1 // Copyright (c) 2017-2022, 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/ceed.h> 9 #include <ceed/backend.h> 10 #include <ceed-impl.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_collocated; 21 /// @endcond 22 23 /// @addtogroup CeedBasisUser 24 /// @{ 25 26 /// Indicate that the quadrature points are collocated with the nodes 27 const CeedBasis CEED_BASIS_COLLOCATED = &ceed_basis_collocated; 28 29 /// @} 30 31 /// ---------------------------------------------------------------------------- 32 /// CeedBasis Library Internal Functions 33 /// ---------------------------------------------------------------------------- 34 /// @addtogroup CeedBasisDeveloper 35 /// @{ 36 37 /** 38 @brief Compute Householder reflection 39 40 Computes A = (I - b v v^T) A 41 where A is an mxn matrix indexed as A[i*row + j*col] 42 43 @param[in,out] A Matrix to apply Householder reflection to, in place 44 @param v Householder vector 45 @param b Scaling factor 46 @param m Number of rows in A 47 @param n Number of columns in A 48 @param row Row stride 49 @param col Col stride 50 51 @return An error code: 0 - success, otherwise - failure 52 53 @ref Developer 54 **/ 55 static int CeedHouseholderReflect(CeedScalar *A, const CeedScalar *v, 56 CeedScalar b, CeedInt m, CeedInt n, 57 CeedInt row, CeedInt col) { 58 for (CeedInt j=0; j<n; j++) { 59 CeedScalar w = A[0*row + j*col]; 60 for (CeedInt i=1; i<m; i++) 61 w += v[i] * A[i*row + j*col]; 62 A[0*row + j*col] -= b * w; 63 for (CeedInt i=1; i<m; i++) 64 A[i*row + j*col] -= b * w * v[i]; 65 } 66 return CEED_ERROR_SUCCESS; 67 } 68 69 /** 70 @brief Apply Householder Q matrix 71 72 Compute A = Q A where Q is mxm and A is mxn. 73 74 @param[in,out] A Matrix to apply Householder Q to, in place 75 @param Q Householder Q matrix 76 @param tau Householder scaling factors 77 @param t_mode Transpose mode for application 78 @param m Number of rows in A 79 @param n Number of columns in A 80 @param k Number of elementary reflectors in Q, k<m 81 @param row Row stride in A 82 @param col Col stride in A 83 84 @return An error code: 0 - success, otherwise - failure 85 86 @ref Developer 87 **/ 88 int CeedHouseholderApplyQ(CeedScalar *A, const CeedScalar *Q, 89 const CeedScalar *tau, CeedTransposeMode t_mode, 90 CeedInt m, CeedInt n, CeedInt k, 91 CeedInt row, CeedInt col) { 92 int ierr; 93 CeedScalar *v; 94 ierr = CeedMalloc(m, &v); CeedChk(ierr); 95 for (CeedInt ii=0; ii<k; ii++) { 96 CeedInt i = t_mode == CEED_TRANSPOSE ? ii : k-1-ii; 97 for (CeedInt j=i+1; j<m; j++) 98 v[j] = Q[j*k+i]; 99 // Apply Householder reflector (I - tau v v^T) collo_grad_1d^T 100 ierr = CeedHouseholderReflect(&A[i*row], &v[i], tau[i], m-i, n, row, col); 101 CeedChk(ierr); 102 } 103 ierr = CeedFree(&v); CeedChk(ierr); 104 return CEED_ERROR_SUCCESS; 105 } 106 107 /** 108 @brief Compute Givens rotation 109 110 Computes A = G A (or G^T A in transpose mode) 111 where A is an mxn matrix indexed as A[i*n + j*m] 112 113 @param[in,out] A Row major matrix to apply Givens rotation to, in place 114 @param c Cosine factor 115 @param s Sine factor 116 @param t_mode @ref CEED_NOTRANSPOSE to rotate the basis counter-clockwise, 117 which has the effect of rotating columns of A clockwise; 118 @ref CEED_TRANSPOSE for the opposite rotation 119 @param i First row/column to apply rotation 120 @param k Second row/column to apply rotation 121 @param m Number of rows in A 122 @param n Number of columns in A 123 124 @return An error code: 0 - success, otherwise - failure 125 126 @ref Developer 127 **/ 128 static int CeedGivensRotation(CeedScalar *A, CeedScalar c, CeedScalar s, 129 CeedTransposeMode t_mode, CeedInt i, CeedInt k, 130 CeedInt m, CeedInt n) { 131 CeedInt stride_j = 1, stride_ik = m, num_its = n; 132 if (t_mode == CEED_NOTRANSPOSE) { 133 stride_j = n; stride_ik = 1; num_its = m; 134 } 135 136 // Apply rotation 137 for (CeedInt j=0; j<num_its; j++) { 138 CeedScalar tau1 = A[i*stride_ik+j*stride_j], tau2 = A[k*stride_ik+j*stride_j]; 139 A[i*stride_ik+j*stride_j] = c*tau1 - s*tau2; 140 A[k*stride_ik+j*stride_j] = s*tau1 + c*tau2; 141 } 142 return CEED_ERROR_SUCCESS; 143 } 144 145 /** 146 @brief View an array stored in a CeedBasis 147 148 @param[in] name Name of array 149 @param[in] fp_fmt Printing format 150 @param[in] m Number of rows in array 151 @param[in] n Number of columns in array 152 @param[in] a Array to be viewed 153 @param[in] stream Stream to view to, e.g., stdout 154 155 @return An error code: 0 - success, otherwise - failure 156 157 @ref Developer 158 **/ 159 static int CeedScalarView(const char *name, const char *fp_fmt, CeedInt m, 160 CeedInt n, const CeedScalar *a, FILE *stream) { 161 for (CeedInt i=0; i<m; i++) { 162 if (m > 1) 163 fprintf(stream, "%12s[%d]:", name, i); 164 else 165 fprintf(stream, "%12s:", name); 166 for (CeedInt j=0; j<n; j++) 167 fprintf(stream, fp_fmt, fabs(a[i*n+j]) > 1E-14 ? a[i*n+j] : 0); 168 fputs("\n", stream); 169 } 170 return CEED_ERROR_SUCCESS; 171 } 172 173 /// @} 174 175 /// ---------------------------------------------------------------------------- 176 /// Ceed Backend API 177 /// ---------------------------------------------------------------------------- 178 /// @addtogroup CeedBasisBackend 179 /// @{ 180 181 /** 182 @brief Return collocated grad matrix 183 184 @param basis CeedBasis 185 @param[out] collo_grad_1d Row-major (Q_1d * Q_1d) matrix expressing derivatives of 186 basis functions at quadrature points 187 188 @return An error code: 0 - success, otherwise - failure 189 190 @ref Backend 191 **/ 192 int CeedBasisGetCollocatedGrad(CeedBasis basis, CeedScalar *collo_grad_1d) { 193 int i, j, k; 194 Ceed ceed; 195 CeedInt ierr, P_1d=(basis)->P_1d, Q_1d=(basis)->Q_1d; 196 CeedScalar *interp_1d, *grad_1d, *tau; 197 198 ierr = CeedMalloc(Q_1d*P_1d, &interp_1d); CeedChk(ierr); 199 ierr = CeedMalloc(Q_1d*P_1d, &grad_1d); CeedChk(ierr); 200 ierr = CeedMalloc(Q_1d, &tau); CeedChk(ierr); 201 memcpy(interp_1d, (basis)->interp_1d, Q_1d*P_1d*sizeof(basis)->interp_1d[0]); 202 memcpy(grad_1d, (basis)->grad_1d, Q_1d*P_1d*sizeof(basis)->interp_1d[0]); 203 204 // QR Factorization, interp_1d = Q R 205 ierr = CeedBasisGetCeed(basis, &ceed); CeedChk(ierr); 206 ierr = CeedQRFactorization(ceed, interp_1d, tau, Q_1d, P_1d); CeedChk(ierr); 207 // Note: This function is for backend use, so all errors are terminal 208 // and we do not need to clean up memory on failure. 