1 /// @file 2 /// Test creation and use of FDM element inverse 3 /// \test Test creation and use of FDM element inverse 4 #include "t541-operator.h" 5 6 #include <ceed.h> 7 #include <math.h> 8 #include <stdlib.h> 9 #include <string.h> 10 11 int main(int argc, char **argv) { 12 Ceed ceed; 13 CeedElemRestriction elem_restr_x_i, elem_restr_u_i, elem_restr_qd_i; 14 CeedBasis basis_x, basis_u; 15 CeedQFunction qf_setup_diff, qf_apply; 16 CeedOperator op_setup_diff, op_apply, op_inv; 17 CeedVector q_data_diff, X, U, V, W; 18 CeedInt num_elem = 1, P = 4, Q = 5, dim = 2; 19 CeedInt num_dofs = P * P, num_qpts = num_elem * Q * Q, q_data_size = dim * (dim + 1) / 2; 20 CeedScalar x[dim * num_elem * (2 * 2)]; 21 22 CeedInit(argv[1], &ceed); 23 24 // Test skipped if using single precision 25 if (CEED_SCALAR_TYPE == CEED_SCALAR_FP32) return CeedError(ceed, CEED_ERROR_UNSUPPORTED, "Test not implemented in single precision"); 26 27 // DoF Coordinates 28 for (CeedInt i = 0; i < 2; i++) { 29 for (CeedInt j = 0; j < 2; j++) { 30 x[i + j * 2 + 0 * 4] = i; 31 x[i + j * 2 + 1 * 4] = j; 32 } 33 } 34 CeedVectorCreate(ceed, dim * num_elem * (2 * 2), &X); 35 CeedVectorSetArray(X, CEED_MEM_HOST, CEED_USE_POINTER, x); 36 37 // Qdata Vector 38 CeedVectorCreate(ceed, q_data_size * num_qpts, &q_data_diff); 39 40 // Element Setup 41 42 // Restrictions 43 CeedInt strides_x[3] = {1, 2 * 2, 2 * 2 * dim}; 44 CeedElemRestrictionCreateStrided(ceed, num_elem, 2 * 2, dim, dim * num_elem * 2 * 2, strides_x, &elem_restr_x_i); 45 46 CeedInt strides_u[3] = {1, P * P, P * P}; 47 CeedElemRestrictionCreateStrided(ceed, num_elem, P * P, 1, num_dofs, strides_u, &elem_restr_u_i); 48 49 CeedInt strides_qd[3] = {1, Q * Q, q_data_size * Q * Q}; 50 CeedElemRestrictionCreateStrided(ceed, num_elem, Q * Q, q_data_size, num_qpts * q_data_size, strides_qd, &elem_restr_qd_i); 51 52 // Bases 53 CeedBasisCreateTensorH1Lagrange(ceed, dim, dim, 2, Q, CEED_GAUSS, &basis_x); 54 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, P, Q, CEED_GAUSS, &basis_u); 55 56 // QFunction - setup diff 57 CeedQFunctionCreateInterior(ceed, 1, setup_diff, setup_diff_loc, &qf_setup_diff); 58 CeedQFunctionAddInput(qf_setup_diff, "dx", dim * dim, CEED_EVAL_GRAD); 59 CeedQFunctionAddInput(qf_setup_diff, "weight", 1, CEED_EVAL_WEIGHT); 60 CeedQFunctionAddOutput(qf_setup_diff, "qdata", q_data_size, CEED_EVAL_NONE); 61 62 // Operator - setup diff 63 CeedOperatorCreate(ceed, qf_setup_diff, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_setup_diff); 64 CeedOperatorSetField(op_setup_diff, "dx", elem_restr_x_i, basis_x, CEED_VECTOR_ACTIVE); 65 CeedOperatorSetField(op_setup_diff, "weight", CEED_ELEMRESTRICTION_NONE, basis_x, CEED_VECTOR_NONE); 66 CeedOperatorSetField(op_setup_diff, "qdata", elem_restr_qd_i, CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE); 67 68 // Apply Setup Operator 69 