xref: /petsc/src/mat/impls/h2opus/cuda/math2opus.cu (revision ae1ee55146a7ad071171b861759b85940c7e5c67)

#include <h2opusconf.h>
/* skip compilation of this .cu file if H2OPUS is CPU only while PETSc has GPU support */
#if !defined(__CUDACC__) || defined(H2OPUS_USE_GPU)
  #include <h2opus.h>
  #if defined(H2OPUS_USE_MPI)
    #include <h2opus/distributed/distributed_h2opus_handle.h>
    #include <h2opus/distributed/distributed_geometric_construction.h>
    #include <h2opus/distributed/distributed_hgemv.h>
    #include <h2opus/distributed/distributed_horthog.h>
    #include <h2opus/distributed/distributed_hcompress.h>
  #endif
  #include <h2opus/util/boxentrygen.h>
  #include <petsc/private/matimpl.h>
  #include <petsc/private/vecimpl.h>
  #include <petsc/private/deviceimpl.h> /*I "petscmat.h"   I*/
  #include <petscsf.h>

/* math2opusutils */
PETSC_INTERN PetscErrorCode MatDenseGetH2OpusStridedSF(Mat, PetscSF, PetscSF *);
PETSC_INTERN PetscErrorCode VecSign(Vec, Vec);
PETSC_INTERN PetscErrorCode VecSetDelta(Vec, PetscInt);
PETSC_INTERN PetscErrorCode MatApproximateNorm_Private(Mat, NormType, PetscInt, PetscReal *);

  #define MatH2OpusGetThrustPointer(v) thrust::raw_pointer_cast((v).data())

  /* Use GPU only if H2OPUS is configured for GPU */
  #if defined(PETSC_HAVE_CUDA) && defined(H2OPUS_USE_GPU)
    #define PETSC_H2OPUS_USE_GPU
  #endif
  #if defined(PETSC_H2OPUS_USE_GPU)
    #define MatH2OpusUpdateIfNeeded(A, B) MatBindToCPU(A, (PetscBool)((A)->boundtocpu || (B)))
  #else
    #define MatH2OpusUpdateIfNeeded(A, B) PETSC_SUCCESS
  #endif

// TODO H2OPUS:
// DistributedHMatrix
//   unsymmetric ?
//   transpose for distributed_hgemv?
//   clearData()
// Unify interface for sequential and parallel?
// Reuse geometric construction (almost possible, only the unsymmetric case is explicitly handled)
//
template <class T>
class PetscPointCloud : public H2OpusDataSet<T> {
private:
  int            dimension;
  size_t         num_points;
  std::vector<T> pts;

public:
  PetscPointCloud(int dim, size_t num_pts, const T coords[])
  {
    dim              = dim > 0 ? dim : 1;
    this->dimension  = dim;
    this->num_points = num_pts;

    pts.resize(num_pts * dim);
    if (coords) {
      for (size_t n = 0; n < num_pts; n++)
        for (int i = 0; i < dim; i++) pts[n * dim + i] = coords[n * dim + i];
    } else {
      PetscReal h = 1.0; //num_pts > 1 ? 1./(num_pts - 1) : 0.0;
      for (size_t n = 0; n < num_pts; n++) {
        pts[n * dim] = n * h;
        for (int i = 1; i < dim; i++) pts[n * dim + i] = 0.0;
      }
    }
  }

  PetscPointCloud(const PetscPointCloud<T> &other)
  {
    size_t N         = other.dimension * other.num_points;
    this->dimension  = other.dimension;
    this->num_points = other.num_points;
    this->pts.resize(N);
    for (size_t i = 0; i < N; i++) this->pts[i] = other.pts[i];
  }

  int getDimension() const { return dimension; }

  size_t getDataSetSize() const { return num_points; }

  T getDataPoint(size_t idx, int dim) const
  {
    assert(dim < dimension && idx < num_points);
    return pts[idx * dimension + dim];
  }

  void Print(std::ostream &out = std::cout)
  {
    out << "Dimension: " << dimension << std::endl;
    out << "NumPoints: " << num_points << std::endl;
    for (size_t n = 0; n < num_points; n++) {
      for (int d = 0; d < dimension; d++) out << pts[n * dimension + d] << " ";
      out << std::endl;
    }
  }
};

template <class T>
class PetscFunctionGenerator {
private:
  MatH2OpusKernelFn *k;
  int                dim;
  void              *ctx;

public:
  PetscFunctionGenerator(MatH2OpusKernelFn *k, int dim, PetscCtx ctx)
  {
    this->k   = k;
    this->dim = dim;
    this->ctx = ctx;
  }
  PetscFunctionGenerator(PetscFunctionGenerator &other)
  {
    this->k   = other.k;
    this->dim = other.dim;
    this->ctx = other.ctx;
  }
  T operator()(PetscReal *pt1, PetscReal *pt2) { return (T)((*this->k)(this->dim, pt1, pt2, this->ctx)); }
};

  #include <../src/mat/impls/h2opus/math2opussampler.hpp>

  /* just to not clutter the code */
  #if !defined(H2OPUS_USE_GPU)
typedef HMatrix HMatrix_GPU;
    #if defined(H2OPUS_USE_MPI)
typedef DistributedHMatrix DistributedHMatrix_GPU;
    #endif
  #endif

typedef struct {
  #if defined(H2OPUS_USE_MPI)
  distributedH2OpusHandle_t handle;
  #else
  h2opusHandle_t handle;
  #endif
  /* Sequential and parallel matrices are two different classes at the moment */
  HMatrix *hmatrix;
  #if defined(H2OPUS_USE_MPI)
  DistributedHMatrix *dist_hmatrix;
  #else
  HMatrix *dist_hmatrix; /* just to not clutter the code */
  #endif
  /* May use permutations */
  PetscSF                           sf;
  PetscLayout                       h2opus_rmap, h2opus_cmap;
  IS                                h2opus_indexmap;
  thrust::host_vector<PetscScalar> *xx, *yy;
  PetscInt                          xxs, yys;
  PetscBool                         multsetup;

  /* GPU */
  HMatrix_GPU *hmatrix_gpu;
  #if defined(H2OPUS_USE_MPI)
  DistributedHMatrix_GPU *dist_hmatrix_gpu;
  #else
  HMatrix_GPU *dist_hmatrix_gpu; /* just to not clutter the code */
  #endif
  #if defined(PETSC_H2OPUS_USE_GPU)
  thrust::device_vector<PetscScalar> *xx_gpu, *yy_gpu;
  PetscInt                            xxs_gpu, yys_gpu;
  #endif

  /* construction from matvecs */
  PetscMatrixSampler *sampler;
  PetscBool           nativemult;

  /* Admissibility */
  PetscReal eta;
  PetscInt  leafsize;

  /* for dof reordering */
  PetscPointCloud<PetscReal> *ptcloud;

  /* kernel for generating matrix entries */
  PetscFunctionGenerator<PetscScalar> *kernel;

  /* basis orthogonalized? */
  PetscBool orthogonal;

  /* customization */
  PetscInt  basisord;
  PetscInt  max_rank;
  PetscInt  bs;
  PetscReal rtol;
  PetscInt  norm_max_samples;
  PetscBool check_construction;
  PetscBool hara_verbose;
  PetscBool resize;

  /* keeps track of MatScale values */
  PetscScalar s;
} Mat_H2OPUS;

static PetscErrorCode MatDestroy_H2OPUS(Mat A)
{
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;

  PetscFunctionBegin;
  #if defined(H2OPUS_USE_MPI)
  h2opusDestroyDistributedHandle(a->handle);
  #else
  h2opusDestroyHandle(a->handle);
  #endif
  delete a->dist_hmatrix;
  delete a->hmatrix;
  PetscCall(PetscSFDestroy(&a->sf));
  PetscCall(PetscLayoutDestroy(&a->h2opus_rmap));
  PetscCall(PetscLayoutDestroy(&a->h2opus_cmap));
  PetscCall(ISDestroy(&a->h2opus_indexmap));
  delete a->xx;
  delete a->yy;
  delete a->hmatrix_gpu;
  delete a->dist_hmatrix_gpu;
  #if defined(PETSC_H2OPUS_USE_GPU)
  delete a->xx_gpu;
  delete a->yy_gpu;
  #endif
  delete a->sampler;
  delete a->ptcloud;
  delete a->kernel;
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_h2opus_seqdense_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_h2opus_seqdensecuda_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_h2opus_mpidense_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_h2opus_mpidensecuda_C", NULL));
  PetscCall(PetscObjectChangeTypeName((PetscObject)A, NULL));
  PetscCall(PetscFree(A->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatH2OpusSetNativeMult(Mat A, PetscBool nm)
{
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;
  PetscBool   ish2opus;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidLogicalCollectiveBool(A, nm, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATH2OPUS, &ish2opus));
  if (ish2opus) {
    if (a->h2opus_rmap) { /* need to swap layouts for vector creation */
      if ((!a->nativemult && nm) || (a->nativemult && !nm)) {
        PetscLayout t;
        t              = A->rmap;
        A->rmap        = a->h2opus_rmap;
        a->h2opus_rmap = t;
        t              = A->cmap;
        A->cmap        = a->h2opus_cmap;
        a->h2opus_cmap = t;
      }
    }
    a->nativemult = nm;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode MatH2OpusGetNativeMult(Mat A, PetscBool *nm)
{
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;
  PetscBool   ish2opus;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscAssertPointer(nm, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATH2OPUS, &ish2opus));
  PetscCheck(ish2opus, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for type %s", ((PetscObject)A)->type_name);
  *nm = a->nativemult;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_EXTERN PetscErrorCode MatNorm_H2OPUS(Mat A, NormType normtype, PetscReal *n)
{
  PetscBool   ish2opus;
  PetscInt    nmax = PETSC_DECIDE;
  Mat_H2OPUS *a    = NULL;
  PetscBool   mult = PETSC_FALSE;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATH2OPUS, &ish2opus));
  if (ish2opus) { /* set userdefine number of samples and fastpath for mult (norms are order independent) */
    a = (Mat_H2OPUS *)A->data;

    nmax = a->norm_max_samples;
    mult = a->nativemult;
    PetscCall(MatH2OpusSetNativeMult(A, PETSC_TRUE));
  } else {
    PetscCall(PetscOptionsGetInt(((PetscObject)A)->options, ((PetscObject)A)->prefix, "-mat_approximate_norm_samples", &nmax, NULL));
  }
  PetscCall(MatApproximateNorm_Private(A, normtype, nmax, n));
  if (a) PetscCall(MatH2OpusSetNativeMult(A, mult));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatH2OpusResizeBuffers_Private(Mat A, PetscInt xN, PetscInt yN)
{
  Mat_H2OPUS *h2opus = (Mat_H2OPUS *)A->data;
  PetscInt    n;
  PetscBool   boundtocpu = PETSC_TRUE;

