetscCount k = jmap[i]; k < jmap[i + 1]; k++) sum += kv[perm[k]];
    a[i] = (imode == INSERT_VALUES ? 0.0 : a[i]) + sum;
  }
}

static PetscErrorCode MatSetValuesCOO_SeqAIJCUSPARSE(Mat A, const PetscScalar v[], InsertMode imode)
{
  Mat_SeqAIJ          *seq  = (Mat_SeqAIJ *)A->data;
  Mat_SeqAIJCUSPARSE  *dev  = (Mat_SeqAIJCUSPARSE *)A->spptr;
  PetscCount           Annz = seq->nz;
  PetscMemType         memtype;
  const PetscScalar   *v1 = v;
  PetscScalar         *Aa;
  PetscContainer       container;
  MatCOOStruct_SeqAIJ *coo;

  PetscFunctionBegin;
  if (!dev->mat) PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));

  PetscCall(PetscObjectQuery((PetscObject)A, "__PETSc_MatCOOStruct_Device", (PetscObject *)&container));
  PetscCall(PetscContainerGetPointer(container, (void **)&coo));

  PetscCall(PetscGetMemType(v, &memtype));
  if (PetscMemTypeHost(memtype)) { /* If user gave v[] in host, we might need to copy it to device if any */
    PetscCallCUDA(cudaMalloc((void **)&v1, coo->n * sizeof(PetscScalar)));
    PetscCallCUDA(cudaMemcpy((void *)v1, v, coo->n * sizeof(PetscScalar), cudaMemcpyHostToDevice));
  }

  if (imode == INSERT_VALUES) PetscCall(MatSeqAIJCUSPARSEGetArrayWrite(A, &Aa));
  else PetscCall(MatSeqAIJCUSPARSEGetArray(A, &Aa));

  PetscCall(PetscLogGpuTimeBegin());
  if (Annz) {
    MatAddCOOValues<<<(Annz + 255) / 256, 256>>>(v1, Annz, coo->jmap, coo->perm, imode, Aa);
    PetscCallCUDA(cudaPeekAtLastError());
  }
  PetscCall(PetscLogGpuTimeEnd());

  if (imode == INSERT_VALUES) PetscCall(MatSeqAIJCUSPARSERestoreArrayWrite(A, &Aa));
  else PetscCall(MatSeqAIJCUSPARSERestoreArray(A, &Aa));

  if (PetscMemTypeHost(memtype)) PetscCallCUDA(cudaFree((void *)v1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqAIJCUSPARSEGetIJ - returns the device row storage `i` and `j` indices for `MATSEQAIJCUSPARSE` matrices.

  Not Collective

  Input Parameters:
+ A          - the matrix
- compressed - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be always returned in compressed form

  Output Parameters:
+ i - the CSR row pointers
- j - the CSR column indices

  Level: developer

  Note:
  When compressed is true, the CSR structure does not contain empty rows

.seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSERestoreIJ()`, `MatSeqAIJCUSPARSEGetArrayRead()`
@*/
PetscErrorCode MatSeqAIJCUSPARSEGetIJ(Mat A, PetscBool compressed, const int **i, const int **j)
{
  Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
  CsrMatrix          *csr;
  Mat_SeqAIJ         *a = (Mat_SeqAIJ *)A->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  if (!i || !j) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
  PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
  csr = (CsrMatrix *)cusp->mat->mat;
  if (i) {
    if (!compressed && a->compressedrow.use) { /* need full row offset */
      if (!cusp->rowoffsets_gpu) {
        cusp->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
        cusp->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
        PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
      }
      *i = cusp->rowoffsets_gpu->data().get();
    } else *i = csr->row_offsets->data().get();
  }
  if (j) *j = csr->column_indices->data().get();
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqAIJCUSPARSERestoreIJ - restore the device row storage `i` and `j` indices obtained with `MatSeqAIJCUSPARSEGetIJ()`

  Not Collective

  Input Parameters:
+ A          - the matrix
. compressed - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be always returned in compressed form
. i          - the CSR row pointers
- j          - the CSR column indices

