xref: /petsc/src/mat/impls/aij/seq/kokkos/aijkok.kokkos.cxx (revision a1e4e190b393703c9d1e1a9f7db7c9c55e8c8427)

#include <petscvec_kokkos.hpp>
#include <petscpkg_version.h>
#include <petsc/private/petscimpl.h>
#include <petsc/private/sfimpl.h>
#include <petscsystypes.h>
#include <petscerror.h>

#include <Kokkos_Core.hpp>
#include <KokkosBlas.hpp>
#include <KokkosSparse_CrsMatrix.hpp>
#include <KokkosSparse_spmv.hpp>
#include <KokkosSparse_spiluk.hpp>
#include <KokkosSparse_sptrsv.hpp>
#include <KokkosSparse_spgemm.hpp>
#include <KokkosSparse_spadd.hpp>

#include <../src/mat/impls/aij/seq/kokkos/aijkok.hpp>

#if PETSC_PKG_KOKKOS_KERNELS_VERSION_GE(3, 7, 0)
  #include <KokkosSparse_Utils.hpp>
using KokkosSparse::sort_crs_matrix;
using KokkosSparse::Impl::transpose_matrix;
#else
  #include <KokkosKernels_Sorting.hpp>
using KokkosKernels::sort_crs_matrix;
using KokkosKernels::Impl::transpose_matrix;
#endif

static PetscErrorCode MatSetOps_SeqAIJKokkos(Mat); /* Forward declaration */

/* MatAssemblyEnd_SeqAIJKokkos() happens when we finalized nonzeros of the matrix, either after
   we assembled the matrix on host, or after we directly produced the matrix data on device (ex., through MatMatMult).
   In the latter case, it is important to set a_dual's sync state correctly.
 */
static PetscErrorCode MatAssemblyEnd_SeqAIJKokkos(Mat A, MatAssemblyType mode)
{
  Mat_SeqAIJ       *aijseq;
  Mat_SeqAIJKokkos *aijkok;

  PetscFunctionBegin;
  if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(MatAssemblyEnd_SeqAIJ(A, mode));

  aijseq = static_cast<Mat_SeqAIJ *>(A->data);
  aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  /* If aijkok does not exist, we just copy i, j to device.
     If aijkok already exists, but the device's nonzero pattern does not match with the host's, we assume the latest data is on host.
     In both cases, we build a new aijkok structure.
  */
  if (!aijkok || aijkok->nonzerostate != A->nonzerostate) { /* aijkok might not exist yet or nonzero pattern has changed */
    delete aijkok;
    aijkok   = new Mat_SeqAIJKokkos(A->rmap->n, A->cmap->n, aijseq->nz, aijseq->i, aijseq->j, aijseq->a, A->nonzerostate, PETSC_FALSE /*don't copy mat values to device*/);
    A->spptr = aijkok;
  }

  if (aijkok->device_mat_d.data()) {
    A->offloadmask = PETSC_OFFLOAD_GPU; // in GPU mode, no going back. MatSetValues checks this
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Sync CSR data to device if not yet */
PETSC_INTERN PetscErrorCode MatSeqAIJKokkosSyncDevice(Mat A)
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  PetscFunctionBegin;
  PetscCheck(A->factortype == MAT_FACTOR_NONE, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Can't sync factorized matrix from host to device");
  PetscCheck(aijkok, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Unexpected NULL (Mat_SeqAIJKokkos*)A->spptr");
  if (aijkok->a_dual.need_sync_device()) {
    aijkok->a_dual.sync_device();
    aijkok->transpose_updated = PETSC_FALSE; /* values of the transpose is out-of-date */
    aijkok->hermitian_updated = PETSC_FALSE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Mark the CSR data on device as modified */
PETSC_INTERN PetscErrorCode MatSeqAIJKokkosModifyDevice(Mat A)
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  PetscFunctionBegin;
  PetscCheck(A->factortype == MAT_FACTOR_NONE, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Not supported for factorized matries");
  aijkok->a_dual.clear_sync_state();
  aijkok->a_dual.modify_device();
  aijkok->transpose_updated = PETSC_FALSE;
  aijkok->hermitian_updated = PETSC_FALSE;
  PetscCall(MatSeqAIJInvalidateDiagonal(A));
  PetscCall(PetscObjectStateIncrease((PetscObject)A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJKokkosSyncHost(Mat A)
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  PetscFunctionBegin;
  PetscCheckTypeName(A, MATSEQAIJKOKKOS);
  /* We do not expect one needs factors on host  */
  PetscCheck(A->factortype == MAT_FACTOR_NONE, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Can't sync factorized matrix from device to host");
  PetscCheck(aijkok, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing AIJKOK");
  aijkok->a_dual.sync_host();
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJGetArray_SeqAIJKokkos(Mat A, PetscScalar *array[])
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  PetscFunctionBegin;
  /* aijkok contains valid pointers only if the host's nonzerostate matches with the device's.
    Calling MatSeqAIJSetPreallocation() or MatSetValues() on host, where aijseq->{i,j,a} might be
    reallocated, will lead to stale {i,j,a}_dual in aijkok. In both operations, the hosts's nonzerostate
    must have been updated. The stale aijkok will be rebuilt during MatAssemblyEnd.
  */
  if (aijkok && A->nonzerostate == aijkok->nonzerostate) {
    aijkok->a_dual.sync_host();
    *array = aijkok->a_dual.view_host().data();
  } else { /* Happens when calling MatSetValues on a newly created matrix */
    *array = static_cast<Mat_SeqAIJ *>(A->data)->a;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJRestoreArray_SeqAIJKokkos(Mat A, PetscScalar *array[])
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  PetscFunctionBegin;
  if (aijkok && A->nonzerostate == aijkok->nonzerostate) aijkok->a_dual.modify_host();
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJGetArrayRead_SeqAIJKokkos(Mat A, const PetscScalar *array[])
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  PetscFunctionBegin;
  if (aijkok && A->nonzerostate == aijkok->nonzerostate) {
    aijkok->a_dual.sync_host();
    *array = aijkok->a_dual.view_host().data();
  } else {
    *array = static_cast<Mat_SeqAIJ *>(A->data)->a;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

static PetscErrorCode MatSeqAIJGetArrayWrite_SeqAIJKokkos(Mat A, PetscScalar *array[])
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  PetscFunctionBegin;
  if (aijkok && A->nonzerostate == aijkok->nonzerostate) {
    *array = aijkok->a_dual.view_host().data();
  } else { /* Ex. happens with MatZeroEntries on a preallocated but not assembled matrix */
    *array = static_cast<Mat_SeqAIJ *>(A->data)->a;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJRestoreArrayWrite_SeqAIJKokkos(Mat A, PetscScalar *array[])
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  PetscFunctionBegin;
  if (aijkok && A->nonzerostate == aijkok->nonzerostate) {
    aijkok->a_dual.clear_sync_state();
    aijkok->a_dual.modify_host();
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJGetCSRAndMemType_SeqAIJKokkos(Mat A, const PetscInt **i, const PetscInt **j, PetscScalar **a, PetscMemType *mtype)
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  PetscFunctionBegin;
  PetscCheck(aijkok != NULL, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "aijkok is NULL");

  if (i) *i = aijkok->i_device_data();
  if (j) *j = aijkok->j_device_data();
  if (a) {
    aijkok->a_dual.sync_device();
    *a = aijkok->a_device_data();
  }
  if (mtype) *mtype = PETSC_MEMTYPE_KOKKOS;
  PetscFunctionReturn(PETSC_SUCCESS);
}

// MatSeqAIJKokkosSetDeviceMat takes a PetscSplitCSRDataStructure with device data and copies it to the device. Note, "deep_copy" here is really a shallow copy
PetscErrorCode MatSeqAIJKokkosSetDeviceMat(Mat A, PetscSplitCSRDataStructure h_mat)
{
  Mat_SeqAIJKokkos                            *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  Kokkos::View<SplitCSRMat, Kokkos::HostSpace> h_mat_k(h_mat);

  PetscFunctionBegin;
  PetscCheck(aijkok, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Unexpected NULL (Mat_SeqAIJKokkos*)A->spptr");
  aijkok->device_mat_d = create_mirror(DefaultMemorySpace(), h_mat_k);
  Kokkos::deep_copy(aijkok->device_mat_d, h_mat_k);
  PetscFunctionReturn(PETSC_SUCCESS);
}

// MatSeqAIJKokkosGetDeviceMat gets the device if it is here, otherwise it creates a place for it and returns NULL
PetscErrorCode MatSeqAIJKokkosGetDeviceMat(Mat A, PetscSplitCSRDataStructure *d_mat)
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  PetscFunctionBegin;
  if (aijkok && aijkok->device_mat_d.data()) {
    *d_mat = aijkok->device_mat_d.data();
  } else {
    PetscCall(MatSeqAIJKokkosSyncDevice(A)); // create aijkok (we are making d_mat now so make a place for it)
    *d_mat = NULL;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Generate the sparsity pattern of a MatSeqAIJKokkos matrix's transpose on device.

  Input Parameter:
.  A       - the MATSEQAIJKOKKOS matrix

  Output Parameters:
+  perm_d - the permutation array on device, which connects Ta(i) = Aa(perm(i))
-  T_d    - the transpose on device, whose value array is allocated but not initialized
*/
static PetscErrorCode MatSeqAIJKokkosGenerateTransposeStructure(Mat A, MatRowMapKokkosView &perm_d, KokkosCsrMatrix &T_d)
{
  Mat_SeqAIJ             *aseq = static_cast<Mat_SeqAIJ *>(A->data);
  PetscInt                nz = aseq->nz, m = A->rmap->N, n = A->cmap->n;
  const PetscInt         *Ai = aseq->i, *Aj = aseq->j;
  MatRowMapKokkosViewHost Ti_h("Ti", n + 1);
  MatRowMapType          *Ti = Ti_h.data();
  MatColIdxKokkosViewHost Tj_h("Tj", nz);
  MatRowMapKokkosViewHost perm_h("permutation", nz);
  PetscInt               *Tj   = Tj_h.data();
  PetscInt               *perm = perm_h.data();
  PetscInt               *offset;

  PetscFunctionBegin;
  // Populate Ti
  PetscCallCXX(Kokkos::deep_copy(Ti_h, 0));
  Ti++;
  for (PetscInt i = 0; i < nz; i++) Ti[Aj[i]]++;
  Ti--;
  for (PetscInt i = 0; i < n; i++) Ti[i + 1] += Ti[i];

  // Populate Tj and the permutation array
  PetscCall(PetscCalloc1(n, &offset)); // offset in each T row to fill in its column indices
  for (PetscInt i = 0; i < m; i++) {
    for (PetscInt j = Ai[i]; j < Ai[i + 1]; j++) { // A's (i,j) is T's (j,i)
      PetscInt r    = Aj[j];                       // row r of T
      PetscInt disp = Ti[r] + offset[r];

      Tj[disp]   = i; // col i of T
      perm[disp] = j;
      offset[r]++;
    }
  }
  PetscCall(PetscFree(offset));

  // Sort each row of T, along with the permutation array
  for (PetscInt i = 0; i < n; i++) PetscCall(PetscSortIntWithArray(Ti[i + 1] - Ti[i], Tj + Ti[i], perm + Ti[i]));

  // Output perm and T on device
  auto Ti_d = Kokkos::create_mirror_view_and_copy(DefaultMemorySpace(), Ti_h);
  auto Tj_d = Kokkos::create_mirror_view_and_copy(DefaultMemorySpace(), Tj_h);
  PetscCallCXX(T_d = KokkosCsrMatrix("csrmatT", n, m, nz, MatScalarKokkosView("Ta", nz), Ti_d, Tj_d));
  PetscCallCXX(perm_d = Kokkos::create_mirror_view_and_copy(DefaultMemorySpace(), perm_h));
  PetscFunctionReturn(PETSC_SUCCESS);
}

