xref: /libCEED/backends/ref/ceed-ref-operator.c (revision de5bf46bcc909da70680c51facd7097145cfeaa6)

// Copyright (c) 2017-2025, 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.h>
#include <ceed/backend.h>
#include <stdbool.h>
#include <stddef.h>
#include <stdint.h>

#include "ceed-ref.h"

//------------------------------------------------------------------------------
// Setup Input/Output Fields
//------------------------------------------------------------------------------
static int CeedOperatorSetupFields_Ref(CeedQFunction qf, CeedOperator op, bool is_input, bool *skip_rstr, CeedInt *e_data_out_indices,
                                       bool *apply_add_basis, CeedVector *e_vecs_full, CeedVector *e_vecs, CeedVector *q_vecs, CeedInt start_e,
                                       CeedInt num_fields, CeedInt Q) {
  Ceed                ceed;
  CeedSize            e_size, q_size;
  CeedInt             num_comp, size, P;
  CeedQFunctionField *qf_fields;
  CeedOperatorField  *op_fields;

  {
    Ceed ceed_parent;

    CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
    CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
    CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
    CeedCallBackend(CeedDestroy(&ceed_parent));
  }
  if (is_input) {
    CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
    CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
  } else {
    CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
    CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
  }

  // Loop over fields
  for (CeedInt i = 0; i < num_fields; i++) {
    CeedEvalMode        eval_mode;
    CeedElemRestriction elem_rstr;
    CeedBasis           basis;

    CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
    if (eval_mode != CEED_EVAL_WEIGHT) {
      CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
      CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
      CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
    }

    switch (eval_mode) {
      case CEED_EVAL_NONE:
        CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
        q_size = (CeedSize)Q * size;
        CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
        break;
      case CEED_EVAL_INTERP:
      case CEED_EVAL_GRAD:
      case CEED_EVAL_DIV:
      case CEED_EVAL_CURL:
        CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
        CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
        CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
        CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
        e_size = (CeedSize)P * num_comp;
        CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
        q_size = (CeedSize)Q * size;
        CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
        CeedCallBackend(CeedBasisDestroy(&basis));
        break;
      case CEED_EVAL_WEIGHT:  // Only on input fields
        CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
        q_size = (CeedSize)Q;
        CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
        CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, q_vecs[i]));
        CeedCallBackend(CeedBasisDestroy(&basis));
        break;
    }
  }
  // Drop duplicate restrictions
  if (is_input) {
    for (CeedInt i = 0; i < num_fields; i++) {
      CeedVector          vec_i;
      CeedElemRestriction rstr_i;

      CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
      CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
      for (CeedInt j = i + 1; j < num_fields; j++) {
        CeedVector          vec_j;
        CeedElemRestriction rstr_j;

        CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
        CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
        if (vec_i == vec_j && rstr_i == rstr_j) {
          CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
          CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i + start_e], &e_vecs_full[j + start_e]));
          skip_rstr[j] = true;
        }
        CeedCallBackend(CeedVectorDestroy(&vec_j));
        CeedCallBackend(CeedElemRestrictionDestroy(&rstr_j));
      }
      CeedCallBackend(CeedVectorDestroy(&vec_i));
      CeedCallBackend(CeedElemRestrictionDestroy(&rstr_i));
    }
  } else {
    for (CeedInt i = num_fields - 1; i >= 0; i--) {
      CeedVector          vec_i;
      CeedElemRestriction rstr_i;

      CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
      CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
      for (CeedInt j = i - 1; j >= 0; j--) {
        CeedVector          vec_j;
        CeedElemRestriction rstr_j;

        CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
        CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
        if (vec_i == vec_j && rstr_i == rstr_j) {
          CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
          CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i + start_e], &e_vecs_full[j + start_e]));
          skip_rstr[j]          = true;
          apply_add_basis[i]    = true;
          e_data_out_indices[j] = i;
        }
        CeedCallBackend(CeedVectorDestroy(&vec_j));
        CeedCallBackend(CeedElemRestrictionDestroy(&rstr_j));
      }
      CeedCallBackend(CeedVectorDestroy(&vec_i));
      CeedCallBackend(CeedElemRestrictionDestroy(&rstr_i));
    }
  }
  CeedCallBackend(CeedDestroy(&ceed));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Setup Operator
//------------------------------------------------------------------------------/*
static int CeedOperatorSetup_Ref(CeedOperator op) {
  bool                is_setup_done;
  CeedInt             Q, num_input_fields, num_output_fields;
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  CeedQFunction       qf;
  CeedOperatorField  *op_input_fields, *op_output_fields;
  CeedOperator_Ref   *impl;

  CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
  if (is_setup_done) return CEED_ERROR_SUCCESS;

  CeedCallBackend(CeedOperatorGetData(op, &impl));
  CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
  CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
  CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
  CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
  CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));

  // Allocate
  CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));

  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_in));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_out));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_data_out_indices));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->apply_add_basis_out));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));

  impl->num_inputs  = num_input_fields;
  impl->num_outputs = num_output_fields;

  // Set up infield and outfield e_vecs and q_vecs
  // Infields
  CeedCallBackend(CeedOperatorSetupFields_Ref(qf, op, true, impl->skip_rstr_in, NULL, NULL, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0,
                                              num_input_fields, Q));
  // Outfields
  CeedCallBackend(CeedOperatorSetupFields_Ref(qf, op, false, impl->skip_rstr_out, impl->e_data_out_indices, impl->apply_add_basis_out,
                                              impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields, num_output_fields, Q));

  // Identity QFunctions
  if (impl->is_identity_qf) {
    CeedEvalMode        in_mode, out_mode;
    CeedQFunctionField *in_fields, *out_fields;

    CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &in_fields, NULL, &out_fields));
    CeedCallBackend(CeedQFunctionFieldGetEvalMode(in_fields[0], &in_mode));
    CeedCallBackend(CeedQFunctionFieldGetEvalMode(out_fields[0], &out_mode));

    if (in_mode == CEED_EVAL_NONE && out_mode == CEED_EVAL_NONE) {
      impl->is_identity_rstr_op = true;
    } else {
      CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
    }
  }

  CeedCallBackend(CeedOperatorSetSetupDone(op));
  CeedCallBackend(CeedQFunctionDestroy(&qf));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Setup Operator Inputs
//------------------------------------------------------------------------------
static inline int CeedOperatorSetupInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
                                              CeedVector in_vec, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
                                              CeedOperator_Ref *impl, CeedRequest *request) {
  for (CeedInt i = 0; i < num_input_fields; i++) {
    bool         is_active;
    uint64_t     state;
    CeedEvalMode eval_mode;
    CeedVector   vec;

    // Get input vector
    CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
    is_active = vec == CEED_VECTOR_ACTIVE;
    if (is_active) {
      if (skip_active) continue;
      else vec = in_vec;
    }

    CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
    // Restrict and Evec
    if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
    } else {
      // Restrict
      CeedCallBackend(CeedVectorGetState(vec, &state));
      // Skip restriction if input is unchanged
      if ((state != impl->input_states[i] || vec == in_vec) && !impl->skip_rstr_in[i]) {
        CeedElemRestriction elem_rstr;

        CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
        CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, vec, impl->e_vecs_full[i], request));
        CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
      }
      impl->input_states[i] = state;
      // Get evec
      CeedCallBackend(CeedVectorGetArrayRead(impl->e_vecs_full[i], CEED_MEM_HOST, (const CeedScalar **)&e_data_full[i]));
    }
    if (!is_active) CeedCallBackend(CeedVectorDestroy(&vec));
  }
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Input Basis Action
//------------------------------------------------------------------------------
static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
                                             CeedInt num_input_fields, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
                                             CeedOperator_Ref *impl) {
  for (CeedInt i = 0; i < num_input_fields; i++) {
    CeedInt             elem_size, size, num_comp;
    CeedEvalMode        eval_mode;
    CeedElemRestriction elem_rstr;
    CeedBasis           basis;

    // Skip active input
    if (skip_active) {
      bool       is_active;
      CeedVector vec;

      CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
      is_active = vec == CEED_VECTOR_ACTIVE;
      CeedCallBackend(CeedVectorDestroy(&vec));
      if (is_active) continue;
    }
    // Get elem_size, eval_mode, size
    CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
    CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
    CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
    CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
    CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
    // Basis action
    switch (eval_mode) {
      case CEED_EVAL_NONE:
        CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][(CeedSize)e * Q * size]));
        break;
      case CEED_EVAL_INTERP:
      case CEED_EVAL_GRAD:
      case CEED_EVAL_DIV:
      case CEED_EVAL_CURL:
        CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
        CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
        CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][(CeedSize)e * elem_size * num_comp]));
        CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, eval_mode, impl->e_vecs_in[i], impl->q_vecs_in[i]));
        CeedCallBackend(CeedBasisDestroy(&basis));
        break;
      case CEED_EVAL_WEIGHT:
        break;  // No action
    }
  }
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Output Basis Action
//------------------------------------------------------------------------------
static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_output_fields, CeedOperatorField *op_output_fields,
                                              CeedInt num_input_fields, CeedInt num_output_fields, bool *apply_add_basis, CeedOperator op,
                                              CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
  for (CeedInt i = 0; i < num_output_fields; i++) {
    CeedInt             elem_size, num_comp;
    CeedEvalMode        eval_mode;
    CeedElemRestriction elem_rstr;
    CeedBasis           basis;

    // Get elem_size, eval_mode
    CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
    CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
    CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
    CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
    // Basis action
    switch (eval_mode) {
      case CEED_EVAL_NONE:
        break;  // No action
      case CEED_EVAL_INTERP:
      case CEED_EVAL_GRAD:
      case CEED_EVAL_DIV:
      case CEED_EVAL_CURL:
        CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
        CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
        CeedCallBackend(CeedVectorSetArray(impl->e_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER,
                                           &e_data_full[i + num_input_fields][(CeedSize)e * elem_size * num_comp]));
        if (apply_add_basis[i]) {
          CeedCallBackend(CeedBasisApplyAdd(basis, 1, CEED_TRANSPOSE, eval_mode, impl->q_vecs_out[i], impl->e_vecs_out[i]));
        } else {
          CeedCallBackend(CeedBasisApply(basis, 1, CEED_TRANSPOSE, eval_mode, impl->q_vecs_out[i], impl->e_vecs_out[i]));
        }
        CeedCallBackend(CeedBasisDestroy(&basis));
        break;
      // LCOV_EXCL_START
      case CEED_EVAL_WEIGHT: {
        return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
        // LCOV_EXCL_STOP
      }
    }
  }
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Restore Input Vectors
//------------------------------------------------------------------------------
static inline int CeedOperatorRestoreInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
                                                const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
  for (CeedInt i = 0; i < num_input_fields; i++) {
    CeedEvalMode eval_mode;

    // Skip active inputs
    if (skip_active) {
      bool       is_active;
      CeedVector vec;

      CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
      is_active = vec == CEED_VECTOR_ACTIVE;
      CeedCallBackend(CeedVectorDestroy(&vec));
      if (is_active) continue;
    }
    // Restore input
    CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
    if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
    } else {
      CeedCallBackend(CeedVectorRestoreArrayRead(impl->e_vecs_full[i], (const CeedScalar **)&e_data_full[i]));
    }
  }
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Operator Apply
//------------------------------------------------------------------------------
static int CeedOperatorApplyAdd_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
  CeedInt             Q, num_elem, num_input_fields, num_output_fields, size;
  CeedEvalMode        eval_mode;
  CeedScalar         *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  CeedQFunction       qf;
  CeedOperatorField  *op_input_fields, *op_output_fields;
  CeedOperator_Ref   *impl;

  // Setup
  CeedCallBackend(CeedOperatorSetup_Ref(op));

  CeedCallBackend(CeedOperatorGetData(op, &impl));
  CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));

  // Restriction only operator
  if (impl->is_identity_rstr_op) {
    CeedElemRestriction elem_rstr;

    CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[0], &elem_rstr));
    CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_full[0], request));
    CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
    CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[0], &elem_rstr));
    CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[0], out_vec, request));
    CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
    return CEED_ERROR_SUCCESS;
  }

  CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
  CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
  CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
  CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));

  // Input Evecs and Restriction
  CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, in_vec, false, e_data_full, impl, request));

  // Output Evecs
  for (CeedInt i = num_output_fields - 1; i >= 0; i--) {
    if (impl->skip_rstr_out[i]) {
      e_data_full[i + num_input_fields] = e_data_full[impl->e_data_out_indices[i] + num_input_fields];
    } else {
      CeedCallBackend(CeedVectorGetArrayWrite(impl->e_vecs_full[i + impl->num_inputs], CEED_MEM_HOST, &e_data_full[i + num_input_fields]));
    }
  }

  // Loop through elements
  for (CeedInt e = 0; e < num_elem; e++) {
    // Output pointers
    for (CeedInt i = 0; i < num_output_fields; i++) {
      CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
      if (eval_mode == CEED_EVAL_NONE) {
        CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
        CeedCallBackend(
            CeedVectorSetArray(impl->q_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][(CeedSize)e * Q * size]));
      }
    }

    // Input basis apply
    CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, false, e_data_full, impl));

    // Q function
    if (!impl->is_identity_qf) {
      CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
    }

    // Output basis apply
    CeedCallBackend(CeedOperatorOutputBasis_Ref(e, Q, qf_output_fields, op_output_fields, num_input_fields, num_output_fields,
                                                impl->apply_add_basis_out, op, e_data_full, impl));
  }

