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 <stdio.h> 9 #include <stdlib.h> 10 #include <string.h> 11 12 int main(int argc, char **argv) { 13 Ceed ceed; 14 CeedElemRestriction elem_restriction_x, elem_restriction_u, elem_restriction_q_data; 15 CeedBasis basis_x, basis_u; 16 CeedQFunction qf_setup_diff, qf_apply; 17 CeedOperator op_setup_diff, op_apply, op_inverse; 18 CeedVector q_data_diff, x, u, v, w; 19 CeedInt num_elem = 1, p = 4, q = 5, dim = 2; 20 CeedInt num_dofs = p * p, num_qpts = num_elem * q * q, q_data_size = dim * (dim + 1) / 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 // Vectors 28 CeedVectorCreate(ceed, dim * num_elem * (2 * 2), &x); 29 { 30 CeedScalar x_array[dim * num_elem * (2 * 2)]; 31 32 for (CeedInt i = 0; i < 2; i++) { 33 for (CeedInt j = 0; j < 2; j++) { 34 x_array[i + j * 2 + 0 * 4] = i; 35 x_array[i + j * 2 + 1 * 4] = j; 36 } 37 } 38 CeedVectorSetArray(x, CEED_MEM_HOST, CEED_COPY_VALUES, x_array); 39 } 40 CeedVectorCreate(ceed, num_dofs, &u); 41 CeedVectorCreate(ceed, num_dofs, &v); 42 CeedVectorCreate(ceed, num_dofs, &w); 43 CeedVectorCreate(ceed, q_data_size * num_qpts, &q_data_diff); 44 45 // Restrictions 46 CeedInt strides_x[3] = {1, 2 * 2, 2 * 2 * dim}; 47 CeedElemRestrictionCreateStrided(ceed, num_elem, 2 * 2, dim, dim * num_elem * 2 * 2, strides_x, &elem_restriction_x); 48 49 CeedInt strides_u[3] = {1, p * p, p * p}; 50 CeedElemRestrictionCreateStrided(ceed, num_elem, p * p, 1, num_dofs, strides_u, &elem_restriction_u); 51 52 CeedInt strides_q_data[3] = {1, q * q, q_data_size * q * q}; 53 CeedElemRestrictionCreateStrided(ceed, num_elem, q * q, q_data_size, num_qpts * q_data_size, strides_q_data, &elem_restriction_q_data); 54 55 // Bases 56 CeedBasisCreateTensorH1Lagrange(ceed, dim, dim, 2, q, CEED_GAUSS, &basis_x); 57 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, p, q, CEED_GAUSS, &basis_u); 58 59 // QFunction - setup diff 60 CeedQFunctionCreateInterior(ceed, 1, setup_diff, setup_diff_loc, &qf_setup_diff); 61 CeedQFunctionAddInput(qf_setup_diff, "dx", dim * dim, CEED_EVAL_GRAD); 62 CeedQFunctionAddInput(qf_setup_diff, "weight", 1, CEED_EVAL_WEIGHT); 63 CeedQFunctionAddOutput(qf_setup_diff, "q data", q_data_size, CEED_EVAL_NONE); 64 65 // Operator - setup diff 66 CeedOperatorCreate(ceed, qf_setup_diff, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_setup_diff); 67 CeedOperatorSetField(op_setup_diff, "dx", elem_restriction_x, basis_x, CEED_VECTOR_ACTIVE); 68 CeedOperatorSetField(op_setup_diff, "weight", CEED_ELEMRESTRICTION_NONE, basis_x, CEED_VECTOR_NONE); 69 CeedOperatorSetField(op_setup_diff, "q data", elem_restriction_q_data, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE); 70 71 // Apply Setup Operator 72 CeedOperatorApply(op_setup_diff, x, q_data_diff, CEED_REQUEST_IMMEDIATE); 73 74 // QFunction - apply 75 CeedQFunctionCreateInterior(ceed, 1, apply, apply_loc, &qf_apply); 76 CeedQFunctionAddInput(qf_apply, "u", dim, CEED_EVAL_GRAD); 77 CeedQFunctionAddInput(qf_apply, "q data diff", q_data_size, CEED_EVAL_NONE); 78 CeedQFunctionAddOutput(qf_apply, "v", dim, CEED_EVAL_GRAD); 79 80 // Operator - apply 81 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply); 82 CeedOperatorSetField(op_apply, "u", elem_restriction_u, basis_u, CEED_VECTOR_ACTIVE); 83 CeedOperatorSetField(op_apply, "q data diff", elem_restriction_q_data, CEED_BASIS_NONE, q_data_diff); 84 CeedOperatorSetField(op_apply, "v", elem_restriction_u, basis_u, CEED_VECTOR_ACTIVE); 85 86 // Create FDM element inverse 87 CeedOperatorCreateFDMElementInverse(op_apply, &op_inverse, CEED_REQUEST_IMMEDIATE); 88 89 // Create Schur complement for element corners 90 CeedScalar S[16]; 91 for (CeedInt i = 0; i < 4; i++) { 