backends/magma/ceed-magma.c

// Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
// reserved. See files LICENSE and NOTICE for details.
//
// This file is part of CEED, a collection of benchmarks, miniapps, software
// libraries and APIs for efficient high-order finite element and spectral
// element discretizations for exascale applications. For more information and
// source code availability see http://github.com/ceed.
//
// The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
// a collaborative effort of two U.S. Department of Energy organizations (Office
// of Science and the National Nuclear Security Administration) responsible for
// the planning and preparation of a capable exascale ecosystem, including
// software, applications, hardware, advanced system engineering and early
// testbed platforms, in support of the nation's exascale computing imperative.

#include "ceed-magma.h"
#include <string.h>

typedef struct {
  CeedScalar *array;
  CeedScalar *darray;
  int  own_;
  int down_;
} CeedVector_Magma;

typedef struct {
  CeedInt *indices;
  CeedInt *dindices;
  int  own_;
  int down_;            // cover a case where we own Device memory
} CeedElemRestriction_Magma;

typedef struct {
  CeedVector etmp;
  CeedVector qdata;
} CeedOperator_Magma;

// *****************************************************************************
// * Initialize vector vec (after free mem) with values from array based on cmode
// *   CEED_COPY_VALUES: memory is allocated in vec->array_allocated, made equal
// *                     to array, and data is copied (not store passed pointer)
// *   CEED_OWN_POINTER: vec->data->array_allocated and vec->data->array = array
// *   CEED_USE_POINTER: vec->data->array = array (can modify; no ownership)
// * mtype: CEED_MEM_HOST or CEED_MEM_DEVICE
// *****************************************************************************
static int CeedVectorSetArray_Magma(CeedVector vec, CeedMemType mtype,
                                    CeedCopyMode cmode, CeedScalar *array) {
  CeedVector_Magma *impl = vec->data;
  int ierr;

  // If own data, free the "old" data, e.g., as it may be of different size
  if (impl->own_) {
    magma_free( impl->darray );
    magma_free_pinned( impl->array );
    impl->darray = NULL;
    impl->array  = NULL;
    impl->own_ = 0;
    impl->down_= 0;
  }

  if (mtype == CEED_MEM_HOST) {
    // memory is on the host; own_ = 0
    switch (cmode) {
    case CEED_COPY_VALUES:
      ierr = magma_malloc( (void**)&impl->darray,
                           vec->length * sizeof(CeedScalar)); CeedChk(ierr);
      ierr = magma_malloc_pinned( (void**)&impl->array,
                                  vec->length * sizeof(CeedScalar)); CeedChk(ierr);
      impl->own_ = 1;

      if (array != NULL)
        magma_setvector(vec->length, sizeof(array[0]),
                        array, 1, impl->darray, 1);
      break;
    case CEED_OWN_POINTER:
      ierr = magma_malloc( (void**)&impl->darray,
                           vec->length * sizeof(CeedScalar)); CeedChk(ierr);
      // TODO: possible problem here is if we are passed non-pinned memory;
      //       (as we own it, lter in destroy, we use free for pinned memory).
      impl->array = array;
      impl->own_ = 1;

      if (array != NULL)
        magma_setvector(vec->length, sizeof(array[0]),
                        array, 1, impl->darray, 1);
      break;
    case CEED_USE_POINTER:
      ierr = magma_malloc( (void**)&impl->darray,
                           vec->length * sizeof(CeedScalar)); CeedChk(ierr);
      magma_setvector(vec->length, sizeof(array[0]),
                      array, 1, impl->darray, 1);

      impl->down_  = 1;
      impl->array  = array;
    }
  } else if (mtype == CEED_MEM_DEVICE) {
    // memory is on the device; own = 0
    switch (cmode) {
    case CEED_COPY_VALUES:
      ierr = magma_malloc( (void**)&impl->darray,
                           vec->length * sizeof(CeedScalar)); CeedChk(ierr);
      ierr = magma_malloc_pinned( (void**)&impl->array,
                                  vec->length * sizeof(CeedScalar)); CeedChk(ierr);
      impl->own_ = 1;

      if (array)
        magma_copyvector(vec->length, sizeof(array[0]),
                         array, 1, impl->darray, 1);
      else
        // t30 assumes allocation initializes with 0s
        magma_setvector(vec->length, sizeof(array[0]),
                        impl->array, 1, impl->darray, 1);
      break;
    case CEED_OWN_POINTER:
      impl->darray = array;
      ierr = magma_malloc_pinned( (void**)&impl->array,
                                  vec->length * sizeof(CeedScalar)); CeedChk(ierr);
      impl->own_ = 1;

      break;
    case CEED_USE_POINTER:
      impl->darray = array;
      impl->array  = NULL;
    }