209 210 // Apply Rinv, collo_grad_1d = grad_1d Rinv 211 for (i=0; i<Q_1d; i++) { // Row i 212 collo_grad_1d[Q_1d*i] = grad_1d[P_1d*i]/interp_1d[0]; 213 for (j=1; j<P_1d; j++) { // Column j 214 collo_grad_1d[j+Q_1d*i] = grad_1d[j+P_1d*i]; 215 for (k=0; k<j; k++) 216 collo_grad_1d[j+Q_1d*i] -= interp_1d[j+P_1d*k]*collo_grad_1d[k+Q_1d*i]; 217 collo_grad_1d[j+Q_1d*i] /= interp_1d[j+P_1d*j]; 218 } 219 for (j=P_1d; j<Q_1d; j++) 220 collo_grad_1d[j+Q_1d*i] = 0; 221 } 222 223 // Apply Qtranspose, collo_grad = collo_grad Q_transpose 224 ierr = CeedHouseholderApplyQ(collo_grad_1d, interp_1d, tau, CEED_NOTRANSPOSE, 225 Q_1d, Q_1d, P_1d, 1, Q_1d); CeedChk(ierr); 226 227 ierr = CeedFree(&interp_1d); CeedChk(ierr); 228 ierr = CeedFree(&grad_1d); CeedChk(ierr); 229 ierr = CeedFree(&tau); CeedChk(ierr); 230 return CEED_ERROR_SUCCESS; 231 } 232 233 /** 234 @brief Get tensor status for given CeedBasis 235 236 @param basis CeedBasis 237 @param[out] is_tensor Variable to store tensor status 238 239 @return An error code: 0 - success, otherwise - failure 240 241 @ref Backend 242 **/ 243 int CeedBasisIsTensor(CeedBasis basis, bool *is_tensor) { 244 *is_tensor = basis->tensor_basis; 245 return CEED_ERROR_SUCCESS; 246 } 247 248 /** 249 @brief Get backend data of a CeedBasis 250 251 @param basis CeedBasis 252 @param[out] data Variable to store data 253 254 @return An error code: 0 - success, otherwise - failure 255 256 @ref Backend 257 **/ 258 int CeedBasisGetData(CeedBasis basis, void *data) { 259 *(void **)data = basis->data; 260 return CEED_ERROR_SUCCESS; 261 } 262 263 /** 264 @brief Set backend data of a CeedBasis 265 266 @param[out] basis CeedBasis 267 @param data Data to set 268 269 @return An error code: 0 - success, otherwise - failure 270 271 @ref Backend 272 **/ 273 int CeedBasisSetData(CeedBasis basis, void *data) { 274 basis->data = data; 275 return CEED_ERROR_SUCCESS; 276 } 277 278 /** 279 @brief Increment the reference counter for a CeedBasis 280 281 @param basis Basis to increment the reference counter 282 283 @return An error code: 0 - success, otherwise - failure 284 285 @ref Backend 286 **/ 287 int CeedBasisReference(CeedBasis basis) { 288 basis->ref_count++; 289 return CEED_ERROR_SUCCESS; 290 } 291 292 /** 293 @brief Estimate number of FLOPs required to apply CeedBasis in t_mode and eval_mode 294 295 @param basis Basis to estimate FLOPs for 296 @param t_mode Apply basis or transpose 297 @param eval_mode Basis evaluation mode 298 @param flops Address of variable to hold FLOPs estimate 299 300 @ref Backend 301 **/ 302 int CeedBasisGetFlopsEstimate(CeedBasis basis, CeedTransposeMode t_mode, 303 CeedEvalMode eval_mode, CeedSize *flops) { 304 int ierr; 305 bool is_tensor; 306 307 ierr = CeedBasisIsTensor(basis, &is_tensor); CeedChk(ierr); 308 if (is_tensor) { 309 CeedInt dim, num_comp, P_1d, Q_1d; 310 ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr); 311 ierr = CeedBasisGetNumComponents(basis, &num_comp); CeedChk(ierr); 312 ierr = CeedBasisGetNumNodes1D(basis, &P_1d); CeedChk(ierr); 313 ierr = CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d); CeedChk(ierr); 314 if (t_mode == CEED_TRANSPOSE) { 315 P_1d = Q_1d; Q_1d = P_1d; 316 } 317 CeedInt tensor_flops = 0, pre = num_comp * CeedIntPow(P_1d, dim-1), post = 1; 318 for (CeedInt d = 0; d < dim; d++) { 319 tensor_flops += 2 * pre * P_1d * post * Q_1d; 320 pre /= P_1d; 321 post *= Q_1d; 322 } 323 switch (eval_mode) { 324 case CEED_EVAL_NONE: *flops = 0; break; 325 case CEED_EVAL_INTERP: *flops = tensor_flops; break; 326 case CEED_EVAL_GRAD: *flops = tensor_flops * 2; break; 327 case CEED_EVAL_DIV: 328 // LCOV_EXCL_START 329 return CeedError(basis->ceed, CEED_ERROR_INCOMPATIBLE, 330 "Tensor CEED_EVAL_DIV not supported"); break; 331 case CEED_EVAL_CURL: 332 return CeedError(basis->ceed, CEED_ERROR_INCOMPATIBLE, 333 "Tensor CEED_EVAL_CURL not supported"); break; 334 // LCOV_EXCL_STOP 335 case CEED_EVAL_WEIGHT: *flops = dim * CeedIntPow(Q_1d, dim); break; 336 } 337 } else { 338 CeedInt dim, num_comp, num_nodes, num_qpts, Q_comp; 339 ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr); 340 ierr = CeedBasisGetNumComponents(basis, &num_comp); CeedChk(ierr); 341 ierr = CeedBasisGetNumNodes(basis, &num_nodes); CeedChk(ierr); 342 ierr = CeedBasisGetNumQuadraturePoints(basis, &num_qpts); CeedChk(ierr); 343 ierr = CeedBasisGetNumQuadratureComponents(basis, &Q_comp); CeedChk(ierr); 344 switch (eval_mode) { 345 case CEED_EVAL_NONE: *flops = 0; break; 346 case CEED_EVAL_INTERP: *flops = num_nodes * num_qpts * num_comp; break; 347 case CEED_EVAL_GRAD: *flops = num_nodes * num_qpts * num_comp * dim; break; 348 case CEED_EVAL_DIV: *flops = num_nodes * num_qpts; break; 349 case CEED_EVAL_CURL: *flops = num_nodes * num_qpts * dim; break; 350 case CEED_EVAL_WEIGHT: *flops = 0; break; 351 } 352 } 353 354 return CEED_ERROR_SUCCESS; 355 } 356 357 /** 358 @brief Get dimension for given CeedElemTopology 359 360 @param topo CeedElemTopology 361 @param[out] dim Variable to store dimension of topology 362 363 @return An error code: 0 - success, otherwise - failure 364 365 @ref Backend 366 **/ 367 int CeedBasisGetTopologyDimension(CeedElemTopology topo, CeedInt *dim) { 368 *dim = (CeedInt) topo >> 16; 369 return CEED_ERROR_SUCCESS; 370 } 371 372 /** 373 @brief Get CeedTensorContract of a CeedBasis 374 375 @param basis CeedBasis 376 @param[out] contract Variable to store CeedTensorContract 377 378 @return An error code: 0 - success, otherwise - failure 379 380 @ref Backend 381 **/ 382 int CeedBasisGetTensorContract(CeedBasis basis, CeedTensorContract *contract) { 383 *contract = basis->contract; 384 return CEED_ERROR_SUCCESS; 385 } 386 387 /** 388 @brief Set CeedTensorContract of a CeedBasis 389 390 @param[out] basis CeedBasis 391 @param contract CeedTensorContract to set 392 393 @return An error code: 0 - success, otherwise - failure 394 395 @ref Backend 396 **/ 397 int CeedBasisSetTensorContract(CeedBasis basis, CeedTensorContract contract) { 398 int ierr; 399 basis->contract = contract; 400 ierr = CeedTensorContractReference(contract); CeedChk(ierr); 401 return CEED_ERROR_SUCCESS; 402 } 403 404 /** 405 @brief Return a reference implementation of matrix multiplication C = A B. 406 Note, this is a reference implementation for CPU CeedScalar pointers 407 that is not intended for high performance. 408 409 @param ceed A Ceed context for error handling 410 @param[in] mat_A Row-major matrix A 411 @param[in] mat_B Row-major matrix B 412 @param[out] mat_C Row-major output matrix C 413 @param m Number of rows of C 414 @param n Number of columns of C 415 @param kk Number of columns of A/rows of B 416 417 @return An error code: 0 - success, otherwise - failure 418 419 @ref Utility 420 **/ 421 int CeedMatrixMultiply(Ceed ceed, const CeedScalar *mat_A, 422 const CeedScalar *mat_B, CeedScalar *mat_C, CeedInt m, 423 CeedInt n, CeedInt kk) { 424 for (CeedInt i=0; i<m; i++) 425 for (CeedInt j=0; j<n; j++) { 426 CeedScalar sum = 0; 427 for (CeedInt k=0; k<kk; k++) 428 sum += mat_A[k+i*kk]*mat_B[j+k*n]; 429 mat_C[j+i*n] = sum; 430 } 431 return CEED_ERROR_SUCCESS; 432 } 433 434 /// @} 435 436 /// ---------------------------------------------------------------------------- 437 /// CeedBasis Public API 438 /// ---------------------------------------------------------------------------- 439 /// @addtogroup CeedBasisUser 440 /// @{ 441 442 /** 443 @brief Create a tensor-product basis for H^1 discretizations 444 445 @param ceed A Ceed object where the CeedBasis will be created 446 @param dim Topological dimension 447 @param num_comp Number of field components (1 for scalar fields) 448 @param P_1d Number of nodes in one dimension 449 @param Q_1d Number of quadrature points in one dimension 450 @param interp_1d Row-major (Q_1d * P_1d) matrix expressing the values of nodal 451 basis functions at quadrature points 452 @param grad_1d Row-major (Q_1d * P_1d) matrix expressing derivatives of nodal 453 basis functions at quadrature points 454 @param q_ref_1d Array of length Q_1d holding the locations of quadrature points 455 on the 1D reference element [-1, 1] 456 @param q_weight_1d Array of length Q_1d holding the quadrature weights on the 457 reference element 458 @param[out] basis Address of the variable where the newly created 459 CeedBasis will be stored. 