xref: /libCEED/interface/ceed-elemrestriction.c (revision 3ac8f562f5621e25a98112671345ef9a265ba6d0)

// Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors.
// All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
//
// SPDX-License-Identifier: BSD-2-Clause
//
// This file is part of CEED:  http://github.com/ceed

#include <ceed-impl.h>
#include <ceed.h>
#include <ceed/backend.h>
#include <stdbool.h>
#include <stdio.h>
#include <string.h>

/// @file
/// Implementation of CeedElemRestriction interfaces

/// ----------------------------------------------------------------------------
/// CeedElemRestriction Library Internal Functions
/// ----------------------------------------------------------------------------
/// @addtogroup CeedElemRestrictionDeveloper
/// @{

/**
  @brief Permute and pad offsets for a blocked restriction

  @param[in]  offsets        Array of shape [@a num_elem, @a elem_size].
  @param[out] block_offsets  Array of permuted and padded array values of shape [@a num_block, @a elem_size, @a block_size].
  @param[in]  num_block      Number of blocks
  @param[in]  num_elem       Number of elements
  @param[in]  block_size     Number of elements in a block
  @param[in]  elem_size      Size of each element

  @return An error code: 0 - success, otherwise - failure

  @ref Utility
**/
int CeedPermutePadOffsets(const CeedInt *offsets, CeedInt *block_offsets, CeedInt num_block, CeedInt num_elem, CeedInt block_size,
                          CeedInt elem_size) {
  for (CeedInt e = 0; e < num_block * block_size; e += block_size) {
    for (CeedInt j = 0; j < block_size; j++) {
      for (CeedInt k = 0; k < elem_size; k++) {
        block_offsets[e * elem_size + k * block_size + j] = offsets[CeedIntMin(e + j, num_elem - 1) * elem_size + k];
      }
    }
  }
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Permute and pad orientations for a blocked restriction

  @param[in]  orients       Array of shape [@a num_elem, @a elem_size].
  @param[out] block_orients Array of permuted and padded array values of shape [@a num_block, @a elem_size, @a block_size].
  @param[in]  num_block     Number of blocks
  @param[in]  num_elem      Number of elements
  @param[in]  block_size    Number of elements in a block
  @param[in]  elem_size     Size of each element

  @return An error code: 0 - success, otherwise - failure

  @ref Utility
**/
int CeedPermutePadOrients(const bool *orients, bool *block_orients, CeedInt num_block, CeedInt num_elem, CeedInt block_size, CeedInt elem_size) {
  for (CeedInt e = 0; e < num_block * block_size; e += block_size) {
    for (CeedInt j = 0; j < block_size; j++) {
      for (CeedInt k = 0; k < elem_size; k++) {
        block_orients[e * elem_size + k * block_size + j] = orients[CeedIntMin(e + j, num_elem - 1) * elem_size + k];
      }
    }
  }
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Permute and pad curl-conforming orientations for a blocked restriction

  @param[in]  curl_orients       Array of shape [@a num_elem, @a 3 * elem_size].
  @param[out] block_curl_orients Array of permuted and padded array values of shape [@a num_block, @a elem_size, @a block_size].
  @param[in]  num_block          Number of blocks
  @param[in]  num_elem           Number of elements
  @param[in]  block_size         Number of elements in a block
  @param[in]  elem_size          Size of each element

  @return An error code: 0 - success, otherwise - failure

  @ref Utility
**/
int CeedPermutePadCurlOrients(const CeedInt8 *curl_orients, CeedInt8 *block_curl_orients, CeedInt num_block, CeedInt num_elem, CeedInt block_size,
                              CeedInt elem_size) {
  for (CeedInt e = 0; e < num_block * block_size; e += block_size) {
    for (CeedInt j = 0; j < block_size; j++) {
      for (CeedInt k = 0; k < elem_size; k++) {
        block_curl_orients[e * elem_size + k * block_size + j] = curl_orients[CeedIntMin(e + j, num_elem - 1) * elem_size + k];
      }
    }
  }
  return CEED_ERROR_SUCCESS;
}

/// @}

/// ----------------------------------------------------------------------------
/// CeedElemRestriction Backend API
/// ----------------------------------------------------------------------------
/// @addtogroup CeedElemRestrictionBackend
/// @{

/**
  @brief Get the type of a CeedElemRestriction

  @param[in]  rstr      CeedElemRestriction
  @param[out] rstr_type Variable to store restriction type

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
**/
int CeedElemRestrictionGetType(CeedElemRestriction rstr, CeedRestrictionType *rstr_type) {
  *rstr_type = rstr->rstr_type;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the strided status of a CeedElemRestriction

  @param[in]  rstr       CeedElemRestriction
  @param[out] is_strided Variable to store strided status, 1 if strided else 0
**/
int CeedElemRestrictionIsStrided(CeedElemRestriction rstr, bool *is_strided) {
  *is_strided = (rstr->rstr_type == CEED_RESTRICTION_STRIDED);
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the points status of a CeedElemRestriction

  @param[in]  rstr      CeedElemRestriction
  @param[out] is_points Variable to store points status, 1 if points else 0
**/
int CeedElemRestrictionIsPoints(CeedElemRestriction rstr, bool *is_points) {
  *is_points = (rstr->rstr_type == CEED_RESTRICTION_POINTS);
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the strides of a strided CeedElemRestriction

  @param[in]  rstr    CeedElemRestriction
  @param[out] strides Variable to store strides array

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
**/
int CeedElemRestrictionGetStrides(CeedElemRestriction rstr, CeedInt (*strides)[3]) {
  CeedCheck(rstr->strides, rstr->ceed, CEED_ERROR_MINOR, "ElemRestriction has no stride data");
  for (CeedInt i = 0; i < 3; i++) (*strides)[i] = rstr->strides[i];
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the backend stride status of a CeedElemRestriction

  @param[in]  rstr                 CeedElemRestriction
  @param[out] has_backend_strides  Variable to store stride status

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
**/
int CeedElemRestrictionHasBackendStrides(CeedElemRestriction rstr, bool *has_backend_strides) {
  CeedCheck(rstr->strides, rstr->ceed, CEED_ERROR_MINOR, "ElemRestriction has no stride data");
  *has_backend_strides = ((rstr->strides[0] == CEED_STRIDES_BACKEND[0]) && (rstr->strides[1] == CEED_STRIDES_BACKEND[1]) &&
                          (rstr->strides[2] == CEED_STRIDES_BACKEND[2]));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get read-only access to a CeedElemRestriction offsets array by memtype

  @param[in]  rstr     CeedElemRestriction to retrieve offsets
  @param[in]  mem_type Memory type on which to access the array.
                         If the backend uses a different memory type, this will perform a copy (possibly cached).
  @param[out] offsets  Array on memory type mem_type

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionGetOffsets(CeedElemRestriction rstr, CeedMemType mem_type, const CeedInt **offsets) {
  if (rstr->rstr_base) {
    CeedCall(CeedElemRestrictionGetOffsets(rstr->rstr_base, mem_type, offsets));
  } else {
    CeedCheck(rstr->GetOffsets, rstr->ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support GetOffsets");
    CeedCall(rstr->GetOffsets(rstr, mem_type, offsets));
    rstr->num_readers++;
  }
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Restore an offsets array obtained using CeedElemRestrictionGetOffsets()

  @param[in] rstr    CeedElemRestriction to restore
  @param[in] offsets Array of offset data

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionRestoreOffsets(CeedElemRestriction rstr, const CeedInt **offsets) {
  if (rstr->rstr_base) {
    CeedCall(CeedElemRestrictionRestoreOffsets(rstr->rstr_base, offsets));
  } else {
    *offsets = NULL;
    rstr->num_readers--;
  }
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get read-only access to a CeedElemRestriction orientations array by memtype

  @param[in]  rstr     CeedElemRestriction to retrieve orientations
  @param[in]  mem_type Memory type on which to access the array.
                         If the backend uses a different memory type, this will perform a copy (possibly cached).
  @param[out] orients  Array on memory type mem_type