  } else
    return CeedError(vec->ceed, 1, "Only MemType = HOST or DEVICE supported");

  return 0;
}

// *****************************************************************************
// * Give data pointer from vector vec to array (on HOST or DEVICE)
// *****************************************************************************
static int CeedVectorGetArray_Magma(CeedVector vec, CeedMemType mtype,
                                    CeedScalar **array) {
  CeedVector_Magma *impl = vec->data;
  int ierr;

  if (mtype == CEED_MEM_HOST) {
    if (impl->own_) {
      // data is owned so GPU had the most up-to-date version; copy it
      // TTT - apparantly it doesn't have most up to date data
      magma_getvector(vec->length, sizeof(*array[0]),
                      impl->darray, 1, impl->array, 1);
      CeedDebug("\033[31m[CeedVectorGetArray_Magma]");
      //fprintf(stderr,"rrrrrrrrrrrrrrr\n");
    } else if (impl->array == NULL) {
      // Vector doesn't own the data and was set on GPU
      if (impl->darray == NULL) {
        // call was made just to allocate memory
        ierr = CeedVectorSetArray(vec, mtype, CEED_COPY_VALUES, NULL);
        CeedChk(ierr);
      } else
        return CeedError(vec->ceed, 1, "Can not access DEVICE vector on HOST");
    }
    *array = impl->array;
  } else if (mtype == CEED_MEM_DEVICE) {
    if (impl->darray == NULL) {
      // Vector doesn't own the data and was set on the CPU
      if (impl->array == NULL) {
        // call was made just to allocate memory
        ierr = CeedVectorSetArray(vec, mtype, CEED_COPY_VALUES, NULL);
        CeedChk(ierr);
      } else
        return CeedError(vec->ceed, 1, "Can not access HOST vector on DEVICE");
    }
    *array = impl->darray;
  } else
    return CeedError(vec->ceed, 1, "Can only provide to HOST or DEVICE memory");

  return 0;
}

// *****************************************************************************
// * Give data pointer from vector vec to array (on HOST or DEVICE) to read it
// *****************************************************************************
static int CeedVectorGetArrayRead_Magma(CeedVector vec, CeedMemType mtype,
                                        const CeedScalar **array) {
  CeedVector_Magma *impl = vec->data;
  int ierr;

  if (mtype == CEED_MEM_HOST) {
    if (impl->own_) {
      // data is owned so GPU had the most up-to-date version; copy it
      magma_getvector(vec->length, sizeof(*array[0]),
                      impl->darray, 1, impl->array, 1);
    } else if (impl->array == NULL) {
      // Vector doesn't own the data and was set on GPU
      if (impl->darray == NULL) {
        // call was made just to allocate memory
        ierr = CeedVectorSetArray(vec, mtype, CEED_COPY_VALUES, NULL);
        CeedChk(ierr);
      } else
        return CeedError(vec->ceed, 1, "Can not access DEVICE vector on HOST");
    }
    *array = impl->array;
  } else if (mtype == CEED_MEM_DEVICE) {
    if (impl->darray == NULL) {
      // Vector doesn't own the data and was set on the CPU
      if (impl->array == NULL) {
        // call was made just to allocate memory
        ierr = CeedVectorSetArray(vec, mtype, CEED_COPY_VALUES, NULL);
        CeedChk(ierr);
      } else
        return CeedError(vec->ceed, 1, "Can not access HOST vector on DEVICE");
    }
    *array = impl->darray;
  } else
    return CeedError(vec->ceed, 1, "Can only provide to HOST or DEVICE memory");

  return 0;
}

// *****************************************************************************
// * There is no mtype here for array so it is not clear if we restore from HOST
// * memory or from DEVICE memory. We assume that it is CPU memory because if
// * it was GPU memory we would not call this routine at all.
// * Restore vector vec with values from array, where array received its values
// * from vec and possibly modified them.
// *****************************************************************************
static int CeedVectorRestoreArray_Magma(CeedVector vec, CeedScalar **array) {
  CeedVector_Magma *impl = vec->data;

  // Check if the array is a CPU pointer
  if (*array == impl->array) {
    // Update device, if the device pointer is not NULL
    if (impl->darray != NULL) {
      magma_setvector(vec->length, sizeof(*array[0]),
                      *array, 1, impl->darray, 1);
    } else {
      // nothing to do (case of CPU use pointer)
    }