// Generate the transpose on device and cache it internally
// Note: KK transpose_matrix() does not have support symbolic/numeric transpose, so we do it on our own
PETSC_INTERN PetscErrorCode MatSeqAIJKokkosGenerateTranspose_Private(Mat A, KokkosCsrMatrix *csrmatT)
{
  Mat_SeqAIJ       *aseq = static_cast<Mat_SeqAIJ *>(A->data);
  Mat_SeqAIJKokkos *akok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  PetscInt          nz = aseq->nz, m = A->rmap->N, n = A->cmap->n;
  KokkosCsrMatrix  &T = akok->csrmatT;

  PetscFunctionBegin;
  PetscCheck(akok, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Unexpected NULL (Mat_SeqAIJKokkos*)A->spptr");
  PetscCallCXX(akok->a_dual.sync_device()); // Sync A's valeus since we are going to access them on device

  const auto &Aa = akok->a_dual.view_device();

  if (A->symmetric == PETSC_BOOL3_TRUE) {
    *csrmatT = akok->csrmat;
  } else {
    // See if we already have a cached transpose and its value is up to date
    if (T.numRows() == n && T.numCols() == m) {  // this indicates csrmatT had been generated before, otherwise T has 0 rows/cols after construction
      if (!akok->transpose_updated) {            // if the value is out of date, update the cached version
        const auto &perm = akok->transpose_perm; // get the permutation array
        auto       &Ta   = T.values;

        PetscCallCXX(Kokkos::parallel_for(
          nz, KOKKOS_LAMBDA(const PetscInt i) { Ta(i) = Aa(perm(i)); }));
      }
    } else { // Generate T of size n x m for the first time
      MatRowMapKokkosView perm;

      PetscCall(MatSeqAIJKokkosGenerateTransposeStructure(A, perm, T));
      akok->transpose_perm = perm; // cache the perm in this matrix for reuse
      PetscCallCXX(Kokkos::parallel_for(
        nz, KOKKOS_LAMBDA(const PetscInt i) { T.values(i) = Aa(perm(i)); }));
    }
    akok->transpose_updated = PETSC_TRUE;
    *csrmatT                = akok->csrmatT;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

// Generate the Hermitian on device and cache it internally
static PetscErrorCode MatSeqAIJKokkosGenerateHermitian_Private(Mat A, KokkosCsrMatrix *csrmatH)
{
  Mat_SeqAIJ       *aseq = static_cast<Mat_SeqAIJ *>(A->data);
  Mat_SeqAIJKokkos *akok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  PetscInt          nz = aseq->nz, m = A->rmap->N, n = A->cmap->n;
  KokkosCsrMatrix  &T = akok->csrmatH;

  PetscFunctionBegin;
  PetscCheck(akok, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Unexpected NULL (Mat_SeqAIJKokkos*)A->spptr");
  PetscCallCXX(akok->a_dual.sync_device()); // Sync A's values since we are going to access them on device

  const auto &Aa = akok->a_dual.view_device();

  if (A->hermitian == PETSC_BOOL3_TRUE) {
    *csrmatH = akok->csrmat;
  } else {
    // See if we already have a cached hermitian and its value is up to date
    if (T.numRows() == n && T.numCols() == m) {  // this indicates csrmatT had been generated before, otherwise T has 0 rows/cols after construction
      if (!akok->hermitian_updated) {            // if the value is out of date, update the cached version
        const auto &perm = akok->transpose_perm; // get the permutation array
        auto       &Ta   = T.values;

        PetscCallCXX(Kokkos::parallel_for(
          nz, KOKKOS_LAMBDA(const PetscInt i) { Ta(i) = PetscConj(Aa(perm(i))); }));
      }
    } else { // Generate T of size n x m for the first time
      MatRowMapKokkosView perm;

      PetscCall(MatSeqAIJKokkosGenerateTransposeStructure(A, perm, T));
      akok->transpose_perm = perm; // cache the perm in this matrix for reuse
      PetscCallCXX(Kokkos::parallel_for(
        nz, KOKKOS_LAMBDA(const PetscInt i) { T.values(i) = PetscConj(Aa(perm(i))); }));
    }
    akok->hermitian_updated = PETSC_TRUE;
    *csrmatH                = akok->csrmatH;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* y = A x */
static PetscErrorCode MatMult_SeqAIJKokkos(Mat A, Vec xx, Vec yy)
{
  Mat_SeqAIJKokkos          *aijkok;
  ConstPetscScalarKokkosView xv;
  PetscScalarKokkosView      yv;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  PetscCall(VecGetKokkosView(xx, &xv));
  PetscCall(VecGetKokkosViewWrite(yy, &yv));
  aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  PetscCallCXX(KokkosSparse::spmv("N", 1.0 /*alpha*/, aijkok->csrmat, xv, 0.0 /*beta*/, yv)); /* y = alpha A x + beta y */
  PetscCall(VecRestoreKokkosView(xx, &xv));
  PetscCall(VecRestoreKokkosViewWrite(yy, &yv));
  /* 2.0*nnz - numRows seems more accurate here but assumes there are no zero-rows. So a little sloppy here. */
  PetscCall(PetscLogGpuFlops(2.0 * aijkok->csrmat.nnz()));
  PetscCall(PetscLogGpuTimeEnd());
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* y = A^T x */
static PetscErrorCode MatMultTranspose_SeqAIJKokkos(Mat A, Vec xx, Vec yy)
{
  Mat_SeqAIJKokkos          *aijkok;
  const char                *mode;
  ConstPetscScalarKokkosView xv;
  PetscScalarKokkosView      yv;
  KokkosCsrMatrix            csrmat;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  PetscCall(VecGetKokkosView(xx, &xv));
  PetscCall(VecGetKokkosViewWrite(yy, &yv));
  if (A->form_explicit_transpose) {
    PetscCall(MatSeqAIJKokkosGenerateTranspose_Private(A, &csrmat));
    mode = "N";
  } else {
    aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
    csrmat = aijkok->csrmat;
    mode   = "T";
  }
  PetscCallCXX(KokkosSparse::spmv(mode, 1.0 /*alpha*/, csrmat, xv, 0.0 /*beta*/, yv)); /* y = alpha A^T x + beta y */
  PetscCall(VecRestoreKokkosView(xx, &xv));
  PetscCall(VecRestoreKokkosViewWrite(yy, &yv));
  PetscCall(PetscLogGpuFlops(2.0 * csrmat.nnz()));
  PetscCall(PetscLogGpuTimeEnd());
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* y = A^H x */
static PetscErrorCode MatMultHermitianTranspose_SeqAIJKokkos(Mat A, Vec xx, Vec yy)
{
  Mat_SeqAIJKokkos          *aijkok;
  const char                *mode;
  ConstPetscScalarKokkosView xv;
  PetscScalarKokkosView      yv;
  KokkosCsrMatrix            csrmat;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  PetscCall(VecGetKokkosView(xx, &xv));
  PetscCall(VecGetKokkosViewWrite(yy, &yv));
  if (A->form_explicit_transpose) {
    PetscCall(MatSeqAIJKokkosGenerateHermitian_Private(A, &csrmat));
    mode = "N";
  } else {
    aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
    csrmat = aijkok->csrmat;
    mode   = "C";
  }
  PetscCallCXX(KokkosSparse::spmv(mode, 1.0 /*alpha*/, csrmat, xv, 0.0 /*beta*/, yv)); /* y = alpha A^H x + beta y */
  PetscCall(VecRestoreKokkosView(xx, &xv));
  PetscCall(VecRestoreKokkosViewWrite(yy, &yv));
  PetscCall(PetscLogGpuFlops(2.0 * csrmat.nnz()));
  PetscCall(PetscLogGpuTimeEnd());
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* z = A x + y */
static PetscErrorCode MatMultAdd_SeqAIJKokkos(Mat A, Vec xx, Vec yy, Vec zz)
{
  Mat_SeqAIJKokkos          *aijkok;
  ConstPetscScalarKokkosView xv, yv;
  PetscScalarKokkosView      zv;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  PetscCall(VecGetKokkosView(xx, &xv));
  PetscCall(VecGetKokkosView(yy, &yv));
  PetscCall(VecGetKokkosViewWrite(zz, &zv));
  if (zz != yy) Kokkos::deep_copy(zv, yv);
  aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  PetscCallCXX(KokkosSparse::spmv("N", 1.0 /*alpha*/, aijkok->csrmat, xv, 1.0 /*beta*/, zv)); /* z = alpha A x + beta z */
  PetscCall(VecRestoreKokkosView(xx, &xv));
  PetscCall(VecRestoreKokkosView(yy, &yv));
  PetscCall(VecRestoreKokkosViewWrite(zz, &zv));
  PetscCall(PetscLogGpuFlops(2.0 * aijkok->csrmat.nnz()));
  PetscCall(PetscLogGpuTimeEnd());
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* z = A^T x + y */
static PetscErrorCode MatMultTransposeAdd_SeqAIJKokkos(Mat A, Vec xx, Vec yy, Vec zz)
{
  Mat_SeqAIJKokkos          *aijkok;
  const char                *mode;
  ConstPetscScalarKokkosView xv, yv;
  PetscScalarKokkosView      zv;
  KokkosCsrMatrix            csrmat;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  PetscCall(VecGetKokkosView(xx, &xv));
  PetscCall(VecGetKokkosView(yy, &yv));
  PetscCall(VecGetKokkosViewWrite(zz, &zv));
  if (zz != yy) Kokkos::deep_copy(zv, yv);
  if (A->form_explicit_transpose) {
    PetscCall(MatSeqAIJKokkosGenerateTranspose_Private(A, &csrmat));
    mode = "N";
  } else {
    aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
    csrmat = aijkok->csrmat;
    mode   = "T";
  }
  PetscCallCXX(KokkosSparse::spmv(mode, 1.0 /*alpha*/, csrmat, xv, 1.0 /*beta*/, zv)); /* z = alpha A^T x + beta z */
  PetscCall(VecRestoreKokkosView(xx, &xv));
  PetscCall(VecRestoreKokkosView(yy, &yv));
  PetscCall(VecRestoreKokkosViewWrite(zz, &zv));
  PetscCall(PetscLogGpuFlops(2.0 * csrmat.nnz()));
  PetscCall(PetscLogGpuTimeEnd());
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* z = A^H x + y */
static PetscErrorCode MatMultHermitianTransposeAdd_SeqAIJKokkos(Mat A, Vec xx, Vec yy, Vec zz)
{
  Mat_SeqAIJKokkos          *aijkok;
  const char                *mode;
  ConstPetscScalarKokkosView xv, yv;
  PetscScalarKokkosView      zv;
  KokkosCsrMatrix            csrmat;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  PetscCall(VecGetKokkosView(xx, &xv));
  PetscCall(VecGetKokkosView(yy, &yv));
  PetscCall(VecGetKokkosViewWrite(zz, &zv));
  if (zz != yy) Kokkos::deep_copy(zv, yv);
  if (A->form_explicit_transpose) {
    PetscCall(MatSeqAIJKokkosGenerateHermitian_Private(A, &csrmat));
    mode = "N";
  } else {
    aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
    csrmat = aijkok->csrmat;
    mode   = "C";
  }
  PetscCallCXX(KokkosSparse::spmv(mode, 1.0 /*alpha*/, csrmat, xv, 1.0 /*beta*/, zv)); /* z = alpha A^H x + beta z */
  PetscCall(VecRestoreKokkosView(xx, &xv));
  PetscCall(VecRestoreKokkosView(yy, &yv));
  PetscCall(VecRestoreKokkosViewWrite(zz, &zv));
  PetscCall(PetscLogGpuFlops(2.0 * csrmat.nnz()));
  PetscCall(PetscLogGpuTimeEnd());
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSetOption_SeqAIJKokkos(Mat A, MatOption op, PetscBool flg)
{
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  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 && aijkok) PetscCall(aijkok->DestroyMatTranspose());
    A->form_explicit_transpose = flg;
    break;
  default:
    PetscCall(MatSetOption_SeqAIJ(A, op, flg));
    break;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Depending on reuse, either build a new mat, or use the existing mat */
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJKokkos(Mat A, MatType mtype, MatReuse reuse, Mat *newmat)
{
  Mat_SeqAIJ *aseq;

