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 bool are_both_tensor; 198 CeedInt Q, Q_to, Q_from, P_to, P_from; 199 200 // Check for compatible quadrature spaces 201 CeedCall(CeedBasisGetNumQuadraturePoints(basis_to, &Q_to)); 202 CeedCall(CeedBasisGetNumQuadraturePoints(basis_from, &Q_from)); 203 CeedCheck(Q_to == Q_from, CeedBasisReturnCeed(basis_to), CEED_ERROR_DIMENSION, 204 "Bases must have compatible quadrature spaces." 205 " 'basis_from' has %" CeedInt_FMT " points and 'basis_to' has %" CeedInt_FMT, 206 Q_from, Q_to); 207 Q = Q_to; 208 209 // Check for matching tensor or non-tensor 210 { 211 bool is_tensor_to, is_tensor_from; 212 213 CeedCall(CeedBasisIsTensor(basis_to, &is_tensor_to)); 214 CeedCall(CeedBasisIsTensor(basis_from, &is_tensor_from)); 215 are_both_tensor = is_tensor_to && is_tensor_from; 216 } 217 if (are_both_tensor) { 218 CeedCall(CeedBasisGetNumNodes1D(basis_to, &P_to)); 219 CeedCall(CeedBasisGetNumNodes1D(basis_from, &P_from)); 220 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis_from, &Q)); 221 } else { 222 CeedCall(CeedBasisGetNumNodes(basis_to, &P_to)); 223 CeedCall(CeedBasisGetNumNodes(basis_from, &P_from)); 224 } 225 226 // Check for matching FE space 227 CeedFESpace fe_space_to, fe_space_from; 228 229 CeedCall(CeedBasisGetFESpace(basis_to, &fe_space_to)); 230 CeedCall(CeedBasisGetFESpace(basis_from, &fe_space_from)); 231 CeedCheck(fe_space_to == fe_space_from, CeedBasisReturnCeed(basis_to), CEED_ERROR_MINOR, 232 "Bases must both be the same FE space type." 233 " 'basis_from' is a %s and 'basis_to' is a %s", 234 CeedFESpaces[fe_space_from], CeedFESpaces[fe_space_to]); 235 236 // Get source matrices 237 CeedInt dim, q_comp = 1; 238 CeedScalar *interp_to_inv, *interp_from; 239 const CeedScalar *interp_to_source = NULL, *interp_from_source = NULL, *grad_from_source = NULL; 240 241 CeedCall(CeedBasisGetDimension(basis_from, &dim)); 242 if (are_both_tensor) { 243 CeedCall(CeedBasisGetInterp1D(basis_to, &interp_to_source)); 244 CeedCall(CeedBasisGetInterp1D(basis_from, &interp_from_source)); 245 } else { 246 CeedCall(CeedBasisGetNumQuadratureComponents(basis_from, CEED_EVAL_INTERP, &q_comp)); 247 CeedCall(CeedBasisGetInterp(basis_to, &interp_to_source)); 248 CeedCall(CeedBasisGetInterp(basis_from, &interp_from_source)); 249 } 250 CeedCall(CeedMalloc(Q * P_from * q_comp, &interp_from)); 251 CeedCall(CeedCalloc(P_to * P_from, interp_project)); 252 253 // `grad_project = interp_to^+ * grad_from` is computed for the H^1 space case so the 254 // projection basis will have a gradient operation (allocated even if not H^1 for the 255 // basis construction later on) 256 if (fe_space_to == CEED_FE_SPACE_H1) { 257 if (are_both_tensor) { 258 CeedCall(CeedBasisGetGrad1D(basis_from, &grad_from_source)); 259 } else { 260 CeedCall(CeedBasisGetGrad(basis_from, &grad_from_source)); 261 } 262 } 263 CeedCall(CeedCalloc(P_to * P_from * (are_both_tensor ? 1 : dim), grad_project)); 264 265 // Compute interp_to^+, pseudoinverse of interp_to 266 CeedCall(CeedCalloc(Q * q_comp * P_to, &interp_to_inv)); 267 CeedCall(CeedMatrixPseudoinverse(CeedBasisReturnCeed(basis_to), interp_to_source, Q * q_comp, P_to, interp_to_inv)); 268 // Build matrices 269 CeedInt num_matrices = 1 + (fe_space_to == CEED_FE_SPACE_H1) * (are_both_tensor ? 1 : dim); 270 CeedScalar *input_from[num_matrices], *output_project[num_matrices]; 271 272 input_from[0] = (CeedScalar *)interp_from_source; 273 output_project[0] = *interp_project; 274 for (CeedInt m = 1; m < num_matrices; m++) { 275 input_from[m] = (CeedScalar *)&grad_from_source[(m - 1) * Q * P_from]; 276 output_project[m] = &((*grad_project)[(m - 1) * P_to * P_from]); 277 } 278 for (CeedInt m = 0; m < num_matrices; m++) { 279 // output_project = interp_to^+ * interp_from 280 memcpy(interp_from, input_from[m], Q * P_from * q_comp * sizeof(input_from[m][0])); 281 CeedCall(CeedMatrixMatrixMultiply(CeedBasisReturnCeed(basis_to), interp_to_inv, input_from[m], output_project[m], P_to, P_from, Q * q_comp)); 282 // Round zero to machine precision 283 for (CeedInt i = 0; i < P_to * P_from; i++) { 284 if (fabs(output_project[m][i]) < 10 * CEED_EPSILON) output_project[m][i] = 0.0; 285 } 286 } 287 288 // Cleanup 289 CeedCall(CeedFree(&interp_to_inv)); 290 CeedCall(CeedFree(&interp_from)); 291 return CEED_ERROR_SUCCESS; 292 } 293 294 /** 295 @brief Check input vector dimensions for CeedBasisApply[Add]AtPoints 296 297 @param[in] basis `CeedBasis` to evaluate 298 @param[in] num_elem The number of elements to apply the basis evaluation to; 299 the backend will specify the ordering in @ref CeedElemRestrictionCreate() 300 @param[in] num_points Array of the number of points to apply the basis evaluation to in each element, size `num_elem` 301 @param[in] t_mode @ref CEED_NOTRANSPOSE to evaluate from nodes to points; 302 @ref CEED_TRANSPOSE to apply the transpose, mapping from points to nodes 303 @param[in] eval_mode @ref CEED_EVAL_INTERP to use interpolated values, 304 @ref CEED_EVAL_GRAD to use gradients, 305 @ref CEED_EVAL_WEIGHT to use quadrature weights 306 @param[in] x_ref `CeedVector` holding reference coordinates of each point 307 @param[in] u Input `CeedVector`, of length `num_nodes * num_comp` for @ref CEED_NOTRANSPOSE 308 @param[out] v Output `CeedVector`, of length `num_points * num_q_comp` for @ref CEED_NOTRANSPOSE with @ref CEED_EVAL_INTERP 309 310 @return An error code: 0 - success, otherwise - failure 311 312 @ref Developer 313 **/ 314 static int CeedBasisApplyAtPointsCheckDims(CeedBasis basis, CeedInt num_elem, const CeedInt *num_points, CeedTransposeMode t_mode, 315 CeedEvalMode eval_mode, CeedVector x_ref, CeedVector u, CeedVector v) { 316 CeedInt dim, num_comp, num_q_comp, num_nodes, P_1d = 1, Q_1d = 1, total_num_points = 0; 317 CeedSize x_length = 0, u_length = 0, v_length; 318 319 CeedCall(CeedBasisGetDimension(basis, &dim)); 320 CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d)); 321 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d)); 322 CeedCall(CeedBasisGetNumComponents(basis, &num_comp)); 323 CeedCall(CeedBasisGetNumQuadratureComponents(basis, eval_mode, &num_q_comp)); 324 CeedCall(CeedBasisGetNumNodes(basis, &num_nodes)); 325 CeedCall(CeedVectorGetLength(v, &v_length)); 326 if (x_ref != CEED_VECTOR_NONE) CeedCall(CeedVectorGetLength(x_ref, &x_length)); 327 if (u != CEED_VECTOR_NONE) CeedCall(CeedVectorGetLength(u, &u_length)); 328 329 // Check compatibility coordinates vector 330 for (CeedInt i = 0; i < num_elem; i++) total_num_points += num_points[i]; 331 CeedCheck((x_length >= (CeedSize)total_num_points * (CeedSize)dim) || (eval_mode == CEED_EVAL_WEIGHT), CeedBasisReturnCeed(basis), 332 CEED_ERROR_DIMENSION, 333 "Length of reference coordinate vector incompatible with basis dimension and number of points." 334 " Found reference coordinate vector of length %" CeedSize_FMT ", not of length %" CeedSize_FMT ".", 335 x_length, (CeedSize)total_num_points * (CeedSize)dim); 336 337 // Check CEED_EVAL_WEIGHT only on CEED_NOTRANSPOSE 338 CeedCheck(eval_mode != CEED_EVAL_WEIGHT || t_mode == CEED_NOTRANSPOSE, CeedBasisReturnCeed(basis), CEED_ERROR_UNSUPPORTED, 339 "CEED_EVAL_WEIGHT only supported with CEED_NOTRANSPOSE"); 340 341 // Check vector lengths to prevent out of bounds issues 342 bool has_good_dims = true; 343 switch (eval_mode) { 344 case CEED_EVAL_INTERP: 345 has_good_dims = ((t_mode == CEED_TRANSPOSE && (u_length >= (CeedSize)total_num_points * (CeedSize)num_q_comp || 346 v_length >= (CeedSize)num_elem * (CeedSize)num_nodes * (CeedSize)num_comp)) || 347 (t_mode == CEED_NOTRANSPOSE && (v_length >= (CeedSize)total_num_points * (CeedSize)num_q_comp || 348 u_length >= (CeedSize)num_elem * (CeedSize)num_nodes * (CeedSize)num_comp))); 349 break; 350 case CEED_EVAL_GRAD: 351 has_good_dims = ((t_mode == CEED_TRANSPOSE && (u_length >= (CeedSize)total_num_points * (CeedSize)num_q_comp * (CeedSize)dim || 352 v_length >= (CeedSize)num_elem * (CeedSize)num_nodes * (CeedSize)num_comp)) || 353 (t_mode == CEED_NOTRANSPOSE && (v_length >= (CeedSize)total_num_points * (CeedSize)num_q_comp * (CeedSize)dim || 354 u_length >= (CeedSize)num_elem * (CeedSize)num_nodes * (CeedSize)num_comp))); 355 break; 356 case CEED_EVAL_WEIGHT: 357 has_good_dims = t_mode == CEED_NOTRANSPOSE && (v_length >= total_num_points); 358 break; 359 // LCOV_EXCL_START 360 case CEED_EVAL_NONE: 361 case CEED_EVAL_DIV: 362 case CEED_EVAL_CURL: 363 return CeedError(CeedBasisReturnCeed(basis), CEED_ERROR_UNSUPPORTED, "Evaluation at arbitrary points not supported for %s", 364 CeedEvalModes[eval_mode]); 365 // LCOV_EXCL_STOP 366 } 367 CeedCheck(has_good_dims, CeedBasisReturnCeed(basis), CEED_ERROR_DIMENSION, "Input/output vectors too short for basis and evaluation mode"); 368 return CEED_ERROR_SUCCESS; 369 } 370 371 /** 372 @brief Default implimentation to apply basis evaluation from nodes to arbitrary points 373 374 @param[in] basis `CeedBasis` to evaluate 375 @param[in] apply_add Sum result into target vector or overwrite 376 @param[in] num_elem The number of elements to apply the basis evaluation to; 377 the backend will specify the ordering in @ref CeedElemRestrictionCreate() 378 @param[in] num_points Array of the number of points to apply the basis evaluation to in each element, size `num_elem` 379 @param[in] t_mode @ref CEED_NOTRANSPOSE to evaluate from nodes to points; 380 @ref CEED_TRANSPOSE to apply the transpose, mapping from points to nodes 381 @param[in] eval_mode @ref CEED_EVAL_INTERP to use interpolated values, 382 @ref CEED_EVAL_GRAD to use gradients, 383 @ref CEED_EVAL_WEIGHT to use quadrature weights 384 @param[in] x_ref `CeedVector` holding reference coordinates of each point 385 @param[in] u Input `CeedVector`, of length `num_nodes * num_comp` for @ref CEED_NOTRANSPOSE 386 @param[out] v Output `CeedVector`, of length `num_points * num_q_comp` for @ref CEED_NOTRANSPOSE with @ref CEED_EVAL_INTERP 387 388 @return An error code: 0 - success, otherwise - failure 389 390 @ref Developer 391 **/ 392 static int CeedBasisApplyAtPoints_Core(CeedBasis basis, bool apply_add, CeedInt num_elem, const CeedInt *num_points, CeedTransposeMode t_mode, 393 