  Level: developer

.seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetIJ()`
@*/
PetscErrorCode MatSeqAIJCUSPARSERestoreIJ(Mat A, PetscBool compressed, const int **i, const int **j)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
  if (i) *i = NULL;
  if (j) *j = NULL;
  (void)compressed;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqAIJCUSPARSEGetArrayRead - gives read-only access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored

  Not Collective

  Input Parameter:
. A - a `MATSEQAIJCUSPARSE` matrix

  Output Parameter:
. a - pointer to the device data

  Level: developer

  Note:
  May trigger host-device copies if up-to-date matrix data is on host

.seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`, `MatSeqAIJCUSPARSEGetArrayWrite()`, `MatSeqAIJCUSPARSERestoreArrayRead()`
@*/
PetscErrorCode MatSeqAIJCUSPARSEGetArrayRead(Mat A, const PetscScalar **a)
{
  Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
  CsrMatrix          *csr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscAssertPointer(a, 2);
  PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
  PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
  csr = (CsrMatrix *)cusp->mat->mat;
  PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
  *a = csr->values->data().get();
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqAIJCUSPARSERestoreArrayRead - restore the read-only access array obtained from `MatSeqAIJCUSPARSEGetArrayRead()`

  Not Collective

  Input Parameters:
+ A - a `MATSEQAIJCUSPARSE` matrix
- a - pointer to the device data

  Level: developer

.seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayRead()`
@*/
PetscErrorCode MatSeqAIJCUSPARSERestoreArrayRead(Mat A, const PetscScalar **a)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscAssertPointer(a, 2);
  PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqAIJCUSPARSEGetArray - gives read-write access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored

  Not Collective

  Input Parameter:
. A - a `MATSEQAIJCUSPARSE` matrix

  Output Parameter:
. a - pointer to the device data

  Level: developer

  Note:
  May trigger host-device copies if up-to-date matrix data is on host

.seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayRead()`, `MatSeqAIJCUSPARSEGetArrayWrite()`, `MatSeqAIJCUSPARSERestoreArray()`
@*/
PetscErrorCode MatSeqAIJCUSPARSEGetArray(Mat A, PetscScalar **a)
{
  Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
  CsrMatrix          *csr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscAssertPointer(a, 2);
  PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
  PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
  PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
  PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
  csr = (CsrMatrix *)cusp->mat->mat;
  PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
  *a             = csr->values->data().get();
  A->offloadmask = PETSC_OFFLOAD_GPU;
  PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}
/*@C
  MatSeqAIJCUSPARSERestoreArray - restore the read-write access array obtained from `MatSeqAIJCUSPARSEGetArray()`

  Not Collective

  Input Parameters:
+ A - a `MATSEQAIJCUSPARSE` matrix
- a - pointer to the device data

  Level: developer

.seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`
@*/
PetscErrorCode MatSeqAIJCUSPARSERestoreArray(Mat A, PetscScalar **a)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscAssertPointer(a, 2);
  PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  PetscCall(PetscObjectStateIncrease((PetscObject)A));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqAIJCUSPARSEGetArrayWrite - gives write access to the array where the device data for a `MATSEQAIJCUSPARSE` matrix is stored

  Not Collective

  Input Parameter:
. A - a `MATSEQAIJCUSPARSE` matrix

  Output Parameter:
. a - pointer to the device data

  Level: developer

  Note:
  Does not trigger host-device copies and flags data validity on the GPU

.seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArray()`, `MatSeqAIJCUSPARSEGetArrayRead()`, `MatSeqAIJCUSPARSERestoreArrayWrite()`
@*/
PetscErrorCode MatSeqAIJCUSPARSEGetArrayWrite(Mat A, PetscScalar **a)
{
  Mat_SeqAIJCUSPARSE *cusp = (Mat_SeqAIJCUSPARSE *)A->spptr;
  CsrMatrix          *csr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscAssertPointer(a, 2);
  PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
  PetscCheck(cusp->format != MAT_CUSPARSE_ELL && cusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
  PetscCheck(cusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
  csr = (CsrMatrix *)cusp->mat->mat;
  PetscCheck(csr->values, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing CUDA memory");
  *a             = csr->values->data().get();
  A->offloadmask = PETSC_OFFLOAD_GPU;
  PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(A, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatSeqAIJCUSPARSERestoreArrayWrite - restore the write-only access array obtained from `MatSeqAIJCUSPARSEGetArrayWrite()`