  PetscFunctionBegin;
  PetscCall(PetscKokkosInitializeCheck());
  if (reuse == MAT_INITIAL_MATRIX) {                      /* Build a brand new mat */
    PetscCall(MatDuplicate(A, MAT_COPY_VALUES, newmat));  /* the returned newmat is a SeqAIJKokkos */
  } else if (reuse == MAT_REUSE_MATRIX) {                 /* Reuse the mat created before */
    PetscCall(MatCopy(A, *newmat, SAME_NONZERO_PATTERN)); /* newmat is already a SeqAIJKokkos */
  } else if (reuse == MAT_INPLACE_MATRIX) {               /* newmat is A */
    PetscCheck(A == *newmat, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "A != *newmat with MAT_INPLACE_MATRIX");
    PetscCall(PetscFree(A->defaultvectype));
    PetscCall(PetscStrallocpy(VECKOKKOS, &A->defaultvectype)); /* Allocate and copy the string */
    PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATSEQAIJKOKKOS));
    PetscCall(MatSetOps_SeqAIJKokkos(A));
    aseq = static_cast<Mat_SeqAIJ *>(A->data);
    if (A->assembled) { /* Copy i, j (but not values) to device for an assembled matrix if not yet */
      PetscCheck(!A->spptr, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Expect NULL (Mat_SeqAIJKokkos*)A->spptr");
      A->spptr = new Mat_SeqAIJKokkos(A->rmap->n, A->cmap->n, aseq->nz, aseq->i, aseq->j, aseq->a, A->nonzerostate, PETSC_FALSE);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* MatDuplicate always creates a new matrix. MatDuplicate can be called either on an assembled matrix or
   an unassembled matrix, even though MAT_COPY_VALUES is not allowed for unassembled matrix.
 */
static PetscErrorCode MatDuplicate_SeqAIJKokkos(Mat A, MatDuplicateOption dupOption, Mat *B)
{
  Mat_SeqAIJ       *bseq;
  Mat_SeqAIJKokkos *akok = static_cast<Mat_SeqAIJKokkos *>(A->spptr), *bkok;
  Mat               mat;

  PetscFunctionBegin;
  /* Do not copy values on host as A's latest values might be on device. We don't want to do sync blindly */
  PetscCall(MatDuplicate_SeqAIJ(A, MAT_DO_NOT_COPY_VALUES, B));
  mat = *B;
  if (A->assembled) {
    bseq = static_cast<Mat_SeqAIJ *>(mat->data);
    bkok = new Mat_SeqAIJKokkos(mat->rmap->n, mat->cmap->n, bseq->nz, bseq->i, bseq->j, bseq->a, mat->nonzerostate, PETSC_FALSE);
    bkok->a_dual.clear_sync_state(); /* Clear B's sync state as it will be decided below */
    /* Now copy values to B if needed */
    if (dupOption == MAT_COPY_VALUES) {
      if (akok->a_dual.need_sync_device()) {
        Kokkos::deep_copy(bkok->a_dual.view_host(), akok->a_dual.view_host());
        bkok->a_dual.modify_host();
      } else { /* If device has the latest data, we only copy data on device */
        Kokkos::deep_copy(bkok->a_dual.view_device(), akok->a_dual.view_device());
        bkok->a_dual.modify_device();
      }
    } else { /* MAT_DO_NOT_COPY_VALUES or MAT_SHARE_NONZERO_PATTERN. B's values should be zeroed */
      /* B's values on host should be already zeroed by MatDuplicate_SeqAIJ() */
      bkok->a_dual.modify_host();
    }
    mat->spptr = bkok;
  }

  PetscCall(PetscFree(mat->defaultvectype));
  PetscCall(PetscStrallocpy(VECKOKKOS, &mat->defaultvectype)); /* Allocate and copy the string */
  PetscCall(PetscObjectChangeTypeName((PetscObject)mat, MATSEQAIJKOKKOS));
  PetscCall(MatSetOps_SeqAIJKokkos(mat));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatTranspose_SeqAIJKokkos(Mat A, MatReuse reuse, Mat *B)
{
  Mat               At;
  KokkosCsrMatrix   internT;
  Mat_SeqAIJKokkos *atkok, *bkok;

  PetscFunctionBegin;
  if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *B));
  PetscCall(MatSeqAIJKokkosGenerateTranspose_Private(A, &internT)); /* Generate a transpose internally */
  if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_INPLACE_MATRIX) {
    /* Deep copy internT, as we want to isolate the internal transpose */
    PetscCallCXX(atkok = new Mat_SeqAIJKokkos(KokkosCsrMatrix("csrmat", internT)));
    PetscCall(MatCreateSeqAIJKokkosWithCSRMatrix(PetscObjectComm((PetscObject)A), atkok, &At));
    if (reuse == MAT_INITIAL_MATRIX) *B = At;
    else PetscCall(MatHeaderReplace(A, &At)); /* Replace A with At inplace */
  } else {                                    /* MAT_REUSE_MATRIX, just need to copy values to B on device */
    if ((*B)->assembled) {
      bkok = static_cast<Mat_SeqAIJKokkos *>((*B)->spptr);
      PetscCallCXX(Kokkos::deep_copy(bkok->a_dual.view_device(), internT.values));
      PetscCall(MatSeqAIJKokkosModifyDevice(*B));
    } else if ((*B)->preallocated) { /* It is ok for B to be only preallocated, as needed in MatTranspose_MPIAIJ */
      Mat_SeqAIJ             *bseq = static_cast<Mat_SeqAIJ *>((*B)->data);
      MatScalarKokkosViewHost a_h(bseq->a, internT.nnz()); /* bseq->nz = 0 if unassembled */
      MatColIdxKokkosViewHost j_h(bseq->j, internT.nnz());
      PetscCallCXX(Kokkos::deep_copy(a_h, internT.values));
      PetscCallCXX(Kokkos::deep_copy(j_h, internT.graph.entries));
    } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "B must be assembled or preallocated");
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDestroy_SeqAIJKokkos(Mat A)
{
  Mat_SeqAIJKokkos *aijkok;

  PetscFunctionBegin;
  if (A->factortype == MAT_FACTOR_NONE) {
    aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
    delete aijkok;
  } else {
    delete static_cast<Mat_SeqAIJKokkosTriFactors *>(A->spptr);
  }
  A->spptr = NULL;
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
  PetscCall(MatDestroy_SeqAIJ(A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
   MATSEQAIJKOKKOS - MATAIJKOKKOS = "(seq)aijkokkos" - A matrix type to be used for sparse matrices with Kokkos

   A matrix type type using Kokkos-Kernels CrsMatrix type for portability across different device types

   Options Database Key:
.  -mat_type aijkokkos - sets the matrix type to `MATSEQAIJKOKKOS` during a call to `MatSetFromOptions()`

  Level: beginner

.seealso: [](chapter_matrices), `Mat`, `MatCreateSeqAIJKokkos()`, `MATMPIAIJKOKKOS`
M*/
PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJKokkos(Mat A)
{
  PetscFunctionBegin;
  PetscCall(PetscKokkosInitializeCheck());
  PetscCall(MatCreate_SeqAIJ(A));
  PetscCall(MatConvert_SeqAIJ_SeqAIJKokkos(A, MATSEQAIJKOKKOS, MAT_INPLACE_MATRIX, &A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Merge A, B into a matrix C. A is put before B. C's size would be A->rmap->n by (A->cmap->n + B->cmap->n) */
PetscErrorCode MatSeqAIJKokkosMergeMats(Mat A, Mat B, MatReuse reuse, Mat *C)
{
  Mat_SeqAIJ         *a, *b;
  Mat_SeqAIJKokkos   *akok, *bkok, *ckok;
  MatScalarKokkosView aa, ba, ca;
  MatRowMapKokkosView ai, bi, ci;
  MatColIdxKokkosView aj, bj, cj;
  PetscInt            m, n, nnz, aN;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidHeaderSpecific(B, MAT_CLASSID, 2);
  PetscValidPointer(C, 4);
  PetscCheckTypeName(A, MATSEQAIJKOKKOS);
  PetscCheckTypeName(B, MATSEQAIJKOKKOS);
  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");

  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  PetscCall(MatSeqAIJKokkosSyncDevice(B));
  a    = static_cast<Mat_SeqAIJ *>(A->data);
  b    = static_cast<Mat_SeqAIJ *>(B->data);
  akok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  bkok = static_cast<Mat_SeqAIJKokkos *>(B->spptr);
  aa   = akok->a_dual.view_device();
  ai   = akok->i_dual.view_device();
  ba   = bkok->a_dual.view_device();
  bi   = bkok->i_dual.view_device();
  m    = A->rmap->n; /* M, N and nnz of C */
  n    = A->cmap->n + B->cmap->n;
  nnz  = a->nz + b->nz;
  aN   = A->cmap->n; /* N of A */
  if (reuse == MAT_INITIAL_MATRIX) {
    aj           = akok->j_dual.view_device();
    bj           = bkok->j_dual.view_device();
    auto ca_dual = MatScalarKokkosDualView("a", aa.extent(0) + ba.extent(0));
    auto ci_dual = MatRowMapKokkosDualView("i", ai.extent(0));
    auto cj_dual = MatColIdxKokkosDualView("j", aj.extent(0) + bj.extent(0));
    ca           = ca_dual.view_device();
    ci           = ci_dual.view_device();
    cj           = cj_dual.view_device();

    /* Concatenate A and B in parallel using Kokkos hierarchical parallelism */
    Kokkos::parallel_for(
      Kokkos::TeamPolicy<>(m, Kokkos::AUTO()), KOKKOS_LAMBDA(const KokkosTeamMemberType &t) {
        PetscInt i       = t.league_rank(); /* row i */
        PetscInt coffset = ai(i) + bi(i), alen = ai(i + 1) - ai(i), blen = bi(i + 1) - bi(i);

        Kokkos::single(Kokkos::PerTeam(t), [=]() { /* this side effect only happens once per whole team */
                                                   ci(i) = coffset;
                                                   if (i == m - 1) ci(m) = ai(m) + bi(m);
        });

        Kokkos::parallel_for(Kokkos::TeamThreadRange(t, alen + blen), [&](PetscInt k) {
          if (k < alen) {
            ca(coffset + k) = aa(ai(i) + k);
            cj(coffset + k) = aj(ai(i) + k);
          } else {
            ca(coffset + k) = ba(bi(i) + k - alen);
            cj(coffset + k) = bj(bi(i) + k - alen) + aN; /* Entries in B get new column indices in C */
          }
        });
      });
    ca_dual.modify_device();
    ci_dual.modify_device();
    cj_dual.modify_device();
    PetscCallCXX(ckok = new Mat_SeqAIJKokkos(m, n, nnz, ci_dual, cj_dual, ca_dual));
    PetscCall(MatCreateSeqAIJKokkosWithCSRMatrix(PETSC_COMM_SELF, ckok, C));
  } else if (reuse == MAT_REUSE_MATRIX) {
    PetscValidHeaderSpecific(*C, MAT_CLASSID, 4);
    PetscCheckTypeName(*C, MATSEQAIJKOKKOS);
    ckok = static_cast<Mat_SeqAIJKokkos *>((*C)->spptr);
    ca   = ckok->a_dual.view_device();
    ci   = ckok->i_dual.view_device();

    Kokkos::parallel_for(
      Kokkos::TeamPolicy<>(m, Kokkos::AUTO()), KOKKOS_LAMBDA(const KokkosTeamMemberType &t) {
        PetscInt i    = t.league_rank(); /* row i */
        PetscInt alen = ai(i + 1) - ai(i), blen = bi(i + 1) - bi(i);
        Kokkos::parallel_for(Kokkos::TeamThreadRange(t, alen + blen), [&](PetscInt k) {
          if (k < alen) ca(ci(i) + k) = aa(ai(i) + k);
          else ca(ci(i) + k) = ba(bi(i) + k - alen);
        });
      });
    PetscCall(MatSeqAIJKokkosModifyDevice(*C));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatProductDataDestroy_SeqAIJKokkos(void *pdata)
{
  PetscFunctionBegin;
  delete static_cast<MatProductData_SeqAIJKokkos *>(pdata);
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatProductNumeric_SeqAIJKokkos_SeqAIJKokkos(Mat C)
{
  Mat_Product                 *product = C->product;
  Mat                          A, B;
  bool                         transA, transB; /* use bool, since KK needs this type */
  Mat_SeqAIJKokkos            *akok, *bkok, *ckok;
  Mat_SeqAIJ                  *c;
  MatProductData_SeqAIJKokkos *pdata;
  KokkosCsrMatrix              csrmatA, csrmatB;