  PetscFunctionBegin;
  #if defined(PETSC_H2OPUS_USE_GPU)
  boundtocpu = A->boundtocpu;
  #endif
  PetscCall(PetscSFGetGraph(h2opus->sf, NULL, &n, NULL, NULL));
  if (boundtocpu) {
    if (h2opus->xxs < xN) {
      h2opus->xx->resize(n * xN);
      h2opus->xxs = xN;
    }
    if (h2opus->yys < yN) {
      h2opus->yy->resize(n * yN);
      h2opus->yys = yN;
    }
  }
  #if defined(PETSC_H2OPUS_USE_GPU)
  if (!boundtocpu) {
    if (h2opus->xxs_gpu < xN) {
      h2opus->xx_gpu->resize(n * xN);
      h2opus->xxs_gpu = xN;
    }
    if (h2opus->yys_gpu < yN) {
      h2opus->yy_gpu->resize(n * yN);
      h2opus->yys_gpu = yN;
    }
  }
  #endif
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultNKernel_H2OPUS(Mat A, PetscBool transA, Mat B, Mat C)
{
  Mat_H2OPUS *h2opus = (Mat_H2OPUS *)A->data;
  #if defined(H2OPUS_USE_MPI)
  h2opusHandle_t handle = h2opus->handle->handle;
  #else
  h2opusHandle_t handle = h2opus->handle;
  #endif
  PetscBool    boundtocpu = PETSC_TRUE;
  PetscScalar *xx, *yy, *uxx, *uyy;
  PetscInt     blda, clda;
  PetscMPIInt  size;
  PetscSF      bsf, csf;
  PetscBool    usesf = (PetscBool)(h2opus->sf && !h2opus->nativemult);

  PetscFunctionBegin;
  HLibProfile::clear();
  #if defined(PETSC_H2OPUS_USE_GPU)
  boundtocpu = A->boundtocpu;
  #endif
  PetscCall(MatDenseGetLDA(B, &blda));
  PetscCall(MatDenseGetLDA(C, &clda));
  if (usesf) {
    PetscInt n;

    PetscCall(MatDenseGetH2OpusStridedSF(B, h2opus->sf, &bsf));
    PetscCall(MatDenseGetH2OpusStridedSF(C, h2opus->sf, &csf));

    PetscCall(MatH2OpusResizeBuffers_Private(A, B->cmap->N, C->cmap->N));
    PetscCall(PetscSFGetGraph(h2opus->sf, NULL, &n, NULL, NULL));
    blda = n;
    clda = n;
  }
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  if (boundtocpu) {
    PetscCall(MatDenseGetArrayRead(B, (const PetscScalar **)&xx));
    PetscCall(MatDenseGetArrayWrite(C, &yy));
    if (usesf) {
      uxx = MatH2OpusGetThrustPointer(*h2opus->xx);
      uyy = MatH2OpusGetThrustPointer(*h2opus->yy);
      PetscCall(PetscSFBcastBegin(bsf, MPIU_SCALAR, xx, uxx, MPI_REPLACE));
      PetscCall(PetscSFBcastEnd(bsf, MPIU_SCALAR, xx, uxx, MPI_REPLACE));
    } else {
      uxx = xx;
      uyy = yy;
    }
    if (size > 1) {
      PetscCheck(h2opus->dist_hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing distributed CPU matrix");
      PetscCheck(!transA || A->symmetric, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MatMultTranspose not yet coded in parallel");
  #if defined(H2OPUS_USE_MPI)
      distributed_hgemv(/* transA ? H2Opus_Trans : H2Opus_NoTrans, */ h2opus->s, *h2opus->dist_hmatrix, uxx, blda, 0.0, uyy, clda, B->cmap->N, h2opus->handle);
  #endif
    } else {
      PetscCheck(h2opus->hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing CPU matrix");
      hgemv(transA ? H2Opus_Trans : H2Opus_NoTrans, h2opus->s, *h2opus->hmatrix, uxx, blda, 0.0, uyy, clda, B->cmap->N, handle);
    }
    PetscCall(MatDenseRestoreArrayRead(B, (const PetscScalar **)&xx));
    if (usesf) {
      PetscCall(PetscSFReduceBegin(csf, MPIU_SCALAR, uyy, yy, MPI_REPLACE));
      PetscCall(PetscSFReduceEnd(csf, MPIU_SCALAR, uyy, yy, MPI_REPLACE));
    }
    PetscCall(MatDenseRestoreArrayWrite(C, &yy));
  #if defined(PETSC_H2OPUS_USE_GPU)
  } else {
    PetscBool ciscuda, biscuda;

    /* If not of type seqdensecuda, convert on the fly (i.e. allocate GPU memory) */
    PetscCall(PetscObjectTypeCompareAny((PetscObject)B, &biscuda, MATSEQDENSECUDA, MATMPIDENSECUDA, ""));
    if (!biscuda) PetscCall(MatConvert(B, MATDENSECUDA, MAT_INPLACE_MATRIX, &B));
    PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &ciscuda, MATSEQDENSECUDA, MATMPIDENSECUDA, ""));
    if (!ciscuda) {
      C->assembled = PETSC_TRUE;
      PetscCall(MatConvert(C, MATDENSECUDA, MAT_INPLACE_MATRIX, &C));
    }
    PetscCall(MatDenseCUDAGetArrayRead(B, (const PetscScalar **)&xx));
    PetscCall(MatDenseCUDAGetArrayWrite(C, &yy));
    if (usesf) {
      uxx = MatH2OpusGetThrustPointer(*h2opus->xx_gpu);
      uyy = MatH2OpusGetThrustPointer(*h2opus->yy_gpu);
      PetscCall(PetscSFBcastBegin(bsf, MPIU_SCALAR, xx, uxx, MPI_REPLACE));
      PetscCall(PetscSFBcastEnd(bsf, MPIU_SCALAR, xx, uxx, MPI_REPLACE));
    } else {
      uxx = xx;
      uyy = yy;
    }
    PetscCall(PetscLogGpuTimeBegin());
    if (size > 1) {
      PetscCheck(h2opus->dist_hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing distributed GPU matrix");
      PetscCheck(!transA || A->symmetric, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MatMultTranspose not yet coded in parallel");
    #if defined(H2OPUS_USE_MPI)
      distributed_hgemv(/* transA ? H2Opus_Trans : H2Opus_NoTrans, */ h2opus->s, *h2opus->dist_hmatrix_gpu, uxx, blda, 0.0, uyy, clda, B->cmap->N, h2opus->handle);
    #endif
    } else {
      PetscCheck(h2opus->hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing GPU matrix");
      hgemv(transA ? H2Opus_Trans : H2Opus_NoTrans, h2opus->s, *h2opus->hmatrix_gpu, uxx, blda, 0.0, uyy, clda, B->cmap->N, handle);
    }
    PetscCall(PetscLogGpuTimeEnd());
    PetscCall(MatDenseCUDARestoreArrayRead(B, (const PetscScalar **)&xx));
    if (usesf) {
      PetscCall(PetscSFReduceBegin(csf, MPIU_SCALAR, uyy, yy, MPI_REPLACE));
      PetscCall(PetscSFReduceEnd(csf, MPIU_SCALAR, uyy, yy, MPI_REPLACE));
    }
    PetscCall(MatDenseCUDARestoreArrayWrite(C, &yy));
    if (!biscuda) PetscCall(MatConvert(B, MATDENSE, MAT_INPLACE_MATRIX, &B));
    if (!ciscuda) PetscCall(MatConvert(C, MATDENSE, MAT_INPLACE_MATRIX, &C));
  #endif
  }
  { /* log flops */
    double gops, time, perf, dev;
    HLibProfile::getHgemvPerf(gops, time, perf, dev);
  #if defined(PETSC_H2OPUS_USE_GPU)
    if (boundtocpu) {
      PetscCall(PetscLogFlops(1e9 * gops));
    } else {
      PetscCall(PetscLogGpuFlops(1e9 * gops));
    }
  #else
    PetscCall(PetscLogFlops(1e9 * gops));
  #endif
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatProductNumeric_H2OPUS(Mat C)
{
  Mat_Product *product = C->product;

  PetscFunctionBegin;
  MatCheckProduct(C, 1);
  switch (product->type) {
  case MATPRODUCT_AB:
    PetscCall(MatMultNKernel_H2OPUS(product->A, PETSC_FALSE, product->B, C));
    break;
  case MATPRODUCT_AtB:
    PetscCall(MatMultNKernel_H2OPUS(product->A, PETSC_TRUE, product->B, C));
    break;
  default:
    SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type %s is not supported", MatProductTypes[product->type]);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatProductSymbolic_H2OPUS(Mat C)
{
  Mat_Product *product = C->product;
  PetscBool    cisdense;
  Mat          A, B;

  PetscFunctionBegin;
  MatCheckProduct(C, 1);
  A = product->A;
  B = product->B;
  switch (product->type) {
  case MATPRODUCT_AB:
    PetscCall(MatSetSizes(C, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
    PetscCall(MatSetBlockSizesFromMats(C, product->A, product->B));
    PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATMPIDENSE, MATSEQDENSECUDA, MATMPIDENSECUDA, ""));
    if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)product->B)->type_name));
    PetscCall(MatSetUp(C));
    break;
  case MATPRODUCT_AtB:
    PetscCall(MatSetSizes(C, A->cmap->n, B->cmap->n, A->cmap->N, B->cmap->N));
    PetscCall(MatSetBlockSizesFromMats(C, product->A, product->B));
    PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATMPIDENSE, MATSEQDENSECUDA, MATMPIDENSECUDA, ""));
    if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)product->B)->type_name));
    PetscCall(MatSetUp(C));
    break;
  default:
    SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type %s is not supported", MatProductTypes[product->type]);
  }
  C->ops->productsymbolic = NULL;
  C->ops->productnumeric  = MatProductNumeric_H2OPUS;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatProductSetFromOptions_H2OPUS(Mat C)
{
  PetscFunctionBegin;
  MatCheckProduct(C, 1);
  if (C->product->type == MATPRODUCT_AB || C->product->type == MATPRODUCT_AtB) C->ops->productsymbolic = MatProductSymbolic_H2OPUS;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultKernel_H2OPUS(Mat A, Vec x, PetscScalar sy, Vec y, PetscBool trans)
{
  Mat_H2OPUS *h2opus = (Mat_H2OPUS *)A->data;
  #if defined(H2OPUS_USE_MPI)
  h2opusHandle_t handle = h2opus->handle->handle;
  #else
  h2opusHandle_t handle = h2opus->handle;
  #endif
  PetscBool    boundtocpu = PETSC_TRUE;
  PetscInt     n;
  PetscScalar *xx, *yy, *uxx, *uyy;
  PetscMPIInt  size;
  PetscBool    usesf = (PetscBool)(h2opus->sf && !h2opus->nativemult);

  PetscFunctionBegin;
  HLibProfile::clear();
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  #if defined(PETSC_H2OPUS_USE_GPU)
  boundtocpu = A->boundtocpu;
  #endif
  if (usesf) PetscCall(PetscSFGetGraph(h2opus->sf, NULL, &n, NULL, NULL));
  else n = A->rmap->n;
  if (boundtocpu) {
    PetscCall(VecGetArrayRead(x, (const PetscScalar **)&xx));
    if (sy == 0.0) {
      PetscCall(VecGetArrayWrite(y, &yy));
    } else {
      PetscCall(VecGetArray(y, &yy));
    }
    if (usesf) {
      uxx = MatH2OpusGetThrustPointer(*h2opus->xx);
      uyy = MatH2OpusGetThrustPointer(*h2opus->yy);