CeedEvalMode eval_mode, CeedVector x_ref, CeedVector u, CeedVector v) { 394 CeedInt dim, num_comp, P_1d = 1, Q_1d = 1, total_num_points = num_points[0]; 395 396 CeedCall(CeedBasisGetDimension(basis, &dim)); 397 // Inserting check because clang-tidy doesn't understand this cannot occur 398 CeedCheck(dim > 0, CeedBasisReturnCeed(basis), CEED_ERROR_UNSUPPORTED, "Malformed CeedBasis, dim > 0 is required"); 399 CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d)); 400 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d)); 401 CeedCall(CeedBasisGetNumComponents(basis, &num_comp)); 402 403 // Default implementation 404 { 405 bool is_tensor_basis; 406 407 CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis)); 408 CeedCheck(is_tensor_basis, CeedBasisReturnCeed(basis), CEED_ERROR_UNSUPPORTED, 409 "Evaluation at arbitrary points only supported for tensor product bases"); 410 } 411 CeedCheck(num_elem == 1, CeedBasisReturnCeed(basis), CEED_ERROR_UNSUPPORTED, 412 "Evaluation at arbitrary points only supported for a single element at a time"); 413 if (eval_mode == CEED_EVAL_WEIGHT) { 414 CeedCall(CeedVectorSetValue(v, 1.0)); 415 return CEED_ERROR_SUCCESS; 416 } 417 if (!basis->basis_chebyshev) { 418 // Build basis mapping from nodes to Chebyshev coefficients 419 CeedScalar *chebyshev_interp_1d, *chebyshev_grad_1d, *chebyshev_q_weight_1d; 420 const CeedScalar *q_ref_1d; 421 Ceed ceed; 422 423 CeedCall(CeedCalloc(P_1d * Q_1d, &chebyshev_interp_1d)); 424 CeedCall(CeedCalloc(P_1d * Q_1d, &chebyshev_grad_1d)); 425 CeedCall(CeedCalloc(Q_1d, &chebyshev_q_weight_1d)); 426 CeedCall(CeedBasisGetQRef(basis, &q_ref_1d)); 427 CeedCall(CeedBasisGetChebyshevInterp1D(basis, chebyshev_interp_1d)); 428 429 CeedCall(CeedBasisGetCeed(basis, &ceed)); 430 CeedCall(CeedVectorCreate(ceed, num_comp * CeedIntPow(Q_1d, dim), &basis->vec_chebyshev)); 431 CeedCall(CeedBasisCreateTensorH1(ceed, dim, num_comp, P_1d, Q_1d, chebyshev_interp_1d, chebyshev_grad_1d, q_ref_1d, chebyshev_q_weight_1d, 432 &basis->basis_chebyshev)); 433 434 // Cleanup 435 CeedCall(CeedFree(&chebyshev_interp_1d)); 436 CeedCall(CeedFree(&chebyshev_grad_1d)); 437 CeedCall(CeedFree(&chebyshev_q_weight_1d)); 438 CeedCall(CeedDestroy(&ceed)); 439 } 440 441 // Create TensorContract object if needed, such as a basis from the GPU backends 442 if (!basis->contract) { 443 Ceed ceed_ref; 444 CeedBasis basis_ref = NULL; 445 446 CeedCall(CeedInit("/cpu/self", &ceed_ref)); 447 // Only need matching tensor contraction dimensions, any type of basis will work 448 CeedCall(CeedBasisCreateTensorH1Lagrange(ceed_ref, dim, num_comp, P_1d, Q_1d, CEED_GAUSS, &basis_ref)); 449 // Note - clang-tidy doesn't know basis_ref->contract must be valid here 450 CeedCheck(basis_ref && basis_ref->contract, CeedBasisReturnCeed(basis), CEED_ERROR_UNSUPPORTED, 451 "Reference CPU ceed failed to create a tensor contraction object"); 452 CeedCall(CeedTensorContractReferenceCopy(basis_ref->contract, &basis->contract)); 453 CeedCall(CeedBasisDestroy(&basis_ref)); 454 CeedCall(CeedDestroy(&ceed_ref)); 455 } 456 457 // Basis evaluation 458 switch (t_mode) { 459 case CEED_NOTRANSPOSE: { 460 // Nodes to arbitrary points 461 CeedScalar *v_array; 462 const CeedScalar *chebyshev_coeffs, *x_array_read; 463 464 // -- Interpolate to Chebyshev coefficients 465 CeedCall(CeedBasisApply(basis->basis_chebyshev, 1, CEED_NOTRANSPOSE, CEED_EVAL_INTERP, u, basis->vec_chebyshev)); 466 467 // -- Evaluate Chebyshev polynomials at arbitrary points 468 CeedCall(CeedVectorGetArrayRead(basis->vec_chebyshev, CEED_MEM_HOST, &chebyshev_coeffs)); 469 CeedCall(CeedVectorGetArrayRead(x_ref, CEED_MEM_HOST, &x_array_read)); 470 CeedCall(CeedVectorGetArrayWrite(v, CEED_MEM_HOST, &v_array)); 471 switch (eval_mode) { 472 case CEED_EVAL_INTERP: { 473 CeedScalar tmp[2][num_comp * CeedIntPow(Q_1d, dim)], chebyshev_x[Q_1d]; 474 475 // ---- Values at point 476 for (CeedInt p = 0; p < total_num_points; p++) { 477 CeedInt pre = num_comp * CeedIntPow(Q_1d, dim - 1), post = 1; 478 479 for (CeedInt d = 0; d < dim; d++) { 480 // ------ Tensor contract with current Chebyshev polynomial values 481 CeedCall(CeedChebyshevPolynomialsAtPoint(x_array_read[d * total_num_points + p], Q_1d, chebyshev_x)); 482 CeedCall(CeedTensorContractApply(basis->contract, pre, Q_1d, post, 1, chebyshev_x, t_mode, false, 483 d == 0 ? chebyshev_coeffs : tmp[d % 2], tmp[(d + 1) % 2])); 484 pre /= Q_1d; 485 post *= 1; 486 } 487 for (CeedInt c = 0; c < num_comp; c++) v_array[c * total_num_points + p] = tmp[dim % 2][c]; 488 } 489 break; 490 } 491 case CEED_EVAL_GRAD: { 492 CeedScalar tmp[2][num_comp * CeedIntPow(Q_1d, dim)], chebyshev_x[Q_1d]; 493 494 // ---- Values at point 495 for (CeedInt p = 0; p < total_num_points; p++) { 496 // Dim**2 contractions, apply grad when pass == dim 497 for (CeedInt pass = 0; pass < dim; pass++) { 498 CeedInt pre = num_comp * CeedIntPow(Q_1d, dim - 1), post = 1; 499 500 for (CeedInt d = 0; d < dim; d++) { 501 // ------ Tensor contract with current Chebyshev polynomial values 502 if (pass == d) CeedCall(CeedChebyshevDerivativeAtPoint(x_array_read[d * total_num_points + p], Q_1d, chebyshev_x)); 503 else CeedCall(CeedChebyshevPolynomialsAtPoint(x_array_read[d * total_num_points + p], Q_1d, chebyshev_x)); 504 CeedCall(CeedTensorContractApply(basis->contract, pre, Q_1d, post, 1, chebyshev_x, t_mode, false, 505 d == 0 ? chebyshev_coeffs : tmp[d % 2], tmp[(d + 1) % 2])); 506 pre /= Q_1d; 507 post *= 1; 508 } 509 for (CeedInt c = 0; c < num_comp; c++) v_array[(pass * num_comp + c) * total_num_points + p] = tmp[dim % 2][c]; 510 } 511 } 512 break; 513 } 514 default: 515 // Nothing to do, excluded above 516 break; 517 } 518 CeedCall(CeedVectorRestoreArrayRead(basis->vec_chebyshev, &chebyshev_coeffs)); 519 CeedCall(CeedVectorRestoreArrayRead(x_ref, &x_array_read)); 520 CeedCall(CeedVectorRestoreArray(v, &v_array)); 521 break; 522 } 523 case CEED_TRANSPOSE: { 524 // Note: No switch on e_mode here because only CEED_EVAL_INTERP is supported at this time 525 // Arbitrary points to nodes 526 CeedScalar *chebyshev_coeffs; 527 const CeedScalar *u_array, *x_array_read; 528 529 // -- Transpose of evaluation of Chebyshev polynomials at arbitrary points 530 CeedCall(CeedVectorGetArrayWrite(basis->vec_chebyshev, CEED_MEM_HOST, &chebyshev_coeffs)); 531 CeedCall(CeedVectorGetArrayRead(x_ref, CEED_MEM_HOST, &x_array_read)); 532 CeedCall(CeedVectorGetArrayRead(u, CEED_MEM_HOST, &u_array)); 533 534 switch (eval_mode) { 535 case CEED_EVAL_INTERP: { 536 CeedScalar tmp[2][num_comp * CeedIntPow(Q_1d, dim)], chebyshev_x[Q_1d]; 537 538 // ---- Values at point 539 for (CeedInt p = 0; p < total_num_points; p++) { 540 CeedInt pre = num_comp * 1, post = 1; 541 542 for (CeedInt c = 0; c < num_comp; c++) tmp[0][c] = u_array[c * total_num_points + p]; 543 for (CeedInt d = 0; d < dim; d++) { 544 // ------ Tensor contract with current Chebyshev polynomial values 545 CeedCall(CeedChebyshevPolynomialsAtPoint(x_array_read[d * total_num_points + p], Q_1d, chebyshev_x)); 546 CeedCall(CeedTensorContractApply(basis->contract, pre, 1, post, Q_1d, chebyshev_x, t_mode, p > 0 && d == (dim - 1), tmp[d % 2], 547 d == (dim - 1) ? chebyshev_coeffs : tmp[(d + 1) % 2])); 548 pre /= 1; 549 post *= Q_1d; 550 } 551 } 552 break; 553 } 554 case CEED_EVAL_GRAD: { 555 CeedScalar tmp[2][num_comp * CeedIntPow(Q_1d, dim)], chebyshev_x[Q_1d]; 556 557 // ---- Values at point 558 for (CeedInt p = 0; p < total_num_points; p++) { 559 // Dim**2 contractions, apply grad when pass == dim 560 for (CeedInt pass = 0; pass < dim; pass++) { 561 CeedInt pre = num_comp * 1, post = 1; 562 563 for (CeedInt c = 0; c < num_comp; c++) tmp[0][c] = u_array[(pass * num_comp + c) * total_num_points + p]; 564 for (CeedInt d = 0; d < dim; d++) { 565 // ------ Tensor contract with current Chebyshev polynomial values 566 if (pass == d) CeedCall(CeedChebyshevDerivativeAtPoint(x_array_read[d * total_num_points + p], Q_1d, chebyshev_x)); 567 else CeedCall(CeedChebyshevPolynomialsAtPoint(x_array_read[d * total_num_points + p], Q_1d, chebyshev_x)); 568 CeedCall(CeedTensorContractApply(basis->contract, pre, 1, post, Q_1d, chebyshev_x, t_mode, 569 (p > 0 || (p == 0 && pass > 0)) && d == (dim - 1), tmp[d % 2], 570 d == (dim - 1) ? chebyshev_coeffs : tmp[(d + 1) % 2])); 571 pre /= 1; 572 post *= Q_1d; 573 } 574 } 575 } 576 break; 577 } 578 default: 579 // Nothing to do, excluded above 580 break; 581 } 582 CeedCall(CeedVectorRestoreArray(basis->vec_chebyshev, &chebyshev_coeffs)); 583 CeedCall(CeedVectorRestoreArrayRead(x_ref, &x_array_read)); 584 CeedCall(CeedVectorRestoreArrayRead(u, &u_array)); 585 586 // -- Interpolate transpose from Chebyshev coefficients 587 if (apply_add) CeedCall(CeedBasisApplyAdd(basis->basis_chebyshev, 1, CEED_TRANSPOSE, CEED_EVAL_INTERP, basis->vec_chebyshev, v)); 588 else CeedCall(CeedBasisApply(basis->basis_chebyshev, 1, CEED_TRANSPOSE, CEED_EVAL_INTERP, basis->vec_chebyshev, v)); 589 break; 590 } 591 } 592 return CEED_ERROR_SUCCESS; 593 } 594 595 /// @} 596 597 /// ---------------------------------------------------------------------------- 598 /// Ceed Backend API 599 /// ---------------------------------------------------------------------------- 600 /// @addtogroup CeedBasisBackend 601 /// @{ 602 603 /** 604 @brief Return collocated gradient matrix 605 606 @param[in] basis `CeedBasis` 607 @param[out] collo_grad_1d Row-major (`Q_1d * Q_1d`) matrix expressing derivatives of basis functions at quadrature points 608 609 @return An error code: 0 - success, otherwise - failure 610 611 @ref Backend 612 **/ 613 int CeedBasisGetCollocatedGrad(CeedBasis basis, CeedScalar *collo_grad_1d) { 614 Ceed ceed; 615 CeedInt P_1d, Q_1d; 616 CeedScalar *interp_1d_pinv; 617 const CeedScalar *grad_1d, *interp_1d; 618 619 // Note: This function is for backend use, so all errors are terminal and we do not need to clean up memory on failure. 