CeedOperatorApply(op_setup_diff, X, q_data_diff, CEED_REQUEST_IMMEDIATE); 70 71 // QFunction - apply 72 CeedQFunctionCreateInterior(ceed, 1, apply, apply_loc, &qf_apply); 73 CeedQFunctionAddInput(qf_apply, "u", dim, CEED_EVAL_GRAD); 74 CeedQFunctionAddInput(qf_apply, "qdata_diff", q_data_size, CEED_EVAL_NONE); 75 CeedQFunctionAddOutput(qf_apply, "v", dim, CEED_EVAL_GRAD); 76 77 // Operator - apply 78 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply); 79 CeedOperatorSetField(op_apply, "u", elem_restr_u_i, basis_u, CEED_VECTOR_ACTIVE); 80 CeedOperatorSetField(op_apply, "qdata_diff", elem_restr_qd_i, CEED_BASIS_COLLOCATED, q_data_diff); 81 CeedOperatorSetField(op_apply, "v", elem_restr_u_i, basis_u, CEED_VECTOR_ACTIVE); 82 83 // Create FDM element inverse 84 CeedOperatorCreateFDMElementInverse(op_apply, &op_inv, CEED_REQUEST_IMMEDIATE); 85 86 // Create vectors 87 CeedVectorCreate(ceed, num_dofs, &U); 88 CeedVectorCreate(ceed, num_dofs, &V); 89 CeedVectorCreate(ceed, num_dofs, &W); 90 91 // Create Schur complement for element corners 92 CeedScalar S[16]; 93 for (CeedInt i = 0; i < 4; i++) { 94 CeedScalar *u; 95 CeedVectorSetValue(U, 0.0); 96 CeedVectorGetArray(U, CEED_MEM_HOST, &u); 97 switch (i) { 98 case 0: 99 u[0] = 1.0; 100 break; 101 case 1: 102 u[P - 1] = 1.0; 103 break; 104 case 2: 105 u[P * P - P] = 1.0; 106 break; 107 case 3: 108 u[P * P - 1] = 1.0; 109 break; 110 } 111 CeedVectorRestoreArray(U, &u); 112 113 CeedOperatorApply(op_inv, U, V, CEED_REQUEST_IMMEDIATE); 114 115 const CeedScalar *v; 116 CeedVectorGetArrayRead(V, CEED_MEM_HOST, &v); 117 S[0 * 4 + i] = -v[0]; 118 S[1 * 4 + i] = -v[P - 1]; 119 S[2 * 4 + i] = -v[P * P - P]; 120 S[3 * 4 + i] = -v[P * P - 1]; 121 CeedVectorRestoreArrayRead(V, &v); 122 } 123 CeedScalar S_inv[16]; 124 { 125 CeedScalar det; 126 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]; 127 128 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]; 129 130 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]; 131 132 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]; 133 134 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]; 135 136 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]; 137 138 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]; 139 140 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]; 141 142 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]; 143 144 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]; 145 146 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]; 147 148 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]; 149 150 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]; 151 152 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]; 153 154 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]; 155 156 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]; 157 158 det = 1 / (S[0] * S_inv[0] + S[1] * S_inv[4] + S[2] * S_inv[8] + S[3] * S_inv[12]); 159 160 for (CeedInt i = 0; i < 16; i++) S_inv[i] *= det; 161 } 162 163 // Set initial values 164 { 165 CeedScalar nodes[P]; 166 CeedLobattoQuadrature(P, nodes, NULL); 167 CeedScalar *u; 168 CeedVectorGetArray(U, CEED_MEM_HOST, &u); 169 for (CeedInt i = 0; i < P; i++) { 170 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); 171 } 172 CeedVectorRestoreArray(U, &u); 173 } 174 175 // Apply original operator 176 CeedOperatorApply(op_apply, U, V, CEED_REQUEST_IMMEDIATE); 177 178 // Apply FDM element inverse 179 { 180 // -- Zero corners 181 CeedScalar *v; 182 CeedVectorGetArray(V, CEED_MEM_HOST, &v); 183 v[0] = 0.0; 184 v[P - 1] = 0.0; 185 v[P * P - P] = 0.0; 186 v[P * P - 1] = 0.0; 187 CeedVectorRestoreArray(V, &v); 188 189 // -- Apply FDM inverse to interior 190 CeedOperatorApply(op_inv, V, W, CEED_REQUEST_IMMEDIATE); 191 192 // -- Pick off corners 193 const CeedScalar *w; 194 CeedScalar w_Pi[4]; 195 CeedVectorGetArrayRead(W, CEED_MEM_HOST, &w); 196 w_Pi[0] = w[0]; 197 w_Pi[1] = w[P - 1]; 198 w_Pi[2] = w[P * P - P]; 199 w_Pi[3] = w[P * P - 1]; 200 CeedVectorRestoreArrayRead(W, &w); 201 202 // -- Apply inverse of Schur complement 203 CeedScalar v_Pi[4]; 204 for (CeedInt i = 0; i < 4; i++) { 205 CeedScalar sum = 0.0; 206 for (CeedInt j = 0; j < 4; j++) { 207 sum += w_Pi[j] * S_inv[i * 4 + j]; 208 } 209 v_Pi[i] = sum; 210 } 211 212 // -- Set corners 213 CeedVectorGetArray(V, CEED_MEM_HOST, &v); 214 v[0] = v_Pi[0]; 215 v[P - 1] = v_Pi[1]; 216 v[P * P - P] = v_Pi[2]; 217 v[P * P - 1] = v_Pi[3]; 218 CeedVectorRestoreArray(V, &v); 219 220 // -- Apply full FDM inverse again 221 CeedOperatorApply(op_inv, V, W, CEED_REQUEST_IMMEDIATE); 222 } 223 224 // Check output 225 { 226 const CeedScalar *u, *w; 227 CeedVectorGetArrayRead(U, CEED_MEM_HOST, &u); 228 CeedVectorGetArrayRead(W, CEED_MEM_HOST, &w); 229 for (CeedInt i = 0; i < P; i++) { 230 for (CeedInt j = 0; j < P; j++) { 231 if (fabs(u[i * P + j] - w[i * P + j]) > 2e-3) { 232 // LCOV_EXCL_START 233 printf("[%" CeedInt_FMT ", %" CeedInt_FMT "] Error in inverse: %e != %e\n", i, j, w[i * P + j], u[i * P + j]); 234 // LCOV_EXCL_STOP 235 } 236 } 237 } 238 CeedVectorRestoreArrayRead(U, &u); 239 CeedVectorRestoreArrayRead(W, &w); 240 } 241 242 // Cleanup 243 CeedQFunctionDestroy(&qf_setup_diff); 244 CeedQFunctionDestroy(&qf_apply); 245 CeedOperatorDestroy(&op_setup_diff); 246 CeedOperatorDestroy(&op_apply); 247 CeedOperatorDestroy(&op_inv); 248 CeedElemRestrictionDestroy(&elem_restr_u_i); 249 CeedElemRestrictionDestroy(&elem_restr_x_i); 250 CeedElemRestrictionDestroy(&elem_restr_qd_i); 251 CeedBasisDestroy(&basis_x); 252 CeedBasisDestroy(&basis_u); 253 CeedVectorDestroy(&X); 254 CeedVectorDestroy(&q_data_diff); 255 CeedVectorDestroy(&U); 256 CeedVectorDestroy(&V); 257 CeedVectorDestroy(&W); 258 CeedDestroy(&ceed); 259 return 0; 260 } 261