  } else if (impl->down_) {
    // nothing to do if array is on GPU, except if down_=1(case CPU use pointer)
    magma_getvector(vec->length, sizeof(*array[0]),
                    impl->darray, 1, impl->array, 1);
  }

  *array = NULL;
  return 0;
}

// *****************************************************************************
// * There is no mtype here for array so it is not clear if we restore from HOST
// * memory or from DEVICE memory. We assume that it is CPU memory because if
// * it was GPU memory we would not call this routine at all.
// * Restore vector vec with values from array, where array received its values
// * from vec to only read them; in this case vec may have been modified meanwhile
// * and needs to be restored here.
// *****************************************************************************
static int CeedVectorRestoreArrayRead_Magma(CeedVector vec,
    const CeedScalar **array) {
  CeedVector_Magma *impl = vec->data;

  // Check if the array is a CPU pointer
  if (*array == impl->array) {
    // Update device, if the device pointer is not NULL
    if (impl->darray != NULL) {
      magma_setvector(vec->length, sizeof(*array[0]),
                      *array, 1, impl->darray, 1);
    } else {
      // nothing to do (case of CPU use pointer)
    }

  } else if (impl->down_) {
    // nothing to do if array is on GPU, except if down_=1(case CPU use pointer)
    magma_getvector(vec->length, sizeof(*array[0]),
                    impl->darray, 1, impl->array, 1);
  }

  *array = NULL;
  return 0;
}

static int CeedVectorDestroy_Magma(CeedVector vec) {
  CeedVector_Magma *impl = vec->data;
  int ierr;

  // Free if we own the data
  if (impl->own_) {
    ierr = magma_free_pinned(impl->array); CeedChk(ierr);
    ierr = magma_free(impl->darray);       CeedChk(ierr);
  } else if (impl->down_) {
    ierr = magma_free(impl->darray);       CeedChk(ierr);
  }
  ierr = CeedFree(&vec->data); CeedChk(ierr);
  return 0;
}

// *****************************************************************************
// * Create vector vec of size n
// *****************************************************************************
static int CeedVectorCreate_Magma(Ceed ceed, CeedInt n, CeedVector vec) {
  CeedVector_Magma *impl;
  int ierr;

  vec->SetArray = CeedVectorSetArray_Magma;
  vec->GetArray = CeedVectorGetArray_Magma;
  vec->GetArrayRead = CeedVectorGetArrayRead_Magma;
  vec->RestoreArray = CeedVectorRestoreArray_Magma;
  vec->RestoreArrayRead = CeedVectorRestoreArrayRead_Magma;
  vec->Destroy = CeedVectorDestroy_Magma;
  ierr = CeedCalloc(1,&impl); CeedChk(ierr);
  impl->darray = NULL;
  impl->array  = NULL;
  impl->own_ = 0;
  impl->down_= 0;
  vec->data = impl;
  return 0;
}

// *****************************************************************************
// * Apply restriction operator r to u: v = r(rmode) u
// *****************************************************************************
static int CeedElemRestrictionApply_Magma(CeedElemRestriction r,
    CeedTransposeMode tmode, CeedInt ncomp,
    CeedTransposeMode lmode, CeedVector u,
    CeedVector v, CeedRequest *request) {
  CeedElemRestriction_Magma *impl = r->data;
  int ierr;
  const CeedScalar *uu;
  CeedScalar *vv;
  CeedInt nelem = r->nelem, elemsize = r->elemsize, ndof = r->ndof;
  CeedInt esize = nelem * elemsize;

#ifdef USE_MAGMA_BATCH2
  CeedInt *dindices = impl->dindices;
  // Get pointers on the device
  ierr = CeedVectorGetArrayRead(u, CEED_MEM_DEVICE, &uu); CeedChk(ierr);
  ierr = CeedVectorGetArray(v, CEED_MEM_DEVICE, &vv); CeedChk(ierr);
#else
  CeedInt *indices = impl->indices;
  ierr = CeedVectorGetArrayRead(u, CEED_MEM_HOST, &uu); CeedChk(ierr);
  ierr = CeedVectorGetArray(v, CEED_MEM_HOST, &vv); CeedChk(ierr);
#endif

