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
main(int argc,char ** argv)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