xref: /libCEED/tests/t541-operator.c (revision 66ce82e0a71c19ea7217385b30cf4d3e9f880c71)

/// @file
/// Test creation and use of FDM element inverse
/// \test Test creation and use of FDM element inverse
#include <ceed.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "t541-operator.h"

int main(int argc, char **argv) {
  Ceed ceed;
  CeedElemRestriction elem_restr_x_i, elem_restr_u_i, elem_restr_qd_i;
  CeedBasis basis_x, basis_u;
  CeedQFunction qf_setup_diff, qf_apply;
  CeedOperator op_setup_diff, op_apply, op_inv;
  CeedVector q_data_diff, X, U, V, W;
  CeedInt num_elem = 1, P = 4, Q = 5, dim = 2;
  CeedInt num_dofs = P*P, num_qpts = num_elem*Q*Q, q_data_size = dim*(dim+1)/2;
  CeedScalar x[dim*num_elem*(2*2)];

  CeedInit(argv[1], &ceed);

  // DoF Coordinates
  for (CeedInt i=0; i<2; i++)
    for (CeedInt j=0; j<2; j++) {
      x[i+j*2+0*4] = i;
      x[i+j*2+1*4] = j;
    }
  CeedVectorCreate(ceed, dim*num_elem*(2*2), &X);
  CeedVectorSetArray(X, CEED_MEM_HOST, CEED_USE_POINTER, x);

  // Qdata Vector
  CeedVectorCreate(ceed, q_data_size*num_qpts, &q_data_diff);

  // Element Setup

  // Restrictions
  CeedInt strides_x[3] = {1, 2*2, 2*2*dim};
  CeedElemRestrictionCreateStrided(ceed, num_elem, 2*2, dim, dim*num_elem*2*2,
                                   strides_x, &elem_restr_x_i);

  CeedInt strides_u[3] = {1, P*P, P*P};
  CeedElemRestrictionCreateStrided(ceed, num_elem, P*P, 1, num_dofs, strides_u,
                                   &elem_restr_u_i);

  CeedInt strides_qd[3] = {1, Q*Q, q_data_size *Q*Q};
  CeedElemRestrictionCreateStrided(ceed, num_elem, Q*Q, q_data_size,
                                   num_qpts*q_data_size, strides_qd, &elem_restr_qd_i);

  // Bases
  CeedBasisCreateTensorH1Lagrange(ceed, dim, dim, 2, Q, CEED_GAUSS, &basis_x);
  CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, P, Q, CEED_GAUSS, &basis_u);

  // QFunction - setup diff
  CeedQFunctionCreateInterior(ceed, 1, setup_diff, setup_diff_loc,
                              &qf_setup_diff);
  CeedQFunctionAddInput(qf_setup_diff, "dx", dim*dim, CEED_EVAL_GRAD);
  CeedQFunctionAddInput(qf_setup_diff, "weight", 1, CEED_EVAL_WEIGHT);
  CeedQFunctionAddOutput(qf_setup_diff, "qdata", q_data_size, CEED_EVAL_NONE);

  // Operator - setup diff
  CeedOperatorCreate(ceed, qf_setup_diff, CEED_QFUNCTION_NONE,
                     CEED_QFUNCTION_NONE, &op_setup_diff);
  CeedOperatorSetField(op_setup_diff, "dx", elem_restr_x_i, basis_x,
                       CEED_VECTOR_ACTIVE);
  CeedOperatorSetField(op_setup_diff, "weight", CEED_ELEMRESTRICTION_NONE,
                       basis_x, CEED_VECTOR_NONE);
  CeedOperatorSetField(op_setup_diff, "qdata", elem_restr_qd_i,
                       CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);

  // Apply Setup Operator
  CeedOperatorApply(op_setup_diff, X, q_data_diff, CEED_REQUEST_IMMEDIATE);

  // QFunction - apply
  CeedQFunctionCreateInterior(ceed, 1, apply, apply_loc, &qf_apply);
  CeedQFunctionAddInput(qf_apply, "u", dim, CEED_EVAL_GRAD);
  CeedQFunctionAddInput(qf_apply, "qdata_diff", q_data_size, CEED_EVAL_NONE);
  CeedQFunctionAddOutput(qf_apply, "v", dim, CEED_EVAL_GRAD);

  // Operator - apply
  CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE,
                     &op_apply);
  CeedOperatorSetField(op_apply, "u", elem_restr_u_i, basis_u,
                       CEED_VECTOR_ACTIVE);
  CeedOperatorSetField(op_apply, "qdata_diff", elem_restr_qd_i,
                       CEED_BASIS_COLLOCATED, q_data_diff);
  CeedOperatorSetField(op_apply, "v", elem_restr_u_i, basis_u,
                       CEED_VECTOR_ACTIVE);

  // Create FDM element inverse
  CeedOperatorCreateFDMElementInverse(op_apply, &op_inv, CEED_REQUEST_IMMEDIATE);

  // Create vectors
  CeedVectorCreate(ceed, num_dofs, &U);
  CeedVectorCreate(ceed, num_dofs, &V);
  CeedVectorCreate(ceed, num_dofs, &W);