  PetscFunctionBegin;
  MatCheckProduct(C, 1);
  PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
  pdata = static_cast<MatProductData_SeqAIJKokkos *>(C->product->data);

  // See if numeric has already been done in symbolic (e.g., user calls MatMatMult(A,B,MAT_INITIAL_MATRIX,..,C)).
  // If yes, skip the numeric, but reset the flag so that next time when user calls MatMatMult(E,F,MAT_REUSE_MATRIX,..,C),
  // we still do numeric.
  if (pdata->reusesym) { // numeric reuses results from symbolic
    pdata->reusesym = PETSC_FALSE;
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  switch (product->type) {
  case MATPRODUCT_AB:
    transA = false;
    transB = false;
    break;
  case MATPRODUCT_AtB:
    transA = true;
    transB = false;
    break;
  case MATPRODUCT_ABt:
    transA = false;
    transB = true;
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Unsupported product type %s", MatProductTypes[product->type]);
  }

  A = product->A;
  B = product->B;
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  PetscCall(MatSeqAIJKokkosSyncDevice(B));
  akok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  bkok = static_cast<Mat_SeqAIJKokkos *>(B->spptr);
  ckok = static_cast<Mat_SeqAIJKokkos *>(C->spptr);

  PetscCheck(ckok, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Device data structure spptr is empty");

  csrmatA = akok->csrmat;
  csrmatB = bkok->csrmat;

  /* TODO: Once KK spgemm implements transpose, we can get rid of the explicit transpose here */
  if (transA) {
    PetscCall(MatSeqAIJKokkosGenerateTranspose_Private(A, &csrmatA));
    transA = false;
  }

  if (transB) {
    PetscCall(MatSeqAIJKokkosGenerateTranspose_Private(B, &csrmatB));
    transB = false;
  }
  PetscCall(PetscLogGpuTimeBegin());
  PetscCallCXX(KokkosSparse::spgemm_numeric(pdata->kh, csrmatA, transA, csrmatB, transB, ckok->csrmat));
#if PETSC_PKG_KOKKOS_KERNELS_VERSION_LT(4, 0, 0)
  auto spgemmHandle = pdata->kh.get_spgemm_handle();
  if (spgemmHandle->get_sort_option() != 1) PetscCallCXX(sort_crs_matrix(ckok->csrmat)); /* without sort, mat_tests-ex62_14_seqaijkokkos fails */
#endif

  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(MatSeqAIJKokkosModifyDevice(C));
  /* shorter version of MatAssemblyEnd_SeqAIJ */
  c = (Mat_SeqAIJ *)C->data;
  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_SeqAIJKokkos_SeqAIJKokkos(Mat C)
{
  Mat_Product                 *product = C->product;
  MatProductType               ptype;
  Mat                          A, B;
  bool                         transA, transB;
  Mat_SeqAIJKokkos            *akok, *bkok, *ckok;
  MatProductData_SeqAIJKokkos *pdata;
  MPI_Comm                     comm;
  KokkosCsrMatrix              csrmatA, csrmatB, csrmatC;

  PetscFunctionBegin;
  MatCheckProduct(C, 1);
  PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
  PetscCheck(!product->data, comm, PETSC_ERR_PLIB, "Product data not empty");
  A = product->A;
  B = product->B;
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  PetscCall(MatSeqAIJKokkosSyncDevice(B));
  akok    = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  bkok    = static_cast<Mat_SeqAIJKokkos *>(B->spptr);
  csrmatA = akok->csrmat;
  csrmatB = bkok->csrmat;

  ptype = product->type;
  // Take advantage of the symmetry if true
  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;
  }

  switch (ptype) {
  case MATPRODUCT_AB:
    transA = false;
    transB = false;
    break;
  case MATPRODUCT_AtB:
    transA = true;
    transB = false;
    break;
  case MATPRODUCT_ABt:
    transA = false;
    transB = true;
    break;
  default:
    SETERRQ(comm, PETSC_ERR_PLIB, "Unsupported product type %s", MatProductTypes[product->type]);
  }
  PetscCallCXX(product->data = pdata = new MatProductData_SeqAIJKokkos());
  pdata->reusesym = product->api_user;

  /* TODO: add command line options to select spgemm algorithms */
  auto spgemm_alg = KokkosSparse::SPGEMMAlgorithm::SPGEMM_DEFAULT; /* default alg is TPL if enabled, otherwise KK */

  /* CUDA-10.2's spgemm has bugs. We prefer the SpGEMMreuse APIs introduced in cuda-11.4 */
#if defined(KOKKOSKERNELS_ENABLE_TPL_CUSPARSE)
  #if PETSC_PKG_CUDA_VERSION_LT(11, 4, 0)
  spgemm_alg = KokkosSparse::SPGEMMAlgorithm::SPGEMM_KK;
  #endif
#endif
  PetscCallCXX(pdata->kh.create_spgemm_handle(spgemm_alg));

  PetscCall(PetscLogGpuTimeBegin());
  /* TODO: Get rid of the explicit transpose once KK-spgemm implements the transpose option */
  if (transA) {
    PetscCall(MatSeqAIJKokkosGenerateTranspose_Private(A, &csrmatA));
    transA = false;
  }

  if (transB) {
    PetscCall(MatSeqAIJKokkosGenerateTranspose_Private(B, &csrmatB));
    transB = false;
  }

  PetscCallCXX(KokkosSparse::spgemm_symbolic(pdata->kh, csrmatA, transA, csrmatB, transB, csrmatC));
  /* spgemm_symbolic() only populates C's rowmap, but not C's column indices.
    So we have to do a fake spgemm_numeric() here to get csrmatC.j_d setup, before
    calling new Mat_SeqAIJKokkos().
    TODO: Remove the fake spgemm_numeric() after KK fixed this problem.
  */
  PetscCallCXX(KokkosSparse::spgemm_numeric(pdata->kh, csrmatA, transA, csrmatB, transB, csrmatC));
#if PETSC_PKG_KOKKOS_KERNELS_VERSION_LT(4, 0, 0)
  /* Query if KK outputs a sorted matrix. If not, we need to sort it */
  auto spgemmHandle = pdata->kh.get_spgemm_handle();
  if (spgemmHandle->get_sort_option() != 1) PetscCallCXX(sort_crs_matrix(csrmatC)); /* sort_option defaults to -1 in KK!*/
#endif
  PetscCall(PetscLogGpuTimeEnd());

  PetscCallCXX(ckok = new Mat_SeqAIJKokkos(csrmatC));
  PetscCall(MatSetSeqAIJKokkosWithCSRMatrix(C, ckok));
  C->product->destroy = MatProductDataDestroy_SeqAIJKokkos;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* handles sparse matrix matrix ops */
static PetscErrorCode MatProductSetFromOptions_SeqAIJKokkos(Mat mat)
{
  Mat_Product *product = mat->product;
  PetscBool    Biskok = PETSC_FALSE, Ciskok = PETSC_TRUE;

  PetscFunctionBegin;
  MatCheckProduct(mat, 1);
  PetscCall(PetscObjectTypeCompare((PetscObject)product->B, MATSEQAIJKOKKOS, &Biskok));
  if (product->type == MATPRODUCT_ABC) PetscCall(PetscObjectTypeCompare((PetscObject)product->C, MATSEQAIJKOKKOS, &Ciskok));
  if (Biskok && Ciskok) {
    switch (product->type) {
    case MATPRODUCT_AB:
    case MATPRODUCT_AtB:
    case MATPRODUCT_ABt:
      mat->ops->productsymbolic = MatProductSymbolic_SeqAIJKokkos_SeqAIJKokkos;
      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 MatScale_SeqAIJKokkos(Mat A, PetscScalar a)
{
  Mat_SeqAIJKokkos *aijkok;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  KokkosBlas::scal(aijkok->a_dual.view_device(), a, aijkok->a_dual.view_device());
  PetscCall(MatSeqAIJKokkosModifyDevice(A));
  PetscCall(PetscLogGpuFlops(aijkok->a_dual.extent(0)));
  PetscCall(PetscLogGpuTimeEnd());
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroEntries_SeqAIJKokkos(Mat A)
{
  Mat_SeqAIJKokkos *aijkok;

  PetscFunctionBegin;
  aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  if (aijkok) { /* Only zero the device if data is already there */
    KokkosBlas::fill(aijkok->a_dual.view_device(), 0.0);
    PetscCall(MatSeqAIJKokkosModifyDevice(A));
  } else { /* Might be preallocated but not assembled */
    PetscCall(MatZeroEntries_SeqAIJ(A));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetDiagonal_SeqAIJKokkos(Mat A, Vec x)
{
  Mat_SeqAIJ           *aijseq;
  Mat_SeqAIJKokkos     *aijkok;
  PetscInt              n;
  PetscScalarKokkosView xv;

  PetscFunctionBegin;
  PetscCall(VecGetLocalSize(x, &n));
  PetscCheck(n == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
  PetscCheck(A->factortype == MAT_FACTOR_NONE, PETSC_COMM_SELF, PETSC_ERR_SUP, "MatGetDiagonal_SeqAIJKokkos not supported on factored matrices");

  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);

  if (A->rmap->n && aijkok->diag_dual.extent(0) == 0) { /* Set the diagonal pointer if not already */
    PetscCall(MatMarkDiagonal_SeqAIJ(A));
    aijseq = static_cast<Mat_SeqAIJ *>(A->data);
    aijkok->SetDiagonal(aijseq->diag);
  }

  const auto &Aa    = aijkok->a_dual.view_device();
  const auto &Ai    = aijkok->i_dual.view_device();
  const auto &Adiag = aijkok->diag_dual.view_device();

  PetscCall(VecGetKokkosViewWrite(x, &xv));
  Kokkos::parallel_for(
    n, KOKKOS_LAMBDA(const PetscInt i) {
      if (Adiag(i) < Ai(i + 1)) xv(i) = Aa(Adiag(i));
      else xv(i) = 0;
    });
  PetscCall(VecRestoreKokkosViewWrite(x, &xv));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Get a Kokkos View from a mat of type MatSeqAIJKokkos */
PetscErrorCode MatSeqAIJGetKokkosView(Mat A, ConstMatScalarKokkosView *kv)
{
  Mat_SeqAIJKokkos *aijkok;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidPointer(kv, 2);
  PetscCheckTypeName(A, MATSEQAIJKOKKOS);
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  *kv    = aijkok->a_dual.view_device();
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSeqAIJRestoreKokkosView(Mat A, ConstMatScalarKokkosView *kv)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidPointer(kv, 2);
  PetscCheckTypeName(A, MATSEQAIJKOKKOS);
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSeqAIJGetKokkosView(Mat A, MatScalarKokkosView *kv)
{
  Mat_SeqAIJKokkos *aijkok;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidPointer(kv, 2);
  PetscCheckTypeName(A, MATSEQAIJKOKKOS);
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  *kv    = aijkok->a_dual.view_device();
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSeqAIJRestoreKokkosView(Mat A, MatScalarKokkosView *kv)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidPointer(kv, 2);
  PetscCheckTypeName(A, MATSEQAIJKOKKOS);
  PetscCall(MatSeqAIJKokkosModifyDevice(A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSeqAIJGetKokkosViewWrite(Mat A, MatScalarKokkosView *kv)
{
  Mat_SeqAIJKokkos *aijkok;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidPointer(kv, 2);
  PetscCheckTypeName(A, MATSEQAIJKOKKOS);
  aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  *kv    = aijkok->a_dual.view_device();
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatSeqAIJRestoreKokkosViewWrite(Mat A, MatScalarKokkosView *kv)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidPointer(kv, 2);
  PetscCheckTypeName(A, MATSEQAIJKOKKOS);
  PetscCall(MatSeqAIJKokkosModifyDevice(A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Computes Y += alpha X */
static PetscErrorCode MatAXPY_SeqAIJKokkos(Mat Y, PetscScalar alpha, Mat X, MatStructure pattern)
{
  Mat_SeqAIJ              *x = (Mat_SeqAIJ *)X->data, *y = (Mat_SeqAIJ *)Y->data;
  Mat_SeqAIJKokkos        *xkok, *ykok, *zkok;
  ConstMatScalarKokkosView Xa;
  MatScalarKokkosView      Ya;