460 461 @return An error code: 0 - success, otherwise - failure 462 463 @ref User 464 **/ 465 int CeedBasisCreateTensorH1(Ceed ceed, CeedInt dim, CeedInt num_comp, 466 CeedInt P_1d, CeedInt Q_1d, 467 const CeedScalar *interp_1d, 468 const CeedScalar *grad_1d, const CeedScalar *q_ref_1d, 469 const CeedScalar *q_weight_1d, CeedBasis *basis) { 470 int ierr; 471 472 if (!ceed->BasisCreateTensorH1) { 473 Ceed delegate; 474 ierr = CeedGetObjectDelegate(ceed, &delegate, "Basis"); CeedChk(ierr); 475 476 if (!delegate) 477 // LCOV_EXCL_START 478 return CeedError(ceed, CEED_ERROR_UNSUPPORTED, 479 "Backend does not support BasisCreateTensorH1"); 480 // LCOV_EXCL_STOP 481 482 ierr = CeedBasisCreateTensorH1(delegate, dim, num_comp, P_1d, 483 Q_1d, interp_1d, grad_1d, q_ref_1d, 484 q_weight_1d, basis); CeedChk(ierr); 485 return CEED_ERROR_SUCCESS; 486 } 487 488 if (dim < 1) 489 // LCOV_EXCL_START 490 return CeedError(ceed, CEED_ERROR_DIMENSION, 491 "Basis dimension must be a positive value"); 492 // LCOV_EXCL_STOP 493 494 if (num_comp < 1) 495 // LCOV_EXCL_START 496 return CeedError(ceed, CEED_ERROR_DIMENSION, 497 "Basis must have at least 1 component"); 498 // LCOV_EXCL_STOP 499 500 if (P_1d < 1) 501 // LCOV_EXCL_START 502 return CeedError(ceed, CEED_ERROR_DIMENSION, 503 "Basis must have at least 1 node"); 504 // LCOV_EXCL_STOP 505 506 if (Q_1d < 1) 507 // LCOV_EXCL_START 508 return CeedError(ceed, CEED_ERROR_DIMENSION, 509 "Basis must have at least 1 quadrature point"); 510 // LCOV_EXCL_STOP 511 512 CeedElemTopology topo = dim == 1 ? CEED_TOPOLOGY_LINE 513 : dim == 2 ? CEED_TOPOLOGY_QUAD 514 : CEED_TOPOLOGY_HEX; 515 516 ierr = CeedCalloc(1, basis); CeedChk(ierr); 517 (*basis)->ceed = ceed; 518 ierr = CeedReference(ceed); CeedChk(ierr); 519 (*basis)->ref_count = 1; 520 (*basis)->tensor_basis = 1; 521 (*basis)->dim = dim; 522 (*basis)->topo = topo; 523 (*basis)->num_comp = num_comp; 524 (*basis)->P_1d = P_1d; 525 (*basis)->Q_1d = Q_1d; 526 (*basis)->P = CeedIntPow(P_1d, dim); 527 (*basis)->Q = CeedIntPow(Q_1d, dim); 528 (*basis)->Q_comp = 1; 529 (*basis)->basis_space = 1; // 1 for H^1 space 530 ierr = CeedCalloc(Q_1d, &(*basis)->q_ref_1d); CeedChk(ierr); 531 ierr = CeedCalloc(Q_1d, &(*basis)->q_weight_1d); CeedChk(ierr); 532 if (q_ref_1d) memcpy((*basis)->q_ref_1d, q_ref_1d, Q_1d*sizeof(q_ref_1d[0])); 533 if (q_weight_1d) memcpy((*basis)->q_weight_1d, q_weight_1d, 534 Q_1d*sizeof(q_weight_1d[0])); 535 ierr = CeedCalloc(Q_1d*P_1d, &(*basis)->interp_1d); CeedChk(ierr); 536 ierr = CeedCalloc(Q_1d*P_1d, &(*basis)->grad_1d); CeedChk(ierr); 537 if (interp_1d) memcpy((*basis)->interp_1d, interp_1d, 538 Q_1d*P_1d*sizeof(interp_1d[0])); 539 if (grad_1d) memcpy((*basis)->grad_1d, grad_1d, Q_1d*P_1d*sizeof(grad_1d[0])); 540 ierr = ceed->BasisCreateTensorH1(dim, P_1d, Q_1d, interp_1d, grad_1d, q_ref_1d, 541 q_weight_1d, *basis); CeedChk(ierr); 542 return CEED_ERROR_SUCCESS; 543 } 544 545 /** 546 @brief Create a tensor-product Lagrange basis 547 548 @param ceed A Ceed object where the CeedBasis will be created 549 @param dim Topological dimension of element 550 @param num_comp Number of field components (1 for scalar fields) 551 @param P Number of Gauss-Lobatto nodes in one dimension. The 552 polynomial degree of the resulting Q_k element is k=P-1. 553 @param Q Number of quadrature points in one dimension. 554 @param quad_mode Distribution of the Q quadrature points (affects order of 555 accuracy for the quadrature) 556 @param[out] basis Address of the variable where the newly created 557 CeedBasis will be stored. 558 559 @return An error code: 0 - success, otherwise - failure 560 561 @ref User 562 **/ 563 int CeedBasisCreateTensorH1Lagrange(Ceed ceed, CeedInt dim, CeedInt num_comp, 564 CeedInt P, CeedInt Q, CeedQuadMode quad_mode, 565 CeedBasis *basis) { 566 // Allocate 567 int ierr, ierr2, i, j, k; 568 CeedScalar c1, c2, c3, c4, dx, *nodes, *interp_1d, *grad_1d, *q_ref_1d, 569 *q_weight_1d; 570 571 if (dim < 1) 572 // LCOV_EXCL_START 573 return CeedError(ceed, CEED_ERROR_DIMENSION, 574 "Basis dimension must be a positive value"); 575 // LCOV_EXCL_STOP 576 577 if (num_comp < 1) 578 // LCOV_EXCL_START 579 return CeedError(ceed, CEED_ERROR_DIMENSION, 580 "Basis must have at least 1 component"); 581 // LCOV_EXCL_STOP 582 583 if (P < 1) 584 // LCOV_EXCL_START 585 return CeedError(ceed, CEED_ERROR_DIMENSION, 586 "Basis must have at least 1 node"); 587 // LCOV_EXCL_STOP 588 589 if (Q < 1) 590 // LCOV_EXCL_START 591 return CeedError(ceed, CEED_ERROR_DIMENSION, 592 "Basis must have at least 1 quadrature point"); 593 // LCOV_EXCL_STOP 594 595 // Get Nodes and Weights 596 ierr = CeedCalloc(P*Q, &interp_1d); CeedChk(ierr); 597 ierr = CeedCalloc(P*Q, &grad_1d); CeedChk(ierr); 598 ierr = CeedCalloc(P, &nodes); CeedChk(ierr); 599 ierr = CeedCalloc(Q, &q_ref_1d); CeedChk(ierr); 600 ierr = CeedCalloc(Q, &q_weight_1d); CeedChk(ierr); 601 ierr = CeedLobattoQuadrature(P, nodes, NULL); 602 if (ierr) { goto cleanup; } CeedChk(ierr); 603 switch (quad_mode) { 604 case CEED_GAUSS: 605 ierr = CeedGaussQuadrature(Q, q_ref_1d, q_weight_1d); 606 break; 607 case CEED_GAUSS_LOBATTO: 608 ierr = CeedLobattoQuadrature(Q, q_ref_1d, q_weight_1d); 609 break; 610 } 611 if (ierr) { goto cleanup; } CeedChk(ierr); 612 613 // Build B, D matrix 614 // Fornberg, 1998 615 for (i = 0; i < Q; i++) { 616 c1 = 1.0; 617 c3 = nodes[0] - q_ref_1d[i]; 618 interp_1d[i*P+0] = 1.0; 619 for (j = 1; j < P; j++) { 620 c2 = 1.0; 621 c4 = c3; 622 c3 = nodes[j] - q_ref_1d[i]; 623 for (k = 0; k < j; k++) { 624 dx = nodes[j] - nodes[k]; 625 c2 *= dx; 626 if (k == j - 1) { 627 grad_1d[i*P + j] = c1*(interp_1d[i*P + k] - c4*grad_1d[i*P + k]) / c2; 628 interp_1d[i*P + j] = - c1*c4*interp_1d[i*P + k] / c2; 629 } 630 grad_1d[i*P + k] = (c3*grad_1d[i*P + k] - interp_1d[i*P + k]) / dx; 631 interp_1d[i*P + k] = c3*interp_1d[i*P + k] / dx; 632 } 633 c1 = c2; 634 } 635 } 636 // Pass to CeedBasisCreateTensorH1 637 ierr = CeedBasisCreateTensorH1(ceed, dim, num_comp, P, Q, interp_1d, grad_1d, 638 q_ref_1d, q_weight_1d, basis); CeedChk(ierr); 639 cleanup: 640 ierr2 = CeedFree(&interp_1d); CeedChk(ierr2); 641 ierr2 = CeedFree(&grad_1d); CeedChk(ierr2); 642 ierr2 = CeedFree(&nodes); CeedChk(ierr2); 643 ierr2 = CeedFree(&q_ref_1d); CeedChk(ierr2); 644 ierr2 = CeedFree(&q_weight_1d); CeedChk(ierr2); 645 CeedChk(ierr); 646 return CEED_ERROR_SUCCESS; 647 } 648 649 /** 650 @brief Create a non tensor-product basis for H^1 discretizations 651 652 @param ceed A Ceed object where the CeedBasis will be created 653 @param topo Topology of element, e.g. hypercube, simplex, ect 654 @param num_comp Number of field components (1 for scalar fields) 655 @param num_nodes Total number of nodes 656 @param num_qpts Total number of quadrature points 657 @param interp Row-major (num_qpts * num_nodes) matrix expressing the values of 658 nodal basis functions at quadrature points 659 @param grad Row-major (num_qpts * dim * num_nodes) matrix expressing 660 derivatives of nodal basis functions at quadrature points 661 @param q_ref Array of length num_qpts holding the locations of quadrature 662 points on the reference element 663 @param q_weight Array of length num_qpts holding the quadrature weights on the 664 reference element 665 @param[out] basis Address of the variable where the newly created 666 CeedBasis will be stored. 