  // Output restriction
  for (CeedInt i = 0; i < num_output_fields; i++) {
    bool                is_active;
    CeedVector          vec;
    CeedElemRestriction elem_rstr;

    if (impl->skip_rstr_out[i]) continue;
    // Restore Evec
    CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_full[i + impl->num_inputs], &e_data_full[i + num_input_fields]));
    // Get output vector
    CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
    // Active
    is_active = vec == CEED_VECTOR_ACTIVE;
    if (is_active) vec = out_vec;
    // Restrict
    CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
    CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[i + impl->num_inputs], vec, request));
    if (!is_active) CeedCallBackend(CeedVectorDestroy(&vec));
    CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
  }

  // Restore input arrays
  CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, false, e_data_full, impl));
  CeedCallBackend(CeedQFunctionDestroy(&qf));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Core code for assembling linear QFunction
//------------------------------------------------------------------------------
static inline int CeedOperatorLinearAssembleQFunctionCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled, CeedElemRestriction *rstr,
                                                              CeedRequest *request) {
  Ceed                ceed_parent;
  CeedInt             qf_size_in, qf_size_out, Q, num_elem, num_input_fields, num_output_fields;
  CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  CeedQFunction       qf;
  CeedOperatorField  *op_input_fields, *op_output_fields;
  CeedOperator_Ref   *impl;

  CeedCallBackend(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
  CeedCallBackend(CeedOperatorGetData(op, &impl));
  qf_size_in  = impl->qf_size_in;
  qf_size_out = impl->qf_size_out;
  CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
  CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
  CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
  CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
  CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));

  // Setup
  CeedCallBackend(CeedOperatorSetup_Ref(op));

  // Check for restriction only operator
  CeedCheck(!impl->is_identity_rstr_op, CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");

  // Input Evecs and Restriction
  CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));

  // Count number of active input fields
  if (qf_size_in == 0) {
    for (CeedInt i = 0; i < num_input_fields; i++) {
      CeedInt    field_size;
      CeedVector vec;

      // Get input vector
      CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
      // Check if active input
      if (vec == CEED_VECTOR_ACTIVE) {
        CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
        CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
        qf_size_in += field_size;
      }
      CeedCallBackend(CeedVectorDestroy(&vec));
    }
    CeedCheck(qf_size_in > 0, CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
    impl->qf_size_in = qf_size_in;
  }

  // Count number of active output fields
  if (qf_size_out == 0) {
    for (CeedInt i = 0; i < num_output_fields; i++) {
      CeedInt    field_size;
      CeedVector vec;

      // Get output vector
      CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
      // Check if active output
      if (vec == CEED_VECTOR_ACTIVE) {
        CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
        qf_size_out += field_size;
      }
      CeedCallBackend(CeedVectorDestroy(&vec));
    }
    CeedCheck(qf_size_out > 0, CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
    impl->qf_size_out = qf_size_out;
  }

  // Build objects if needed
  if (build_objects) {
    const CeedSize l_size     = (CeedSize)num_elem * Q * qf_size_in * qf_size_out;
    CeedInt        strides[3] = {1, Q, qf_size_in * qf_size_out * Q}; /* *NOPAD* */

    // Create output restriction
    CeedCallBackend(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, Q, qf_size_in * qf_size_out,
                                                     (CeedSize)qf_size_in * (CeedSize)qf_size_out * (CeedSize)num_elem * (CeedSize)Q, strides, rstr));
    // Create assembled vector
    CeedCallBackend(CeedVectorCreate(ceed_parent, l_size, assembled));
  }
  // Clear output vector
  CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
  CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));

  // Loop through elements
  for (CeedInt e = 0; e < num_elem; e++) {
    // Input basis apply
    CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, true, e_data_full, impl));

    // Assemble QFunction

    for (CeedInt i = 0; i < num_input_fields; i++) {
      bool       is_active;
      CeedInt    field_size;
      CeedVector vec;

      // Set Inputs
      CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
      is_active = vec == CEED_VECTOR_ACTIVE;
      CeedCallBackend(CeedVectorDestroy(&vec));
      if (!is_active) continue;
      CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
      for (CeedInt field = 0; field < field_size; field++) {
        // Set current portion of input to 1.0
        {
          CeedScalar *array;

          CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
          for (CeedInt j = 0; j < Q; j++) array[field * Q + j] = 1.0;
          CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
        }

        if (!impl->is_identity_qf) {
          // Set Outputs
          for (CeedInt out = 0; out < num_output_fields; out++) {
            CeedVector vec;

            // Get output vector
            CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
            // Check if active output
            if (vec == CEED_VECTOR_ACTIVE) {
              CeedInt field_size;

              CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
              CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
              assembled_array += field_size * Q;  // Advance the pointer by the size of the output
            }
            CeedCallBackend(CeedVectorDestroy(&vec));
          }
          // Apply QFunction
          CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
        } else {
          CeedInt           field_size;
          const CeedScalar *array;

          // Copy Identity Outputs
          CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
          CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &array));
          for (CeedInt j = 0; j < field_size * Q; j++) assembled_array[j] = array[j];
          CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &array));
          assembled_array += field_size * Q;
        }
        // Reset input to 0.0
        {
          CeedScalar *array;

          CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
          for (CeedInt j = 0; j < Q; j++) array[field * Q + j] = 0.0;
          CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
        }
      }
    }
  }

  // Un-set output Qvecs to prevent accidental overwrite of Assembled
  if (!impl->is_identity_qf) {
    for (CeedInt out = 0; out < num_output_fields; out++) {
      CeedVector vec;

      // Get output vector
      CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
      // Check if active output
      if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
        CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
      }
      CeedCallBackend(CeedVectorDestroy(&vec));
    }
  }

  // Restore input arrays
  CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));

  // Restore output
  CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
  CeedCallBackend(CeedDestroy(&ceed_parent));
  CeedCallBackend(CeedQFunctionDestroy(&qf));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Assemble Linear QFunction
//------------------------------------------------------------------------------
static int CeedOperatorLinearAssembleQFunction_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
  return CeedOperatorLinearAssembleQFunctionCore_Ref(op, true, assembled, rstr, request);
}

//------------------------------------------------------------------------------
// Update Assembled Linear QFunction
//------------------------------------------------------------------------------
static int CeedOperatorLinearAssembleQFunctionUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr, CeedRequest *request) {
  return CeedOperatorLinearAssembleQFunctionCore_Ref(op, false, &assembled, &rstr, request);
}

//------------------------------------------------------------------------------
// Setup Input/Output Fields
//------------------------------------------------------------------------------
static int CeedOperatorSetupFieldsAtPoints_Ref(CeedQFunction qf, CeedOperator op, bool is_input, bool *skip_rstr, bool *apply_add_basis,
                                               CeedVector *e_vecs_full, CeedVector *e_vecs, CeedVector *q_vecs, CeedInt start_e, CeedInt num_fields,
                                               CeedInt Q) {
  Ceed                ceed;
  CeedSize            e_size, q_size;
  CeedInt             max_num_points, num_comp, size, P;
  CeedQFunctionField *qf_fields;
  CeedOperatorField  *op_fields;