      PetscCall(PetscSFBcastBegin(h2opus->sf, MPIU_SCALAR, xx, uxx, MPI_REPLACE));
      PetscCall(PetscSFBcastEnd(h2opus->sf, MPIU_SCALAR, xx, uxx, MPI_REPLACE));
      if (sy != 0.0) {
        PetscCall(PetscSFBcastBegin(h2opus->sf, MPIU_SCALAR, yy, uyy, MPI_REPLACE));
        PetscCall(PetscSFBcastEnd(h2opus->sf, MPIU_SCALAR, yy, uyy, MPI_REPLACE));
      }
    } else {
      uxx = xx;
      uyy = yy;
    }
    if (size > 1) {
      PetscCheck(h2opus->dist_hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing distributed CPU matrix");
      PetscCheck(!trans || A->symmetric, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MatMultTranspose not yet coded in parallel");
  #if defined(H2OPUS_USE_MPI)
      distributed_hgemv(/*trans ? H2Opus_Trans : H2Opus_NoTrans, */ h2opus->s, *h2opus->dist_hmatrix, uxx, n, sy, uyy, n, 1, h2opus->handle);
  #endif
    } else {
      PetscCheck(h2opus->hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing CPU matrix");
      hgemv(trans ? H2Opus_Trans : H2Opus_NoTrans, h2opus->s, *h2opus->hmatrix, uxx, n, sy, uyy, n, 1, handle);
    }
    PetscCall(VecRestoreArrayRead(x, (const PetscScalar **)&xx));
    if (usesf) {
      PetscCall(PetscSFReduceBegin(h2opus->sf, MPIU_SCALAR, uyy, yy, MPI_REPLACE));
      PetscCall(PetscSFReduceEnd(h2opus->sf, MPIU_SCALAR, uyy, yy, MPI_REPLACE));
    }
    if (sy == 0.0) {
      PetscCall(VecRestoreArrayWrite(y, &yy));
    } else {
      PetscCall(VecRestoreArray(y, &yy));
    }
  #if defined(PETSC_H2OPUS_USE_GPU)
  } else {
    PetscCall(VecCUDAGetArrayRead(x, (const PetscScalar **)&xx));
    if (sy == 0.0) {
      PetscCall(VecCUDAGetArrayWrite(y, &yy));
    } else {
      PetscCall(VecCUDAGetArray(y, &yy));
    }
    if (usesf) {
      uxx = MatH2OpusGetThrustPointer(*h2opus->xx_gpu);
      uyy = MatH2OpusGetThrustPointer(*h2opus->yy_gpu);

      PetscCall(PetscSFBcastBegin(h2opus->sf, MPIU_SCALAR, xx, uxx, MPI_REPLACE));
      PetscCall(PetscSFBcastEnd(h2opus->sf, MPIU_SCALAR, xx, uxx, MPI_REPLACE));
      if (sy != 0.0) {
        PetscCall(PetscSFBcastBegin(h2opus->sf, MPIU_SCALAR, yy, uyy, MPI_REPLACE));
        PetscCall(PetscSFBcastEnd(h2opus->sf, MPIU_SCALAR, yy, uyy, MPI_REPLACE));
      }
    } else {
      uxx = xx;
      uyy = yy;
    }
    PetscCall(PetscLogGpuTimeBegin());
    if (size > 1) {
      PetscCheck(h2opus->dist_hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing distributed GPU matrix");
      PetscCheck(!trans || A->symmetric, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MatMultTranspose not yet coded in parallel");
    #if defined(H2OPUS_USE_MPI)
      distributed_hgemv(/*trans ? H2Opus_Trans : H2Opus_NoTrans, */ h2opus->s, *h2opus->dist_hmatrix_gpu, uxx, n, sy, uyy, n, 1, h2opus->handle);
    #endif
    } else {
      PetscCheck(h2opus->hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing GPU matrix");
      hgemv(trans ? H2Opus_Trans : H2Opus_NoTrans, h2opus->s, *h2opus->hmatrix_gpu, uxx, n, sy, uyy, n, 1, handle);
    }
    PetscCall(PetscLogGpuTimeEnd());
    PetscCall(VecCUDARestoreArrayRead(x, (const PetscScalar **)&xx));
    if (usesf) {
      PetscCall(PetscSFReduceBegin(h2opus->sf, MPIU_SCALAR, uyy, yy, MPI_REPLACE));
      PetscCall(PetscSFReduceEnd(h2opus->sf, MPIU_SCALAR, uyy, yy, MPI_REPLACE));
    }
    if (sy == 0.0) {
      PetscCall(VecCUDARestoreArrayWrite(y, &yy));
    } else {
      PetscCall(VecCUDARestoreArray(y, &yy));
    }
  #endif
  }
  { /* log flops */
    double gops, time, perf, dev;
    HLibProfile::getHgemvPerf(gops, time, perf, dev);
  #if defined(PETSC_H2OPUS_USE_GPU)
    if (boundtocpu) {
      PetscCall(PetscLogFlops(1e9 * gops));
    } else {
      PetscCall(PetscLogGpuFlops(1e9 * gops));
    }
  #else
    PetscCall(PetscLogFlops(1e9 * gops));
  #endif
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultTranspose_H2OPUS(Mat A, Vec x, Vec y)
{
  PetscBool xiscuda, yiscuda;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompareAny((PetscObject)x, &xiscuda, VECSEQCUDA, VECMPICUDA, ""));
  PetscCall(PetscObjectTypeCompareAny((PetscObject)y, &yiscuda, VECSEQCUDA, VECMPICUDA, ""));
  PetscCall(MatH2OpusUpdateIfNeeded(A, !xiscuda || !yiscuda));
  PetscCall(MatMultKernel_H2OPUS(A, x, 0.0, y, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMult_H2OPUS(Mat A, Vec x, Vec y)
{
  PetscBool xiscuda, yiscuda;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompareAny((PetscObject)x, &xiscuda, VECSEQCUDA, VECMPICUDA, ""));
  PetscCall(PetscObjectTypeCompareAny((PetscObject)y, &yiscuda, VECSEQCUDA, VECMPICUDA, ""));
  PetscCall(MatH2OpusUpdateIfNeeded(A, !xiscuda || !yiscuda));
  PetscCall(MatMultKernel_H2OPUS(A, x, 0.0, y, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultTransposeAdd_H2OPUS(Mat A, Vec x, Vec y, Vec z)
{
  PetscBool xiscuda, ziscuda;

  PetscFunctionBegin;
  PetscCall(VecCopy(y, z));
  PetscCall(PetscObjectTypeCompareAny((PetscObject)x, &xiscuda, VECSEQCUDA, VECMPICUDA, ""));
  PetscCall(PetscObjectTypeCompareAny((PetscObject)z, &ziscuda, VECSEQCUDA, VECMPICUDA, ""));
  PetscCall(MatH2OpusUpdateIfNeeded(A, !xiscuda || !ziscuda));
  PetscCall(MatMultKernel_H2OPUS(A, x, 1.0, z, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultAdd_H2OPUS(Mat A, Vec x, Vec y, Vec z)
{
  PetscBool xiscuda, ziscuda;

  PetscFunctionBegin;
  PetscCall(VecCopy(y, z));
  PetscCall(PetscObjectTypeCompareAny((PetscObject)x, &xiscuda, VECSEQCUDA, VECMPICUDA, ""));
  PetscCall(PetscObjectTypeCompareAny((PetscObject)z, &ziscuda, VECSEQCUDA, VECMPICUDA, ""));
  PetscCall(MatH2OpusUpdateIfNeeded(A, !xiscuda || !ziscuda));
  PetscCall(MatMultKernel_H2OPUS(A, x, 1.0, z, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatScale_H2OPUS(Mat A, PetscScalar s)
{
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;

  PetscFunctionBegin;
  a->s *= s;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetFromOptions_H2OPUS(Mat A, PetscOptionItems PetscOptionsObject)
{
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "H2OPUS options");
  PetscCall(PetscOptionsInt("-mat_h2opus_leafsize", "Leaf size of cluster tree", NULL, a->leafsize, &a->leafsize, NULL));
  PetscCall(PetscOptionsReal("-mat_h2opus_eta", "Admissibility condition tolerance", NULL, a->eta, &a->eta, NULL));
  PetscCall(PetscOptionsInt("-mat_h2opus_order", "Basis order for off-diagonal sampling when constructed from kernel", NULL, a->basisord, &a->basisord, NULL));
  PetscCall(PetscOptionsInt("-mat_h2opus_maxrank", "Maximum rank when constructed from matvecs", NULL, a->max_rank, &a->max_rank, NULL));
  PetscCall(PetscOptionsInt("-mat_h2opus_samples", "Maximum number of samples to be taken concurrently when constructing from matvecs", NULL, a->bs, &a->bs, NULL));
  PetscCall(PetscOptionsInt("-mat_h2opus_normsamples", "Maximum number of samples to be when estimating norms", NULL, a->norm_max_samples, &a->norm_max_samples, NULL));
  PetscCall(PetscOptionsReal("-mat_h2opus_rtol", "Relative tolerance for construction from sampling", NULL, a->rtol, &a->rtol, NULL));
  PetscCall(PetscOptionsBool("-mat_h2opus_check", "Check error when constructing from sampling during MatAssemblyEnd()", NULL, a->check_construction, &a->check_construction, NULL));
  PetscCall(PetscOptionsBool("-mat_h2opus_hara_verbose", "Verbose output from hara construction", NULL, a->hara_verbose, &a->hara_verbose, NULL));
  PetscCall(PetscOptionsBool("-mat_h2opus_resize", "Resize after compression", NULL, a->resize, &a->resize, NULL));
  PetscOptionsHeadEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatH2OpusSetCoords_H2OPUS(Mat, PetscInt, const PetscReal[], PetscBool, MatH2OpusKernelFn *, void *);

static PetscErrorCode MatH2OpusInferCoordinates_Private(Mat A)
{
  Mat_H2OPUS        *a = (Mat_H2OPUS *)A->data;
  Vec                c;
  PetscInt           spacedim;
  const PetscScalar *coords;

  PetscFunctionBegin;
  if (a->ptcloud) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscObjectQuery((PetscObject)A, "__math2opus_coords", (PetscObject *)&c));
  if (!c && a->sampler) {
    Mat S = a->sampler->GetSamplingMat();

    PetscCall(PetscObjectQuery((PetscObject)S, "__math2opus_coords", (PetscObject *)&c));
  }
  if (!c) {
    PetscCall(MatH2OpusSetCoords_H2OPUS(A, -1, NULL, PETSC_FALSE, NULL, NULL));
  } else {
    PetscCall(VecGetArrayRead(c, &coords));
    PetscCall(VecGetBlockSize(c, &spacedim));
    PetscCall(MatH2OpusSetCoords_H2OPUS(A, spacedim, coords, PETSC_FALSE, NULL, NULL));
    PetscCall(VecRestoreArrayRead(c, &coords));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetUpMultiply_H2OPUS(Mat A)
{
  MPI_Comm      comm;
  PetscMPIInt   size;
  Mat_H2OPUS   *a = (Mat_H2OPUS *)A->data;
  PetscInt      n = 0, *idx = NULL;
  int          *iidx = NULL;
  PetscCopyMode own;
  PetscBool     rid;