  Not Collective

  Input Parameters:
+ A - a `MATSEQAIJCUSPARSE` matrix
- a - pointer to the device data

  Level: developer

.seealso: [](ch_matrices), `Mat`, `MatSeqAIJCUSPARSEGetArrayWrite()`
@*/
PetscErrorCode MatSeqAIJCUSPARSERestoreArrayWrite(Mat A, PetscScalar **a)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscAssertPointer(a, 2);
  PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  PetscCall(PetscObjectStateIncrease((PetscObject)A));
  *a = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

struct IJCompare4 {
  __host__ __device__ inline bool operator()(const thrust::tuple<int, int, PetscScalar, int> &t1, const thrust::tuple<int, int, PetscScalar, int> &t2)
  {
    if (t1.get<0>() < t2.get<0>()) return true;
    if (t1.get<0>() == t2.get<0>()) return t1.get<1>() < t2.get<1>();
    return false;
  }
};

struct Shift {
  int _shift;

  Shift(int shift) : _shift(shift) { }
  __host__ __device__ inline int operator()(const int &c) { return c + _shift; }
};

/* merges two SeqAIJCUSPARSE matrices A, B by concatenating their rows. [A';B']' operation in MATLAB notation */
PetscErrorCode MatSeqAIJCUSPARSEMergeMats(Mat A, Mat B, MatReuse reuse, Mat *C)
{
  Mat_SeqAIJ                   *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
  Mat_SeqAIJCUSPARSE           *Acusp = (Mat_SeqAIJCUSPARSE *)A->spptr, *Bcusp = (Mat_SeqAIJCUSPARSE *)B->spptr, *Ccusp;
  Mat_SeqAIJCUSPARSEMultStruct *Cmat;
  CsrMatrix                    *Acsr, *Bcsr, *Ccsr;
  PetscInt                      Annz, Bnnz;
  cusparseStatus_t              stat;
  PetscInt                      i, m, n, zero = 0;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidHeaderSpecific(B, MAT_CLASSID, 2);
  PetscAssertPointer(C, 4);
  PetscCheckTypeName(A, MATSEQAIJCUSPARSE);
  PetscCheckTypeName(B, MATSEQAIJCUSPARSE);
  PetscCheck(A->rmap->n == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Invalid number or rows %" PetscInt_FMT " != %" PetscInt_FMT, A->rmap->n, B->rmap->n);
  PetscCheck(reuse != MAT_INPLACE_MATRIX, PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_INPLACE_MATRIX not supported");
  PetscCheck(Acusp->format != MAT_CUSPARSE_ELL && Acusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
  PetscCheck(Bcusp->format != MAT_CUSPARSE_ELL && Bcusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
  if (reuse == MAT_INITIAL_MATRIX) {
    m = A->rmap->n;
    n = A->cmap->n + B->cmap->n;
    PetscCall(MatCreate(PETSC_COMM_SELF, C));
    PetscCall(MatSetSizes(*C, m, n, m, n));
    PetscCall(MatSetType(*C, MATSEQAIJCUSPARSE));
    c                       = (Mat_SeqAIJ *)(*C)->data;
    Ccusp                   = (Mat_SeqAIJCUSPARSE *)(*C)->spptr;
    Cmat                    = new Mat_SeqAIJCUSPARSEMultStruct;
    Ccsr                    = new CsrMatrix;
    Cmat->cprowIndices      = NULL;
    c->compressedrow.use    = PETSC_FALSE;
    c->compressedrow.nrows  = 0;
    c->compressedrow.i      = NULL;
    c->compressedrow.rindex = NULL;
    Ccusp->workVector       = NULL;
    Ccusp->nrows            = m;
    Ccusp->mat              = Cmat;
    Ccusp->mat->mat         = Ccsr;
    Ccsr->num_rows          = m;
    Ccsr->num_cols          = n;
    PetscCallCUSPARSE(cusparseCreateMatDescr(&Cmat->descr));
    PetscCallCUSPARSE(cusparseSetMatIndexBase(Cmat->descr, CUSPARSE_INDEX_BASE_ZERO));
    PetscCallCUSPARSE(cusparseSetMatType(Cmat->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
    PetscCallCUDA(cudaMalloc((void **)&Cmat->alpha_one, sizeof(PetscScalar)));
    PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_zero, sizeof(PetscScalar)));
    PetscCallCUDA(cudaMalloc((void **)&Cmat->beta_one, sizeof(PetscScalar)));
    PetscCallCUDA(cudaMemcpy(Cmat->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
    PetscCallCUDA(cudaMemcpy(Cmat->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
    PetscCallCUDA(cudaMemcpy(Cmat->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
    PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
    PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
    PetscCheck(Acusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
    PetscCheck(Bcusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");