  PetscFunctionBegin;
  PetscCheckTypeName(Y, MATSEQAIJKOKKOS);
  PetscCheckTypeName(X, MATSEQAIJKOKKOS);
  PetscCall(MatSeqAIJKokkosSyncDevice(Y));
  PetscCall(MatSeqAIJKokkosSyncDevice(X));
  PetscCall(PetscLogGpuTimeBegin());

  if (pattern != SAME_NONZERO_PATTERN && x->nz == y->nz) {
    PetscBool e;
    PetscCall(PetscArraycmp(x->i, y->i, Y->rmap->n + 1, &e));
    if (e) {
      PetscCall(PetscArraycmp(x->j, y->j, y->nz, &e));
      if (e) pattern = SAME_NONZERO_PATTERN;
    }
  }

  /* cusparseDcsrgeam2() computes C = alpha A + beta B. If one knew sparsity pattern of C, one can skip
    cusparseScsrgeam2_bufferSizeExt() / cusparseXcsrgeam2Nnz(), and directly call cusparseScsrgeam2().
    If X is SUBSET_NONZERO_PATTERN of Y, we could take advantage of this cusparse feature. However,
    KokkosSparse::spadd(alpha,A,beta,B,C) has symbolic and numeric phases, MatAXPY does not.
  */
  ykok = static_cast<Mat_SeqAIJKokkos *>(Y->spptr);
  xkok = static_cast<Mat_SeqAIJKokkos *>(X->spptr);
  Xa   = xkok->a_dual.view_device();
  Ya   = ykok->a_dual.view_device();

  if (pattern == SAME_NONZERO_PATTERN) {
    KokkosBlas::axpy(alpha, Xa, Ya);
    PetscCall(MatSeqAIJKokkosModifyDevice(Y));
  } else if (pattern == SUBSET_NONZERO_PATTERN) {
    MatRowMapKokkosView Xi = xkok->i_dual.view_device(), Yi = ykok->i_dual.view_device();
    MatColIdxKokkosView Xj = xkok->j_dual.view_device(), Yj = ykok->j_dual.view_device();

    Kokkos::parallel_for(
      Kokkos::TeamPolicy<>(Y->rmap->n, 1), KOKKOS_LAMBDA(const KokkosTeamMemberType &t) {
        PetscInt i = t.league_rank(); // row i
        Kokkos::single(Kokkos::PerTeam(t), [=]() {
          // Only one thread works in a team
          PetscInt p, q = Yi(i);
          for (p = Xi(i); p < Xi(i + 1); p++) {          // For each nonzero on row i of X,
            while (Xj(p) != Yj(q) && q < Yi(i + 1)) q++; // find the matching nonzero on row i of Y.
            if (Xj(p) == Yj(q)) {                        // Found it
              Ya(q) += alpha * Xa(p);
              q++;
            } else {
            // If not found, it indicates the input is wrong (X is not a SUBSET_NONZERO_PATTERN of Y).
            // Just insert a NaN at the beginning of row i if it is not empty, to make the result wrong.
#if PETSC_PKG_KOKKOS_VERSION_GE(3, 7, 0)
              if (Yi(i) != Yi(i + 1)) Ya(Yi(i)) = Kokkos::ArithTraits<PetscScalar>::nan();
#else
              if (Yi(i) != Yi(i + 1)) Ya(Yi(i)) = Kokkos::Experimental::nan("1");
#endif
            }
          }
        });
      });
    PetscCall(MatSeqAIJKokkosModifyDevice(Y));
  } else { // different nonzero patterns
    Mat             Z;
    KokkosCsrMatrix zcsr;
    KernelHandle    kh;
    kh.create_spadd_handle(true); // X, Y are sorted
    KokkosSparse::spadd_symbolic(&kh, xkok->csrmat, ykok->csrmat, zcsr);
    KokkosSparse::spadd_numeric(&kh, alpha, xkok->csrmat, (PetscScalar)1.0, ykok->csrmat, zcsr);
    zkok = new Mat_SeqAIJKokkos(zcsr);
    PetscCall(MatCreateSeqAIJKokkosWithCSRMatrix(PETSC_COMM_SELF, zkok, &Z));
    PetscCall(MatHeaderReplace(Y, &Z));
    kh.destroy_spadd_handle();
  }
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(PetscLogGpuFlops(xkok->a_dual.extent(0) * 2)); // Because we scaled X and then added it to Y
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetPreallocationCOO_SeqAIJKokkos(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
{
  Mat_SeqAIJKokkos *akok;
  Mat_SeqAIJ       *aseq;

  PetscFunctionBegin;
  PetscCall(MatSetPreallocationCOO_SeqAIJ(mat, coo_n, coo_i, coo_j));
  aseq = static_cast<Mat_SeqAIJ *>(mat->data);
  akok = static_cast<Mat_SeqAIJKokkos *>(mat->spptr);
  delete akok;
  mat->spptr = akok = new Mat_SeqAIJKokkos(mat->rmap->n, mat->cmap->n, aseq->nz, aseq->i, aseq->j, aseq->a, mat->nonzerostate + 1, PETSC_FALSE);
  PetscCall(MatZeroEntries_SeqAIJKokkos(mat));
  akok->SetUpCOO(aseq);
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetValuesCOO_SeqAIJKokkos(Mat A, const PetscScalar v[], InsertMode imode)
{
  Mat_SeqAIJ                 *aseq = static_cast<Mat_SeqAIJ *>(A->data);
  Mat_SeqAIJKokkos           *akok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  PetscCount                  Annz = aseq->nz;
  const PetscCountKokkosView &jmap = akok->jmap_d;
  const PetscCountKokkosView &perm = akok->perm_d;
  MatScalarKokkosView         Aa;
  ConstMatScalarKokkosView    kv;
  PetscMemType                memtype;

  PetscFunctionBegin;
  PetscCall(PetscGetMemType(v, &memtype));
  if (PetscMemTypeHost(memtype)) { /* If user gave v[] in host, we might need to copy it to device if any */
    kv = Kokkos::create_mirror_view_and_copy(DefaultMemorySpace(), ConstMatScalarKokkosViewHost(v, aseq->coo_n));
  } else {
    kv = ConstMatScalarKokkosView(v, aseq->coo_n); /* Directly use v[]'s memory */
  }

  if (imode == INSERT_VALUES) PetscCall(MatSeqAIJGetKokkosViewWrite(A, &Aa)); /* write matrix values */
  else PetscCall(MatSeqAIJGetKokkosView(A, &Aa));                             /* read & write matrix values */

  Kokkos::parallel_for(
    Annz, KOKKOS_LAMBDA(const PetscCount i) {
      PetscScalar sum = 0.0;
      for (PetscCount k = jmap(i); k < jmap(i + 1); k++) sum += kv(perm(k));
      Aa(i) = (imode == INSERT_VALUES ? 0.0 : Aa(i)) + sum;
    });

  if (imode == INSERT_VALUES) PetscCall(MatSeqAIJRestoreKokkosViewWrite(A, &Aa));
  else PetscCall(MatSeqAIJRestoreKokkosView(A, &Aa));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatSeqAIJMoveDiagonalValuesFront_SeqAIJKokkos(Mat A, const PetscInt *diag)
{
  Mat_SeqAIJKokkos          *akok = static_cast<Mat_SeqAIJKokkos *>(A->spptr);
  MatScalarKokkosView        Aa;
  const MatRowMapKokkosView &Ai = akok->i_dual.view_device();
  PetscInt                   m  = A->rmap->n;
  ConstMatRowMapKokkosView   Adiag(diag, m); /* diag is a device pointer */

  PetscFunctionBegin;
  PetscCall(MatSeqAIJGetKokkosViewWrite(A, &Aa));
  Kokkos::parallel_for(
    m, KOKKOS_LAMBDA(const PetscInt i) {
      PetscScalar tmp;
      if (Adiag(i) >= Ai(i) && Adiag(i) < Ai(i + 1)) { /* The diagonal element exists */
        tmp          = Aa(Ai(i));
        Aa(Ai(i))    = Aa(Adiag(i));
        Aa(Adiag(i)) = tmp;
      }
    });
  PetscCall(MatSeqAIJRestoreKokkosViewWrite(A, &Aa));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatLUFactorNumeric_SeqAIJKokkos(Mat B, Mat A, const MatFactorInfo *info)
{
  PetscFunctionBegin;
  PetscCall(MatSeqAIJKokkosSyncHost(A));
  PetscCall(MatLUFactorNumeric_SeqAIJ(B, A, info));
  B->offloadmask = PETSC_OFFLOAD_CPU;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetOps_SeqAIJKokkos(Mat A)
{
  Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;

  PetscFunctionBegin;
  A->offloadmask = PETSC_OFFLOAD_KOKKOS; /* We do not really use this flag */
  A->boundtocpu  = PETSC_FALSE;

  A->ops->assemblyend               = MatAssemblyEnd_SeqAIJKokkos;
  A->ops->destroy                   = MatDestroy_SeqAIJKokkos;
  A->ops->duplicate                 = MatDuplicate_SeqAIJKokkos;
  A->ops->axpy                      = MatAXPY_SeqAIJKokkos;
  A->ops->scale                     = MatScale_SeqAIJKokkos;
  A->ops->zeroentries               = MatZeroEntries_SeqAIJKokkos;
  A->ops->productsetfromoptions     = MatProductSetFromOptions_SeqAIJKokkos;
  A->ops->mult                      = MatMult_SeqAIJKokkos;
  A->ops->multadd                   = MatMultAdd_SeqAIJKokkos;
  A->ops->multtranspose             = MatMultTranspose_SeqAIJKokkos;
  A->ops->multtransposeadd          = MatMultTransposeAdd_SeqAIJKokkos;
  A->ops->multhermitiantranspose    = MatMultHermitianTranspose_SeqAIJKokkos;
  A->ops->multhermitiantransposeadd = MatMultHermitianTransposeAdd_SeqAIJKokkos;
  A->ops->productnumeric            = MatProductNumeric_SeqAIJKokkos_SeqAIJKokkos;
  A->ops->transpose                 = MatTranspose_SeqAIJKokkos;
  A->ops->setoption                 = MatSetOption_SeqAIJKokkos;
  A->ops->getdiagonal               = MatGetDiagonal_SeqAIJKokkos;
  a->ops->getarray                  = MatSeqAIJGetArray_SeqAIJKokkos;
  a->ops->restorearray              = MatSeqAIJRestoreArray_SeqAIJKokkos;
  a->ops->getarrayread              = MatSeqAIJGetArrayRead_SeqAIJKokkos;
  a->ops->restorearrayread          = MatSeqAIJRestoreArrayRead_SeqAIJKokkos;
  a->ops->getarraywrite             = MatSeqAIJGetArrayWrite_SeqAIJKokkos;
  a->ops->restorearraywrite         = MatSeqAIJRestoreArrayWrite_SeqAIJKokkos;
  a->ops->getcsrandmemtype          = MatSeqAIJGetCSRAndMemType_SeqAIJKokkos;

  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_SeqAIJKokkos));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", MatSetValuesCOO_SeqAIJKokkos));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatSetSeqAIJKokkosWithCSRMatrix(Mat A, Mat_SeqAIJKokkos *akok)
{
  Mat_SeqAIJ *aseq;
  PetscInt    i, m, n;

  PetscFunctionBegin;
  PetscCheck(!A->spptr, PETSC_COMM_SELF, PETSC_ERR_PLIB, "A->spptr is supposed to be empty");

  m = akok->nrows();
  n = akok->ncols();
  PetscCall(MatSetSizes(A, m, n, m, n));
  PetscCall(MatSetType(A, MATSEQAIJKOKKOS));

