1 // Copyright (c) 2017-2024, Lawrence Livermore National Security, LLC and other CEED contributors. 2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details. 3 // 4 // SPDX-License-Identifier: BSD-2-Clause 5 // 6 // This file is part of CEED: http://github.com/ceed 7 8 #include <ceed-impl.h> 9 #include <ceed.h> 10 #include <ceed/backend.h> 11 #include <math.h> 12 #include <stdbool.h> 13 #include <stdio.h> 14 #include <string.h> 15 16 /// @file 17 /// Implementation of CeedBasis interfaces 18 19 /// @cond DOXYGEN_SKIP 20 static struct CeedBasis_private ceed_basis_none; 21 /// @endcond 22 23 /// @addtogroup CeedBasisUser 24 /// @{ 25 26 /// Argument for @ref CeedOperatorSetField() indicating that the field does not require a `CeedBasis` 27 const CeedBasis CEED_BASIS_NONE = &ceed_basis_none; 28 29 /// @} 30 31 /// ---------------------------------------------------------------------------- 32 /// CeedBasis Library Internal Functions 33 /// ---------------------------------------------------------------------------- 34 /// @addtogroup CeedBasisDeveloper 35 /// @{ 36 37 /** 38 @brief Compute Chebyshev polynomial values at a point 39 40 @param[in] x Coordinate to evaluate Chebyshev polynomials at 41 @param[in] n Number of Chebyshev polynomials to evaluate, `n >= 2` 42 @param[out] chebyshev_x Array of Chebyshev polynomial values 43 44 @return An error code: 0 - success, otherwise - failure 45 46 @ref Developer 47 **/ 48 static int CeedChebyshevPolynomialsAtPoint(CeedScalar x, CeedInt n, CeedScalar *chebyshev_x) { 49 chebyshev_x[0] = 1.0; 50 chebyshev_x[1] = 2 * x; 51 for (CeedInt i = 2; i < n; i++) chebyshev_x[i] = 2 * x * chebyshev_x[i - 1] - chebyshev_x[i - 2]; 52 return CEED_ERROR_SUCCESS; 53 } 54 55 /** 56 @brief Compute values of the derivative of Chebyshev polynomials at a point 57 58 @param[in] x Coordinate to evaluate derivative of Chebyshev polynomials at 59 @param[in] n Number of Chebyshev polynomials to evaluate, `n >= 2` 60 @param[out] chebyshev_dx Array of Chebyshev polynomial derivative values 61 62 @return An error code: 0 - success, otherwise - failure 63 64 @ref Developer 65 **/ 66 static int CeedChebyshevDerivativeAtPoint(CeedScalar x, CeedInt n, CeedScalar *chebyshev_dx) { 67 CeedScalar chebyshev_x[3]; 68 69 chebyshev_x[1] = 1.0; 70 chebyshev_x[2] = 2 * x; 71 chebyshev_dx[0] = 0.0; 72 chebyshev_dx[1] = 2.0; 73 for (CeedInt i = 2; i < n; i++) { 74 chebyshev_x[0] = chebyshev_x[1]; 75 chebyshev_x[1] = chebyshev_x[2]; 76 chebyshev_x[2] = 2 * x * chebyshev_x[1] - chebyshev_x[0]; 77 chebyshev_dx[i] = 2 * x * chebyshev_dx[i - 1] + 2 * chebyshev_x[1] - chebyshev_dx[i - 2]; 78 } 79 return CEED_ERROR_SUCCESS; 80 } 81 82 /** 83 @brief Compute Householder reflection. 84 85 Computes \f$A = (I - b v v^T) A\f$, where \f$A\f$ is an \f$m \times n\f$ matrix indexed as `A[i*row + j*col]`. 86 87 @param[in,out] A Matrix to apply Householder reflection to, in place 88 @param[in] v Householder vector 89 @param[in] b Scaling factor 90 @param[in] m Number of rows in `A` 91 @param[in] n Number of columns in `A` 92 @param[in] row Row stride 93 @param[in] col Col stride 94 95 @return An error code: 0 - success, otherwise - failure 96 97 @ref Developer 98 **/ 99 static int CeedHouseholderReflect(CeedScalar *A, const CeedScalar *v, CeedScalar b, CeedInt m, CeedInt n, CeedInt row, CeedInt col) { 100 for (CeedInt j = 0; j < n; j++) { 101 CeedScalar w = A[0 * row + j * col]; 102 103 for (CeedInt i = 1; i < m; i++) w += v[i] * A[i * row + j * col]; 104 A[0 * row + j * col] -= b * w; 105 for (CeedInt i = 1; i < m; i++) A[i * row + j * col] -= b * w * v[i]; 106 } 107 return CEED_ERROR_SUCCESS; 108 } 109 110 /** 111 @brief Compute Givens rotation 112 113 Computes \f$A = G A\f$ (or \f$G^T A\f$ in transpose mode), where \f$A\f$ is an \f$m \times n\f$ matrix indexed as `A[i*n + j*m]`. 114 115 @param[in,out] A Row major matrix to apply Givens rotation to, in place 116 @param[in] c Cosine factor 117 @param[in] s Sine factor 118 @param[in] t_mode @ref CEED_NOTRANSPOSE to rotate the basis counter-clockwise, which has the effect of rotating columns of `A` clockwise; 119 @ref CEED_TRANSPOSE for the opposite rotation 120 @param[in] i First row/column to apply rotation 121 @param[in] k Second row/column to apply rotation 122 @param[in] m Number of rows in `A` 123 @param[in] n Number of columns in `A` 124 125 @return An error code: 0 - success, otherwise - failure 126 127 @ref Developer 128 **/ 129 static int CeedGivensRotation(CeedScalar *A, CeedScalar c, CeedScalar s, CeedTransposeMode t_mode, CeedInt i, CeedInt k, CeedInt m, CeedInt n) { 130 CeedInt stride_j = 1, stride_ik = m, num_its = n; 131 132 if (t_mode == CEED_NOTRANSPOSE) { 133 stride_j = n; 134 stride_ik = 1; 135 num_its = m; 136 } 137 138 // Apply rotation 139 for (CeedInt j = 0; j < num_its; j++) { 140 CeedScalar tau1 = A[i * stride_ik + j * stride_j], tau2 = A[k * stride_ik + j * stride_j]; 141 142 A[i * stride_ik + j * stride_j] = c * tau1 - s * tau2; 143 A[k * stride_ik + j * stride_j] = s * tau1 + c * tau2; 144 } 145 return CEED_ERROR_SUCCESS; 146 } 147 148 /** 149 @brief View an array stored in a `CeedBasis` 150 151 @param[in] name Name of array 152 @param[in] fp_fmt Printing format 153 @param[in] m Number of rows in array 154 @param[in] n Number of columns in array 155 @param[in] a Array to be viewed 156 @param[in] stream Stream to view to, e.g., `stdout` 157 158 @return An error code: 0 - success, otherwise - failure 159 160 @ref Developer 161 **/ 162 static int CeedScalarView(const char *name, const char *fp_fmt, CeedInt m, CeedInt n, const CeedScalar *a, FILE *stream) { 163 if (m > 1) { 164 fprintf(stream, " %s:\n", name); 165 } else { 166 char padded_name[12]; 167 168 snprintf(padded_name, 11, "%s:", name); 169 fprintf(stream, " %-10s", padded_name); 170 } 171 for (CeedInt i = 0; i < m; i++) { 172 if (m > 1) fprintf(stream, " [%" CeedInt_FMT "]", i); 173 for (CeedInt j = 0; j < n; j++) fprintf(stream, fp_fmt, fabs(a[i * n + j]) > 1E-14 ? a[i * n + j] : 0); 174 fputs("\n", stream); 175 } 176 return CEED_ERROR_SUCCESS; 177 } 178 179 /** 180 @brief Create the interpolation and gradient matrices for projection from the nodes of `basis_from` to the nodes of `basis_to`. 181 182 The interpolation is given by `interp_project = interp_to^+ * interp_from`, where the pseudoinverse `interp_to^+` is given by QR factorization. 183 The gradient is given by `grad_project = interp_to^+ * grad_from`, and is only computed for \f$H^1\f$ spaces otherwise it should not be used. 184 185 Note: `basis_from` and `basis_to` must have compatible quadrature spaces. 186 187 @param[in] basis_from `CeedBasis` to project from 188 @param[in] basis_to `CeedBasis` to project to 189 @param[out] interp_project Address of the variable where the newly created interpolation matrix will be stored 190 @param[out] grad_project Address of the variable where the newly created gradient matrix will be stored 191 192 @return An error code: 0 - success, otherwise - failure 193 194 @ref Developer 195 **/ 196 static int CeedBasisCreateProjectionMatrices(CeedBasis basis_from, CeedBasis basis_to, CeedScalar **interp_project, CeedScalar **grad_project) { 197 Ceed ceed; 198 bool is_tensor_to, is_tensor_from; 199 CeedInt Q, Q_to, Q_from, P_to, P_from; 200 201 CeedCall(CeedBasisGetCeed(basis_to, &ceed)); 202 203 // Check for compatible quadrature spaces 204 CeedCall(CeedBasisGetNumQuadraturePoints(basis_to, &Q_to)); 205 CeedCall(CeedBasisGetNumQuadraturePoints(basis_from, &Q_from)); 206 CeedCheck(Q_to == Q_from, ceed, CEED_ERROR_DIMENSION, "Bases must have compatible quadrature spaces"); 207 Q = Q_to; 208 209 // Check for matching tensor or non-tensor 210 CeedCall(CeedBasisIsTensor(basis_to, &is_tensor_to)); 211 CeedCall(CeedBasisIsTensor(basis_from, &is_tensor_from)); 212 CeedCheck(is_tensor_to == is_tensor_from, ceed, CEED_ERROR_MINOR, "Bases must both be tensor or non-tensor"); 213 if (is_tensor_to) { 214 CeedCall(CeedBasisGetNumNodes1D(basis_to, &P_to)); 215 CeedCall(CeedBasisGetNumNodes1D(basis_from, &P_from)); 216 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis_from, &Q)); 217 } else { 218 CeedCall(CeedBasisGetNumNodes(basis_to, &P_to)); 219 CeedCall(CeedBasisGetNumNodes(basis_from, &P_from)); 220 } 221 222 // Check for matching FE space 223 CeedFESpace fe_space_to, fe_space_from; 224 CeedCall(CeedBasisGetFESpace(basis_to, &fe_space_to)); 225 CeedCall(CeedBasisGetFESpace(basis_from, &fe_space_from)); 226 CeedCheck(fe_space_to == fe_space_from, ceed, CEED_ERROR_MINOR, "Bases must both be the same FE space type"); 227 228 // Get source matrices 229 CeedInt dim, q_comp = 1; 230 CeedScalar *interp_to_inv, *interp_from; 231 const CeedScalar *interp_to_source = NULL, *interp_from_source = NULL, *grad_from_source = NULL; 232 233 CeedCall(CeedBasisGetDimension(basis_to, &dim)); 234 if (is_tensor_to) { 235 CeedCall(CeedBasisGetInterp1D(basis_to, &interp_to_source)); 236 CeedCall(CeedBasisGetInterp1D(basis_from, &interp_from_source)); 237 } else { 238 CeedCall(CeedBasisGetNumQuadratureComponents(basis_from, CEED_EVAL_INTERP, &q_comp)); 239 CeedCall(CeedBasisGetInterp(basis_to, &interp_to_source)); 240 CeedCall(CeedBasisGetInterp(basis_from, &interp_from_source)); 241 } 242 CeedCall(CeedMalloc(Q * P_from * q_comp, &interp_from)); 243 CeedCall(CeedCalloc(P_to * P_from, interp_project)); 244 245 // `grad_project = interp_to^+ * grad_from` is computed for the H^1 space case so the 246 // projection basis will have a gradient operation (allocated even if not H^1 for the 247 // basis construction later on) 248 if (fe_space_to == CEED_FE_SPACE_H1) { 249 if (is_tensor_to) { 250 CeedCall(CeedBasisGetGrad1D(basis_from, &grad_from_source)); 251 } else { 252 CeedCall(CeedBasisGetGrad(basis_from, &grad_from_source)); 253 } 254 } 255 CeedCall(CeedCalloc(P_to * P_from * (is_tensor_to ? 1 : dim), grad_project)); 256 257 // Compute interp_to^+, pseudoinverse of interp_to 258 CeedCall(CeedCalloc(Q * q_comp * P_to, &interp_to_inv)); 259 CeedCall(CeedMatrixPseudoinverse(ceed, interp_to_source, Q * q_comp, P_to, interp_to_inv)); 260 // Build matrices 261 CeedInt num_matrices = 1 + (fe_space_to == CEED_FE_SPACE_H1) * (is_tensor_to ? 