xref: /libCEED/backends/ref/ceed-ref-operator.c (revision a0162de9bfaf277d9d50534bbae669b234f08437)

// Copyright (c) 2017-2018, Lawrence Livermore National Security, LLC.
// Produced at the Lawrence Livermore National Laboratory. LLNL-CODE-734707.
// All Rights reserved. See files LICENSE and NOTICE for details.
//
// This file is part of CEED, a collection of benchmarks, miniapps, software
// libraries and APIs for efficient high-order finite element and spectral
// element discretizations for exascale applications. For more information and
// source code availability see http://github.com/ceed.
//
// The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
// a collaborative effort of two U.S. Department of Energy organizations (Office
// of Science and the National Nuclear Security Administration) responsible for
// the planning and preparation of a capable exascale ecosystem, including
// software, applications, hardware, advanced system engineering and early
// testbed platforms, in support of the nation's exascale computing imperative.

#include <ceed/ceed.h>
#include <ceed/backend.h>
#include <math.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 inOrOut,
                                       CeedVector *full_evecs, CeedVector *e_vecs,
                                       CeedVector *q_vecs, CeedInt starte,
                                       CeedInt num_fields, CeedInt Q) {
  CeedInt dim, ierr, size, P;
  Ceed ceed;
  ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
  CeedBasis basis;
  CeedElemRestriction elem_restr;
  CeedOperatorField *op_fields;
  CeedQFunctionField *qf_fields;
  if (inOrOut) {
    ierr = CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields);
    CeedChkBackend(ierr);
    ierr = CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields);
    CeedChkBackend(ierr);
  } else {
    ierr = CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL);
    CeedChkBackend(ierr);
    ierr = CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL);
    CeedChkBackend(ierr);
  }

  // Loop over fields
  for (CeedInt i=0; i<num_fields; i++) {
    CeedEvalMode eval_mode;
    ierr = CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode);
    CeedChkBackend(ierr);

    if (eval_mode != CEED_EVAL_WEIGHT) {
      ierr = CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_restr);
      CeedChkBackend(ierr);
      ierr = CeedElemRestrictionCreateVector(elem_restr, NULL,
                                             &full_evecs[i+starte]);
      CeedChkBackend(ierr);
    }

    switch(eval_mode) {
    case CEED_EVAL_NONE:
      ierr = CeedQFunctionFieldGetSize(qf_fields[i], &size); CeedChkBackend(ierr);
      ierr = CeedVectorCreate(ceed, Q*size, &q_vecs[i]); CeedChkBackend(ierr);
      break;
    case CEED_EVAL_INTERP:
      ierr = CeedQFunctionFieldGetSize(qf_fields[i], &size); CeedChkBackend(ierr);
      ierr = CeedElemRestrictionGetElementSize(elem_restr, &P);
      CeedChkBackend(ierr);
      ierr = CeedVectorCreate(ceed, P*size, &e_vecs[i]); CeedChkBackend(ierr);
      ierr = CeedVectorCreate(ceed, Q*size, &q_vecs[i]); CeedChkBackend(ierr);
      break;
    case CEED_EVAL_GRAD:
      ierr = CeedOperatorFieldGetBasis(op_fields[i], &basis); CeedChkBackend(ierr);
      ierr = CeedQFunctionFieldGetSize(qf_fields[i], &size); CeedChkBackend(ierr);
      ierr = CeedBasisGetDimension(basis, &dim); CeedChkBackend(ierr);
      ierr = CeedElemRestrictionGetElementSize(elem_restr, &P);
      CeedChkBackend(ierr);
      ierr = CeedVectorCreate(ceed, P*size/dim, &e_vecs[i]); CeedChkBackend(ierr);
      ierr = CeedVectorCreate(ceed, Q*size, &q_vecs[i]); CeedChkBackend(ierr);
      break;
    case CEED_EVAL_WEIGHT: // Only on input fields
      ierr = CeedOperatorFieldGetBasis(op_fields[i], &basis); CeedChkBackend(ierr);
      ierr = CeedVectorCreate(ceed, Q, &q_vecs[i]); CeedChkBackend(ierr);
      ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
                            CEED_VECTOR_NONE, q_vecs[i]); CeedChkBackend(ierr);
      break;
    case CEED_EVAL_DIV:
      break; // Not implemented
    case CEED_EVAL_CURL:
      break; // Not implemented
    }
  }
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Setup Operator
//------------------------------------------------------------------------------/*
static int CeedOperatorSetup_Ref(CeedOperator op) {
  int ierr;
  bool setup_done;
  ierr = CeedOperatorIsSetupDone(op, &setup_done); CeedChkBackend(ierr);
  if (setup_done) return CEED_ERROR_SUCCESS;
  Ceed ceed;
  ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
  CeedOperator_Ref *impl;
  ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
  CeedQFunction qf;
  ierr = CeedOperatorGetQFunction(op, &qf); CeedChkBackend(ierr);
  CeedInt Q, num_input_fields, num_output_fields;
  ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChkBackend(ierr);
  ierr = CeedQFunctionIsIdentity(qf, &impl->is_identity_qf); CeedChkBackend(ierr);
  CeedOperatorField *op_input_fields, *op_output_fields;
  ierr = CeedOperatorGetFields(op, &num_input_fields, &op_input_fields,
                               &num_output_fields, &op_output_fields);
  CeedChkBackend(ierr);
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  ierr = CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL,
                                &qf_output_fields);
  CeedChkBackend(ierr);