  /* Set up data structures of A as a MATSEQAIJ */
  PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(A, MAT_SKIP_ALLOCATION, NULL));
  aseq = (Mat_SeqAIJ *)(A)->data;

  akok->i_dual.sync_host(); /* We always need sync'ed i, j on host */
  akok->j_dual.sync_host();

  aseq->i            = akok->i_host_data();
  aseq->j            = akok->j_host_data();
  aseq->a            = akok->a_host_data();
  aseq->nonew        = -1; /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
  aseq->singlemalloc = PETSC_FALSE;
  aseq->free_a       = PETSC_FALSE;
  aseq->free_ij      = PETSC_FALSE;
  aseq->nz           = akok->nnz();
  aseq->maxnz        = aseq->nz;

  PetscCall(PetscMalloc1(m, &aseq->imax));
  PetscCall(PetscMalloc1(m, &aseq->ilen));
  for (i = 0; i < m; i++) aseq->ilen[i] = aseq->imax[i] = aseq->i[i + 1] - aseq->i[i];

  /* It is critical to set the nonzerostate, as we use it to check if sparsity pattern (hence data) has changed on host in MatAssemblyEnd */
  akok->nonzerostate = A->nonzerostate;
  A->spptr           = akok; /* Set A->spptr before MatAssembly so that A->spptr won't be allocated again there */
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatSeqAIJKokkosGetKokkosCsrMatrix(Mat A, KokkosCsrMatrix *csr)
{
  PetscFunctionBegin;
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  *csr = static_cast<Mat_SeqAIJKokkos *>(A->spptr)->csrmat;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatCreateSeqAIJKokkosWithKokkosCsrMatrix(MPI_Comm comm, KokkosCsrMatrix csr, Mat *A)
{
  Mat_SeqAIJKokkos *akok;
  PetscFunctionBegin;
  PetscCallCXX(akok = new Mat_SeqAIJKokkos(csr));
  PetscCall(MatCreate(comm, A));
  PetscCall(MatSetSeqAIJKokkosWithCSRMatrix(*A, akok));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Crete a SEQAIJKOKKOS matrix with a Mat_SeqAIJKokkos data structure

   Note we have names like MatSeqAIJSetPreallocationCSR, so I use capitalized CSR
 */
PETSC_INTERN PetscErrorCode MatCreateSeqAIJKokkosWithCSRMatrix(MPI_Comm comm, Mat_SeqAIJKokkos *akok, Mat *A)
{
  PetscFunctionBegin;
  PetscCall(MatCreate(comm, A));
  PetscCall(MatSetSeqAIJKokkosWithCSRMatrix(*A, akok));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   MatCreateSeqAIJKokkos - Creates a sparse matrix in `MATSEQAIJKOKKOS` (compressed row) format
   (the default parallel PETSc format). This matrix will ultimately be handled by
   Kokkos for calculations.

   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 provided
-  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:
   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: [](chapter_matrices), `Mat`, `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`, `MatCreateAIJ()`
@*/
PetscErrorCode MatCreateSeqAIJKokkos(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt nz, const PetscInt nnz[], Mat *A)
{
  PetscFunctionBegin;
  PetscCall(PetscKokkosInitializeCheck());
  PetscCall(MatCreate(comm, A));
  PetscCall(MatSetSizes(*A, m, n, m, n));
  PetscCall(MatSetType(*A, MATSEQAIJKOKKOS));
  PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*A, nz, (PetscInt *)nnz));
  PetscFunctionReturn(PETSC_SUCCESS);
}

typedef Kokkos::TeamPolicy<>::member_type team_member;
//
// This factorization exploits block diagonal matrices with "Nf" (not used).
// Use -pc_factor_mat_ordering_type rcm to order decouple blocks of size N/Nf for this optimization
//
static PetscErrorCode MatLUFactorNumeric_SeqAIJKOKKOSDEVICE(Mat B, Mat A, const MatFactorInfo *info)
{
  Mat_SeqAIJ       *b      = (Mat_SeqAIJ *)B->data;
  Mat_SeqAIJKokkos *aijkok = static_cast<Mat_SeqAIJKokkos *>(A->spptr), *baijkok = static_cast<Mat_SeqAIJKokkos *>(B->spptr);
  IS                isrow = b->row, isicol = b->icol;
  const PetscInt   *r_h, *ic_h;
  const PetscInt n = A->rmap->n, *ai_d = aijkok->i_dual.view_device().data(), *aj_d = aijkok->j_dual.view_device().data(), *bi_d = baijkok->i_dual.view_device().data(), *bj_d = baijkok->j_dual.view_device().data(), *bdiag_d = baijkok->diag_d.data();
  const PetscScalar *aa_d = aijkok->a_dual.view_device().data();
  PetscScalar       *ba_d = baijkok->a_dual.view_device().data();
  PetscBool          row_identity, col_identity;
  PetscInt           nc, Nf = 1, nVec = 32; // should be a parameter, Nf is batch size - not used

  PetscFunctionBegin;
  PetscCheck(A->rmap->n == n, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "square matrices only supported %" PetscInt_FMT " %" PetscInt_FMT, A->rmap->n, n);
  PetscCall(MatIsStructurallySymmetric(A, &row_identity));
  PetscCheck(row_identity, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "structurally symmetric matrices only supported");
  PetscCall(ISGetIndices(isrow, &r_h));
  PetscCall(ISGetIndices(isicol, &ic_h));
  PetscCall(ISGetSize(isicol, &nc));
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  {
#define KOKKOS_SHARED_LEVEL 1
    using scr_mem_t    = Kokkos::DefaultExecutionSpace::scratch_memory_space;
    using sizet_scr_t  = Kokkos::View<size_t, scr_mem_t>;
    using scalar_scr_t = Kokkos::View<PetscScalar, scr_mem_t>;
    const Kokkos::View<const PetscInt *, Kokkos::LayoutLeft, Kokkos::HostSpace, Kokkos::MemoryTraits<Kokkos::Unmanaged>> h_r_k(r_h, n);
    Kokkos::View<PetscInt *, Kokkos::LayoutLeft>                                                                         d_r_k("r", n);
    const Kokkos::View<const PetscInt *, Kokkos::LayoutLeft, Kokkos::HostSpace, Kokkos::MemoryTraits<Kokkos::Unmanaged>> h_ic_k(ic_h, nc);
    Kokkos::View<PetscInt *, Kokkos::LayoutLeft>                                                                         d_ic_k("ic", nc);
    size_t                                                                                                               flops_h = 0.0;
    Kokkos::View<size_t, Kokkos::HostSpace>                                                                              h_flops_k(&flops_h);
    Kokkos::View<size_t>                                                                                                 d_flops_k("flops");
    const int                                                                                                            conc = Kokkos::DefaultExecutionSpace().concurrency(), team_size = conc > 1 ? 16 : 1; // 8*32 = 256
    const int                                                                                                            nloc = n / Nf, Ni = (conc > 8) ? 1 /* some intelligent number of SMs -- but need league_barrier */ : 1;
    Kokkos::deep_copy(d_flops_k, h_flops_k);
    Kokkos::deep_copy(d_r_k, h_r_k);
    Kokkos::deep_copy(d_ic_k, h_ic_k);
    // Fill A --> fact
    Kokkos::parallel_for(
      Kokkos::TeamPolicy<>(Nf * Ni, team_size, nVec), KOKKOS_LAMBDA(const team_member team) {
        const PetscInt  field = team.league_rank() / Ni, field_block = team.league_rank() % Ni; // use grid.x/y in CUDA
        const PetscInt  nloc_i = (nloc / Ni + !!(nloc % Ni)), start_i = field * nloc + field_block * nloc_i, end_i = (start_i + nloc_i) > (field + 1) * nloc ? (field + 1) * nloc : (start_i + nloc_i);
        const PetscInt *ic = d_ic_k.data(), *r = d_r_k.data();
        // zero rows of B
        Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start_i, end_i), [=](const int &rowb) {
          PetscInt     nzbL = bi_d[rowb + 1] - bi_d[rowb], nzbU = bdiag_d[rowb] - bdiag_d[rowb + 1]; // with diag
          PetscScalar *baL = ba_d + bi_d[rowb];
          PetscScalar *baU = ba_d + bdiag_d[rowb + 1] + 1;
          /* zero (unfactored row) */
          for (int j = 0; j < nzbL; j++) baL[j] = 0;
          for (int j = 0; j < nzbU; j++) baU[j] = 0;
        });
        // copy A into B
        Kokkos::parallel_for(Kokkos::TeamVectorRange(team, start_i, end_i), [=](const int &rowb) {
          PetscInt           rowa = r[rowb], nza = ai_d[rowa + 1] - ai_d[rowa];
          const PetscScalar *av    = aa_d + ai_d[rowa];
          const PetscInt    *ajtmp = aj_d + ai_d[rowa];
          /* load in initial (unfactored row) */
          for (int j = 0; j < nza; j++) {
            PetscInt    colb = ic[ajtmp[j]];
            PetscScalar vala = av[j];
            if (colb == rowb) {
              *(ba_d + bdiag_d[rowb]) = vala;
            } else {
              const PetscInt *pbj = bj_d + ((colb > rowb) ? bdiag_d[rowb + 1] + 1 : bi_d[rowb]);
              PetscScalar    *pba = ba_d + ((colb > rowb) ? bdiag_d[rowb + 1] + 1 : bi_d[rowb]);
              PetscInt        nz = (colb > rowb) ? bdiag_d[rowb] - (bdiag_d[rowb + 1] + 1) : bi_d[rowb + 1] - bi_d[rowb], set = 0;
              for (int j = 0; j < nz; j++) {
                if (pbj[j] == colb) {
                  pba[j] = vala;
                  set++;
                  break;
                }
              }
#if !defined(PETSC_HAVE_SYCL)
              if (set != 1) printf("\t\t\t ERROR DID NOT SET ?????\n");
#else
              (void)set;
#endif
            }
          }
        });
      });
    Kokkos::fence();