  {
    Ceed ceed_parent;

    CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
    CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
    CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
    CeedCallBackend(CeedDestroy(&ceed_parent));
  }
  if (is_input) {
    CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
    CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
  } else {
    CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
    CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
  }

  // Get max number of points
  {
    CeedInt             dim;
    CeedElemRestriction rstr_points = NULL;
    CeedOperator_Ref   *impl;

    CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, NULL));
    CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
    CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr_points, &dim));
    CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
    CeedCallBackend(CeedOperatorGetData(op, &impl));
    if (is_input) {
      CeedCallBackend(CeedVectorCreate(ceed, dim * max_num_points, &impl->point_coords_elem));
      CeedCallBackend(CeedVectorSetValue(impl->point_coords_elem, 0.0));
    }
  }

  // Loop over fields
  for (CeedInt i = 0; i < num_fields; i++) {
    CeedEvalMode eval_mode;
    CeedBasis    basis;

    CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
    if (eval_mode != CEED_EVAL_WEIGHT) {
      CeedElemRestriction elem_rstr;

      CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
      CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
      CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
      CeedCallBackend(CeedVectorSetValue(e_vecs_full[i + start_e], 0.0));
    }

    switch (eval_mode) {
      case CEED_EVAL_NONE: {
        CeedVector vec;

        CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
        e_size = (CeedSize)max_num_points * size;
        CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
        CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec));
        if (vec == CEED_VECTOR_ACTIVE || !is_input) {
          CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &q_vecs[i]));
        } else {
          q_size = (CeedSize)max_num_points * size;
          CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
        }
        CeedCallBackend(CeedVectorDestroy(&vec));
        break;
      }
      case CEED_EVAL_INTERP:
      case CEED_EVAL_GRAD:
      case CEED_EVAL_DIV:
      case CEED_EVAL_CURL:
        CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
        CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
        CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
        CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
        e_size = (CeedSize)P * num_comp;
        CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
        q_size = (CeedSize)max_num_points * size;
        CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
        CeedCallBackend(CeedBasisDestroy(&basis));
        break;
      case CEED_EVAL_WEIGHT:  // Only on input fields
        CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
        q_size = (CeedSize)max_num_points;
        CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
        CeedCallBackend(
            CeedBasisApplyAtPoints(basis, 1, &max_num_points, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, CEED_VECTOR_NONE, q_vecs[i]));
        CeedCallBackend(CeedBasisDestroy(&basis));
        break;
    }
    // Initialize full arrays for E-vectors and Q-vectors
    if (e_vecs[i]) CeedCallBackend(CeedVectorSetValue(e_vecs[i], 0.0));
    if (eval_mode != CEED_EVAL_WEIGHT) CeedCallBackend(CeedVectorSetValue(q_vecs[i], 0.0));
  }
  // Drop duplicate restrictions
  if (is_input) {
    for (CeedInt i = 0; i < num_fields; i++) {
      CeedVector          vec_i;
      CeedElemRestriction rstr_i;

      CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
      CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
      for (CeedInt j = i + 1; j < num_fields; j++) {
        CeedVector          vec_j;
        CeedElemRestriction rstr_j;

        CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
        CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
        if (vec_i == vec_j && rstr_i == rstr_j) {
          CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
          CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i + start_e], &e_vecs_full[j + start_e]));
          skip_rstr[j] = true;
        }
        CeedCallBackend(CeedVectorDestroy(&vec_j));
        CeedCallBackend(CeedElemRestrictionDestroy(&rstr_j));
      }
      CeedCallBackend(CeedVectorDestroy(&vec_i));
      CeedCallBackend(CeedElemRestrictionDestroy(&rstr_i));
    }
  } else {
    for (CeedInt i = num_fields - 1; i >= 0; i--) {
      CeedVector          vec_i;
      CeedElemRestriction rstr_i;

      CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
      CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
      for (CeedInt j = i - 1; j >= 0; j--) {
        CeedVector          vec_j;
        CeedElemRestriction rstr_j;

        CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
        CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
        if (vec_i == vec_j && rstr_i == rstr_j) {
          CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
          CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i + start_e], &e_vecs_full[j + start_e]));
          skip_rstr[j]       = true;
          apply_add_basis[i] = true;
        }
        CeedCallBackend(CeedVectorDestroy(&vec_j));
        CeedCallBackend(CeedElemRestrictionDestroy(&rstr_j));
      }
      CeedCallBackend(CeedVectorDestroy(&vec_i));
      CeedCallBackend(CeedElemRestrictionDestroy(&rstr_i));
    }
  }
  CeedCallBackend(CeedDestroy(&ceed));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Setup Operator
//------------------------------------------------------------------------------
static int CeedOperatorSetupAtPoints_Ref(CeedOperator op) {
  bool                is_setup_done;
  CeedInt             Q, num_input_fields, num_output_fields;
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  CeedQFunction       qf;
  CeedOperatorField  *op_input_fields, *op_output_fields;
  CeedOperator_Ref   *impl;

  CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
  if (is_setup_done) return CEED_ERROR_SUCCESS;

  CeedCallBackend(CeedOperatorGetData(op, &impl));
  CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
  CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
  CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
  CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
  CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));

  // Allocate
  CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));

  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_in));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_out));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->apply_add_basis_out));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
  CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));

  impl->num_inputs  = num_input_fields;
  impl->num_outputs = num_output_fields;

  // Set up infield and outfield pointer arrays
  // Infields
  CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, true, impl->skip_rstr_in, NULL, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0,
                                                      num_input_fields, Q));
  // Outfields
  CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, false, impl->skip_rstr_out, impl->apply_add_basis_out, impl->e_vecs_full,
                                                      impl->e_vecs_out, impl->q_vecs_out, num_input_fields, num_output_fields, Q));

  // Identity QFunctions
  if (impl->is_identity_qf) {
    CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
    CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->e_vecs_out[0]));
  }

  CeedCallBackend(CeedOperatorSetSetupDone(op));
  CeedCallBackend(CeedQFunctionDestroy(&qf));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Input Basis Action
//------------------------------------------------------------------------------
static inline int CeedOperatorInputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_input_fields,
                                                     CeedOperatorField *op_input_fields, CeedInt num_input_fields, CeedVector in_vec,
                                                     CeedVector point_coords_elem, bool skip_active, bool skip_passive,
                                                     CeedScalar *e_data[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl, CeedRequest *request) {
  for (CeedInt i = 0; i < num_input_fields; i++) {
    bool                is_active;
    CeedInt             elem_size, size, num_comp;
    CeedRestrictionType rstr_type;
    CeedEvalMode        eval_mode;
    CeedVector          vec;
    CeedElemRestriction elem_rstr;
    CeedBasis           basis;