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionGetOrientations(CeedElemRestriction rstr, CeedMemType mem_type, const bool **orients) {
  CeedCheck(rstr->GetOrientations, rstr->ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support GetOrientations");
  CeedCall(rstr->GetOrientations(rstr, mem_type, orients));
  rstr->num_readers++;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Restore an orientations array obtained using CeedElemRestrictionGetOrientations()

  @param[in] rstr    CeedElemRestriction to restore
  @param[in] orients Array of orientation data

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionRestoreOrientations(CeedElemRestriction rstr, const bool **orients) {
  *orients = NULL;
  rstr->num_readers--;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get read-only access to a CeedElemRestriction curl-conforming orientations array by memtype

  @param[in]  rstr         CeedElemRestriction to retrieve curl-conforming orientations
  @param[in]  mem_type     Memory type on which to access the array.
                             If the backend uses a different memory type, this will perform a copy (possibly cached).
  @param[out] curl_orients Array on memory type mem_type

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionGetCurlOrientations(CeedElemRestriction rstr, CeedMemType mem_type, const CeedInt8 **curl_orients) {
  CeedCheck(rstr->GetCurlOrientations, rstr->ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support GetCurlOrientations");
  CeedCall(rstr->GetCurlOrientations(rstr, mem_type, curl_orients));
  rstr->num_readers++;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Restore an orientations array obtained using CeedElemRestrictionGetCurlOrientations()

  @param[in] rstr         CeedElemRestriction to restore
  @param[in] curl_orients Array of orientation data

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionRestoreCurlOrientations(CeedElemRestriction rstr, const CeedInt8 **curl_orients) {
  *curl_orients = NULL;
  rstr->num_readers--;
  return CEED_ERROR_SUCCESS;
}

/**

  @brief Get the number of points in an element of a points CeedElemRestriction

  @param[in]  rstr       CeedElemRestriction
  @param[in]  elem       Index number of element to retrieve the number of points for
  @param[out] num_points The number of points in the element at index elem

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
**/
int CeedElemRestrictionGetNumPointsInElement(CeedElemRestriction rstr, CeedInt elem, CeedInt *num_points) {
  Ceed           ceed;
  const CeedInt *offsets;

  CeedCall(CeedElemRestrictionGetCeed(rstr, &ceed));
  CeedCheck(rstr->rstr_type == CEED_RESTRICTION_POINTS, ceed, CEED_ERROR_INCOMPATIBLE,
            "Can only retrieve the number of points for a points CeedElemRestriction");

  CeedCall(CeedElemRestrictionGetOffsets(rstr, CEED_MEM_HOST, &offsets));
  *num_points = offsets[elem - 1] - offsets[elem];
  CeedCall(CeedElemRestrictionRestoreOffsets(rstr, &offsets));
  return CEED_ERROR_SUCCESS;
}

/**

  @brief Get the E-vector layout of a CeedElemRestriction

  @param[in]  rstr    CeedElemRestriction
  @param[out] layout  Variable to store layout array, stored as [nodes, components, elements].
                        The data for node i, component j, element k in the E-vector is given by i*layout[0] + j*layout[1] + k*layout[2]

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
**/
int CeedElemRestrictionGetELayout(CeedElemRestriction rstr, CeedInt (*layout)[3]) {
  CeedCheck(rstr->layout[0], rstr->ceed, CEED_ERROR_MINOR, "ElemRestriction has no layout data");
  for (CeedInt i = 0; i < 3; i++) (*layout)[i] = rstr->layout[i];
  return CEED_ERROR_SUCCESS;
}

/**

  @brief Set the E-vector layout of a CeedElemRestriction

  @param[in] rstr   CeedElemRestriction
  @param[in] layout Variable to containing layout array, stored as [nodes, components, elements].
                      The data for node i, component j, element k in the E-vector is given by i*layout[0] + j*layout[1] + k*layout[2]

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
**/
int CeedElemRestrictionSetELayout(CeedElemRestriction rstr, CeedInt layout[3]) {
  for (CeedInt i = 0; i < 3; i++) rstr->layout[i] = layout[i];
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the backend data of a CeedElemRestriction

  @param[in]  rstr CeedElemRestriction
  @param[out] data Variable to store data

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
**/
int CeedElemRestrictionGetData(CeedElemRestriction rstr, void *data) {
  *(void **)data = rstr->data;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Set the backend data of a CeedElemRestriction

  @param[in,out] rstr CeedElemRestriction
  @param[in]     data Data to set

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
**/
int CeedElemRestrictionSetData(CeedElemRestriction rstr, void *data) {
  rstr->data = data;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Increment the reference counter for a CeedElemRestriction

  @param[in,out] rstr ElemRestriction to increment the reference counter

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
**/
int CeedElemRestrictionReference(CeedElemRestriction rstr) {
  rstr->ref_count++;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Estimate number of FLOPs required to apply CeedElemRestriction in t_mode

  @param[in]  rstr   ElemRestriction to estimate FLOPs for
  @param[in]  t_mode Apply restriction or transpose
  @param[out] flops  Address of variable to hold FLOPs estimate

  @ref Backend
**/
int CeedElemRestrictionGetFlopsEstimate(CeedElemRestriction rstr, CeedTransposeMode t_mode, CeedSize *flops) {
  CeedInt             e_size = rstr->num_block * rstr->block_size * rstr->elem_size * rstr->num_comp, scale = 0;
  CeedRestrictionType rstr_type;

  CeedCall(CeedElemRestrictionGetType(rstr, &rstr_type));
  if (rstr_type == CEED_RESTRICTION_POINTS) e_size = rstr->num_points * rstr->num_comp;
  if (t_mode == CEED_TRANSPOSE) {
    switch (rstr_type) {
      case CEED_RESTRICTION_POINTS:
        scale = 0;
        break;
      case CEED_RESTRICTION_STRIDED:
      case CEED_RESTRICTION_STANDARD:
        scale = 1;
        break;
      case CEED_RESTRICTION_ORIENTED:
        scale = 2;
        break;
      case CEED_RESTRICTION_CURL_ORIENTED:
        scale = 6;
        break;
    }
  } else {
    switch (rstr_type) {
      case CEED_RESTRICTION_STRIDED:
      case CEED_RESTRICTION_STANDARD:
      case CEED_RESTRICTION_POINTS:
        scale = 0;
        break;
      case CEED_RESTRICTION_ORIENTED:
        scale = 1;
        break;
      case CEED_RESTRICTION_CURL_ORIENTED:
        scale = 5;
        break;
    }
  }
  *flops = e_size * scale;
  return CEED_ERROR_SUCCESS;
}

/// @}

/// @cond DOXYGEN_SKIP
static struct CeedElemRestriction_private ceed_elemrestriction_none;
/// @endcond

/// ----------------------------------------------------------------------------
/// CeedElemRestriction Public API
/// ----------------------------------------------------------------------------
/// @addtogroup CeedElemRestrictionUser
/// @{

/// Indicate that the stride is determined by the backend
const CeedInt CEED_STRIDES_BACKEND[3] = {0};

/// Argument for CeedOperatorSetField indicating that the field does not requre a CeedElemRestriction
const CeedElemRestriction CEED_ELEMRESTRICTION_NONE = &ceed_elemrestriction_none;

/**
  @brief Create a CeedElemRestriction

  @param[in]  ceed        Ceed object where the CeedElemRestriction will be created
  @param[in]  num_elem    Number of elements described in the @a offsets array
  @param[in]  elem_size   Size (number of "nodes") per element
  @param[in]  num_comp    Number of field components per interpolation node (1 for scalar fields)
  @param[in]  comp_stride Stride between components for the same L-vector "node".
                            Data for node i, component j, element k can be found in the L-vector at index offsets[i + k*elem_size] + j*comp_stride.
  @param[in]  l_size      The size of the L-vector.
                            This vector may be larger than the elements and fields given by this restriction.
  @param[in]  mem_type    Memory type of the @a offsets array, see CeedMemType
  @param[in]  copy_mode   Copy mode for the @a offsets array, see CeedCopyMode
  @param[in]  offsets     Array of shape [@a num_elem, @a elem_size].
                            Row i holds the ordered list of the offsets (into the input CeedVector) for the unknowns corresponding to element i, where
0 <= i < @a num_elem. All offsets must be in the range [0, @a l_size - 1].
  @param[out] rstr        Address of the variable where the newly created CeedElemRestriction will be stored