667 668 @return An error code: 0 - success, otherwise - failure 669 670 @ref User 671 **/ 672 int CeedBasisCreateH1(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, 673 CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, 674 const CeedScalar *grad, const CeedScalar *q_ref, 675 const CeedScalar *q_weight, CeedBasis *basis) { 676 int ierr; 677 CeedInt P = num_nodes, Q = num_qpts, dim = 0; 678 679 if (!ceed->BasisCreateH1) { 680 Ceed delegate; 681 ierr = CeedGetObjectDelegate(ceed, &delegate, "Basis"); CeedChk(ierr); 682 683 if (!delegate) 684 // LCOV_EXCL_START 685 return CeedError(ceed, CEED_ERROR_UNSUPPORTED, 686 "Backend does not support BasisCreateH1"); 687 // LCOV_EXCL_STOP 688 689 ierr = CeedBasisCreateH1(delegate, topo, num_comp, num_nodes, 690 num_qpts, interp, grad, q_ref, 691 q_weight, basis); CeedChk(ierr); 692 return CEED_ERROR_SUCCESS; 693 } 694 695 if (num_comp < 1) 696 // LCOV_EXCL_START 697 return CeedError(ceed, CEED_ERROR_DIMENSION, 698 "Basis must have at least 1 component"); 699 // LCOV_EXCL_STOP 700 701 if (num_nodes < 1) 702 // LCOV_EXCL_START 703 return CeedError(ceed, CEED_ERROR_DIMENSION, 704 "Basis must have at least 1 node"); 705 // LCOV_EXCL_STOP 706 707 if (num_qpts < 1) 708 // LCOV_EXCL_START 709 return CeedError(ceed, CEED_ERROR_DIMENSION, 710 "Basis must have at least 1 quadrature point"); 711 // LCOV_EXCL_STOP 712 713 ierr = CeedCalloc(1, basis); CeedChk(ierr); 714 715 ierr = CeedBasisGetTopologyDimension(topo, &dim); CeedChk(ierr); 716 717 (*basis)->ceed = ceed; 718 ierr = CeedReference(ceed); CeedChk(ierr); 719 (*basis)->ref_count = 1; 720 (*basis)->tensor_basis = 0; 721 (*basis)->dim = dim; 722 (*basis)->topo = topo; 723 (*basis)->num_comp = num_comp; 724 (*basis)->P = P; 725 (*basis)->Q = Q; 726 (*basis)->Q_comp = 1; 727 (*basis)->basis_space = 1; // 1 for H^1 space 728 ierr = CeedCalloc(Q*dim, &(*basis)->q_ref_1d); CeedChk(ierr); 729 ierr = CeedCalloc(Q, &(*basis)->q_weight_1d); CeedChk(ierr); 730 if (q_ref) memcpy((*basis)->q_ref_1d, q_ref, Q*dim*sizeof(q_ref[0])); 731 if(q_weight) memcpy((*basis)->q_weight_1d, q_weight, Q*sizeof(q_weight[0])); 732 ierr = CeedCalloc(Q*P, &(*basis)->interp); CeedChk(ierr); 733 ierr = CeedCalloc(dim*Q*P, &(*basis)->grad); CeedChk(ierr); 734 if(interp) memcpy((*basis)->interp, interp, Q*P*sizeof(interp[0])); 735 if(grad) memcpy((*basis)->grad, grad, dim*Q*P*sizeof(grad[0])); 736 ierr = ceed->BasisCreateH1(topo, dim, P, Q, interp, grad, q_ref, 737 q_weight, *basis); CeedChk(ierr); 738 return CEED_ERROR_SUCCESS; 739 } 740 741 /** 742 @brief Create a non tensor-product basis for H(div) discretizations 743 744 @param ceed A Ceed object where the CeedBasis will be created 745 @param topo Topology of element (`CEED_TOPOLOGY_QUAD`, `CEED_TOPOLOGY_PRISM`, etc.), 746 dimension of which is used in some array sizes below 747 @param num_comp Number of components (usually 1 for vectors in H(div) bases) 748 @param num_nodes Total number of nodes (dofs per element) 749 @param num_qpts Total number of quadrature points 750 @param interp Row-major (dim*num_qpts * num_nodes) matrix expressing the values of 751 nodal basis functions at quadrature points 752 @param div Row-major (num_qpts * num_nodes) matrix expressing 753 divergence of nodal basis functions at quadrature points 754 @param q_ref Array of length num_qpts holding the locations of quadrature 755 points on the reference element 756 @param q_weight Array of length num_qpts holding the quadrature weights on the 757 reference element 758 @param[out] basis Address of the variable where the newly created 759 CeedBasis will be stored. 760 761 @return An error code: 0 - success, otherwise - failure 762 763 @ref User 764 **/ 765 int CeedBasisCreateHdiv(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, 766 CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, 767 const CeedScalar *div, const CeedScalar *q_ref, 768 const CeedScalar *q_weight, CeedBasis *basis) { 769 int ierr; 770 CeedInt Q = num_qpts, P = num_nodes, dim = 0; 771 ierr = CeedBasisGetTopologyDimension(topo, &dim); CeedChk(ierr); 772 if (!ceed->BasisCreateHdiv) { 773 Ceed delegate; 774 ierr = CeedGetObjectDelegate(ceed, &delegate, "Basis"); CeedChk(ierr); 775 776 if (!delegate) 777 // LCOV_EXCL_START 778 return CeedError(ceed, CEED_ERROR_UNSUPPORTED, 779 "Backend does not implement BasisCreateHdiv"); 780 // LCOV_EXCL_STOP 781 782 ierr = CeedBasisCreateHdiv(delegate, topo, num_comp, num_nodes, 783 num_qpts, interp, div, q_ref, 784 q_weight, basis); CeedChk(ierr); 785 return CEED_ERROR_SUCCESS; 786 } 787 788 if (num_comp < 1) 789 // LCOV_EXCL_START 790 return CeedError(ceed, CEED_ERROR_DIMENSION, 791 "Basis must have at least 1 component"); 792 // LCOV_EXCL_STOP 793 794 if (num_nodes < 1) 795 // LCOV_EXCL_START 796 return CeedError(ceed, CEED_ERROR_DIMENSION, 797 "Basis must have at least 1 node"); 798 // LCOV_EXCL_STOP 799 800 if (num_qpts < 1) 801 // LCOV_EXCL_START 802 return CeedError(ceed, CEED_ERROR_DIMENSION, 803 "Basis must have at least 1 quadrature point"); 804 // LCOV_EXCL_STOP 805 806 ierr = CeedCalloc(1, basis); CeedChk(ierr); 807 808 (*basis)->ceed = ceed; 809 ierr = CeedReference(ceed); CeedChk(ierr); 810 (*basis)->ref_count = 1; 811 (*basis)->tensor_basis = 0; 812 (*basis)->dim = dim; 813 (*basis)->topo = topo; 814 (*basis)->num_comp = num_comp; 815 (*basis)->P = P; 816 (*basis)->Q = Q; 817 (*basis)->Q_comp = dim; 818 (*basis)->basis_space = 2; // 2 for H(div) space 819 ierr = CeedMalloc(Q*dim, &(*basis)->q_ref_1d); CeedChk(ierr); 820 ierr = CeedMalloc(Q, &(*basis)->q_weight_1d); CeedChk(ierr); 821 if (q_ref) memcpy((*basis)->q_ref_1d, q_ref, Q*dim*sizeof(q_ref[0])); 822 if (q_weight) memcpy((*basis)->q_weight_1d, q_weight, Q*sizeof(q_weight[0])); 823 ierr = CeedMalloc(dim*Q*P, &(*basis)->interp); CeedChk(ierr); 824 ierr = CeedMalloc(Q*P, &(*basis)->div); CeedChk(ierr); 825 if (interp) memcpy((*basis)->interp, interp, dim*Q*P*sizeof(interp[0])); 826 if (div) memcpy((*basis)->div, div, Q*P*sizeof(div[0])); 827 ierr = ceed->BasisCreateHdiv(topo, dim, P, Q, interp, div, q_ref, 828 q_weight, *basis); CeedChk(ierr); 829 return CEED_ERROR_SUCCESS; 830 } 831 832 /** 833 @brief Copy the pointer to a CeedBasis. Both pointers should 834 be destroyed with `CeedBasisDestroy()`; 835 Note: If `*basis_copy` is non-NULL, then it is assumed that 836 `*basis_copy` is a pointer to a CeedBasis. This CeedBasis 837 will be destroyed if `*basis_copy` is the only 838 reference to this CeedBasis. 