1 : dim); 262 CeedScalar *input_from[num_matrices], *output_project[num_matrices]; 263 264 input_from[0] = (CeedScalar *)interp_from_source; 265 output_project[0] = *interp_project; 266 for (CeedInt m = 1; m < num_matrices; m++) { 267 input_from[m] = (CeedScalar *)&grad_from_source[(m - 1) * Q * P_from]; 268 output_project[m] = &((*grad_project)[(m - 1) * P_to * P_from]); 269 } 270 for (CeedInt m = 0; m < num_matrices; m++) { 271 // output_project = interp_to^+ * interp_from 272 memcpy(interp_from, input_from[m], Q * P_from * q_comp * sizeof(input_from[m][0])); 273 CeedCall(CeedMatrixMatrixMultiply(ceed, interp_to_inv, input_from[m], output_project[m], P_to, P_from, Q * q_comp)); 274 // Round zero to machine precision 275 for (CeedInt i = 0; i < P_to * P_from; i++) { 276 if (fabs(output_project[m][i]) < 10 * CEED_EPSILON) output_project[m][i] = 0.0; 277 } 278 } 279 280 // Cleanup 281 CeedCall(CeedFree(&interp_to_inv)); 282 CeedCall(CeedFree(&interp_from)); 283 return CEED_ERROR_SUCCESS; 284 } 285 286 /// @} 287 288 /// ---------------------------------------------------------------------------- 289 /// Ceed Backend API 290 /// ---------------------------------------------------------------------------- 291 /// @addtogroup CeedBasisBackend 292 /// @{ 293 294 /** 295 @brief Return collocated gradient matrix 296 297 @param[in] basis `CeedBasis` 298 @param[out] collo_grad_1d Row-major (`Q_1d * Q_1d`) matrix expressing derivatives of basis functions at quadrature points 299 300 @return An error code: 0 - success, otherwise - failure 301 302 @ref Backend 303 **/ 304 int CeedBasisGetCollocatedGrad(CeedBasis basis, CeedScalar *collo_grad_1d) { 305 Ceed ceed; 306 CeedInt P_1d, Q_1d; 307 CeedScalar *interp_1d_pinv; 308 const CeedScalar *grad_1d, *interp_1d; 309 310 // Note: This function is for backend use, so all errors are terminal and we do not need to clean up memory on failure. 311 CeedCall(CeedBasisGetCeed(basis, &ceed)); 312 CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d)); 313 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d)); 314 315 // Compute interp_1d^+, pseudoinverse of interp_1d 316 CeedCall(CeedCalloc(P_1d * Q_1d, &interp_1d_pinv)); 317 CeedCall(CeedBasisGetInterp1D(basis, &interp_1d)); 318 CeedCall(CeedMatrixPseudoinverse(ceed, interp_1d, Q_1d, P_1d, interp_1d_pinv)); 319 CeedCall(CeedBasisGetGrad1D(basis, &grad_1d)); 320 CeedCall(CeedMatrixMatrixMultiply(ceed, grad_1d, (const CeedScalar *)interp_1d_pinv, collo_grad_1d, Q_1d, Q_1d, P_1d)); 321 322 CeedCall(CeedFree(&interp_1d_pinv)); 323 return CEED_ERROR_SUCCESS; 324 } 325 326 /** 327 @brief Get tensor status for given `CeedBasis` 328 329 @param[in] basis `CeedBasis` 330 @param[out] is_tensor Variable to store tensor status 331 332 @return An error code: 0 - success, otherwise - failure 333 334 @ref Backend 335 **/ 336 int CeedBasisIsTensor(CeedBasis basis, bool *is_tensor) { 337 *is_tensor = basis->is_tensor_basis; 338 return CEED_ERROR_SUCCESS; 339 } 340 341 /** 342 @brief Get backend data of a `CeedBasis` 343 344 @param[in] basis `CeedBasis` 345 @param[out] data Variable to store data 346 347 @return An error code: 0 - success, otherwise - failure 348 349 @ref Backend 350 **/ 351 int CeedBasisGetData(CeedBasis basis, void *data) { 352 *(void **)data = basis->data; 353 return CEED_ERROR_SUCCESS; 354 } 355 356 /** 357 @brief Set backend data of a `CeedBasis` 358 359 @param[in,out] basis `CeedBasis` 360 @param[in] data Data to set 361 362 @return An error code: 0 - success, otherwise - failure 363 364 @ref Backend 365 **/ 366 int CeedBasisSetData(CeedBasis basis, void *data) { 367 basis->data = data; 368 return CEED_ERROR_SUCCESS; 369 } 370 371 /** 372 @brief Increment the reference counter for a `CeedBasis` 373 374 @param[in,out] basis `CeedBasis` to increment the reference counter 375 376 @return An error code: 0 - success, otherwise - failure 377 378 @ref Backend 379 **/ 380 int CeedBasisReference(CeedBasis basis) { 381 basis->ref_count++; 382 return CEED_ERROR_SUCCESS; 383 } 384 385 /** 386 @brief Get number of Q-vector components for given `CeedBasis` 387 388 @param[in] basis `CeedBasis` 389 @param[in] eval_mode @ref CEED_EVAL_INTERP to use interpolated values, 390 @ref CEED_EVAL_GRAD to use gradients, 391 @ref CEED_EVAL_DIV to use divergence, 392 @ref CEED_EVAL_CURL to use curl 393 @param[out] q_comp Variable to store number of Q-vector components of basis 394 395 @return An error code: 0 - success, otherwise - failure 396 397 @ref Backend 398 **/ 399 int CeedBasisGetNumQuadratureComponents(CeedBasis basis, CeedEvalMode eval_mode, CeedInt *q_comp) { 400 CeedInt dim; 401 402 CeedCall(CeedBasisGetDimension(basis, &dim)); 403 switch (eval_mode) { 404 case CEED_EVAL_INTERP: { 405 CeedFESpace fe_space; 406 407 CeedCall(CeedBasisGetFESpace(basis, &fe_space)); 408 *q_comp = (fe_space == CEED_FE_SPACE_H1) ? 1 : dim; 409 } break; 410 case CEED_EVAL_GRAD: 411 *q_comp = dim; 412 break; 413 case CEED_EVAL_DIV: 414 *q_comp = 1; 415 break; 416 case CEED_EVAL_CURL: 417 *q_comp = (dim < 3) ? 1 : dim; 418 break; 419 case CEED_EVAL_NONE: 420 case CEED_EVAL_WEIGHT: 421 *q_comp = 1; 422 break; 423 } 424 return CEED_ERROR_SUCCESS; 425 } 426 427 /** 428 @brief Estimate number of FLOPs required to apply `CeedBasis` in `t_mode` and `eval_mode` 429 430 @param[in] basis `CeedBasis` to estimate FLOPs for 431 @param[in] t_mode Apply basis or transpose 432 @param[in] eval_mode @ref CeedEvalMode 433 @param[out] flops Address of variable to hold FLOPs estimate 434 435 @ref Backend 436 **/ 437 int CeedBasisGetFlopsEstimate(CeedBasis basis, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedSize *flops) { 438 bool is_tensor; 439 440 CeedCall(CeedBasisIsTensor(basis, &is_tensor)); 441 if (is_tensor) { 442 CeedInt dim, num_comp, P_1d, Q_1d; 443 444 CeedCall(CeedBasisGetDimension(basis, &dim)); 445 CeedCall(CeedBasisGetNumComponents(basis, &num_comp)); 446 CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d)); 447 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d)); 448 if (t_mode == CEED_TRANSPOSE) { 449 P_1d = Q_1d; 450 Q_1d = P_1d; 451 } 452 CeedInt tensor_flops = 0, pre = num_comp * CeedIntPow(P_1d, dim - 1), post = 1; 453 for (CeedInt d = 0; d < dim; d++) { 454 tensor_flops += 2 * pre * P_1d * post * Q_1d; 455 pre /= P_1d; 456 post *= Q_1d; 457 } 458 switch (eval_mode) { 459 case CEED_EVAL_NONE: 460 *flops = 0; 461 break; 462 case CEED_EVAL_INTERP: 463 *flops = tensor_flops; 464 break; 465 case CEED_EVAL_GRAD: 466 *flops = tensor_flops * 2; 467 break; 468 case CEED_EVAL_DIV: 469 case CEED_EVAL_CURL: { 470 // LCOV_EXCL_START 471 return CeedError(CeedBasisReturnCeed(basis), CEED_ERROR_INCOMPATIBLE, "Tensor basis evaluation for %s not supported", 472 CeedEvalModes[eval_mode]); 473 break; 474 // LCOV_EXCL_STOP 475 } 476 case CEED_EVAL_WEIGHT: 477 *flops = dim * CeedIntPow(Q_1d, dim); 478 break; 479 } 480 } else { 481 CeedInt dim, num_comp, q_comp, num_nodes, num_qpts; 482 483 CeedCall(CeedBasisGetDimension(basis, &dim)); 484 CeedCall(CeedBasisGetNumComponents(basis, &num_comp)); 485 CeedCall(CeedBasisGetNumQuadratureComponents(basis, eval_mode, &q_comp)); 486 CeedCall(CeedBasisGetNumNodes(basis, &num_nodes)); 487 CeedCall(CeedBasisGetNumQuadraturePoints(basis, &num_qpts)); 488 switch (eval_mode) { 489 case CEED_EVAL_NONE: 490 *flops = 0; 491 break; 492 case CEED_EVAL_INTERP: 493 case CEED_EVAL_GRAD: 494 case CEED_EVAL_DIV: 495 case CEED_EVAL_CURL: 496 *flops = num_nodes * num_qpts * num_comp * q_comp; 497 break; 498 case CEED_EVAL_WEIGHT: 499 *flops = 0; 500 break; 501 } 502 } 503 return CEED_ERROR_SUCCESS; 504 } 505 506 /** 507 @brief Get `CeedFESpace` for a `CeedBasis` 508 509 @param[in] basis `CeedBasis` 510 @param[out] fe_space Variable to store `CeedFESpace` 511 512 @return An error code: 0 - success, otherwise - failure 513 514 @ref Backend 515 **/ 516 int CeedBasisGetFESpace(CeedBasis basis, CeedFESpace *fe_space) { 517 *fe_space = basis->fe_space; 518 return CEED_ERROR_SUCCESS; 519 } 520 521 /** 522 @brief Get dimension for given `CeedElemTopology` 523 524 @param[in] topo `CeedElemTopology` 525 @param[out] dim Variable to store dimension of topology 526 527 @return An error code: 0 - success, otherwise - failure 528 529 @ref Backend 530 **/ 531 int CeedBasisGetTopologyDimension(CeedElemTopology topo, CeedInt *dim) { 532 *dim = (CeedInt)topo >> 16; 533 return CEED_ERROR_SUCCESS; 534 } 535 536 /** 537 @brief Get `CeedTensorContract` of a `CeedBasis` 538 539 @param[in] basis `CeedBasis` 540 @param[out] contract Variable to store `CeedTensorContract` 541 542 @return An error code: 0 - success, otherwise - failure 543 544 @ref Backend 545 **/ 546 int CeedBasisGetTensorContract(CeedBasis basis, CeedTensorContract *contract) { 547 *contract = basis->contract; 548 return CEED_ERROR_SUCCESS; 549 } 550 551 /** 552 @brief Set `CeedTensorContract` of a `CeedBasis` 553 554 @param[in,out] basis `CeedBasis` 555 @param[in] contract `CeedTensorContract` to set 556 557 @return An error code: 0 - success, otherwise - failure 558 559 @ref Backend 560 **/ 561 int CeedBasisSetTensorContract(CeedBasis basis, CeedTensorContract contract) { 562 basis->contract = contract; 563 CeedCall(CeedTensorContractReference(contract)); 564 return CEED_ERROR_SUCCESS; 565 } 566 567 /** 568 @brief Return a reference implementation of matrix multiplication \f$C = A B\f$. 569 570 Note: This is a reference implementation for CPU `CeedScalar` pointers that is not intended for high performance. 571 572 @param[in] ceed `Ceed` context for error handling 573 @param[in] mat_A Row-major matrix `A` 574 @param[in] mat_B Row-major matrix `B` 575 @param[out] mat_C Row-major output matrix `C` 576 @param[in] m Number of rows of `C` 577 @param[in] n Number of columns of `C` 578 @param[in] kk Number of columns of `A`/rows of `B` 579 580 @return An error code: 0 - success, otherwise - failure 581 582 @ref Utility 583 **/ 584 int CeedMatrixMatrixMultiply(Ceed ceed, const CeedScalar *mat_A, const CeedScalar *mat_B, CeedScalar *mat_C, CeedInt m, CeedInt n, CeedInt kk) { 585 for (CeedInt i = 0; i < m; i++) { 586 for (CeedInt j = 0; j < n; j++) { 587 CeedScalar sum = 0; 588 589 for (CeedInt k = 0; k < kk; k++) sum += mat_A[k + i * kk] * mat_B[j + k * n]; 590 mat_C[j + i * n] = sum; 591 } 592 } 593 return CEED_ERROR_SUCCESS; 594 } 595 596 /** 597 @brief Return QR Factorization of a matrix 598 599 @param[in] ceed `Ceed` context for error handling 600 @param[in,out] mat Row-major matrix to be factorized in place 601 @param[in,out] tau Vector of length `m` of scaling factors 602 @param[in] m Number of rows 603 @param[in] n Number of columns 604 605 @return An error code: 0 - success, otherwise - failure 606 607 @ref Utility 608 **/ 609 int CeedQRFactorization(Ceed ceed, CeedScalar *mat, CeedScalar *tau, CeedInt m, CeedInt n) { 610 CeedScalar v[m]; 611 612 // Check matrix shape 613 CeedCheck(n <= m, ceed, CEED_ERROR_UNSUPPORTED, "Cannot compute QR factorization with n > m"); 614 615 for (CeedInt i = 0; i < n; i++) { 616 CeedScalar sigma = 0.0; 617 618 if (i >= m - 1) { // last row of matrix, no reflection needed 619 tau[i] = 0.; 620 break; 621 } 622 // Calculate Householder vector, magnitude 623 v[i] = mat[i + n * i]; 624 for (CeedInt j = i + 1; j < m; j++) { 625 v[j] = mat[i + n * j]; 626 sigma += v[j] * v[j]; 627 } 628 const CeedScalar norm = sqrt(v[i] * v[i] + sigma); // norm of v[i:m] 629 const CeedScalar R_ii = -copysign(norm, v[i]); 630 631 v[i] -= R_ii; 632 // norm of v[i:m] after modification above and scaling below 633 // norm = sqrt(v[i]*v[i] + sigma) / v[i]; 634 // tau = 2 / (norm*norm) 635 tau[i] = 2 * v[i] * v[i] / (v[i] * v[i] + sigma); 636 for (CeedInt j = i + 1; j < m; j++) v[j] /= v[i]; 637 638 // Apply Householder reflector to lower right panel 639 CeedHouseholderReflect(&mat[i * n + i + 1], &v[i], tau[i], m - i, n - i - 1, n, 1); 640 // Save v 641 mat[i + n * i] = R_ii; 642 for (CeedInt j = i + 1; j < m; j++) mat[i + n * j] = v[j]; 643 } 644 return CEED_ERROR_SUCCESS; 645 } 646 647 /** 648 @brief Apply Householder Q matrix 649 650 Compute `mat_A = mat_Q mat_A`, where `mat_Q` is \f$m \times m\f$ and `mat_A` is \f$m \times n\f$. 