xref: /libCEED/backends/ref/ceed-ref-operator.c (revision a7b7f929ab476a681f8a846f95c06992dbac3dd3)

// 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-ref.h"

static int CeedOperatorDestroy_Ref(CeedOperator op) {
  int ierr;
  CeedOperator_Ref *impl;
  ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);

  for (CeedInt i=0; i<impl->numein+impl->numeout; i++) {
    ierr = CeedVectorDestroy(&impl->evecs[i]); CeedChk(ierr);
  }
  ierr = CeedFree(&impl->evecs); CeedChk(ierr);
  ierr = CeedFree(&impl->edata); CeedChk(ierr);
  ierr = CeedFree(&impl->inputstate); CeedChk(ierr);

  for (CeedInt i=0; i<impl->numein; i++) {
    ierr = CeedVectorDestroy(&impl->evecsin[i]); CeedChk(ierr);
    ierr = CeedVectorDestroy(&impl->qvecsin[i]); CeedChk(ierr);
  }
  ierr = CeedFree(&impl->evecsin); CeedChk(ierr);
  ierr = CeedFree(&impl->qvecsin); CeedChk(ierr);

  for (CeedInt i=0; i<impl->numeout; i++) {
    ierr = CeedVectorDestroy(&impl->evecsout[i]); CeedChk(ierr);
    ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
  }
  ierr = CeedFree(&impl->evecsout); CeedChk(ierr);
  ierr = CeedFree(&impl->qvecsout); CeedChk(ierr);

  ierr = CeedFree(&impl); CeedChk(ierr);
  return 0;
}

/*
  Setup infields or outfields
 */
static int CeedOperatorSetupFields_Ref(CeedQFunction qf, CeedOperator op,
                                       bool inOrOut,
                                       CeedVector *fullevecs, CeedVector *evecs,
                                       CeedVector *qvecs, CeedInt starte,
                                       CeedInt numfields, CeedInt Q) {
  CeedInt dim, ierr, size, P;
  Ceed ceed;
  ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
  CeedBasis basis;
  CeedElemRestriction Erestrict;
  CeedOperatorField *opfields;
  CeedQFunctionField *qffields;
  if (inOrOut) {
    ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
    ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
  } else {
    ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
    ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
  }

  // Loop over fields
  for (CeedInt i=0; i<numfields; i++) {
    CeedEvalMode emode;
    ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);

    if (emode != CEED_EVAL_WEIGHT) {
      ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &Erestrict);
      CeedChk(ierr);
      ierr = CeedElemRestrictionCreateVector(Erestrict, NULL,
                                             &fullevecs[i+starte]);
      CeedChk(ierr);
    }

    switch(emode) {
    case CEED_EVAL_NONE:
      ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
      ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
      break;
    case CEED_EVAL_INTERP:
      ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
      ierr = CeedElemRestrictionGetElementSize(Erestrict, &P);
      CeedChk(ierr);
      ierr = CeedVectorCreate(ceed, P*size, &evecs[i]); CeedChk(ierr);
      ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
      break;
    case CEED_EVAL_GRAD:
      ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
      ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
      ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
      ierr = CeedElemRestrictionGetElementSize(Erestrict, &P);
      CeedChk(ierr);
      ierr = CeedVectorCreate(ceed, P*size/dim, &evecs[i]); CeedChk(ierr);
      ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
      break;
    case CEED_EVAL_WEIGHT: // Only on input fields
      ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
      ierr = CeedVectorCreate(ceed, Q, &qvecs[i]); CeedChk(ierr);
      ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
                            CEED_VECTOR_NONE, qvecs[i]); CeedChk(ierr);
      break;
    case CEED_EVAL_DIV:
      break; // Not implemented
    case CEED_EVAL_CURL:
      break; // Not implemented
    }
  }
  return 0;
}