  PetscFunctionBegin;
  if (a->multsetup) PetscFunctionReturn(PETSC_SUCCESS);
  if (a->sf) { /* MatDuplicate_H2OPUS takes reference to the SF */
    PetscCall(PetscSFGetGraph(a->sf, NULL, &n, NULL, NULL));
  #if defined(PETSC_H2OPUS_USE_GPU)
    a->xx_gpu  = new thrust::device_vector<PetscScalar>(n);
    a->yy_gpu  = new thrust::device_vector<PetscScalar>(n);
    a->xxs_gpu = 1;
    a->yys_gpu = 1;
  #endif
    a->xx  = new thrust::host_vector<PetscScalar>(n);
    a->yy  = new thrust::host_vector<PetscScalar>(n);
    a->xxs = 1;
    a->yys = 1;
  } else {
    IS is;
    PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    PetscCallMPI(MPI_Comm_size(comm, &size));
    if (!a->h2opus_indexmap) {
      if (size > 1) {
        PetscCheck(a->dist_hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing distributed CPU matrix");
  #if defined(H2OPUS_USE_MPI)
        iidx = MatH2OpusGetThrustPointer(a->dist_hmatrix->basis_tree.basis_branch.index_map);
        n    = a->dist_hmatrix->basis_tree.basis_branch.index_map.size();
  #endif
      } else {
        iidx = MatH2OpusGetThrustPointer(a->hmatrix->u_basis_tree.index_map);
        n    = a->hmatrix->u_basis_tree.index_map.size();
      }

      if (PetscDefined(USE_64BIT_INDICES)) {
        PetscInt i;

        own = PETSC_OWN_POINTER;
        PetscCall(PetscMalloc1(n, &idx));
        for (i = 0; i < n; i++) idx[i] = iidx[i];
      } else {
        own = PETSC_COPY_VALUES;
        idx = (PetscInt *)iidx;
      }
      PetscCall(ISCreateGeneral(comm, n, idx, own, &is));
      PetscCall(ISSetPermutation(is));
      PetscCall(ISViewFromOptions(is, (PetscObject)A, "-mat_h2opus_indexmap_view"));
      a->h2opus_indexmap = is;
    }
    PetscCall(ISGetLocalSize(a->h2opus_indexmap, &n));
    PetscCall(ISGetIndices(a->h2opus_indexmap, (const PetscInt **)&idx));
    rid = (PetscBool)(n == A->rmap->n);
    PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &rid, 1, MPI_C_BOOL, MPI_LAND, comm));
    if (rid) PetscCall(ISIdentity(a->h2opus_indexmap, &rid));
    if (!rid) {
      if (size > 1) { /* Parallel distribution may be different, save it here for fast path in MatMult (see MatH2OpusSetNativeMult) */
        PetscCall(PetscLayoutCreate(comm, &a->h2opus_rmap));
        PetscCall(PetscLayoutSetLocalSize(a->h2opus_rmap, n));
        PetscCall(PetscLayoutSetUp(a->h2opus_rmap));
        PetscCall(PetscLayoutReference(a->h2opus_rmap, &a->h2opus_cmap));
      }
      PetscCall(PetscSFCreate(comm, &a->sf));
      PetscCall(PetscSFSetGraphLayout(a->sf, A->rmap, n, NULL, PETSC_OWN_POINTER, idx));
      PetscCall(PetscSFSetUp(a->sf));
      PetscCall(PetscSFViewFromOptions(a->sf, (PetscObject)A, "-mat_h2opus_sf_view"));
  #if defined(PETSC_H2OPUS_USE_GPU)
      a->xx_gpu  = new thrust::device_vector<PetscScalar>(n);
      a->yy_gpu  = new thrust::device_vector<PetscScalar>(n);
      a->xxs_gpu = 1;
      a->yys_gpu = 1;
  #endif
      a->xx  = new thrust::host_vector<PetscScalar>(n);
      a->yy  = new thrust::host_vector<PetscScalar>(n);
      a->xxs = 1;
      a->yys = 1;
    }
    PetscCall(ISRestoreIndices(a->h2opus_indexmap, (const PetscInt **)&idx));
  }
  a->multsetup = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAssemblyEnd_H2OPUS(Mat A, MatAssemblyType assemblytype)
{
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;
  #if defined(H2OPUS_USE_MPI)
  h2opusHandle_t handle = a->handle->handle;
  #else
  h2opusHandle_t handle = a->handle;
  #endif
  PetscBool   kernel       = PETSC_FALSE;
  PetscBool   boundtocpu   = PETSC_TRUE;
  PetscBool   samplingdone = PETSC_FALSE;
  MPI_Comm    comm;
  PetscMPIInt size;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
  PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Different row and column local sizes are not supported");
  PetscCheck(A->rmap->N == A->cmap->N, comm, PETSC_ERR_SUP, "Rectangular matrices are not supported");

  /* XXX */
  a->leafsize = PetscMin(a->leafsize, PetscMin(A->rmap->N, A->cmap->N));

  PetscCallMPI(MPI_Comm_size(comm, &size));
  /* TODO REUSABILITY of geometric construction */
  delete a->hmatrix;
  delete a->dist_hmatrix;
  #if defined(PETSC_H2OPUS_USE_GPU)
  delete a->hmatrix_gpu;
  delete a->dist_hmatrix_gpu;
  #endif
  a->orthogonal = PETSC_FALSE;

  /* TODO: other? */
  H2OpusBoxCenterAdmissibility adm(a->eta);

  PetscCall(PetscLogEventBegin(MAT_H2Opus_Build, A, 0, 0, 0));
  if (size > 1) {
  #if defined(H2OPUS_USE_MPI)
    a->dist_hmatrix = new DistributedHMatrix(A->rmap->n /* ,A->symmetric */);
  #else
    a->dist_hmatrix = NULL;
  #endif
  } else a->hmatrix = new HMatrix(A->rmap->n, A->symmetric == PETSC_BOOL3_TRUE);
  PetscCall(MatH2OpusInferCoordinates_Private(A));
  PetscCheck(a->ptcloud, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing pointcloud");
  if (a->kernel) {
    BoxEntryGen<PetscScalar, H2OPUS_HWTYPE_CPU, PetscFunctionGenerator<PetscScalar>> entry_gen(*a->kernel);
    if (size > 1) {
      PetscCheck(a->dist_hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing distributed CPU matrix");
  #if defined(H2OPUS_USE_MPI)
      buildDistributedHMatrix(*a->dist_hmatrix, a->ptcloud, adm, entry_gen, a->leafsize, a->basisord, a->handle);
  #endif
    } else {
      buildHMatrix(*a->hmatrix, a->ptcloud, adm, entry_gen, a->leafsize, a->basisord);
    }
    kernel = PETSC_TRUE;
  } else {
    PetscCheck(size <= 1, comm, PETSC_ERR_SUP, "Construction from sampling not supported in parallel");
    buildHMatrixStructure(*a->hmatrix, a->ptcloud, a->leafsize, adm);
  }
  PetscCall(MatSetUpMultiply_H2OPUS(A));

  #if defined(PETSC_H2OPUS_USE_GPU)
  boundtocpu = A->boundtocpu;
  if (!boundtocpu) {
    if (size > 1) {
      PetscCheck(a->dist_hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing distributed CPU matrix");
    #if defined(H2OPUS_USE_MPI)
      a->dist_hmatrix_gpu = new DistributedHMatrix_GPU(*a->dist_hmatrix);
    #endif
    } else {
      a->hmatrix_gpu = new HMatrix_GPU(*a->hmatrix);
    }
  }
  #endif
  if (size == 1) {
    if (!kernel && a->sampler && a->sampler->GetSamplingMat()) {
      PetscReal Anorm;
      bool      verbose;

      PetscCall(PetscOptionsGetBool(((PetscObject)A)->options, ((PetscObject)A)->prefix, "-mat_h2opus_hara_verbose", &a->hara_verbose, NULL));
      verbose = a->hara_verbose;
      PetscCall(MatApproximateNorm_Private(a->sampler->GetSamplingMat(), NORM_2, a->norm_max_samples, &Anorm));
      if (a->hara_verbose) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Sampling uses max rank %d, tol %g (%g*%g), %s samples %d\n", a->max_rank, a->rtol * Anorm, a->rtol, Anorm, boundtocpu ? "CPU" : "GPU", a->bs));
      if (a->sf && !a->nativemult) a->sampler->SetIndexMap(a->hmatrix->u_basis_tree.index_map.size(), a->hmatrix->u_basis_tree.index_map.data());
      a->sampler->SetStream(handle->getMainStream());
      if (boundtocpu) {
        a->sampler->SetGPUSampling(false);
        hara(a->sampler, *a->hmatrix, a->max_rank, 10 /* TODO */, a->rtol * Anorm, a->bs, handle, verbose);
  #if defined(PETSC_H2OPUS_USE_GPU)
      } else {
        a->sampler->SetGPUSampling(true);
        hara(a->sampler, *a->hmatrix_gpu, a->max_rank, 10 /* TODO */, a->rtol * Anorm, a->bs, handle, verbose);
  #endif
      }
      samplingdone = PETSC_TRUE;
    }
  }
  #if defined(PETSC_H2OPUS_USE_GPU)
  if (!boundtocpu) {
    delete a->hmatrix;
    delete a->dist_hmatrix;
    a->hmatrix      = NULL;
    a->dist_hmatrix = NULL;
  }
  A->offloadmask = boundtocpu ? PETSC_OFFLOAD_CPU : PETSC_OFFLOAD_GPU;
  #endif
  PetscCall(PetscLogEventEnd(MAT_H2Opus_Build, A, 0, 0, 0));

  if (!a->s) a->s = 1.0;
  A->assembled = PETSC_TRUE;

  if (samplingdone) {
    PetscBool check  = a->check_construction;
    PetscBool checke = PETSC_FALSE;

    PetscCall(PetscOptionsGetBool(((PetscObject)A)->options, ((PetscObject)A)->prefix, "-mat_h2opus_check", &check, NULL));
    PetscCall(PetscOptionsGetBool(((PetscObject)A)->options, ((PetscObject)A)->prefix, "-mat_h2opus_check_explicit", &checke, NULL));
    if (check) {
      Mat               E, Ae;
      PetscReal         n1, ni, n2;
      PetscReal         n1A, niA, n2A;
      PetscErrorCodeFn *normfunc;

      Ae = a->sampler->GetSamplingMat();
      PetscCall(MatConvert(A, MATSHELL, MAT_INITIAL_MATRIX, &E));
      PetscCall(MatShellSetOperation(E, MATOP_NORM, (PetscErrorCodeFn *)MatNorm_H2OPUS));
      PetscCall(MatAXPY(E, -1.0, Ae, DIFFERENT_NONZERO_PATTERN));
      PetscCall(MatNorm(E, NORM_1, &n1));
      PetscCall(MatNorm(E, NORM_INFINITY, &ni));
      PetscCall(MatNorm(E, NORM_2, &n2));
      if (checke) {
        Mat eA, eE, eAe;