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionCreate(Ceed ceed, CeedInt num_elem, CeedInt elem_size, CeedInt num_comp, CeedInt comp_stride, CeedSize l_size,
                              CeedMemType mem_type, CeedCopyMode copy_mode, const CeedInt *offsets, CeedElemRestriction *rstr) {
  if (!ceed->ElemRestrictionCreate) {
    Ceed delegate;

    CeedCall(CeedGetObjectDelegate(ceed, &delegate, "ElemRestriction"));
    CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement ElemRestrictionCreate");
    CeedCall(CeedElemRestrictionCreate(delegate, num_elem, elem_size, num_comp, comp_stride, l_size, mem_type, copy_mode, offsets, rstr));
    return CEED_ERROR_SUCCESS;
  }

  CeedCheck(num_elem >= 0, ceed, CEED_ERROR_DIMENSION, "Number of elements must be non-negative");
  CeedCheck(elem_size > 0, ceed, CEED_ERROR_DIMENSION, "Element size must be at least 1");
  CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction must have at least 1 component");
  CeedCheck(num_comp == 1 || comp_stride > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction component stride must be at least 1");

  CeedCall(CeedCalloc(1, rstr));
  CeedCall(CeedReferenceCopy(ceed, &(*rstr)->ceed));
  (*rstr)->ref_count   = 1;
  (*rstr)->num_elem    = num_elem;
  (*rstr)->elem_size   = elem_size;
  (*rstr)->num_comp    = num_comp;
  (*rstr)->comp_stride = comp_stride;
  (*rstr)->l_size      = l_size;
  (*rstr)->num_block   = num_elem;
  (*rstr)->block_size  = 1;
  (*rstr)->rstr_type   = CEED_RESTRICTION_STANDARD;
  CeedCall(ceed->ElemRestrictionCreate(mem_type, copy_mode, offsets, NULL, NULL, *rstr));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Create a CeedElemRestriction with orientation signs

  @param[in]  ceed        Ceed object where the CeedElemRestriction will be created
  @param[in]  num_elem    Number of elements described in the @a offsets array
  @param[in]  elem_size   Size (number of "nodes") per element
  @param[in]  num_comp    Number of field components per interpolation node (1 for scalar fields)
  @param[in]  comp_stride Stride between components for the same L-vector "node".
                            Data for node i, component j, element k can be found in the L-vector at index offsets[i + k*elem_size] + j*comp_stride.
  @param[in]  l_size      The size of the L-vector.
                            This vector may be larger than the elements and fields given by this restriction.
  @param[in]  mem_type    Memory type of the @a offsets array, see CeedMemType
  @param[in]  copy_mode   Copy mode for the @a offsets array, see CeedCopyMode
  @param[in]  offsets     Array of shape [@a num_elem, @a elem_size].
                            Row i holds the ordered list of the offsets (into the input CeedVector) for the unknowns corresponding to element i, where
0 <= i < @a num_elem. All offsets must be in the range [0, @a l_size - 1].
  @param[in]  orients     Array of shape [@a num_elem, @a elem_size] with bool false for positively oriented and true to flip the orientation.
  @param[out] rstr        Address of the variable where the newly created CeedElemRestriction will be stored

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionCreateOriented(Ceed ceed, CeedInt num_elem, CeedInt elem_size, CeedInt num_comp, CeedInt comp_stride, CeedSize l_size,
                                      CeedMemType mem_type, CeedCopyMode copy_mode, const CeedInt *offsets, const bool *orients,
                                      CeedElemRestriction *rstr) {
  if (!ceed->ElemRestrictionCreate) {
    Ceed delegate;

    CeedCall(CeedGetObjectDelegate(ceed, &delegate, "ElemRestriction"));
    CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement ElemRestrictionCreate");
    CeedCall(
        CeedElemRestrictionCreateOriented(delegate, num_elem, elem_size, num_comp, comp_stride, l_size, mem_type, copy_mode, offsets, orients, rstr));
    return CEED_ERROR_SUCCESS;
  }

  CeedCheck(num_elem >= 0, ceed, CEED_ERROR_DIMENSION, "Number of elements must be non-negative");
  CeedCheck(elem_size > 0, ceed, CEED_ERROR_DIMENSION, "Element size must be at least 1");
  CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction must have at least 1 component");
  CeedCheck(num_comp == 1 || comp_stride > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction component stride must be at least 1");

  CeedCall(CeedCalloc(1, rstr));
  CeedCall(CeedReferenceCopy(ceed, &(*rstr)->ceed));
  (*rstr)->ref_count   = 1;
  (*rstr)->num_elem    = num_elem;
  (*rstr)->elem_size   = elem_size;
  (*rstr)->num_comp    = num_comp;
  (*rstr)->comp_stride = comp_stride;
  (*rstr)->l_size      = l_size;
  (*rstr)->num_block   = num_elem;
  (*rstr)->block_size  = 1;
  (*rstr)->rstr_type   = CEED_RESTRICTION_ORIENTED;
  CeedCall(ceed->ElemRestrictionCreate(mem_type, copy_mode, offsets, orients, NULL, *rstr));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Create a CeedElemRestriction with a general tridiagonal transformation matrix for curl-conforming elements

  @param[in]  ceed         Ceed object where the CeedElemRestriction will be created
  @param[in]  num_elem     Number of elements described in the @a offsets array
  @param[in]  elem_size    Size (number of "nodes") per element
  @param[in]  num_comp     Number of field components per interpolation node (1 for scalar fields)
  @param[in]  comp_stride  Stride between components for the same L-vector "node".
                             Data for node i, component j, element k can be found in the L-vector at index offsets[i + k*elem_size] + j*comp_stride.
  @param[in]  l_size       The size of the L-vector.
                             This vector may be larger than the elements and fields given by this restriction.
  @param[in]  mem_type     Memory type of the @a offsets array, see CeedMemType
  @param[in]  copy_mode    Copy mode for the @a offsets array, see CeedCopyMode
  @param[in]  offsets      Array of shape [@a num_elem, @a elem_size].
                             Row i holds the ordered list of the offsets (into the input CeedVector) for the unknowns corresponding to element i,
where 0 <= i < @a num_elem. All offsets must be in the range [0, @a l_size - 1].
  @param[in]  curl_orients Array of shape [@a num_elem, @a 3 * elem_size] representing a row-major tridiagonal matrix (curl_orients[i * 3 * elem_size]
= curl_orients[(i + 1) * 3 * elem_size - 1] = 0, where 0 <= i < @a num_elem) which is applied to the element unknowns upon restriction. This
orientation matrix allows for pairs of face degrees of freedom on elements for H(curl) spaces to be coupled in the element restriction operation,
which is a way to resolve face orientation issues for 3D meshes (https://dl.acm.org/doi/pdf/10.1145/3524456).
  @param[out] rstr         Address of the variable where the newly created CeedElemRestriction will be stored

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionCreateCurlOriented(Ceed ceed, CeedInt num_elem, CeedInt elem_size, CeedInt num_comp, CeedInt comp_stride, CeedSize l_size,
                                          CeedMemType mem_type, CeedCopyMode copy_mode, const CeedInt *offsets, const CeedInt8 *curl_orients,
                                          CeedElemRestriction *rstr) {
  if (!ceed->ElemRestrictionCreate) {
    Ceed delegate;

    CeedCall(CeedGetObjectDelegate(ceed, &delegate, "ElemRestriction"));
    CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement ElemRestrictionCreate");
    CeedCall(CeedElemRestrictionCreateCurlOriented(delegate, num_elem, elem_size, num_comp, comp_stride, l_size, mem_type, copy_mode, offsets,
                                                   curl_orients, rstr));
    return CEED_ERROR_SUCCESS;
  }