/*
  CeedOperator needs to connect all the named fields (be they active or passive)
  to the named inputs and outputs of its CeedQFunction.
 */
static int CeedOperatorSetup_Ref(CeedOperator op) {
  int ierr;
  bool setupdone;
  ierr = CeedOperatorGetSetupStatus(op, &setupdone); CeedChk(ierr);
  if (setupdone) return 0;
  Ceed ceed;
  ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
  CeedOperator_Ref *impl;
  ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
  CeedQFunction qf;
  ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
  CeedInt Q, numinputfields, numoutputfields;
  ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
  ierr = CeedQFunctionGetIdentityStatus(qf, &impl->identityqf); CeedChk(ierr);
  ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
  CeedChk(ierr);
  CeedOperatorField *opinputfields, *opoutputfields;
  ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
  CeedChk(ierr);
  CeedQFunctionField *qfinputfields, *qfoutputfields;
  ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
  CeedChk(ierr);

  // Allocate
  ierr = CeedCalloc(numinputfields + numoutputfields, &impl->evecs);
  CeedChk(ierr);
  ierr = CeedCalloc(numinputfields + numoutputfields, &impl->edata);
  CeedChk(ierr);

  ierr = CeedCalloc(16, &impl->inputstate); CeedChk(ierr);
  ierr = CeedCalloc(16, &impl->evecsin); CeedChk(ierr);
  ierr = CeedCalloc(16, &impl->evecsout); CeedChk(ierr);
  ierr = CeedCalloc(16, &impl->qvecsin); CeedChk(ierr);
  ierr = CeedCalloc(16, &impl->qvecsout); CeedChk(ierr);

  impl->numein = numinputfields; impl->numeout = numoutputfields;

  // Set up infield and outfield evecs and qvecs
  // Infields
  ierr = CeedOperatorSetupFields_Ref(qf, op, 0, impl->evecs,
                                     impl->evecsin, impl->qvecsin, 0,
                                     numinputfields, Q);
  CeedChk(ierr);
  // Outfields
  ierr = CeedOperatorSetupFields_Ref(qf, op, 1, impl->evecs,
                                     impl->evecsout, impl->qvecsout,
                                     numinputfields, numoutputfields, Q);
  CeedChk(ierr);

  // Identity QFunctions
  if (impl->identityqf) {
    CeedEvalMode inmode, outmode;
    CeedQFunctionField *infields, *outfields;
    ierr = CeedQFunctionGetFields(qf, &infields, &outfields); CeedChk(ierr);

    for (CeedInt i=0; i<numinputfields; i++) {
      ierr = CeedQFunctionFieldGetEvalMode(infields[i], &inmode);
      CeedChk(ierr);
      ierr = CeedQFunctionFieldGetEvalMode(outfields[i], &outmode);
      CeedChk(ierr);

      ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
      impl->qvecsout[i] = impl->qvecsin[i];
      ierr = CeedVectorAddReference(impl->qvecsin[i]); CeedChk(ierr);
    }
  }

  ierr = CeedOperatorSetSetupDone(op); CeedChk(ierr);

  return 0;
}

// Setup Input fields
static inline int CeedOperatorSetupInputs_Ref(CeedInt numinputfields,
    CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
    CeedVector invec, const bool skipactive, CeedOperator_Ref *impl,
    CeedRequest *request) {
  CeedInt ierr;
  CeedEvalMode emode;
  CeedVector vec;
  CeedElemRestriction Erestrict;
  CeedTransposeMode lmode;
  uint64_t state;

  for (CeedInt i=0; i<numinputfields; i++) {
    // Get input vector
    ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
    if (vec == CEED_VECTOR_ACTIVE) {
      if (skipactive)
        continue;
      else
        vec = invec;
    }

    ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
    CeedChk(ierr);
    // Restrict and Evec
    if (emode == CEED_EVAL_WEIGHT) { // Skip
    } else {
      // Restrict
      ierr = CeedVectorGetState(vec, &state); CeedChk(ierr);
      // Skip restriction if input is unchanged
      if (state != impl->inputstate[i] || vec == invec) {
        ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
        CeedChk(ierr);
        ierr = CeedOperatorFieldGetLMode(opinputfields[i], &lmode);
        CeedChk(ierr);
        ierr = CeedElemRestrictionApply(Erestrict, CEED_NOTRANSPOSE,
                                        lmode, vec, impl->evecs[i],
                                        request); CeedChk(ierr);
        impl->inputstate[i] = state;
      }
      // Get evec
      ierr = CeedVectorGetArrayRead(impl->evecs[i], CEED_MEM_HOST,
                                    (const CeedScalar **) &impl->edata[i]);
      CeedChk(ierr);
    }
  }
  return 0;
}