651 652 @param[in,out] mat_A Matrix to apply Householder Q to, in place 653 @param[in] mat_Q Householder Q matrix 654 @param[in] tau Householder scaling factors 655 @param[in] t_mode Transpose mode for application 656 @param[in] m Number of rows in `A` 657 @param[in] n Number of columns in `A` 658 @param[in] k Number of elementary reflectors in Q, `k < m` 659 @param[in] row Row stride in `A` 660 @param[in] col Col stride in `A` 661 662 @return An error code: 0 - success, otherwise - failure 663 664 @ref Utility 665 **/ 666 int CeedHouseholderApplyQ(CeedScalar *mat_A, const CeedScalar *mat_Q, const CeedScalar *tau, CeedTransposeMode t_mode, CeedInt m, CeedInt n, 667 CeedInt k, CeedInt row, CeedInt col) { 668 CeedScalar *v; 669 670 CeedCall(CeedMalloc(m, &v)); 671 for (CeedInt ii = 0; ii < k; ii++) { 672 CeedInt i = t_mode == CEED_TRANSPOSE ? ii : k - 1 - ii; 673 for (CeedInt j = i + 1; j < m; j++) v[j] = mat_Q[j * k + i]; 674 // Apply Householder reflector (I - tau v v^T) collo_grad_1d^T 675 CeedCall(CeedHouseholderReflect(&mat_A[i * row], &v[i], tau[i], m - i, n, row, col)); 676 } 677 CeedCall(CeedFree(&v)); 678 return CEED_ERROR_SUCCESS; 679 } 680 681 /** 682 @brief Return pseudoinverse of a matrix 683 684 @param[in] ceed Ceed context for error handling 685 @param[in] mat Row-major matrix to compute pseudoinverse of 686 @param[in] m Number of rows 687 @param[in] n Number of columns 688 @param[out] mat_pinv Row-major pseudoinverse matrix 689 690 @return An error code: 0 - success, otherwise - failure 691 692 @ref Utility 693 **/ 694 int CeedMatrixPseudoinverse(Ceed ceed, const CeedScalar *mat, CeedInt m, CeedInt n, CeedScalar *mat_pinv) { 695 CeedScalar *tau, *I, *mat_copy; 696 697 CeedCall(CeedCalloc(m, &tau)); 698 CeedCall(CeedCalloc(m * m, &I)); 699 CeedCall(CeedCalloc(m * n, &mat_copy)); 700 memcpy(mat_copy, mat, m * n * sizeof mat[0]); 701 702 // QR Factorization, mat = Q R 703 CeedCall(CeedQRFactorization(ceed, mat_copy, tau, m, n)); 704 705 // -- Apply Q^T, I = Q^T * I 706 for (CeedInt i = 0; i < m; i++) I[i * m + i] = 1.0; 707 CeedCall(CeedHouseholderApplyQ(I, mat_copy, tau, CEED_TRANSPOSE, m, m, n, m, 1)); 708 // -- Apply R_inv, mat_pinv = R_inv * Q^T 709 for (CeedInt j = 0; j < m; j++) { // Column j 710 mat_pinv[j + m * (n - 1)] = I[j + m * (n - 1)] / mat_copy[n * n - 1]; 711 for (CeedInt i = n - 2; i >= 0; i--) { // Row i 712 mat_pinv[j + m * i] = I[j + m * i]; 713 for (CeedInt k = i + 1; k < n; k++) mat_pinv[j + m * i] -= mat_copy[k + n * i] * mat_pinv[j + m * k]; 714 mat_pinv[j + m * i] /= mat_copy[i + n * i]; 715 } 716 } 717 718 // Cleanup 719 CeedCall(CeedFree(&I)); 720 CeedCall(CeedFree(&tau)); 721 CeedCall(CeedFree(&mat_copy)); 722 return CEED_ERROR_SUCCESS; 723 } 724 725 /** 726 @brief Return symmetric Schur decomposition of the symmetric matrix mat via symmetric QR factorization 727 728 @param[in] ceed `Ceed` context for error handling 729 @param[in,out] mat Row-major matrix to be factorized in place 730 @param[out] lambda Vector of length n of eigenvalues 731 @param[in] n Number of rows/columns 732 733 @return An error code: 0 - success, otherwise - failure 734 735 @ref Utility 736 **/ 737 CeedPragmaOptimizeOff 738 int CeedSymmetricSchurDecomposition(Ceed ceed, CeedScalar *mat, CeedScalar *lambda, CeedInt n) { 739 // Check bounds for clang-tidy 740 CeedCheck(n > 1, ceed, CEED_ERROR_UNSUPPORTED, "Cannot compute symmetric Schur decomposition of scalars"); 741 742 CeedScalar v[n - 1], tau[n - 1], mat_T[n * n]; 743 744 // Copy mat to mat_T and set mat to I 745 memcpy(mat_T, mat, n * n * sizeof(mat[0])); 746 for (CeedInt i = 0; i < n; i++) { 747 for (CeedInt j = 0; j < n; j++) mat[j + n * i] = (i == j) ? 1 : 0; 748 } 749 750 // Reduce to tridiagonal 751 for (CeedInt i = 0; i < n - 1; i++) { 752 // Calculate Householder vector, magnitude 753 CeedScalar sigma = 0.0; 754 755 v[i] = mat_T[i + n * (i + 1)]; 756 for (CeedInt j = i + 1; j < n - 1; j++) { 757 v[j] = mat_T[i + n * (j + 1)]; 758 sigma += v[j] * v[j]; 759 } 760 const CeedScalar norm = sqrt(v[i] * v[i] + sigma); // norm of v[i:n-1] 761 const CeedScalar R_ii = -copysign(norm, v[i]); 762 763 v[i] -= R_ii; 764 // norm of v[i:m] after modification above and scaling below 765 // norm = sqrt(v[i]*v[i] + sigma) / v[i]; 766 // tau = 2 / (norm*norm) 767 tau[i] = i == n - 2 ? 2 : 2 * v[i] * v[i] / (v[i] * v[i] + sigma); 768 for (CeedInt j = i + 1; j < n - 1; j++) v[j] /= v[i]; 769 770 // Update sub and super diagonal 771 for (CeedInt j = i + 2; j < n; j++) { 772 mat_T[i + n * j] = 0; 773 mat_T[j + n * i] = 0; 774 } 775 // Apply symmetric Householder reflector to lower right panel 776 CeedHouseholderReflect(&mat_T[(i + 1) + n * (i + 1)], &v[i], tau[i], n - (i + 1), n - (i + 1), n, 1); 777 CeedHouseholderReflect(&mat_T[(i + 1) + n * (i + 1)], &v[i], tau[i], n - (i + 1), n - (i + 1), 1, n); 778 779 // Save v 780 mat_T[i + n * (i + 1)] = R_ii; 781 mat_T[(i + 1) + n * i] = R_ii; 782 for (CeedInt j = i + 1; j < n - 1; j++) { 783 mat_T[i + n * (j + 1)] = v[j]; 784 } 785 } 786 // Backwards accumulation of Q 787 for (CeedInt i = n - 2; i >= 0; i--) { 788 if (tau[i] > 0.0) { 789 v[i] = 1; 790 for (CeedInt j = i + 1; j < n - 1; j++) { 791 v[j] = mat_T[i + n * (j + 1)]; 792 mat_T[i + n * (j + 1)] = 0; 793 } 794 CeedHouseholderReflect(&mat[(i + 1) + n * (i + 1)], &v[i], tau[i], n - (i + 1), n - (i + 1), n, 1); 795 } 796 } 797 798 // Reduce sub and super diagonal 799 CeedInt p = 0, q = 0, itr = 0, max_itr = n * n * n * n; 800 CeedScalar tol = CEED_EPSILON; 801 802 while (itr < max_itr) { 803 // Update p, q, size of reduced portions of diagonal 804 p = 0; 805 q = 0; 806 for (CeedInt i = n - 2; i >= 0; i--) { 807 if (fabs(mat_T[i + n * (i + 1)]) < tol) q += 1; 808 else break; 809 } 810 for (CeedInt i = 0; i < n - q - 1; i++) { 811 if (fabs(mat_T[i + n * (i + 1)]) < tol) p += 1; 812 else break; 813 } 814 if (q == n - 1) break; // Finished reducing 815 816 // Reduce tridiagonal portion 817 CeedScalar t_nn = mat_T[(n - 1 - q) + n * (n - 1 - q)], t_nnm1 = mat_T[(n - 2 - q) + n * (n - 1 - q)]; 818 CeedScalar d = (mat_T[(n - 2 - q) + n * (n - 2 - q)] - t_nn) / 2; 819 CeedScalar mu = t_nn - t_nnm1 * t_nnm1 / (d + copysign(sqrt(d * d + t_nnm1 * t_nnm1), d)); 820 CeedScalar x = mat_T[p + n * p] - mu; 821 CeedScalar z = mat_T[p + n * (p + 1)]; 822 823 for (CeedInt k = p; k < n - q - 1; k++) { 824 // Compute Givens rotation 825 CeedScalar c = 1, s = 0; 826 827 if (fabs(z) > tol) { 828 if (fabs(z) > fabs(x)) { 829 const CeedScalar tau = -x / z; 830 831 s = 1 / sqrt(1 + tau * tau); 832 c = s * tau; 833 } else { 834 const CeedScalar tau = -z / x; 835 836 c = 1 / sqrt(1 + tau * tau); 837 s = c * tau; 838 } 839 } 840 841 // Apply Givens rotation to T 842 CeedGivensRotation(mat_T, c, s, CEED_NOTRANSPOSE, k, k + 1, n, n); 843 CeedGivensRotation(mat_T, c, s, CEED_TRANSPOSE, k, k + 1, n, n); 844 845 // Apply Givens rotation to Q 846 CeedGivensRotation(mat, c, s, CEED_NOTRANSPOSE, k, k + 1, n, n); 847 848 // Update x, z 849 if (k < n - q - 2) { 850 x = mat_T[k + n * (k + 1)]; 851 z = mat_T[k + n * (k + 2)]; 852 } 853 } 854 itr++; 855 } 856 857 // Save eigenvalues 858 for (CeedInt i = 0; i < n; i++) lambda[i] = mat_T[i + n * i]; 859 860 // Check convergence 861 CeedCheck(itr < max_itr || q > n, ceed, CEED_ERROR_MINOR, "Symmetric QR failed to converge"); 862 return CEED_ERROR_SUCCESS; 863 } 864 CeedPragmaOptimizeOn 865 866 /** 867 @brief Return Simultaneous Diagonalization of two matrices. 868 869 This solves the generalized eigenvalue problem `A x = lambda B x`, where `A` and `B` are symmetric and `B` is positive definite. 870 We generate the matrix `X` and vector `Lambda` such that `X^T A X = Lambda` and `X^T B X = I`. 871 This is equivalent to the LAPACK routine 'sygv' with `TYPE = 1`. 872 873 @param[in] ceed `Ceed` context for error handling 874 @param[in] mat_A Row-major matrix to be factorized with eigenvalues 875 @param[in] mat_B Row-major matrix to be factorized to identity 876 @param[out] mat_X Row-major orthogonal matrix 877 @param[out] lambda Vector of length `n` of generalized eigenvalues 878 @param[in] n Number of rows/columns 879 880 @return An error code: 0 - success, otherwise - failure 881 882 @ref Utility 883 **/ 884 CeedPragmaOptimizeOff 885 int CeedSimultaneousDiagonalization(Ceed ceed, CeedScalar *mat_A, CeedScalar *mat_B, CeedScalar *mat_X, CeedScalar *lambda, CeedInt n) { 886 CeedScalar *mat_C, *mat_G, *vec_D; 887 888 CeedCall(CeedCalloc(n * n, &mat_C)); 889 CeedCall(CeedCalloc(n * n, &mat_G)); 890 CeedCall(CeedCalloc(n, &vec_D)); 891 892 // Compute B = G D G^T 893 memcpy(mat_G, mat_B, n * n * sizeof(mat_B[0])); 894 CeedCall(CeedSymmetricSchurDecomposition(ceed, mat_G, vec_D, n)); 895 896 // Sort eigenvalues 897 for (CeedInt i = n - 1; i >= 0; i--) { 898 for (CeedInt j = 0; j < i; j++) { 899 if (fabs(vec_D[j]) > fabs(vec_D[j + 1])) { 900 CeedScalarSwap(vec_D[j], vec_D[j + 1]); 901 for (CeedInt k = 0; k < n; k++) CeedScalarSwap(mat_G[k * n + j], mat_G[k * n + j + 1]); 902 } 903 } 904 } 905 906 // Compute C = (G D^1/2)^-1 A (G D^1/2)^-T 907 // = D^-1/2 G^T A G D^-1/2 908 // -- D = D^-1/2 909 for (CeedInt i = 0; i < n; i++) vec_D[i] = 1. / sqrt(vec_D[i]); 910 // -- G = G D^-1/2 911 // -- C = D^-1/2 G^T 912 for (CeedInt i = 0; i < n; i++) { 913 for (CeedInt j = 0; j < n; j++) { 914 mat_G[i * n + j] *= vec_D[j]; 915 mat_C[j * n + i] = mat_G[i * n + j]; 916 } 917 } 918 // -- X = (D^-1/2 G^T) A 919 CeedCall(CeedMatrixMatrixMultiply(ceed, (const CeedScalar *)mat_C, (const CeedScalar *)mat_A, mat_X, n, n, n)); 920 // -- C = (D^-1/2 G^T A) (G D^-1/2) 921 CeedCall(CeedMatrixMatrixMultiply(ceed, (const CeedScalar *)mat_X, (const CeedScalar *)mat_G, mat_C, n, n, n)); 922 923 // Compute Q^T C Q = lambda 924 CeedCall(CeedSymmetricSchurDecomposition(ceed, mat_C, lambda, n)); 925 926 // Sort eigenvalues 927 for (CeedInt i = n - 1; i >= 0; i--) { 928 for (CeedInt j = 0; j < i; j++) { 929 if (fabs(lambda[j]) > fabs(lambda[j + 1])) { 930 CeedScalarSwap(lambda[j], lambda[j + 1]); 931 for (CeedInt k = 0; k < n; k++) CeedScalarSwap(mat_C[k * n + j], mat_C[k * n + j + 1]); 932 } 933 } 934 } 935 936 // Set X = (G D^1/2)^-T Q 937 // = G D^-1/2 Q 938 CeedCall(CeedMatrixMatrixMultiply(ceed, (const CeedScalar *)mat_G, (const CeedScalar *)mat_C, mat_X, n, n, n)); 939 940 // Cleanup 