92 CeedScalar *u_array; 93 94 CeedVectorSetValue(u, 0.0); 95 CeedVectorGetArray(u, CEED_MEM_HOST, &u_array); 96 switch (i) { 97 case 0: 98 u_array[0] = 1.0; 99 break; 100 case 1: 101 u_array[p - 1] = 1.0; 102 break; 103 case 2: 104 u_array[p * p - p] = 1.0; 105 break; 106 case 3: 107 u_array[p * p - 1] = 1.0; 108 break; 109 } 110 CeedVectorRestoreArray(u, &u_array); 111 112 CeedOperatorApply(op_inverse, u, v, CEED_REQUEST_IMMEDIATE); 113 114 const CeedScalar *v_array; 115 116 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 117 S[0 * 4 + i] = -v_array[0]; 118 S[1 * 4 + i] = -v_array[p - 1]; 119 S[2 * 4 + i] = -v_array[p * p - p]; 120 S[3 * 4 + i] = -v_array[p * p - 1]; 121 CeedVectorRestoreArrayRead(v, &v_array); 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 CeedScalar *u_array; 167 168 CeedLobattoQuadrature(p, nodes, NULL); 169 CeedVectorGetArray(u, CEED_MEM_HOST, &u_array); 170 for (CeedInt i = 0; i < p; i++) { 171 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); 172 } 173 CeedVectorRestoreArray(u, &u_array); 174 } 175 176 // Apply original operator 177 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 178 179 // Apply FDM element inverse 180 { 181 // -- Zero corners 182 CeedScalar *v_array; 183 184 CeedVectorGetArray(v, CEED_MEM_HOST, &v_array); 185 v_array[0] = 0.0; 186 v_array[p - 1] = 0.0; 187 v_array[p * p - p] = 0.0; 188 v_array[p * p - 1] = 0.0; 189 CeedVectorRestoreArray(v, &v_array); 190 191 // -- Apply FDM inverse to interior 192 CeedOperatorApply(op_inverse, v, w, CEED_REQUEST_IMMEDIATE); 193 194 // -- Pick off corners 195 const CeedScalar *w_array; 196 CeedScalar w_Pi[4]; 197 198 CeedVectorGetArrayRead(w, CEED_MEM_HOST, &w_array); 199 w_Pi[0] = w_array[0]; 200 w_Pi[1] = w_array[p - 1]; 201 w_Pi[2] = w_array[p * p - p]; 202 w_Pi[3] = w_array[p * p - 1]; 203 CeedVectorRestoreArrayRead(w, &w_array); 204 205 // -- Apply inverse of Schur complement 206 CeedScalar v_Pi[4]; 207 for (CeedInt i = 0; i < 4; i++) { 208 CeedScalar sum = 0.0; 209 for (CeedInt j = 0; j < 4; j++) { 210 sum += w_Pi[j] * S_inv[i * 4 + j]; 211 } 212 v_Pi[i] = sum; 213 } 214 215 // -- Set corners 216 CeedVectorGetArray(v, CEED_MEM_HOST, &v_array); 217 v_array[0] = v_Pi[0]; 218 v_array[p - 1] = v_Pi[1]; 219 v_array[p * p - p] = v_Pi[2]; 220 v_array[p * p - 1] = v_Pi[3]; 221 CeedVectorRestoreArray(v, &v_array); 222 223 // -- Apply full FDM inverse again 224 CeedOperatorApply(op_inverse, v, w, CEED_REQUEST_IMMEDIATE); 225 } 226 227 // Check output 228 { 229 const CeedScalar *u_array, *w_array; 230 CeedVectorGetArrayRead(u, CEED_MEM_HOST, &u_array); 231 CeedVectorGetArrayRead(w, CEED_MEM_HOST, &w_array); 232 for (CeedInt i = 0; i < p; i++) { 233 for (CeedInt j = 0; j < p; j++) { 234 if (fabs(u_array[i * p + j] - w_array[i * p + j]) > 2e-3) { 235 // LCOV_EXCL_START 236 printf("[%" CeedInt_FMT ", %" CeedInt_FMT "] Error in inverse: %e != %e\n", i, j, w_array[i * p + j], u_array[i * p + j]); 237 // LCOV_EXCL_STOP 238 } 239 } 240 } 241 CeedVectorRestoreArrayRead(u, &u_array); 242 CeedVectorRestoreArrayRead(w, &w_array); 243 } 244 245 // Cleanup 246 CeedVectorDestroy(&x); 247 CeedVectorDestroy(&q_data_diff); 248 CeedVectorDestroy(&u); 249 CeedVectorDestroy(&v); 250 CeedVectorDestroy(&w); 251 CeedElemRestrictionDestroy(&elem_restriction_u); 252 CeedElemRestrictionDestroy(&elem_restriction_x); 253 CeedElemRestrictionDestroy(&elem_restriction_q_data); 254 CeedBasisDestroy(&basis_x); 255 CeedBasisDestroy(&basis_u); 256 CeedQFunctionDestroy(&qf_setup_diff); 257 CeedQFunctionDestroy(&qf_apply); 258 CeedOperatorDestroy(&op_setup_diff); 259 CeedOperatorDestroy(&op_apply); 260 CeedOperatorDestroy(&op_inverse); 261 CeedDestroy(&ceed); 262 return 0; 263 } 264