  // Allocate
  ierr = CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs);
  CeedChkBackend(ierr);

  ierr = CeedCalloc(CEED_FIELD_MAX, &impl->input_state); CeedChkBackend(ierr);
  ierr = CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in); CeedChkBackend(ierr);
  ierr = CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out); CeedChkBackend(ierr);
  ierr = CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in); CeedChkBackend(ierr);
  ierr = CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out); CeedChkBackend(ierr);

  impl->num_e_vecs_in = num_input_fields;
  impl->num_e_vecs_out = num_output_fields;

  // Set up infield and outfield e_vecs and q_vecs
  // Infields
  ierr = CeedOperatorSetupFields_Ref(qf, op, 0, impl->e_vecs,
                                     impl->e_vecs_in, impl->q_vecs_in, 0,
                                     num_input_fields, Q);
  CeedChkBackend(ierr);
  // Outfields
  ierr = CeedOperatorSetupFields_Ref(qf, op, 1, impl->e_vecs,
                                     impl->e_vecs_out, impl->q_vecs_out,
                                     num_input_fields, num_output_fields, Q);
  CeedChkBackend(ierr);

  // Identity QFunctions
  if (impl->is_identity_qf) {
    CeedEvalMode in_mode, out_mode;
    CeedQFunctionField *in_fields, *out_fields;
    ierr = CeedQFunctionGetFields(qf, NULL, &in_fields, NULL, &out_fields);
    CeedChkBackend(ierr);
    ierr = CeedQFunctionFieldGetEvalMode(in_fields[0], &in_mode);
    CeedChkBackend(ierr);
    ierr = CeedQFunctionFieldGetEvalMode(out_fields[0], &out_mode);
    CeedChkBackend(ierr);

    if (in_mode == CEED_EVAL_NONE && out_mode == CEED_EVAL_NONE) {
      impl->is_identity_restr_op = true;
    } else {
      ierr = CeedVectorDestroy(&impl->q_vecs_out[0]); CeedChkBackend(ierr);
      impl->q_vecs_out[0] = impl->q_vecs_in[0];
      ierr = CeedVectorAddReference(impl->q_vecs_in[0]); CeedChkBackend(ierr);
    }
  }

  ierr = CeedOperatorSetSetupDone(op); CeedChkBackend(ierr);