941 CeedCall(CeedFree(&mat_C)); 942 CeedCall(CeedFree(&mat_G)); 943 CeedCall(CeedFree(&vec_D)); 944 return CEED_ERROR_SUCCESS; 945 } 946 CeedPragmaOptimizeOn 947 948 /// @} 949 950 /// ---------------------------------------------------------------------------- 951 /// CeedBasis Public API 952 /// ---------------------------------------------------------------------------- 953 /// @addtogroup CeedBasisUser 954 /// @{ 955 956 /** 957 @brief Create a tensor-product basis for \f$H^1\f$ discretizations 958 959 @param[in] ceed `Ceed` object used to create the `CeedBasis` 960 @param[in] dim Topological dimension 961 @param[in] num_comp Number of field components (1 for scalar fields) 962 @param[in] P_1d Number of nodes in one dimension 963 @param[in] Q_1d Number of quadrature points in one dimension 964 @param[in] interp_1d Row-major (`Q_1d * P_1d`) matrix expressing the values of nodal basis functions at quadrature points 965 @param[in] grad_1d Row-major (`Q_1d * P_1d`) matrix expressing derivatives of nodal basis functions at quadrature points 966 @param[in] q_ref_1d Array of length `Q_1d` holding the locations of quadrature points on the 1D reference element `[-1, 1]` 967 @param[in] q_weight_1d Array of length `Q_1d` holding the quadrature weights on the reference element 968 @param[out] basis Address of the variable where the newly created `CeedBasis` will be stored 969 970 @return An error code: 0 - success, otherwise - failure 971 972 @ref User 973 **/ 974 int CeedBasisCreateTensorH1(Ceed ceed, CeedInt dim, CeedInt num_comp, CeedInt P_1d, CeedInt Q_1d, const CeedScalar *interp_1d, 975 const CeedScalar *grad_1d, const CeedScalar *q_ref_1d, const CeedScalar *q_weight_1d, CeedBasis *basis) { 976 if (!ceed->BasisCreateTensorH1) { 977 Ceed delegate; 978 979 CeedCall(CeedGetObjectDelegate(ceed, &delegate, "Basis")); 980 CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support BasisCreateTensorH1"); 981 CeedCall(CeedBasisCreateTensorH1(delegate, dim, num_comp, P_1d, Q_1d, interp_1d, grad_1d, q_ref_1d, q_weight_1d, basis)); 982 return CEED_ERROR_SUCCESS; 983 } 984 985 CeedCheck(dim > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis dimension must be a positive value"); 986 CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 component"); 987 CeedCheck(P_1d > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 node"); 988 CeedCheck(Q_1d > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 quadrature point"); 989 990 CeedElemTopology topo = dim == 1 ? CEED_TOPOLOGY_LINE : dim == 2 ? CEED_TOPOLOGY_QUAD : CEED_TOPOLOGY_HEX; 991 992 CeedCall(CeedCalloc(1, basis)); 993 CeedCall(CeedReferenceCopy(ceed, &(*basis)->ceed)); 994 (*basis)->ref_count = 1; 995 (*basis)->is_tensor_basis = true; 996 (*basis)->dim = dim; 997 (*basis)->topo = topo; 998 (*basis)->num_comp = num_comp; 999 (*basis)->P_1d = P_1d; 1000 (*basis)->Q_1d = Q_1d; 1001 (*basis)->P = CeedIntPow(P_1d, dim); 1002 (*basis)->Q = CeedIntPow(Q_1d, dim); 1003 (*basis)->fe_space = CEED_FE_SPACE_H1; 1004 CeedCall(CeedCalloc(Q_1d, &(*basis)->q_ref_1d)); 1005 CeedCall(CeedCalloc(Q_1d, &(*basis)->q_weight_1d)); 1006 if (q_ref_1d) memcpy((*basis)->q_ref_1d, q_ref_1d, Q_1d * sizeof(q_ref_1d[0])); 1007 if (q_weight_1d) memcpy((*basis)->q_weight_1d, q_weight_1d, Q_1d * sizeof(q_weight_1d[0])); 1008 CeedCall(CeedCalloc(Q_1d * P_1d, &(*basis)->interp_1d)); 1009 CeedCall(CeedCalloc(Q_1d * P_1d, &(*basis)->grad_1d)); 1010 if (interp_1d) memcpy((*basis)->interp_1d, interp_1d, Q_1d * P_1d * sizeof(interp_1d[0])); 1011 if (grad_1d) memcpy((*basis)->grad_1d, grad_1d, Q_1d * P_1d * sizeof(grad_1d[0])); 1012 CeedCall(ceed->BasisCreateTensorH1(dim, P_1d, Q_1d, interp_1d, grad_1d, q_ref_1d, q_weight_1d, *basis)); 1013 return CEED_ERROR_SUCCESS; 1014 } 1015 1016 /** 1017 @brief Create a tensor-product \f$H^1\f$ Lagrange basis 1018 1019 @param[in] ceed `Ceed` object used to create the `CeedBasis` 1020 @param[in] dim Topological dimension of element 1021 @param[in] num_comp Number of field components (1 for scalar fields) 1022 @param[in] P Number of Gauss-Lobatto nodes in one dimension. 1023 The polynomial degree of the resulting `Q_k` element is `k = P - 1`. 1024 @param[in] Q Number of quadrature points in one dimension. 1025 @param[in] quad_mode Distribution of the `Q` quadrature points (affects order of accuracy for the quadrature) 1026 @param[out] basis Address of the variable where the newly created `CeedBasis` will be stored 1027 1028 @return An error code: 0 - success, otherwise - failure 1029 1030 @ref User 1031 **/ 1032 int CeedBasisCreateTensorH1Lagrange(Ceed ceed, CeedInt dim, CeedInt num_comp, CeedInt P, CeedInt Q, CeedQuadMode quad_mode, CeedBasis *basis) { 1033 // Allocate 1034 int ierr = CEED_ERROR_SUCCESS; 1035 CeedScalar c1, c2, c3, c4, dx, *nodes, *interp_1d, *grad_1d, *q_ref_1d, *q_weight_1d; 1036 1037 CeedCheck(dim > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis dimension must be a positive value"); 1038 CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 component"); 1039 CeedCheck(P > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 node"); 1040 CeedCheck(Q > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 quadrature point"); 1041 1042 // Get Nodes and Weights 1043 CeedCall(CeedCalloc(P * Q, &interp_1d)); 1044 CeedCall(CeedCalloc(P * Q, &grad_1d)); 1045 CeedCall(CeedCalloc(P, &nodes)); 1046 CeedCall(CeedCalloc(Q, &q_ref_1d)); 1047 CeedCall(CeedCalloc(Q, &q_weight_1d)); 1048 if (CeedLobattoQuadrature(P, nodes, NULL) != CEED_ERROR_SUCCESS) goto cleanup; 1049 switch (quad_mode) { 1050 case CEED_GAUSS: 1051 ierr = CeedGaussQuadrature(Q, q_ref_1d, q_weight_1d); 1052 break; 1053 case CEED_GAUSS_LOBATTO: 1054 ierr = CeedLobattoQuadrature(Q, q_ref_1d, q_weight_1d); 1055 break; 1056 } 1057 if (ierr != CEED_ERROR_SUCCESS) goto cleanup; 1058 1059 // Build B, D matrix 1060 // Fornberg, 1998 1061 for (CeedInt i = 0; i < Q; i++) { 1062 c1 = 1.0; 1063 c3 = nodes[0] - q_ref_1d[i]; 1064 interp_1d[i * P + 0] = 1.0; 1065 for (CeedInt j = 1; j < P; j++) { 1066 c2 = 1.0; 1067 c4 = c3; 1068 c3 = nodes[j] - q_ref_1d[i]; 1069 for (CeedInt k = 0; k < j; k++) { 1070 dx = nodes[j] - nodes[k]; 1071 c2 *= dx; 1072 if (k == j - 1) { 1073 grad_1d[i * P + j] = c1 * (interp_1d[i * P + k] - c4 * grad_1d[i * P + k]) / c2; 1074 interp_1d[i * P + j] = -c1 * c4 * interp_1d[i * P + k] / c2; 1075 } 1076 grad_1d[i * P + k] = (c3 * grad_1d[i * P + k] - interp_1d[i * P + k]) / dx; 1077 interp_1d[i * P + k] = c3 * interp_1d[i * P + k] / dx; 1078 } 1079 c1 = c2; 1080 } 1081 } 1082 // Pass to CeedBasisCreateTensorH1 1083 CeedCall(CeedBasisCreateTensorH1(ceed, dim, num_comp, P, Q, interp_1d, grad_1d, q_ref_1d, q_weight_1d, basis)); 1084 cleanup: 1085 CeedCall(CeedFree(&interp_1d)); 1086 CeedCall(CeedFree(&grad_1d)); 1087 CeedCall(CeedFree(&nodes)); 1088 CeedCall(CeedFree(&q_ref_1d)); 1089 CeedCall(CeedFree(&q_weight_1d)); 1090 return CEED_ERROR_SUCCESS; 1091 } 1092 1093 /** 1094 @brief Create a non tensor-product basis for \f$H^1\f$ discretizations 1095 1096 @param[in] ceed `Ceed` object used to create the `CeedBasis` 1097 @param[in] topo Topology of element, e.g. hypercube, simplex, ect 1098 @param[in] num_comp Number of field components (1 for scalar fields) 1099 @param[in] num_nodes Total number of nodes 1100 @param[in] num_qpts Total number of quadrature points 1101 @param[in] interp Row-major (`num_qpts * num_nodes`) matrix expressing the values of nodal basis functions at quadrature points 1102 @param[in] grad Row-major (`dim * num_qpts * num_nodes`) matrix expressing derivatives of nodal basis functions at quadrature points 1103 @param[in] q_ref Array of length `num_qpts` * dim holding the locations of quadrature points on the reference element 1104 @param[in] q_weight Array of length `num_qpts` holding the quadrature weights on the reference element 1105 @param[out] basis Address of the variable where the newly created `CeedBasis` will be stored 1106 1107 @return An error code: 0 - success, otherwise - failure 1108 1109 @ref User 1110 **/ 1111 int CeedBasisCreateH1(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, 1112 const CeedScalar *grad, const CeedScalar *q_ref, const CeedScalar *q_weight, CeedBasis *basis) { 1113 CeedInt P = num_nodes, Q = num_qpts, dim = 0; 1114 1115 if (!ceed->BasisCreateH1) { 1116 Ceed delegate; 1117 1118 CeedCall(CeedGetObjectDelegate(ceed, &delegate, "Basis")); 1119 CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support BasisCreateH1"); 1120 CeedCall(CeedBasisCreateH1(delegate, topo, num_comp, num_nodes, num_qpts, interp, grad, q_ref, q_weight, basis)); 1121 return CEED_ERROR_SUCCESS; 1122 } 1123 1124 CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 component"); 1125 CeedCheck(num_nodes > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 node"); 1126 CeedCheck(num_qpts > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 quadrature point"); 1127 1128 CeedCall(CeedBasisGetTopologyDimension(topo, &dim)); 1129 1130 CeedCall(CeedCalloc(1, basis)); 1131 CeedCall(CeedReferenceCopy(ceed, &(*basis)->ceed)); 1132 (*basis)->ref_count = 1; 1133 (*basis)->is_tensor_basis = false; 1134 (*basis)->dim = dim; 1135 (*basis)->topo = topo; 1136 (*basis)->num_comp = num_comp; 1137 (*basis)->P = P; 1138 (*basis)->Q = Q; 1139 (*basis)->fe_space = CEED_FE_SPACE_H1; 1140 CeedCall(CeedCalloc(Q * dim, &(*basis)->q_ref_1d)); 1141 CeedCall(CeedCalloc(Q, &(*basis)->q_weight_1d)); 1142 if (q_ref) memcpy((*basis)->q_ref_1d, q_ref, Q * dim * sizeof(q_ref[0])); 1143 if (q_weight) memcpy((*basis)->q_weight_1d, q_weight, Q * sizeof(q_weight[0])); 1144 CeedCall(CeedCalloc(Q * P, &(*basis)->interp)); 1145 CeedCall(CeedCalloc(dim * Q * P, &(*basis)->grad)); 1146 if (interp) memcpy((*basis)->interp, interp, Q * P * sizeof(interp[0])); 1147 if (grad) memcpy((*basis)->grad, grad, dim * Q * P * sizeof(grad[0])); 1148 CeedCall(ceed->BasisCreateH1(topo, dim, P, Q, interp, grad, q_ref, q_weight, *basis)); 1149 return CEED_ERROR_SUCCESS; 1150 } 1151 1152 /** 1153 @brief Create a non tensor-product basis for \f$H(\mathrm{div})\f$ discretizations 1154 1155 @param[in] ceed `Ceed` object used to create the `CeedBasis` 1156 @param[in] topo Topology of element (`CEED_TOPOLOGY_QUAD`, `CEED_TOPOLOGY_PRISM`, etc.), dimension of which is used in some array sizes below 1157 @param[in] num_comp Number of components (usually 1 for vectors in H(div) bases) 1158 @param[in] num_nodes Total number of nodes (DoFs per element) 1159 @param[in] num_qpts Total number of quadrature points 1160 @param[in] interp Row-major (`dim * num_qpts * num_nodes`) matrix expressing the values of basis functions at quadrature points 1161 @param[in] div Row-major (`num_qpts * num_nodes`) matrix expressing divergence of basis functions at quadrature points 1162 @param[in] q_ref Array of length `num_qpts` * dim holding the locations of quadrature points on the reference element 