  if (tmode == CEED_NOTRANSPOSE) {
    // Perform: v = r * u
    if (ncomp == 1) {
#ifdef USE_MAGMA_BATCH2
magma_template<<i=0:esize>>
      (const CeedScalar *uu, CeedScalar *vv, CeedInt *dindices) {
        vv[i] = uu[dindices[i]];
      }
#else
      for (CeedInt i=0; i<esize; i++) vv[i] = uu[indices[i]];
#endif
    } else {
      // vv is (elemsize x ncomp x nelem), column-major
      if (lmode == CEED_NOTRANSPOSE) { // u is (ndof x ncomp), column-major
#ifdef USE_MAGMA_BATCH2
magma_template<<e=0:nelem, d=0:ncomp, i=0:elemsize>>
        (const CeedScalar *uu, CeedScalar *vv, CeedInt *dindices, int ndof) {
          vv[i + iend*(d+dend*e)] = uu[dindices[i+iend*e]+ndof*d];
        }
#else
        for (CeedInt e = 0; e < nelem; e++)
          for (CeedInt d = 0; d < ncomp; d++)
            for (CeedInt i=0; i < elemsize; i++) {
              vv[i + elemsize*(d+ncomp*e)] =
                uu[indices[i+elemsize*e]+ndof*d];
            }
#endif
      } else { // u is (ncomp x ndof), column-major
#ifdef USE_MAGMA_BATCH2
magma_template<<e=0:nelem, d=0:ncomp, i=0:elemsize>>
        (const CeedScalar *uu, CeedScalar *vv, CeedInt *dindices) {
          vv[i + iend*(d+dend*e)] = uu[d+dend*dindices[i + iend*e]];
        }
#else
        for (CeedInt e = 0; e < nelem; e++)
          for (CeedInt d = 0; d < ncomp; d++)
            for (CeedInt i=0; i< elemsize; i++) {
              vv[i + elemsize*(d+ncomp*e)] =
                uu[d+ncomp*indices[i+elemsize*e]];
            }
#endif
      }
    }
  } else {
    // Note: in transpose mode, we perform: v += r^t * u
    if (ncomp == 1) {
      // fprintf(stderr,"3 ---------\n");
#ifdef USE_MAGMA_BATCH2
magma_template<<i=0:esize>>
      (const CeedScalar *uu, CeedScalar *vv, CeedInt *dindices) {
        magmablas_datomic_add( &vv[dindices[i]], uu[i]);
      }
#else
      for (CeedInt i=0; i<esize; i++) vv[indices[i]] += uu[i];
#endif
    } else { // u is (elemsize x ncomp x nelem)
      fprintf(stderr,"2 ---------\n");

      if (lmode == CEED_NOTRANSPOSE) { // vv is (ndof x ncomp), column-major
#ifdef USE_MAGMA_BATCH2
magma_template<<e=0:nelem, d=0:ncomp, i=0:elemsize>>
        (const CeedScalar *uu, CeedScalar *vv, CeedInt *dindices, CeedInt ndof) {
          magmablas_datomic_add( &vv[dindices[i+iend*e]+ndof*d],
                                 uu[i+iend*(d+e*dend)]);
        }
#else
        for (CeedInt e = 0; e < nelem; e++)
          for (CeedInt d = 0; d < ncomp; d++)
            for (CeedInt i=0; i < elemsize; i++) {
              vv[indices[i + elemsize*e]+ndof*d] +=
                uu[i + elemsize*(d+e*ncomp)];
            }
#endif
      } else { // vv is (ncomp x ndof), column-major
#ifdef USE_MAGMA_BATCH2
magma_template<<e=0:nelem, d=0:ncomp, i=0:elemsize>>
        (const CeedScalar *uu, CeedScalar *vv, CeedInt *dindices) {
          magmablas_datomic_add( &vv[d+dend*dindices[i + iend*e]],
                                 uu[i+iend*(d+e*dend)]);
        }
#else
        for (CeedInt e = 0; e < nelem; e++)
          for (CeedInt d = 0; d < ncomp; d++)
            for (CeedInt i=0; i < elemsize; i++) {
              vv[d+ncomp*indices[i + elemsize*e]] +=
                uu[i + elemsize*(d+e*ncomp)];
            }
#endif
      }
    }
  }

  ierr = CeedVectorRestoreArrayRead(u, &uu); CeedChk(ierr);
  ierr = CeedVectorRestoreArray(v, &vv); CeedChk(ierr);

  if (request != CEED_REQUEST_IMMEDIATE && request != CEED_REQUEST_ORDERED)
    *request = NULL;
  return 0;
}

static int CeedElemRestrictionDestroy_Magma(CeedElemRestriction r) {
  CeedElemRestriction_Magma *impl = r->data;
  int ierr;