620 CeedCall(CeedBasisGetCeed(basis, &ceed)); 621 CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d)); 622 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d)); 623 624 // Compute interp_1d^+, pseudoinverse of interp_1d 625 CeedCall(CeedCalloc(P_1d * Q_1d, &interp_1d_pinv)); 626 CeedCall(CeedBasisGetInterp1D(basis, &interp_1d)); 627 CeedCall(CeedMatrixPseudoinverse(ceed, interp_1d, Q_1d, P_1d, interp_1d_pinv)); 628 CeedCall(CeedBasisGetGrad1D(basis, &grad_1d)); 629 CeedCall(CeedMatrixMatrixMultiply(ceed, grad_1d, (const CeedScalar *)interp_1d_pinv, collo_grad_1d, Q_1d, Q_1d, P_1d)); 630 631 CeedCall(CeedFree(&interp_1d_pinv)); 632 CeedCall(CeedDestroy(&ceed)); 633 return CEED_ERROR_SUCCESS; 634 } 635 636 /** 637 @brief Return 1D interpolation matrix to Chebyshev polynomial coefficients on quadrature space 638 639 @param[in] basis `CeedBasis` 640 @param[out] chebyshev_interp_1d Row-major (`P_1d * Q_1d`) matrix interpolating from basis nodes to Chebyshev polynomial coefficients 641 642 @return An error code: 0 - success, otherwise - failure 643 644 @ref Backend 645 **/ 646 int CeedBasisGetChebyshevInterp1D(CeedBasis basis, CeedScalar *chebyshev_interp_1d) { 647 CeedInt P_1d, Q_1d; 648 CeedScalar *C, *chebyshev_coeffs_1d_inv; 649 const CeedScalar *interp_1d, *q_ref_1d; 650 Ceed ceed; 651 652 CeedCall(CeedBasisGetCeed(basis, &ceed)); 653 CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d)); 654 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d)); 655 656 // Build coefficient matrix 657 // -- Note: Clang-tidy needs this check 658 CeedCheck((P_1d > 0) && (Q_1d > 0), ceed, CEED_ERROR_INCOMPATIBLE, "CeedBasis dimensions are malformed"); 659 CeedCall(CeedCalloc(Q_1d * Q_1d, &C)); 660 CeedCall(CeedBasisGetQRef(basis, &q_ref_1d)); 661 for (CeedInt i = 0; i < Q_1d; i++) CeedCall(CeedChebyshevPolynomialsAtPoint(q_ref_1d[i], Q_1d, &C[i * Q_1d])); 662 663 // Compute C^+, pseudoinverse of coefficient matrix 664 CeedCall(CeedCalloc(Q_1d * Q_1d, &chebyshev_coeffs_1d_inv)); 665 CeedCall(CeedMatrixPseudoinverse(ceed, C, Q_1d, Q_1d, chebyshev_coeffs_1d_inv)); 666 667 // Build mapping from nodes to Chebyshev coefficients 668 CeedCall(CeedBasisGetInterp1D(basis, &interp_1d)); 669 CeedCall(CeedMatrixMatrixMultiply(ceed, chebyshev_coeffs_1d_inv, interp_1d, chebyshev_interp_1d, Q_1d, P_1d, Q_1d)); 670 671 // Cleanup 672 CeedCall(CeedFree(&C)); 673 CeedCall(CeedFree(&chebyshev_coeffs_1d_inv)); 674 CeedCall(CeedDestroy(&ceed)); 675 return CEED_ERROR_SUCCESS; 676 } 677 678 /** 679 @brief Get tensor status for given `CeedBasis` 680 681 @param[in] basis `CeedBasis` 682 @param[out] is_tensor Variable to store tensor status 683 684 @return An error code: 0 - success, otherwise - failure 685 686 @ref Backend 687 **/ 688 int CeedBasisIsTensor(CeedBasis basis, bool *is_tensor) { 689 *is_tensor = basis->is_tensor_basis; 690 return CEED_ERROR_SUCCESS; 691 } 692 693 /** 694 @brief Get backend data of a `CeedBasis` 695 696 @param[in] basis `CeedBasis` 697 @param[out] data Variable to store data 698 699 @return An error code: 0 - success, otherwise - failure 700 701 @ref Backend 702 **/ 703 int CeedBasisGetData(CeedBasis basis, void *data) { 704 *(void **)data = basis->data; 705 return CEED_ERROR_SUCCESS; 706 } 707 708 /** 709 @brief Set backend data of a `CeedBasis` 710 711 @param[in,out] basis `CeedBasis` 712 @param[in] data Data to set 713 714 @return An error code: 0 - success, otherwise - failure 715 716 @ref Backend 717 **/ 718 int CeedBasisSetData(CeedBasis basis, void *data) { 719 basis->data = data; 720 return CEED_ERROR_SUCCESS; 721 } 722 723 /** 724 @brief Increment the reference counter for a `CeedBasis` 725 726 @param[in,out] basis `CeedBasis` to increment the reference counter 727 728 @return An error code: 0 - success, otherwise - failure 729 730 @ref Backend 731 **/ 732 int CeedBasisReference(CeedBasis basis) { 733 basis->ref_count++; 734 return CEED_ERROR_SUCCESS; 735 } 736 737 /** 738 @brief Get number of Q-vector components for given `CeedBasis` 739 740 @param[in] basis `CeedBasis` 741 @param[in] eval_mode @ref CEED_EVAL_INTERP to use interpolated values, 742 @ref CEED_EVAL_GRAD to use gradients, 743 @ref CEED_EVAL_DIV to use divergence, 744 @ref CEED_EVAL_CURL to use curl 745 @param[out] q_comp Variable to store number of Q-vector components of basis 746 747 @return An error code: 0 - success, otherwise - failure 748 749 @ref Backend 750 **/ 751 int CeedBasisGetNumQuadratureComponents(CeedBasis basis, CeedEvalMode eval_mode, CeedInt *q_comp) { 752 CeedInt dim; 753 754 CeedCall(CeedBasisGetDimension(basis, &dim)); 755 switch (eval_mode) { 756 case CEED_EVAL_INTERP: { 757 CeedFESpace fe_space; 758 759 CeedCall(CeedBasisGetFESpace(basis, &fe_space)); 760 *q_comp = (fe_space == CEED_FE_SPACE_H1) ? 1 : dim; 761 } break; 762 case CEED_EVAL_GRAD: 763 *q_comp = dim; 764 break; 765 case CEED_EVAL_DIV: 766 *q_comp = 1; 767 break; 768 case CEED_EVAL_CURL: 769 *q_comp = (dim < 3) ? 1 : dim; 770 break; 771 case CEED_EVAL_NONE: 772 case CEED_EVAL_WEIGHT: 773 *q_comp = 1; 774 break; 775 } 776 return CEED_ERROR_SUCCESS; 777 } 778 779 /** 780 @brief Estimate number of FLOPs required to apply `CeedBasis` in `t_mode` and `eval_mode` 781 782 @param[in] basis `CeedBasis` to estimate FLOPs for 783 @param[in] t_mode Apply basis or transpose 784 @param[in] eval_mode @ref CeedEvalMode 785 @param[out] flops Address of variable to hold FLOPs estimate 786 787 @ref Backend 788 **/ 789 int CeedBasisGetFlopsEstimate(CeedBasis basis, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedSize *flops) { 790 bool is_tensor; 791 792 CeedCall(CeedBasisIsTensor(basis, &is_tensor)); 793 if (is_tensor) { 794 CeedInt dim, num_comp, P_1d, Q_1d; 795 796 CeedCall(CeedBasisGetDimension(basis, &dim)); 797 CeedCall(CeedBasisGetNumComponents(basis, &num_comp)); 798 CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d)); 799 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d)); 800 if (t_mode == CEED_TRANSPOSE) { 801 P_1d = Q_1d; 802 Q_1d = P_1d; 803 } 804 CeedInt tensor_flops = 0, pre = num_comp * CeedIntPow(P_1d, dim - 1), post = 1; 805 for (CeedInt d = 0; d < dim; d++) { 806 tensor_flops += 2 * pre * P_1d * post * Q_1d; 807 pre /= P_1d; 808 post *= Q_1d; 809 } 810 switch (eval_mode) { 811 case CEED_EVAL_NONE: 812 *flops = 0; 813 break; 814 case CEED_EVAL_INTERP: 815 *flops = tensor_flops; 816 break; 817 case CEED_EVAL_GRAD: 818 *flops = tensor_flops * 2; 819 break; 820 case CEED_EVAL_DIV: 821 case CEED_EVAL_CURL: { 822 // LCOV_EXCL_START 823 return CeedError(CeedBasisReturnCeed(basis), CEED_ERROR_INCOMPATIBLE, "Tensor basis evaluation for %s not supported", 824 CeedEvalModes[eval_mode]); 825 break; 826 // LCOV_EXCL_STOP 827 } 828 case CEED_EVAL_WEIGHT: 829 *flops = dim * CeedIntPow(Q_1d, dim); 830 break; 831 } 832 } else { 833 CeedInt dim, num_comp, q_comp, num_nodes, num_qpts; 834 835 CeedCall(CeedBasisGetDimension(basis, &dim)); 836 CeedCall(CeedBasisGetNumComponents(basis, &num_comp)); 837 CeedCall(CeedBasisGetNumQuadratureComponents(basis, eval_mode, &q_comp)); 838 CeedCall(CeedBasisGetNumNodes(basis, &num_nodes)); 839 CeedCall(CeedBasisGetNumQuadraturePoints(basis, &num_qpts)); 840 switch (eval_mode) { 841 case CEED_EVAL_NONE: 842 *flops = 0; 843 break; 844 case CEED_EVAL_INTERP: 845 case CEED_EVAL_GRAD: 846 case CEED_EVAL_DIV: 847 case CEED_EVAL_CURL: 848 *flops = num_nodes * num_qpts * num_comp * q_comp; 849 break; 850 case CEED_EVAL_WEIGHT: 851 *flops = 0; 852 break; 853 } 854 } 855 return CEED_ERROR_SUCCESS; 856 } 857 858 /** 859 @brief Get `CeedFESpace` for a `CeedBasis` 860 861 @param[in] basis `CeedBasis` 862 @param[out] fe_space Variable to store `CeedFESpace` 863 864 @return An error code: 0 - success, otherwise - failure 865 866 @ref Backend 867 **/ 868 int CeedBasisGetFESpace(CeedBasis basis, CeedFESpace *fe_space) { 869 *fe_space = basis->fe_space; 870 return CEED_ERROR_SUCCESS; 871 } 872 873 /** 874 @brief Get dimension for given `CeedElemTopology` 875 876 @param[in] topo `CeedElemTopology` 877 @param[out] dim Variable to store dimension of topology 878 879 @return An error code: 0 - success, otherwise - failure 880 881 @ref Backend 882 **/ 883 int CeedBasisGetTopologyDimension(CeedElemTopology topo, CeedInt *dim) { 884 *dim = (CeedInt)topo >> 16; 885 return CEED_ERROR_SUCCESS; 886 } 887 888 /** 889 @brief Get `CeedTensorContract` of a `CeedBasis` 890 891 @param[in] basis `CeedBasis` 892 @param[out] contract Variable to store `CeedTensorContract` 893 894 @return An error code: 0 - success, otherwise - failure 895 896 @ref Backend 897 **/ 898 int CeedBasisGetTensorContract(CeedBasis basis, CeedTensorContract *contract) { 899 *contract = basis->contract; 900 return CEED_ERROR_SUCCESS; 901 } 902 903 /** 904 @brief Set `CeedTensorContract` of a `CeedBasis` 905 906 @param[in,out] basis `CeedBasis` 907 @param[in] contract `CeedTensorContract` to set 908 909 @return An error code: 0 - success, otherwise - failure 910 911 @ref Backend 912 **/ 913 int CeedBasisSetTensorContract(CeedBasis basis, CeedTensorContract contract) { 914 basis->contract = contract; 915 CeedCall(CeedTensorContractReference(contract)); 916 return CEED_ERROR_SUCCESS; 917 } 918 919 /** 920 @brief Return a reference implementation of matrix multiplication \f$C = A B\f$. 921 922 Note: This is a reference implementation for CPU `CeedScalar` pointers that is not intended for high performance. 