        PetscCall(MatComputeOperator(A, MATAIJ, &eA));
        PetscCall(MatComputeOperator(E, MATAIJ, &eE));
        PetscCall(MatComputeOperator(Ae, MATAIJ, &eAe));
        PetscCall(MatFilter(eA, PETSC_SMALL, PETSC_FALSE, PETSC_FALSE));
        PetscCall(MatFilter(eE, PETSC_SMALL, PETSC_FALSE, PETSC_FALSE));
        PetscCall(MatFilter(eAe, PETSC_SMALL, PETSC_FALSE, PETSC_FALSE));
        PetscCall(PetscObjectSetName((PetscObject)eA, "H2Mat"));
        PetscCall(MatView(eA, NULL));
        PetscCall(PetscObjectSetName((PetscObject)eAe, "S"));
        PetscCall(MatView(eAe, NULL));
        PetscCall(PetscObjectSetName((PetscObject)eE, "H2Mat - S"));
        PetscCall(MatView(eE, NULL));
        PetscCall(MatDestroy(&eA));
        PetscCall(MatDestroy(&eE));
        PetscCall(MatDestroy(&eAe));
      }

      PetscCall(MatGetOperation(Ae, MATOP_NORM, &normfunc));
      PetscCall(MatSetOperation(Ae, MATOP_NORM, (PetscErrorCodeFn *)MatNorm_H2OPUS));
      PetscCall(MatNorm(Ae, NORM_1, &n1A));
      PetscCall(MatNorm(Ae, NORM_INFINITY, &niA));
      PetscCall(MatNorm(Ae, NORM_2, &n2A));
      n1A = PetscMax(n1A, PETSC_SMALL);
      n2A = PetscMax(n2A, PETSC_SMALL);
      niA = PetscMax(niA, PETSC_SMALL);
      PetscCall(MatSetOperation(Ae, MATOP_NORM, normfunc));
      PetscCall(PetscPrintf(PetscObjectComm((PetscObject)A), "MATH2OPUS construction errors: NORM_1 %g, NORM_INFINITY %g, NORM_2 %g (%g %g %g)\n", (double)n1, (double)ni, (double)n2, (double)(n1 / n1A), (double)(ni / niA), (double)(n2 / n2A)));
      PetscCall(MatDestroy(&E));
    }
    a->sampler->SetSamplingMat(NULL);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroEntries_H2OPUS(Mat A)
{
  PetscMPIInt size;
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  PetscCheck(size <= 1, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not yet supported");
  a->hmatrix->clearData();
  #if defined(PETSC_H2OPUS_USE_GPU)
  if (a->hmatrix_gpu) a->hmatrix_gpu->clearData();
  #endif
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDuplicate_H2OPUS(Mat B, MatDuplicateOption op, Mat *nA)
{
  Mat         A;
  Mat_H2OPUS *a, *b = (Mat_H2OPUS *)B->data;
  PetscBool   iscpu = PetscDefined(H2OPUS_USE_GPU) ? PETSC_FALSE : PETSC_TRUE;
  MPI_Comm    comm;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)B, &comm));
  PetscCall(MatCreate(comm, &A));
  PetscCall(MatSetSizes(A, B->rmap->n, B->cmap->n, B->rmap->N, B->cmap->N));
  PetscCall(MatSetType(A, MATH2OPUS));
  PetscCall(MatPropagateSymmetryOptions(B, A));
  a = (Mat_H2OPUS *)A->data;

  a->eta              = b->eta;
  a->leafsize         = b->leafsize;
  a->basisord         = b->basisord;
  a->max_rank         = b->max_rank;
  a->bs               = b->bs;
  a->rtol             = b->rtol;
  a->norm_max_samples = b->norm_max_samples;
  if (op == MAT_COPY_VALUES) a->s = b->s;

  a->ptcloud = new PetscPointCloud<PetscReal>(*b->ptcloud);
  if (op == MAT_COPY_VALUES && b->kernel) a->kernel = new PetscFunctionGenerator<PetscScalar>(*b->kernel);

  #if defined(H2OPUS_USE_MPI)
  if (b->dist_hmatrix) a->dist_hmatrix = new DistributedHMatrix(*b->dist_hmatrix);
    #if defined(PETSC_H2OPUS_USE_GPU)
  if (b->dist_hmatrix_gpu) a->dist_hmatrix_gpu = new DistributedHMatrix_GPU(*b->dist_hmatrix_gpu);
    #endif
  #endif
  if (b->hmatrix) {
    a->hmatrix = new HMatrix(*b->hmatrix);
    if (op == MAT_DO_NOT_COPY_VALUES) a->hmatrix->clearData();
  }
  #if defined(PETSC_H2OPUS_USE_GPU)
  if (b->hmatrix_gpu) {
    a->hmatrix_gpu = new HMatrix_GPU(*b->hmatrix_gpu);
    if (op == MAT_DO_NOT_COPY_VALUES) a->hmatrix_gpu->clearData();
  }
  #endif
  if (b->sf) {
    PetscCall(PetscObjectReference((PetscObject)b->sf));
    a->sf = b->sf;
  }
  if (b->h2opus_indexmap) {
    PetscCall(PetscObjectReference((PetscObject)b->h2opus_indexmap));
    a->h2opus_indexmap = b->h2opus_indexmap;
  }

  PetscCall(MatSetUp(A));
  PetscCall(MatSetUpMultiply_H2OPUS(A));
  if (op == MAT_COPY_VALUES) {
    A->assembled  = PETSC_TRUE;
    a->orthogonal = b->orthogonal;
  #if defined(PETSC_H2OPUS_USE_GPU)
    A->offloadmask = B->offloadmask;
  #endif
  }
  #if defined(PETSC_H2OPUS_USE_GPU)
  iscpu = B->boundtocpu;
  #endif
  PetscCall(MatBindToCPU(A, iscpu));

  *nA = A;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatView_H2OPUS(Mat A, PetscViewer view)
{
  Mat_H2OPUS       *h2opus = (Mat_H2OPUS *)A->data;
  PetscBool         isascii, vieweps;
  PetscMPIInt       size;
  PetscViewerFormat format;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)view, PETSCVIEWERASCII, &isascii));
  PetscCall(PetscViewerGetFormat(view, &format));
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  if (isascii) {
    if (format == PETSC_VIEWER_ASCII_MATLAB) {
      if (size == 1) {
        FILE *fp;
        PetscCall(PetscViewerASCIIGetPointer(view, &fp));
        dumpHMatrix(*h2opus->hmatrix, 6, fp);
      }
    } else {
      PetscCall(PetscViewerASCIIPrintf(view, "  H-Matrix constructed from %s\n", h2opus->kernel ? "Kernel" : "Mat"));
      PetscCall(PetscViewerASCIIPrintf(view, "  PointCloud dim %" PetscInt_FMT "\n", h2opus->ptcloud ? h2opus->ptcloud->getDimension() : 0));
      PetscCall(PetscViewerASCIIPrintf(view, "  Admissibility parameters: leaf size %" PetscInt_FMT ", eta %g\n", h2opus->leafsize, (double)h2opus->eta));
      if (!h2opus->kernel) {
        PetscCall(PetscViewerASCIIPrintf(view, "  Sampling parameters: max_rank %" PetscInt_FMT ", samples %" PetscInt_FMT ", tolerance %g\n", h2opus->max_rank, h2opus->bs, (double)h2opus->rtol));
      } else {
        PetscCall(PetscViewerASCIIPrintf(view, "  Off-diagonal blocks approximation order %" PetscInt_FMT "\n", h2opus->basisord));
      }
      PetscCall(PetscViewerASCIIPrintf(view, "  Number of samples for norms %" PetscInt_FMT "\n", h2opus->norm_max_samples));
      if (size == 1) {
        double dense_mem_cpu = h2opus->hmatrix ? h2opus->hmatrix->getDenseMemoryUsage() : 0;
        double low_rank_cpu  = h2opus->hmatrix ? h2opus->hmatrix->getLowRankMemoryUsage() : 0;
  #if defined(PETSC_HAVE_CUDA)
        double dense_mem_gpu = h2opus->hmatrix_gpu ? h2opus->hmatrix_gpu->getDenseMemoryUsage() : 0;
        double low_rank_gpu  = h2opus->hmatrix_gpu ? h2opus->hmatrix_gpu->getLowRankMemoryUsage() : 0;
  #endif
        PetscCall(PetscViewerASCIIPrintf(view, "  Memory consumption GB (CPU): %g (dense) %g (low rank) %g (total)\n", dense_mem_cpu, low_rank_cpu, low_rank_cpu + dense_mem_cpu));
  #if defined(PETSC_HAVE_CUDA)
        PetscCall(PetscViewerASCIIPrintf(view, "  Memory consumption GB (GPU): %g (dense) %g (low rank) %g (total)\n", dense_mem_gpu, low_rank_gpu, low_rank_gpu + dense_mem_gpu));
  #endif
      } else {
  #if defined(PETSC_HAVE_CUDA)
        double      matrix_mem[4] = {0., 0., 0., 0.};
        PetscMPIInt rsize         = 4;
  #else
        double      matrix_mem[2] = {0., 0.};
        PetscMPIInt rsize         = 2;
  #endif
  #if defined(H2OPUS_USE_MPI)
        matrix_mem[0] = h2opus->dist_hmatrix ? h2opus->dist_hmatrix->getLocalDenseMemoryUsage() : 0;
        matrix_mem[1] = h2opus->dist_hmatrix ? h2opus->dist_hmatrix->getLocalLowRankMemoryUsage() : 0;
    #if defined(PETSC_HAVE_CUDA)
        matrix_mem[2] = h2opus->dist_hmatrix_gpu ? h2opus->dist_hmatrix_gpu->getLocalDenseMemoryUsage() : 0;
        matrix_mem[3] = h2opus->dist_hmatrix_gpu ? h2opus->dist_hmatrix_gpu->getLocalLowRankMemoryUsage() : 0;
    #endif
  #endif
        PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, matrix_mem, rsize, MPI_DOUBLE_PRECISION, MPI_SUM, PetscObjectComm((PetscObject)A)));
        PetscCall(PetscViewerASCIIPrintf(view, "  Memory consumption GB (CPU): %g (dense) %g (low rank) %g (total)\n", matrix_mem[0], matrix_mem[1], matrix_mem[0] + matrix_mem[1]));
  #if defined(PETSC_HAVE_CUDA)
        PetscCall(PetscViewerASCIIPrintf(view, "  Memory consumption GB (GPU): %g (dense) %g (low rank) %g (total)\n", matrix_mem[2], matrix_mem[3], matrix_mem[2] + matrix_mem[3]));
  #endif
      }
    }
  }
  vieweps = PETSC_FALSE;
  PetscCall(PetscOptionsGetBool(((PetscObject)A)->options, ((PetscObject)A)->prefix, "-mat_h2opus_vieweps", &vieweps, NULL));
  if (vieweps) {
    char        filename[256];
    const char *name;

    PetscCall(PetscObjectGetName((PetscObject)A, &name));
    PetscCall(PetscSNPrintf(filename, sizeof(filename), "%s_structure.eps", name));
    PetscCall(PetscOptionsGetString(((PetscObject)A)->options, ((PetscObject)A)->prefix, "-mat_h2opus_vieweps_filename", filename, sizeof(filename), NULL));
    outputEps(*h2opus->hmatrix, filename);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatH2OpusSetCoords_H2OPUS(Mat A, PetscInt spacedim, const PetscReal coords[], PetscBool cdist, MatH2OpusKernelFn *kernel, void *kernelctx)
{
  Mat_H2OPUS *h2opus = (Mat_H2OPUS *)A->data;
  PetscReal  *gcoords;
  PetscInt    N;
  MPI_Comm    comm;
  PetscMPIInt size;
  PetscBool   cong;