  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[2*CEED_FIELD_MAX],
    CeedOperator_Ref *impl, CeedRequest *request) {
  CeedInt ierr;
  CeedEvalMode eval_mode;
  CeedVector vec;
  CeedElemRestriction elem_restr;
  uint64_t state;

  for (CeedInt i=0; i<num_input_fields; i++) {
    // Get input vector
    ierr = CeedOperatorFieldGetVector(op_input_fields[i], &vec);
    CeedChkBackend(ierr);
    if (vec == CEED_VECTOR_ACTIVE) {
      if (skip_active)
        continue;
      else
        vec = in_vec;
    }

    ierr = CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode);
    CeedChkBackend(ierr);
    // Restrict and Evec
    if (eval_mode == CEED_EVAL_WEIGHT) { // Skip
    } else {
      // Restrict
      ierr = CeedVectorGetState(vec, &state); CeedChkBackend(ierr);
      // Skip restriction if input is unchanged
      if (state != impl->input_state[i] || vec == in_vec) {
        ierr = CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_restr);
        CeedChkBackend(ierr);
        ierr = CeedElemRestrictionApply(elem_restr, CEED_NOTRANSPOSE, vec,
                                        impl->e_vecs[i], request); CeedChkBackend(ierr);
        impl->input_state[i] = state;
      }
      // Get evec
      ierr = CeedVectorGetArrayRead(impl->e_vecs[i], CEED_MEM_HOST,
                                    (const CeedScalar **) &e_data[i]);
      CeedChkBackend(ierr);
    }
  }
  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[2*CEED_FIELD_MAX], CeedOperator_Ref *impl) {
  CeedInt ierr;
  CeedInt dim, elem_size, size;
  CeedElemRestriction elem_restr;
  CeedEvalMode eval_mode;
  CeedBasis basis;

  for (CeedInt i=0; i<num_input_fields; i++) {
    // Skip active input
    if (skip_active) {
      CeedVector vec;
      ierr = CeedOperatorFieldGetVector(op_input_fields[i], &vec);
      CeedChkBackend(ierr);
      if (vec == CEED_VECTOR_ACTIVE)
        continue;
    }
    // Get elem_size, eval_mode, size
    ierr = CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_restr);
    CeedChkBackend(ierr);
    ierr = CeedElemRestrictionGetElementSize(elem_restr, &elem_size);
    CeedChkBackend(ierr);
    ierr = CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode);
    CeedChkBackend(ierr);
    ierr = CeedQFunctionFieldGetSize(qf_input_fields[i], &size);
    CeedChkBackend(ierr);
    // Basis action
    switch(eval_mode) {
    case CEED_EVAL_NONE:
      ierr = CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST,
                                CEED_USE_POINTER, &e_data[i][e*Q*size]);
      CeedChkBackend(ierr);
      break;
    case CEED_EVAL_INTERP:
      ierr = CeedOperatorFieldGetBasis(op_input_fields[i], &basis);
      CeedChkBackend(ierr);
      ierr = CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST,
                                CEED_USE_POINTER, &e_data[i][e*elem_size*size]);
      CeedChkBackend(ierr);
      ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP,
                            impl->e_vecs_in[i], impl->q_vecs_in[i]); CeedChkBackend(ierr);
      break;
    case CEED_EVAL_GRAD:
      ierr = CeedOperatorFieldGetBasis(op_input_fields[i], &basis);
      CeedChkBackend(ierr);
      ierr = CeedBasisGetDimension(basis, &dim); CeedChkBackend(ierr);
      ierr = CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST,
                                CEED_USE_POINTER, &e_data[i][e*elem_size*size/dim]);
      CeedChkBackend(ierr);
      ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
                            CEED_EVAL_GRAD, impl->e_vecs_in[i],
                            impl->q_vecs_in[i]); CeedChkBackend(ierr);
      break;
    case CEED_EVAL_WEIGHT:
      break;  // No action
    // LCOV_EXCL_START
    case CEED_EVAL_DIV:
    case CEED_EVAL_CURL: {
      ierr = CeedOperatorFieldGetBasis(op_input_fields[i], &basis);
      CeedChkBackend(ierr);
      Ceed ceed;
      ierr = CeedBasisGetCeed(basis, &ceed); CeedChkBackend(ierr);
      return CeedError(ceed, CEED_ERROR_BACKEND,
                       "Ceed evaluation mode not implemented");
      // LCOV_EXCL_STOP
    }
    }
  }
  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, CeedOperator op,
    CeedScalar *e_data[2*CEED_FIELD_MAX], CeedOperator_Ref *impl) {
  CeedInt ierr;
  CeedInt dim, elem_size, size;
  CeedElemRestriction elem_restr;
  CeedEvalMode eval_mode;
  CeedBasis basis;

