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_restriction_x, elem_restriction_u, elem_restriction_q_data; 14 CeedBasis basis_x, basis_u; 15 CeedQFunction qf_setup_diff, qf_apply; 16 CeedOperator op_setup_diff, op_apply, op_inverse; 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 21 CeedInit(argv[1], &ceed); 22 23 // Test skipped if using single precision 24 if (CEED_SCALAR_TYPE == CEED_SCALAR_FP32) return CeedError(ceed, CEED_ERROR_UNSUPPORTED, "Test not implemented in single precision"); 25 26 // Vectors 27 CeedVectorCreate(ceed, dim * num_elem * (2 * 2), &x); 28 { 29 CeedScalar x_array[dim * num_elem * (2 * 2)]; 30 31 for (CeedInt i = 0; i < 2; i++) { 32 for (CeedInt j = 0; j < 2; j++) { 33 x_array[i + j * 2 + 0 * 4] = i; 34 x_array[i + j * 2 + 1 * 4] = j; 35 } 36 } 37 CeedVectorSetArray(x, CEED_MEM_HOST, CEED_COPY_VALUES, x_array); 38 } 39 CeedVectorCreate(ceed, num_dofs, &u); 40 CeedVectorCreate(ceed, num_dofs, &v); 41 CeedVectorCreate(ceed, num_dofs, &w); 42 CeedVectorCreate(ceed, q_data_size * num_qpts, &q_data_diff); 43 44 // Restrictions 45 CeedInt strides_x[3] = {1, 2 * 2, 2 * 2 * dim}; 46 CeedElemRestrictionCreateStrided(ceed, num_elem, 2 * 2, dim, dim * num_elem * 2 * 2, strides_x, &elem_restriction_x); 47 48 CeedInt strides_u[3] = {1, p * p, p * p}; 49 CeedElemRestrictionCreateStrided(ceed, num_elem, p * p, 1, num_dofs, strides_u, &elem_restriction_u); 50 51 CeedInt strides_q_data[3] = {1, q * q, q_data_size * q * q}; 52 CeedElemRestrictionCreateStrided(ceed, num_elem, q * q, q_data_size, num_qpts * q_data_size, strides_q_data, &elem_restriction_q_data); 53 54 // Bases 55 CeedBasisCreateTensorH1Lagrange(ceed, dim, dim, 2, q, CEED_GAUSS, &basis_x); 56 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, p, q, CEED_GAUSS, &basis_u); 57 58 // QFunction - setup diff 59 CeedQFunctionCreateInterior(ceed, 1, setup_diff, setup_diff_loc, &qf_setup_diff); 60 CeedQFunctionAddInput(qf_setup_diff, "dx", dim * dim, CEED_EVAL_GRAD); 61 CeedQFunctionAddInput(qf_setup_diff, "weight", 1, CEED_EVAL_WEIGHT); 62 CeedQFunctionAddOutput(qf_setup_diff, "q data", q_data_size, CEED_EVAL_NONE); 63 64 // Operator - setup diff 65 CeedOperatorCreate(ceed, qf_setup_diff, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_setup_diff); 66 CeedOperatorSetField(op_setup_diff, "dx", elem_restriction_x, basis_x, CEED_VECTOR_ACTIVE); 67 CeedOperatorSetField(op_setup_diff, "weight", CEED_ELEMRESTRICTION_NONE, basis_x, CEED_VECTOR_NONE); 68 CeedOperatorSetField(op_setup_diff, "q data", elem_restriction_q_data, CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE); 69 70 // Apply Setup Operator 71 CeedOperatorApply(op_setup_diff, x, q_data_diff, CEED_REQUEST_IMMEDIATE); 72 73 // QFunction - apply 74 CeedQFunctionCreateInterior(ceed, 1, apply, apply_loc, &qf_apply); 75 CeedQFunctionAddInput(qf_apply, "u", dim, CEED_EVAL_GRAD); 76 CeedQFunctionAddInput(qf_apply, "q data diff", q_data_size, CEED_EVAL_NONE); 77 CeedQFunctionAddOutput(qf_apply, "v", dim, CEED_EVAL_GRAD); 78 79 // Operator - apply 80 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply); 81 CeedOperatorSetField(op_apply, "u", elem_restriction_u, basis_u, CEED_VECTOR_ACTIVE); 82 CeedOperatorSetField(op_apply, "q data diff", elem_restriction_q_data, CEED_BASIS_COLLOCATED, q_data_diff); 83 CeedOperatorSetField(op_apply, "v", elem_restriction_u, basis_u, CEED_VECTOR_ACTIVE); 84 85 // Create FDM element inverse 86 CeedOperatorCreateFDMElementInverse(op_apply, &op_inverse, CEED_REQUEST_IMMEDIATE); 87 88 // Create Schur complement for element corners 89 CeedScalar S[16]; 90 for (CeedInt i = 0; i < 4; i++) { 91 CeedScalar *u_array; 92 93 CeedVectorSetValue(u, 0.0); 94 CeedVectorGetArray(u, CEED_MEM_HOST, &u_array); 95 switch (i) { 96 case 0: 97 u_array[0] = 1.0; 98 break; 99 case 1: 100 u_array[p - 1] = 1.0; 101 break; 102 case 2: 103 u_array[p * p - p] = 1.0; 104 break; 105 case 3: 106 u_array[p * p - 1] = 1.0; 107 break; 108 } 109 CeedVectorRestoreArray(u, &u_array); 110 111 CeedOperatorApply(op_inverse, u, v, CEED_REQUEST_IMMEDIATE); 112 113 const CeedScalar *v_array; 114 115 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 116 S[0 * 4 + i] = -v_array[0]; 117 S[1 * 4 + i] = -v_array[p - 1]; 118 S[2 * 4 + i] = -v_array[p * p - p]; 119 S[3 * 4 + i] = -v_array[p * p - 1]; 120 CeedVectorRestoreArrayRead(v, &v_array); 121 } 122 CeedScalar S_inv[16]; 123 { 124 CeedScalar det; 125 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]; 126 127 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]; 128 129 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]; 130 131 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]; 132 133 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]; 134 135 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]; 136 137 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]; 138 139 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]; 140 141 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]; 142 143 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]; 144 145 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]; 146 147 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]; 148 149 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]; 150 151 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]; 152 153 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]; 154 155 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]; 156 157 det = 1 / (S[0] * S_inv[0] + S[1] * S_inv[4] + S[2] * S_inv[8] + S[3] * S_inv[12]); 158 159 for (CeedInt i = 0; i < 16; i++) S_inv[i] *= det; 160 } 161 162 // Set initial values 163 { 164 CeedScalar nodes[p]; 165 CeedScalar *u_array; 166 167 CeedLobattoQuadrature(p, nodes, NULL); 168 CeedVectorGetArray(u, CEED_MEM_HOST, &u_array); 169 for (CeedInt i = 0; i < p; i++) { 170 for (CeedInt j = 0; j < p; j++) u_array[i * p + j] = -(nodes[i] - 1.0) * (nodes[i] + 1.0) - (nodes[j] - 1.0) * (nodes[j] + 1.0); 171 } 172 CeedVectorRestoreArray(u, &u_array); 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_array; 182 183 CeedVectorGetArray(v, CEED_MEM_HOST, &v_array); 184 v_array[0] = 0.0; 185 v_array[p - 1] = 0.0; 186 v_array[p * p - p] = 0.0; 187 v_array[p * p - 1] = 0.0; 188 CeedVectorRestoreArray(v, &v_array); 189 190 // -- Apply FDM inverse to interior 191 CeedOperatorApply(op_inverse, v, w, CEED_REQUEST_IMMEDIATE); 192 193 // -- Pick off corners 194 const CeedScalar *w_array; 195 CeedScalar w_Pi[4]; 196 197 CeedVectorGetArrayRead(w, CEED_MEM_HOST, &w_array); 198 w_Pi[0] = w_array[0]; 199 w_Pi[1] = w_array[p - 1]; 200 w_Pi[2] = w_array[p * p - p]; 201 w_Pi[3] = w_array[p * p - 1]; 202 CeedVectorRestoreArrayRead(w, &w_array); 203 204 // -- Apply inverse of Schur complement 205 CeedScalar v_Pi[4]; 206 for (CeedInt i = 0; i < 4; i++) { 207 CeedScalar sum = 0.0; 208 for (CeedInt j = 0; j < 4; j++) { 209 sum += w_Pi[j] * S_inv[i * 4 + j]; 210 } 211 v_Pi[i] = sum; 212 } 213 214 // -- Set corners 215 CeedVectorGetArray(v, CEED_MEM_HOST, &v_array); 216 v_array[0] = v_Pi[0]; 217 v_array[p - 1] = v_Pi[1]; 218 v_array[p * p - p] = v_Pi[2]; 219 v_array[p * p - 1] = v_Pi[3]; 220 CeedVectorRestoreArray(v, &v_array); 221 222 // -- Apply full FDM inverse again 223 CeedOperatorApply(op_inverse, v, w, CEED_REQUEST_IMMEDIATE); 224 } 225 226 // Check output 227 { 228 const CeedScalar *u_array, *w_array; 229 CeedVectorGetArrayRead(u, CEED_MEM_HOST, &u_array); 230 CeedVectorGetArrayRead(w, CEED_MEM_HOST, &w_array); 231 for (CeedInt i = 0; i < p; i++) { 232 for (CeedInt j = 0; j < p; j++) { 233 if (fabs(u_array[i * p + j] - w_array[i * p + j]) > 2e-3) { 234 // LCOV_EXCL_START 235 printf("[%" CeedInt_FMT ", %" CeedInt_FMT "] Error in inverse: %e != %e\n", i, j, w_array[i * p + j], u_array[i * p + j]); 236 // LCOV_EXCL_STOP 237 } 238 } 239 } 240 CeedVectorRestoreArrayRead(u, &u_array); 241 CeedVectorRestoreArrayRead(w, &w_array); 242 } 243 244 // Cleanup 245 CeedVectorDestroy(&x); 246 CeedVectorDestroy(&q_data_diff); 247 CeedVectorDestroy(&u); 248 CeedVectorDestroy(&v); 249 CeedVectorDestroy(&w); 250 CeedElemRestrictionDestroy(&elem_restriction_u); 251 CeedElemRestrictionDestroy(&elem_restriction_x); 252 CeedElemRestrictionDestroy(&elem_restriction_q_data); 253 CeedBasisDestroy(&basis_x); 254 CeedBasisDestroy(&basis_u); 255 CeedQFunctionDestroy(&qf_setup_diff); 256 CeedQFunctionDestroy(&qf_apply); 257 CeedOperatorDestroy(&op_setup_diff); 258 CeedOperatorDestroy(&op_apply); 259 CeedOperatorDestroy(&op_inverse); 260 CeedDestroy(&ceed); 261 return 0; 262 } 263