  // Free if we own the data
  if (impl->own_) {
    ierr = magma_free_pinned(impl->indices); CeedChk(ierr);
    ierr = magma_free(impl->dindices);       CeedChk(ierr);
  } else if (impl->down_) {
    ierr = magma_free(impl->dindices);       CeedChk(ierr);
  }
  ierr = CeedFree(&r->data); CeedChk(ierr);
  return 0;
}

static int CeedElemRestrictionCreate_Magma(CeedElemRestriction r,
    CeedMemType mtype,
    CeedCopyMode cmode,
    const CeedInt *indices) {
  int ierr, size = r->nelem*r->elemsize;
  CeedElemRestriction_Magma *impl;

  // Allocate memory for the MAGMA Restricton and initializa pointers to NULL
  ierr = CeedCalloc(1,&impl); CeedChk(ierr);
  impl->dindices = NULL;
  impl->indices  = NULL;
  impl->own_ = 0;
  impl->down_= 0;

  if (mtype == CEED_MEM_HOST) {
    // memory is on the host; own_ = 0
    switch (cmode) {
    case CEED_COPY_VALUES:
      ierr = magma_malloc( (void**)&impl->dindices,
                           size * sizeof(CeedInt)); CeedChk(ierr);
      ierr = magma_malloc_pinned( (void**)&impl->indices,
                                  size * sizeof(CeedInt)); CeedChk(ierr);
      impl->own_ = 1;

      if (indices != NULL) {
        memcpy(impl->indices, indices, size * sizeof(indices[0]));
        magma_setvector(size, sizeof(CeedInt),
                        impl->indices, 1, impl->dindices, 1);
      }
      break;
    case CEED_OWN_POINTER:
      ierr = magma_malloc( (void**)&impl->dindices,
                           size * sizeof(CeedInt)); CeedChk(ierr);
      // TODO: possible problem here is if we are passed non-pinned memory;
      //       (as we own it, lter in destroy, we use free for pinned memory).
      impl->indices = (CeedInt *)indices;
      impl->own_ = 1;

      if (indices != NULL)
        magma_setvector(size, sizeof(CeedInt),
                        indices, 1, impl->dindices, 1);
      break;
    case CEED_USE_POINTER:
      ierr = magma_malloc( (void**)&impl->dindices,
                           size * sizeof(CeedInt)); CeedChk(ierr);
      magma_setvector(size, sizeof(CeedInt),
                      indices, 1, impl->dindices, 1);
      impl->down_ = 1;
      impl->indices  = (CeedInt *)indices;
    }
  } else if (mtype == CEED_MEM_DEVICE) {
    // memory is on the device; own = 0
    switch (cmode) {
    case CEED_COPY_VALUES:
      ierr = magma_malloc( (void**)&impl->dindices,
                           size * sizeof(CeedInt)); CeedChk(ierr);
      ierr = magma_malloc_pinned( (void**)&impl->indices,
                                  size * sizeof(CeedInt)); CeedChk(ierr);
      impl->own_ = 1;

      if (indices)
        magma_copyvector(size, sizeof(CeedInt),
                         indices, 1, impl->dindices, 1);
      break;
    case CEED_OWN_POINTER:
      impl->dindices = (CeedInt *)indices;
      ierr = magma_malloc_pinned( (void**)&impl->indices,
                                  size * sizeof(CeedInt)); CeedChk(ierr);
      impl->own_ = 1;

      break;
    case CEED_USE_POINTER:
      impl->dindices = (CeedInt *)indices;
      impl->indices  = NULL;
    }

  } else
    return CeedError(r->ceed, 1, "Only MemType = HOST or DEVICE supported");

  r->data    = impl;
  r->Apply   = CeedElemRestrictionApply_Magma;
  r->Destroy = CeedElemRestrictionDestroy_Magma;