  for (CeedInt i=0; i<num_output_fields; i++) {
    // Get elem_size, eval_mode, size
    ierr = CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_restr);
    CeedChkBackend(ierr);
    ierr = CeedElemRestrictionGetElementSize(elem_restr, &elem_size);
    CeedChkBackend(ierr);
    ierr = CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode);
    CeedChkBackend(ierr);
    ierr = CeedQFunctionFieldGetSize(qf_output_fields[i], &size);
    CeedChkBackend(ierr);
    // Basis action
    switch(eval_mode) {
    case CEED_EVAL_NONE:
      break; // No action
    case CEED_EVAL_INTERP:
      ierr = CeedOperatorFieldGetBasis(op_output_fields[i], &basis);
      CeedChkBackend(ierr);
      ierr = CeedVectorSetArray(impl->e_vecs_out[i], CEED_MEM_HOST,
                                CEED_USE_POINTER,
                                &e_data[i + num_input_fields][e*elem_size*size]);
      CeedChkBackend(ierr);
      ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
                            CEED_EVAL_INTERP, impl->q_vecs_out[i],
                            impl->e_vecs_out[i]); CeedChkBackend(ierr);
      break;
    case CEED_EVAL_GRAD:
      ierr = CeedOperatorFieldGetBasis(op_output_fields[i], &basis);
      CeedChkBackend(ierr);
      ierr = CeedBasisGetDimension(basis, &dim); CeedChkBackend(ierr);
      ierr = CeedVectorSetArray(impl->e_vecs_out[i], CEED_MEM_HOST,
                                CEED_USE_POINTER,
                                &e_data[i + num_input_fields][e*elem_size*size/dim]);
      CeedChkBackend(ierr);
      ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
                            CEED_EVAL_GRAD, impl->q_vecs_out[i],
                            impl->e_vecs_out[i]); CeedChkBackend(ierr);
      break;
    // LCOV_EXCL_START
    case CEED_EVAL_WEIGHT: {
      Ceed ceed;
      ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
      return CeedError(ceed, CEED_ERROR_BACKEND,
                       "CEED_EVAL_WEIGHT cannot be an output "
                       "evaluation mode");
    }
    case CEED_EVAL_DIV:
    case CEED_EVAL_CURL: {
      Ceed ceed;
      ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
      return CeedError(ceed, CEED_ERROR_BACKEND,
                       "Ceed evaluation mode not implemented");
      // 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[2*CEED_FIELD_MAX],
    CeedOperator_Ref *impl) {
  CeedInt ierr;
  CeedEvalMode eval_mode;

  for (CeedInt i=0; i<num_input_fields; i++) {
    // Skip active inputs
    if (skip_active) {
      CeedVector vec;
      ierr = CeedOperatorFieldGetVector(op_input_fields[i], &vec);
      CeedChkBackend(ierr);
      if (vec == CEED_VECTOR_ACTIVE)
        continue;
    }
    // Restore input
    ierr = CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode);
    CeedChkBackend(ierr);
    if (eval_mode == CEED_EVAL_WEIGHT) { // Skip
    } else {
      ierr = CeedVectorRestoreArrayRead(impl->e_vecs[i],
                                        (const CeedScalar **) &e_data[i]);
      CeedChkBackend(ierr);
    }
  }
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Operator Apply
//------------------------------------------------------------------------------
static int CeedOperatorApplyAdd_Ref(CeedOperator op, CeedVector in_vec,
                                    CeedVector out_vec, CeedRequest *request) {
  int ierr;
  CeedOperator_Ref *impl;
  ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
  CeedQFunction qf;
  ierr = CeedOperatorGetQFunction(op, &qf); CeedChkBackend(ierr);
  CeedInt Q, num_elem, num_input_fields, num_output_fields, size;
  ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChkBackend(ierr);
  ierr = CeedOperatorGetNumElements(op, &num_elem); CeedChkBackend(ierr);
  CeedOperatorField *op_input_fields, *op_output_fields;
  ierr = CeedOperatorGetFields(op, &num_input_fields, &op_input_fields,
                               &num_output_fields, &op_output_fields);
  CeedChkBackend(ierr);
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  ierr = CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL,
                                &qf_output_fields);
  CeedChkBackend(ierr);
  CeedEvalMode eval_mode;
  CeedVector vec;
  CeedElemRestriction elem_restr;
  CeedScalar *e_data[2*CEED_FIELD_MAX] = {0};