// Input basis action
static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q,
    CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
    CeedInt numinputfields, const bool skipactive, CeedOperator_Ref *impl) {
  CeedInt ierr;
  CeedInt dim, elemsize, size;
  CeedElemRestriction Erestrict;
  CeedEvalMode emode;
  CeedBasis basis;

  for (CeedInt i=0; i<numinputfields; i++) {
    // Skip active input
    if (skipactive) {
      CeedVector vec;
      ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
      if (vec == CEED_VECTOR_ACTIVE)
        continue;
    }
    // Get elemsize, emode, size
    ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
    CeedChk(ierr);
    ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
    CeedChk(ierr);
    ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
    CeedChk(ierr);
    ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
    // Basis action
    switch(emode) {
    case CEED_EVAL_NONE:
      ierr = CeedVectorSetArray(impl->qvecsin[i], CEED_MEM_HOST,
                                CEED_USE_POINTER,
                                &impl->edata[i][e*Q*size]); CeedChk(ierr);
      break;
    case CEED_EVAL_INTERP:
      ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
      ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
                                CEED_USE_POINTER,
                                &impl->edata[i][e*elemsize*size]);
      CeedChk(ierr);
      ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
                            CEED_EVAL_INTERP, impl->evecsin[i],
                            impl->qvecsin[i]); CeedChk(ierr);
      break;
    case CEED_EVAL_GRAD:
      ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
      ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
      ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
                                CEED_USE_POINTER,
                                &impl->edata[i][e*elemsize*size/dim]);
      CeedChk(ierr);
      ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
                            CEED_EVAL_GRAD, impl->evecsin[i],
                            impl->qvecsin[i]); CeedChk(ierr);
      break;
    case CEED_EVAL_WEIGHT:
      break;  // No action
    case CEED_EVAL_DIV:
    case CEED_EVAL_CURL: {
      // LCOV_EXCL_START
      ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis);
      CeedChk(ierr);
      Ceed ceed;
      ierr = CeedBasisGetCeed(basis, &ceed); CeedChk(ierr);
      return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
      // LCOV_EXCL_STOP
      break; // Not implemented
    }
    }
  }
  return 0;
}

// Output basis action
static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q,
    CeedQFunctionField *qfoutputfields, CeedOperatorField *opoutputfields,
    CeedInt numinputfields, CeedInt numoutputfields, CeedOperator op,
    CeedOperator_Ref *impl) {
  CeedInt ierr;
  CeedInt dim, elemsize, size;
  CeedElemRestriction Erestrict;
  CeedEvalMode emode;
  CeedBasis basis;

  for (CeedInt i=0; i<numoutputfields; i++) {
    // Get elemsize, emode, size
    ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
    CeedChk(ierr);
    ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
    CeedChk(ierr);
    ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
    CeedChk(ierr);
    ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
    // Basis action
    switch(emode) {
    case CEED_EVAL_NONE:
      break; // No action
    case CEED_EVAL_INTERP:
      ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
      CeedChk(ierr);
      ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
                                CEED_USE_POINTER,
                                &impl->edata[i + numinputfields][e*elemsize*size]);
      CeedChk(ierr);
      ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
                            CEED_EVAL_INTERP, impl->qvecsout[i],
                            impl->evecsout[i]); CeedChk(ierr);
      break;
    case CEED_EVAL_GRAD:
      ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
      CeedChk(ierr);
      ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
      ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
                                CEED_USE_POINTER,
                                &impl->edata[i + numinputfields][e*elemsize*size/dim]);
      CeedChk(ierr);
      ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
                            CEED_EVAL_GRAD, impl->qvecsout[i],
                            impl->evecsout[i]); CeedChk(ierr);
      break;
    case CEED_EVAL_WEIGHT: {
      // LCOV_EXCL_START
      Ceed ceed;
      ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
      return CeedError(ceed, 1, "CEED_EVAL_WEIGHT cannot be an output "
                       "evaluation mode");
      // LCOV_EXCL_STOP
      break; // Should not occur
    }
    case CEED_EVAL_DIV:
    case CEED_EVAL_CURL: {
      // LCOV_EXCL_START
      Ceed ceed;
      ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
      return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
      // LCOV_EXCL_STOP
      break; // Not implemented
    }
    }
  }
  return 0;
}