  return 0;
}

// Contracts on the middle index
// NOTRANSPOSE: V_ajc = T_jb U_abc
// TRANSPOSE:   V_ajc = T_bj U_abc
// If Add != 0, "=" is replaced by "+="
static int CeedTensorContract_Magma(Ceed ceed,
                                    CeedInt A, CeedInt B, CeedInt C, CeedInt J,
                                    const CeedScalar *t, CeedTransposeMode tmode,
                                    const CeedInt Add,
                                    const CeedScalar *u, CeedScalar *v) {
#ifdef USE_MAGMA_BATCH
  magma_dtensor_contract(ceed, A, B, C, J, t, tmode, Add, u, v);
#else
  CeedInt tstride0 = B, tstride1 = 1;
  if (tmode == CEED_TRANSPOSE) {
    tstride0 = 1; tstride1 = J;
  }
  CeedDebug("\033[31m[CeedTensorContract] A=%d, J=%d, C=%d, B=%d: %d %d %d",
            A,J,C,B,A*J*B*C, C*J*A, C*B*A);
  for (CeedInt a=0; a<A; a++) {
    for (CeedInt j=0; j<J; j++) {
      if (!Add) {
        for (CeedInt c=0; c<C; c++)
          v[(a*J+j)*C+c] = 0;
      }
      for (CeedInt b=0; b<B; b++) {
        for (CeedInt c=0; c<C; c++) {
          v[(a*J+j)*C+c] += t[j*tstride0 + b*tstride1] * u[(a*B+b)*C+c];
        }
      }
    }
  }
#endif
  return 0;
}

static int CeedBasisApply_Magma(CeedBasis basis, CeedTransposeMode tmode,
                                CeedEvalMode emode,
                                const CeedScalar *u, CeedScalar *v) {
  int ierr;
  const CeedInt dim = basis->dim;
  const CeedInt ndof = basis->ndof;
  const CeedInt nqpt = ndof*CeedPowInt(basis->Q1d, dim);
  const CeedInt add = (tmode == CEED_TRANSPOSE);

  CeedDebug("\033[01m[CeedBasisApply_Magma] vsize=%d",
            ndof*CeedPowInt(basis->P1d, dim));

  if (tmode == CEED_TRANSPOSE) {
    const CeedInt vsize = ndof*CeedPowInt(basis->P1d, dim);
    for (CeedInt i = 0; i < vsize; i++)
      v[i] = (CeedScalar) 0;
  }
  if (emode & CEED_EVAL_INTERP) {
    CeedInt P = basis->P1d, Q = basis->Q1d;
    if (tmode == CEED_TRANSPOSE) {
      P = basis->Q1d; Q = basis->P1d;
    }
    CeedInt pre = ndof*CeedPowInt(P, dim-1), post = 1;
    CeedScalar tmp[2][ndof*Q*CeedPowInt(P>Q?P:Q, dim-1)];
    CeedDebug("\033[01m[CeedBasisApply_Magma] tmpsize = %d",
              ndof*Q*CeedPowInt(P>Q?P:Q, dim-1));
    for (CeedInt d=0; d<dim; d++) {
      ierr = CeedTensorContract_Magma(basis->ceed, pre, P, post, Q, basis->interp1d,
                                      tmode, add&&(d==dim-1),
                                      d==0?u:tmp[d%2], d==dim-1?v:tmp[(d+1)%2]);
      CeedChk(ierr);
      pre /= P;
      post *= Q;
    }
    if (tmode == CEED_NOTRANSPOSE) {
      v += nqpt;
    } else {
      u += nqpt;
    }
  }
  if (emode & CEED_EVAL_GRAD) {
    CeedInt P = basis->P1d, Q = basis->Q1d;
    // In CEED_NOTRANSPOSE mode:
    // u is (P^dim x nc), column-major layout (nc = ndof)
    // v is (Q^dim x nc x dim), column-major layout (nc = ndof)
    // In CEED_TRANSPOSE mode, the sizes of u and v are switched.
    if (tmode == CEED_TRANSPOSE) {
      P = basis->Q1d, Q = basis->P1d;
    }
    CeedScalar tmp[2][ndof*Q*CeedPowInt(P>Q?P:Q, dim-1)];
    CeedDebug("\033[01m[CeedBasisApply_Magma] tmpsize = %d",
              ndof*Q*CeedPowInt(P>Q?P:Q, dim-1));
    for (CeedInt p = 0; p < dim; p++) {
      CeedInt pre = ndof*CeedPowInt(P, dim-1), post = 1;
      for (CeedInt d=0; d<dim; d++) {
        ierr = CeedTensorContract_Magma(basis->ceed, pre, P, post, Q,
                                        (p==d)?basis->grad1d:basis->interp1d,
                                        tmode, add&&(d==dim-1),
                                        d==0?u:tmp[d%2], d==dim-1?v:tmp[(d+1)%2]);
        CeedChk(ierr);
        pre /= P;
        post *= Q;
      }
      if (tmode == CEED_NOTRANSPOSE) {
        v += nqpt;
      } else {
        u += nqpt;
      }
    }
  }
  if (emode & CEED_EVAL_WEIGHT) {
    if (tmode == CEED_TRANSPOSE)
      return CeedError(basis->ceed, 1,
                       "CEED_EVAL_WEIGHT incompatible with CEED_TRANSPOSE");
    CeedInt Q = basis->Q1d;
    for (CeedInt d=0; d<dim; d++) {
      CeedInt pre = CeedPowInt(Q, dim-d-1), post = CeedPowInt(Q, d);
      for (CeedInt i=0; i<pre; i++) {
        for (CeedInt j=0; j<Q; j++) {
          for (CeedInt k=0; k<post; k++) {
            v[(i*Q + j)*post + k] = basis->qweight1d[j]
                                    * (d == 0 ? 1 : v[(i*Q + j)*post + k]);
          }
        }
      }
    }
  }
  return 0;
}