923 924 @param[in] ceed `Ceed` context for error handling 925 @param[in] mat_A Row-major matrix `A` 926 @param[in] mat_B Row-major matrix `B` 927 @param[out] mat_C Row-major output matrix `C` 928 @param[in] m Number of rows of `C` 929 @param[in] n Number of columns of `C` 930 @param[in] kk Number of columns of `A`/rows of `B` 931 932 @return An error code: 0 - success, otherwise - failure 933 934 @ref Utility 935 **/ 936 int CeedMatrixMatrixMultiply(Ceed ceed, const CeedScalar *mat_A, const CeedScalar *mat_B, CeedScalar *mat_C, CeedInt m, CeedInt n, CeedInt kk) { 937 for (CeedInt i = 0; i < m; i++) { 938 for (CeedInt j = 0; j < n; j++) { 939 CeedScalar sum = 0; 940 941 for (CeedInt k = 0; k < kk; k++) sum += mat_A[k + i * kk] * mat_B[j + k * n]; 942 mat_C[j + i * n] = sum; 943 } 944 } 945 return CEED_ERROR_SUCCESS; 946 } 947 948 /** 949 @brief Return QR Factorization of a matrix 950 951 @param[in] ceed `Ceed` context for error handling 952 @param[in,out] mat Row-major matrix to be factorized in place 953 @param[in,out] tau Vector of length `m` of scaling factors 954 @param[in] m Number of rows 955 @param[in] n Number of columns 956 957 @return An error code: 0 - success, otherwise - failure 958 959 @ref Utility 960 **/ 961 int CeedQRFactorization(Ceed ceed, CeedScalar *mat, CeedScalar *tau, CeedInt m, CeedInt n) { 962 CeedScalar v[m]; 963 964 // Check matrix shape 965 CeedCheck(n <= m, ceed, CEED_ERROR_UNSUPPORTED, "Cannot compute QR factorization with n > m"); 966 967 for (CeedInt i = 0; i < n; i++) { 968 CeedScalar sigma = 0.0; 969 970 if (i >= m - 1) { // last row of matrix, no reflection needed 971 tau[i] = 0.; 972 break; 973 } 974 // Calculate Householder vector, magnitude 975 v[i] = mat[i + n * i]; 976 for (CeedInt j = i + 1; j < m; j++) { 977 v[j] = mat[i + n * j]; 978 sigma += v[j] * v[j]; 979 } 980 const CeedScalar norm = sqrt(v[i] * v[i] + sigma); // norm of v[i:m] 981 const CeedScalar R_ii = -copysign(norm, v[i]); 982 983 v[i] -= R_ii; 984 // norm of v[i:m] after modification above and scaling below 985 // norm = sqrt(v[i]*v[i] + sigma) / v[i]; 986 // tau = 2 / (norm*norm) 987 tau[i] = 2 * v[i] * v[i] / (v[i] * v[i] + sigma); 988 for (CeedInt j = i + 1; j < m; j++) v[j] /= v[i]; 989 990 // Apply Householder reflector to lower right panel 991 CeedHouseholderReflect(&mat[i * n + i + 1], &v[i], tau[i], m - i, n - i - 1, n, 1); 992 // Save v 993 mat[i + n * i] = R_ii; 994 for (CeedInt j = i + 1; j < m; j++) mat[i + n * j] = v[j]; 995 } 996 return CEED_ERROR_SUCCESS; 997 } 998 999 /** 1000 @brief Apply Householder Q matrix 1001 1002 Compute `mat_A = mat_Q mat_A`, where `mat_Q` is \f$m \times m\f$ and `mat_A` is \f$m \times n\f$. 1003 1004 @param[in,out] mat_A Matrix to apply Householder Q to, in place 1005 @param[in] mat_Q Householder Q matrix 1006 @param[in] tau Householder scaling factors 1007 @param[in] t_mode Transpose mode for application 1008 @param[in] m Number of rows in `A` 1009 @param[in] n Number of columns in `A` 1010 @param[in] k Number of elementary reflectors in Q, `k < m` 1011 @param[in] row Row stride in `A` 1012 @param[in] col Col stride in `A` 1013 1014 @return An error code: 0 - success, otherwise - failure 1015 1016 @ref Utility 1017 **/ 1018 int CeedHouseholderApplyQ(CeedScalar *mat_A, const CeedScalar *mat_Q, const CeedScalar *tau, CeedTransposeMode t_mode, CeedInt m, CeedInt n, 1019 CeedInt k, CeedInt row, CeedInt col) { 1020 CeedScalar *v; 1021 1022 CeedCall(CeedMalloc(m, &v)); 1023 for (CeedInt ii = 0; ii < k; ii++) { 1024 CeedInt i = t_mode == CEED_TRANSPOSE ? ii : k - 1 - ii; 1025 for (CeedInt j = i + 1; j < m; j++) v[j] = mat_Q[j * k + i]; 1026 // Apply Householder reflector (I - tau v v^T) collo_grad_1d^T 1027 CeedCall(CeedHouseholderReflect(&mat_A[i * row], &v[i], tau[i], m - i, n, row, col)); 1028 } 1029 CeedCall(CeedFree(&v)); 1030 return CEED_ERROR_SUCCESS; 1031 } 1032 1033 /** 1034 @brief Return pseudoinverse of a matrix 1035 1036 @param[in] ceed Ceed context for error handling 1037 @param[in] mat Row-major matrix to compute pseudoinverse of 1038 @param[in] m Number of rows 1039 @param[in] n Number of columns 1040 @param[out] mat_pinv Row-major pseudoinverse matrix 1041 1042 @return An error code: 0 - success, otherwise - failure 1043 1044 @ref Utility 1045 **/ 1046 int CeedMatrixPseudoinverse(Ceed ceed, const CeedScalar *mat, CeedInt m, CeedInt n, CeedScalar *mat_pinv) { 1047 CeedScalar *tau, *I, *mat_copy; 1048 1049 CeedCall(CeedCalloc(m, &tau)); 1050 CeedCall(CeedCalloc(m * m, &I)); 1051 CeedCall(CeedCalloc(m * n, &mat_copy)); 1052 memcpy(mat_copy, mat, m * n * sizeof mat[0]); 1053 1054 // QR Factorization, mat = Q R 1055 CeedCall(CeedQRFactorization(ceed, mat_copy, tau, m, n)); 1056 1057 // -- Apply Q^T, I = Q^T * I 1058 for (CeedInt i = 0; i < m; i++) I[i * m + i] = 1.0; 1059 CeedCall(CeedHouseholderApplyQ(I, mat_copy, tau, CEED_TRANSPOSE, m, m, n, m, 1)); 1060 // -- Apply R_inv, mat_pinv = R_inv * Q^T 1061 for (CeedInt j = 0; j < m; j++) { // Column j 1062 mat_pinv[j + m * (n - 1)] = I[j + m * (n - 1)] / mat_copy[n * n - 1]; 1063 for (CeedInt i = n - 2; i >= 0; i--) { // Row i 1064 mat_pinv[j + m * i] = I[j + m * i]; 1065 for (CeedInt k = i + 1; k < n; k++) mat_pinv[j + m * i] -= mat_copy[k + n * i] * mat_pinv[j + m * k]; 1066 mat_pinv[j + m * i] /= mat_copy[i + n * i]; 1067 } 1068 } 1069 1070 // Cleanup 1071 CeedCall(CeedFree(&I)); 1072 CeedCall(CeedFree(&tau)); 1073 CeedCall(CeedFree(&mat_copy)); 1074 return CEED_ERROR_SUCCESS; 1075 } 1076 1077 /** 1078 @brief Return symmetric Schur decomposition of the symmetric matrix mat via symmetric QR factorization 1079 1080 @param[in] ceed `Ceed` context for error handling 1081 @param[in,out] mat Row-major matrix to be factorized in place 1082 @param[out] lambda Vector of length n of eigenvalues 1083 @param[in] n Number of rows/columns 1084 1085 @return An error code: 0 - success, otherwise - failure 1086 1087 @ref Utility 1088 **/ 1089 CeedPragmaOptimizeOff 1090 int CeedSymmetricSchurDecomposition(Ceed ceed, CeedScalar *mat, CeedScalar *lambda, CeedInt n) { 1091 // Check bounds for clang-tidy 1092 CeedCheck(n > 1, ceed, CEED_ERROR_UNSUPPORTED, "Cannot compute symmetric Schur decomposition of scalars"); 1093 1094 CeedScalar v[n - 1], tau[n - 1], mat_T[n * n]; 1095 1096 // Copy mat to mat_T and set mat to I 1097 memcpy(mat_T, mat, n * n * sizeof(mat[0])); 1098 for (CeedInt i = 0; i < n; i++) { 1099 for (CeedInt j = 0; j < n; j++) mat[j + n * i] = (i == j) ? 1 : 0; 1100 } 1101 1102 // Reduce to tridiagonal 1103 for (CeedInt i = 0; i < n - 1; i++) { 1104 // Calculate Householder vector, magnitude 1105 CeedScalar sigma = 0.0; 1106 1107 v[i] = mat_T[i + n * (i + 1)]; 1108 for (CeedInt j = i + 1; j < n - 1; j++) { 1109 v[j] = mat_T[i + n * (j + 1)]; 1110 sigma += v[j] * v[j]; 1111 } 1112 const CeedScalar norm = sqrt(v[i] * v[i] + sigma); // norm of v[i:n-1] 1113 const CeedScalar R_ii = -copysign(norm, v[i]); 1114 1115 v[i] -= R_ii; 1116 // norm of v[i:m] after modification above and scaling below 1117 // norm = sqrt(v[i]*v[i] + sigma) / v[i]; 1118 // tau = 2 / (norm*norm) 1119 tau[i] = i == n - 2 ? 2 : 2 * v[i] * v[i] / (v[i] * v[i] + sigma); 1120 for (CeedInt j = i + 1; j < n - 1; j++) v[j] /= v[i]; 1121 1122 // Update sub and super diagonal 1123 for (CeedInt j = i + 2; j < n; j++) { 1124 mat_T[i + n * j] = 0; 1125 mat_T[j + n * i] = 0; 1126 } 1127 // Apply symmetric Householder reflector to lower right panel 1128 CeedHouseholderReflect(&mat_T[(i + 1) + n * (i + 1)], &v[i], tau[i], n - (i + 1), n - (i + 1), n, 1); 1129 CeedHouseholderReflect(&mat_T[(i + 1) + n * (i + 1)], &v[i], tau[i], n - (i + 1), n - (i + 1), 1, n); 1130 1131 // Save v 1132 mat_T[i + n * (i + 1)] = R_ii; 1133 mat_T[(i + 1) + n * i] = R_ii; 1134 for (CeedInt j = i + 1; j < n - 1; j++) { 1135 mat_T[i + n * (j + 1)] = v[j]; 1136 } 1137 } 1138 // Backwards accumulation of Q 1139 for (CeedInt i = n - 2; i >= 0; i--) { 1140 if (tau[i] > 0.0) { 1141 v[i] = 1; 1142 for (CeedInt j = i + 1; j < n - 1; j++) { 1143 v[j] = mat_T[i + n * (j + 1)]; 1144 mat_T[i + n * (j + 1)] = 0; 1145 } 1146 CeedHouseholderReflect(&mat[(i + 1) + n * (i + 1)], &v[i], tau[i], n - (i + 1), n - (i + 1), n, 1); 1147 } 1148 } 1149 1150 // Reduce sub and super diagonal 1151 CeedInt p = 0, q = 0, itr = 0, max_itr = n * n * n * n; 1152 CeedScalar tol = CEED_EPSILON; 1153 1154 while (itr < max_itr) { 1155 // Update p, q, size of reduced portions of diagonal 1156 p = 0; 1157 q = 0; 1158 for (CeedInt i = n - 2; i >= 0; i--) { 1159 if (fabs(mat_T[i + n * (i + 1)]) < tol) q += 1; 1160 else break; 1161 } 1162 for (CeedInt i = 0; i < n - q - 1; i++) { 1163 if (fabs(mat_T[i + n * (i + 1)]) < tol) p += 1; 1164 else break; 1165 } 1166 if (q == n - 1) break; // Finished reducing 1167 1168 // Reduce tridiagonal portion 1169 CeedScalar t_nn = mat_T[(n - 1 - q) + n * (n - 1 - q)], t_nnm1 = mat_T[(n - 2 - q) + n * (n - 1 - q)]; 1170 CeedScalar d = (mat_T[(n - 2 - q) + n * (n - 2 - q)] - t_nn) / 2; 1171 CeedScalar mu = t_nn - t_nnm1 * t_nnm1 / (d + copysign(sqrt(d * d + t_nnm1 * t_nnm1), d)); 1172 CeedScalar x = mat_T[p + n * p] - mu; 1173 CeedScalar z = mat_T[p + n * (p + 1)]; 1174 1175 for (CeedInt k = p; k < n - q - 1; k++) { 1176 // Compute Givens rotation 1177 CeedScalar c = 1, s = 0; 1178 1179 if (fabs(z) > tol) { 1180 if (fabs(z) > fabs(x)) { 1181 const CeedScalar tau = -x / z; 1182 1183 s = 1 / sqrt(1 + tau * tau); 1184 c = s * tau; 1185 } else { 1186 const CeedScalar tau = -z / x; 1187 1188 c = 1 / sqrt(1 + tau * tau); 1189 s = c * tau; 1190 } 1191 } 1192 1193 // Apply Givens rotation to T 1194 CeedGivensRotation(mat_T, c, s, CEED_NOTRANSPOSE, k, k + 1, n, n); 1195 CeedGivensRotation(mat_T, c, s, CEED_TRANSPOSE, k, k + 1, n, n); 1196 1197 // Apply Givens rotation to Q 1198 CeedGivensRotation(mat, c, s, CEED_NOTRANSPOSE, k, k + 1, n, n); 1199 1200 // Update x, z 1201 if (k < n - q - 2) { 1202 x = mat_T[k + n * (k + 1)]; 1203 z = mat_T[k + n * (k + 2)]; 1204 } 1205 } 1206 itr++; 1207 } 1208 1209 // Save eigenvalues 1210 for (CeedInt i = 0; i < n; i++) lambda[i] = mat_T[i + n * i]; 1211 1212 // Check convergence 1213 CeedCheck(itr < max_itr || q > n, ceed, CEED_ERROR_MINOR, "Symmetric QR failed to converge"); 1214 return CEED_ERROR_SUCCESS; 1215 } 1216 CeedPragmaOptimizeOn 1217 1218 /** 1219 @brief Return Simultaneous Diagonalization of two matrices. 1220 1221 This solves the generalized eigenvalue problem `A x = lambda B x`, where `A` and `B` are symmetric and `B` is positive definite. 1222 We generate the matrix `X` and vector `Lambda` such that `X^T A X = Lambda` and `X^T B X = I`. 1223 This is equivalent to the LAPACK routine 'sygv' with `TYPE = 1`. 