    Kokkos::parallel_for(
      Kokkos::TeamPolicy<>(Nf * Ni, team_size, nVec).set_scratch_size(KOKKOS_SHARED_LEVEL, Kokkos::PerThread(sizet_scr_t::shmem_size() + scalar_scr_t::shmem_size()), Kokkos::PerTeam(sizet_scr_t::shmem_size())), KOKKOS_LAMBDA(const team_member team) {
        sizet_scr_t    colkIdx(team.thread_scratch(KOKKOS_SHARED_LEVEL));
        scalar_scr_t   L_ki(team.thread_scratch(KOKKOS_SHARED_LEVEL));
        sizet_scr_t    flops(team.team_scratch(KOKKOS_SHARED_LEVEL));
        const PetscInt field = team.league_rank() / Ni, field_block_idx = team.league_rank() % Ni; // use grid.x/y in CUDA
        const PetscInt start = field * nloc, end = start + nloc;
        Kokkos::single(Kokkos::PerTeam(team), [=]() { flops() = 0; });
        // A22 panel update for each row A(1,:) and col A(:,1)
        for (int ii = start; ii < end - 1; ii++) {
          const PetscInt    *bjUi = bj_d + bdiag_d[ii + 1] + 1, nzUi = bdiag_d[ii] - (bdiag_d[ii + 1] + 1); // vector, and vector size, of column indices of U(i,(i+1):end)
          const PetscScalar *baUi    = ba_d + bdiag_d[ii + 1] + 1;                                          // vector of data  U(i,i+1:end)
          const PetscInt     nUi_its = nzUi / Ni + !!(nzUi % Ni);
          const PetscScalar  Bii     = *(ba_d + bdiag_d[ii]); // diagonal in its special place
          Kokkos::parallel_for(Kokkos::TeamThreadRange(team, nUi_its), [=](const int j) {
            PetscInt kIdx = j * Ni + field_block_idx;
            if (kIdx >= nzUi) /* void */
              ;
            else {
              const PetscInt  myk = bjUi[kIdx];                // assume symmetric structure, need a transposed meta-data here in general
              const PetscInt *pjL = bj_d + bi_d[myk];          // look for L(myk,ii) in start of row
              const PetscInt  nzL = bi_d[myk + 1] - bi_d[myk]; // size of L_k(:)
              size_t          st_idx;
              // find and do L(k,i) = A(:k,i) / A(i,i)
              Kokkos::single(Kokkos::PerThread(team), [&]() { colkIdx() = PETSC_MAX_INT; });
              // get column, there has got to be a better way
              Kokkos::parallel_reduce(
                Kokkos::ThreadVectorRange(team, nzL),
                [&](const int &j, size_t &idx) {
                  if (pjL[j] == ii) {
                    PetscScalar *pLki = ba_d + bi_d[myk] + j;
                    idx               = j;           // output
                    *pLki             = *pLki / Bii; // column scaling:  L(k,i) = A(:k,i) / A(i,i)
                  }
                },
                st_idx);
              Kokkos::single(Kokkos::PerThread(team), [=]() {
                colkIdx() = st_idx;
                L_ki()    = *(ba_d + bi_d[myk] + st_idx);
              });
#if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
              if (colkIdx() == PETSC_MAX_INT) printf("\t\t\t\t\t\t\tERROR: failed to find L_ki(%d,%d)\n", (int)myk, ii); // uses a register
#endif
              // active row k, do  A_kj -= Lki * U_ij; j \in U(i,:) j != i
              // U(i+1,:end)
              Kokkos::parallel_for(Kokkos::ThreadVectorRange(team, nzUi), [=](const int &uiIdx) { // index into i (U)
                PetscScalar Uij = baUi[uiIdx];
                PetscInt    col = bjUi[uiIdx];
                if (col == myk) {
                  // A_kk = A_kk - L_ki * U_ij(k)
                  PetscScalar *Akkv = (ba_d + bdiag_d[myk]); // diagonal in its special place
                  *Akkv             = *Akkv - L_ki() * Uij;  // UiK
                } else {
                  PetscScalar    *start, *end, *pAkjv = NULL;
                  PetscInt        high, low;
                  const PetscInt *startj;
                  if (col < myk) { // L
                    PetscScalar *pLki = ba_d + bi_d[myk] + colkIdx();
                    PetscInt     idx  = (pLki + 1) - (ba_d + bi_d[myk]); // index into row
                    start             = pLki + 1;                        // start at pLki+1, A22(myk,1)
                    startj            = bj_d + bi_d[myk] + idx;
                    end               = ba_d + bi_d[myk + 1];
                  } else {
                    PetscInt idx = bdiag_d[myk + 1] + 1;
                    start        = ba_d + idx;
                    startj       = bj_d + idx;
                    end          = ba_d + bdiag_d[myk];
                  }
                  // search for 'col', use bisection search - TODO
                  low  = 0;
                  high = (PetscInt)(end - start);
                  while (high - low > 5) {
                    int t = (low + high) / 2;
                    if (startj[t] > col) high = t;
                    else low = t;
                  }
                  for (pAkjv = start + low; pAkjv < start + high; pAkjv++) {
                    if (startj[pAkjv - start] == col) break;
                  }
#if defined(PETSC_USE_DEBUG) && !defined(PETSC_HAVE_SYCL)
                  if (pAkjv == start + high) printf("\t\t\t\t\t\t\t\t\t\t\tERROR: *** failed to find Akj(%d,%d)\n", (int)myk, (int)col); // uses a register
#endif
                  *pAkjv = *pAkjv - L_ki() * Uij; // A_kj = A_kj - L_ki * U_ij
                }
              });
            }
          });
          team.team_barrier(); // this needs to be a league barrier to use more that one SM per block
          if (field_block_idx == 0) Kokkos::single(Kokkos::PerTeam(team), [&]() { Kokkos::atomic_add(flops.data(), (size_t)(2 * (nzUi * nzUi) + 2)); });
        } /* endof for (i=0; i<n; i++) { */
        Kokkos::single(Kokkos::PerTeam(team), [=]() {
          Kokkos::atomic_add(&d_flops_k(), flops());
          flops() = 0;
        });
      });
    Kokkos::fence();
    Kokkos::deep_copy(h_flops_k, d_flops_k);
    PetscCall(PetscLogGpuFlops((PetscLogDouble)h_flops_k()));
    Kokkos::parallel_for(
      Kokkos::TeamPolicy<>(Nf * Ni, 1, 256), KOKKOS_LAMBDA(const team_member team) {
        const PetscInt lg_rank = team.league_rank(), field = lg_rank / Ni;                            //, field_offset = lg_rank%Ni;
        const PetscInt start = field * nloc, end = start + nloc, n_its = (nloc / Ni + !!(nloc % Ni)); // 1/Ni iters
        /* Invert diagonal for simpler triangular solves */
        Kokkos::parallel_for(Kokkos::TeamVectorRange(team, n_its), [=](int outer_index) {
          int i = start + outer_index * Ni + lg_rank % Ni;
          if (i < end) {
            PetscScalar *pv = ba_d + bdiag_d[i];
            *pv             = 1.0 / (*pv);
          }
        });
      });
  }
  PetscCall(PetscLogGpuTimeEnd());
  PetscCall(ISRestoreIndices(isicol, &ic_h));
  PetscCall(ISRestoreIndices(isrow, &r_h));

  PetscCall(ISIdentity(isrow, &row_identity));
  PetscCall(ISIdentity(isicol, &col_identity));
  if (b->inode.size) {
    B->ops->solve = MatSolve_SeqAIJ_Inode;
  } else if (row_identity && col_identity) {
    B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
  } else {
    B->ops->solve = MatSolve_SeqAIJ; // at least this needs to be in Kokkos
  }
  B->offloadmask = PETSC_OFFLOAD_GPU;
  PetscCall(MatSeqAIJKokkosSyncHost(B));          // solve on CPU
  B->ops->solveadd          = MatSolveAdd_SeqAIJ; // and this
  B->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
  B->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
  B->ops->matsolve          = MatMatSolve_SeqAIJ;
  B->assembled              = PETSC_TRUE;
  B->preallocated           = PETSC_TRUE;

  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatLUFactorSymbolic_SeqAIJKokkos(Mat B, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
{
  PetscFunctionBegin;
  PetscCall(MatLUFactorSymbolic_SeqAIJ(B, A, isrow, iscol, info));
  B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJKokkos;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSeqAIJKokkosSymbolicSolveCheck(Mat A)
{
  Mat_SeqAIJKokkosTriFactors *factors = (Mat_SeqAIJKokkosTriFactors *)A->spptr;

  PetscFunctionBegin;
  if (!factors->sptrsv_symbolic_completed) {
    KokkosSparse::Experimental::sptrsv_symbolic(&factors->khU, factors->iU_d, factors->jU_d, factors->aU_d);
    KokkosSparse::Experimental::sptrsv_symbolic(&factors->khL, factors->iL_d, factors->jL_d, factors->aL_d);
    factors->sptrsv_symbolic_completed = PETSC_TRUE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Check if we need to update factors etc for transpose solve */
static PetscErrorCode MatSeqAIJKokkosTransposeSolveCheck(Mat A)
{
  Mat_SeqAIJKokkosTriFactors *factors = (Mat_SeqAIJKokkosTriFactors *)A->spptr;
  MatColIdxType               n       = A->rmap->n;

  PetscFunctionBegin;
  if (!factors->transpose_updated) { /* TODO: KK needs to provide functions to do numeric transpose only */
    /* Update L^T and do sptrsv symbolic */
    factors->iLt_d = MatRowMapKokkosView("factors->iLt_d", n + 1);
    Kokkos::deep_copy(factors->iLt_d, 0); /* KK requires 0 */
    factors->jLt_d = MatColIdxKokkosView("factors->jLt_d", factors->jL_d.extent(0));
    factors->aLt_d = MatScalarKokkosView("factors->aLt_d", factors->aL_d.extent(0));

    transpose_matrix<ConstMatRowMapKokkosView, ConstMatColIdxKokkosView, ConstMatScalarKokkosView, MatRowMapKokkosView, MatColIdxKokkosView, MatScalarKokkosView, MatRowMapKokkosView, DefaultExecutionSpace>(n, n, factors->iL_d, factors->jL_d, factors->aL_d,
                                                                                                                                                                                                              factors->iLt_d, factors->jLt_d, factors->aLt_d);

    /* TODO: KK transpose_matrix() does not sort column indices, however cusparse requires sorted indices.
      We have to sort the indices, until KK provides finer control options.
    */
    sort_crs_matrix<DefaultExecutionSpace, MatRowMapKokkosView, MatColIdxKokkosView, MatScalarKokkosView>(factors->iLt_d, factors->jLt_d, factors->aLt_d);

    KokkosSparse::Experimental::sptrsv_symbolic(&factors->khLt, factors->iLt_d, factors->jLt_d, factors->aLt_d);

    /* Update U^T and do sptrsv symbolic */
    factors->iUt_d = MatRowMapKokkosView("factors->iUt_d", n + 1);
    Kokkos::deep_copy(factors->iUt_d, 0); /* KK requires 0 */
    factors->jUt_d = MatColIdxKokkosView("factors->jUt_d", factors->jU_d.extent(0));
    factors->aUt_d = MatScalarKokkosView("factors->aUt_d", factors->aU_d.extent(0));

    transpose_matrix<ConstMatRowMapKokkosView, ConstMatColIdxKokkosView, ConstMatScalarKokkosView, MatRowMapKokkosView, MatColIdxKokkosView, MatScalarKokkosView, MatRowMapKokkosView, DefaultExecutionSpace>(n, n, factors->iU_d, factors->jU_d, factors->aU_d,
                                                                                                                                                                                                              factors->iUt_d, factors->jUt_d, factors->aUt_d);

    /* Sort indices. See comments above */
    sort_crs_matrix<DefaultExecutionSpace, MatRowMapKokkosView, MatColIdxKokkosView, MatScalarKokkosView>(factors->iUt_d, factors->jUt_d, factors->aUt_d);

    KokkosSparse::Experimental::sptrsv_symbolic(&factors->khUt, factors->iUt_d, factors->jUt_d, factors->aUt_d);
    factors->transpose_updated = PETSC_TRUE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Solve Ax = b, with A = LU */
static PetscErrorCode MatSolve_SeqAIJKokkos(Mat A, Vec b, Vec x)
{
  ConstPetscScalarKokkosView  bv;
  PetscScalarKokkosView       xv;
  Mat_SeqAIJKokkosTriFactors *factors = (Mat_SeqAIJKokkosTriFactors *)A->spptr;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosSymbolicSolveCheck(A));
  PetscCall(VecGetKokkosView(b, &bv));
  PetscCall(VecGetKokkosViewWrite(x, &xv));
  /* Solve L tmpv = b */
  PetscCallCXX(KokkosSparse::Experimental::sptrsv_solve(&factors->khL, factors->iL_d, factors->jL_d, factors->aL_d, bv, factors->workVector));
  /* Solve Ux = tmpv */
  PetscCallCXX(KokkosSparse::Experimental::sptrsv_solve(&factors->khU, factors->iU_d, factors->jU_d, factors->aU_d, factors->workVector, xv));
  PetscCall(VecRestoreKokkosView(b, &bv));
  PetscCall(VecRestoreKokkosViewWrite(x, &xv));
  PetscCall(PetscLogGpuTimeEnd());
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Solve A^T x = b, where A^T = U^T L^T */
static PetscErrorCode MatSolveTranspose_SeqAIJKokkos(Mat A, Vec b, Vec x)
{
  ConstPetscScalarKokkosView  bv;
  PetscScalarKokkosView       xv;
  Mat_SeqAIJKokkosTriFactors *factors = (Mat_SeqAIJKokkosTriFactors *)A->spptr;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosTransposeSolveCheck(A));
  PetscCall(VecGetKokkosView(b, &bv));
  PetscCall(VecGetKokkosViewWrite(x, &xv));
  /* Solve U^T tmpv = b */
  KokkosSparse::Experimental::sptrsv_solve(&factors->khUt, factors->iUt_d, factors->jUt_d, factors->aUt_d, bv, factors->workVector);

  /* Solve L^T x = tmpv */
  KokkosSparse::Experimental::sptrsv_solve(&factors->khLt, factors->iLt_d, factors->jLt_d, factors->aLt_d, factors->workVector, xv);
  PetscCall(VecRestoreKokkosView(b, &bv));
  PetscCall(VecRestoreKokkosViewWrite(x, &xv));
  PetscCall(PetscLogGpuTimeEnd());
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatILUFactorNumeric_SeqAIJKokkos(Mat B, Mat A, const MatFactorInfo *info)
{
  Mat_SeqAIJKokkos           *aijkok   = (Mat_SeqAIJKokkos *)A->spptr;
  Mat_SeqAIJKokkosTriFactors *factors  = (Mat_SeqAIJKokkosTriFactors *)B->spptr;
  PetscInt                    fill_lev = info->levels;