static int CeedBasisDestroy_Magma(CeedBasis basis) {
  return 0;
}

static int CeedBasisCreateTensorH1_Magma(Ceed ceed, CeedInt dim, CeedInt P1d,
    CeedInt Q1d, const CeedScalar *interp1d,
    const CeedScalar *grad1d,
    const CeedScalar *qref1d,
    const CeedScalar *qweight1d,
    CeedBasis basis) {
  basis->Apply = CeedBasisApply_Magma;
  basis->Destroy = CeedBasisDestroy_Magma;
  return 0;
}

static int CeedQFunctionApply_Magma(CeedQFunction qf, void *qdata, CeedInt Q,
                                    const CeedScalar *const *u,
                                    CeedScalar *const *v) {
  int ierr;
  ierr = qf->function(qf->ctx, qdata, Q, u, v); CeedChk(ierr);
  return 0;
}

static int CeedQFunctionDestroy_Magma(CeedQFunction qf) {
  return 0;
}

static int CeedQFunctionCreate_Magma(CeedQFunction qf) {
  qf->Apply = CeedQFunctionApply_Magma;
  qf->Destroy = CeedQFunctionDestroy_Magma;
  return 0;
}

static int CeedOperatorDestroy_Magma(CeedOperator op) {
  CeedOperator_Magma *impl = op->data;
  int ierr;

  ierr = CeedVectorDestroy(&impl->etmp); CeedChk(ierr);
  ierr = CeedVectorDestroy(&impl->qdata); CeedChk(ierr);
  ierr = CeedFree(&op->data); CeedChk(ierr);
  return 0;
}

static int CeedOperatorApply_Magma(CeedOperator op, CeedVector qdata,
                                   CeedVector ustate,
                                   CeedVector residual, CeedRequest *request) {
  CeedOperator_Magma *impl = op->data;
  CeedVector etmp;
  CeedInt Q;
  const CeedInt nc = op->basis->ndof, dim = op->basis->dim;
  CeedScalar *Eu;
  char *qd;
  int ierr;
  CeedTransposeMode lmode = CEED_NOTRANSPOSE;

  if (!impl->etmp) {
    ierr = CeedVectorCreate(op->ceed,
                            nc * op->Erestrict->nelem * op->Erestrict->elemsize,
                            &impl->etmp); CeedChk(ierr);
    // etmp is allocated when CeedVectorGetArray is called below
  }
  etmp = impl->etmp;
  if (op->qf->inmode & ~CEED_EVAL_WEIGHT) {
    ierr = CeedElemRestrictionApply(op->Erestrict, CEED_NOTRANSPOSE,
                                    nc, lmode, ustate, etmp,
                                    CEED_REQUEST_IMMEDIATE); CeedChk(ierr);
  }
  ierr = CeedBasisGetNumQuadraturePoints(op->basis, &Q); CeedChk(ierr);
  ierr = CeedVectorGetArray(etmp, CEED_MEM_HOST, &Eu); CeedChk(ierr);
  ierr = CeedVectorGetArray(qdata, CEED_MEM_HOST, (CeedScalar**)&qd);
  CeedChk(ierr);