1163 @param[in] q_weight Array of length `num_qpts` holding the quadrature weights on the reference element 1164 @param[out] basis Address of the variable where the newly created `CeedBasis` will be stored 1165 1166 @return An error code: 0 - success, otherwise - failure 1167 1168 @ref User 1169 **/ 1170 int CeedBasisCreateHdiv(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, 1171 const CeedScalar *div, const CeedScalar *q_ref, const CeedScalar *q_weight, CeedBasis *basis) { 1172 CeedInt Q = num_qpts, P = num_nodes, dim = 0; 1173 1174 if (!ceed->BasisCreateHdiv) { 1175 Ceed delegate; 1176 1177 CeedCall(CeedGetObjectDelegate(ceed, &delegate, "Basis")); 1178 CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement BasisCreateHdiv"); 1179 CeedCall(CeedBasisCreateHdiv(delegate, topo, num_comp, num_nodes, num_qpts, interp, div, q_ref, q_weight, basis)); 1180 return CEED_ERROR_SUCCESS; 1181 } 1182 1183 CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 component"); 1184 CeedCheck(num_nodes > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 node"); 1185 CeedCheck(num_qpts > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 quadrature point"); 1186 1187 CeedCall(CeedBasisGetTopologyDimension(topo, &dim)); 1188 1189 CeedCall(CeedCalloc(1, basis)); 1190 CeedCall(CeedReferenceCopy(ceed, &(*basis)->ceed)); 1191 (*basis)->ref_count = 1; 1192 (*basis)->is_tensor_basis = false; 1193 (*basis)->dim = dim; 1194 (*basis)->topo = topo; 1195 (*basis)->num_comp = num_comp; 1196 (*basis)->P = P; 1197 (*basis)->Q = Q; 1198 (*basis)->fe_space = CEED_FE_SPACE_HDIV; 1199 CeedCall(CeedMalloc(Q * dim, &(*basis)->q_ref_1d)); 1200 CeedCall(CeedMalloc(Q, &(*basis)->q_weight_1d)); 1201 if (q_ref) memcpy((*basis)->q_ref_1d, q_ref, Q * dim * sizeof(q_ref[0])); 1202 if (q_weight) memcpy((*basis)->q_weight_1d, q_weight, Q * sizeof(q_weight[0])); 1203 CeedCall(CeedMalloc(dim * Q * P, &(*basis)->interp)); 1204 CeedCall(CeedMalloc(Q * P, &(*basis)->div)); 1205 if (interp) memcpy((*basis)->interp, interp, dim * Q * P * sizeof(interp[0])); 1206 if (div) memcpy((*basis)->div, div, Q * P * sizeof(div[0])); 1207 CeedCall(ceed->BasisCreateHdiv(topo, dim, P, Q, interp, div, q_ref, q_weight, *basis)); 1208 return CEED_ERROR_SUCCESS; 1209 } 1210 1211 /** 1212 @brief Create a non tensor-product basis for \f$H(\mathrm{curl})\f$ discretizations 1213 1214 @param[in] ceed `Ceed` object used to create the `CeedBasis` 1215 @param[in] topo Topology of element (`CEED_TOPOLOGY_QUAD`, `CEED_TOPOLOGY_PRISM`, etc.), dimension of which is used in some array sizes below 1216 @param[in] num_comp Number of components (usually 1 for vectors in \f$H(\mathrm{curl})\f$ bases) 1217 @param[in] num_nodes Total number of nodes (DoFs per element) 1218 @param[in] num_qpts Total number of quadrature points 1219 @param[in] interp Row-major (`dim * num_qpts * num_nodes`) matrix expressing the values of basis functions at quadrature points 1220 @param[in] curl Row-major (`curl_comp * num_qpts * num_nodes`, `curl_comp = 1` if `dim < 3` otherwise `curl_comp = dim`) matrix expressing curl of basis functions at quadrature points 1221 @param[in] q_ref Array of length `num_qpts * dim` holding the locations of quadrature points on the reference element 1222 @param[in] q_weight Array of length `num_qpts` holding the quadrature weights on the reference element 1223 @param[out] basis Address of the variable where the newly created `CeedBasis` will be stored 1224 1225 @return An error code: 0 - success, otherwise - failure 1226 1227 @ref User 1228 **/ 1229 int CeedBasisCreateHcurl(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, 1230 const CeedScalar *curl, const CeedScalar *q_ref, const CeedScalar *q_weight, CeedBasis *basis) { 1231 CeedInt Q = num_qpts, P = num_nodes, dim = 0, curl_comp = 0; 1232 1233 if (!ceed->BasisCreateHcurl) { 1234 Ceed delegate; 1235 1236 CeedCall(CeedGetObjectDelegate(ceed, &delegate, "Basis")); 1237 CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement BasisCreateHcurl"); 1238 CeedCall(CeedBasisCreateHcurl(delegate, topo, num_comp, num_nodes, num_qpts, interp, curl, q_ref, q_weight, basis)); 1239 return CEED_ERROR_SUCCESS; 1240 } 1241 1242 CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 component"); 1243 CeedCheck(num_nodes > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 node"); 1244 CeedCheck(num_qpts > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 quadrature point"); 1245 1246 CeedCall(CeedBasisGetTopologyDimension(topo, &dim)); 1247 curl_comp = (dim < 3) ? 1 : dim; 1248 1249 CeedCall(CeedCalloc(1, basis)); 1250 CeedCall(CeedReferenceCopy(ceed, &(*basis)->ceed)); 1251 (*basis)->ref_count = 1; 1252 (*basis)->is_tensor_basis = false; 1253 (*basis)->dim = dim; 1254 (*basis)->topo = topo; 1255 (*basis)->num_comp = num_comp; 1256 (*basis)->P = P; 1257 (*basis)->Q = Q; 1258 (*basis)->fe_space = CEED_FE_SPACE_HCURL; 1259 CeedCall(CeedMalloc(Q * dim, &(*basis)->q_ref_1d)); 1260 CeedCall(CeedMalloc(Q, &(*basis)->q_weight_1d)); 1261 if (q_ref) memcpy((*basis)->q_ref_1d, q_ref, Q * dim * sizeof(q_ref[0])); 1262 if (q_weight) memcpy((*basis)->q_weight_1d, q_weight, Q * sizeof(q_weight[0])); 1263 CeedCall(CeedMalloc(dim * Q * P, &(*basis)->interp)); 1264 CeedCall(CeedMalloc(curl_comp * Q * P, &(*basis)->curl)); 1265 if (interp) memcpy((*basis)->interp, interp, dim * Q * P * sizeof(interp[0])); 1266 if (curl) memcpy((*basis)->curl, curl, curl_comp * Q * P * sizeof(curl[0])); 1267 CeedCall(ceed->BasisCreateHcurl(topo, dim, P, Q, interp, curl, q_ref, q_weight, *basis)); 1268 return CEED_ERROR_SUCCESS; 1269 } 1270 1271 /** 1272 @brief Create a `CeedBasis` for projection from the nodes of `basis_from` to the nodes of `basis_to`. 1273 1274 Only @ref CEED_EVAL_INTERP will be valid for the new basis, `basis_project`. 1275 For \f$H^1\f$ spaces, @ref CEED_EVAL_GRAD will also be valid. 1276 The interpolation is given by `interp_project = interp_to^+ * interp_from`, where the pseudoinverse `interp_to^+` is given by QR factorization. 1277 The gradient (for the \f$H^1\f$ case) is given by `grad_project = interp_to^+ * grad_from`. 1278 1279 Note: `basis_from` and `basis_to` must have compatible quadrature spaces. 1280 1281 Note: `basis_project` will have the same number of components as `basis_from`, regardless of the number of components that `basis_to` has. 1282 If `basis_from` has 3 components and `basis_to` has 5 components, then `basis_project` will have 3 components. 1283 1284 @param[in] basis_from `CeedBasis` to prolong from 1285 @param[in] basis_to `CeedBasis` to prolong to 1286 @param[out] basis_project Address of the variable where the newly created `CeedBasis` will be stored 1287 1288 @return An error code: 0 - success, otherwise - failure 1289 1290 @ref User 1291 **/ 1292 int CeedBasisCreateProjection(CeedBasis basis_from, CeedBasis basis_to, CeedBasis *basis_project) { 1293 Ceed ceed; 1294 bool is_tensor; 1295 CeedInt dim, num_comp; 1296 CeedScalar *q_ref, *q_weight, *interp_project, *grad_project; 1297 1298 CeedCall(CeedBasisGetCeed(basis_to, &ceed)); 1299 1300 // Create projection matrix 1301 CeedCall(CeedBasisCreateProjectionMatrices(basis_from, basis_to, &interp_project, &grad_project)); 1302 1303 // Build basis 1304 CeedCall(CeedBasisIsTensor(basis_to, &is_tensor)); 1305 CeedCall(CeedBasisGetDimension(basis_to, &dim)); 1306 CeedCall(CeedBasisGetNumComponents(basis_from, &num_comp)); 1307 if (is_tensor) { 1308 CeedInt P_1d_to, P_1d_from; 1309 1310 CeedCall(CeedBasisGetNumNodes1D(basis_from, &P_1d_from)); 1311 CeedCall(CeedBasisGetNumNodes1D(basis_to, &P_1d_to)); 1312 CeedCall(CeedCalloc(P_1d_to, &q_ref)); 1313 CeedCall(CeedCalloc(P_1d_to, &q_weight)); 1314 CeedCall(CeedBasisCreateTensorH1(ceed, dim, num_comp, P_1d_from, P_1d_to, interp_project, grad_project, q_ref, q_weight, basis_project)); 1315 } else { 1316 // Even if basis_to and basis_from are not H1, the resulting basis is H1 for interpolation to work 1317 CeedInt num_nodes_to, num_nodes_from; 1318 CeedElemTopology topo; 1319 1320 CeedCall(CeedBasisGetTopology(basis_to, &topo)); 1321 CeedCall(CeedBasisGetNumNodes(basis_from, &num_nodes_from)); 1322 CeedCall(CeedBasisGetNumNodes(basis_to, &num_nodes_to)); 1323 CeedCall(CeedCalloc(num_nodes_to * dim, &q_ref)); 1324 CeedCall(CeedCalloc(num_nodes_to, &q_weight)); 1325 CeedCall(CeedBasisCreateH1(ceed, topo, num_comp, num_nodes_from, num_nodes_to, interp_project, grad_project, q_ref, q_weight, basis_project)); 1326 } 1327 1328 // Cleanup 1329 CeedCall(CeedFree(&interp_project)); 1330 CeedCall(CeedFree(&grad_project)); 1331 CeedCall(CeedFree(&q_ref)); 1332 CeedCall(CeedFree(&q_weight)); 1333 return CEED_ERROR_SUCCESS; 1334 } 1335 1336 /** 1337 @brief Copy the pointer to a `CeedBasis`. 1338 1339 Note: If the value of `*basis_copy` passed into this function is non-`NULL`, then it is assumed that `*basis_copy` is a pointer to a `CeedBasis`. 1340 This `CeedBasis` will be destroyed if `*basis_copy` is the only reference to this `CeedBasis`. 1341 1342 @param[in] basis `CeedBasis` to copy reference to 1343 @param[in,out] basis_copy Variable to store copied reference 1344 1345 @return An error code: 0 - success, otherwise - failure 1346 1347 @ref User 1348 **/ 1349 int CeedBasisReferenceCopy(CeedBasis basis, CeedBasis *basis_copy) { 1350 if (basis != CEED_BASIS_NONE) CeedCall(CeedBasisReference(basis)); 1351 CeedCall(CeedBasisDestroy(basis_copy)); 1352 *basis_copy = basis; 1353 return CEED_ERROR_SUCCESS; 1354 } 1355 1356 /** 1357 @brief View a `CeedBasis` 1358 1359 @param[in] basis `CeedBasis` to view 1360 @param[in] stream Stream to view to, e.g., `stdout` 1361 1362 @return An error code: 0 - success, otherwise - failure 1363 1364 @ref User 1365 **/ 1366 int CeedBasisView(CeedBasis basis, FILE *stream) { 1367 bool is_tensor_basis; 1368 CeedElemTopology topo; 1369 CeedFESpace fe_space; 1370 1371 // Basis data 1372 CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis)); 1373 CeedCall(CeedBasisGetTopology(basis, &topo)); 1374 CeedCall(CeedBasisGetFESpace(basis, &fe_space)); 1375 1376 // Print FE space and element topology of the basis 1377 fprintf(stream, "CeedBasis in a %s on a %s element\n", CeedFESpaces[fe_space], CeedElemTopologies[topo]); 1378 if (is_tensor_basis) { 1379 fprintf(stream, " P: %" CeedInt_FMT "\n Q: %" CeedInt_FMT "\n", basis->P_1d, basis->Q_1d); 1380 } else { 1381 fprintf(stream, " P: %" CeedInt_FMT "\n Q: %" CeedInt_FMT "\n", basis->P, basis->Q); 1382 } 1383 fprintf(stream, " dimension: %" CeedInt_FMT "\n field components: %" CeedInt_FMT "\n", basis->dim, basis->num_comp); 1384 // Print quadrature data, interpolation/gradient/divergence/curl of the basis 1385 if (is_tensor_basis) { // tensor basis 1386 CeedInt P_1d, Q_1d; 1387 const CeedScalar *q_ref_1d, *q_weight_1d, *interp_1d, *grad_1d; 1388 1389 CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d)); 1390 