  CeedCheck(num_elem >= 0, ceed, CEED_ERROR_DIMENSION, "Number of elements must be non-negative");
  CeedCheck(elem_size > 0, ceed, CEED_ERROR_DIMENSION, "Element size must be at least 1");
  CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction must have at least 1 component");
  CeedCheck(num_comp == 1 || comp_stride > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction component stride must be at least 1");

  CeedCall(CeedCalloc(1, rstr));
  CeedCall(CeedReferenceCopy(ceed, &(*rstr)->ceed));
  (*rstr)->ref_count   = 1;
  (*rstr)->num_elem    = num_elem;
  (*rstr)->elem_size   = elem_size;
  (*rstr)->num_comp    = num_comp;
  (*rstr)->comp_stride = comp_stride;
  (*rstr)->l_size      = l_size;
  (*rstr)->num_block   = num_elem;
  (*rstr)->block_size  = 1;
  (*rstr)->rstr_type   = CEED_RESTRICTION_CURL_ORIENTED;
  CeedCall(ceed->ElemRestrictionCreate(mem_type, copy_mode, offsets, NULL, curl_orients, *rstr));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Create a strided CeedElemRestriction

  @param[in]  ceed      Ceed object where the CeedElemRestriction will be created
  @param[in]  num_elem  Number of elements described by the restriction
  @param[in]  elem_size Size (number of "nodes") per element
  @param[in]  num_comp  Number of field components per interpolation "node" (1 for scalar fields)
  @param[in]  l_size    The size of the L-vector.
                          This vector may be larger than the elements and fields given by this restriction.
  @param[in]  strides   Array for strides between [nodes, components, elements].
                          Data for node i, component j, element k can be found in the L-vector at index i*strides[0] + j*strides[1] + k*strides[2].
                          @a CEED_STRIDES_BACKEND may be used with vectors created by a Ceed backend.
  @param[out] rstr      Address of the variable where the newly created CeedElemRestriction will be stored

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionCreateStrided(Ceed ceed, CeedInt num_elem, CeedInt elem_size, CeedInt num_comp, CeedSize l_size, const CeedInt strides[3],
                                     CeedElemRestriction *rstr) {
  if (!ceed->ElemRestrictionCreate) {
    Ceed delegate;

    CeedCall(CeedGetObjectDelegate(ceed, &delegate, "ElemRestriction"));
    CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement ElemRestrictionCreate");
    CeedCall(CeedElemRestrictionCreateStrided(delegate, num_elem, elem_size, num_comp, l_size, strides, rstr));
    return CEED_ERROR_SUCCESS;
  }

  CeedCheck(num_elem >= 0, ceed, CEED_ERROR_DIMENSION, "Number of elements must be non-negative");
  CeedCheck(elem_size > 0, ceed, CEED_ERROR_DIMENSION, "Element size must be at least 1");
  CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction must have at least 1 component");
  CeedCheck(l_size >= num_elem * elem_size * num_comp, ceed, CEED_ERROR_DIMENSION, "L-vector size must be at least num_elem * elem_size * num_comp");

  CeedCall(CeedCalloc(1, rstr));
  CeedCall(CeedReferenceCopy(ceed, &(*rstr)->ceed));
  (*rstr)->ref_count  = 1;
  (*rstr)->num_elem   = num_elem;
  (*rstr)->elem_size  = elem_size;
  (*rstr)->num_comp   = num_comp;
  (*rstr)->l_size     = l_size;
  (*rstr)->num_block  = num_elem;
  (*rstr)->block_size = 1;
  (*rstr)->rstr_type  = CEED_RESTRICTION_STRIDED;
  CeedCall(CeedMalloc(3, &(*rstr)->strides));
  for (CeedInt i = 0; i < 3; i++) (*rstr)->strides[i] = strides[i];
  CeedCall(ceed->ElemRestrictionCreate(CEED_MEM_HOST, CEED_OWN_POINTER, NULL, NULL, NULL, *rstr));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Create a points CeedElemRestriction, for restricting for restricting from a all local points to the current element in which they are
 located.

  The offsets array is arranged as

  element_0_start_index
  element_1_start_index
  ...
  element_n_start_index
  element_n_stop_index
  element_0_point_0
  element_0_point_1
  ...

  @param[in]  ceed          Ceed object where the CeedElemRestriction will be created
  @param[in]  num_elem      Number of elements described in the @a offsets array
  @param[in]  num_points    Number of points described in the @a offsets array
  @param[in]  num_comp      Number of field components per interpolation node (1 for scalar fields).
                              Components are assumed to be contiguous by point.
  @param[in]  l_size        The size of the L-vector.
                              This vector may be larger than the elements and fields given by this restriction.
  @param[in]  mem_type      Memory type of the @a offsets array, see CeedMemType
  @param[in]  copy_mode     Copy mode for the @a offsets array, see CeedCopyMode
  @param[in]  offsets       Array of size num_elem + 1 + num_points.
                              The first portion of the offsets array holds the ranges of indices corresponding to each element.
                              The second portion holds the indices for each element.
  @param[out] rstr          Address of the variable where the newly created CeedElemRestriction will be stored

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
 **/
int CeedElemRestrictionCreateAtPoints(Ceed ceed, CeedInt num_elem, CeedInt num_points, CeedInt num_comp, CeedSize l_size, CeedMemType mem_type,
                                CeedCopyMode copy_mode, const CeedInt *offsets, CeedElemRestriction *rstr) {
  if (!ceed->ElemRestrictionCreateAtPoints) {
    Ceed delegate;

    CeedCall(CeedGetObjectDelegate(ceed, &delegate, "ElemRestriction"));
    CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement ElemRestrictionCreateAtPoints");
    CeedCall(CeedElemRestrictionCreateAtPoints(delegate, num_elem, num_points, num_comp, l_size, mem_type, copy_mode, offsets, rstr));
    return CEED_ERROR_SUCCESS;
  }

  CeedCheck(num_elem >= 0, ceed, CEED_ERROR_DIMENSION, "Number of elements must be non-negative");
  CeedCheck(num_points >= 0, ceed, CEED_ERROR_DIMENSION, "Number of points must be non-negative");
  CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction must have at least 1 component");
  CeedCheck(l_size >= num_points * num_comp, ceed, CEED_ERROR_DIMENSION, "L-vector must be at least num_points * num_comp");

  CeedCall(CeedCalloc(1, rstr));
  CeedCall(CeedReferenceCopy(ceed, &(*rstr)->ceed));
  (*rstr)->ref_count  = 1;
  (*rstr)->num_elem   = num_elem;
  (*rstr)->num_points = num_points;
  (*rstr)->num_comp   = num_comp;
  (*rstr)->l_size     = l_size;
  (*rstr)->block_size = 1;
  (*rstr)->rstr_type  = CEED_RESTRICTION_POINTS;
  CeedCall(ceed->ElemRestrictionCreateAtPoints(mem_type, copy_mode, offsets, NULL, NULL, *rstr));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Create a blocked CeedElemRestriction, typically only called by backends

  @param[in]  ceed          Ceed object where the CeedElemRestriction will be created
  @param[in]  num_elem      Number of elements described in the @a offsets array
  @param[in]  elem_size     Size (number of unknowns) per element
  @param[in]  block_size    Number of elements in a block
  @param[in]  num_comp      Number of field components per interpolation node (1 for scalar fields)
  @param[in]  comp_stride   Stride between components for the same L-vector "node".
                              Data for node i, component j, element k can be found in the L-vector at index offsets[i + k*elem_size] + j*comp_stride.
  @param[in]  l_size        The size of the L-vector.
                              This vector may be larger than the elements and fields given by this restriction.
  @param[in]  mem_type      Memory type of the @a offsets array, see CeedMemType
  @param[in]  copy_mode     Copy mode for the @a offsets array, see CeedCopyMode
  @param[in]  offsets       Array of shape [@a num_elem, @a elem_size].
                              Row i holds the ordered list of the offsets (into the input CeedVector) for the unknowns corresponding to element i,
 where 0 <= i < @a num_elem. All offsets must be in the range [0, @a l_size - 1]. The backend will permute and pad this array to the desired ordering
 for the blocksize, which is typically given by the backend. The default reordering is to interlace elements.
  @param[out] rstr          Address of the variable where the newly created CeedElemRestriction will be stored