  PetscFunctionBegin;
  PetscCall(PetscLayoutSetUp(A->rmap));
  PetscCall(PetscLayoutSetUp(A->cmap));
  PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
  PetscCall(MatHasCongruentLayouts(A, &cong));
  PetscCheck(cong, comm, PETSC_ERR_SUP, "Only for square matrices with congruent layouts");
  N = A->rmap->N;
  PetscCallMPI(MPI_Comm_size(comm, &size));
  if (spacedim > 0 && size > 1 && cdist) {
    PetscSF      sf;
    MPI_Datatype dtype;

    PetscCallMPI(MPI_Type_contiguous(spacedim, MPIU_REAL, &dtype));
    PetscCallMPI(MPI_Type_commit(&dtype));

    PetscCall(PetscSFCreate(comm, &sf));
    PetscCall(PetscSFSetGraphWithPattern(sf, A->rmap, PETSCSF_PATTERN_ALLGATHER));
    PetscCall(PetscMalloc1(spacedim * N, &gcoords));
    PetscCall(PetscSFBcastBegin(sf, dtype, coords, gcoords, MPI_REPLACE));
    PetscCall(PetscSFBcastEnd(sf, dtype, coords, gcoords, MPI_REPLACE));
    PetscCall(PetscSFDestroy(&sf));
    PetscCallMPI(MPI_Type_free(&dtype));
  } else gcoords = (PetscReal *)coords;

  delete h2opus->ptcloud;
  delete h2opus->kernel;
  h2opus->ptcloud = new PetscPointCloud<PetscReal>(spacedim, N, gcoords);
  if (kernel) h2opus->kernel = new PetscFunctionGenerator<PetscScalar>(kernel, spacedim, kernelctx);
  if (gcoords != coords) PetscCall(PetscFree(gcoords));
  A->preallocated = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

  #if defined(PETSC_H2OPUS_USE_GPU)
static PetscErrorCode MatBindToCPU_H2OPUS(Mat A, PetscBool flg)
{
  PetscMPIInt size;
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  if (flg && A->offloadmask == PETSC_OFFLOAD_GPU) {
    if (size > 1) {
      PetscCheck(a->dist_hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing GPU matrix");
    #if defined(H2OPUS_USE_MPI)
      if (!a->dist_hmatrix) a->dist_hmatrix = new DistributedHMatrix(*a->dist_hmatrix_gpu);
      else *a->dist_hmatrix = *a->dist_hmatrix_gpu;
    #endif
    } else {
      PetscCheck(a->hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing GPU matrix");
      if (!a->hmatrix) a->hmatrix = new HMatrix(*a->hmatrix_gpu);
      else *a->hmatrix = *a->hmatrix_gpu;
    }
    delete a->hmatrix_gpu;
    delete a->dist_hmatrix_gpu;
    a->hmatrix_gpu      = NULL;
    a->dist_hmatrix_gpu = NULL;
    A->offloadmask      = PETSC_OFFLOAD_CPU;
  } else if (!flg && A->offloadmask == PETSC_OFFLOAD_CPU) {
    if (size > 1) {
      PetscCheck(a->dist_hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing CPU matrix");
    #if defined(H2OPUS_USE_MPI)
      if (!a->dist_hmatrix_gpu) a->dist_hmatrix_gpu = new DistributedHMatrix_GPU(*a->dist_hmatrix);
      else *a->dist_hmatrix_gpu = *a->dist_hmatrix;
    #endif
    } else {
      PetscCheck(a->hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing CPU matrix");
      if (!a->hmatrix_gpu) a->hmatrix_gpu = new HMatrix_GPU(*a->hmatrix);
      else *a->hmatrix_gpu = *a->hmatrix;
    }
    delete a->hmatrix;
    delete a->dist_hmatrix;
    a->hmatrix      = NULL;
    a->dist_hmatrix = NULL;
    A->offloadmask  = PETSC_OFFLOAD_GPU;
  }
  PetscCall(PetscFree(A->defaultvectype));
  if (!flg) {
    PetscCall(PetscStrallocpy(VECCUDA, &A->defaultvectype));
  } else {
    PetscCall(PetscStrallocpy(VECSTANDARD, &A->defaultvectype));
  }
  A->boundtocpu = flg;
  PetscFunctionReturn(PETSC_SUCCESS);
}
  #endif

/*MC
   MATH2OPUS = "h2opus" - A matrix type for hierarchical matrices using the H2Opus package {cite}`zampinibouakaramturkiyyahkniokeyes2022`.

   Options Database Key:
.  -mat_type h2opus - matrix type to "h2opus"

   Level: beginner

   Notes:
   H2Opus implements hierarchical matrices in the $H^2$ flavour. It supports CPU or NVIDIA GPUs.

   For CPU only builds, use `./configure --download-h2opus --download-thrust` to install PETSc to use H2Opus.
   In order to run on NVIDIA GPUs, use `./configure --download-h2opus --download-magma --download-kblas`.

.seealso: [](ch_matrices), `Mat`, `MATH2OPUS`, `MATHTOOL`, `MATDENSE`, `MatCreateH2OpusFromKernel()`, `MatCreateH2OpusFromMat()`
M*/
PETSC_EXTERN PetscErrorCode MatCreate_H2OPUS(Mat A)
{
  Mat_H2OPUS *a;
  PetscMPIInt size;

  PetscFunctionBegin;
  #if defined(PETSC_H2OPUS_USE_GPU)
  PetscCall(PetscDeviceInitialize(PETSC_DEVICE_CUDA));
  #endif
  PetscCall(PetscNew(&a));
  A->data = (void *)a;

  a->eta              = 0.9;
  a->leafsize         = 32;
  a->basisord         = 4;
  a->max_rank         = 64;
  a->bs               = 32;
  a->rtol             = 1.e-4;
  a->s                = 1.0;
  a->norm_max_samples = 10;
  a->resize           = PETSC_TRUE; /* reallocate after compression */
  #if defined(H2OPUS_USE_MPI)
  h2opusCreateDistributedHandleComm(&a->handle, PetscObjectComm((PetscObject)A));
  #else
  h2opusCreateHandle(&a->handle);
  #endif
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATH2OPUS));
  PetscCall(PetscMemzero(A->ops, sizeof(struct _MatOps)));

  A->ops->destroy          = MatDestroy_H2OPUS;
  A->ops->view             = MatView_H2OPUS;
  A->ops->assemblyend      = MatAssemblyEnd_H2OPUS;
  A->ops->mult             = MatMult_H2OPUS;
  A->ops->multtranspose    = MatMultTranspose_H2OPUS;
  A->ops->multadd          = MatMultAdd_H2OPUS;
  A->ops->multtransposeadd = MatMultTransposeAdd_H2OPUS;
  A->ops->scale            = MatScale_H2OPUS;
  A->ops->duplicate        = MatDuplicate_H2OPUS;
  A->ops->setfromoptions   = MatSetFromOptions_H2OPUS;
  A->ops->norm             = MatNorm_H2OPUS;
  A->ops->zeroentries      = MatZeroEntries_H2OPUS;
  #if defined(PETSC_H2OPUS_USE_GPU)
  A->ops->bindtocpu = MatBindToCPU_H2OPUS;
  #endif

  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_h2opus_seqdense_C", MatProductSetFromOptions_H2OPUS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_h2opus_seqdensecuda_C", MatProductSetFromOptions_H2OPUS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_h2opus_mpidense_C", MatProductSetFromOptions_H2OPUS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_h2opus_mpidensecuda_C", MatProductSetFromOptions_H2OPUS));
  #if defined(PETSC_H2OPUS_USE_GPU)
  PetscCall(PetscFree(A->defaultvectype));
  PetscCall(PetscStrallocpy(VECCUDA, &A->defaultvectype));
  #endif
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatH2OpusOrthogonalize - Orthogonalize the basis tree of a hierarchical matrix.

  Input Parameter:
. A - the matrix

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MATH2OPUS`, `MatCreateH2OpusFromMat()`, `MatCreateH2OpusFromKernel()`, `MatH2OpusCompress()`
@*/
PetscErrorCode MatH2OpusOrthogonalize(Mat A)
{
  PetscBool   ish2opus;
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;
  PetscMPIInt size;
  PetscBool   boundtocpu = PETSC_TRUE;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidType(A, 1);
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATH2OPUS, &ish2opus));
  if (!ish2opus) PetscFunctionReturn(PETSC_SUCCESS);
  if (a->orthogonal) PetscFunctionReturn(PETSC_SUCCESS);
  HLibProfile::clear();
  PetscCall(PetscLogEventBegin(MAT_H2Opus_Orthog, A, 0, 0, 0));
  #if defined(PETSC_H2OPUS_USE_GPU)
  boundtocpu = A->boundtocpu;
  #endif
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  if (size > 1) {
    if (boundtocpu) {
      PetscCheck(a->dist_hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing CPU matrix");
  #if defined(H2OPUS_USE_MPI)
      distributed_horthog(*a->dist_hmatrix, a->handle);
  #endif
  #if defined(PETSC_H2OPUS_USE_GPU)
      A->offloadmask = PETSC_OFFLOAD_CPU;
    } else {
      PetscCheck(a->dist_hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing GPU matrix");
      PetscCall(PetscLogGpuTimeBegin());
    #if defined(H2OPUS_USE_MPI)
      distributed_horthog(*a->dist_hmatrix_gpu, a->handle);
    #endif
      PetscCall(PetscLogGpuTimeEnd());
  #endif
    }
  } else {
  #if defined(H2OPUS_USE_MPI)
    h2opusHandle_t handle = a->handle->handle;
  #else
    h2opusHandle_t handle = a->handle;
  #endif
    if (boundtocpu) {
      PetscCheck(a->hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing CPU matrix");
      horthog(*a->hmatrix, handle);
  #if defined(PETSC_H2OPUS_USE_GPU)
      A->offloadmask = PETSC_OFFLOAD_CPU;
    } else {
      PetscCheck(a->hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing GPU matrix");
      PetscCall(PetscLogGpuTimeBegin());
      horthog(*a->hmatrix_gpu, handle);
      PetscCall(PetscLogGpuTimeEnd());
  #endif
    }
  }
  a->orthogonal = PETSC_TRUE;
  { /* log flops */
    double gops, time, perf, dev;
    HLibProfile::getHorthogPerf(gops, time, perf, dev);
  #if defined(PETSC_H2OPUS_USE_GPU)
    if (boundtocpu) {
      PetscCall(PetscLogFlops(1e9 * gops));
    } else {
      PetscCall(PetscLogGpuFlops(1e9 * gops));
    }
  #else
    PetscCall(PetscLogFlops(1e9 * gops));
  #endif
  }
  PetscCall(PetscLogEventEnd(MAT_H2Opus_Orthog, A, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatH2OpusCompress - Compress a hierarchical matrix.