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d)); 1391 CeedCall(CeedBasisGetQRef(basis, &q_ref_1d)); 1392 CeedCall(CeedBasisGetQWeights(basis, &q_weight_1d)); 1393 CeedCall(CeedBasisGetInterp1D(basis, &interp_1d)); 1394 CeedCall(CeedBasisGetGrad1D(basis, &grad_1d)); 1395 1396 CeedCall(CeedScalarView("qref1d", "\t% 12.8f", 1, Q_1d, q_ref_1d, stream)); 1397 CeedCall(CeedScalarView("qweight1d", "\t% 12.8f", 1, Q_1d, q_weight_1d, stream)); 1398 CeedCall(CeedScalarView("interp1d", "\t% 12.8f", Q_1d, P_1d, interp_1d, stream)); 1399 CeedCall(CeedScalarView("grad1d", "\t% 12.8f", Q_1d, P_1d, grad_1d, stream)); 1400 } else { // non-tensor basis 1401 CeedInt P, Q, dim, q_comp; 1402 const CeedScalar *q_ref, *q_weight, *interp, *grad, *div, *curl; 1403 1404 CeedCall(CeedBasisGetNumNodes(basis, &P)); 1405 CeedCall(CeedBasisGetNumQuadraturePoints(basis, &Q)); 1406 CeedCall(CeedBasisGetDimension(basis, &dim)); 1407 CeedCall(CeedBasisGetQRef(basis, &q_ref)); 1408 CeedCall(CeedBasisGetQWeights(basis, &q_weight)); 1409 CeedCall(CeedBasisGetInterp(basis, &interp)); 1410 CeedCall(CeedBasisGetGrad(basis, &grad)); 1411 CeedCall(CeedBasisGetDiv(basis, &div)); 1412 CeedCall(CeedBasisGetCurl(basis, &curl)); 1413 1414 CeedCall(CeedScalarView("qref", "\t% 12.8f", 1, Q * dim, q_ref, stream)); 1415 CeedCall(CeedScalarView("qweight", "\t% 12.8f", 1, Q, q_weight, stream)); 1416 CeedCall(CeedBasisGetNumQuadratureComponents(basis, CEED_EVAL_INTERP, &q_comp)); 1417 CeedCall(CeedScalarView("interp", "\t% 12.8f", q_comp * Q, P, interp, stream)); 1418 if (grad) { 1419 CeedCall(CeedBasisGetNumQuadratureComponents(basis, CEED_EVAL_GRAD, &q_comp)); 1420 CeedCall(CeedScalarView("grad", "\t% 12.8f", q_comp * Q, P, grad, stream)); 1421 } 1422 if (div) { 1423 CeedCall(CeedBasisGetNumQuadratureComponents(basis, CEED_EVAL_DIV, &q_comp)); 1424 CeedCall(CeedScalarView("div", "\t% 12.8f", q_comp * Q, P, div, stream)); 1425 } 1426 if (curl) { 1427 CeedCall(CeedBasisGetNumQuadratureComponents(basis, CEED_EVAL_CURL, &q_comp)); 1428 CeedCall(CeedScalarView("curl", "\t% 12.8f", q_comp * Q, P, curl, stream)); 1429 } 1430 } 1431 return CEED_ERROR_SUCCESS; 1432 } 1433 1434 /** 1435 @brief Apply basis evaluation from nodes to quadrature points or vice versa 1436 1437 @param[in] basis `CeedBasis` to evaluate 1438 @param[in] num_elem The number of elements to apply the basis evaluation to; 1439 the backend will specify the ordering in @ref CeedElemRestrictionCreate() 1440 @param[in] t_mode @ref CEED_NOTRANSPOSE to evaluate from nodes to quadrature points; 1441 @ref CEED_TRANSPOSE to apply the transpose, mapping from quadrature points to nodes 1442 @param[in] eval_mode @ref CEED_EVAL_NONE to use values directly, 1443 @ref CEED_EVAL_INTERP to use interpolated values, 1444 @ref CEED_EVAL_GRAD to use gradients, 1445 @ref CEED_EVAL_DIV to use divergence, 1446 @ref CEED_EVAL_CURL to use curl, 1447 @ref CEED_EVAL_WEIGHT to use quadrature weights 1448 @param[in] u Input `CeedVector` 1449 @param[out] v Output `CeedVector` 1450 1451 @return An error code: 0 - success, otherwise - failure 1452 1453 @ref User 1454 **/ 1455 int CeedBasisApply(CeedBasis basis, CeedInt num_elem, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedVector u, CeedVector v) { 1456 CeedInt dim, num_comp, q_comp, num_nodes, num_qpts; 1457 CeedSize u_length = 0, v_length; 1458 Ceed ceed; 1459 1460 CeedCall(CeedBasisGetCeed(basis, &ceed)); 1461 CeedCall(CeedBasisGetDimension(basis, &dim)); 1462 CeedCall(CeedBasisGetNumComponents(basis, &num_comp)); 1463 CeedCall(CeedBasisGetNumQuadratureComponents(basis, eval_mode, &q_comp)); 1464 CeedCall(CeedBasisGetNumNodes(basis, &num_nodes)); 1465 CeedCall(CeedBasisGetNumQuadraturePoints(basis, &num_qpts)); 1466 CeedCall(CeedVectorGetLength(v, &v_length)); 1467 if (u) CeedCall(CeedVectorGetLength(u, &u_length)); 1468 1469 CeedCheck(basis->Apply, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support CeedBasisApply"); 1470 1471 // Check compatibility of topological and geometrical dimensions 1472 CeedCheck((t_mode == CEED_TRANSPOSE && v_length % num_nodes == 0 && u_length % num_qpts == 0) || 1473 (t_mode == CEED_NOTRANSPOSE && u_length % num_nodes == 0 && v_length % num_qpts == 0), 1474 ceed, CEED_ERROR_DIMENSION, "Length of input/output vectors incompatible with basis dimensions"); 1475 1476 // Check vector lengths to prevent out of bounds issues 1477 bool has_good_dims = true; 1478 switch (eval_mode) { 1479 case CEED_EVAL_NONE: 1480 case CEED_EVAL_INTERP: 1481 case CEED_EVAL_GRAD: 1482 case CEED_EVAL_DIV: 1483 case CEED_EVAL_CURL: 1484 has_good_dims = 1485 ((t_mode == CEED_TRANSPOSE && u_length >= num_elem * num_comp * num_qpts * q_comp && v_length >= num_elem * num_comp * num_nodes) || 1486 (t_mode == CEED_NOTRANSPOSE && v_length >= num_elem * num_qpts * num_comp * q_comp && u_length >= num_elem * num_comp * num_nodes)); 1487 break; 1488 case CEED_EVAL_WEIGHT: 1489 has_good_dims = v_length >= num_elem * num_qpts; 1490 break; 1491 } 1492 CeedCheck(has_good_dims, ceed, CEED_ERROR_DIMENSION, "Input/output vectors too short for basis and evaluation mode"); 1493 1494 CeedCall(basis->Apply(basis, num_elem, t_mode, eval_mode, u, v)); 1495 return CEED_ERROR_SUCCESS; 1496 } 1497 1498 /** 1499 @brief Apply basis evaluation from nodes to arbitrary points 1500 1501 @param[in] basis `CeedBasis` to evaluate 1502 @param[in] num_points The number of points to apply the basis evaluation to 1503 @param[in] t_mode @ref CEED_NOTRANSPOSE to evaluate from nodes to points; 1504 @ref CEED_TRANSPOSE to apply the transpose, mapping from points to nodes 1505 @param[in] eval_mode @ref CEED_EVAL_INTERP to use interpolated values, 1506 @ref CEED_EVAL_GRAD to use gradients, 1507 @ref CEED_EVAL_WEIGHT to use quadrature weights 1508 @param[in] x_ref `CeedVector` holding reference coordinates of each point 1509 @param[in] u Input `CeedVector`, of length `num_nodes * num_comp` for @ref CEED_NOTRANSPOSE 1510 @param[out] v Output `CeedVector`, of length `num_points * num_q_comp` for @ref CEED_NOTRANSPOSE with @ref CEED_EVAL_INTERP 1511 1512 @return An error code: 0 - success, otherwise - failure 1513 1514 @ref User 1515 **/ 1516 int CeedBasisApplyAtPoints(CeedBasis basis, CeedInt num_points, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedVector x_ref, CeedVector u, 1517 CeedVector v) { 1518 bool is_tensor_basis; 1519 CeedInt dim, num_comp, num_q_comp, num_nodes, P_1d = 1, Q_1d = 1; 1520 CeedSize x_length = 0, u_length = 0, v_length; 1521 Ceed ceed; 1522 1523 CeedCall(CeedBasisGetCeed(basis, &ceed)); 1524 CeedCall(CeedBasisGetDimension(basis, &dim)); 1525 CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d)); 1526 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d)); 1527 CeedCall(CeedBasisGetNumComponents(basis, &num_comp)); 1528 CeedCall(CeedBasisGetNumQuadratureComponents(basis, eval_mode, &num_q_comp)); 1529 CeedCall(CeedBasisGetNumNodes(basis, &num_nodes)); 1530 CeedCall(CeedVectorGetLength(v, &v_length)); 1531 if (x_ref != CEED_VECTOR_NONE) CeedCall(CeedVectorGetLength(x_ref, &x_length)); 1532 if (u != CEED_VECTOR_NONE) CeedCall(CeedVectorGetLength(u, &u_length)); 1533 1534 // Check compatibility of topological and geometrical dimensions 1535 CeedCheck((t_mode == CEED_TRANSPOSE && v_length % num_nodes == 0) || (t_mode == CEED_NOTRANSPOSE && u_length % num_nodes == 0) || 1536 (eval_mode == CEED_EVAL_WEIGHT), 1537 ceed, CEED_ERROR_DIMENSION, "Length of input/output vectors incompatible with basis dimensions and number of points"); 1538 1539 // Check compatibility coordinates vector 1540 CeedCheck((x_length >= num_points * dim) || (eval_mode == CEED_EVAL_WEIGHT), ceed, CEED_ERROR_DIMENSION, 1541 "Length of reference coordinate vector incompatible with basis dimension and number of points"); 1542 1543 // Check CEED_EVAL_WEIGHT only on CEED_NOTRANSPOSE 1544 CeedCheck(eval_mode != CEED_EVAL_WEIGHT || t_mode == CEED_NOTRANSPOSE, ceed, CEED_ERROR_UNSUPPORTED, 1545 "CEED_EVAL_WEIGHT only supported with CEED_NOTRANSPOSE"); 1546 1547 // Check vector lengths to prevent out of bounds issues 1548 bool has_good_dims = true; 1549 switch (eval_mode) { 1550 case CEED_EVAL_INTERP: 1551 has_good_dims = ((t_mode == CEED_TRANSPOSE && (u_length >= num_points * num_q_comp || v_length >= num_nodes * num_comp)) || 1552 (t_mode == CEED_NOTRANSPOSE && (v_length >= num_points * num_q_comp || u_length >= num_nodes * num_comp))); 1553 break; 1554 case CEED_EVAL_GRAD: 1555 has_good_dims = ((t_mode == CEED_TRANSPOSE && (u_length >= num_points * num_q_comp * dim || v_length >= num_nodes * num_comp)) || 1556 (t_mode == CEED_NOTRANSPOSE && (v_length >= num_points * num_q_comp * dim || u_length >= num_nodes * num_comp))); 1557 break; 1558 case CEED_EVAL_WEIGHT: 1559 has_good_dims = t_mode == CEED_NOTRANSPOSE && (v_length >= num_points); 1560 break; 1561 // LCOV_EXCL_START 1562 case CEED_EVAL_NONE: 1563 case CEED_EVAL_DIV: 1564 case CEED_EVAL_CURL: 1565 return CeedError(ceed, CEED_ERROR_UNSUPPORTED, "Evaluation at arbitrary points not supported for %s", CeedEvalModes[eval_mode]); 1566 // LCOV_EXCL_STOP 1567 } 1568 CeedCheck(has_good_dims, ceed, CEED_ERROR_DIMENSION, "Input/output vectors too short for basis and evaluation mode"); 1569 1570 // Backend method 1571 if (basis->ApplyAtPoints) { 1572 CeedCall(basis->ApplyAtPoints(basis, num_points, t_mode, eval_mode, x_ref, u, v)); 1573 return CEED_ERROR_SUCCESS; 1574 } 1575 1576 // Default implementation 1577 CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis)); 1578 CeedCheck(is_tensor_basis, ceed, CEED_ERROR_UNSUPPORTED, "Evaluation at arbitrary points only supported for tensor product bases"); 1579 if (eval_mode == CEED_EVAL_WEIGHT) { 1580 CeedCall(CeedVectorSetValue(v, 1.0)); 1581 return CEED_ERROR_SUCCESS; 1582 } 1583 if (!basis->basis_chebyshev) { 1584 // Build matrix mapping from quadrature point values to Chebyshev coefficients 1585 CeedScalar *C, *chebyshev_coeffs_1d_inv; 1586 const CeedScalar *q_ref_1d; 1587 1588 // Build coefficient matrix 1589 // -- Note: Clang-tidy needs this check because it does not understand the is_tensor_basis check above 1590 CeedCheck(P_1d > 0 && Q_1d > 0, ceed, CEED_ERROR_INCOMPATIBLE, "CeedBasis dimensions are malformed"); 1591 CeedCall(CeedCalloc(Q_1d * Q_1d, &C)); 1592 CeedCall(CeedBasisGetQRef(basis, &q_ref_1d)); 1593 for (CeedInt i = 0; i < Q_1d; i++) CeedCall(CeedChebyshevPolynomialsAtPoint(q_ref_1d[i], Q_1d, &C[i * Q_1d])); 1594 1595 // Compute C^+, pseudoinverse of coefficient matrix 1596 CeedCall(CeedCalloc(Q_1d * Q_1d, &chebyshev_coeffs_1d_inv)); 1597 CeedCall(CeedMatrixPseudoinverse(ceed, C, Q_1d, Q_1d, chebyshev_coeffs_1d_inv)); 1598 1599 // Build basis mapping from nodes to Chebyshev coefficients 1600 CeedScalar *chebyshev_interp_1d, *chebyshev_grad_1d, *chebyshev_q_weight_1d; 1601 const CeedScalar *interp_1d; 1602 1603 CeedCall(CeedCalloc(P_1d * Q_1d, &chebyshev_interp_1d)); 1604 CeedCall(CeedCalloc(P_1d * Q_1d, &chebyshev_grad_1d)); 1605 CeedCall(CeedCalloc(Q_1d, &chebyshev_q_weight_1d)); 1606 CeedCall(CeedBasisGetInterp1D(basis, &interp_1d)); 1607 CeedCall(CeedMatrixMatrixMultiply(ceed, chebyshev_coeffs_1d_inv, interp_1d, chebyshev_interp_1d, Q_1d, P_1d, Q_1d)); 1608 1609 CeedCall(CeedVectorCreate(ceed, num_comp * CeedIntPow(Q_1d, dim), &basis->vec_chebyshev)); 1610 CeedCall(CeedBasisCreateTensorH1(ceed, dim, num_comp, P_1d, Q_1d, chebyshev_interp_1d, chebyshev_grad_1d, q_ref_1d, chebyshev_q_weight_1d, 1611 &basis->basis_chebyshev)); 1612 1613 // Cleanup 1614 CeedCall(CeedFree(&C)); 1615 CeedCall(CeedFree(&chebyshev_coeffs_1d_inv)); 1616 CeedCall(CeedFree(&chebyshev_interp_1d)); 1617 CeedCall(CeedFree(&chebyshev_grad_1d)); 1618 CeedCall(CeedFree(&chebyshev_q_weight_1d)); 1619 } 1620 1621 // Create TensorContract object if needed, such as a basis from the GPU backends 1622 if (!basis->contract) { 1623 Ceed ceed_ref; 1624 CeedBasis basis_ref = NULL; 1625 1626 CeedCall(CeedInit("/cpu/self", &ceed_ref)); 1627 // Only need matching tensor contraction dimensions, any type of basis will work 1628 CeedCall(CeedBasisCreateTensorH1Lagrange(ceed_ref, dim, num_comp, P_1d, Q_1d, CEED_GAUSS, &basis_ref)); 1629 // Note - clang-tidy doesn't know basis_ref->contract must be valid here 1630 CeedCheck(basis_ref && basis_ref->contract, ceed, CEED_ERROR_UNSUPPORTED, "Reference CPU ceed failed to create a tensor contraction object"); 1631 CeedCall(CeedTensorContractReferenceCopy(basis_ref->contract, &basis->contract)); 1632 CeedCall(CeedBasisDestroy(&basis_ref)); 1633 CeedCall(CeedDestroy(&ceed_ref)); 1634 } 1635 1636 // Basis evaluation 1637 switch (t_mode) { 1638 case CEED_NOTRANSPOSE: { 1639 // Nodes to arbitrary points 1640 CeedScalar *v_array; 1641 const CeedScalar *chebyshev_coeffs, *x_array_read; 1642 1643 // -- Interpolate to Chebyshev coefficients 1644 CeedCall(CeedBasisApply(basis->basis_chebyshev, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, u, basis->vec_chebyshev)); 1645 1646 // -- Evaluate Chebyshev polynomials at arbitrary points 1647 CeedCall(CeedVectorGetArrayRead(basis->vec_chebyshev, CEED_MEM_HOST, &chebyshev_coeffs)); 1648 CeedCall(CeedVectorGetArrayRead(x_ref, CEED_MEM_HOST, &x_array_read)); 1649 CeedCall(CeedVectorGetArrayWrite(v, CEED_MEM_HOST, &v_array)); 1650 switch (eval_mode) { 1651 case CEED_EVAL_INTERP: { 1652 CeedScalar tmp[2][num_comp * CeedIntPow(Q_1d, dim)], chebyshev_x[Q_1d]; 1653 1654 // ---- Values at point 1655 for (CeedInt p = 0; p < num_points; p++) { 1656 CeedInt pre = num_comp * CeedIntPow(Q_1d, dim - 1), post = 1; 1657 1658 for (CeedInt d = 0; d < dim; d++) { 1659 // ------ Tensor contract with current Chebyshev polynomial values 1660 CeedCall(CeedChebyshevPolynomialsAtPoint(x_array_read[d * num_points + p], Q_1d, chebyshev_x)); 1661 CeedCall(CeedTensorContractApply(basis->contract, pre, Q_1d, post, 1, chebyshev_x, t_mode, false, 1662 d == 0 ? chebyshev_coeffs : tmp[d % 2], tmp[(d + 1) % 2])); 1663 pre /= Q_1d; 1664 post *= 1; 1665 } 1666 for (CeedInt c = 0; c < num_comp; c++) v_array[c * num_points + p] = tmp[dim % 2][c]; 1667 } 1668 break; 1669 } 1670 case CEED_EVAL_GRAD: { 1671 CeedScalar tmp[2][num_comp * CeedIntPow(Q_1d, dim)], chebyshev_x[Q_1d]; 1672 1673 // ---- Values at point 1674 for (CeedInt p = 0; p < num_points; p++) { 1675 // Dim**2 contractions, apply grad when pass == dim 1676 for (CeedInt pass = 0; pass < dim; pass++) { 1677 CeedInt pre = num_comp * CeedIntPow(Q_1d, dim - 1), post = 1; 1678 1679 for (CeedInt d = 0; d < dim; d++) { 1680 // ------ Tensor contract with current Chebyshev polynomial values 1681 if (pass == d) CeedCall(CeedChebyshevDerivativeAtPoint(x_array_read[d * num_points + p], Q_1d, chebyshev_x)); 1682 else CeedCall(CeedChebyshevPolynomialsAtPoint(x_array_read[d * num_points + p], Q_1d, chebyshev_x)); 1683 CeedCall(CeedTensorContractApply(basis->contract, pre, Q_1d, post, 1, chebyshev_x, t_mode, false, 1684 d == 0 ? chebyshev_coeffs : tmp[d % 2], tmp[(d + 1) % 2])); 1685 pre /= Q_1d; 1686 post *= 1; 1687 } 1688 for (CeedInt c = 0; c < num_comp; c++) v_array[(pass * num_comp + c) * num_points + p] = tmp[dim % 2][c]; 1689 } 1690 } 1691 break; 1692 } 1693 default: 1694 // Nothing to do, excluded above 1695 break; 1696 } 1697 CeedCall(CeedVectorRestoreArrayRead(basis->vec_chebyshev, &chebyshev_coeffs)); 1698 CeedCall(CeedVectorRestoreArrayRead(x_ref, &x_array_read)); 1699 CeedCall(CeedVectorRestoreArray(v, &v_array)); 1700 break; 1701 } 1702 case CEED_TRANSPOSE: { 1703 // Note: No switch on e_mode here because only CEED_EVAL_INTERP is supported at this time 1704 // Arbitrary points to nodes 1705 CeedScalar *chebyshev_coeffs; 1706 const CeedScalar *u_array, *x_array_read; 1707 1708 // -- Transpose of evaluation of Chebyshev polynomials at arbitrary points 1709 CeedCall(CeedVectorGetArrayWrite(basis->vec_chebyshev, CEED_MEM_HOST, &chebyshev_coeffs)); 1710 CeedCall(CeedVectorGetArrayRead(x_ref, CEED_MEM_HOST, &x_array_read)); 1711 CeedCall(CeedVectorGetArrayRead(u, CEED_MEM_HOST, &u_array)); 1712 1713 switch (eval_mode) { 1714 case CEED_EVAL_INTERP: { 1715 CeedScalar tmp[2][num_comp * CeedIntPow(Q_1d, dim)], chebyshev_x[Q_1d]; 1716 1717 // ---- Values at point 1718 for (CeedInt p = 0; p < num_points; p++) { 1719 CeedInt pre = num_comp * 1, post = 1; 1720 1721 for (CeedInt c = 0; c < num_comp; c++) tmp[0][c] = u_array[c * num_points + p]; 1722 for (CeedInt d = 0; d < dim; d++) { 1723 // ------ Tensor contract with current Chebyshev polynomial values 1724 CeedCall(CeedChebyshevPolynomialsAtPoint(x_array_read[d * num_points + p], Q_1d, chebyshev_x)); 1725 CeedCall(CeedTensorContractApply(basis->contract, pre, 1, post, Q_1d, chebyshev_x, t_mode, p > 0 && d == (dim - 1), tmp[d % 2], 1726 d == (dim - 1) ? chebyshev_coeffs : tmp[(d + 1) % 2])); 1727 pre /= 1; 1728 post *= Q_1d; 1729 } 1730 } 1731 break; 1732 } 1733 case CEED_EVAL_GRAD: { 1734 CeedScalar tmp[2][num_comp * CeedIntPow(Q_1d, dim)], chebyshev_x[Q_1d]; 1735 1736 // ---- Values at point 1737 for (CeedInt p = 0; p < num_points; p++) { 1738 // Dim**2 contractions, apply grad when pass == dim 1739 for (CeedInt pass = 0; pass < dim; pass++) { 1740 CeedInt pre = num_comp * 1, post = 1; 1741 1742 for (CeedInt c = 0; c < num_comp; c++) tmp[0][c] = u_array[(pass * num_comp + c) * num_points + p]; 1743 for (CeedInt d = 0; d < dim; d++) { 1744 // ------ Tensor contract with current Chebyshev polynomial values 1745 if (pass == d) CeedCall(CeedChebyshevDerivativeAtPoint(x_array_read[d * num_points + p], Q_1d, chebyshev_x)); 1746 else CeedCall(CeedChebyshevPolynomialsAtPoint(x_array_read[d * num_points + p], Q_1d, chebyshev_x)); 1747 CeedCall(CeedTensorContractApply(basis->contract, pre, 1, post, Q_1d, chebyshev_x, t_mode, 1748 (p > 0 || (p == 0 && pass > 0)) && d == (dim - 1), tmp[d % 2], 1749 d == (dim - 1) ? chebyshev_coeffs : tmp[(d + 1) % 2])); 1750 pre /= 1; 1751 post *= Q_1d; 1752 } 1753 } 1754 } 1755 break; 1756 } 1757 default: 1758 // Nothing to do, excluded above 1759 break; 1760 } 1761 CeedCall(CeedVectorRestoreArray(basis->vec_chebyshev, &chebyshev_coeffs)); 1762 CeedCall(CeedVectorRestoreArrayRead(x_ref, &x_array_read)); 1763 CeedCall(CeedVectorRestoreArrayRead(u, &u_array)); 1764 1765 // -- Interpolate transpose from Chebyshev coefficients 1766 CeedCall(CeedBasisApply(basis->basis_chebyshev, 1, CEED_TRANSPOSE, CEED_EVAL_INTERP, basis->vec_chebyshev, v)); 1767 break; 1768 } 1769 } 1770 return CEED_ERROR_SUCCESS; 1771 } 1772 1773 /** 1774 @brief Get the `Ceed` associated with a `CeedBasis` 1775 1776 @param[in] basis `CeedBasis` 1777 @param[out] ceed Variable to store `Ceed` 1778 1779 @return An error code: 0 - success, otherwise - failure 1780 1781 @ref Advanced 1782 **/ 1783 int CeedBasisGetCeed(CeedBasis basis, Ceed *ceed) { 1784 *ceed = CeedBasisReturnCeed(basis); 1785 return CEED_ERROR_SUCCESS; 1786 } 1787 1788 /** 1789 @brief Return the `Ceed` associated with a `CeedBasis` 1790 1791 @param[in] basis `CeedBasis` 1792 1793 @return `Ceed` associated with the `basis` 1794 1795 @ref Advanced 1796 **/ 1797 Ceed CeedBasisReturnCeed(CeedBasis basis) { return basis->ceed; } 1798 1799 /** 1800 @brief Get dimension for given `CeedBasis` 1801 1802 @param[in] basis `CeedBasis` 1803 @param[out] dim Variable to store dimension of basis 1804 1805 @return An error code: 0 - success, otherwise - failure 1806 1807 @ref Advanced 1808 **/ 1809 int CeedBasisGetDimension(CeedBasis basis, CeedInt *dim) { 1810 *dim = basis->dim; 1811 return CEED_ERROR_SUCCESS; 1812 } 1813 1814 /** 1815 @brief Get topology for given `CeedBasis` 1816 1817 @param[in] basis `CeedBasis` 1818 @param[out] topo Variable to store topology of basis 1819 1820 @return An error code: 0 - success, otherwise - failure 1821 1822 @ref Advanced 1823 **/ 1824 int CeedBasisGetTopology(CeedBasis basis, CeedElemTopology *topo) { 1825 *topo = basis->topo; 1826 return CEED_ERROR_SUCCESS; 1827 } 1828 1829 /** 1830 @brief Get number of components for given `CeedBasis` 1831 1832 @param[in] basis `CeedBasis` 1833 @param[out] num_comp Variable to store number of components 1834 1835 @return An error code: 0 - success, otherwise - failure 1836 1837 @ref Advanced 1838 **/ 1839 int CeedBasisGetNumComponents(CeedBasis basis, CeedInt *num_comp) { 1840 *num_comp = basis->num_comp; 1841 return CEED_ERROR_SUCCESS; 1842 } 1843 1844 /** 1845 @brief Get total number of nodes (in `dim` dimensions) of a `CeedBasis` 1846 1847 @param[in] basis `CeedBasis` 1848 @param[out] P Variable to store number of nodes 1849 1850 @return An error code: 0 - success, otherwise - failure 1851 1852 @ref Utility 1853 **/ 1854 int CeedBasisGetNumNodes(CeedBasis basis, CeedInt *P) { 1855 *P = basis->P; 1856 return CEED_ERROR_SUCCESS; 1857 } 1858 1859 /** 1860 @brief Get total number of nodes (in 1 dimension) of a `CeedBasis` 1861 1862 @param[in] basis `CeedBasis` 1863 @param[out] P_1d Variable to store number of nodes 1864 1865 @return An error code: 0 - success, otherwise - failure 1866 1867 @ref Advanced 1868 **/ 1869 int CeedBasisGetNumNodes1D(CeedBasis basis, CeedInt *P_1d) { 1870 CeedCheck(basis->is_tensor_basis, CeedBasisReturnCeed(basis), CEED_ERROR_MINOR, "Cannot supply P_1d for non-tensor CeedBasis"); 1871 *P_1d = basis->P_1d; 1872 return CEED_ERROR_SUCCESS; 1873 } 1874 1875 /** 1876 @brief Get total number of quadrature points (in `dim` dimensions) of a `CeedBasis` 1877 1878 @param[in] basis `CeedBasis` 1879 @param[out] Q Variable to store number of quadrature points 1880 1881 @return An error code: 0 - success, otherwise - failure 1882 1883 @ref Utility 1884 **/ 1885 int CeedBasisGetNumQuadraturePoints(CeedBasis basis, CeedInt *Q) { 1886 *Q = basis->Q; 1887 return CEED_ERROR_SUCCESS; 1888 } 1889 1890 /** 1891 @brief Get total number of quadrature points (in 1 dimension) of a `CeedBasis` 1892 1893 @param[in] basis `CeedBasis` 1894 @param[out] Q_1d