    // Skip active input
    CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
    is_active = vec == CEED_VECTOR_ACTIVE;
    CeedCallBackend(CeedVectorDestroy(&vec));
    if (skip_active && is_active) continue;
    if (skip_passive && !is_active) continue;

    // Get elem_size, eval_mode, size
    CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
    CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
    CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
    CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
    // Restrict block active input
    // When skipping passive inputs, we're doing assembly and should not restrict
    if (is_active && !impl->skip_rstr_in[i] && !skip_passive) {
      if (rstr_type == CEED_RESTRICTION_POINTS) {
        CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
      } else {
        CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
      }
    }
    // Basis action
    switch (eval_mode) {
      case CEED_EVAL_NONE:
        if (!is_active) {
          CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][num_points_offset * size]));
        }
        break;
      // Note - these basis eval modes require FEM fields
      case CEED_EVAL_INTERP:
      case CEED_EVAL_GRAD:
      case CEED_EVAL_DIV:
      case CEED_EVAL_CURL:
        CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
        if (!is_active) {
          CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
          CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
          CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][(CeedSize)e * elem_size * num_comp]));
        }
        CeedCallBackend(
            CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_NOTRANSPOSE, eval_mode, point_coords_elem, impl->e_vecs_in[i], impl->q_vecs_in[i]));
        CeedCallBackend(CeedBasisDestroy(&basis));
        break;
      case CEED_EVAL_WEIGHT:
        break;  // No action
    }
    CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
  }
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Output Basis Action
//------------------------------------------------------------------------------
static inline int CeedOperatorOutputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_output_fields,
                                                      CeedOperatorField *op_output_fields, CeedInt num_input_fields, CeedInt num_output_fields,
                                                      bool *apply_add_basis, bool *skip_rstr, CeedOperator op, CeedVector out_vec,
                                                      CeedVector point_coords_elem, bool skip_passive, CeedOperator_Ref *impl, CeedRequest *request) {
  for (CeedInt i = 0; i < num_output_fields; i++) {
    bool                is_active;
    CeedRestrictionType rstr_type;
    CeedEvalMode        eval_mode;
    CeedVector          vec;
    CeedElemRestriction elem_rstr;
    CeedBasis           basis;

    // Skip active input
    CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
    is_active = vec == CEED_VECTOR_ACTIVE;
    CeedCallBackend(CeedVectorDestroy(&vec));
    if (skip_passive && !is_active) continue;

    // Get elem_size, eval_mode, size
    CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
    CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
    // Basis action
    switch (eval_mode) {
      case CEED_EVAL_NONE:
        break;  // No action
      case CEED_EVAL_INTERP:
      case CEED_EVAL_GRAD:
      case CEED_EVAL_DIV:
      case CEED_EVAL_CURL:
        CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
        if (apply_add_basis[i]) {
          CeedCallBackend(CeedBasisApplyAddAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i],
                                                    impl->e_vecs_out[i]));
        } else {
          CeedCallBackend(
              CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i], impl->e_vecs_out[i]));
        }
        CeedCallBackend(CeedBasisDestroy(&basis));
        break;
      // LCOV_EXCL_START
      case CEED_EVAL_WEIGHT: {
        return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
        // LCOV_EXCL_STOP
      }
    }
    // Restrict output block
    // When skipping passive outputs, we're doing assembly and should not restrict
    if (skip_rstr[i] || skip_passive) {
      CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
      continue;
    }

    // Get output vector
    CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
    CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
    if (is_active) vec = out_vec;
    // Restrict
    if (rstr_type == CEED_RESTRICTION_POINTS) {
      CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
    } else {
      CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
    }
    if (!is_active) CeedCallBackend(CeedVectorDestroy(&vec));
    CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
  }
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Operator Apply
//------------------------------------------------------------------------------
static int CeedOperatorApplyAddAtPoints_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
  CeedInt             num_points_offset          = 0, num_input_fields, num_output_fields, num_elem;
  CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
  CeedVector          point_coords               = NULL;
  CeedElemRestriction rstr_points                = NULL;
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  CeedQFunction       qf;
  CeedOperatorField  *op_input_fields, *op_output_fields;
  CeedOperator_Ref   *impl;

  CeedCallBackend(CeedOperatorGetData(op, &impl));
  CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
  CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
  CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
  CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));

  // Setup
  CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));

  // Point coordinates
  CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));

  // Input Evecs and Restriction
  CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));

  // Loop through elements
  for (CeedInt e = 0; e < num_elem; e++) {
    CeedInt num_points;

    // Setup points for element
    CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
    CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
    if (num_points < 1) continue;

    // Input basis apply
    CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
                                                       impl->point_coords_elem, false, false, e_data, impl, request));

    // Q function
    if (!impl->is_identity_qf) {
      CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
    }

    // Output basis apply and restriction
    CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
                                                        num_output_fields, impl->apply_add_basis_out, impl->skip_rstr_out, op, out_vec,
                                                        impl->point_coords_elem, false, impl, request));

    num_points_offset += num_points;
  }

  // Restore input arrays
  CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));

  // Cleanup point coordinates
  CeedCallBackend(CeedVectorDestroy(&point_coords));
  CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
  CeedCallBackend(CeedQFunctionDestroy(&qf));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Core code for assembling linear QFunction
//------------------------------------------------------------------------------
static inline int CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled,
                                                                      CeedElemRestriction *rstr, CeedRequest *request) {
  Ceed                ceed;
  CeedInt             qf_size_in, qf_size_out, max_num_points, num_elem, num_input_fields, num_output_fields, num_points_offset = 0;
  CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
  CeedVector          point_coords = NULL;
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  CeedQFunction       qf;
  CeedOperatorField  *op_input_fields, *op_output_fields;
  CeedOperator_Ref   *impl;
  CeedElemRestriction rstr_points = NULL;

  CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
  CeedCallBackend(CeedOperatorGetData(op, &impl));
  qf_size_in  = impl->qf_size_in;
  qf_size_out = impl->qf_size_out;
  CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
  CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
  CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
  CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));

  // Setup
  CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));

  // Check for restriction only operator
  CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");

  // Point coordinates
  CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
  CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));

  // Input Evecs and Restriction
  CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));

  // Count number of active input fields
  if (qf_size_in == 0) {
    for (CeedInt i = 0; i < num_input_fields; i++) {
      CeedInt    field_size;
      CeedVector vec;

      // Get input vector
      CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
      // Check if active input
      if (vec == CEED_VECTOR_ACTIVE) {
        // Check that all active inputs are nodal fields
        {
          CeedElemRestriction elem_rstr;
          bool                is_at_points = false;

          CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
          CeedCallBackend(CeedElemRestrictionIsAtPoints(elem_rstr, &is_at_points));
          CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
          CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
        }
        // Get size of active input
        CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
        qf_size_in += field_size;
      }
      CeedCallBackend(CeedVectorDestroy(&vec));
    }
    CeedCheck(qf_size_in, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
    impl->qf_size_in = qf_size_in;
  }

  // Count number of active output fields
  if (qf_size_out == 0) {
    for (CeedInt i = 0; i < num_output_fields; i++) {
      CeedInt    field_size;
      CeedVector vec;

      // Get output vector
      CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
      // Check if active output
      if (vec == CEED_VECTOR_ACTIVE) {
        // Check that all active inputs are nodal fields
        {
          CeedElemRestriction elem_rstr;
          bool                is_at_points = false;

          CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
          CeedCallBackend(CeedElemRestrictionIsAtPoints(elem_rstr, &is_at_points));
          CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
          CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
        }
        // Get size of active output
        CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
        CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
        qf_size_out += field_size;
      }
      CeedCallBackend(CeedVectorDestroy(&vec));
    }
    CeedCheck(qf_size_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
    impl->qf_size_out = qf_size_out;
  }

  // Build objects if needed
  if (build_objects) {
    CeedInt        num_points_total;
    const CeedInt *offsets;

    CeedCallBackend(CeedElemRestrictionGetNumPoints(rstr_points, &num_points_total));

    // Create output restriction (at points)
    CeedCallBackend(CeedElemRestrictionGetOffsets(rstr_points, CEED_MEM_HOST, &offsets));
    CeedCallBackend(CeedElemRestrictionCreateAtPoints(ceed, num_elem, num_points_total, qf_size_in * qf_size_out,
                                                      qf_size_in * qf_size_out * num_points_total, CEED_MEM_HOST, CEED_COPY_VALUES, offsets, rstr));
    CeedCallBackend(CeedElemRestrictionRestoreOffsets(rstr_points, &offsets));

    // Create assembled vector
    CeedCallBackend(CeedElemRestrictionCreateVector(*rstr, assembled, NULL));
  }
  // Clear output vector
  CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
  CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));

  // Loop through elements
  for (CeedInt e = 0; e < num_elem; e++) {
    CeedInt num_points;

    // Setup points for element
    CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
    CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));

    // Input basis apply
    CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, NULL,
                                                       impl->point_coords_elem, true, false, e_data_full, impl, request));

    // Assemble QFunction
    for (CeedInt i = 0; i < num_input_fields; i++) {
      bool       is_active;
      CeedInt    field_size;
      CeedVector vec;

      // Get input vector
      CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
      is_active = vec == CEED_VECTOR_ACTIVE;
      CeedCallBackend(CeedVectorDestroy(&vec));
      // Check if active input
      if (!is_active) continue;
      // Get size of active input
      CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
      for (CeedInt field = 0; field < field_size; field++) {
        // Set current portion of input to 1.0
        {
          CeedScalar *array;

          CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
          for (CeedInt j = 0; j < num_points; j++) array[field * num_points + j] = 1.0;
          CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
        }

        if (!impl->is_identity_qf) {
          // Set Outputs
          for (CeedInt out = 0; out < num_output_fields; out++) {
            CeedVector vec;
            CeedInt    field_size;

            // Get output vector
            CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
            // Check if active output
            if (vec == CEED_VECTOR_ACTIVE) {
              CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
              CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
              assembled_array += field_size * num_points;  // Advance the pointer by the size of the output
            }
            CeedCallBackend(CeedVectorDestroy(&vec));
          }
          // Apply QFunction
          CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
        } else {
          const CeedScalar *array;
          CeedInt           field_size;

          // Copy Identity Outputs
          CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
          CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &array));
          for (CeedInt j = 0; j < field_size * num_points; j++) assembled_array[j] = array[j];
          CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &array));
          assembled_array += field_size * num_points;
        }
        // Reset input to 0.0
        {
          CeedScalar *array;

          CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
          for (CeedInt j = 0; j < num_points; j++) array[field * num_points + j] = 0.0;
          CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
        }
      }
    }
    num_points_offset += num_points;
  }

  // Un-set output Qvecs to prevent accidental overwrite of Assembled
  if (!impl->is_identity_qf) {
    for (CeedInt out = 0; out < num_output_fields; out++) {
      CeedVector vec;

      // Get output vector
      CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
      // Check if active output
      if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
        CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
      }
      CeedCallBackend(CeedVectorDestroy(&vec));
    }
  }

  // Restore input arrays
  CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));

  // Restore output
  CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));

  // Cleanup
  CeedCallBackend(CeedDestroy(&ceed));
  CeedCallBackend(CeedVectorDestroy(&point_coords));
  CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
  CeedCallBackend(CeedQFunctionDestroy(&qf));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Assemble Linear QFunction
//------------------------------------------------------------------------------
static int CeedOperatorLinearAssembleQFunctionAtPoints_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
  return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, true, assembled, rstr, request);
}

//------------------------------------------------------------------------------
// Update Assembled Linear QFunction
//------------------------------------------------------------------------------
static int CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr,
                                                                 CeedRequest *request) {
  return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, false, &assembled, &rstr, request);
}

//------------------------------------------------------------------------------
// Assemble Operator Diagonal AtPoints
//------------------------------------------------------------------------------
static int CeedOperatorLinearAssembleAddDiagonalAtPoints_Ref(CeedOperator op, CeedVector assembled, CeedRequest *request) {
  CeedInt             num_points_offset = 0, num_input_fields, num_output_fields, num_elem, num_comp_active = 1;
  CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
  Ceed                ceed;
  CeedVector          point_coords = NULL, in_vec, out_vec;
  CeedElemRestriction rstr_points  = NULL;
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  CeedQFunction       qf;
  CeedOperatorField  *op_input_fields, *op_output_fields;
  CeedOperator_Ref   *impl;

  CeedCallBackend(CeedOperatorGetData(op, &impl));
  CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
  CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
  CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
  CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));

  // Setup
  CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));

  // Ceed
  {
    Ceed ceed_parent;

    CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
    CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
    CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
    CeedCallBackend(CeedDestroy(&ceed_parent));
  }

  // Point coordinates
  CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));

  // Input and output vectors
  {
    CeedSize input_size, output_size;

    CeedCallBackend(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
    CeedCallBackend(CeedVectorCreate(ceed, input_size, &in_vec));
    CeedCallBackend(CeedVectorCreate(ceed, output_size, &out_vec));
    CeedCallBackend(CeedVectorSetValue(out_vec, 0.0));
  }

  // Clear input Evecs
  for (CeedInt i = 0; i < num_input_fields; i++) {
    bool       is_active;
    CeedVector vec;

    CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
    is_active = vec == CEED_VECTOR_ACTIVE;
    CeedCallBackend(CeedVectorDestroy(&vec));
    if (!is_active || impl->skip_rstr_in[i]) continue;
    CeedCallBackend(CeedVectorSetValue(impl->e_vecs_in[i], 0.0));
  }