  for (CeedInt e=0; e<op->Erestrict->nelem; e++) {
    CeedScalar BEu[Q*nc*(dim+2)], BEv[Q*nc*(dim+2)], *out[5] = {0,0,0,0,0};
    const CeedScalar *in[5] = {0,0,0,0,0};
    // TODO: quadrature weights can be computed just once
    CeedDebug("\033[11m[CeedOperatorApply_Magma] e=%d: Eu+%d, %d",
              e, e*op->Erestrict->elemsize*nc, Q*nc*(dim+2));
    ierr = CeedBasisApply(op->basis, CEED_NOTRANSPOSE, op->qf->inmode,
                          &Eu[e*op->Erestrict->elemsize*nc], BEu);
    CeedChk(ierr);
    CeedScalar *u_ptr = BEu, *v_ptr = BEv;
    if (op->qf->inmode & CEED_EVAL_INTERP) { in[0] = u_ptr; u_ptr += Q*nc; }
    if (op->qf->inmode & CEED_EVAL_GRAD) { in[1] = u_ptr; u_ptr += Q*nc*dim; }
    if (op->qf->inmode & CEED_EVAL_WEIGHT) { in[4] = u_ptr; u_ptr += Q; }
    if (op->qf->outmode & CEED_EVAL_INTERP) { out[0] = v_ptr; v_ptr += Q*nc; }
    if (op->qf->outmode & CEED_EVAL_GRAD) { out[1] = v_ptr; v_ptr += Q*nc*dim; }
    ierr = CeedQFunctionApply(op->qf, &qd[e*Q*op->qf->qdatasize], Q, in, out);
    CeedChk(ierr);
    CeedDebug("\033[31m[CeedOperatorApply_Magma] e=%d: ",e);
    ierr = CeedBasisApply(op->basis, CEED_TRANSPOSE, op->qf->outmode, BEv,
                          &Eu[e*op->Erestrict->elemsize*nc]);
    CeedChk(ierr);
  }
  ierr = CeedVectorRestoreArray(etmp, &Eu); CeedChk(ierr);
  // qdata must be restored
  ierr = CeedVectorRestoreArray(qdata, (CeedScalar**)&qd); CeedChk(ierr);
  if (residual) {
    CeedScalar *res;
    CeedVectorGetArray(residual, CEED_MEM_HOST, &res);
    for (int i = 0; i < residual->length; i++)
      res[i] = (CeedScalar)0;
    // residual must be restored
    CeedVectorRestoreArray(residual, &res);
    ierr = CeedElemRestrictionApply(op->Erestrict, CEED_TRANSPOSE,
                                    nc, lmode, etmp, residual,
                                    CEED_REQUEST_IMMEDIATE); CeedChk(ierr);
  }
  if (request != CEED_REQUEST_IMMEDIATE && request != CEED_REQUEST_ORDERED)
    *request = NULL;
  return 0;
}

static int CeedOperatorGetQData_Magma(CeedOperator op, CeedVector *qdata) {
  CeedOperator_Magma *impl = op->data;
  int ierr;

  if (!impl->qdata) {
    CeedInt Q;
    ierr = CeedBasisGetNumQuadraturePoints(op->basis, &Q); CeedChk(ierr);
    ierr = CeedVectorCreate(op->ceed,
                            op->Erestrict->nelem * Q
                            * op->qf->qdatasize / sizeof(CeedScalar),
                            &impl->qdata); CeedChk(ierr);
  }
  *qdata = impl->qdata;
  return 0;
}

static int CeedOperatorCreate_Magma(CeedOperator op) {
  CeedOperator_Magma *impl;
  int ierr;

  ierr = CeedCalloc(1, &impl); CeedChk(ierr);
  op->data = impl;
  op->Destroy  = CeedOperatorDestroy_Magma;
  op->Apply    = CeedOperatorApply_Magma;
  op->GetQData = CeedOperatorGetQData_Magma;
  return 0;
}

// *****************************************************************************
// * INIT
// *****************************************************************************
static int CeedInit_Magma(const char *resource, Ceed ceed) {
  int ierr;
  if (strcmp(resource, "/gpu/magma"))
    return CeedError(ceed, 1, "MAGMA backend cannot use resource: %s", resource);

  ierr = magma_init();
  if (ierr) return CeedError(ceed, 1, "error in magma_init(): %d\n", ierr);
  //magma_print_environment();

  ceed->VecCreate = CeedVectorCreate_Magma;
  ceed->BasisCreateTensorH1 = CeedBasisCreateTensorH1_Magma;
  ceed->ElemRestrictionCreate = CeedElemRestrictionCreate_Magma;
  ceed->QFunctionCreate = CeedQFunctionCreate_Magma;
  ceed->OperatorCreate = CeedOperatorCreate_Magma;
  return 0;
}

// *****************************************************************************
// * REGISTER
// *****************************************************************************
__attribute__((constructor))
static void Register(void) {
  CeedRegister("/gpu/magma", CeedInit_Magma, 20);
}