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
 **/
int CeedElemRestrictionCreateBlocked(Ceed ceed, CeedInt num_elem, CeedInt elem_size, CeedInt block_size, CeedInt num_comp, CeedInt comp_stride,
                                     CeedSize l_size, CeedMemType mem_type, CeedCopyMode copy_mode, const CeedInt *offsets,
                                     CeedElemRestriction *rstr) {
  CeedInt *block_offsets, num_block = (num_elem / block_size) + !!(num_elem % block_size);

  if (!ceed->ElemRestrictionCreateBlocked) {
    Ceed delegate;

    CeedCall(CeedGetObjectDelegate(ceed, &delegate, "ElemRestriction"));
    CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement ElemRestrictionCreateBlocked");
    CeedCall(CeedElemRestrictionCreateBlocked(delegate, num_elem, elem_size, block_size, num_comp, comp_stride, l_size, mem_type, copy_mode, offsets,
                                              rstr));
    return CEED_ERROR_SUCCESS;
  }

  CeedCheck(num_elem >= 0, ceed, CEED_ERROR_DIMENSION, "Number of elements must be non-negative");
  CeedCheck(elem_size > 0, ceed, CEED_ERROR_DIMENSION, "Element size must be at least 1");
  CeedCheck(block_size > 0, ceed, CEED_ERROR_DIMENSION, "Block size must be at least 1");
  CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction must have at least 1 component");
  CeedCheck(num_comp == 1 || comp_stride > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction component stride must be at least 1");

  CeedCall(CeedCalloc(num_block * block_size * elem_size, &block_offsets));
  CeedCall(CeedPermutePadOffsets(offsets, block_offsets, num_block, num_elem, block_size, elem_size));

  CeedCall(CeedCalloc(1, rstr));
  CeedCall(CeedReferenceCopy(ceed, &(*rstr)->ceed));
  (*rstr)->ref_count   = 1;
  (*rstr)->num_elem    = num_elem;
  (*rstr)->elem_size   = elem_size;
  (*rstr)->num_comp    = num_comp;
  (*rstr)->comp_stride = comp_stride;
  (*rstr)->l_size      = l_size;
  (*rstr)->num_block   = num_block;
  (*rstr)->block_size  = block_size;
  (*rstr)->rstr_type   = CEED_RESTRICTION_STANDARD;
  CeedCall(ceed->ElemRestrictionCreateBlocked(CEED_MEM_HOST, CEED_OWN_POINTER, (const CeedInt *)block_offsets, NULL, NULL, *rstr));
  if (copy_mode == CEED_OWN_POINTER) CeedCall(CeedFree(&offsets));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Create a blocked oriented CeedElemRestriction, typically only called by backends

  @param[in]  ceed          Ceed object where the CeedElemRestriction will be created.
  @param[in]  num_elem      Number of elements described in the @a offsets array.
  @param[in]  elem_size     Size (number of unknowns) per element
  @param[in]  block_size    Number of elements in a block
  @param[in]  num_comp      Number of field components per interpolation node (1 for scalar fields)
  @param[in]  comp_stride   Stride between components for the same L-vector "node".
                              Data for node i, component j, element k can be found in the L-vector at index offsets[i + k*elem_size] + j*comp_stride.
  @param[in]  l_size        The size of the L-vector.
                              This vector may be larger than the elements and fields given by this restriction.
  @param[in]  mem_type      Memory type of the @a offsets array, see CeedMemType
  @param[in]  copy_mode     Copy mode for the @a offsets array, see CeedCopyMode
  @param[in]  offsets       Array of shape [@a num_elem, @a elem_size].
                            Row i holds the ordered list of the offsets (into the input CeedVector) for the unknowns corresponding to element i, where
 0 <= i < @a num_elem. All offsets must be in the range [0, @a l_size - 1]. The backend will permute and pad this array to the desired ordering for
 the blocksize, which is typically given by the backend. The default reordering is to interlace elements.
  @param[in]  orients       Array of shape [@a num_elem, @a elem_size] with bool false for positively oriented and true to flip the orientation.
                              Will also be permuted and padded similarly to @a offsets.
  @param[out] rstr          Address of the variable where the newly created CeedElemRestriction will be stored

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
 **/
int CeedElemRestrictionCreateBlockedOriented(Ceed ceed, CeedInt num_elem, CeedInt elem_size, CeedInt block_size, CeedInt num_comp,
                                             CeedInt comp_stride, CeedSize l_size, CeedMemType mem_type, CeedCopyMode copy_mode,
                                             const CeedInt *offsets, const bool *orients, CeedElemRestriction *rstr) {
  bool    *block_orients;
  CeedInt *block_offsets, num_block = (num_elem / block_size) + !!(num_elem % block_size);

  if (!ceed->ElemRestrictionCreateBlocked) {
    Ceed delegate;

    CeedCall(CeedGetObjectDelegate(ceed, &delegate, "ElemRestriction"));
    CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement ElemRestrictionCreateBlocked");
    CeedCall(CeedElemRestrictionCreateBlockedOriented(delegate, num_elem, elem_size, block_size, num_comp, comp_stride, l_size, mem_type, copy_mode,
                                                      offsets, orients, rstr));
    return CEED_ERROR_SUCCESS;
  }

  CeedCheck(elem_size > 0, ceed, CEED_ERROR_DIMENSION, "Element size must be at least 1");
  CeedCheck(block_size > 0, ceed, CEED_ERROR_DIMENSION, "Block size must be at least 1");
  CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction must have at least 1 component");
  CeedCheck(num_comp == 1 || comp_stride > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction component stride must be at least 1");

  CeedCall(CeedCalloc(num_block * block_size * elem_size, &block_offsets));
  CeedCall(CeedCalloc(num_block * block_size * elem_size, &block_orients));
  CeedCall(CeedPermutePadOffsets(offsets, block_offsets, num_block, num_elem, block_size, elem_size));
  CeedCall(CeedPermutePadOrients(orients, block_orients, num_block, num_elem, block_size, elem_size));

  CeedCall(CeedCalloc(1, rstr));
  CeedCall(CeedReferenceCopy(ceed, &(*rstr)->ceed));
  (*rstr)->ref_count   = 1;
  (*rstr)->num_elem    = num_elem;
  (*rstr)->elem_size   = elem_size;
  (*rstr)->num_comp    = num_comp;
  (*rstr)->comp_stride = comp_stride;
  (*rstr)->l_size      = l_size;
  (*rstr)->num_block   = num_block;
  (*rstr)->block_size  = block_size;
  (*rstr)->rstr_type   = CEED_RESTRICTION_ORIENTED;
  CeedCall(
      ceed->ElemRestrictionCreateBlocked(CEED_MEM_HOST, CEED_OWN_POINTER, (const CeedInt *)block_offsets, (const bool *)block_orients, NULL, *rstr));
  if (copy_mode == CEED_OWN_POINTER) CeedCall(CeedFree(&offsets));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Create a blocked curl-oriented CeedElemRestriction, typically only called by backends

  @param[in]  ceed           Ceed object where the CeedElemRestriction will be created.
  @param[in]  num_elem       Number of elements described in the @a offsets array.
  @param[in]  elem_size      Size (number of unknowns) per element
  @param[in]  block_size     Number of elements in a block
  @param[in]  num_comp       Number of field components per interpolation node (1 for scalar fields)
  @param[in]  comp_stride    Stride between components for the same L-vector "node".
                               Data for node i, component j, element k can be found in the L-vector at index offsets[i + k*elem_size] + j*comp_stride.
  @param[in]  l_size         The size of the L-vector.
                               This vector may be larger than the elements and fields given by this restriction.
  @param[in]  mem_type       Memory type of the @a offsets array, see CeedMemType
  @param[in]  copy_mode      Copy mode for the @a offsets array, see CeedCopyMode
  @param[in]  offsets        Array of shape [@a num_elem, @a elem_size].
                             Row i holds the ordered list of the offsets (into the input CeedVector) for the unknowns corresponding to element i,
where 0 <= i < @a num_elem. All offsets must be in the range [0, @a l_size - 1]. The backend will permute and pad this array to the desired ordering
for the blocksize, which is typically given by the backend. The default reordering is to interlace elements.
  @param[in]  curl_orients Array of shape [@a num_elem, @a 3 * elem_size] representing a row-major tridiagonal matrix (curl_orients[i * 3 * elem_size]
= curl_orients[(i + 1) * 3 * elem_size - 1] = 0, where 0 <= i < @a num_elem) which is applied to the element unknowns upon restriction. This
orientation matrix allows for pairs of face degrees of freedom on elements for H(curl) spaces to be coupled in the element restriction operation,
which is a way to resolve face orientation issues for 3D meshes (https://dl.acm.org/doi/pdf/10.1145/3524456). Will also be permuted and padded
similarly to @a offsets.
  @param[out] rstr           Address of the variable where the newly created CeedElemRestriction will be stored