839 840 @param basis CeedBasis to copy reference to 841 @param[out] basis_copy Variable to store copied reference 842 843 @return An error code: 0 - success, otherwise - failure 844 845 @ref User 846 **/ 847 int CeedBasisReferenceCopy(CeedBasis basis, CeedBasis *basis_copy) { 848 int ierr; 849 850 ierr = CeedBasisReference(basis); CeedChk(ierr); 851 ierr = CeedBasisDestroy(basis_copy); CeedChk(ierr); 852 *basis_copy = basis; 853 return CEED_ERROR_SUCCESS; 854 } 855 856 /** 857 @brief View a CeedBasis 858 859 @param basis CeedBasis to view 860 @param stream Stream to view to, e.g., stdout 861 862 @return An error code: 0 - success, otherwise - failure 863 864 @ref User 865 **/ 866 int CeedBasisView(CeedBasis basis, FILE *stream) { 867 int ierr; 868 CeedFESpace FE_space = basis->basis_space; 869 CeedElemTopology topo = basis->topo; 870 // Print FE space and element topology of the basis 871 if (basis->tensor_basis) { 872 fprintf(stream, "CeedBasis (%s on a %s element): dim=%d P=%d Q=%d\n", 873 CeedFESpaces[FE_space], CeedElemTopologies[topo], 874 basis->dim, basis->P_1d, basis->Q_1d); 875 } else { 876 fprintf(stream, "CeedBasis (%s on a %s element): dim=%d P=%d Q=%d\n", 877 CeedFESpaces[FE_space], CeedElemTopologies[topo], 878 basis->dim, basis->P, basis->Q); 879 } 880 // Print quadrature data, interpolation/gradient/divergene/curl of the basis 881 if (basis->tensor_basis) { // tensor basis 882 ierr = CeedScalarView("qref1d", "\t% 12.8f", 1, basis->Q_1d, basis->q_ref_1d, 883 stream); CeedChk(ierr); 884 ierr = CeedScalarView("qweight1d", "\t% 12.8f", 1, basis->Q_1d, 885 basis->q_weight_1d, stream); CeedChk(ierr); 886 ierr = CeedScalarView("interp1d", "\t% 12.8f", basis->Q_1d, basis->P_1d, 887 basis->interp_1d, stream); CeedChk(ierr); 888 ierr = CeedScalarView("grad1d", "\t% 12.8f", basis->Q_1d, basis->P_1d, 889 basis->grad_1d, stream); CeedChk(ierr); 890 } else { // non-tensor basis 891 ierr = CeedScalarView("qref", "\t% 12.8f", 1, basis->Q*basis->dim, 892 basis->q_ref_1d, 893 stream); CeedChk(ierr); 894 ierr = CeedScalarView("qweight", "\t% 12.8f", 1, basis->Q, basis->q_weight_1d, 895 stream); CeedChk(ierr); 896 ierr = CeedScalarView("interp", "\t% 12.8f", basis->Q_comp*basis->Q, basis->P, 897 basis->interp, stream); CeedChk(ierr); 898 if (basis->grad) { 899 ierr = CeedScalarView("grad", "\t% 12.8f", basis->dim*basis->Q, basis->P, 900 basis->grad, stream); CeedChk(ierr); 901 } 902 if (basis->div) { 903 ierr = CeedScalarView("div", "\t% 12.8f", basis->Q, basis->P, 904 basis->div, stream); CeedChk(ierr); 905 } 906 } 907 return CEED_ERROR_SUCCESS; 908 } 909 910 /** 911 @brief Apply basis evaluation from nodes to quadrature points or vice versa 912 913 @param basis CeedBasis to evaluate 914 @param num_elem The number of elements to apply the basis evaluation to; 915 the backend will specify the ordering in 916 CeedElemRestrictionCreateBlocked() 917 @param t_mode \ref CEED_NOTRANSPOSE to evaluate from nodes to quadrature 918 points, \ref CEED_TRANSPOSE to apply the transpose, mapping 919 from quadrature points to nodes 920 @param eval_mode \ref CEED_EVAL_NONE to use values directly, 921 \ref CEED_EVAL_INTERP to use interpolated values, 922 \ref CEED_EVAL_GRAD to use gradients, 923 \ref CEED_EVAL_WEIGHT to use quadrature weights. 924 @param[in] u Input CeedVector 925 @param[out] v Output CeedVector 926 927 @return An error code: 0 - success, otherwise - failure 928 929 @ref User 930 **/ 931 int CeedBasisApply(CeedBasis basis, CeedInt num_elem, CeedTransposeMode t_mode, 932 CeedEvalMode eval_mode, CeedVector u, CeedVector v) { 933 int ierr; 934 CeedSize u_length = 0, v_length; 935 CeedInt dim, num_comp, num_nodes, num_qpts; 936 ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr); 937 ierr = CeedBasisGetNumComponents(basis, &num_comp); CeedChk(ierr); 938 ierr = CeedBasisGetNumNodes(basis, &num_nodes); CeedChk(ierr); 939 ierr = CeedBasisGetNumQuadraturePoints(basis, &num_qpts); CeedChk(ierr); 940 ierr = CeedVectorGetLength(v, &v_length); CeedChk(ierr); 941 if (u) { 942 ierr = CeedVectorGetLength(u, &u_length); CeedChk(ierr); 943 } 944 945 if (!basis->Apply) 946 // LCOV_EXCL_START 947 return CeedError(basis->ceed, CEED_ERROR_UNSUPPORTED, 948 "Backend does not support BasisApply"); 949 // LCOV_EXCL_STOP 950 951 // Check compatibility of topological and geometrical dimensions 952 if ((t_mode == CEED_TRANSPOSE && (v_length%num_nodes != 0 || 953 u_length%num_qpts != 0)) || 954 (t_mode == CEED_NOTRANSPOSE && (u_length%num_nodes != 0 || 955 v_length%num_qpts != 0))) 956 // LCOV_EXCL_START 957 return CeedError(basis->ceed, CEED_ERROR_DIMENSION, 958 "Length of input/output vectors " 959 "incompatible with basis dimensions"); 960 // LCOV_EXCL_STOP 961 962 // Check vector lengths to prevent out of bounds issues 963 bool bad_dims = false; 964 switch (eval_mode) { 965 case CEED_EVAL_NONE: 966 case CEED_EVAL_INTERP: bad_dims = 967 ((t_mode == CEED_TRANSPOSE && (u_length < num_elem*num_comp*num_qpts || 968 v_length < num_elem*num_comp*num_nodes)) || 969 (t_mode == CEED_NOTRANSPOSE && (v_length < num_elem*num_qpts*num_comp || 970 u_length < num_elem*num_comp*num_nodes))); 971 break; 972 case CEED_EVAL_GRAD: bad_dims = 973 ((t_mode == CEED_TRANSPOSE && (u_length < num_elem*num_comp*num_qpts*dim || 974 v_length < num_elem*num_comp*num_nodes)) || 975 (t_mode == CEED_NOTRANSPOSE && (v_length < num_elem*num_qpts*num_comp*dim || 976 u_length < num_elem*num_comp*num_nodes))); 977 break; 978 case CEED_EVAL_WEIGHT: 979 bad_dims = v_length < num_elem*num_qpts; 980 break; 981 // LCOV_EXCL_START 982 case CEED_EVAL_DIV: bad_dims = 983 ((t_mode == CEED_TRANSPOSE && (u_length < num_elem*num_comp*num_qpts || 984 v_length < num_elem*num_comp*num_nodes)) || 985 (t_mode == CEED_NOTRANSPOSE && (v_length < num_elem*num_qpts*num_comp || 986 u_length < num_elem*num_comp*num_nodes))); 987 break; 988 case CEED_EVAL_CURL: bad_dims = 989 ((t_mode == CEED_TRANSPOSE && (u_length < num_elem*num_comp*num_qpts || 990 v_length < num_elem*num_comp*num_nodes)) || 991 (t_mode == CEED_NOTRANSPOSE && (v_length < num_elem*num_qpts*num_comp || 992 u_length < num_elem*num_comp*num_nodes))); 993 break; 994 // LCOV_EXCL_STOP 995 } 996 if (bad_dims) 997 // LCOV_EXCL_START 998 return CeedError(basis->ceed, CEED_ERROR_DIMENSION, 999 "Input/output vectors too short for basis and evaluation mode"); 1000 // LCOV_EXCL_STOP 1001 1002 ierr = basis->Apply(basis, num_elem, t_mode, eval_mode, u, v); CeedChk(ierr); 1003 return CEED_ERROR_SUCCESS; 1004 } 1005 1006 /** 1007 @brief Get Ceed associated with a CeedBasis 1008 1009 @param basis CeedBasis 1010 @param[out] ceed Variable to store Ceed 1011 1012 @return An error code: 0 - success, otherwise - failure 1013 1014 @ref Advanced 1015 **/ 1016 int CeedBasisGetCeed(CeedBasis basis, Ceed *ceed) { 1017 *ceed = basis->ceed; 1018 return CEED_ERROR_SUCCESS; 1019 } 1020 1021 /** 1022 @brief Get dimension for given CeedBasis 1023 1024 @param basis CeedBasis 1025 @param[out] dim Variable to store dimension of basis 1026 1027 @return An error code: 0 - success, otherwise - failure 1028 1029 @ref Advanced 1030 **/ 1031 int CeedBasisGetDimension(CeedBasis basis, CeedInt *dim) { 1032 *dim = basis->dim; 1033 return CEED_ERROR_SUCCESS; 1034 } 1035 1036 /** 1037 @brief Get topology for given CeedBasis 1038 1039 @param basis CeedBasis 1040 @param[out] topo Variable to store topology of basis 1041 1042 @return An error code: 0 - success, otherwise - failure 1043 1044 @ref Advanced 1045 **/ 1046 int CeedBasisGetTopology(CeedBasis basis, CeedElemTopology *topo) { 1047 *topo = basis->topo; 1048 return CEED_ERROR_SUCCESS; 1049 } 1050 1051 /** 1052 @brief Get number of Q-vector components for given CeedBasis 1053 1054 @param basis CeedBasis 1055 @param[out] Q_comp Variable to store number of Q-vector components of basis 1056 1057 @return An error code: 0 - success, otherwise - failure 1058 1059 @ref Advanced 1060 **/ 1061 int CeedBasisGetNumQuadratureComponents(CeedBasis basis, CeedInt *Q_comp) { 1062 *Q_comp = basis->Q_comp; 1063 return CEED_ERROR_SUCCESS; 1064 } 1065 1066 /** 1067 @brief