    Acsr                 = (CsrMatrix *)Acusp->mat->mat;
    Bcsr                 = (CsrMatrix *)Bcusp->mat->mat;
    Annz                 = (PetscInt)Acsr->column_indices->size();
    Bnnz                 = (PetscInt)Bcsr->column_indices->size();
    c->nz                = Annz + Bnnz;
    Ccsr->row_offsets    = new THRUSTINTARRAY32(m + 1);
    Ccsr->column_indices = new THRUSTINTARRAY32(c->nz);
    Ccsr->values         = new THRUSTARRAY(c->nz);
    Ccsr->num_entries    = c->nz;
    Ccusp->coords        = new THRUSTINTARRAY(c->nz);
    if (c->nz) {
      auto              Acoo = new THRUSTINTARRAY32(Annz);
      auto              Bcoo = new THRUSTINTARRAY32(Bnnz);
      auto              Ccoo = new THRUSTINTARRAY32(c->nz);
      THRUSTINTARRAY32 *Aroff, *Broff;

      if (a->compressedrow.use) { /* need full row offset */
        if (!Acusp->rowoffsets_gpu) {
          Acusp->rowoffsets_gpu = new THRUSTINTARRAY32(A->rmap->n + 1);
          Acusp->rowoffsets_gpu->assign(a->i, a->i + A->rmap->n + 1);
          PetscCall(PetscLogCpuToGpu((A->rmap->n + 1) * sizeof(PetscInt)));
        }
        Aroff = Acusp->rowoffsets_gpu;
      } else Aroff = Acsr->row_offsets;
      if (b->compressedrow.use) { /* need full row offset */
        if (!Bcusp->rowoffsets_gpu) {
          Bcusp->rowoffsets_gpu = new THRUSTINTARRAY32(B->rmap->n + 1);
          Bcusp->rowoffsets_gpu->assign(b->i, b->i + B->rmap->n + 1);
          PetscCall(PetscLogCpuToGpu((B->rmap->n + 1) * sizeof(PetscInt)));
        }
        Broff = Bcusp->rowoffsets_gpu;
      } else Broff = Bcsr->row_offsets;
      PetscCall(PetscLogGpuTimeBegin());
      stat = cusparseXcsr2coo(Acusp->handle, Aroff->data().get(), Annz, m, Acoo->data().get(), CUSPARSE_INDEX_BASE_ZERO);
      PetscCallCUSPARSE(stat);
      stat = cusparseXcsr2coo(Bcusp->handle, Broff->data().get(), Bnnz, m, Bcoo->data().get(), CUSPARSE_INDEX_BASE_ZERO);
      PetscCallCUSPARSE(stat);
      /* Issues when using bool with large matrices on SUMMIT 10.2.89 */
      auto Aperm = thrust::make_constant_iterator(1);
      auto Bperm = thrust::make_constant_iterator(0);
#if PETSC_PKG_CUDA_VERSION_GE(10, 0, 0)
      auto Bcib = thrust::make_transform_iterator(Bcsr->column_indices->begin(), Shift(A->cmap->n));
      auto Bcie = thrust::make_transform_iterator(Bcsr->column_indices->end(), Shift(A->cmap->n));
#else
      /* there are issues instantiating the merge operation using a transform iterator for the columns of B */
      auto Bcib = Bcsr->column_indices->begin();
      auto Bcie = Bcsr->column_indices->end();
      thrust::transform(Bcib, Bcie, Bcib, Shift(A->cmap->n));
#endif
      auto wPerm = new THRUSTINTARRAY32(Annz + Bnnz);
      auto Azb   = thrust::make_zip_iterator(thrust::make_tuple(Acoo->begin(), Acsr->column_indices->begin(), Acsr->values->begin(), Aperm));
      auto Aze   = thrust::make_zip_iterator(thrust::make_tuple(Acoo->end(), Acsr->column_indices->end(), Acsr->values->end(), Aperm));
      auto Bzb   = thrust::make_zip_iterator(thrust::make_tuple(Bcoo->begin(), Bcib, Bcsr->values->begin(), Bperm));
      auto Bze   = thrust::make_zip_iterator(thrust::make_tuple(Bcoo->end(), Bcie, Bcsr->values->end(), Bperm));
      auto Czb   = thrust::make_zip_iterator(thrust::make_tuple(Ccoo->begin(), Ccsr->column_indices->begin(), Ccsr->values->begin(), wPerm->begin()));
      auto p1    = Ccusp->coords->begin();
      auto p2    = Ccusp->coords->begin();
      thrust::advance(p2, Annz);
      PetscCallThrust(thrust::merge(thrust::device, Azb, Aze, Bzb, Bze, Czb, IJCompare4()));
#if PETSC_PKG_CUDA_VERSION_LT(10, 0, 0)
      thrust::transform(Bcib, Bcie, Bcib, Shift(-A->cmap->n));
#endif
      auto cci = thrust::make_counting_iterator(zero);
      auto cce = thrust::make_counting_iterator(c->nz);
#if 0 //Errors on SUMMIT cuda 11.1.0
      PetscCallThrust(thrust::partition_copy(thrust::device,cci,cce,wPerm->begin(),p1,p2,thrust::identity<int>()));
#else
      auto pred = thrust::identity<int>();
      PetscCallThrust(thrust::copy_if(thrust::device, cci, cce, wPerm->begin(), p1, pred));
      PetscCallThrust(thrust::remove_copy_if(thrust::device, cci, cce, wPerm->begin(), p2, pred));
#endif
      stat = cusparseXcoo2csr(Ccusp->handle, Ccoo->data().get(), c->nz, m, Ccsr->row_offsets->data().get(), CUSPARSE_INDEX_BASE_ZERO);
      PetscCallCUSPARSE(stat);
      PetscCall(PetscLogGpuTimeEnd());
      delete wPerm;
      delete Acoo;
      delete Bcoo;
      delete Ccoo;
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
      stat = cusparseCreateCsr(&Cmat->matDescr, Ccsr->num_rows, Ccsr->num_cols, Ccsr->num_entries, Ccsr->row_offsets->data().get(), Ccsr->column_indices->data().get(), Ccsr->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
      PetscCallCUSPARSE(stat);
#endif
      if (A->form_explicit_transpose && B->form_explicit_transpose) { /* if A and B have the transpose, generate C transpose too */
        PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(A));
        PetscCall(MatSeqAIJCUSPARSEFormExplicitTranspose(B));
        PetscBool                     AT = Acusp->matTranspose ? PETSC_TRUE : PETSC_FALSE, BT = Bcusp->matTranspose ? PETSC_TRUE : PETSC_FALSE;
        Mat_SeqAIJCUSPARSEMultStruct *CmatT = new Mat_SeqAIJCUSPARSEMultStruct;
        CsrMatrix                    *CcsrT = new CsrMatrix;
        CsrMatrix                    *AcsrT = AT ? (CsrMatrix *)Acusp->matTranspose->mat : NULL;
        CsrMatrix                    *BcsrT = BT ? (CsrMatrix *)Bcusp->matTranspose->mat : NULL;

        (*C)->form_explicit_transpose = PETSC_TRUE;
        (*C)->transupdated            = PETSC_TRUE;
        Ccusp->rowoffsets_gpu         = NULL;
        CmatT->cprowIndices           = NULL;
        CmatT->mat                    = CcsrT;
        CcsrT->num_rows               = n;
        CcsrT->num_cols               = m;
        CcsrT->num_entries            = c->nz;

        CcsrT->row_offsets    = new THRUSTINTARRAY32(n + 1);
        CcsrT->column_indices = new THRUSTINTARRAY32(c->nz);
        CcsrT->values         = new THRUSTARRAY(c->nz);