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
 **/
int CeedElemRestrictionCreateBlockedCurlOriented(Ceed ceed, CeedInt num_elem, CeedInt elem_size, CeedInt block_size, CeedInt num_comp,
                                                 CeedInt comp_stride, CeedSize l_size, CeedMemType mem_type, CeedCopyMode copy_mode,
                                                 const CeedInt *offsets, const CeedInt8 *curl_orients, CeedElemRestriction *rstr) {
  CeedInt8 *block_curl_orients;
  CeedInt  *block_offsets, num_block = (num_elem / block_size) + !!(num_elem % block_size);

  if (!ceed->ElemRestrictionCreateBlocked) {
    Ceed delegate;

    CeedCall(CeedGetObjectDelegate(ceed, &delegate, "ElemRestriction"));
    CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement ElemRestrictionCreateBlocked");
    CeedCall(CeedElemRestrictionCreateBlockedCurlOriented(delegate, num_elem, elem_size, block_size, num_comp, comp_stride, l_size, mem_type,
                                                          copy_mode, offsets, curl_orients, rstr));
    return CEED_ERROR_SUCCESS;
  }

  CeedCheck(num_elem >= 0, ceed, CEED_ERROR_DIMENSION, "Number of elements must be non-negative");
  CeedCheck(elem_size > 0, ceed, CEED_ERROR_DIMENSION, "Element size must be at least 1");
  CeedCheck(block_size > 0, ceed, CEED_ERROR_DIMENSION, "Block size must be at least 1");
  CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction must have at least 1 component");
  CeedCheck(num_comp == 1 || comp_stride > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction component stride must be at least 1");

  CeedCall(CeedCalloc(num_block * block_size * elem_size, &block_offsets));
  CeedCall(CeedCalloc(num_block * block_size * 3 * elem_size, &block_curl_orients));
  CeedCall(CeedPermutePadOffsets(offsets, block_offsets, num_block, num_elem, block_size, elem_size));
  CeedCall(CeedPermutePadCurlOrients(curl_orients, block_curl_orients, num_block, num_elem, block_size, 3 * elem_size));

  CeedCall(CeedCalloc(1, rstr));
  CeedCall(CeedReferenceCopy(ceed, &(*rstr)->ceed));
  (*rstr)->ref_count   = 1;
  (*rstr)->num_elem    = num_elem;
  (*rstr)->elem_size   = elem_size;
  (*rstr)->num_comp    = num_comp;
  (*rstr)->comp_stride = comp_stride;
  (*rstr)->l_size      = l_size;
  (*rstr)->num_block   = num_block;
  (*rstr)->block_size  = block_size;
  (*rstr)->rstr_type   = CEED_RESTRICTION_CURL_ORIENTED;
  CeedCall(ceed->ElemRestrictionCreateBlocked(CEED_MEM_HOST, CEED_OWN_POINTER, (const CeedInt *)block_offsets, NULL,
                                              (const CeedInt8 *)block_curl_orients, *rstr));
  if (copy_mode == CEED_OWN_POINTER) CeedCall(CeedFree(&offsets));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Create a blocked strided CeedElemRestriction, typically only called by backends

  @param[in]  ceed        Ceed object where the CeedElemRestriction will be created
  @param[in]  num_elem    Number of elements described by the restriction
  @param[in]  elem_size   Size (number of "nodes") per element
  @param[in]  block_size  Number of elements in a block
  @param[in]  num_comp    Number of field components per interpolation node (1 for scalar fields)
  @param[in]  l_size      The size of the L-vector.
                            This vector may be larger than the elements and fields given by this restriction.
  @param[in]  strides     Array for strides between [nodes, components, elements].
                            Data for node i, component j, element k can be found in the L-vector at index i*strides[0] + j*strides[1] + k*strides[2].
                            @a CEED_STRIDES_BACKEND may be used with vectors created by a Ceed backend.
  @param[out] rstr        Address of the variable where the newly created CeedElemRestriction will be stored

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionCreateBlockedStrided(Ceed ceed, CeedInt num_elem, CeedInt elem_size, CeedInt block_size, CeedInt num_comp, CeedSize l_size,
                                            const CeedInt strides[3], CeedElemRestriction *rstr) {
  CeedInt num_block = (num_elem / block_size) + !!(num_elem % block_size);

  if (!ceed->ElemRestrictionCreateBlocked) {
    Ceed delegate;

    CeedCall(CeedGetObjectDelegate(ceed, &delegate, "ElemRestriction"));
    CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement ElemRestrictionCreateBlocked");
    CeedCall(CeedElemRestrictionCreateBlockedStrided(delegate, num_elem, elem_size, block_size, num_comp, l_size, strides, rstr));
    return CEED_ERROR_SUCCESS;
  }

  CeedCheck(num_elem >= 0, ceed, CEED_ERROR_DIMENSION, "Number of elements must be non-negative");
  CeedCheck(elem_size > 0, ceed, CEED_ERROR_DIMENSION, "Element size must be at least 1");
  CeedCheck(block_size > 0, ceed, CEED_ERROR_DIMENSION, "Block size must be at least 1");
  CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "ElemRestriction must have at least 1 component");
  CeedCheck(l_size >= num_elem * elem_size * num_comp, ceed, CEED_ERROR_DIMENSION, "L-vector size must be at least num_elem * elem_size * num_comp");

  CeedCall(CeedCalloc(1, rstr));
  CeedCall(CeedReferenceCopy(ceed, &(*rstr)->ceed));
  (*rstr)->ref_count  = 1;
  (*rstr)->num_elem   = num_elem;
  (*rstr)->elem_size  = elem_size;
  (*rstr)->num_comp   = num_comp;
  (*rstr)->l_size     = l_size;
  (*rstr)->num_block  = num_block;
  (*rstr)->block_size = block_size;
  (*rstr)->rstr_type  = CEED_RESTRICTION_STRIDED;
  CeedCall(CeedMalloc(3, &(*rstr)->strides));
  for (CeedInt i = 0; i < 3; i++) (*rstr)->strides[i] = strides[i];
  CeedCall(ceed->ElemRestrictionCreateBlocked(CEED_MEM_HOST, CEED_OWN_POINTER, NULL, NULL, NULL, *rstr));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Copy the pointer to a CeedElemRestriction and set `CeedElemRestrictionApply()` implementation to use the unsigned version.

  Both pointers should be destroyed with `CeedElemRestrictionDestroy()`.

  @param[in]     rstr          CeedElemRestriction to create unsigned reference to
  @param[in,out] rstr_unsigned Variable to store unsigned CeedElemRestriction

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionCreateUnsignedCopy(CeedElemRestriction rstr, CeedElemRestriction *rstr_unsigned) {
  CeedCall(CeedCalloc(1, rstr_unsigned));

  // Copy old rstr
  memcpy(*rstr_unsigned, rstr, sizeof(struct CeedElemRestriction_private));
  (*rstr_unsigned)->ceed = NULL;
  CeedCall(CeedReferenceCopy(rstr->ceed, &(*rstr_unsigned)->ceed));
  (*rstr_unsigned)->ref_count = 1;
  (*rstr_unsigned)->strides   = NULL;
  if (rstr->strides) {
    CeedCall(CeedMalloc(3, &(*rstr_unsigned)->strides));
    for (CeedInt i = 0; i < 3; i++) (*rstr_unsigned)->strides[i] = rstr->strides[i];
  }
  CeedCall(CeedElemRestrictionReferenceCopy(rstr, &(*rstr_unsigned)->rstr_base));

  // Override Apply
  (*rstr_unsigned)->Apply = rstr->ApplyUnsigned;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Copy the pointer to a CeedElemRestriction and set `CeedElemRestrictionApply()` implementation to use the unoriented version.