Get number of components for given CeedBasis 1068 1069 @param basis CeedBasis 1070 @param[out] num_comp Variable to store number of components of basis 1071 1072 @return An error code: 0 - success, otherwise - failure 1073 1074 @ref Advanced 1075 **/ 1076 int CeedBasisGetNumComponents(CeedBasis basis, CeedInt *num_comp) { 1077 *num_comp = basis->num_comp; 1078 return CEED_ERROR_SUCCESS; 1079 } 1080 1081 /** 1082 @brief Get total number of nodes (in dim dimensions) of a CeedBasis 1083 1084 @param basis CeedBasis 1085 @param[out] P Variable to store number of nodes 1086 1087 @return An error code: 0 - success, otherwise - failure 1088 1089 @ref Utility 1090 **/ 1091 int CeedBasisGetNumNodes(CeedBasis basis, CeedInt *P) { 1092 *P = basis->P; 1093 return CEED_ERROR_SUCCESS; 1094 } 1095 1096 /** 1097 @brief Get total number of nodes (in 1 dimension) of a CeedBasis 1098 1099 @param basis CeedBasis 1100 @param[out] P_1d Variable to store number of nodes 1101 1102 @return An error code: 0 - success, otherwise - failure 1103 1104 @ref Advanced 1105 **/ 1106 int CeedBasisGetNumNodes1D(CeedBasis basis, CeedInt *P_1d) { 1107 if (!basis->tensor_basis) 1108 // LCOV_EXCL_START 1109 return CeedError(basis->ceed, CEED_ERROR_MINOR, 1110 "Cannot supply P_1d for non-tensor basis"); 1111 // LCOV_EXCL_STOP 1112 1113 *P_1d = basis->P_1d; 1114 return CEED_ERROR_SUCCESS; 1115 } 1116 1117 /** 1118 @brief Get total number of quadrature points (in dim dimensions) of a CeedBasis 1119 1120 @param basis CeedBasis 1121 @param[out] Q Variable to store number of quadrature points 1122 1123 @return An error code: 0 - success, otherwise - failure 1124 1125 @ref Utility 1126 **/ 1127 int CeedBasisGetNumQuadraturePoints(CeedBasis basis, CeedInt *Q) { 1128 *Q = basis->Q; 1129 return CEED_ERROR_SUCCESS; 1130 } 1131 1132 /** 1133 @brief Get total number of quadrature points (in 1 dimension) of a CeedBasis 1134 1135 @param basis CeedBasis 1136 @param[out] Q_1d Variable to store number of quadrature points 1137 1138 @return An error code: 0 - success, otherwise - failure 1139 1140 @ref Advanced 1141 **/ 1142 int CeedBasisGetNumQuadraturePoints1D(CeedBasis basis, CeedInt *Q_1d) { 1143 if (!basis->tensor_basis) 1144 // LCOV_EXCL_START 1145 return CeedError(basis->ceed, CEED_ERROR_MINOR, 1146 "Cannot supply Q_1d for non-tensor basis"); 1147 // LCOV_EXCL_STOP 1148 1149 *Q_1d = basis->Q_1d; 1150 return CEED_ERROR_SUCCESS; 1151 } 1152 1153 /** 1154 @brief Get reference coordinates of quadrature points (in dim dimensions) 1155 of a CeedBasis 1156 1157 @param basis CeedBasis 1158 @param[out] q_ref Variable to store reference coordinates of quadrature points 1159 1160 @return An error code: 0 - success, otherwise - failure 1161 1162 @ref Advanced 1163 **/ 1164 int CeedBasisGetQRef(CeedBasis basis, const CeedScalar **q_ref) { 1165 *q_ref = basis->q_ref_1d; 1166 return CEED_ERROR_SUCCESS; 1167 } 1168 1169 /** 1170 @brief Get quadrature weights of quadrature points (in dim dimensions) 1171 of a CeedBasis 1172 1173 @param basis CeedBasis 1174 @param[out] q_weight Variable to store quadrature weights 1175 1176 @return An error code: 0 - success, otherwise - failure 1177 1178 @ref Advanced 1179 **/ 1180 int CeedBasisGetQWeights(CeedBasis basis, const CeedScalar **q_weight) { 1181 *q_weight = basis->q_weight_1d; 1182 return CEED_ERROR_SUCCESS; 1183 } 1184 1185 /** 1186 @brief Get interpolation matrix of a CeedBasis 1187 1188 @param basis CeedBasis 1189 @param[out] interp Variable to store interpolation matrix 1190 1191 @return An error code: 0 - success, otherwise - failure 1192 1193 @ref Advanced 1194 **/ 1195 int CeedBasisGetInterp(CeedBasis basis, const CeedScalar **interp) { 1196 if (!basis->interp && basis->tensor_basis) { 1197 // Allocate 1198 int ierr; 1199 ierr = CeedMalloc(basis->Q*basis->P, &basis->interp); CeedChk(ierr); 1200 1201 // Initialize 1202 for (CeedInt i=0; i<basis->Q*basis->P; i++) 1203 basis->interp[i] = 1.0; 1204 1205 // Calculate 1206 for (CeedInt d=0; d<basis->dim; d++) 1207 for (CeedInt qpt=0; qpt<basis->Q; qpt++) 1208 for (CeedInt node=0; node<basis->P; node++) { 1209 CeedInt p = (node / CeedIntPow(basis->P_1d, d)) % basis->P_1d; 1210 CeedInt q = (qpt / CeedIntPow(basis->Q_1d, d)) % basis->Q_1d; 1211 basis->interp[qpt*(basis->P)+node] *= basis->interp_1d[q*basis->P_1d+p]; 1212 } 1213 } 1214 *interp = basis->interp; 1215 return CEED_ERROR_SUCCESS; 1216 } 1217 1218 /** 1219 @brief Get 1D interpolation matrix of a tensor product CeedBasis 1220 1221 @param basis CeedBasis 1222 @param[out] interp_1d Variable to store interpolation matrix 1223 1224 @return An error code: 0 - success, otherwise - failure 1225 1226 @ref Backend 1227 **/ 1228 int CeedBasisGetInterp1D(CeedBasis basis, const CeedScalar **interp_1d) { 1229 if (!basis->tensor_basis) 1230 // LCOV_EXCL_START 1231 return CeedError(basis->ceed, CEED_ERROR_MINOR, 1232 "CeedBasis is not a tensor product basis."); 1233 // LCOV_EXCL_STOP 1234 1235 *interp_1d = basis->interp_1d; 1236 return CEED_ERROR_SUCCESS; 1237 } 1238 1239 /** 1240 @brief Get gradient matrix of a CeedBasis 1241 1242 @param basis CeedBasis 1243 @param[out] grad Variable to store gradient matrix 1244 1245 @return An error code: 0 - success, otherwise - failure 1246 1247 @ref Advanced 1248 **/ 1249 int CeedBasisGetGrad(CeedBasis basis, const CeedScalar **grad) { 1250 if (!basis->grad && basis->tensor_basis) { 1251 // Allocate 1252 int ierr; 1253 ierr = CeedMalloc(basis->dim*basis->Q*basis->P, &basis->grad); 1254 CeedChk(ierr); 1255 1256 // Initialize 1257 for (CeedInt i=0; i<basis->dim*basis->Q*basis->P; i++) 1258 basis->grad[i] = 1.0; 1259 1260 // Calculate 1261 for (CeedInt d=0; d<basis->dim; d++) 1262 for (CeedInt i=0; i<basis->dim; i++) 1263 for (CeedInt qpt=0; qpt<basis->Q; qpt++) 1264 for (CeedInt node=0; node<basis->P; node++) { 1265 CeedInt p = (node / CeedIntPow(basis->P_1d, d)) % basis->P_1d; 1266 CeedInt q = (qpt / CeedIntPow(basis->Q_1d, d)) % basis->Q_1d; 1267 if (i == d) 1268 basis->grad[(i*basis->Q+qpt)*(basis->P)+node] *= 1269 basis->grad_1d[q*basis->P_1d+p]; 1270 else 1271 basis->grad[(i*basis->Q+qpt)*(basis->P)+node] *= 1272 basis->interp_1d[q*basis->P_1d+p]; 1273 } 1274 } 1275 *grad = basis->grad; 1276 return CEED_ERROR_SUCCESS; 1277 } 1278 1279 /** 1280 @brief Get 1D gradient matrix of a tensor product CeedBasis 1281 1282 @param basis CeedBasis 1283 @param[out] grad_1d Variable to store gradient matrix 1284 1285 @return An error code: 0 - success, otherwise - failure 1286 1287 @ref Advanced 1288 **/ 1289 int CeedBasisGetGrad1D(CeedBasis basis, const CeedScalar **grad_1d) { 1290 if (!basis->tensor_basis) 1291 // LCOV_EXCL_START 1292 return CeedError(basis->ceed, CEED_ERROR_MINOR, 1293 "CeedBasis is not a tensor product basis."); 1294 // LCOV_EXCL_STOP 1295 1296 *grad_1d = basis->grad_1d; 1297 return CEED_ERROR_SUCCESS; 1298 } 1299 1300 /** 1301 @brief Get divergence matrix of a CeedBasis 1302 1303 @param basis CeedBasis 1304 @param[out] div Variable to store divergence matrix 1305 1306 @return An error code: 0 - success, otherwise - failure 1307 1308 @ref Advanced 1309 **/ 1310 int CeedBasisGetDiv(CeedBasis basis, const CeedScalar **div) { 1311 if (!basis->div) 1312 // LCOV_EXCL_START 1313 return CeedError(basis->ceed, CEED_ERROR_MINOR, 1314 "CeedBasis does not have divergence matrix."); 1315 // LCOV_EXCL_STOP 1316 1317 *div = basis->div; 1318 return CEED_ERROR_SUCCESS; 1319 } 1320 1321 /** 1322 @brief Destroy a CeedBasis 1323 1324 @param basis CeedBasis to destroy 1325 1326 @return An error code: 0 - success, otherwise - failure 1327 1328 @ref User 1329 **/ 1330 int CeedBasisDestroy(CeedBasis *basis) { 1331 int ierr; 1332 1333 if (!