  // Input Evecs and Restriction
  CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));

  // Loop through elements
  for (CeedInt e = 0; e < num_elem; e++) {
    CeedInt num_points, e_vec_size = 0;

    // Setup points for element
    CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
    CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));

    // Input basis apply for non-active bases
    CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
                                                       impl->point_coords_elem, true, false, e_data, impl, request));

    // Loop over points on element
    for (CeedInt i = 0; i < num_input_fields; i++) {
      bool                is_active_at_points = true, is_active;
      CeedInt             elem_size_active    = 1;
      CeedRestrictionType rstr_type;
      CeedVector          vec;
      CeedElemRestriction elem_rstr;

      // -- Skip non-active input
      CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
      is_active = vec == CEED_VECTOR_ACTIVE;
      CeedCallBackend(CeedVectorDestroy(&vec));
      if (!is_active || impl->skip_rstr_in[i]) continue;

      // -- Get active restriction type
      CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
      CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
      is_active_at_points = rstr_type == CEED_RESTRICTION_POINTS;
      if (!is_active_at_points) CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size_active));
      else elem_size_active = num_points;
      CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp_active));
      CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));

      e_vec_size = elem_size_active * num_comp_active;
      for (CeedInt s = 0; s < e_vec_size; s++) {
        // -- Update unit vector
        {
          CeedScalar *array;

          CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
          array[s] = 1.0;
          if (s > 0) array[s - 1] = 0.0;
          CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
        }
        // Input basis apply for active bases
        CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields,
                                                           in_vec, impl->point_coords_elem, false, true, e_data, impl, request));

        // -- Q function
        if (!impl->is_identity_qf) {
          CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
        }

        // -- Output basis apply and restriction
        CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
                                                            num_output_fields, impl->apply_add_basis_out, impl->skip_rstr_out, op, out_vec,
                                                            impl->point_coords_elem, true, impl, request));

        // -- Grab diagonal value
        for (CeedInt j = 0; j < num_output_fields; j++) {
          bool                is_active;
          CeedInt             elem_size = 0;
          CeedRestrictionType rstr_type;
          CeedVector          vec;
          CeedElemRestriction elem_rstr;

          // ---- Skip non-active output
          CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[j], &vec));
          is_active = vec == CEED_VECTOR_ACTIVE;
          CeedCallBackend(CeedVectorDestroy(&vec));
          if (!is_active || impl->skip_rstr_out[j]) continue;

          // ---- Check if elem size matches
          CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[j], &elem_rstr));
          CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
          if (is_active_at_points && rstr_type != CEED_RESTRICTION_POINTS) {
            CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
            continue;
          }
          if (rstr_type == CEED_RESTRICTION_POINTS) {
            CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(elem_rstr, e, &elem_size));
          } else {
            CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
          }
          {
            CeedInt num_comp = 0;

            CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
            if (e_vec_size != num_comp * elem_size) {
              CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
              continue;
            }
          }
          // ---- Update output vector
          {
            CeedScalar *array, current_value = 0.0;

            CeedCallBackend(CeedVectorGetArray(impl->e_vecs_out[j], CEED_MEM_HOST, &array));
            current_value = array[s];
            CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_out[j], &array));
            CeedCallBackend(CeedVectorSetValue(impl->e_vecs_out[j], 0.0));
            CeedCallBackend(CeedVectorGetArray(impl->e_vecs_out[j], CEED_MEM_HOST, &array));
            array[s] = current_value;
            CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_out[j], &array));
          }
          // ---- Restrict output block
          if (rstr_type == CEED_RESTRICTION_POINTS) {
            CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[j], assembled, request));
          } else {
            CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[j], assembled, request));
          }
          CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
        }
        // -- Reset unit vector
        if (s == e_vec_size - 1) {
          CeedScalar *array;

          CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
          array[s] = 0.0;
          CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
        }
      }
    }
    num_points_offset += num_points;
  }

  // Restore input arrays
  CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));

  // Cleanup
  CeedCallBackend(CeedDestroy(&ceed));
  CeedCallBackend(CeedVectorDestroy(&in_vec));
  CeedCallBackend(CeedVectorDestroy(&out_vec));
  CeedCallBackend(CeedVectorDestroy(&point_coords));
  CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
  CeedCallBackend(CeedQFunctionDestroy(&qf));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Assemble Operator AtPoints
//------------------------------------------------------------------------------
static int CeedOperatorAssembleSingleAtPoints_Ref(CeedOperator op, CeedInt offset, CeedVector values) {
  CeedInt             num_points_offset = 0, num_input_fields, num_output_fields, num_elem, num_comp_active = 1;
  CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0}, *assembled;
  Ceed                ceed;
  CeedVector          point_coords = NULL, in_vec, out_vec;
  CeedElemRestriction rstr_points  = NULL;
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  CeedQFunction       qf;
  CeedOperatorField  *op_input_fields, *op_output_fields;
  CeedOperator_Ref   *impl;

  CeedCallBackend(CeedOperatorGetData(op, &impl));
  CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
  CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
  CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
  CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));

  // Setup
  CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));

  // Ceed
  {
    Ceed ceed_parent;

    CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
    CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
    CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
    CeedCallBackend(CeedDestroy(&ceed_parent));
  }

  // Point coordinates
  CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));

  // Input and output vectors
  {
    CeedSize input_size, output_size;

    CeedCallBackend(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
    CeedCallBackend(CeedVectorCreate(ceed, input_size, &in_vec));
    CeedCallBackend(CeedVectorCreate(ceed, output_size, &out_vec));
    CeedCallBackend(CeedVectorSetValue(out_vec, 0.0));
  }

  // Assembled array
  CeedCallBackend(CeedVectorGetArray(values, CEED_MEM_HOST, &assembled));

  // Clear input Evecs
  for (CeedInt i = 0; i < num_input_fields; i++) {
    bool       is_active;
    CeedVector vec;

    CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
    is_active = vec == CEED_VECTOR_ACTIVE;
    CeedCallBackend(CeedVectorDestroy(&vec));
    if (!is_active || impl->skip_rstr_in[i]) continue;
    CeedCallBackend(CeedVectorSetValue(impl->e_vecs_in[i], 0.0));
  }

  // Input Evecs and Restriction
  CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, CEED_REQUEST_IMMEDIATE));

  // Loop through elements
  for (CeedInt e = 0; e < num_elem; e++) {
    CeedInt num_points, e_vec_size = 0;

    // Setup points for element
    CeedCallBackend(
        CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, CEED_REQUEST_IMMEDIATE));
    CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));

    // Input basis apply for non-active bases
    CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
                                                       impl->point_coords_elem, true, false, e_data, impl, CEED_REQUEST_IMMEDIATE));