  Input Parameters:
+ A   - the matrix
- tol - the absolute truncation threshold

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MATH2OPUS`, `MatCreateH2OpusFromMat()`, `MatCreateH2OpusFromKernel()`, `MatH2OpusOrthogonalize()`
@*/
PetscErrorCode MatH2OpusCompress(Mat A, PetscReal tol)
{
  PetscBool   ish2opus;
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;
  PetscMPIInt size;
  PetscBool   boundtocpu = PETSC_TRUE;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidType(A, 1);
  PetscValidLogicalCollectiveReal(A, tol, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATH2OPUS, &ish2opus));
  if (!ish2opus || tol <= 0.0) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(MatH2OpusOrthogonalize(A));
  HLibProfile::clear();
  PetscCall(PetscLogEventBegin(MAT_H2Opus_Compress, A, 0, 0, 0));
  #if defined(PETSC_H2OPUS_USE_GPU)
  boundtocpu = A->boundtocpu;
  #endif
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
  if (size > 1) {
    if (boundtocpu) {
      PetscCheck(a->dist_hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing CPU matrix");
  #if defined(H2OPUS_USE_MPI)
      distributed_hcompress(*a->dist_hmatrix, tol, a->handle);
      if (a->resize) {
        DistributedHMatrix *dist_hmatrix = new DistributedHMatrix(*a->dist_hmatrix);
        delete a->dist_hmatrix;
        a->dist_hmatrix = dist_hmatrix;
      }
  #endif
  #if defined(PETSC_H2OPUS_USE_GPU)
      A->offloadmask = PETSC_OFFLOAD_CPU;
    } else {
      PetscCheck(a->dist_hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing GPU matrix");
      PetscCall(PetscLogGpuTimeBegin());
    #if defined(H2OPUS_USE_MPI)
      distributed_hcompress(*a->dist_hmatrix_gpu, tol, a->handle);

      if (a->resize) {
        DistributedHMatrix_GPU *dist_hmatrix_gpu = new DistributedHMatrix_GPU(*a->dist_hmatrix_gpu);
        delete a->dist_hmatrix_gpu;
        a->dist_hmatrix_gpu = dist_hmatrix_gpu;
      }
    #endif
      PetscCall(PetscLogGpuTimeEnd());
  #endif
    }
  } else {
  #if defined(H2OPUS_USE_MPI)
    h2opusHandle_t handle = a->handle->handle;
  #else
    h2opusHandle_t handle = a->handle;
  #endif
    if (boundtocpu) {
      PetscCheck(a->hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing CPU matrix");
      hcompress(*a->hmatrix, tol, handle);

      if (a->resize) {
        HMatrix *hmatrix = new HMatrix(*a->hmatrix);
        delete a->hmatrix;
        a->hmatrix = hmatrix;
      }
  #if defined(PETSC_H2OPUS_USE_GPU)
      A->offloadmask = PETSC_OFFLOAD_CPU;
    } else {
      PetscCheck(a->hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing GPU matrix");
      PetscCall(PetscLogGpuTimeBegin());
      hcompress(*a->hmatrix_gpu, tol, handle);
      PetscCall(PetscLogGpuTimeEnd());

      if (a->resize) {
        HMatrix_GPU *hmatrix_gpu = new HMatrix_GPU(*a->hmatrix_gpu);
        delete a->hmatrix_gpu;
        a->hmatrix_gpu = hmatrix_gpu;
      }
  #endif
    }
  }
  { /* log flops */
    double gops, time, perf, dev;
    HLibProfile::getHcompressPerf(gops, time, perf, dev);
  #if defined(PETSC_H2OPUS_USE_GPU)
    if (boundtocpu) {
      PetscCall(PetscLogFlops(1e9 * gops));
    } else {
      PetscCall(PetscLogGpuFlops(1e9 * gops));
    }
  #else
    PetscCall(PetscLogFlops(1e9 * gops));
  #endif
  }
  PetscCall(PetscLogEventEnd(MAT_H2Opus_Compress, A, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatH2OpusSetSamplingMat - Set a matrix to be sampled from matrix-vector products on another matrix to construct a hierarchical matrix.

  Input Parameters:
+ A   - the hierarchical matrix
. B   - the matrix to be sampled
. bs  - maximum number of samples to be taken concurrently
- tol - relative tolerance for construction

  Level: intermediate

  Notes:
  You need to call `MatAssemblyBegin()` and `MatAssemblyEnd()` to update the hierarchical matrix.

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MATH2OPUS`, `MatCreateH2OpusFromMat()`, `MatCreateH2OpusFromKernel()`, `MatH2OpusCompress()`, `MatH2OpusOrthogonalize()`
@*/
PetscErrorCode MatH2OpusSetSamplingMat(Mat A, Mat B, PetscInt bs, PetscReal tol)
{
  PetscBool ish2opus;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidType(A, 1);
  if (B) PetscValidHeaderSpecific(B, MAT_CLASSID, 2);
  PetscValidLogicalCollectiveInt(A, bs, 3);
  PetscValidLogicalCollectiveReal(A, tol, 4);
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATH2OPUS, &ish2opus));
  if (ish2opus) {
    Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;

    if (!a->sampler) a->sampler = new PetscMatrixSampler();
    a->sampler->SetSamplingMat(B);
    if (bs > 0) a->bs = bs;
    if (tol > 0.) a->rtol = tol;
    delete a->kernel;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatCreateH2OpusFromKernel - Creates a `MATH2OPUS` from a user-supplied kernel.

  Input Parameters:
+ comm      - MPI communicator
. m         - number of local rows (or `PETSC_DECIDE` to have calculated if `M` is given)
. n         - number of local columns (or `PETSC_DECIDE` to have calculated if `N` is given)
. M         - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
. N         - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
. spacedim  - dimension of the space coordinates
. coords    - coordinates of the points
. cdist     - whether or not coordinates are distributed
. kernel    - computational kernel (or `NULL`)
. kernelctx - kernel context
. eta       - admissibility condition tolerance
. leafsize  - leaf size in cluster tree
- basisord  - approximation order for Chebychev interpolation of low-rank blocks

  Output Parameter:
. nA - matrix

  Options Database Keys:
+ -mat_h2opus_leafsize <`PetscInt`>    - Leaf size of cluster tree
. -mat_h2opus_eta <`PetscReal`>        - Admissibility condition tolerance
. -mat_h2opus_order <`PetscInt`>       - Chebychev approximation order
- -mat_h2opus_normsamples <`PetscInt`> - Maximum number of samples to be used when estimating norms

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MATH2OPUS`, `MatCreateH2OpusFromMat()`
@*/
PetscErrorCode MatCreateH2OpusFromKernel(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, PetscInt spacedim, const PetscReal coords[], PetscBool cdist, MatH2OpusKernelFn *kernel, void *kernelctx, PetscReal eta, PetscInt leafsize, PetscInt basisord, Mat *nA)
{
  Mat         A;
  Mat_H2OPUS *h2opus;
  PetscBool   iscpu = PetscDefined(H2OPUS_USE_GPU) ? PETSC_FALSE : PETSC_TRUE;

  PetscFunctionBegin;
  PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Different row and column local sizes are not supported");
  PetscCall(MatCreate(comm, &A));
  PetscCall(MatSetSizes(A, m, n, M, N));
  PetscCheck(M == N, comm, PETSC_ERR_SUP, "Rectangular matrices are not supported");
  PetscCall(MatSetType(A, MATH2OPUS));
  PetscCall(MatBindToCPU(A, iscpu));
  PetscCall(MatH2OpusSetCoords_H2OPUS(A, spacedim, coords, cdist, kernel, kernelctx));

  h2opus = (Mat_H2OPUS *)A->data;
  if (eta > 0.) h2opus->eta = eta;
  if (leafsize > 0) h2opus->leafsize = leafsize;
  if (basisord > 0) h2opus->basisord = basisord;

  *nA = A;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatCreateH2OpusFromMat - Creates a `MATH2OPUS` sampling from a user-supplied operator.

  Input Parameters:
+ B        - the matrix to be sampled
. spacedim - dimension of the space coordinates
. coords   - coordinates of the points
. cdist    - whether or not coordinates are distributed
. eta      - admissibility condition tolerance
. leafsize - leaf size in cluster tree
. maxrank  - maximum rank allowed
. bs       - maximum number of samples to be taken concurrently
- rtol     - relative tolerance for construction

  Output Parameter:
. nA - matrix

  Options Database Keys:
+ -mat_h2opus_leafsize <`PetscInt`>      - Leaf size of cluster tree
. -mat_h2opus_eta <`PetscReal`>          - Admissibility condition tolerance
. -mat_h2opus_maxrank <`PetscInt`>       - Maximum rank when constructed from matvecs
. -mat_h2opus_samples <`PetscInt`>       - Maximum number of samples to be taken concurrently when constructing from matvecs
. -mat_h2opus_rtol <`PetscReal`>         - Relative tolerance for construction from sampling
. -mat_h2opus_check <`PetscBool`>        - Check error when constructing from sampling during MatAssemblyEnd()
. -mat_h2opus_hara_verbose <`PetscBool`> - Verbose output from hara construction
- -mat_h2opus_normsamples <`PetscInt`>   - Maximum number of samples to be when estimating norms

  Level: intermediate

  Note:
  Not available in parallel

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MATH2OPUS`, `MatCreateH2OpusFromKernel()`
@*/
PetscErrorCode MatCreateH2OpusFromMat(Mat B, PetscInt spacedim, const PetscReal coords[], PetscBool cdist, PetscReal eta, PetscInt leafsize, PetscInt maxrank, PetscInt bs, PetscReal rtol, Mat *nA)
{
  Mat         A;
  Mat_H2OPUS *h2opus;
  MPI_Comm    comm;
  PetscBool   boundtocpu = PETSC_TRUE;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
  PetscValidLogicalCollectiveInt(B, spacedim, 2);
  PetscValidLogicalCollectiveBool(B, cdist, 4);
  PetscValidLogicalCollectiveReal(B, eta, 5);
  PetscValidLogicalCollectiveInt(B, leafsize, 6);
  PetscValidLogicalCollectiveInt(B, maxrank, 7);
  PetscValidLogicalCollectiveInt(B, bs, 8);
  PetscValidLogicalCollectiveReal(B, rtol, 9);
  PetscAssertPointer(nA, 10);
  PetscCall(PetscObjectGetComm((PetscObject)B, &comm));
  PetscCheck(B->rmap->n == B->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Different row and column local sizes are not supported");
  PetscCheck(B->rmap->N == B->cmap->N, comm, PETSC_ERR_SUP, "Rectangular matrices are not supported");
  PetscCall(MatCreate(comm, &A));
  PetscCall(MatSetSizes(A, B->rmap->n, B->cmap->n, B->rmap->N, B->cmap->N));
  #if defined(PETSC_H2OPUS_USE_GPU)
  {
    VecType   vtype;
    PetscBool isstd, iscuda, iskok;

    PetscCall(MatGetVecType(B, &vtype));
    PetscCall(PetscStrcmpAny(vtype, &isstd, VECSTANDARD, VECSEQ, VECMPI, ""));
    PetscCall(PetscStrcmpAny(vtype, &iscuda, VECCUDA, VECSEQCUDA, VECMPICUDA, ""));
    PetscCall(PetscStrcmpAny(vtype, &iskok, VECKOKKOS, VECSEQKOKKOS, VECMPIKOKKOS, ""));
    PetscCheck(isstd || iscuda || iskok, comm, PETSC_ERR_SUP, "Not for type %s", vtype);
    if (iscuda && !B->boundtocpu) boundtocpu = PETSC_FALSE;
    if (iskok && PetscDefined(HAVE_MACRO_KOKKOS_ENABLE_CUDA)) boundtocpu = PETSC_FALSE;
  }
  #endif
  PetscCall(MatSetType(A, MATH2OPUS));
  PetscCall(MatBindToCPU(A, boundtocpu));
  if (spacedim) PetscCall(MatH2OpusSetCoords_H2OPUS(A, spacedim, coords, cdist, NULL, NULL));
  PetscCall(MatPropagateSymmetryOptions(B, A));
  /* PetscCheck(A->symmetric,comm,PETSC_ERR_SUP,"Unsymmetric sampling does not work"); */

  h2opus          = (Mat_H2OPUS *)A->data;
  h2opus->sampler = new PetscMatrixSampler(B);
  if (eta > 0.) h2opus->eta = eta;
  if (leafsize > 0) h2opus->leafsize = leafsize;
  if (maxrank > 0) h2opus->max_rank = maxrank;
  if (bs > 0) h2opus->bs = bs;
  if (rtol > 0.) h2opus->rtol = rtol;
  *nA             = A;
  A->preallocated = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatH2OpusGetIndexMap - Access reordering index set.