  // Create Schur complement for element corners
  CeedScalar S[16];
  for (CeedInt i = 0; i < 4; i++) {
    CeedScalar *u;
    CeedVectorSetValue(U, 0.0);
    CeedVectorGetArray(U, CEED_MEM_HOST, &u);
    switch (i) {
    case 0: u[0]     = 1.0; break;
    case 1: u[P-1]   = 1.0; break;
    case 2: u[P*P-P] = 1.0; break;
    case 3: u[P*P-1] = 1.0; break;
    }
    CeedVectorRestoreArray(U, &u);

    CeedOperatorApply(op_inv, U, V, CEED_REQUEST_IMMEDIATE);

    const CeedScalar *v;
    CeedVectorGetArrayRead(V, CEED_MEM_HOST, &v);
    S[0*4+i] = v[0];
    S[1*4+i] = v[P-1];
    S[2*4+i] = v[P*P-P];
    S[3*4+i] = v[P*P-1];
    CeedVectorRestoreArrayRead(V, &v);
  }
  CeedScalar S_inv[16];
  {
    CeedScalar det;
    S_inv[0] =  S[5]  * S[10] * S[15] -
                S[5]  * S[11] * S[14] -
                S[9]  * S[6]  * S[15] +
                S[9]  * S[7]  * S[14] +
                S[13] * S[6]  * S[11] -
                S[13] * S[7]  * S[10];

    S_inv[4] =  -S[4] * S[10] * S[15] +
                S[4]  * S[11] * S[14] +
                S[8]  * S[6]  * S[15] -
                S[8]  * S[7]  * S[14] -
                S[12] * S[6]  * S[11] +
                S[12] * S[7]  * S[10];

    S_inv[8] =  S[4]  * S[9]  * S[15] -
                S[4]  * S[11] * S[13] -
                S[8]  * S[5]  * S[15] +
                S[8]  * S[7]  * S[13] +
                S[12] * S[5]  * S[11] -
                S[12] * S[7]  * S[9];

    S_inv[12] = -S[4] * S[9]  * S[14] +
                S[4]  * S[10] * S[13] +
                S[8]  * S[5]  * S[14] -
                S[8]  * S[6]  * S[13] -
                S[12] * S[5]  * S[10] +
                S[12] * S[6]  * S[9];

    S_inv[1] =  -S[1] * S[10] * S[15] +
                S[1]  * S[11] * S[14] +
                S[9]  * S[2]  * S[15] -
                S[9]  * S[3]  * S[14] -
                S[13] * S[2]  * S[11] +
                S[13] * S[3]  * S[10];

    S_inv[5] =  S[0]  * S[10] * S[15] -
                S[0]  * S[11] * S[14] -
                S[8]  * S[2]  * S[15] +
                S[8]  * S[3]  * S[14] +
                S[12] * S[2]  * S[11] -
                S[12] * S[3]  * S[10];

    S_inv[9] =  -S[0] * S[9]  * S[15] +
                S[0]  * S[11] * S[13] +
                S[8]  * S[1]  * S[15] -
                S[8]  * S[3]  * S[13] -
                S[12] * S[1]  * S[11] +
                S[12] * S[3]  * S[9];

    S_inv[13] = S[0]  * S[9]  * S[14] -
                S[0]  * S[10] * S[13] -
                S[8]  * S[1]  * S[14] +
                S[8]  * S[2]  * S[13] +
                S[12] * S[1]  * S[10] -
                S[12] * S[2]  * S[9];

    S_inv[2] =  S[1]  * S[6]  * S[15] -
                S[1]  * S[7]  * S[14] -
                S[5]  * S[2]  * S[15] +
                S[5]  * S[3]  * S[14] +
                S[13] * S[2]  * S[7]  -
                S[13] * S[3]  * S[6];

    S_inv[6] =  -S[0] * S[6]  * S[15] +
                S[0]  * S[7]  * S[14] +
                S[4]  * S[2]  * S[15] -
                S[4]  * S[3]  * S[14] -
                S[12] * S[2]  * S[7] +
                S[12] * S[3]  * S[6];

    S_inv[10] = S[0]  * S[5]  * S[15] -
                S[0]  * S[7]  * S[13] -
                S[4]  * S[1]  * S[15] +
                S[4]  * S[3]  * S[13] +
                S[12] * S[1]  * S[7]  -
                S[12] * S[3]  * S[5];

    S_inv[14] = -S[0] * S[5]  * S[14] +
                S[0]  * S[6]  * S[13] +
                S[4]  * S[1]  * S[14] -
                S[4]  * S[2]  * S[13] -
                S[12] * S[1]  * S[6]  +
                S[12] * S[2]  * S[5];

    S_inv[3] =  -S[1] * S[6]  * S[11] +
                S[1]  * S[7]  * S[10] +
                S[5]  * S[2]  * S[11] -
                S[5]  * S[3]  * S[10] -
                S[9]  * S[2]  * S[7]  +
                S[9]  * S[3]  * S[6];