        PetscCall(PetscLogGpuTimeBegin());
        auto rT = CcsrT->row_offsets->begin();
        if (AT) {
          rT = thrust::copy(AcsrT->row_offsets->begin(), AcsrT->row_offsets->end(), rT);
          thrust::advance(rT, -1);
        }
        if (BT) {
          auto titb = thrust::make_transform_iterator(BcsrT->row_offsets->begin(), Shift(a->nz));
          auto tite = thrust::make_transform_iterator(BcsrT->row_offsets->end(), Shift(a->nz));
          thrust::copy(titb, tite, rT);
        }
        auto cT = CcsrT->column_indices->begin();
        if (AT) cT = thrust::copy(AcsrT->column_indices->begin(), AcsrT->column_indices->end(), cT);
        if (BT) thrust::copy(BcsrT->column_indices->begin(), BcsrT->column_indices->end(), cT);
        auto vT = CcsrT->values->begin();
        if (AT) vT = thrust::copy(AcsrT->values->begin(), AcsrT->values->end(), vT);
        if (BT) thrust::copy(BcsrT->values->begin(), BcsrT->values->end(), vT);
        PetscCall(PetscLogGpuTimeEnd());

        PetscCallCUSPARSE(cusparseCreateMatDescr(&CmatT->descr));
        PetscCallCUSPARSE(cusparseSetMatIndexBase(CmatT->descr, CUSPARSE_INDEX_BASE_ZERO));
        PetscCallCUSPARSE(cusparseSetMatType(CmatT->descr, CUSPARSE_MATRIX_TYPE_GENERAL));
        PetscCallCUDA(cudaMalloc((void **)&CmatT->alpha_one, sizeof(PetscScalar)));
        PetscCallCUDA(cudaMalloc((void **)&CmatT->beta_zero, sizeof(PetscScalar)));
        PetscCallCUDA(cudaMalloc((void **)&CmatT->beta_one, sizeof(PetscScalar)));
        PetscCallCUDA(cudaMemcpy(CmatT->alpha_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
        PetscCallCUDA(cudaMemcpy(CmatT->beta_zero, &PETSC_CUSPARSE_ZERO, sizeof(PetscScalar), cudaMemcpyHostToDevice));
        PetscCallCUDA(cudaMemcpy(CmatT->beta_one, &PETSC_CUSPARSE_ONE, sizeof(PetscScalar), cudaMemcpyHostToDevice));
#if PETSC_PKG_CUDA_VERSION_GE(11, 0, 0)
        stat = cusparseCreateCsr(&CmatT->matDescr, CcsrT->num_rows, CcsrT->num_cols, CcsrT->num_entries, CcsrT->row_offsets->data().get(), CcsrT->column_indices->data().get(), CcsrT->values->data().get(), CUSPARSE_INDEX_32I, CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, cusparse_scalartype);
        PetscCallCUSPARSE(stat);
#endif
        Ccusp->matTranspose = CmatT;
      }
    }