// Restore Inputs
static inline int CeedOperatorRestoreInputs_Ref(CeedInt numinputfields,
    CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
    const bool skipactive, CeedOperator_Ref *impl) {
  CeedInt ierr;
  CeedEvalMode emode;

  for (CeedInt i=0; i<numinputfields; i++) {
    // Skip active inputs
    if (skipactive) {
      CeedVector vec;
      ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
      if (vec == CEED_VECTOR_ACTIVE)
        continue;
    }
    // Restore input
    ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
    CeedChk(ierr);
    if (emode == CEED_EVAL_WEIGHT) { // Skip
    } else {
      ierr = CeedVectorRestoreArrayRead(impl->evecs[i],
                                        (const CeedScalar **) &impl->edata[i]);
      CeedChk(ierr);
    }
  }
  return 0;
}

// Apply Operator
static int CeedOperatorApply_Ref(CeedOperator op, CeedVector invec,
                                 CeedVector outvec, CeedRequest *request) {
  int ierr;
  CeedOperator_Ref *impl;
  ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
  CeedQFunction qf;
  ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
  CeedInt Q, numelements, numinputfields, numoutputfields, size;
  ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
  ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
  ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
  CeedChk(ierr);
  CeedTransposeMode lmode;
  CeedOperatorField *opinputfields, *opoutputfields;
  ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
  CeedChk(ierr);
  CeedQFunctionField *qfinputfields, *qfoutputfields;
  ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
  CeedChk(ierr);
  CeedEvalMode emode;
  CeedVector vec;
  CeedElemRestriction Erestrict;

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

  // Input Evecs and Restriction
  ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
                                     opinputfields, invec, false, impl,
                                     request); CeedChk(ierr);

  // Output Evecs
  for (CeedInt i=0; i<numoutputfields; i++) {
    ierr = CeedVectorGetArray(impl->evecs[i+impl->numein], CEED_MEM_HOST,
                              &impl->edata[i + numinputfields]); CeedChk(ierr);
  }

  // Loop through elements
  for (CeedInt e=0; e<numelements; e++) {
    // Output pointers
    for (CeedInt i=0; i<numoutputfields; i++) {
      ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
      CeedChk(ierr);
      if (emode == CEED_EVAL_NONE) {
        ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size);
        CeedChk(ierr);
        ierr = CeedVectorSetArray(impl->qvecsout[i], CEED_MEM_HOST,
                                  CEED_USE_POINTER,
                                  &impl->edata[i + numinputfields][e*Q*size]);
        CeedChk(ierr);
      }
    }

    // Input basis apply
    ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
                                      numinputfields, false, impl);
    CeedChk(ierr);

    // Q function
    if (!impl->identityqf) {
      ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
      CeedChk(ierr);
    }

    // Output basis apply
    ierr = CeedOperatorOutputBasis_Ref(e, Q, qfoutputfields, opoutputfields,
                                       numinputfields, numoutputfields, op, impl);
    CeedChk(ierr);
  }

  // Zero lvecs
  for (CeedInt i=0; i<numoutputfields; i++) {
    ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
    if (vec == CEED_VECTOR_ACTIVE) {
      if (!impl->add) {
        vec = outvec;
        ierr = CeedVectorSetValue(vec, 0.0); CeedChk(ierr);
      }
    } else {
      ierr = CeedVectorSetValue(vec, 0.0); CeedChk(ierr);
    }
  }
  impl->add = false;