    S_inv[7] =  S[0]  * S[6]  * S[11] -
                S[0]  * S[7]  * S[10] -
                S[4]  * S[2]  * S[11] +
                S[4]  * S[3]  * S[10] +
                S[8]  * S[2]  * S[7]  -
                S[8]  * S[3]  * S[6];

    S_inv[11] = -S[0] * S[5]  * S[11] +
                S[0]  * S[7]  * S[9]  +
                S[4]  * S[1]  * S[11] -
                S[4]  * S[3]  * S[9]  -
                S[8]  * S[1]  * S[7]  +
                S[8]  * S[3]  * S[5];

    S_inv[15] = S[0]  * S[5]  * S[10] -
                S[0]  * S[6]  * S[9]  -
                S[4]  * S[1]  * S[10] +
                S[4]  * S[2]  * S[9]  +
                S[8]  * S[1]  * S[6]  -
                S[8]  * S[2]  * S[5];

    det = 1/(S[0]*S_inv[0] + S[1]*S_inv[4] + S[2]*S_inv[8] + S[3]*S_inv[12]);

    for (CeedInt i = 0; i < 16; i++)
      S_inv[i] *= det;
  }

  // Set initial values
  {
    CeedScalar nodes[P];
    CeedLobattoQuadrature(P, nodes, NULL);
    CeedScalar *u;
    CeedVectorGetArray(U, CEED_MEM_HOST, &u);
    for (CeedInt i=0; i<P; i++)
      for (CeedInt j=0; j<P; j++)
        u[i*P+j] = -(nodes[i] - 1.0)*(nodes[i] + 1.0) -
                   (nodes[j] - 1.0)*(nodes[j] + 1.0);
    CeedVectorRestoreArray(U, &u);
  }

  // Apply original operator
  CeedOperatorApply(op_apply, U, V, CEED_REQUEST_IMMEDIATE);

  // Apply FDM element inverse
  {
    // -- Zero corners
    CeedScalar *v;
    CeedVectorGetArray(V, CEED_MEM_HOST, &v);
    v[0]     = 0.0;
    v[P-1]   = 0.0;
    v[P*P-P] = 0.0;
    v[P*P-1] = 0.0;
    CeedVectorRestoreArray(V, &v);

    // -- Apply FDM inverse to interior
    CeedOperatorApply(op_inv, V, W, CEED_REQUEST_IMMEDIATE);

    // -- Pick off corners
    const CeedScalar *w;
    CeedScalar w_Pi[4];
    CeedVectorGetArrayRead(W, CEED_MEM_HOST, &w);
    w_Pi[0] = w[0];
    w_Pi[1] = w[P-1];
    w_Pi[2] = w[P*P-P];
    w_Pi[3] = w[P*P-1];
    CeedVectorRestoreArrayRead(W, &w);

    // -- Apply inverse of Schur complement
    CeedScalar v_Pi[4];
    for (CeedInt i=0; i<4; i++) {
      CeedScalar sum = 0.0;
      for (CeedInt j=0; j<4; j++) {
        sum += w_Pi[j] * S_inv[i*4+j];
      }
      v_Pi[i] = -sum;
    }

    // -- Set corners
    CeedVectorGetArray(V, CEED_MEM_HOST, &v);
    v[0]     = v_Pi[0];
    v[P-1]   = v_Pi[1];
    v[P*P-P] = v_Pi[2];
    v[P*P-1] = v_Pi[3];
    CeedVectorRestoreArray(V, &v);

    // -- Apply full FDM inverse again
    CeedOperatorApply(op_inv, V, W, CEED_REQUEST_IMMEDIATE);
  }


  // Check output
  {
    const CeedScalar *u, *w;
    CeedVectorGetArrayRead(U, CEED_MEM_HOST, &u);
    CeedVectorGetArrayRead(W, CEED_MEM_HOST, &w);
    for (CeedInt i=0; i<P; i++)
      for (CeedInt j=0; j<P; j++)
        if (fabs(u[i*P+j] - w[i*P+j]) > 5e-14)
          // LCOV_EXCL_START
          printf("[%d, %d] Error in inverse: %e != %e\n", i, j, w[i*P+j], u[i*P+j]);
    // LCOV_EXCL_STOP
    CeedVectorRestoreArrayRead(U, &u);
    CeedVectorRestoreArrayRead(W, &w);
  }

  // Cleanup
  CeedQFunctionDestroy(&qf_setup_diff);
  CeedQFunctionDestroy(&qf_apply);
  CeedOperatorDestroy(&op_setup_diff);
  CeedOperatorDestroy(&op_apply);
  CeedOperatorDestroy(&op_inv);
  CeedElemRestrictionDestroy(&elem_restr_u_i);
  CeedElemRestrictionDestroy(&elem_restr_x_i);
  CeedElemRestrictionDestroy(&elem_restr_qd_i);
  CeedBasisDestroy(&basis_x);
  CeedBasisDestroy(&basis_u);
  CeedVectorDestroy(&X);
  CeedVectorDestroy(&q_data_diff);
  CeedVectorDestroy(&U);
  CeedVectorDestroy(&V);
  CeedVectorDestroy(&W);
  CeedDestroy(&ceed);
  return 0;
}