    // Loop over points on element
    for (CeedInt i = 0; i < num_input_fields; i++) {
      bool                is_active_at_points = true, is_active;
      CeedInt             elem_size_active    = 1;
      CeedRestrictionType rstr_type;
      CeedVector          vec;
      CeedElemRestriction elem_rstr;

      // -- Skip non-active input
      CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
      is_active = vec == CEED_VECTOR_ACTIVE;
      CeedCallBackend(CeedVectorDestroy(&vec));
      if (!is_active || impl->skip_rstr_in[i]) continue;

      // -- Get active restriction type
      CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
      CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
      is_active_at_points = rstr_type == CEED_RESTRICTION_POINTS;
      if (!is_active_at_points) CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size_active));
      else elem_size_active = num_points;
      CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp_active));
      CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));

      e_vec_size = elem_size_active * num_comp_active;
      for (CeedInt s = 0; s < e_vec_size; s++) {
        const CeedInt comp_in = s / elem_size_active;
        const CeedInt node_in = s % elem_size_active;

        // -- Update unit vector
        {
          CeedScalar *array;

          if (s == 0) CeedCallBackend(CeedVectorSetValue(impl->e_vecs_in[i], 0.0));
          CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
          array[s] = 1.0;
          if (s > 0) array[s - 1] = 0.0;
          CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
        }
        // Input basis apply for active bases
        CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields,
                                                           in_vec, impl->point_coords_elem, false, true, e_data, impl, CEED_REQUEST_IMMEDIATE));

        // -- Q function
        if (!impl->is_identity_qf) {
          CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
        }

        // -- Output basis apply and restriction
        CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
                                                            num_output_fields, impl->apply_add_basis_out, impl->skip_rstr_out, op, out_vec,
                                                            impl->point_coords_elem, true, impl, CEED_REQUEST_IMMEDIATE));

        // -- Build element matrix
        for (CeedInt j = 0; j < num_output_fields; j++) {
          bool                is_active;
          CeedInt             elem_size = 0;
          CeedRestrictionType rstr_type;
          CeedVector          vec;
          CeedElemRestriction elem_rstr;

          // ---- Skip non-active output
          CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[j], &vec));
          is_active = vec == CEED_VECTOR_ACTIVE;
          CeedCallBackend(CeedVectorDestroy(&vec));
          if (!is_active || impl->skip_rstr_out[j]) continue;

          // ---- Check if elem size matches
          CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[j], &elem_rstr));
          CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
          if (is_active_at_points && rstr_type != CEED_RESTRICTION_POINTS) {
            CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
            continue;
          }
          if (rstr_type == CEED_RESTRICTION_POINTS) {
            CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(elem_rstr, e, &elem_size));
          } else {
            CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
          }
          {
            CeedInt num_comp = 0;

            CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
            CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
            if (e_vec_size != num_comp * elem_size) continue;
          }
          // ---- Copy output
          {
            const CeedScalar *output;

            CeedCallBackend(CeedVectorGetArrayRead(impl->e_vecs_out[j], CEED_MEM_HOST, &output));
            for (CeedInt k = 0; k < e_vec_size; k++) {
              const CeedInt comp_out = k / elem_size_active;
              const CeedInt node_out = k % elem_size_active;

              assembled[offset + e * e_vec_size * e_vec_size + (comp_in * num_comp_active + comp_out) * elem_size_active * elem_size_active +
                        node_out * elem_size_active + node_in] = output[k];
            }
            CeedCallBackend(CeedVectorRestoreArrayRead(impl->e_vecs_out[j], &output));
          }
        }
        // -- Reset unit vector
        if (s == e_vec_size - 1) {
          CeedScalar *array;

          CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
          array[s] = 0.0;
          CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
        }
      }
    }
    num_points_offset += num_points;
  }

  // Restore input arrays
  CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));

  // Restore assembled values
  CeedCallBackend(CeedVectorRestoreArray(values, &assembled));

  // Cleanup
  CeedCallBackend(CeedDestroy(&ceed));
  CeedCallBackend(CeedVectorDestroy(&in_vec));
  CeedCallBackend(CeedVectorDestroy(&out_vec));
  CeedCallBackend(CeedVectorDestroy(&point_coords));
  CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
  CeedCallBackend(CeedQFunctionDestroy(&qf));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Operator Destroy
//------------------------------------------------------------------------------
static int CeedOperatorDestroy_Ref(CeedOperator op) {
  CeedOperator_Ref *impl;

  CeedCallBackend(CeedOperatorGetData(op, &impl));
  CeedCallBackend(CeedFree(&impl->skip_rstr_in));
  CeedCallBackend(CeedFree(&impl->skip_rstr_out));
  CeedCallBackend(CeedFree(&impl->e_data_out_indices));
  CeedCallBackend(CeedFree(&impl->apply_add_basis_out));
  for (CeedInt i = 0; i < impl->num_inputs + impl->num_outputs; i++) {
    CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_full[i]));
  }
  CeedCallBackend(CeedFree(&impl->e_vecs_full));
  CeedCallBackend(CeedFree(&impl->input_states));

  for (CeedInt i = 0; i < impl->num_inputs; i++) {
    CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_in[i]));
    CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_in[i]));
  }
  CeedCallBackend(CeedFree(&impl->e_vecs_in));
  CeedCallBackend(CeedFree(&impl->q_vecs_in));

  for (CeedInt i = 0; i < impl->num_outputs; i++) {
    CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_out[i]));
    CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_out[i]));
  }
  CeedCallBackend(CeedFree(&impl->e_vecs_out));
  CeedCallBackend(CeedFree(&impl->q_vecs_out));
  CeedCallBackend(CeedVectorDestroy(&impl->point_coords_elem));

  CeedCallBackend(CeedFree(&impl));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Operator Create
//------------------------------------------------------------------------------
int CeedOperatorCreate_Ref(CeedOperator op) {
  Ceed              ceed;
  CeedOperator_Ref *impl;

  CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
  CeedCallBackend(CeedCalloc(1, &impl));
  CeedCallBackend(CeedOperatorSetData(op, impl));
  CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunction_Ref));
  CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionUpdate_Ref));
  CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAdd_Ref));
  CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
  CeedCallBackend(CeedDestroy(&ceed));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Operator Create At Points
//------------------------------------------------------------------------------
int CeedOperatorCreateAtPoints_Ref(CeedOperator op) {
  Ceed              ceed;
  CeedOperator_Ref *impl;

  CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
  CeedCallBackend(CeedCalloc(1, &impl));
  CeedCallBackend(CeedOperatorSetData(op, impl));
  CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunctionAtPoints_Ref));
  CeedCallBackend(
      CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref));
  CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleAddDiagonal", CeedOperatorLinearAssembleAddDiagonalAtPoints_Ref));
  CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleSingle", CeedOperatorAssembleSingleAtPoints_Ref));
  CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAddAtPoints_Ref));
  CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
  CeedCallBackend(CeedDestroy(&ceed));
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------