*basis || --(*basis)->ref_count > 0) return CEED_ERROR_SUCCESS; 1334 if ((*basis)->Destroy) { 1335 ierr = (*basis)->Destroy(*basis); CeedChk(ierr); 1336 } 1337 if ((*basis)->contract) { 1338 ierr = CeedTensorContractDestroy(&(*basis)->contract); CeedChk(ierr); 1339 } 1340 ierr = CeedFree(&(*basis)->interp); CeedChk(ierr); 1341 ierr = CeedFree(&(*basis)->interp_1d); CeedChk(ierr); 1342 ierr = CeedFree(&(*basis)->grad); CeedChk(ierr); 1343 ierr = CeedFree(&(*basis)->div); CeedChk(ierr); 1344 ierr = CeedFree(&(*basis)->grad_1d); CeedChk(ierr); 1345 ierr = CeedFree(&(*basis)->q_ref_1d); CeedChk(ierr); 1346 ierr = CeedFree(&(*basis)->q_weight_1d); CeedChk(ierr); 1347 ierr = CeedDestroy(&(*basis)->ceed); CeedChk(ierr); 1348 ierr = CeedFree(basis); CeedChk(ierr); 1349 return CEED_ERROR_SUCCESS; 1350 } 1351 1352 /** 1353 @brief Construct a Gauss-Legendre quadrature 1354 1355 @param Q Number of quadrature points (integrates polynomials of 1356 degree 2*Q-1 exactly) 1357 @param[out] q_ref_1d Array of length Q to hold the abscissa on [-1, 1] 1358 @param[out] q_weight_1d Array of length Q to hold the weights 1359 1360 @return An error code: 0 - success, otherwise - failure 1361 1362 @ref Utility 1363 **/ 1364 int CeedGaussQuadrature(CeedInt Q, CeedScalar *q_ref_1d, 1365 CeedScalar *q_weight_1d) { 1366 // Allocate 1367 CeedScalar P0, P1, P2, dP2, xi, wi, PI = 4.0*atan(1.0); 1368 // Build q_ref_1d, q_weight_1d 1369 for (CeedInt i = 0; i <= Q/2; i++) { 1370 // Guess 1371 xi = cos(PI*(CeedScalar)(2*i+1)/((CeedScalar)(2*Q))); 1372 // Pn(xi) 1373 P0 = 1.0; 1374 P1 = xi; 1375 P2 = 0.0; 1376 for (CeedInt j = 2; j <= Q; j++) { 1377 P2 = (((CeedScalar)(2*j-1))*xi*P1-((CeedScalar)(j-1))*P0)/((CeedScalar)(j)); 1378 P0 = P1; 1379 P1 = P2; 1380 } 1381 // First Newton Step 1382 dP2 = (xi*P2 - P0)*(CeedScalar)Q/(xi*xi-1.0); 1383 xi = xi-P2/dP2; 1384 // Newton to convergence 1385 for (CeedInt k=0; k<100 && fabs(P2)>10*CEED_EPSILON; k++) { 1386 P0 = 1.0; 1387 P1 = xi; 1388 for (CeedInt j = 2; j <= Q; j++) { 1389 P2 = (((CeedScalar)(2*j-1))*xi*P1-((CeedScalar)(j-1))*P0)/((CeedScalar)(j)); 1390 P0 = P1; 1391 P1 = P2; 1392 } 1393 dP2 = (xi*P2 - P0)*(CeedScalar)Q/(xi*xi-1.0); 1394 xi = xi-P2/dP2; 1395 } 1396 // Save xi, wi 1397 wi = 2.0/((1.0-xi*xi)*dP2*dP2); 1398 q_weight_1d[i] = wi; 1399 q_weight_1d[Q-1-i] = wi; 1400 q_ref_1d[i] = -xi; 1401 q_ref_1d[Q-1-i]= xi; 1402 } 1403 return CEED_ERROR_SUCCESS; 1404 } 1405 1406 /** 1407 @brief Construct a Gauss-Legendre-Lobatto quadrature 1408 1409 @param Q Number of quadrature points (integrates polynomials of 1410 degree 2*Q-3 exactly) 1411 @param[out] q_ref_1d Array of length Q to hold the abscissa on [-1, 1] 1412 @param[out] q_weight_1d Array of length Q to hold the weights 1413 1414 @return An error code: 0 - success, otherwise - failure 1415 1416 @ref Utility 1417 **/ 1418 int CeedLobattoQuadrature(CeedInt Q, CeedScalar *q_ref_1d, 1419 CeedScalar *q_weight_1d) { 1420 // Allocate 1421 CeedScalar P0, P1, P2, dP2, d2P2, xi, wi, PI = 4.0*atan(1.0); 1422 // Build q_ref_1d, q_weight_1d 1423 // Set endpoints 1424 if (Q < 2) 1425 // LCOV_EXCL_START 1426 return CeedError(NULL, CEED_ERROR_DIMENSION, 1427 "Cannot create Lobatto quadrature with Q=%d < 2 points", Q); 1428 // LCOV_EXCL_STOP 1429 wi = 2.0/((CeedScalar)(Q*(Q-1))); 1430 if (q_weight_1d) { 1431 q_weight_1d[0] = wi; 1432 q_weight_1d[Q-1] = wi; 1433 } 1434 q_ref_1d[0] = -1.0; 1435 q_ref_1d[Q-1] = 1.0; 1436 // Interior 1437 for (CeedInt i = 1; i <= (Q-1)/2; i++) { 1438 // Guess 1439 xi = cos(PI*(CeedScalar)(i)/(CeedScalar)(Q-1)); 1440 // Pn(xi) 1441 P0 = 1.0; 1442 P1 = xi; 1443 P2 = 0.0; 1444 for (CeedInt j = 2; j < Q; j++) { 1445 P2 = (((CeedScalar)(2*j-1))*xi*P1-((CeedScalar)(j-1))*P0)/((CeedScalar)(j)); 1446 P0 = P1; 1447 P1 = P2; 1448 } 1449 // First Newton step 1450 dP2 = (xi*P2 - P0)*(CeedScalar)Q/(xi*xi-1.0); 1451 d2P2 = (2*xi*dP2 - (CeedScalar)(Q*(Q-1))*P2)/(1.0-xi*xi); 1452 xi = xi-dP2/d2P2; 1453 // Newton to convergence 1454 for (CeedInt k=0; k<100 && fabs(dP2)>10*CEED_EPSILON; k++) { 1455 P0 = 1.0; 1456 P1 = xi; 1457 for (CeedInt j = 2; j < Q; j++) { 1458 P2 = (((CeedScalar)(2*j-1))*xi*P1-((CeedScalar)(j-1))*P0)/((CeedScalar)(j)); 1459 P0 = P1; 1460 P1 = P2; 1461 } 1462 dP2 = (xi*P2 - P0)*(CeedScalar)Q/(xi*xi-1.0); 1463 d2P2 = (2*xi*dP2 - (CeedScalar)(Q*(Q-1))*P2)/(1.0-xi*xi); 1464 xi = xi-dP2/d2P2; 1465 } 1466 // Save xi, wi 1467 wi = 2.0/(((CeedScalar)(Q*(Q-1)))*P2*P2); 1468 if (q_weight_1d) { 1469 q_weight_1d[i] = wi; 1470 q_weight_1d[Q-1-i] = wi; 1471 } 1472 q_ref_1d[i] = -xi; 1473 q_ref_1d[Q-1-i]= xi; 1474 } 1475 return CEED_ERROR_SUCCESS; 1476 } 1477 1478 /** 1479 @brief Return QR Factorization of a matrix 1480 1481 @param ceed A Ceed context for error handling 1482 @param[in,out] mat Row-major matrix to be factorized in place 1483 @param[in,out] tau Vector of length m of scaling factors 1484 @param m Number of rows 1485 @param n Number of columns 1486 1487 @return An error code: 0 - success, otherwise - failure 1488 1489 @ref Utility 1490 **/ 1491 int CeedQRFactorization(Ceed ceed, CeedScalar *mat, CeedScalar *tau, 1492 CeedInt m, CeedInt n) { 1493 CeedScalar v[m]; 1494 1495 // Check m >= n 1496 if (n > m) 1497 // LCOV_EXCL_START 1498 return CeedError(ceed, CEED_ERROR_UNSUPPORTED, 1499 "Cannot compute QR factorization with n > m"); 1500 // LCOV_EXCL_STOP 1501 1502 for (CeedInt i=0; i<n; i++) { 1503 if (i >= m-1) { // last row of matrix, no reflection needed 1504 tau[i] = 0.; 1505 break; 1506 } 1507 // Calculate Householder vector, magnitude 1508 CeedScalar sigma = 0.0; 1509 v[i] = mat[i+n*i]; 1510 for (CeedInt j=i+1; j<m; j++) { 1511 v[j] = mat[i+n*j]; 1512 sigma += v[j] * v[j]; 1513 } 1514 CeedScalar norm = sqrt(v[i]*v[i] + sigma); // norm of v[i:m] 1515 CeedScalar R_ii = -copysign(norm, v[i]); 1516 v[i] -= R_ii; 1517 // norm of v[i:m] after modification above and scaling below 1518 // norm = sqrt(v[i]*v[i] + sigma) / v[i]; 1519 // tau = 2 / (norm*norm) 1520 tau[i] = 2 * v[i]*v[i] / (v[i]*v[i] + sigma); 1521 for (CeedInt j=i+1; j<m; j++) 1522 v[j] /= v[i]; 1523 1524 // Apply Householder reflector to lower right panel 1525 CeedHouseholderReflect(&mat[i*n+i+1], &v[i], tau[i], m-i, n-i-1, n, 1); 1526 // Save v 1527 mat[i+n*i] = R_ii; 1528 for (CeedInt j=i+1; j<m; j++) 1529 mat[i+n*j] = v[j]; 1530 } 1531 return CEED_ERROR_SUCCESS; 1532 } 1533 1534 /** 1535 @brief Return symmetric Schur decomposition of the symmetric matrix mat via 1536 symmetric QR factorization 1537 1538 @param ceed A Ceed context for error handling 1539 @param[in,out] mat Row-major matrix to be factorized in place 1540 @param[out] lambda Vector of length n of eigenvalues 1541 @param n Number of rows/columns 1542 1543 @return An error code: 0 - success, otherwise - failure 1544 1545 @ref Utility 1546 **/ 1547 CeedPragmaOptimizeOff 1548 int CeedSymmetricSchurDecomposition(Ceed ceed, CeedScalar *mat, 1549 CeedScalar *lambda, CeedInt n) { 1550 // Check bounds for clang-tidy 1551 if (n<2) 1552 // LCOV_EXCL_START 1553 return CeedError(ceed, CEED_ERROR_UNSUPPORTED, 1554 "Cannot compute symmetric Schur decomposition of scalars"); 1555 // LCOV_EXCL_STOP 1556 1557 CeedScalar v[n-1], tau[n-1], mat_T[n*n]; 1558 1559 // Copy mat to mat_T and set mat to I 1560 memcpy(mat_T, mat, n*n*sizeof(mat[0])); 1561 for (CeedInt i=0; i<n; i++) 1562 for (CeedInt j=0; j<n; j++) 1563 mat[j+n*i] = (i==j) ? 