  PetscFunctionBegin;
  PetscCall(PetscLogGpuTimeBegin());
  PetscCall(MatSeqAIJKokkosSyncDevice(A));

  auto a_d = aijkok->a_dual.view_device();
  auto i_d = aijkok->i_dual.view_device();
  auto j_d = aijkok->j_dual.view_device();

  KokkosSparse::Experimental::spiluk_numeric(&factors->kh, fill_lev, i_d, j_d, a_d, factors->iL_d, factors->jL_d, factors->aL_d, factors->iU_d, factors->jU_d, factors->aU_d);

  B->assembled              = PETSC_TRUE;
  B->preallocated           = PETSC_TRUE;
  B->ops->solve             = MatSolve_SeqAIJKokkos;
  B->ops->solvetranspose    = MatSolveTranspose_SeqAIJKokkos;
  B->ops->matsolve          = NULL;
  B->ops->matsolvetranspose = NULL;
  B->offloadmask            = PETSC_OFFLOAD_GPU;

  /* Once the factors' value changed, we need to update their transpose and sptrsv handle */
  factors->transpose_updated         = PETSC_FALSE;
  factors->sptrsv_symbolic_completed = PETSC_FALSE;
  /* TODO: log flops, but how to know that? */
  PetscCall(PetscLogGpuTimeEnd());
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatILUFactorSymbolic_SeqAIJKokkos(Mat B, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
{
  Mat_SeqAIJKokkos           *aijkok;
  Mat_SeqAIJ                 *b;
  Mat_SeqAIJKokkosTriFactors *factors  = (Mat_SeqAIJKokkosTriFactors *)B->spptr;
  PetscInt                    fill_lev = info->levels;
  PetscInt                    nnzA     = ((Mat_SeqAIJ *)A->data)->nz, nnzL, nnzU;
  PetscInt                    n        = A->rmap->n;

  PetscFunctionBegin;
  PetscCall(MatSeqAIJKokkosSyncDevice(A));
  /* Rebuild factors */
  if (factors) {
    factors->Destroy();
  } /* Destroy the old if it exists */
  else {
    B->spptr = factors = new Mat_SeqAIJKokkosTriFactors(n);
  }

  /* Create a spiluk handle and then do symbolic factorization */
  nnzL = nnzU = PetscRealIntMultTruncate(info->fill, nnzA);
  factors->kh.create_spiluk_handle(KokkosSparse::Experimental::SPILUKAlgorithm::SEQLVLSCHD_TP1, n, nnzL, nnzU);

  auto spiluk_handle = factors->kh.get_spiluk_handle();

  Kokkos::realloc(factors->iL_d, n + 1); /* Free old arrays and realloc */
  Kokkos::realloc(factors->jL_d, spiluk_handle->get_nnzL());
  Kokkos::realloc(factors->iU_d, n + 1);
  Kokkos::realloc(factors->jU_d, spiluk_handle->get_nnzU());

  aijkok   = (Mat_SeqAIJKokkos *)A->spptr;
  auto i_d = aijkok->i_dual.view_device();
  auto j_d = aijkok->j_dual.view_device();
  KokkosSparse::Experimental::spiluk_symbolic(&factors->kh, fill_lev, i_d, j_d, factors->iL_d, factors->jL_d, factors->iU_d, factors->jU_d);
  /* TODO: if spiluk_symbolic is asynchronous, do we need to sync before calling get_nnzL()? */

  Kokkos::resize(factors->jL_d, spiluk_handle->get_nnzL()); /* Shrink or expand, and retain old value */
  Kokkos::resize(factors->jU_d, spiluk_handle->get_nnzU());
  Kokkos::realloc(factors->aL_d, spiluk_handle->get_nnzL()); /* No need to retain old value */
  Kokkos::realloc(factors->aU_d, spiluk_handle->get_nnzU());

  /* TODO: add options to select sptrsv algorithms */
  /* Create sptrsv handles for L, U and their transpose */
#if defined(KOKKOSKERNELS_ENABLE_TPL_CUSPARSE)
  auto sptrsv_alg = KokkosSparse::Experimental::SPTRSVAlgorithm::SPTRSV_CUSPARSE;
#else
  auto sptrsv_alg = KokkosSparse::Experimental::SPTRSVAlgorithm::SEQLVLSCHD_TP1;
#endif

  factors->khL.create_sptrsv_handle(sptrsv_alg, n, true /* L is lower tri */);
  factors->khU.create_sptrsv_handle(sptrsv_alg, n, false /* U is not lower tri */);
  factors->khLt.create_sptrsv_handle(sptrsv_alg, n, false /* L^T is not lower tri */);
  factors->khUt.create_sptrsv_handle(sptrsv_alg, n, true /* U^T is lower tri */);

  /* Fill fields of the factor matrix B */
  PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(B, MAT_SKIP_ALLOCATION, NULL));
  b     = (Mat_SeqAIJ *)B->data;
  b->nz = b->maxnz          = spiluk_handle->get_nnzL() + spiluk_handle->get_nnzU();
  B->info.fill_ratio_given  = info->fill;
  B->info.fill_ratio_needed = nnzA > 0 ? ((PetscReal)b->nz) / ((PetscReal)nnzA) : 1.0;

  B->offloadmask          = PETSC_OFFLOAD_GPU;
  B->ops->lufactornumeric = MatILUFactorNumeric_SeqAIJKokkos;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatLUFactorSymbolic_SeqAIJKOKKOSDEVICE(Mat B, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
{
  Mat_SeqAIJ    *b     = (Mat_SeqAIJ *)B->data;
  const PetscInt nrows = A->rmap->n;

  PetscFunctionBegin;
  PetscCall(MatLUFactorSymbolic_SeqAIJ(B, A, isrow, iscol, info));
  B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJKOKKOSDEVICE;
  // move B data into Kokkos
  PetscCall(MatSeqAIJKokkosSyncDevice(B)); // create aijkok
  PetscCall(MatSeqAIJKokkosSyncDevice(A)); // create aijkok
  {
    Mat_SeqAIJKokkos *baijkok = static_cast<Mat_SeqAIJKokkos *>(B->spptr);
    if (!baijkok->diag_d.extent(0)) {
      const Kokkos::View<PetscInt *, Kokkos::HostSpace, Kokkos::MemoryTraits<Kokkos::Unmanaged>> h_diag(b->diag, nrows + 1);
      baijkok->diag_d = Kokkos::View<PetscInt *>(Kokkos::create_mirror(DefaultMemorySpace(), h_diag));
      Kokkos::deep_copy(baijkok->diag_d, h_diag);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatFactorGetSolverType_SeqAIJKokkos(Mat A, MatSolverType *type)
{
  PetscFunctionBegin;
  *type = MATSOLVERKOKKOS;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatFactorGetSolverType_seqaij_kokkos_device(Mat A, MatSolverType *type)
{
  PetscFunctionBegin;
  *type = MATSOLVERKOKKOSDEVICE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  MATSOLVERKOKKOS = "Kokkos" - A matrix solver type providing triangular solvers for sequential matrices
  on a single GPU of type, `MATSEQAIJKOKKOS`, `MATAIJKOKKOS`.

  Level: beginner

.seealso: [](chapter_matrices), `Mat`, `PCFactorSetMatSolverType()`, `MatSolverType`, `MatCreateSeqAIJKokkos()`, `MATAIJKOKKOS`, `MatKokkosSetFormat()`, `MatKokkosStorageFormat`, `MatKokkosFormatOperation`
M*/
PETSC_EXTERN PetscErrorCode MatGetFactor_SeqAIJKokkos_Kokkos(Mat A, MatFactorType ftype, Mat *B) /* MatGetFactor_<MatType>_<MatSolverType> */
{
  PetscInt n = A->rmap->n;

  PetscFunctionBegin;
  PetscCall(MatCreate(PetscObjectComm((PetscObject)A), B));
  PetscCall(MatSetSizes(*B, n, n, n, n));
  (*B)->factortype = ftype;
  PetscCall(PetscStrallocpy(MATORDERINGND, (char **)&(*B)->preferredordering[MAT_FACTOR_LU]));
  PetscCall(MatSetType(*B, MATSEQAIJKOKKOS));

  if (ftype == MAT_FACTOR_LU) {
    PetscCall(MatSetBlockSizesFromMats(*B, A, A));
    (*B)->canuseordering        = PETSC_TRUE;
    (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJKokkos;
  } else if (ftype == MAT_FACTOR_ILU) {
    PetscCall(MatSetBlockSizesFromMats(*B, A, A));
    (*B)->canuseordering         = PETSC_FALSE;
    (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJKokkos;
  } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatFactorType %s is not supported by MatType SeqAIJKokkos", MatFactorTypes[ftype]);

  PetscCall(MatSeqAIJSetPreallocation(*B, MAT_SKIP_ALLOCATION, NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)(*B), "MatFactorGetSolverType_C", MatFactorGetSolverType_SeqAIJKokkos));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBegin;
  PetscCall(MatCreate(PetscObjectComm((PetscObject)A), B));
  PetscCall(MatSetSizes(*B, n, n, n, n));
  (*B)->factortype     = ftype;
  (*B)->canuseordering = PETSC_TRUE;
  PetscCall(PetscStrallocpy(MATORDERINGND, (char **)&(*B)->preferredordering[MAT_FACTOR_LU]));
  PetscCall(MatSetType(*B, MATSEQAIJKOKKOS));

  if (ftype == MAT_FACTOR_LU) {
    PetscCall(MatSetBlockSizesFromMats(*B, A, A));
    (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJKOKKOSDEVICE;
  } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor type not supported for KOKKOS Matrix Types");

  PetscCall(MatSeqAIJSetPreallocation(*B, MAT_SKIP_ALLOCATION, NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)(*B), "MatFactorGetSolverType_C", MatFactorGetSolverType_seqaij_kokkos_device));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_EXTERN PetscErrorCode MatSolverTypeRegister_KOKKOS(void)
{
  PetscFunctionBegin;
  PetscCall(MatSolverTypeRegister(MATSOLVERKOKKOS, MATSEQAIJKOKKOS, MAT_FACTOR_LU, MatGetFactor_SeqAIJKokkos_Kokkos));
  PetscCall(MatSolverTypeRegister(MATSOLVERKOKKOS, MATSEQAIJKOKKOS, MAT_FACTOR_ILU, MatGetFactor_SeqAIJKokkos_Kokkos));
  PetscCall(MatSolverTypeRegister(MATSOLVERKOKKOSDEVICE, MATSEQAIJKOKKOS, MAT_FACTOR_LU, MatGetFactor_seqaijkokkos_kokkos_device));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Utility to print out a KokkosCsrMatrix for debugging */
PETSC_INTERN PetscErrorCode PrintCsrMatrix(const KokkosCsrMatrix &csrmat)
{
  const auto        &iv = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), csrmat.graph.row_map);
  const auto        &jv = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), csrmat.graph.entries);
  const auto        &av = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), csrmat.values);
  const PetscInt    *i  = iv.data();
  const PetscInt    *j  = jv.data();
  const PetscScalar *a  = av.data();
  PetscInt           m = csrmat.numRows(), n = csrmat.numCols(), nnz = csrmat.nnz();

  PetscFunctionBegin;
  PetscCall(PetscPrintf(PETSC_COMM_SELF, "%" PetscInt_FMT " x %" PetscInt_FMT " SeqAIJKokkos, with %" PetscInt_FMT " nonzeros\n", m, n, nnz));
  for (PetscInt k = 0; k < m; k++) {
    PetscCall(PetscPrintf(PETSC_COMM_SELF, "%" PetscInt_FMT ": ", k));
    for (PetscInt p = i[k]; p < i[k + 1]; p++) PetscCall(PetscPrintf(PETSC_COMM_SELF, "%" PetscInt_FMT "(%.1f), ", j[p], (double)PetscRealPart(a[p])));
    PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}