  // Output restriction
  for (CeedInt i=0; i<numoutputfields; i++) {
    // Restore evec
    ierr = CeedVectorRestoreArray(impl->evecs[i+impl->numein],
                                  &impl->edata[i + numinputfields]);
    CeedChk(ierr);
    // Get output vector
    ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
    // Active
    if (vec == CEED_VECTOR_ACTIVE)
      vec = outvec;
    // Restrict
    ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
    CeedChk(ierr);
    ierr = CeedOperatorFieldGetLMode(opoutputfields[i], &lmode); CeedChk(ierr);
    ierr = CeedElemRestrictionApply(Erestrict, CEED_TRANSPOSE,
                                    lmode, impl->evecs[i+impl->numein], vec,
                                    request); CeedChk(ierr);
  }

  // Restore input arrays
  ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
                                       opinputfields, false, impl);
  CeedChk(ierr);

  return 0;
}

// Composite operators
static int CeedCompositeOperatorApply_Ref(CeedOperator op, CeedVector invec,
    CeedVector outvec,
    CeedRequest *request) {
  int ierr;
  CeedInt numsub;
  CeedOperator_Ref *impl;
  CeedOperator *suboperators;
  ierr = CeedOperatorGetNumSub(op, &numsub); CeedChk(ierr);
  ierr = CeedOperatorGetSubList(op, &suboperators); CeedChk(ierr);

  // Overwrite outvec with first output
  ierr = CeedOperatorApply(suboperators[0], invec, outvec, request);
  CeedChk(ierr);
  // Add to outvec with subsequent outputs
  for (CeedInt i=1; i<numsub; i++) {
    ierr = CeedOperatorGetData(suboperators[i], (void *)&impl); CeedChk(ierr);
    impl->add = true;
    ierr = CeedOperatorApply(suboperators[i], invec, outvec, request);
    CeedChk(ierr);
  }

  return 0;
}

// Assemble Linear QFunction
static int CeedOperatorAssembleLinearQFunction_Ref(CeedOperator op,
    CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
  int ierr;
  CeedOperator_Ref *impl;
  ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
  CeedQFunction qf;
  ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
  CeedInt Q, numelements, numinputfields, numoutputfields, size;
  ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
  ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
  ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
  CeedChk(ierr);
  CeedOperatorField *opinputfields, *opoutputfields;
  ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
  CeedChk(ierr);
  CeedQFunctionField *qfinputfields, *qfoutputfields;
  ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
  CeedChk(ierr);
  CeedVector vec;
  CeedInt numactivein = 0, numactiveout = 0;
  CeedVector *activein = NULL;
  CeedScalar *a, *tmp;
  Ceed ceed;
  ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);

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

  // Check for identity
  if (impl->identityqf)
    // LCOV_EXCL_START
    return CeedError(ceed, 1, "Assembling identity qfunctions not supported");
  // LCOV_EXCL_STOP

  // Input Evecs and Restriction
  ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
                                     opinputfields, NULL, true, impl, request);
  CeedChk(ierr);

  // Count number of active input fields
  for (CeedInt i=0; i<numinputfields; i++) {
    // Get input vector
    ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
    // Check if active input
    if (vec == CEED_VECTOR_ACTIVE) {
      ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
      ierr = CeedVectorSetValue(impl->qvecsin[i], 0.0); CeedChk(ierr);
      ierr = CeedVectorGetArray(impl->qvecsin[i], CEED_MEM_HOST, &tmp);
      CeedChk(ierr);
      ierr = CeedRealloc(numactivein + size, &activein); CeedChk(ierr);
      for (CeedInt field=0; field<size; field++) {
        ierr = CeedVectorCreate(ceed, Q, &activein[numactivein+field]);
        CeedChk(ierr);
        ierr = CeedVectorSetArray(activein[numactivein+field], CEED_MEM_HOST,
                                  CEED_USE_POINTER, &tmp[field*Q]);
        CeedChk(ierr);
      }
      numactivein += size;
      ierr = CeedVectorRestoreArray(impl->qvecsin[i], &tmp); CeedChk(ierr);
    }
  }