  // Setup
  ierr = CeedOperatorSetup_Ref(op); CeedChkBackend(ierr);

  // Restriction only operator
  if (impl->is_identity_restr_op) {
    ierr = CeedOperatorFieldGetElemRestriction(op_input_fields[0], &elem_restr);
    CeedChkBackend(ierr);
    ierr = CeedElemRestrictionApply(elem_restr, CEED_NOTRANSPOSE, in_vec,
                                    impl->e_vecs[0], request); CeedChkBackend(ierr);
    ierr = CeedOperatorFieldGetElemRestriction(op_output_fields[0], &elem_restr);
    CeedChkBackend(ierr);
    ierr = CeedElemRestrictionApply(elem_restr, CEED_TRANSPOSE, impl->e_vecs[0],
                                    out_vec, request); CeedChkBackend(ierr);
    return CEED_ERROR_SUCCESS;
  }

  // Input Evecs and Restriction
  ierr = CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields,
                                     op_input_fields, in_vec, false, e_data, impl,
                                     request); CeedChkBackend(ierr);

  // Output Evecs
  for (CeedInt i=0; i<num_output_fields; i++) {
    ierr = CeedVectorGetArray(impl->e_vecs[i+impl->num_e_vecs_in], CEED_MEM_HOST,
                              &e_data[i + num_input_fields]); CeedChkBackend(ierr);
  }

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

    // Input basis apply
    ierr = CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields,
                                      num_input_fields, false, e_data, impl);
    CeedChkBackend(ierr);

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

    // Output basis apply
    ierr = CeedOperatorOutputBasis_Ref(e, Q, qf_output_fields, op_output_fields,
                                       num_input_fields, num_output_fields, op,
                                       e_data, impl); CeedChkBackend(ierr);
  }

  // Output restriction
  for (CeedInt i=0; i<num_output_fields; i++) {
    // Restore Evec
    ierr = CeedVectorRestoreArray(impl->e_vecs[i+impl->num_e_vecs_in],
                                  &e_data[i + num_input_fields]);
    CeedChkBackend(ierr);
    // Get output vector
    ierr = CeedOperatorFieldGetVector(op_output_fields[i], &vec);
    CeedChkBackend(ierr);
    // Active
    if (vec == CEED_VECTOR_ACTIVE)
      vec = out_vec;
    // Restrict
    ierr = CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_restr);
    CeedChkBackend(ierr);
    ierr = CeedElemRestrictionApply(elem_restr, CEED_TRANSPOSE,
                                    impl->e_vecs[i+impl->num_e_vecs_in], vec, request);
    CeedChkBackend(ierr);
  }

  // Restore input arrays
  ierr = CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields,
                                       op_input_fields, false, e_data, impl);
  CeedChkBackend(ierr);

  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) {
  int ierr;
  CeedOperator_Ref *impl;
  ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
  CeedQFunction qf;
  ierr = CeedOperatorGetQFunction(op, &qf); CeedChkBackend(ierr);
  CeedInt Q, num_elem, num_input_fields, num_output_fields, size;
  ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChkBackend(ierr);
  ierr = CeedOperatorGetNumElements(op, &num_elem); CeedChkBackend(ierr);
  CeedOperatorField *op_input_fields, *op_output_fields;
  ierr = CeedOperatorGetFields(op, &num_input_fields, &op_input_fields,
                               &num_output_fields, &op_output_fields);
  CeedChkBackend(ierr);
  CeedQFunctionField *qf_input_fields, *qf_output_fields;
  ierr = CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL,
                                &qf_output_fields);
  CeedChkBackend(ierr);
  CeedVector vec;
  CeedInt num_active_in = impl->qf_num_active_in,
          num_active_out = impl->qf_num_active_out;
  CeedVector *active_in = impl->qf_active_in;
  CeedScalar *a, *tmp;
  Ceed ceed, ceed_parent;
  ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
  ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceed_parent);
  CeedChkBackend(ierr);
  ceed_parent = ceed_parent ? ceed_parent : ceed;
  CeedScalar *e_data[2*CEED_FIELD_MAX] = {0};