Variable to store number of quadrature points 1895 1896 @return An error code: 0 - success, otherwise - failure 1897 1898 @ref Advanced 1899 **/ 1900 int CeedBasisGetNumQuadraturePoints1D(CeedBasis basis, CeedInt *Q_1d) { 1901 CeedCheck(basis->is_tensor_basis, CeedBasisReturnCeed(basis), CEED_ERROR_MINOR, "Cannot supply Q_1d for non-tensor CeedBasis"); 1902 *Q_1d = basis->Q_1d; 1903 return CEED_ERROR_SUCCESS; 1904 } 1905 1906 /** 1907 @brief Get reference coordinates of quadrature points (in `dim` dimensions) of a `CeedBasis` 1908 1909 @param[in] basis `CeedBasis` 1910 @param[out] q_ref Variable to store reference coordinates of quadrature points 1911 1912 @return An error code: 0 - success, otherwise - failure 1913 1914 @ref Advanced 1915 **/ 1916 int CeedBasisGetQRef(CeedBasis basis, const CeedScalar **q_ref) { 1917 *q_ref = basis->q_ref_1d; 1918 return CEED_ERROR_SUCCESS; 1919 } 1920 1921 /** 1922 @brief Get quadrature weights of quadrature points (in `dim` dimensions) of a `CeedBasis` 1923 1924 @param[in] basis `CeedBasis` 1925 @param[out] q_weight Variable to store quadrature weights 1926 1927 @return An error code: 0 - success, otherwise - failure 1928 1929 @ref Advanced 1930 **/ 1931 int CeedBasisGetQWeights(CeedBasis basis, const CeedScalar **q_weight) { 1932 *q_weight = basis->q_weight_1d; 1933 return CEED_ERROR_SUCCESS; 1934 } 1935 1936 /** 1937 @brief Get interpolation matrix of a `CeedBasis` 1938 1939 @param[in] basis `CeedBasis` 1940 @param[out] interp Variable to store interpolation matrix 1941 1942 @return An error code: 0 - success, otherwise - failure 1943 1944 @ref Advanced 1945 **/ 1946 int CeedBasisGetInterp(CeedBasis basis, const CeedScalar **interp) { 1947 if (!basis->interp && basis->is_tensor_basis) { 1948 // Allocate 1949 CeedCall(CeedMalloc(basis->Q * basis->P, &basis->interp)); 1950 1951 // Initialize 1952 for (CeedInt i = 0; i < basis->Q * basis->P; i++) basis->interp[i] = 1.0; 1953 1954 // Calculate 1955 for (CeedInt d = 0; d < basis->dim; d++) { 1956 for (CeedInt qpt = 0; qpt < basis->Q; qpt++) { 1957 for (CeedInt node = 0; node < basis->P; node++) { 1958 CeedInt p = (node / CeedIntPow(basis->P_1d, d)) % basis->P_1d; 1959 CeedInt q = (qpt / CeedIntPow(basis->Q_1d, d)) % basis->Q_1d; 1960 1961 basis->interp[qpt * (basis->P) + node] *= basis->interp_1d[q * basis->P_1d + p]; 1962 } 1963 } 1964 } 1965 } 1966 *interp = basis->interp; 1967 return CEED_ERROR_SUCCESS; 1968 } 1969 1970 /** 1971 @brief Get 1D interpolation matrix of a tensor product `CeedBasis` 1972 1973 @param[in] basis `CeedBasis` 1974 @param[out] interp_1d Variable to store interpolation matrix 1975 1976 @return An error code: 0 - success, otherwise - failure 1977 1978 @ref Backend 1979 **/ 1980 int CeedBasisGetInterp1D(CeedBasis basis, const CeedScalar **interp_1d) { 1981 bool is_tensor_basis; 1982 1983 CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis)); 1984 CeedCheck(is_tensor_basis, CeedBasisReturnCeed(basis), CEED_ERROR_MINOR, "CeedBasis is not a tensor product CeedBasis"); 1985 *interp_1d = basis->interp_1d; 1986 return CEED_ERROR_SUCCESS; 1987 } 1988 1989 /** 1990 @brief Get gradient matrix of a `CeedBasis` 1991 1992 @param[in] basis `CeedBasis` 1993 @param[out] grad Variable to store gradient matrix 1994 1995 @return An error code: 0 - success, otherwise - failure 1996 1997 @ref Advanced 1998 **/ 1999 int CeedBasisGetGrad(CeedBasis basis, const CeedScalar **grad) { 2000 if (!basis->grad && basis->is_tensor_basis) { 2001 // Allocate 2002 CeedCall(CeedMalloc(basis->dim * basis->Q * basis->P, &basis->grad)); 2003 2004 // Initialize 2005 for (CeedInt i = 0; i < basis->dim * basis->Q * basis->P; i++) basis->grad[i] = 1.0; 2006 2007 // Calculate 2008 for (CeedInt d = 0; d < basis->dim; d++) { 2009 for (CeedInt i = 0; i < basis->dim; i++) { 2010 for (CeedInt qpt = 0; qpt < basis->Q; qpt++) { 2011 for (CeedInt node = 0; node < basis->P; node++) { 2012 CeedInt p = (node / CeedIntPow(basis->P_1d, d)) % basis->P_1d; 2013 CeedInt q = (qpt / CeedIntPow(basis->Q_1d, d)) % basis->Q_1d; 2014 2015 if (i == d) basis->grad[(i * basis->Q + qpt) * (basis->P) + node] *= basis->grad_1d[q * basis->P_1d + p]; 2016 else basis->grad[(i * basis->Q + qpt) * (basis->P) + node] *= basis->interp_1d[q * basis->P_1d + p]; 2017 } 2018 } 2019 } 2020 } 2021 } 2022 *grad = basis->grad; 2023 return CEED_ERROR_SUCCESS; 2024 } 2025 2026 /** 2027 @brief Get 1D gradient matrix of a tensor product `CeedBasis` 2028 2029 @param[in] basis `CeedBasis` 2030 @param[out] grad_1d Variable to store gradient matrix 2031 2032 @return An error code: 0 - success, otherwise - failure 2033 2034 @ref Advanced 2035 **/ 2036 int CeedBasisGetGrad1D(CeedBasis basis, const CeedScalar **grad_1d) { 2037 bool is_tensor_basis; 2038 2039 CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis)); 2040 CeedCheck(is_tensor_basis, CeedBasisReturnCeed(basis), CEED_ERROR_MINOR, "CeedBasis is not a tensor product CeedBasis"); 2041 *grad_1d = basis->grad_1d; 2042 return CEED_ERROR_SUCCESS; 2043 } 2044 2045 /** 2046 @brief Get divergence matrix of a `CeedBasis` 2047 2048 @param[in] basis `CeedBasis` 2049 @param[out] div Variable to store divergence matrix 2050 2051 @return An error code: 0 - success, otherwise - failure 2052 2053 @ref Advanced 2054 **/ 2055 int CeedBasisGetDiv(CeedBasis basis, const CeedScalar **div) { 2056 *div = basis->div; 2057 return CEED_ERROR_SUCCESS; 2058 } 2059 2060 /** 2061 @brief Get curl matrix of a `CeedBasis` 2062 2063 @param[in] basis `CeedBasis` 2064 @param[out] curl Variable to store curl matrix 2065 2066 @return An error code: 0 - success, otherwise - failure 2067 2068 @ref Advanced 2069 **/ 2070 int CeedBasisGetCurl(CeedBasis basis, const CeedScalar **curl) { 2071 *curl = basis->curl; 2072 return CEED_ERROR_SUCCESS; 2073 } 2074 2075 /** 2076 @brief Destroy a @ref CeedBasis 2077 2078 @param[in,out] basis `CeedBasis` to destroy 2079 2080 @return An error code: 0 - success, otherwise - failure 2081 2082 @ref User 2083 **/ 2084 int CeedBasisDestroy(CeedBasis *basis) { 2085 if (!*basis || *basis == CEED_BASIS_NONE || --(*basis)->ref_count > 0) { 2086 *basis = NULL; 2087 return CEED_ERROR_SUCCESS; 2088 } 2089 if ((*basis)->Destroy) CeedCall((*basis)->Destroy(*basis)); 2090 CeedCall(CeedTensorContractDestroy(&(*basis)->contract)); 2091 CeedCall(CeedFree(&(*basis)->q_ref_1d)); 2092 CeedCall(CeedFree(&(*basis)->q_weight_1d)); 2093 CeedCall(CeedFree(&(*basis)->interp)); 2094 CeedCall(CeedFree(&(*basis)->interp_1d)); 2095 CeedCall(CeedFree(&(*basis)->grad)); 2096 CeedCall(CeedFree(&(*basis)->grad_1d)); 2097 CeedCall(CeedFree(&(*basis)->div)); 2098 CeedCall(CeedFree(&(*basis)->curl)); 2099 CeedCall(CeedVectorDestroy(&(*basis)->vec_chebyshev)); 2100 CeedCall(CeedBasisDestroy(&(*basis)->basis_chebyshev)); 2101 CeedCall(CeedDestroy(&(*basis)->ceed)); 2102 CeedCall(CeedFree(basis)); 2103 return CEED_ERROR_SUCCESS; 2104 } 2105 2106 /** 2107 @brief Construct a Gauss-Legendre quadrature 2108 2109 @param[in] Q Number of quadrature points (integrates polynomials of degree `2*Q-1` exactly) 2110 @param[out] q_ref_1d Array of length `Q` to hold the abscissa on `[-1, 1]` 2111 @param[out] q_weight_1d Array of length `Q` to hold the weights 2112 2113 @return An error code: 0 - success, otherwise - failure 2114 2115 @ref Utility 2116 **/ 2117 int CeedGaussQuadrature(CeedInt Q, CeedScalar *q_ref_1d, CeedScalar *q_weight_1d) { 2118 CeedScalar P0, P1, P2, dP2, xi, wi, PI = 4.0 * atan(1.0); 2119 2120 // Build q_ref_1d, q_weight_1d 2121 for (CeedInt i = 0; i <= Q / 2; i++) { 2122 // Guess 2123 xi = cos(PI * (CeedScalar)(2 * i + 1) / ((CeedScalar)(2 * Q))); 2124 // Pn(xi) 2125 P0 = 1.0; 2126 P1 = xi; 2127 P2 = 0.0; 2128 for (CeedInt j = 2; j <= Q; j++) { 2129 P2 = (((CeedScalar)(2 * j - 1)) * xi * P1 - ((CeedScalar)(j - 1)) * P0) / ((CeedScalar)(j)); 2130 P0 = P1; 2131 P1 = P2; 2132 } 2133 // First Newton Step 2134 dP2 = (xi * P2 - P0) * (CeedScalar)Q / (xi * xi - 1.0); 2135 xi = xi - P2 / dP2; 2136 // Newton to convergence 2137 for (CeedInt k = 0; k < 100 && fabs(P2) > 10 * CEED_EPSILON; k++) { 2138 P0 = 1.0; 2139 P1 = xi; 2140 for (CeedInt j = 2; j <= Q; j++) { 2141 P2 = (((CeedScalar)(2 * j - 1)) * xi * P1 - ((CeedScalar)(j - 1)) * P0) / ((CeedScalar)(j)); 2142 P0 = P1; 2143 P1 = P2; 2144 } 2145 dP2 = (xi * P2 - P0) * (CeedScalar)Q / (xi * xi - 1.0); 2146 xi = xi - P2 / dP2; 2147 } 2148 // Save xi, wi 2149 wi = 2.0 / ((1.0 - xi * xi) * dP2 * dP2); 2150 q_weight_1d[i] = wi; 2151 q_weight_1d[Q - 1 - i] = wi; 2152 q_ref_1d[i] = -xi; 2153 q_ref_1d[Q - 1 - i] = xi; 2154 } 2155 return CEED_ERROR_SUCCESS; 2156 } 2157 2158 /** 2159 @brief Construct a Gauss-Legendre-Lobatto quadrature 2160 2161 @param[in] Q Number of quadrature points (integrates polynomials of degree `2*Q-3` exactly) 2162 @param[out] q_ref_1d Array of length `Q` to hold the abscissa on `[-1, 1]` 2163 @param[out] q_weight_1d Array of length `Q` to hold the weights 2164 2165 @return An error code: 0 - success, otherwise - failure 2166 2167 @ref Utility 2168 **/ 2169 int CeedLobattoQuadrature(CeedInt Q, CeedScalar *q_ref_1d, CeedScalar *q_weight_1d) { 2170 CeedScalar P0, P1, P2, dP2, d2P2, xi, wi, PI = 4.0 * atan(1.0); 2171 2172 // Build q_ref_1d, q_weight_1d 2173 // Set endpoints 2174 CeedCheck(Q > 1, NULL, CEED_ERROR_DIMENSION, "Cannot create Lobatto quadrature with Q=%" CeedInt_FMT " < 2 points", Q); 2175 wi = 2.0 / ((CeedScalar)(Q * (Q - 1))); 2176 if (q_weight_1d) { 2177 q_weight_1d[0] = wi; 2178 q_weight_1d[Q - 1] = wi; 2179 } 2180 q_ref_1d[0] = -1.0; 2181 q_ref_1d[Q - 1] = 1.0; 2182 // Interior 2183 for (CeedInt i = 1; i <= (Q - 1) / 2; i++) { 2184 // Guess 2185 xi = cos(PI * (CeedScalar)(i) / (CeedScalar)(Q - 1)); 2186 // Pn(xi) 2187 P0 = 1.0; 2188 P1 = xi; 2189 P2 = 0.0; 2190 for (CeedInt j = 2; j < Q; j++) { 2191 P2 = (((CeedScalar)(2 * j - 1)) * xi * P1 - ((CeedScalar)(j - 1)) * P0) / ((CeedScalar)(j)); 2192 P0 = P1; 2193 P1 = P2; 2194 } 2195 // First Newton step 2196 dP2 = (xi * P2 - P0) * (CeedScalar)Q / (xi * xi - 1.0); 2197 d2P2 = (2 * xi * dP2 - (CeedScalar)(Q * (Q - 1)) * P2) / (1.0 - xi * xi); 2198 xi = xi - dP2 / d2P2; 2199 // Newton to convergence 2200 for (CeedInt k = 0; k < 100 && fabs(dP2) > 10 * CEED_EPSILON; k++) { 2201 P0 = 1.0; 2202 P1 = xi; 2203 for (CeedInt j = 2; j < Q; j++) { 2204 P2 = (((CeedScalar)(2 * j - 1)) * xi * P1 - ((CeedScalar)(j - 1)) * P0) / ((CeedScalar)(j)); 2205 P0 = P1; 2206 P1 = P2; 2207 } 2208 dP2 = (xi * P2 - P0) * (CeedScalar)Q / (xi * xi - 1.0); 2209 d2P2 = (2 * xi * dP2 - (CeedScalar)(Q * (Q - 1)) * P2) / (1.0 - xi * xi); 2210 xi = xi - dP2 / d2P2; 2211 } 2212 // Save xi, wi 2213 wi = 2.0 / (((CeedScalar)(Q * (Q - 1))) * P2 * P2); 2214 if (q_weight_1d) { 2215 q_weight_1d[i] = wi; 2216 q_weight_1d[Q - 1 - i] = wi; 2217 } 2218 q_ref_1d[i] = -xi; 2219 q_ref_1d[Q - 1 - i] = xi; 2220 } 2221 return CEED_ERROR_SUCCESS; 2222 } 2223 2224 /// @} 2225