  Input Parameter:
. A - the matrix

  Output Parameter:
. indexmap - the index set for the reordering

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MATH2OPUS`, `MatCreateH2OpusFromMat()`, `MatCreateH2OpusFromKernel()`
@*/
PetscErrorCode MatH2OpusGetIndexMap(Mat A, IS *indexmap)
{
  PetscBool   ish2opus;
  Mat_H2OPUS *a = (Mat_H2OPUS *)A->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidType(A, 1);
  PetscAssertPointer(indexmap, 2);
  PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATH2OPUS, &ish2opus));
  PetscCheck(ish2opus, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for type %s", ((PetscObject)A)->type_name);
  *indexmap = a->h2opus_indexmap;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatH2OpusMapVec - Maps a vector between PETSc and H2Opus ordering

  Input Parameters:
+ A             - the matrix
. nativetopetsc - if true, maps from H2Opus ordering to PETSc ordering. If false, applies the reverse map
- in            - the vector to be mapped

  Output Parameter:
. out - the newly created mapped vector

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MATH2OPUS`, `MatCreateH2OpusFromMat()`, `MatCreateH2OpusFromKernel()`
@*/
PetscErrorCode MatH2OpusMapVec(Mat A, PetscBool nativetopetsc, Vec in, Vec *out)
{
  PetscBool    ish2opus;
  Mat_H2OPUS  *a = (Mat_H2OPUS *)A->data;
  PetscScalar *xin, *xout;
  PetscBool    nm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidType(A, 1);
  PetscValidLogicalCollectiveBool(A, nativetopetsc, 2);
  PetscValidHeaderSpecific(in, VEC_CLASSID, 3);
  PetscAssertPointer(out, 4);
  PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATH2OPUS, &ish2opus));
  PetscCheck(ish2opus, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for type %s", ((PetscObject)A)->type_name);
  nm = a->nativemult;
  PetscCall(MatH2OpusSetNativeMult(A, (PetscBool)!nativetopetsc));
  PetscCall(MatCreateVecs(A, out, NULL));
  PetscCall(MatH2OpusSetNativeMult(A, nm));
  if (!a->sf) { /* same ordering */
    PetscCall(VecCopy(in, *out));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(VecGetArrayRead(in, (const PetscScalar **)&xin));
  PetscCall(VecGetArrayWrite(*out, &xout));
  if (nativetopetsc) {
    PetscCall(PetscSFReduceBegin(a->sf, MPIU_SCALAR, xin, xout, MPI_REPLACE));
    PetscCall(PetscSFReduceEnd(a->sf, MPIU_SCALAR, xin, xout, MPI_REPLACE));
  } else {
    PetscCall(PetscSFBcastBegin(a->sf, MPIU_SCALAR, xin, xout, MPI_REPLACE));
    PetscCall(PetscSFBcastEnd(a->sf, MPIU_SCALAR, xin, xout, MPI_REPLACE));
  }
  PetscCall(VecRestoreArrayRead(in, (const PetscScalar **)&xin));
  PetscCall(VecRestoreArrayWrite(*out, &xout));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatH2OpusLowRankUpdate - Perform a low-rank update of the form $ A = A + s * U * V^T $

  Input Parameters:
+ A - the hierarchical `MATH2OPUS` matrix
. s - the scaling factor
. U - the dense low-rank update matrix
- V - (optional) the dense low-rank update matrix (if `NULL`, then `V` = `U` is assumed)

  Note:
  The `U` and `V` matrices must be in `MATDENSE` dense format

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MATH2OPUS`, `MatCreateH2OpusFromMat()`, `MatCreateH2OpusFromKernel()`, `MatH2OpusCompress()`, `MatH2OpusOrthogonalize()`, `MATDENSE`
@*/
PetscErrorCode MatH2OpusLowRankUpdate(Mat A, Mat U, Mat V, PetscScalar s)
{
  PetscBool flg;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidType(A, 1);
  PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
  PetscValidHeaderSpecific(U, MAT_CLASSID, 2);
  PetscCheckSameComm(A, 1, U, 2);
  if (V) {
    PetscValidHeaderSpecific(V, MAT_CLASSID, 3);
    PetscCheckSameComm(A, 1, V, 3);
  }
  PetscValidLogicalCollectiveScalar(A, s, 4);

  if (!V) V = U;
  PetscCheck(U->cmap->N == V->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Non matching rank update %" PetscInt_FMT " != %" PetscInt_FMT, U->cmap->N, V->cmap->N);
  if (!U->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscLayoutCompare(U->rmap, A->rmap, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "A and U must have the same row layout");
  PetscCall(PetscLayoutCompare(V->rmap, A->cmap, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "A column layout must match V row column layout");
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATH2OPUS, &flg));
  if (flg) {
    Mat_H2OPUS        *a = (Mat_H2OPUS *)A->data;
    const PetscScalar *u, *v, *uu, *vv;
    PetscInt           ldu, ldv;
    PetscMPIInt        size;
  #if defined(H2OPUS_USE_MPI)
    h2opusHandle_t handle = a->handle->handle;
  #else
    h2opusHandle_t handle = a->handle;
  #endif
    PetscBool usesf = (PetscBool)(a->sf && !a->nativemult);
    PetscSF   usf, vsf;

    PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    PetscCheck(size <= 1, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not yet implemented in parallel");
    PetscCall(PetscLogEventBegin(MAT_H2Opus_LR, A, 0, 0, 0));
    PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)U, &flg, MATSEQDENSE, MATMPIDENSE, ""));
    PetscCheck(flg, PetscObjectComm((PetscObject)U), PETSC_ERR_SUP, "Not for U of type %s", ((PetscObject)U)->type_name);
    PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)V, &flg, MATSEQDENSE, MATMPIDENSE, ""));
    PetscCheck(flg, PetscObjectComm((PetscObject)V), PETSC_ERR_SUP, "Not for V of type %s", ((PetscObject)V)->type_name);
    PetscCall(MatDenseGetLDA(U, &ldu));
    PetscCall(MatDenseGetLDA(V, &ldv));
    PetscCall(MatBoundToCPU(A, &flg));
    if (usesf) {
      PetscInt n;

      PetscCall(MatDenseGetH2OpusStridedSF(U, a->sf, &usf));
      PetscCall(MatDenseGetH2OpusStridedSF(V, a->sf, &vsf));
      PetscCall(MatH2OpusResizeBuffers_Private(A, U->cmap->N, V->cmap->N));
      PetscCall(PetscSFGetGraph(a->sf, NULL, &n, NULL, NULL));
      ldu = n;
      ldv = n;
    }
    if (flg) {
      PetscCheck(a->hmatrix, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing CPU matrix");
      PetscCall(MatDenseGetArrayRead(U, &u));
      PetscCall(MatDenseGetArrayRead(V, &v));
      if (usesf) {
        vv = MatH2OpusGetThrustPointer(*a->yy);
        PetscCall(PetscSFBcastBegin(vsf, MPIU_SCALAR, v, (PetscScalar *)vv, MPI_REPLACE));
        PetscCall(PetscSFBcastEnd(vsf, MPIU_SCALAR, v, (PetscScalar *)vv, MPI_REPLACE));
        if (U != V) {
          uu = MatH2OpusGetThrustPointer(*a->xx);
          PetscCall(PetscSFBcastBegin(usf, MPIU_SCALAR, u, (PetscScalar *)uu, MPI_REPLACE));
          PetscCall(PetscSFBcastEnd(usf, MPIU_SCALAR, u, (PetscScalar *)uu, MPI_REPLACE));
        } else uu = vv;
      } else {
        uu = u;
        vv = v;
      }
      hlru_global(*a->hmatrix, uu, ldu, vv, ldv, U->cmap->N, s, handle);
      PetscCall(MatDenseRestoreArrayRead(U, &u));
      PetscCall(MatDenseRestoreArrayRead(V, &v));
    } else {
  #if defined(PETSC_H2OPUS_USE_GPU)
      PetscBool flgU, flgV;

      PetscCheck(a->hmatrix_gpu, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing GPU matrix");
      PetscCall(PetscObjectTypeCompareAny((PetscObject)U, &flgU, MATSEQDENSE, MATMPIDENSE, ""));
      if (flgU) PetscCall(MatConvert(U, MATDENSECUDA, MAT_INPLACE_MATRIX, &U));
      PetscCall(PetscObjectTypeCompareAny((PetscObject)V, &flgV, MATSEQDENSE, MATMPIDENSE, ""));
      if (flgV) PetscCall(MatConvert(V, MATDENSECUDA, MAT_INPLACE_MATRIX, &V));
      PetscCall(MatDenseCUDAGetArrayRead(U, &u));
      PetscCall(MatDenseCUDAGetArrayRead(V, &v));
      if (usesf) {
        vv = MatH2OpusGetThrustPointer(*a->yy_gpu);
        PetscCall(PetscSFBcastBegin(vsf, MPIU_SCALAR, v, (PetscScalar *)vv, MPI_REPLACE));
        PetscCall(PetscSFBcastEnd(vsf, MPIU_SCALAR, v, (PetscScalar *)vv, MPI_REPLACE));
        if (U != V) {
          uu = MatH2OpusGetThrustPointer(*a->xx_gpu);
          PetscCall(PetscSFBcastBegin(usf, MPIU_SCALAR, u, (PetscScalar *)uu, MPI_REPLACE));
          PetscCall(PetscSFBcastEnd(usf, MPIU_SCALAR, u, (PetscScalar *)uu, MPI_REPLACE));
        } else uu = vv;
      } else {
        uu = u;
        vv = v;
      }
  #else
      SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "This should not happen");
  #endif
      hlru_global(*a->hmatrix_gpu, uu, ldu, vv, ldv, U->cmap->N, s, handle);
  #if defined(PETSC_H2OPUS_USE_GPU)
      PetscCall(MatDenseCUDARestoreArrayRead(U, &u));
      PetscCall(MatDenseCUDARestoreArrayRead(V, &v));
      if (flgU) PetscCall(MatConvert(U, MATDENSE, MAT_INPLACE_MATRIX, &U));
      if (flgV) PetscCall(MatConvert(V, MATDENSE, MAT_INPLACE_MATRIX, &V));
  #endif
    }
    PetscCall(PetscLogEventEnd(MAT_H2Opus_LR, A, 0, 0, 0));
    a->orthogonal = PETSC_FALSE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
#endif