  // Setup
  ierr = CeedOperatorSetup_Ref(op); CeedChkBackend(ierr);

  // Check for identity
  if (impl->is_identity_qf)
    // LCOV_EXCL_START
    return CeedError(ceed, CEED_ERROR_BACKEND,
                     "Assembling identity QFunctions not supported");
  // LCOV_EXCL_STOP

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

  // Count number of active input fields
  if (!num_active_in) {
    for (CeedInt i=0; i<num_input_fields; i++) {
      // Get input vector
      ierr = CeedOperatorFieldGetVector(op_input_fields[i], &vec);
      CeedChkBackend(ierr);
      // Check if active input
      if (vec == CEED_VECTOR_ACTIVE) {
        ierr = CeedQFunctionFieldGetSize(qf_input_fields[i], &size);
        CeedChkBackend(ierr);
        ierr = CeedVectorSetValue(impl->q_vecs_in[i], 0.0); CeedChkBackend(ierr);
        ierr = CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &tmp);
        CeedChkBackend(ierr);
        ierr = CeedRealloc(num_active_in + size, &active_in); CeedChkBackend(ierr);
        for (CeedInt field=0; field<size; field++) {
          ierr = CeedVectorCreate(ceed, Q, &active_in[num_active_in+field]);
          CeedChkBackend(ierr);
          ierr = CeedVectorSetArray(active_in[num_active_in+field], CEED_MEM_HOST,
                                    CEED_USE_POINTER, &tmp[field*Q]);
          CeedChkBackend(ierr);
        }
        num_active_in += size;
        ierr = CeedVectorRestoreArray(impl->q_vecs_in[i], &tmp); CeedChkBackend(ierr);
      }
    }
    impl->qf_num_active_in = num_active_in;
    impl->qf_active_in = active_in;
  }

  // Count number of active output fields
  if (!num_active_out) {
    for (CeedInt i=0; i<num_output_fields; i++) {
      // Get output vector
      ierr = CeedOperatorFieldGetVector(op_output_fields[i], &vec);
      CeedChkBackend(ierr);
      // Check if active output
      if (vec == CEED_VECTOR_ACTIVE) {
        ierr = CeedQFunctionFieldGetSize(qf_output_fields[i], &size);
        CeedChkBackend(ierr);
        num_active_out += size;
      }
    }
    impl->qf_num_active_out = num_active_out;
  }

  // Check sizes
  if (!num_active_in || !num_active_out)
    // LCOV_EXCL_START
    return CeedError(ceed, CEED_ERROR_BACKEND,
                     "Cannot assemble QFunction without active inputs "
                     "and outputs");
  // LCOV_EXCL_STOP

  // Build objects if needed
  if (build_objects) {
    // Create output restriction
    CeedInt strides[3] = {1, Q, num_active_in*num_active_out*Q}; /* *NOPAD* */
    ierr = CeedElemRestrictionCreateStrided(ceed_parent, num_elem, Q,
                                            num_active_in*num_active_out,
                                            num_active_in*num_active_out*num_elem*Q,
                                            strides, rstr); CeedChkBackend(ierr);
    // Create assembled vector
    ierr = CeedVectorCreate(ceed_parent, num_elem*Q*num_active_in*num_active_out,
                            assembled); CeedChkBackend(ierr);
  }
  // Clear output vector
  ierr = CeedVectorSetValue(*assembled, 0.0); CeedChkBackend(ierr);
  ierr = CeedVectorGetArray(*assembled, CEED_MEM_HOST, &a); CeedChkBackend(ierr);