    c->singlemalloc = PETSC_FALSE;
    c->free_a       = PETSC_TRUE;
    c->free_ij      = PETSC_TRUE;
    PetscCall(PetscMalloc1(m + 1, &c->i));
    PetscCall(PetscMalloc1(c->nz, &c->j));
    if (PetscDefined(USE_64BIT_INDICES)) { /* 32 to 64-bit conversion on the GPU and then copy to host (lazy) */
      THRUSTINTARRAY ii(Ccsr->row_offsets->size());
      THRUSTINTARRAY jj(Ccsr->column_indices->size());
      ii = *Ccsr->row_offsets;
      jj = *Ccsr->column_indices;
      PetscCallCUDA(cudaMemcpy(c->i, ii.data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
      PetscCallCUDA(cudaMemcpy(c->j, jj.data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
    } else {
      PetscCallCUDA(cudaMemcpy(c->i, Ccsr->row_offsets->data().get(), Ccsr->row_offsets->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
      PetscCallCUDA(cudaMemcpy(c->j, Ccsr->column_indices->data().get(), Ccsr->column_indices->size() * sizeof(PetscInt), cudaMemcpyDeviceToHost));
    }
    PetscCall(PetscLogGpuToCpu((Ccsr->column_indices->size() + Ccsr->row_offsets->size()) * sizeof(PetscInt)));
    PetscCall(PetscMalloc1(m, &c->ilen));
    PetscCall(PetscMalloc1(m, &c->imax));
    c->maxnz         = c->nz;
    c->nonzerorowcnt = 0;
    c->rmax          = 0;
    for (i = 0; i < m; i++) {
      const PetscInt nn = c->i[i + 1] - c->i[i];
      c->ilen[i] = c->imax[i] = nn;
      c->nonzerorowcnt += (PetscInt) !!nn;
      c->rmax = PetscMax(c->rmax, nn);
    }
    PetscCall(MatMarkDiagonal_SeqAIJ(*C));
    PetscCall(PetscMalloc1(c->nz, &c->a));
    (*C)->nonzerostate++;
    PetscCall(PetscLayoutSetUp((*C)->rmap));
    PetscCall(PetscLayoutSetUp((*C)->cmap));
    Ccusp->nonzerostate = (*C)->nonzerostate;
    (*C)->preallocated  = PETSC_TRUE;
  } else {
    PetscCheck((*C)->rmap->n == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Invalid number or rows %" PetscInt_FMT " != %" PetscInt_FMT, (*C)->rmap->n, B->rmap->n);
    c = (Mat_SeqAIJ *)(*C)->data;
    if (c->nz) {
      Ccusp = (Mat_SeqAIJCUSPARSE *)(*C)->spptr;
      PetscCheck(Ccusp->coords, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing coords");
      PetscCheck(Ccusp->format != MAT_CUSPARSE_ELL && Ccusp->format != MAT_CUSPARSE_HYB, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
      PetscCheck(Ccusp->nonzerostate == (*C)->nonzerostate, PETSC_COMM_SELF, PETSC_ERR_COR, "Wrong nonzerostate");
      PetscCall(MatSeqAIJCUSPARSECopyToGPU(A));
      PetscCall(MatSeqAIJCUSPARSECopyToGPU(B));
      PetscCheck(Acusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
      PetscCheck(Bcusp->mat, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Mat_SeqAIJCUSPARSEMultStruct");
      Acsr = (CsrMatrix *)Acusp->mat->mat;
      Bcsr = (CsrMatrix *)Bcusp->mat->mat;
      Ccsr = (CsrMatrix *)Ccusp->mat->mat;
      PetscCheck(Acsr->num_entries == (PetscInt)Acsr->values->size(), PETSC_COMM_SELF, PETSC_ERR_COR, "A nnz %" PetscInt_FMT " != %" PetscInt_FMT, Acsr->num_entries, (PetscInt)Acsr->values->size());