  // Count number of active output fields
  for (CeedInt i=0; i<numoutputfields; i++) {
    // Get output vector
    ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
    // Check if active output
    if (vec == CEED_VECTOR_ACTIVE) {
      ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
      numactiveout += size;
    }
  }

  // Check sizes
  if (!numactivein || !numactiveout)
    // LCOV_EXCL_START
    return CeedError(ceed, 1, "Cannot assemble QFunction without active inputs "
                     "and outputs");
  // LCOV_EXCL_STOP

  // Create output restriction
  ierr = CeedElemRestrictionCreateIdentity(ceed, numelements, Q,
         numelements*Q, numactivein*numactiveout, rstr); CeedChk(ierr);
  // Create assembled vector
  ierr = CeedVectorCreate(ceed, numelements*Q*numactivein*numactiveout,
                          assembled); CeedChk(ierr);
  ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
  ierr = CeedVectorGetArray(*assembled, CEED_MEM_HOST, &a); CeedChk(ierr);

  // Loop through elements
  for (CeedInt e=0; e<numelements; e++) {
    // Input basis apply
    ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
                                      numinputfields, true, impl);
    CeedChk(ierr);

    // Assemble QFunction
    for (CeedInt in=0; in<numactivein; in++) {
      // Set Inputs
      ierr = CeedVectorSetValue(activein[in], 1.0); CeedChk(ierr);
      if (numactivein > 1) {
        ierr = CeedVectorSetValue(activein[(in+numactivein-1)%numactivein],
                                  0.0); CeedChk(ierr);
      }
      // Set Outputs
      for (CeedInt out=0; out<numoutputfields; out++) {
        // Get output vector
        ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
        CeedChk(ierr);
        // Check if active output
        if (vec == CEED_VECTOR_ACTIVE) {
          CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST,
                             CEED_USE_POINTER, a); CeedChk(ierr);
          ierr = CeedQFunctionFieldGetSize(qfoutputfields[out], &size);
          CeedChk(ierr);
          a += size*Q; // Advance the pointer by the size of the output
        }
      }
      // Apply QFunction
      ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
      CeedChk(ierr);
    }
  }

  // Un-set output Qvecs to prevent accidental overwrite of Assembled
  for (CeedInt out=0; out<numoutputfields; out++) {
    // Get output vector
    ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
    CeedChk(ierr);
    // Check if active output
    if (vec == CEED_VECTOR_ACTIVE) {
      CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST, CEED_COPY_VALUES,
                         NULL); CeedChk(ierr);
    }
  }

  // Restore input arrays
  ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
                                       opinputfields, true, impl);
  CeedChk(ierr);

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

  // Cleanup
  for (CeedInt i=0; i<numactivein; i++) {
    ierr = CeedVectorDestroy(&activein[i]); CeedChk(ierr);
  }
  ierr = CeedFree(&activein); CeedChk(ierr);

  return 0;
}

int CeedOperatorCreate_Ref(CeedOperator op) {
  int ierr;
  Ceed ceed;
  ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
  CeedOperator_Ref *impl;

  ierr = CeedCalloc(1, &impl); CeedChk(ierr);
  impl->add = false;
  ierr = CeedOperatorSetData(op, (void *)&impl); CeedChk(ierr);

  ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearQFunction",
                                CeedOperatorAssembleLinearQFunction_Ref);
  CeedChk(ierr);
  ierr = CeedSetBackendFunction(ceed, "Operator", op, "Apply",
                                CeedOperatorApply_Ref); CeedChk(ierr);
  ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
                                CeedOperatorDestroy_Ref); CeedChk(ierr);
  return 0;
}

int CeedCompositeOperatorCreate_Ref(CeedOperator op) {
  int ierr;
  Ceed ceed;
  ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);

  ierr = CeedSetBackendFunction(ceed, "Operator", op, "Apply",
                                CeedCompositeOperatorApply_Ref); CeedChk(ierr);
  return 0;
}