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

    // Assemble QFunction
    for (CeedInt in=0; in<num_active_in; in++) {
      // Set Inputs
      ierr = CeedVectorSetValue(active_in[in], 1.0); CeedChkBackend(ierr);
      if (num_active_in > 1) {
        ierr = CeedVectorSetValue(active_in[(in+num_active_in-1)%num_active_in],
                                  0.0); CeedChkBackend(ierr);
      }
      // Set Outputs
      for (CeedInt out=0; out<num_output_fields; out++) {
        // Get output vector
        ierr = CeedOperatorFieldGetVector(op_output_fields[out], &vec);
        CeedChkBackend(ierr);
        // Check if active output
        if (vec == CEED_VECTOR_ACTIVE) {
          CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST,
                             CEED_USE_POINTER, a); CeedChkBackend(ierr);
          ierr = CeedQFunctionFieldGetSize(qf_output_fields[out], &size);
          CeedChkBackend(ierr);
          a += size*Q; // Advance the pointer by the size of the output
        }
      }
      // Apply QFunction
      ierr = CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out);
      CeedChkBackend(ierr);
    }
  }

  // Un-set output Qvecs to prevent accidental overwrite of Assembled
  for (CeedInt out=0; out<num_output_fields; out++) {
    // Get output vector
    ierr = CeedOperatorFieldGetVector(op_output_fields[out], &vec);
    CeedChkBackend(ierr);
    // Check if active output
    if (vec == CEED_VECTOR_ACTIVE) {
      CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL);
      CeedChkBackend(ierr);
    }
  }

  // Restore input arrays
  ierr = CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields,
                                       op_input_fields, true, e_data, impl);
  CeedChkBackend(ierr);

  // Restore output
  ierr = CeedVectorRestoreArray(*assembled, &a); CeedChkBackend(ierr);

  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);
}

//------------------------------------------------------------------------------
// Operator Destroy
//------------------------------------------------------------------------------
static int CeedOperatorDestroy_Ref(CeedOperator op) {
  int ierr;
  CeedOperator_Ref *impl;
  ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);

  for (CeedInt i=0; i<impl->num_e_vecs_in+impl->num_e_vecs_out; i++) {
    ierr = CeedVectorDestroy(&impl->e_vecs[i]); CeedChkBackend(ierr);
  }
  ierr = CeedFree(&impl->e_vecs); CeedChkBackend(ierr);
  ierr = CeedFree(&impl->input_state); CeedChkBackend(ierr);

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

  for (CeedInt i=0; i<impl->num_e_vecs_out; i++) {
    ierr = CeedVectorDestroy(&impl->e_vecs_out[i]); CeedChkBackend(ierr);
    ierr = CeedVectorDestroy(&impl->q_vecs_out[i]); CeedChkBackend(ierr);
  }
  ierr = CeedFree(&impl->e_vecs_out); CeedChkBackend(ierr);
  ierr = CeedFree(&impl->q_vecs_out); CeedChkBackend(ierr);

  // QFunction assembly
  for (CeedInt i=0; i<impl->qf_num_active_in; i++) {
    ierr = CeedVectorDestroy(&impl->qf_active_in[i]); CeedChkBackend(ierr);
  }
  ierr = CeedFree(&impl->qf_active_in); CeedChkBackend(ierr);

  ierr = CeedFree(&impl); CeedChkBackend(ierr);
  return CEED_ERROR_SUCCESS;
}

//------------------------------------------------------------------------------
// Operator Create
//------------------------------------------------------------------------------
int CeedOperatorCreate_Ref(CeedOperator op) {
  int ierr;
  Ceed ceed;
  ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
  CeedOperator_Ref *impl;

  ierr = CeedCalloc(1, &impl); CeedChkBackend(ierr);
  ierr = CeedOperatorSetData(op, impl); CeedChkBackend(ierr);

  ierr = CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction",
                                CeedOperatorLinearAssembleQFunction_Ref);
  CeedChkBackend(ierr);
  ierr = CeedSetBackendFunction(ceed, "Operator", op,
                                "LinearAssembleQFunctionUpdate",
                                CeedOperatorLinearAssembleQFunctionUpdate_Ref);
  CeedChkBackend(ierr);
  ierr = CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd",
                                CeedOperatorApplyAdd_Ref); CeedChkBackend(ierr);
  ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
                                CeedOperatorDestroy_Ref); CeedChkBackend(ierr);
  return CEED_ERROR_SUCCESS;
}