1224 1225 @param[in] ceed `Ceed` context for error handling 1226 @param[in] mat_A Row-major matrix to be factorized with eigenvalues 1227 @param[in] mat_B Row-major matrix to be factorized to identity 1228 @param[out] mat_X Row-major orthogonal matrix 1229 @param[out] lambda Vector of length `n` of generalized eigenvalues 1230 @param[in] n Number of rows/columns 1231 1232 @return An error code: 0 - success, otherwise - failure 1233 1234 @ref Utility 1235 **/ 1236 CeedPragmaOptimizeOff 1237 int CeedSimultaneousDiagonalization(Ceed ceed, CeedScalar *mat_A, CeedScalar *mat_B, CeedScalar *mat_X, CeedScalar *lambda, CeedInt n) { 1238 CeedScalar *mat_C, *mat_G, *vec_D; 1239 1240 CeedCall(CeedCalloc(n * n, &mat_C)); 1241 CeedCall(CeedCalloc(n * n, &mat_G)); 1242 CeedCall(CeedCalloc(n, &vec_D)); 1243 1244 // Compute B = G D G^T 1245 memcpy(mat_G, mat_B, n * n * sizeof(mat_B[0])); 1246 CeedCall(CeedSymmetricSchurDecomposition(ceed, mat_G, vec_D, n)); 1247 1248 // Sort eigenvalues 1249 for (CeedInt i = n - 1; i >= 0; i--) { 1250 for (CeedInt j = 0; j < i; j++) { 1251 if (fabs(vec_D[j]) > fabs(vec_D[j + 1])) { 1252 CeedScalarSwap(vec_D[j], vec_D[j + 1]); 1253 for (CeedInt k = 0; k < n; k++) CeedScalarSwap(mat_G[k * n + j], mat_G[k * n + j + 1]); 1254 } 1255 } 1256 } 1257 1258 // Compute C = (G D^1/2)^-1 A (G D^1/2)^-T 1259 // = D^-1/2 G^T A G D^-1/2 1260 // -- D = D^-1/2 1261 for (CeedInt i = 0; i < n; i++) vec_D[i] = 1. / sqrt(vec_D[i]); 1262 // -- G = G D^-1/2 1263 // -- C = D^-1/2 G^T 1264 for (CeedInt i = 0; i < n; i++) { 1265 for (CeedInt j = 0; j < n; j++) { 1266 mat_G[i * n + j] *= vec_D[j]; 1267 mat_C[j * n + i] = mat_G[i * n + j]; 1268 } 1269 } 1270 // -- X = (D^-1/2 G^T) A 1271 CeedCall(CeedMatrixMatrixMultiply(ceed, (const CeedScalar *)mat_C, (const CeedScalar *)mat_A, mat_X, n, n, n)); 1272 // -- C = (D^-1/2 G^T A) (G D^-1/2) 1273 CeedCall(CeedMatrixMatrixMultiply(ceed, (const CeedScalar *)mat_X, (const CeedScalar *)mat_G, mat_C, n, n, n)); 1274 1275 // Compute Q^T C Q = lambda 1276 CeedCall(CeedSymmetricSchurDecomposition(ceed, mat_C, lambda, n)); 1277 1278 // Sort eigenvalues 1279 for (CeedInt i = n - 1; i >= 0; i--) { 1280 for (CeedInt j = 0; j < i; j++) { 1281 if (fabs(lambda[j]) > fabs(lambda[j + 1])) { 1282 CeedScalarSwap(lambda[j], lambda[j + 1]); 1283 for (CeedInt k = 0; k < n; k++) CeedScalarSwap(mat_C[k * n + j], mat_C[k * n + j + 1]); 1284 } 1285 } 1286 } 1287 1288 // Set X = (G D^1/2)^-T Q 1289 // = G D^-1/2 Q 1290 CeedCall(CeedMatrixMatrixMultiply(ceed, (const CeedScalar *)mat_G, (const CeedScalar *)mat_C, mat_X, n, n, n)); 1291 1292 // Cleanup 1293 CeedCall(CeedFree(&mat_C)); 1294 CeedCall(CeedFree(&mat_G)); 1295 CeedCall(CeedFree(&vec_D)); 1296 return CEED_ERROR_SUCCESS; 1297 } 1298 CeedPragmaOptimizeOn 1299 1300 /// @} 1301 1302 /// ---------------------------------------------------------------------------- 1303 /// CeedBasis Public API 1304 /// ---------------------------------------------------------------------------- 1305 /// @addtogroup CeedBasisUser 1306 /// @{ 1307 1308 /** 1309 @brief Create a tensor-product basis for \f$H^1\f$ discretizations 1310 1311 @param[in] ceed `Ceed` object used to create the `CeedBasis` 1312 @param[in] dim Topological dimension 1313 @param[in] num_comp Number of field components (1 for scalar fields) 1314 @param[in] P_1d Number of nodes in one dimension 1315 @param[in] Q_1d Number of quadrature points in one dimension 1316 @param[in] interp_1d Row-major (`Q_1d * P_1d`) matrix expressing the values of nodal basis functions at quadrature points 1317 @param[in] grad_1d Row-major (`Q_1d * P_1d`) matrix expressing derivatives of nodal basis functions at quadrature points 1318 @param[in] q_ref_1d Array of length `Q_1d` holding the locations of quadrature points on the 1D reference element `[-1, 1]` 1319 @param[in] q_weight_1d Array of length `Q_1d` holding the quadrature weights on the reference element 1320 @param[out] basis Address of the variable where the newly created `CeedBasis` will be stored 1321 1322 @return An error code: 0 - success, otherwise - failure 1323 1324 @ref User 1325 **/ 1326 int CeedBasisCreateTensorH1(Ceed ceed, CeedInt dim, CeedInt num_comp, CeedInt P_1d, CeedInt Q_1d, const CeedScalar *interp_1d, 1327 const CeedScalar *grad_1d, const CeedScalar *q_ref_1d, const CeedScalar *q_weight_1d, CeedBasis *basis) { 1328 if (!ceed->BasisCreateTensorH1) { 1329 Ceed delegate; 1330 1331 CeedCall(CeedGetObjectDelegate(ceed, &delegate, "Basis")); 1332 CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement BasisCreateTensorH1"); 1333 CeedCall(CeedBasisCreateTensorH1(delegate, dim, num_comp, P_1d, Q_1d, interp_1d, grad_1d, q_ref_1d, q_weight_1d, basis)); 1334 CeedCall(CeedDestroy(&delegate)); 1335 return CEED_ERROR_SUCCESS; 1336 } 1337 1338 CeedCheck(dim > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis dimension must be a positive value"); 1339 CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 component"); 1340 CeedCheck(P_1d > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 node"); 1341 CeedCheck(Q_1d > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 quadrature point"); 1342 1343 CeedElemTopology topo = dim == 1 ? CEED_TOPOLOGY_LINE : dim == 2 ? CEED_TOPOLOGY_QUAD : CEED_TOPOLOGY_HEX; 1344 1345 CeedCall(CeedCalloc(1, basis)); 1346 CeedCall(CeedReferenceCopy(ceed, &(*basis)->ceed)); 1347 (*basis)->ref_count = 1; 1348 (*basis)->is_tensor_basis = true; 1349 (*basis)->dim = dim; 1350 (*basis)->topo = topo; 1351 (*basis)->num_comp = num_comp; 1352 (*basis)->P_1d = P_1d; 1353 (*basis)->Q_1d = Q_1d; 1354 (*basis)->P = CeedIntPow(P_1d, dim); 1355 (*basis)->Q = CeedIntPow(Q_1d, dim); 1356 (*basis)->fe_space = CEED_FE_SPACE_H1; 1357 CeedCall(CeedCalloc(Q_1d, &(*basis)->q_ref_1d)); 1358 CeedCall(CeedCalloc(Q_1d, &(*basis)->q_weight_1d)); 1359 if (q_ref_1d) memcpy((*basis)->q_ref_1d, q_ref_1d, Q_1d * sizeof(q_ref_1d[0])); 1360 if (q_weight_1d) memcpy((*basis)->q_weight_1d, q_weight_1d, Q_1d * sizeof(q_weight_1d[0])); 1361 CeedCall(CeedCalloc(Q_1d * P_1d, &(*basis)->interp_1d)); 1362 CeedCall(CeedCalloc(Q_1d * P_1d, &(*basis)->grad_1d)); 1363 if (interp_1d) memcpy((*basis)->interp_1d, interp_1d, Q_1d * P_1d * sizeof(interp_1d[0])); 1364 if (grad_1d) memcpy((*basis)->grad_1d, grad_1d, Q_1d * P_1d * sizeof(grad_1d[0])); 1365 CeedCall(ceed->BasisCreateTensorH1(dim, P_1d, Q_1d, interp_1d, grad_1d, q_ref_1d, q_weight_1d, *basis)); 1366 return CEED_ERROR_SUCCESS; 1367 } 1368 1369 /** 1370 @brief Create a tensor-product \f$H^1\f$ Lagrange basis 1371 1372 @param[in] ceed `Ceed` object used to create the `CeedBasis` 1373 @param[in] dim Topological dimension of element 1374 @param[in] num_comp Number of field components (1 for scalar fields) 1375 @param[in] P Number of Gauss-Lobatto nodes in one dimension. 1376 The polynomial degree of the resulting `Q_k` element is `k = P - 1`. 1377 @param[in] Q Number of quadrature points in one dimension. 1378 @param[in] quad_mode Distribution of the `Q` quadrature points (affects order of accuracy for the quadrature) 1379 @param[out] basis Address of the variable where the newly created `CeedBasis` will be stored 1380 1381 @return An error code: 0 - success, otherwise - failure 1382 1383 @ref User 1384 **/ 1385 int CeedBasisCreateTensorH1Lagrange(Ceed ceed, CeedInt dim, CeedInt num_comp, CeedInt P, CeedInt Q, CeedQuadMode quad_mode, CeedBasis *basis) { 1386 // Allocate 1387 int ierr = CEED_ERROR_SUCCESS; 1388 CeedScalar c1, c2, c3, c4, dx, *nodes, *interp_1d, *grad_1d, *q_ref_1d, *q_weight_1d; 1389 1390 CeedCheck(dim > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis dimension must be a positive value"); 1391 CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 component"); 1392 CeedCheck(P > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 node"); 1393 CeedCheck(Q > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 quadrature point"); 1394 1395 // Get Nodes and Weights 1396 CeedCall(CeedCalloc(P * Q, &interp_1d)); 1397 CeedCall(CeedCalloc(P * Q, &grad_1d)); 1398 CeedCall(CeedCalloc(P, &nodes)); 1399 CeedCall(CeedCalloc(Q, &q_ref_1d)); 1400 CeedCall(CeedCalloc(Q, &q_weight_1d)); 1401 if (CeedLobattoQuadrature(P, nodes, NULL) != CEED_ERROR_SUCCESS) goto cleanup; 1402 switch (quad_mode) { 1403 case CEED_GAUSS: 1404 ierr = CeedGaussQuadrature(Q, q_ref_1d, q_weight_1d); 1405 break; 1406 case CEED_GAUSS_LOBATTO: 1407 ierr = CeedLobattoQuadrature(Q, q_ref_1d, q_weight_1d); 1408 break; 1409 } 1410 if (ierr != CEED_ERROR_SUCCESS) goto cleanup; 1411 1412 // Build B, D matrix 1413 // Fornberg, 1998 1414 for (CeedInt i = 0; i < Q; i++) { 1415 c1 = 1.0; 1416 c3 = nodes[0] - q_ref_1d[i]; 1417 interp_1d[i * P + 0] = 1.0; 1418 for (CeedInt j = 1; j < P; j++) { 1419 c2 = 1.0; 1420 c4 = c3; 1421 c3 = nodes[j] - q_ref_1d[i]; 1422 for (CeedInt k = 0; k < j; k++) { 1423 dx = nodes[j] - nodes[k]; 1424 c2 *= dx; 1425 if (k == j - 1) { 1426 grad_1d[i * P + j] = c1 * (interp_1d[i * P + k] - c4 * grad_1d[i * P + k]) / c2; 1427 interp_1d[i * P + j] = -c1 * c4 * interp_1d[i * P + k] / c2; 1428 } 1429 grad_1d[i * P + k] = (c3 * grad_1d[i * P + k] - interp_1d[i * P + k]) / dx; 1430 interp_1d[i * P + k] = c3 * interp_1d[i * P + k] / dx; 1431 } 1432 c1 = c2; 1433 } 1434 } 1435 // Pass to CeedBasisCreateTensorH1 1436 CeedCall(CeedBasisCreateTensorH1(ceed, dim, num_comp, P, Q, interp_1d, grad_1d, q_ref_1d, q_weight_1d, basis)); 1437 cleanup: 1438 CeedCall(CeedFree(&interp_1d)); 1439 CeedCall(CeedFree(&grad_1d)); 1440 CeedCall(CeedFree(&nodes)); 1441 CeedCall(CeedFree(&q_ref_1d)); 1442 CeedCall(CeedFree(&q_weight_1d)); 1443 return CEED_ERROR_SUCCESS; 1444 } 1445 1446 /** 1447 @brief Create a non tensor-product basis for \f$H^1\f$ discretizations 1448 1449 @param[in] ceed `Ceed` object used to create the `CeedBasis` 1450 @param[in] topo Topology of element, e.g. hypercube, simplex, etc 1451 @param[in] num_comp Number of field components (1 for scalar fields) 1452 @param[in] num_nodes Total number of nodes 1453 @param[in] num_qpts Total number of quadrature points 1454 @param[in] interp Row-major (`num_qpts * num_nodes`) matrix expressing the values of nodal basis functions at quadrature points 1455 @param[in] grad Row-major (`dim * num_qpts * num_nodes`) matrix expressing derivatives of nodal basis functions at quadrature points 1456 @param[in] q_ref Array of length `num_qpts` * dim holding the locations of quadrature points on the reference element 1457 @param[in] q_weight Array of length `num_qpts` holding the quadrature weights on the reference element 1458 @param[out] basis Address of the variable where the newly created `CeedBasis` will be stored 1459 1460 @return An error code: 0 - success, otherwise - failure 1461 1462 @ref User 1463 **/ 1464 int CeedBasisCreateH1(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, 1465 const CeedScalar *grad, const CeedScalar *q_ref, const CeedScalar *q_weight, CeedBasis *basis) { 1466 CeedInt P = num_nodes, Q = num_qpts, dim = 0; 1467 1468 if (!ceed->BasisCreateH1) { 1469 Ceed delegate; 1470 1471 CeedCall(CeedGetObjectDelegate(ceed, &delegate, "Basis")); 1472 CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement BasisCreateH1"); 1473 CeedCall(CeedBasisCreateH1(delegate, topo, num_comp, num_nodes, num_qpts, interp, grad, q_ref, q_weight, basis)); 1474 CeedCall(CeedDestroy(&delegate)); 1475 return CEED_ERROR_SUCCESS; 1476 } 1477 1478 CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 component"); 1479 CeedCheck(num_nodes > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 node"); 1480 CeedCheck(num_qpts > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 quadrature point"); 1481 1482 CeedCall(CeedBasisGetTopologyDimension(topo, &dim)); 1483 1484 CeedCall(CeedCalloc(1, basis)); 1485 CeedCall(CeedReferenceCopy(ceed, &(*basis)->ceed)); 1486 (*basis)->ref_count = 1; 1487 (*basis)->is_tensor_basis = false; 1488 (*basis)->dim = dim; 1489 (*basis)->topo = topo; 1490 (*basis)->num_comp = num_comp; 1491 (*basis)->P = P; 1492 (*basis)->Q = Q; 1493 (*basis)->fe_space = CEED_FE_SPACE_H1; 1494 CeedCall(CeedCalloc(Q * dim, &(*basis)->q_ref_1d)); 1495 CeedCall(CeedCalloc(Q, &(*basis)->q_weight_1d)); 1496 if (q_ref) memcpy((*basis)->q_ref_1d, q_ref, Q * dim * sizeof(q_ref[0])); 1497 if (q_weight) memcpy((*basis)->q_weight_1d, q_weight, Q * sizeof(q_weight[0])); 1498 CeedCall(CeedCalloc(Q * P, &(*basis)->interp)); 1499 CeedCall(CeedCalloc(dim * Q * P, &(*basis)->grad)); 1500 if (interp) memcpy((*basis)->interp, interp, Q * P * sizeof(interp[0])); 1501 if (grad) memcpy((*basis)->grad, grad, dim * Q * P * sizeof(grad[0])); 1502 CeedCall(ceed->BasisCreateH1(topo, dim, P, Q, interp, grad, q_ref, q_weight, *basis)); 1503 return CEED_ERROR_SUCCESS; 1504 } 1505 1506 /** 1507 @brief Create a non tensor-product basis for \f$H(\mathrm{div})\f$ discretizations 1508 1509 @param[in] ceed `Ceed` object used to create the `CeedBasis` 1510 @param[in] topo Topology of element (`CEED_TOPOLOGY_QUAD`, `CEED_TOPOLOGY_PRISM`, etc.), dimension of which is used in some array sizes below 1511 @param[in] num_comp Number of components (usually 1 for vectors in H(div) bases) 1512 @param[in] num_nodes Total number of nodes (DoFs per element) 1513 @param[in] num_qpts Total number of quadrature points 1514 @param[in] interp Row-major (`dim * num_qpts * num_nodes`) matrix expressing the values of basis functions at quadrature points 1515 @param[in] div Row-major (`num_qpts * num_nodes`) matrix expressing divergence of basis functions at quadrature points 1516 @param[in] q_ref Array of length `num_qpts` * dim holding the locations of quadrature points on the reference element 1517 @param[in] q_weight Array of length `num_qpts` holding the quadrature weights on the reference element 1518 @param[out] basis Address of the variable where the newly created `CeedBasis` will be stored 1519 1520 @return An error code: 0 - success, otherwise - failure 1521 1522 @ref User 1523 **/ 1524 int CeedBasisCreateHdiv(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, 1525 const CeedScalar *div, const CeedScalar *q_ref, const CeedScalar *q_weight, CeedBasis *basis) { 1526 CeedInt Q = num_qpts, P = num_nodes, dim = 0; 1527 1528 if (!ceed->BasisCreateHdiv) { 1529 Ceed delegate; 1530 1531 CeedCall(CeedGetObjectDelegate(ceed, &delegate, "Basis")); 1532 CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement BasisCreateHdiv"); 1533 CeedCall(CeedBasisCreateHdiv(delegate, topo, num_comp, num_nodes, num_qpts, interp, div, q_ref, q_weight, basis)); 1534 CeedCall(CeedDestroy(&delegate)); 1535 return CEED_ERROR_SUCCESS; 1536 } 1537 1538 CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 component"); 1539 CeedCheck(num_nodes > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 node"); 1540 CeedCheck(num_qpts > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 quadrature point"); 1541 1542 CeedCall(CeedBasisGetTopologyDimension(topo, &dim)); 1543 1544 CeedCall(CeedCalloc(1, basis)); 1545 CeedCall(CeedReferenceCopy(ceed, &(*basis)->ceed)); 1546 (*basis)->ref_count = 1; 1547 (*basis)->is_tensor_basis = false; 1548 (*basis)->dim = dim; 1549 (*basis)->topo = topo; 1550 (*basis)->num_comp = num_comp; 1551 (*basis)->P = P; 1552 (*basis)->Q = Q; 1553 (*basis)->fe_space = CEED_FE_SPACE_HDIV; 1554 CeedCall(CeedMalloc(Q * dim, &(*basis)->q_ref_1d)); 1555 CeedCall(CeedMalloc(Q, &(*basis)->q_weight_1d)); 1556 if (q_ref) memcpy((*basis)->q_ref_1d, q_ref, Q * dim * sizeof(q_ref[0])); 1557 if (q_weight) memcpy((*basis)->q_weight_1d, q_weight, Q * sizeof(q_weight[0])); 1558 CeedCall(CeedMalloc(dim * Q * P, &(*basis)->interp)); 1559 CeedCall(CeedMalloc(Q * P, &(*basis)->div)); 1560 if (interp) memcpy((*basis)->interp, interp, dim * Q * P * sizeof(interp[0])); 1561 if (div) memcpy((*basis)->div, div, Q * P * sizeof(div[0])); 1562 CeedCall(ceed->BasisCreateHdiv(topo, dim, P, Q, interp, div, q_ref, q_weight, *basis)); 1563 return CEED_ERROR_SUCCESS; 1564 } 1565 1566 /** 1567 @brief Create a non tensor-product basis for \f$H(\mathrm{curl})\f$ discretizations 1568 1569 @param[in] ceed `Ceed` object used to create the `CeedBasis` 1570 @param[in] topo Topology of element (`CEED_TOPOLOGY_QUAD`, `CEED_TOPOLOGY_PRISM`, etc.), dimension of which is used in some array sizes below 1571 @param[in] num_comp Number of components (usually 1 for vectors in \f$H(\mathrm{curl})\f$ bases) 1572 @param[in] num_nodes Total number of nodes (DoFs per element) 1573 @param[in] num_qpts Total number of quadrature points 1574 @param[in] interp Row-major (`dim * num_qpts * num_nodes`) matrix expressing the values of basis functions at quadrature points 1575 @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 1576 @param[in] q_ref Array of length `num_qpts * dim` holding the locations of quadrature points on the reference element 1577 @param[in] q_weight Array of length `num_qpts` holding the quadrature weights on the reference element 1578 @param[out] basis Address of the variable where the newly created `CeedBasis` will be stored 1579 1580 @return An error code: 0 - success, otherwise - failure 1581 1582 @ref User 1583 **/ 1584 int CeedBasisCreateHcurl(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, 1585 const CeedScalar *curl, const CeedScalar *q_ref, const CeedScalar *q_weight, CeedBasis *basis) { 1586 CeedInt Q = num_qpts, P = num_nodes, dim = 0, curl_comp = 0; 1587 1588 if (!ceed->BasisCreateHcurl) { 1589 Ceed delegate; 1590 1591 CeedCall(CeedGetObjectDelegate(ceed, &delegate, "Basis")); 1592 CeedCheck(delegate, ceed, CEED_ERROR_UNSUPPORTED, "Backend does not implement BasisCreateHcurl"); 1593 CeedCall(CeedBasisCreateHcurl(delegate, topo, num_comp, num_nodes, num_qpts, interp, curl, q_ref, q_weight, basis)); 1594 CeedCall(CeedDestroy(&delegate)); 1595 return CEED_ERROR_SUCCESS; 1596 } 1597 1598 CeedCheck(num_comp > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 component"); 1599 CeedCheck(num_nodes > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 node"); 1600 CeedCheck(num_qpts > 0, ceed, CEED_ERROR_DIMENSION, "CeedBasis must have at least 1 quadrature point"); 1601 1602 CeedCall(CeedBasisGetTopologyDimension(topo, &dim)); 1603 curl_comp = (dim < 3) ? 1 : dim; 1604 1605 CeedCall(CeedCalloc(1, basis)); 1606 CeedCall(CeedReferenceCopy(ceed, &(*basis)->ceed)); 1607 (*basis)->ref_count = 1; 1608 (*basis)->is_tensor_basis = false; 1609 (*basis)->dim = dim; 1610 (*basis)->topo = topo; 1611 (*basis)->num_comp = num_comp; 1612 (*basis)->P = P; 1613 (*basis)->Q = Q; 1614 (*basis)->fe_space = CEED_FE_SPACE_HCURL; 1615 CeedCall(CeedMalloc(Q * dim, &(*basis)->q_ref_1d)); 1616 CeedCall(CeedMalloc(Q, &(*basis)->q_weight_1d)); 1617 if (q_ref) memcpy((*basis)->q_ref_1d, q_ref, Q * dim * sizeof(q_ref[0])); 1618 if (q_weight) memcpy((*basis)->q_weight_1d, q_weight, Q * sizeof(q_weight[0])); 1619 CeedCall(CeedMalloc(dim * Q * P, &(*basis)->interp)); 1620 CeedCall(CeedMalloc(curl_comp * Q * P, &(*basis)->curl)); 1621 if (interp) memcpy((*basis)->interp, interp, dim * Q * P * sizeof(interp[0])); 1622 if (curl) memcpy((*basis)->curl, curl, curl_comp * Q * P * sizeof(curl[0])); 1623 CeedCall(ceed->BasisCreateHcurl(topo, dim, P, Q, interp, curl, q_ref, q_weight, *basis)); 1624 return CEED_ERROR_SUCCESS; 1625 } 1626 1627 /** 1628 @brief Create a `CeedBasis` for projection from the nodes of `basis_from` to the nodes of `basis_to`. 1629 1630 Only @ref CEED_EVAL_INTERP will be valid for the new basis, `basis_project`. 1631 For \f$H^1\f$ spaces, @ref CEED_EVAL_GRAD will also be valid. 1632 The interpolation is given by `interp_project = interp_to^+ * interp_from`, where the pseudoinverse `interp_to^+` is given by QR factorization. 1633 The gradient (for the \f$H^1\f$ case) is given by `grad_project = interp_to^+ * grad_from`. 1634 1635 Note: `basis_from` and `basis_to` must have compatible quadrature spaces. 1636 1637 Note: `basis_project` will have the same number of components as `basis_from`, regardless of the number of components that `basis_to` has. 1638 If `basis_from` has 3 components and `basis_to` has 5 components, then `basis_project` will have 3 components. 