  Both pointers should be destroyed with `CeedElemRestrictionDestroy()`.

  @param[in]     rstr            CeedElemRestriction to create unoriented reference to
  @param[in,out] rstr_unoriented Variable to store unoriented CeedElemRestriction

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionCreateUnorientedCopy(CeedElemRestriction rstr, CeedElemRestriction *rstr_unoriented) {
  CeedCall(CeedCalloc(1, rstr_unoriented));

  // Copy old rstr
  memcpy(*rstr_unoriented, rstr, sizeof(struct CeedElemRestriction_private));
  (*rstr_unoriented)->ceed = NULL;
  CeedCall(CeedReferenceCopy(rstr->ceed, &(*rstr_unoriented)->ceed));
  (*rstr_unoriented)->ref_count = 1;
  (*rstr_unoriented)->strides   = NULL;
  if (rstr->strides) {
    CeedCall(CeedMalloc(3, &(*rstr_unoriented)->strides));
    for (CeedInt i = 0; i < 3; i++) (*rstr_unoriented)->strides[i] = rstr->strides[i];
  }
  CeedCall(CeedElemRestrictionReferenceCopy(rstr, &(*rstr_unoriented)->rstr_base));

  // Override Apply
  (*rstr_unoriented)->Apply = rstr->ApplyUnoriented;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Copy the pointer to a CeedElemRestriction.

  Both pointers should be destroyed with `CeedElemRestrictionDestroy()`.

  Note: If the value of `rstr_copy` passed into this function is non-NULL, then it is assumed that `rstr_copy` is a pointer to a CeedElemRestriction.
        This CeedElemRestriction will be destroyed if `rstr_copy` is the only reference to this CeedElemRestriction.

  @param[in]     rstr      CeedElemRestriction to copy reference to
  @param[in,out] rstr_copy Variable to store copied reference

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionReferenceCopy(CeedElemRestriction rstr, CeedElemRestriction *rstr_copy) {
  if (rstr != CEED_ELEMRESTRICTION_NONE) CeedCall(CeedElemRestrictionReference(rstr));
  CeedCall(CeedElemRestrictionDestroy(rstr_copy));
  *rstr_copy = rstr;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Create CeedVectors associated with a CeedElemRestriction

  @param[in]  rstr  CeedElemRestriction
  @param[out] l_vec The address of the L-vector to be created, or NULL
  @param[out] e_vec The address of the E-vector to be created, or NULL

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionCreateVector(CeedElemRestriction rstr, CeedVector *l_vec, CeedVector *e_vec) {
  CeedSize e_size, l_size;
  l_size = rstr->l_size;
  e_size = rstr->num_block * rstr->block_size * rstr->elem_size * rstr->num_comp;
  if (l_vec) CeedCall(CeedVectorCreate(rstr->ceed, l_size, l_vec));
  if (e_vec) CeedCall(CeedVectorCreate(rstr->ceed, e_size, e_vec));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Restrict an L-vector to an E-vector or apply its transpose

  @param[in]  rstr    CeedElemRestriction
  @param[in]  t_mode  Apply restriction or transpose
  @param[in]  u       Input vector (of size @a l_size when t_mode=@ref CEED_NOTRANSPOSE)
  @param[out] ru      Output vector (of shape [@a num_elem * @a elem_size] when t_mode=@ref CEED_NOTRANSPOSE).
                        Ordering of the e-vector is decided by the backend.
  @param[in]  request Request or @ref CEED_REQUEST_IMMEDIATE

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionApply(CeedElemRestriction rstr, CeedTransposeMode t_mode, CeedVector u, CeedVector ru, CeedRequest *request) {
  CeedInt m, n;

  if (t_mode == CEED_NOTRANSPOSE) {
    m = rstr->num_block * rstr->block_size * rstr->elem_size * rstr->num_comp;
    n = rstr->l_size;
  } else {
    m = rstr->l_size;
    n = rstr->num_block * rstr->block_size * rstr->elem_size * rstr->num_comp;
  }
  CeedCheck(n == u->length, rstr->ceed, CEED_ERROR_DIMENSION,
            "Input vector size %" CeedInt_FMT " not compatible with element restriction (%" CeedInt_FMT ", %" CeedInt_FMT ")", u->length, m, n);
  CeedCheck(m == ru->length, rstr->ceed, CEED_ERROR_DIMENSION,
            "Output vector size %" CeedInt_FMT " not compatible with element restriction (%" CeedInt_FMT ", %" CeedInt_FMT ")", ru->length, m, n);
  if (rstr->num_elem > 0) CeedCall(rstr->Apply(rstr, t_mode, u, ru, request));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Restrict an L-vector of points to a single element or apply its transpose

  @param[in]  rstr    CeedElemRestriction
  @param[in]  t_mode  Apply restriction or transpose
  @param[in]  u       Input vector (of size @a l_size when t_mode=@ref CEED_NOTRANSPOSE)
  @param[out] ru      Output vector (of shape [@a num_elem * @a elem_size] when t_mode=@ref CEED_NOTRANSPOSE).
                        Ordering of the e-vector is decided by the backend.
  @param[in]  request Request or @ref CEED_REQUEST_IMMEDIATE

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionApplyAtPoints(CeedElemRestriction rstr, CeedInt elem, CeedTransposeMode t_mode, CeedVector u, CeedVector ru,
                                     CeedRequest *request) {
  CeedInt m, n;

  if (t_mode == CEED_NOTRANSPOSE) {
    CeedCall(CeedElemRestrictionGetNumPointsInElement(rstr, elem, &m));
    n = rstr->l_size;
  } else {
    m = rstr->l_size;
    CeedCall(CeedElemRestrictionGetNumPointsInElement(rstr, elem, &n));
  }
  CeedCheck(n <= u->length, rstr->ceed, CEED_ERROR_DIMENSION,
            "Input vector size %" CeedInt_FMT " not compatible with element restriction (%" CeedInt_FMT ", %" CeedInt_FMT
            ") for element %" CeedInt_FMT,
            u->length, m, n, elem);
  CeedCheck(m <= ru->length, rstr->ceed, CEED_ERROR_DIMENSION,
            "Output vector size %" CeedInt_FMT " not compatible with element restriction (%" CeedInt_FMT ", %" CeedInt_FMT
            ") for element %" CeedInt_FMT,
            ru->length, m, n, elem);
  CeedCheck(elem <= rstr->num_elem, rstr->ceed, CEED_ERROR_DIMENSION,
            "Cannot retrieve element %" CeedInt_FMT ", element %" CeedInt_FMT " > total elements %" CeedInt_FMT "", elem, elem, rstr->num_elem);
  if (rstr->num_elem > 0) CeedCall(rstr->ApplyAtPoints(rstr, elem, t_mode, u, ru, request));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Restrict an L-vector to a block of an E-vector or apply its transpose

  @param[in]  rstr    CeedElemRestriction
  @param[in]  block   Block number to restrict to/from, i.e. block=0 will handle elements [0 : block_size] and block=3 will handle elements
[3*block_size : 4*block_size]
  @param[in]  t_mode  Apply restriction or transpose
  @param[in]  u       Input vector (of size @a l_size when t_mode=@ref CEED_NOTRANSPOSE)
  @param[out] ru      Output vector (of shape [@a block_size * @a elem_size] when t_mode=@ref CEED_NOTRANSPOSE).
                        Ordering of the e-vector is decided by the backend.
  @param[in]  request Request or @ref CEED_REQUEST_IMMEDIATE