      PetscCheck(Bcsr->num_entries == (PetscInt)Bcsr->values->size(), PETSC_COMM_SELF, PETSC_ERR_COR, "B nnz %" PetscInt_FMT " != %" PetscInt_FMT, Bcsr->num_entries, (PetscInt)Bcsr->values->size());
      PetscCheck(Ccsr->num_entries == (PetscInt)Ccsr->values->size(), PETSC_COMM_SELF, PETSC_ERR_COR, "C nnz %" PetscInt_FMT " != %" PetscInt_FMT, Ccsr->num_entries, (PetscInt)Ccsr->values->size());
      PetscCheck(Ccsr->num_entries == Acsr->num_entries + Bcsr->num_entries, PETSC_COMM_SELF, PETSC_ERR_COR, "C nnz %" PetscInt_FMT " != %" PetscInt_FMT " + %" PetscInt_FMT, Ccsr->num_entries, Acsr->num_entries, Bcsr->num_entries);
      PetscCheck(Ccusp->coords->size() == Ccsr->values->size(), PETSC_COMM_SELF, PETSC_ERR_COR, "permSize %" PetscInt_FMT " != %" PetscInt_FMT, (PetscInt)Ccusp->coords->size(), (PetscInt)Ccsr->values->size());
      auto pmid = Ccusp->coords->begin();
      thrust::advance(pmid, Acsr->num_entries);
      PetscCall(PetscLogGpuTimeBegin());
      auto zibait = thrust::make_zip_iterator(thrust::make_tuple(Acsr->values->begin(), thrust::make_permutation_iterator(Ccsr->values->begin(), Ccusp->coords->begin())));
      auto zieait = thrust::make_zip_iterator(thrust::make_tuple(Acsr->values->end(), thrust::make_permutation_iterator(Ccsr->values->begin(), pmid)));
      thrust::for_each(zibait, zieait, VecCUDAEquals());
      auto zibbit = thrust::make_zip_iterator(thrust::make_tuple(Bcsr->values->begin(), thrust::make_permutation_iterator(Ccsr->values->begin(), pmid)));
      auto ziebit = thrust::make_zip_iterator(thrust::make_tuple(Bcsr->values->end(), thrust::make_permutation_iterator(Ccsr->values->begin(), Ccusp->coords->end())));
      thrust::for_each(zibbit, ziebit, VecCUDAEquals());
      PetscCall(MatSeqAIJCUSPARSEInvalidateTranspose(*C, PETSC_FALSE));
      if (A->form_explicit_transpose && B->form_explicit_transpose && (*C)->form_explicit_transpose) {
        PetscCheck(Ccusp->matTranspose, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing transpose Mat_SeqAIJCUSPARSEMultStruct");
        PetscBool  AT = Acusp->matTranspose ? PETSC_TRUE : PETSC_FALSE, BT = Bcusp->matTranspose ? PETSC_TRUE : PETSC_FALSE;
        CsrMatrix *AcsrT = AT ? (CsrMatrix *)Acusp->matTranspose->mat : NULL;
        CsrMatrix *BcsrT = BT ? (CsrMatrix *)Bcusp->matTranspose->mat : NULL;
        CsrMatrix *CcsrT = (CsrMatrix *)Ccusp->matTranspose->mat;
        auto       vT    = CcsrT->values->begin();
        if (AT) vT = thrust::copy(AcsrT->values->begin(), AcsrT->values->end(), vT);
        if (BT) thrust::copy(BcsrT->values->begin(), BcsrT->values->end(), vT);
        (*C)->transupdated = PETSC_TRUE;
      }
      PetscCall(PetscLogGpuTimeEnd());
    }
  }
  PetscCall(PetscObjectStateIncrease((PetscObject)*C));
  (*C)->assembled     = PETSC_TRUE;
  (*C)->was_assembled = PETSC_FALSE;
  (*C)->offloadmask   = PETSC_OFFLOAD_GPU;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJCopySubArray_SeqAIJCUSPARSE(Mat A, PetscInt n, const PetscInt idx[], PetscScalar v[])
{
  bool               dmem;
  const PetscScalar *av;