1 : 0; 1564 1565 // Reduce to tridiagonal 1566 for (CeedInt i=0; i<n-1; i++) { 1567 // Calculate Householder vector, magnitude 1568 CeedScalar sigma = 0.0; 1569 v[i] = mat_T[i+n*(i+1)]; 1570 for (CeedInt j=i+1; j<n-1; j++) { 1571 v[j] = mat_T[i+n*(j+1)]; 1572 sigma += v[j] * v[j]; 1573 } 1574 CeedScalar norm = sqrt(v[i]*v[i] + sigma); // norm of v[i:n-1] 1575 CeedScalar R_ii = -copysign(norm, v[i]); 1576 v[i] -= R_ii; 1577 // norm of v[i:m] after modification above and scaling below 1578 // norm = sqrt(v[i]*v[i] + sigma) / v[i]; 1579 // tau = 2 / (norm*norm) 1580 tau[i] = i == n - 2 ? 2 : 2 * v[i]*v[i] / (v[i]*v[i] + sigma); 1581 for (CeedInt j=i+1; j<n-1; j++) 1582 v[j] /= v[i]; 1583 1584 // Update sub and super diagonal 1585 for (CeedInt j=i+2; j<n; j++) { 1586 mat_T[i+n*j] = 0; mat_T[j+n*i] = 0; 1587 } 1588 // Apply symmetric Householder reflector to lower right panel 1589 CeedHouseholderReflect(&mat_T[(i+1)+n*(i+1)], &v[i], tau[i], 1590 n-(i+1), n-(i+1), n, 1); 1591 CeedHouseholderReflect(&mat_T[(i+1)+n*(i+1)], &v[i], tau[i], 1592 n-(i+1), n-(i+1), 1, n); 1593 1594 // Save v 1595 mat_T[i+n*(i+1)] = R_ii; 1596 mat_T[(i+1)+n*i] = R_ii; 1597 for (CeedInt j=i+1; j<n-1; j++) { 1598 mat_T[i+n*(j+1)] = v[j]; 1599 } 1600 } 1601 // Backwards accumulation of Q 1602 for (CeedInt i=n-2; i>=0; i--) { 1603 if (tau[i] > 0.0) { 1604 v[i] = 1; 1605 for (CeedInt j=i+1; j<n-1; j++) { 1606 v[j] = mat_T[i+n*(j+1)]; 1607 mat_T[i+n*(j+1)] = 0; 1608 } 1609 CeedHouseholderReflect(&mat[(i+1)+n*(i+1)], &v[i], tau[i], 1610 n-(i+1), n-(i+1), n, 1); 1611 } 1612 } 1613 1614 // Reduce sub and super diagonal 1615 CeedInt p = 0, q = 0, itr = 0, max_itr = n*n*n*n; 1616 CeedScalar tol = CEED_EPSILON; 1617 1618 while (itr < max_itr) { 1619 // Update p, q, size of reduced portions of diagonal 1620 p = 0; q = 0; 1621 for (CeedInt i=n-2; i>=0; i--) { 1622 if (fabs(mat_T[i+n*(i+1)]) < tol) 1623 q += 1; 1624 else 1625 break; 1626 } 1627 for (CeedInt i=0; i<n-q-1; i++) { 1628 if (fabs(mat_T[i+n*(i+1)]) < tol) 1629 p += 1; 1630 else 1631 break; 1632 } 1633 if (q == n-1) break; // Finished reducing 1634 1635 // Reduce tridiagonal portion 1636 CeedScalar t_nn = mat_T[(n-1-q)+n*(n-1-q)], 1637 t_nnm1 = mat_T[(n-2-q)+n*(n-1-q)]; 1638 CeedScalar d = (mat_T[(n-2-q)+n*(n-2-q)] - t_nn)/2; 1639 CeedScalar mu = t_nn - t_nnm1*t_nnm1 / 1640 (d + copysign(sqrt(d*d + t_nnm1*t_nnm1), d)); 1641 CeedScalar x = mat_T[p+n*p] - mu; 1642 CeedScalar z = mat_T[p+n*(p+1)]; 1643 for (CeedInt k=p; k<n-q-1; k++) { 1644 // Compute Givens rotation 1645 CeedScalar c = 1, s = 0; 1646 if (fabs(z) > tol) { 1647 if (fabs(z) > fabs(x)) { 1648 CeedScalar tau = -x/z; 1649 s = 1/sqrt(1+tau*tau), c = s*tau; 1650 } else { 1651 CeedScalar tau = -z/x; 1652 c = 1/sqrt(1+tau*tau), s = c*tau; 1653 } 1654 } 1655 1656 // Apply Givens rotation to T 1657 CeedGivensRotation(mat_T, c, s, CEED_NOTRANSPOSE, k, k+1, n, n); 1658 CeedGivensRotation(mat_T, c, s, CEED_TRANSPOSE, k, k+1, n, n); 1659 1660 // Apply Givens rotation to Q 1661 CeedGivensRotation(mat, c, s, CEED_NOTRANSPOSE, k, k+1, n, n); 1662 1663 // Update x, z 1664 if (k < n-q-2) { 1665 x = mat_T[k+n*(k+1)]; 1666 z = mat_T[k+n*(k+2)]; 1667 } 1668 } 1669 itr++; 1670 } 1671 1672 // Save eigenvalues 1673 for (CeedInt i=0; i<n; i++) 1674 lambda[i] = mat_T[i+n*i]; 1675 1676 // Check convergence 1677 if (itr == max_itr && q < n-1) 1678 // LCOV_EXCL_START 1679 return CeedError(ceed, CEED_ERROR_MINOR, 1680 "Symmetric QR failed to converge"); 1681 // LCOV_EXCL_STOP 1682 return CEED_ERROR_SUCCESS; 1683 } 1684 CeedPragmaOptimizeOn 1685 1686 /** 1687 @brief Return Simultaneous Diagonalization of two matrices. This solves the 1688 generalized eigenvalue problem A x = lambda B x, where A and B 1689 are symmetric and B is positive definite. We generate the matrix X 1690 and vector Lambda such that X^T A X = Lambda and X^T B X = I. This 1691 is equivalent to the LAPACK routine 'sygv' with TYPE = 1. 1692 1693 @param ceed A Ceed context for error handling 1694 @param[in] mat_A Row-major matrix to be factorized with eigenvalues 1695 @param[in] mat_B Row-major matrix to be factorized to identity 1696 @param[out] mat_X Row-major orthogonal matrix 1697 @param[out] lambda Vector of length n of generalized eigenvalues 1698 @param n Number of rows/columns 1699 1700 @return An error code: 0 - success, otherwise - failure 1701 1702 @ref Utility 1703 **/ 1704 CeedPragmaOptimizeOff 1705 int CeedSimultaneousDiagonalization(Ceed ceed, CeedScalar *mat_A, 1706 CeedScalar *mat_B, CeedScalar *mat_X, 1707 CeedScalar *lambda, CeedInt n) { 1708 int ierr; 1709 CeedScalar *mat_C, *mat_G, *vec_D; 1710 ierr = CeedCalloc(n*n, &mat_C); CeedChk(ierr); 1711 ierr = CeedCalloc(n*n, &mat_G); CeedChk(ierr); 1712 ierr = CeedCalloc(n, &vec_D); CeedChk(ierr); 1713 1714 // Compute B = G D G^T 1715 memcpy(mat_G, mat_B, n*n*sizeof(mat_B[0])); 1716 ierr = CeedSymmetricSchurDecomposition(ceed, mat_G, vec_D, n); CeedChk(ierr); 1717 1718 // Sort eigenvalues 1719 for (CeedInt i=n-1; i>=0; i--) 1720 for (CeedInt j=0; j<i; j++) { 1721 if (fabs(vec_D[j]) > fabs(vec_D[j+1])) { 1722 CeedScalar temp; 1723 temp = vec_D[j]; vec_D[j] = vec_D[j+1]; vec_D[j+1] = temp; 1724 for (CeedInt k=0; k<n; k++) { 1725 temp = mat_G[k*n+j]; mat_G[k*n+j] = mat_G[k*n+j+1]; mat_G[k*n+j+1] = temp; 1726 } 1727 } 1728 } 1729 1730 // Compute C = (G D^1/2)^-1 A (G D^1/2)^-T 1731 // = D^-1/2 G^T A G D^-1/2 1732 // -- D = D^-1/2 1733 for (CeedInt i=0; i<n; i++) 1734 vec_D[i] = 1./sqrt(vec_D[i]); 1735 // -- G = G D^-1/2 1736 // -- C = D^-1/2 G^T 1737 for (CeedInt i=0; i<n; i++) 1738 for (CeedInt j=0; j<n; j++) { 1739 mat_G[i*n+j] *= vec_D[j]; 1740 mat_C[j*n+i] = mat_G[i*n+j]; 1741 } 1742 // -- X = (D^-1/2 G^T) A 1743 ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)mat_C, 1744 (const CeedScalar *)mat_A, mat_X, n, n, n); 1745 CeedChk(ierr); 1746 // -- C = (D^-1/2 G^T A) (G D^-1/2) 1747 ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)mat_X, 1748 (const CeedScalar *)mat_G, mat_C, n, n, n); 1749 CeedChk(ierr); 1750 1751 // Compute Q^T C Q = lambda 1752 ierr = CeedSymmetricSchurDecomposition(ceed, mat_C, lambda, n); CeedChk(ierr); 1753 1754 // Sort eigenvalues 1755 for (CeedInt i=n-1; i>=0; i--) 1756 for (CeedInt j=0; j<i; j++) { 1757 if (fabs(lambda[j]) > fabs(lambda[j+1])) { 1758 CeedScalar temp; 1759 temp = lambda[j]; lambda[j] = lambda[j+1]; lambda[j+1] = temp; 1760 for (CeedInt k=0; k<n; k++) { 1761 temp = mat_C[k*n+j]; mat_C[k*n+j] = mat_C[k*n+j+1]; mat_C[k*n+j+1] = temp; 1762 } 1763 } 1764 } 1765 1766 // Set X = (G D^1/2)^-T Q 1767 // = G D^-1/2 Q 1768 ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)mat_G, 1769 (const CeedScalar *)mat_C, mat_X, n, n, n); 1770 CeedChk(ierr); 1771 1772 // Cleanup 1773 ierr = CeedFree(&mat_C); CeedChk(ierr); 1774 ierr = CeedFree(&mat_G); CeedChk(ierr); 1775 ierr = CeedFree(&vec_D); CeedChk(ierr); 1776 return CEED_ERROR_SUCCESS; 1777 } 1778 CeedPragmaOptimizeOn 1779 1780 /// @} 1781