  @return An error code: 0 - success, otherwise - failure

  @ref Backend
**/
int CeedElemRestrictionApplyBlock(CeedElemRestriction rstr, CeedInt block, CeedTransposeMode t_mode, CeedVector u, CeedVector ru,
                                  CeedRequest *request) {
  CeedInt m, n;

  CeedCheck(rstr->ApplyBlock, rstr->ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement ElemRestrictionApplyBlock");

  if (t_mode == CEED_NOTRANSPOSE) {
    m = rstr->block_size * rstr->elem_size * rstr->num_comp;
    n = rstr->l_size;
  } else {
    m = rstr->l_size;
    n = rstr->block_size * rstr->elem_size * rstr->num_comp;
  }
  CeedCheck(n == u->length, rstr->ceed, CEED_ERROR_DIMENSION,
            "Input vector size %" CeedInt_FMT " not compatible with element restriction (%" CeedInt_FMT ", %" CeedInt_FMT ")", u->length, m, n);
  CeedCheck(m == ru->length, rstr->ceed, CEED_ERROR_DIMENSION,
            "Output vector size %" CeedInt_FMT " not compatible with element restriction (%" CeedInt_FMT ", %" CeedInt_FMT ")", ru->length, m, n);
  CeedCheck(rstr->block_size * block <= rstr->num_elem, rstr->ceed, CEED_ERROR_DIMENSION,
            "Cannot retrieve block %" CeedInt_FMT ", element %" CeedInt_FMT " > total elements %" CeedInt_FMT "", block, rstr->block_size * block,
            rstr->num_elem);
  CeedCall(rstr->ApplyBlock(rstr, block, t_mode, u, ru, request));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the Ceed associated with a CeedElemRestriction

  @param[in]  rstr CeedElemRestriction
  @param[out] ceed Variable to store Ceed

  @return An error code: 0 - success, otherwise - failure

  @ref Advanced
**/
int CeedElemRestrictionGetCeed(CeedElemRestriction rstr, Ceed *ceed) {
  *ceed = rstr->ceed;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the L-vector component stride

  @param[in]  rstr        CeedElemRestriction
  @param[out] comp_stride Variable to store component stride

  @return An error code: 0 - success, otherwise - failure

  @ref Advanced
**/
int CeedElemRestrictionGetCompStride(CeedElemRestriction rstr, CeedInt *comp_stride) {
  *comp_stride = rstr->comp_stride;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the total number of elements in the range of a CeedElemRestriction

  @param[in] rstr      CeedElemRestriction
  @param[out] num_elem Variable to store number of elements

  @return An error code: 0 - success, otherwise - failure

  @ref Advanced
**/
int CeedElemRestrictionGetNumElements(CeedElemRestriction rstr, CeedInt *num_elem) {
  *num_elem = rstr->num_elem;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the size of elements in the CeedElemRestriction

  @param[in]  rstr      CeedElemRestriction
  @param[out] elem_size Variable to store size of elements

  @return An error code: 0 - success, otherwise - failure

  @ref Advanced
**/
int CeedElemRestrictionGetElementSize(CeedElemRestriction rstr, CeedInt *elem_size) {
  *elem_size = rstr->elem_size;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the size of the l-vector for a CeedElemRestriction

  @param[in]  rstr   CeedElemRestriction
  @param[out] l_size Variable to store number of nodes

  @return An error code: 0 - success, otherwise - failure

  @ref Advanced
**/
int CeedElemRestrictionGetLVectorSize(CeedElemRestriction rstr, CeedSize *l_size) {
  *l_size = rstr->l_size;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the number of components in the elements of a CeedElemRestriction

  @param[in]  rstr     CeedElemRestriction
  @param[out] num_comp Variable to store number of components

  @return An error code: 0 - success, otherwise - failure

  @ref Advanced
**/
int CeedElemRestrictionGetNumComponents(CeedElemRestriction rstr, CeedInt *num_comp) {
  *num_comp = rstr->num_comp;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the number of blocks in a CeedElemRestriction

  @param[in]  rstr      CeedElemRestriction
  @param[out] num_block Variable to store number of blocks

  @return An error code: 0 - success, otherwise - failure

  @ref Advanced
**/
int CeedElemRestrictionGetNumBlocks(CeedElemRestriction rstr, CeedInt *num_block) {
  *num_block = rstr->num_block;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the size of blocks in the CeedElemRestriction

  @param[in]  rstr       CeedElemRestriction
  @param[out] block_size Variable to store size of blocks

  @return An error code: 0 - success, otherwise - failure

  @ref Advanced
**/
int CeedElemRestrictionGetBlockSize(CeedElemRestriction rstr, CeedInt *block_size) {
  *block_size = rstr->block_size;
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Get the multiplicity of nodes in a CeedElemRestriction

  @param[in]  rstr CeedElemRestriction
  @param[out] mult Vector to store multiplicity (of size l_size)

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionGetMultiplicity(CeedElemRestriction rstr, CeedVector mult) {
  CeedVector e_vec;

  // Create e_vec to hold intermediate computation in E^T (E 1)
  CeedCall(CeedElemRestrictionCreateVector(rstr, NULL, &e_vec));

  // Compute e_vec = E * 1
  CeedCall(CeedVectorSetValue(mult, 1.0));
  CeedCall(CeedElemRestrictionApply(rstr, CEED_NOTRANSPOSE, mult, e_vec, CEED_REQUEST_IMMEDIATE));
  // Compute multiplicity, mult = E^T * e_vec = E^T (E 1)
  CeedCall(CeedVectorSetValue(mult, 0.0));
  CeedCall(CeedElemRestrictionApply(rstr, CEED_TRANSPOSE, e_vec, mult, CEED_REQUEST_IMMEDIATE));
  // Cleanup
  CeedCall(CeedVectorDestroy(&e_vec));
  return CEED_ERROR_SUCCESS;
}

/**
  @brief View a CeedElemRestriction

  @param[in] rstr   CeedElemRestriction to view
  @param[in] stream Stream to write; typically stdout/stderr or a file

  @return Error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionView(CeedElemRestriction rstr, FILE *stream) {
  char stridesstr[500];

  if (rstr->strides) {
    sprintf(stridesstr, "[%" CeedInt_FMT ", %" CeedInt_FMT ", %" CeedInt_FMT "]", rstr->strides[0], rstr->strides[1], rstr->strides[2]);
  } else {
    sprintf(stridesstr, "%" CeedInt_FMT, rstr->comp_stride);
  }

  fprintf(stream, "%sCeedElemRestriction from (%td, %" CeedInt_FMT ") to %" CeedInt_FMT " elements with %" CeedInt_FMT " nodes each and %s %s\n",
          rstr->block_size > 1 ? "Blocked " : "", rstr->l_size, rstr->num_comp, rstr->num_elem, rstr->elem_size,
          rstr->strides ? "strides" : "component stride", stridesstr);
  return CEED_ERROR_SUCCESS;
}

/**
  @brief Destroy a CeedElemRestriction

  @param[in,out] rstr CeedElemRestriction to destroy

  @return An error code: 0 - success, otherwise - failure

  @ref User
**/
int CeedElemRestrictionDestroy(CeedElemRestriction *rstr) {
  if (!*rstr || *rstr == CEED_ELEMRESTRICTION_NONE || --(*rstr)->ref_count > 0) {
    *rstr = NULL;
    return CEED_ERROR_SUCCESS;
  }
  CeedCheck((*rstr)->num_readers == 0, (*rstr)->ceed, CEED_ERROR_ACCESS,
            "Cannot destroy CeedElemRestriction, a process has read access to the offset data");

  // Only destroy backend data once between rstr and unsigned copy
  if ((*rstr)->rstr_base) CeedCall(CeedElemRestrictionDestroy(&(*rstr)->rstr_base));
  else if ((*rstr)->Destroy) CeedCall((*rstr)->Destroy(*rstr));

  CeedCall(CeedFree(&(*rstr)->strides));
  CeedCall(CeedDestroy(&(*rstr)->ceed));
  CeedCall(CeedFree(rstr));
  return CEED_ERROR_SUCCESS;
}

/// @}