  PetscFunctionBegin;
  dmem = isCudaMem(v);
  PetscCall(MatSeqAIJCUSPARSEGetArrayRead(A, &av));
  if (n && idx) {
    THRUSTINTARRAY widx(n);
    widx.assign(idx, idx + n);
    PetscCall(PetscLogCpuToGpu(n * sizeof(PetscInt)));

    THRUSTARRAY                    *w = NULL;
    thrust::device_ptr<PetscScalar> dv;
    if (dmem) {
      dv = thrust::device_pointer_cast(v);
    } else {
      w  = new THRUSTARRAY(n);
      dv = w->data();
    }
    thrust::device_ptr<const PetscScalar> dav = thrust::device_pointer_cast(av);

    auto zibit = thrust::make_zip_iterator(thrust::make_tuple(thrust::make_permutation_iterator(dav, widx.begin()), dv));
    auto zieit = thrust::make_zip_iterator(thrust::make_tuple(thrust::make_permutation_iterator(dav, widx.end()), dv + n));
    thrust::for_each(zibit, zieit, VecCUDAEquals());
    if (w) PetscCallCUDA(cudaMemcpy(v, w->data().get(), n * sizeof(PetscScalar), cudaMemcpyDeviceToHost));
    delete w;
  } else {
    PetscCallCUDA(cudaMemcpy(v, av, n * sizeof(PetscScalar), dmem ? cudaMemcpyDeviceToDevice : cudaMemcpyDeviceToHost));
  }
  if (!dmem) PetscCall(PetscLogCpuToGpu(n * sizeof(PetscScalar)));
  PetscCall(MatSeqAIJCUSPARSERestoreArrayRead(A, &av));
  PetscFunctionReturn(PETSC_SUCCESS);
}