1639 1640 Note: If either `basis_from` or `basis_to` are non-tensor, then `basis_project` will also be non-tensor 1641 1642 @param[in] basis_from `CeedBasis` to prolong from 1643 @param[in] basis_to `CeedBasis` to prolong to 1644 @param[out] basis_project Address of the variable where the newly created `CeedBasis` will be stored 1645 1646 @return An error code: 0 - success, otherwise - failure 1647 1648 @ref User 1649 **/ 1650 int CeedBasisCreateProjection(CeedBasis basis_from, CeedBasis basis_to, CeedBasis *basis_project) { 1651 Ceed ceed; 1652 bool create_tensor; 1653 CeedInt dim, num_comp; 1654 CeedScalar *interp_project, *grad_project; 1655 1656 CeedCall(CeedBasisGetCeed(basis_to, &ceed)); 1657 1658 // Create projection matrix 1659 CeedCall(CeedBasisCreateProjectionMatrices(basis_from, basis_to, &interp_project, &grad_project)); 1660 1661 // Build basis 1662 { 1663 bool is_tensor_to, is_tensor_from; 1664 1665 CeedCall(CeedBasisIsTensor(basis_to, &is_tensor_to)); 1666 CeedCall(CeedBasisIsTensor(basis_from, &is_tensor_from)); 1667 create_tensor = is_tensor_from && is_tensor_to; 1668 } 1669 CeedCall(CeedBasisGetDimension(basis_to, &dim)); 1670 CeedCall(CeedBasisGetNumComponents(basis_from, &num_comp)); 1671 if (create_tensor) { 1672 CeedInt P_1d_to, P_1d_from; 1673 1674 CeedCall(CeedBasisGetNumNodes1D(basis_from, &P_1d_from)); 1675 CeedCall(CeedBasisGetNumNodes1D(basis_to, &P_1d_to)); 1676 CeedCall(CeedBasisCreateTensorH1(ceed, dim, num_comp, P_1d_from, P_1d_to, interp_project, grad_project, NULL, NULL, basis_project)); 1677 } else { 1678 // Even if basis_to and basis_from are not H1, the resulting basis is H1 for interpolation to work 1679 CeedInt num_nodes_to, num_nodes_from; 1680 CeedElemTopology topo; 1681 1682 CeedCall(CeedBasisGetTopology(basis_from, &topo)); 1683 CeedCall(CeedBasisGetNumNodes(basis_from, &num_nodes_from)); 1684 CeedCall(CeedBasisGetNumNodes(basis_to, &num_nodes_to)); 1685 CeedCall(CeedBasisCreateH1(ceed, topo, num_comp, num_nodes_from, num_nodes_to, interp_project, grad_project, NULL, NULL, basis_project)); 1686 } 1687 1688 // Cleanup 1689 CeedCall(CeedFree(&interp_project)); 1690 CeedCall(CeedFree(&grad_project)); 1691 CeedCall(CeedDestroy(&ceed)); 1692 return CEED_ERROR_SUCCESS; 1693 } 1694 1695 /** 1696 @brief Copy the pointer to a `CeedBasis`. 1697 1698 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`. 1699 This `CeedBasis` will be destroyed if `*basis_copy` is the only reference to this `CeedBasis`. 1700 1701 @param[in] basis `CeedBasis` to copy reference to 1702 @param[in,out] basis_copy Variable to store copied reference 1703 1704 @return An error code: 0 - success, otherwise - failure 1705 1706 @ref User 1707 **/ 1708 int CeedBasisReferenceCopy(CeedBasis basis, CeedBasis *basis_copy) { 1709 if (basis != CEED_BASIS_NONE) CeedCall(CeedBasisReference(basis)); 1710 CeedCall(CeedBasisDestroy(basis_copy)); 1711 *basis_copy = basis; 1712 return CEED_ERROR_SUCCESS; 1713 } 1714 1715 /** 1716 @brief View a `CeedBasis` 1717 1718 @param[in] basis `CeedBasis` to view 1719 @param[in] stream Stream to view to, e.g., `stdout` 1720 1721 @return An error code: 0 - success, otherwise - failure 1722 1723 @ref User 1724 **/ 1725 int CeedBasisView(CeedBasis basis, FILE *stream) { 1726 bool is_tensor_basis; 1727 CeedElemTopology topo; 1728 CeedFESpace fe_space; 1729 1730 // Basis data 1731 CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis)); 1732 CeedCall(CeedBasisGetTopology(basis, &topo)); 1733 CeedCall(CeedBasisGetFESpace(basis, &fe_space)); 1734 1735 // Print FE space and element topology of the basis 1736 fprintf(stream, "CeedBasis in a %s on a %s element\n", CeedFESpaces[fe_space], CeedElemTopologies[topo]); 1737 if (is_tensor_basis) { 1738 fprintf(stream, " P: %" CeedInt_FMT "\n Q: %" CeedInt_FMT "\n", basis->P_1d, basis->Q_1d); 1739 } else { 1740 fprintf(stream, " P: %" CeedInt_FMT "\n Q: %" CeedInt_FMT "\n", basis->P, basis->Q); 1741 } 1742 fprintf(stream, " dimension: %" CeedInt_FMT "\n field components: %" CeedInt_FMT "\n", basis->dim, basis->num_comp); 1743 // Print quadrature data, interpolation/gradient/divergence/curl of the basis 1744 if (is_tensor_basis) { // tensor basis 1745 CeedInt P_1d, Q_1d; 1746 const CeedScalar *q_ref_1d, *q_weight_1d, *interp_1d, *grad_1d; 1747 1748 CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d)); 1749 CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d)); 1750 CeedCall(CeedBasisGetQRef(basis, &q_ref_1d)); 1751 CeedCall(CeedBasisGetQWeights(basis, &q_weight_1d)); 1752 CeedCall(CeedBasisGetInterp1D(basis, &interp_1d)); 1753 CeedCall(CeedBasisGetGrad1D(basis, &grad_1d)); 1754 1755 CeedCall(CeedScalarView("qref1d", "\t% 12.8f", 1, Q_1d, q_ref_1d, stream)); 1756 CeedCall(CeedScalarView("qweight1d", "\t% 12.8f", 1, Q_1d, q_weight_1d, stream)); 1757 CeedCall(CeedScalarView("interp1d", "\t% 12.8f", Q_1d, P_1d, interp_1d, stream)); 1758 CeedCall(CeedScalarView("grad1d", "\t% 12.8f", Q_1d, P_1d, grad_1d, stream)); 1759 } else { // non-tensor basis 1760 CeedInt P, Q, dim, q_comp; 1761 const CeedScalar *q_ref, *q_weight, *interp, *grad, *div, *curl; 1762 1763 CeedCall(CeedBasisGetNumNodes(basis, &P)); 1764 CeedCall(CeedBasisGetNumQuadraturePoints(basis, &Q)); 1765 CeedCall(CeedBasisGetDimension(basis, &dim)); 1766 CeedCall(CeedBasisGetQRef(basis, &q_ref)); 1767 CeedCall(CeedBasisGetQWeights(basis, &q_weight)); 1768 CeedCall(CeedBasisGetInterp(basis, &interp)); 1769 CeedCall(CeedBasisGetGrad(basis, &grad)); 1770 CeedCall(CeedBasisGetDiv(basis, &div)); 1771 CeedCall(CeedBasisGetCurl(basis, &curl)); 1772 1773 CeedCall(CeedScalarView("qref", "\t% 12.8f", 1, Q * dim, q_ref, stream)); 1774 CeedCall(CeedScalarView("qweight", "\t% 12.8f", 1, Q, q_weight, stream)); 1775 CeedCall(CeedBasisGetNumQuadratureComponents(basis, CEED_EVAL_INTERP, &q_comp)); 1776 CeedCall(CeedScalarView("interp", "\t% 12.8f", q_comp * Q, P, interp, stream)); 1777 if (grad) { 1778 CeedCall(CeedBasisGetNumQuadratureComponents(basis, CEED_EVAL_GRAD, &q_comp)); 1779 CeedCall(CeedScalarView("grad", "\t% 12.8f", q_comp * Q, P, grad, stream)); 1780 } 1781 if (div) { 1782 CeedCall(CeedBasisGetNumQuadratureComponents(basis, CEED_EVAL_DIV, &q_comp)); 1783 CeedCall(CeedScalarView("div", "\t% 12.8f", q_comp * Q, P, div, stream)); 1784 } 1785 if (curl) { 1786 CeedCall(CeedBasisGetNumQuadratureComponents(basis, CEED_EVAL_CURL, &q_comp)); 1787 CeedCall(CeedScalarView("curl", "\t% 12.8f", q_comp * Q, P, curl, stream)); 1788 } 1789 } 1790 return CEED_ERROR_SUCCESS; 1791 } 1792 1793 /** 1794 @brief Check input vector dimensions for CeedBasisApply[Add] 1795 1796 @param[in] basis `CeedBasis` to evaluate 1797 @param[in] num_elem The number of elements to apply the basis evaluation to; 1798 the backend will specify the ordering in @ref CeedElemRestrictionCreate() 1799 @param[in] t_mode @ref CEED_NOTRANSPOSE to evaluate from nodes to quadrature points; 1800 @ref CEED_TRANSPOSE to apply the transpose, mapping from quadrature points to nodes 1801 @param[in] eval_mode @ref CEED_EVAL_NONE to use values directly, 1802 @ref CEED_EVAL_INTERP to use interpolated values, 1803 @ref CEED_EVAL_GRAD to use gradients, 1804 @ref CEED_EVAL_DIV to use divergence, 1805 @ref CEED_EVAL_CURL to use curl, 1806 @ref CEED_EVAL_WEIGHT to use quadrature weights 1807 @param[in] u Input `CeedVector` 1808 @param[out] v Output `CeedVector` 1809 1810 @return An error code: 0 - success, otherwise - failure 1811 1812 @ref Developer 1813 **/ 1814 static int CeedBasisApplyCheckDims(CeedBasis basis, CeedInt num_elem, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedVector u, CeedVector v) { 1815 CeedInt dim, num_comp, q_comp, num_nodes, num_qpts; 1816 CeedSize u_length = 0, v_length; 1817 1818 CeedCall(CeedBasisGetDimension(basis, &dim)); 1819 CeedCall(CeedBasisGetNumComponents(basis, &num_comp)); 1820 CeedCall(CeedBasisGetNumQuadratureComponents(basis, eval_mode, &q_comp)); 1821 CeedCall(CeedBasisGetNumNodes(basis, &num_nodes)); 1822 CeedCall(CeedBasisGetNumQuadraturePoints(basis, &num_qpts)); 1823 CeedCall(CeedVectorGetLength(v, &v_length)); 1824 if (u) CeedCall(CeedVectorGetLength(u, &u_length)); 1825 1826 // Check vector lengths to prevent out of bounds issues 1827 bool has_good_dims = true; 1828 switch (eval_mode) { 1829 case CEED_EVAL_NONE: 1830 case CEED_EVAL_INTERP: 1831 case CEED_EVAL_GRAD: 1832 case CEED_EVAL_DIV: 1833 case CEED_EVAL_CURL: 1834 has_good_dims = ((t_mode == CEED_TRANSPOSE && u_length >= (CeedSize)num_elem * (CeedSize)num_comp * (CeedSize)num_qpts * (CeedSize)q_comp && 1835 v_length >= (CeedSize)num_elem * (CeedSize)num_comp * (CeedSize)num_nodes) || 1836 (t_mode == CEED_NOTRANSPOSE && v_length >= (CeedSize)num_elem * (CeedSize)num_qpts * (CeedSize)num_comp * (CeedSize)q_comp && 1837 u_length >= (CeedSize)num_elem * (CeedSize)num_comp * (CeedSize)num_nodes)); 1838 break; 1839 case CEED_EVAL_WEIGHT: 1840 has_good_dims = v_length >= (CeedSize)num_elem * (CeedSize)num_qpts; 1841 break; 1842 } 1843 CeedCheck(has_good_dims, CeedBasisReturnCeed(basis), CEED_ERROR_DIMENSION, "Input/output vectors too short for basis and evaluation mode"); 1844 return CEED_ERROR_SUCCESS; 1845 } 1846 1847 /** 1848 @brief Apply basis evaluation from nodes to quadrature points or vice versa 1849 1850 @param[in] basis `CeedBasis` to evaluate 1851 @param[in] num_elem The number of elements to apply the basis evaluation to; 1852 the backend will specify the ordering in @ref CeedElemRestrictionCreate() 1853 @param[in] t_mode @ref CEED_NOTRANSPOSE to evaluate from nodes to quadrature points; 1854 @ref CEED_TRANSPOSE to apply the transpose, mapping from quadrature points to nodes 1855 @param[in] eval_mode @ref CEED_EVAL_NONE to use values directly, 1856 @ref CEED_EVAL_INTERP to use interpolated values, 1857 @ref CEED_EVAL_GRAD to use gradients, 1858 @ref CEED_EVAL_DIV to use divergence, 1859 @ref CEED_EVAL_CURL to use curl, 1860 @ref CEED_EVAL_WEIGHT to use quadrature weights 1861 @param[in] u Input `CeedVector` 1862 @param[out] v Output `CeedVector` 1863 1864 @return An error code: 0 - success, otherwise - failure 1865 1866 @ref User 1867 **/ 1868 int CeedBasisApply(CeedBasis basis, CeedInt num_elem, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedVector u, CeedVector v) { 1869 CeedCall(CeedBasisApplyCheckDims(basis, num_elem, t_mode, eval_mode, u, v)); 1870 CeedCheck(basis->Apply, CeedBasisReturnCeed(basis), CEED_ERROR_UNSUPPORTED, "Backend does not support CeedBasisApply"); 1871 CeedCall(basis->Apply(basis, num_elem, t_mode, eval_mode, u, v)); 1872 return CEED_ERROR_SUCCESS; 1873 } 1874 1875 /** 1876 @brief Apply basis evaluation from quadrature points to nodes and sum into target vector 1877 1878 @param[in] basis `CeedBasis` to evaluate 1879 @param[in] num_elem The number of elements to apply the basis evaluation to; 1880 the backend will specify the ordering in @ref CeedElemRestrictionCreate() 1881 @param[in] t_mode @ref CEED_TRANSPOSE to apply the transpose, mapping from quadrature points to nodes; 1882 @ref CEED_NOTRANSPOSE is not valid for `CeedBasisApplyAdd()` 1883 @param[in] eval_mode @ref CEED_EVAL_NONE to use values directly, 1884 @ref CEED_EVAL_INTERP to use interpolated values, 1885 @ref CEED_EVAL_GRAD to use gradients, 1886 @ref CEED_EVAL_DIV to use divergence, 1887 @ref CEED_EVAL_CURL to use curl, 1888 @ref CEED_EVAL_WEIGHT to use quadrature weights 1889 @param[in] u Input `CeedVector` 1890 @param[out] v Output `CeedVector` to sum into 1891 1892 @return An error code: 0 - success, otherwise - failure 1893 1894 @ref User 1895 **/ 1896 int CeedBasisApplyAdd(CeedBasis basis, CeedInt num_elem, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedVector u, CeedVector v) { 1897 CeedCheck(t_mode == CEED_TRANSPOSE, CeedBasisReturnCeed(basis), CEED_ERROR_UNSUPPORTED, "CeedBasisApplyAdd only supports CEED_TRANSPOSE"); 1898 CeedCall(CeedBasisApplyCheckDims(basis, num_elem, t_mode, eval_mode, u, v)); 1899 CeedCheck(basis->ApplyAdd, CeedBasisReturnCeed(basis), CEED_ERROR_UNSUPPORTED, "Backend does not implement CeedBasisApplyAdd"); 1900 CeedCall(basis->ApplyAdd(basis, num_elem, t_mode, eval_mode, u, v)); 1901 return CEED_ERROR_SUCCESS; 1902 } 1903 1904 /** 1905 @brief Apply basis evaluation from nodes to arbitrary points 1906 1907 @param[in] basis `CeedBasis` to evaluate 1908 @param[in] num_elem The number of elements to apply the basis evaluation to; 1909 the backend will specify the ordering in @ref CeedElemRestrictionCreate() 1910 @param[in] num_points Array of the number of points to apply the basis evaluation to in each element, size `num_elem` 1911 @param[in] t_mode @ref CEED_NOTRANSPOSE to evaluate from nodes to points; 1912 @ref CEED_TRANSPOSE to apply the transpose, mapping from points to nodes 1913 @param[in] eval_mode @ref CEED_EVAL_INTERP to use interpolated values, 1914 @ref CEED_EVAL_GRAD to use gradients, 1915 @ref CEED_EVAL_WEIGHT to use quadrature weights 1916 @param[in] x_ref `CeedVector` holding reference coordinates of each point 1917 @param[in] u Input `CeedVector`, of length `num_nodes * num_comp` for @ref CEED_NOTRANSPOSE 1918 @param[out] v Output `CeedVector`, of length `num_points * num_q_comp` for @ref CEED_NOTRANSPOSE with @ref CEED_EVAL_INTERP 1919 1920 @return An error code: 0 - success, otherwise - failure 1921 1922 @ref User 1923 **/ 1924 int CeedBasisApplyAtPoints(CeedBasis basis, CeedInt num_elem, const CeedInt *num_points, CeedTransposeMode t_mode, CeedEvalMode eval_mode, 1925 CeedVector x_ref, CeedVector u, CeedVector v) { 1926 CeedCall(CeedBasisApplyAtPointsCheckDims(basis, num_elem, num_points, t_mode, eval_mode, x_ref, u, v)); 1927 if (basis->ApplyAtPoints) { 1928 CeedCall(basis->ApplyAtPoints(basis, num_elem, num_points, t_mode, eval_mode, x_ref, u, v)); 1929 } else { 1930 CeedCall(CeedBasisApplyAtPoints_Core(basis, false, num_elem, num_points, t_mode, eval_mode, x_ref, u, v)); 1931 } 1932 return CEED_ERROR_SUCCESS; 1933 } 1934 1935 /** 1936 @brief Apply basis evaluation from nodes to arbitrary points and sum into target vector 1937 1938 @param[in] basis `CeedBasis` to evaluate 1939 @param[in] num_elem The number of elements to apply the basis evaluation to; 1940 the backend will specify the ordering in @ref CeedElemRestrictionCreate() 1941 @param[in] num_points Array of the number of points to apply the basis evaluation to in each element, size `num_elem` 1942 @param[in] t_mode @ref CEED_NOTRANSPOSE to evaluate from nodes to points; 1943 @ref CEED_NOTRANSPOSE is not valid for `CeedBasisApplyAddAtPoints()` 1944 @param[in] eval_mode @ref CEED_EVAL_INTERP to use interpolated values, 1945 @ref CEED_EVAL_GRAD to use gradients, 1946 @ref CEED_EVAL_WEIGHT to use quadrature weights 1947 @param[in] x_ref `CeedVector` holding reference coordinates of each point 1948 @param[in] u Input `CeedVector`, of length `num_nodes * num_comp` for @ref CEED_NOTRANSPOSE 1949 @param[out] v Output `CeedVector`, of length `num_points * num_q_comp` for @ref CEED_NOTRANSPOSE with @ref CEED_EVAL_INTERP 1950 1951 @return An error code: 0 - success, otherwise - failure 1952 1953 @ref User 1954 **/ 1955 int CeedBasisApplyAddAtPoints(CeedBasis basis, CeedInt num_elem, const CeedInt *num_points, CeedTransposeMode t_mode, CeedEvalMode eval_mode, 1956 CeedVector x_ref, CeedVector u, CeedVector v) { 1957 CeedCheck(t_mode == CEED_TRANSPOSE, CeedBasisReturnCeed(basis), CEED_ERROR_UNSUPPORTED, "CeedBasisApplyAddAtPoints only supports CEED_TRANSPOSE"); 1958 CeedCall(CeedBasisApplyAtPointsCheckDims(basis, num_elem, num_points, t_mode, eval_mode, x_ref, u, v)); 1959 if (basis->ApplyAddAtPoints) { 1960 CeedCall(basis->ApplyAddAtPoints(basis, num_elem, num_points, t_mode, eval_mode, x_ref, u, v)); 1961 } else { 1962 CeedCall(CeedBasisApplyAtPoints_Core(basis, true, num_elem, num_points, t_mode, eval_mode, x_ref, u, v)); 1963 } 1964 return CEED_ERROR_SUCCESS; 1965 } 1966 1967 /** 1968 @brief Get the `Ceed` associated with a `CeedBasis` 1969 1970 @param[in] basis `CeedBasis` 1971 @param[out] ceed Variable to store `Ceed` 1972 1973 @return An error code: 0 - success, otherwise - failure 1974 1975 @ref Advanced 1976 **/ 1977 int CeedBasisGetCeed(CeedBasis basis, Ceed *ceed) { 1978 *ceed = NULL; 1979 CeedCall(CeedReferenceCopy(CeedBasisReturnCeed(basis), ceed)); 1980 return CEED_ERROR_SUCCESS; 1981 } 1982 1983 /** 1984 @brief Return the `Ceed` associated with a `CeedBasis` 1985 1986 @param[in] basis `CeedBasis` 1987 1988 @return `Ceed` associated with the `basis` 1989 1990 @ref Advanced 1991 **/ 1992 Ceed CeedBasisReturnCeed(CeedBasis basis) { return basis->ceed; } 1993 1994 /** 1995 @brief Get dimension for given `CeedBasis` 1996 1997 @param[in] basis `CeedBasis` 1998 @param[out] dim Variable to store dimension of basis 1999 2000 @return An error code: 0 - success, otherwise - failure 2001 2002 @ref Advanced 2003 **/ 2004 int CeedBasisGetDimension(CeedBasis basis, CeedInt *dim) { 2005 *dim = basis->dim; 2006 return CEED_ERROR_SUCCESS; 2007 } 2008 2009 /** 2010 @brief Get topology for given `CeedBasis` 2011 2012 @param[in] basis `CeedBasis` 2013 @param[out] topo Variable to store topology of basis 2014 2015 @return An error code: 0 - success, otherwise - failure 2016 2017 @ref Advanced 2018 **/ 2019 int CeedBasisGetTopology(CeedBasis basis, CeedElemTopology *topo) { 2020 *topo = basis->topo; 2021 return CEED_ERROR_SUCCESS; 2022 } 2023 2024 /** 2025 @brief Get number of components for given `CeedBasis` 2026 2027 @param[in] basis `CeedBasis` 2028 @param[out] num_comp Variable to store number of components 2029 2030 @return An error code: 0 - success, otherwise - failure 2031 2032 @ref Advanced 2033 **/ 2034 int CeedBasisGetNumComponents(CeedBasis basis, CeedInt *num_comp) { 2035 *num_comp = basis->num_comp; 2036 return CEED_ERROR_SUCCESS; 2037 } 2038 2039 /** 2040 @brief Get total number of nodes (in `dim` dimensions) of a `CeedBasis` 2041 2042 @param[in] basis `CeedBasis` 2043 @param[out] P Variable to store number of nodes 2044 2045 @return An error code: 0 - success, otherwise - failure 2046 2047 @ref Utility 2048 **/ 2049 int CeedBasisGetNumNodes(CeedBasis basis, CeedInt *P) { 2050 *P = basis->P; 2051 return CEED_ERROR_SUCCESS; 2052 } 2053 2054 /** 2055 @brief Get total number of nodes (in 1 dimension) of a `CeedBasis` 2056 2057 @param[in] basis `CeedBasis` 2058 @param[out] P_1d Variable to store number of nodes 2059 2060 @return An error code: 0 - success, otherwise - failure 2061 2062 @ref Advanced 2063 **/ 2064 int CeedBasisGetNumNodes1D(CeedBasis basis, CeedInt *P_1d) { 2065 CeedCheck(basis->is_tensor_basis, CeedBasisReturnCeed(basis), CEED_ERROR_MINOR, "Cannot supply P_1d for non-tensor CeedBasis"); 2066 *P_1d = basis->P_1d; 2067 return CEED_ERROR_SUCCESS; 2068 } 2069 2070 /** 2071 @brief Get total number of quadrature points (in `dim` dimensions) of a `CeedBasis` 2072 2073 @param[in] basis `CeedBasis` 2074 @param[out] Q Variable to store number of quadrature points 2075 2076 @return An error code: 0 - success, otherwise - failure 2077 2078 @ref Utility 2079 **/ 2080 int CeedBasisGetNumQuadraturePoints(CeedBasis basis, CeedInt *Q) { 2081 *Q = basis->Q; 2082 return CEED_ERROR_SUCCESS; 2083 } 2084 2085 /** 2086 @brief Get total number of quadrature points (in 1 dimension) of a `CeedBasis` 2087 2088 @param[in] basis `CeedBasis` 2089 @param[out] Q_1d Variable to store number of quadrature points 2090 2091 @return An error code: 0 - success, otherwise - failure 2092 2093 @ref Advanced 2094 **/ 2095 int CeedBasisGetNumQuadraturePoints1D(CeedBasis basis, CeedInt *Q_1d) { 2096 CeedCheck(basis->is_tensor_basis, CeedBasisReturnCeed(basis), CEED_ERROR_MINOR, "Cannot supply Q_1d for non-tensor CeedBasis"); 2097 *Q_1d = basis->Q_1d; 2098 return CEED_ERROR_SUCCESS; 2099 } 2100 2101 /** 2102 @brief Get reference coordinates of quadrature points (in `dim` dimensions) of a `CeedBasis` 2103 2104 @param[in] basis `CeedBasis` 2105 @param[out] q_ref Variable to store reference coordinates of quadrature points 2106 2107 @return An error code: 0 - success, otherwise - failure 2108 2109 @ref Advanced 2110 **/ 2111 int CeedBasisGetQRef(CeedBasis basis, const CeedScalar **q_ref) { 2112 *q_ref = basis->q_ref_1d; 2113 return CEED_ERROR_SUCCESS; 2114 } 2115 2116 /** 2117 @brief Get quadrature weights of quadrature points (in `dim` dimensions) of a `CeedBasis` 2118 2119 @param[in] basis `CeedBasis` 2120 @param[out] q_weight Variable to store quadrature weights 2121 2122 @return An error code: 0 - success, otherwise - failure 2123 2124 @ref Advanced 2125 **/ 2126 int CeedBasisGetQWeights(CeedBasis basis, const CeedScalar **q_weight) { 2127 *q_weight = basis->q_weight_1d; 2128 return CEED_ERROR_SUCCESS; 2129 } 2130 2131 /** 2132 @brief Get interpolation matrix of a `CeedBasis` 2133 2134 @param[in] basis `CeedBasis` 2135 @param[out] interp Variable to store interpolation matrix 2136 2137 @return An error code: 0 - success, otherwise - failure 2138 2139 @ref Advanced 2140 **/ 2141 int CeedBasisGetInterp(CeedBasis basis, const CeedScalar **interp) { 2142 if (!basis->interp && basis->is_tensor_basis) { 2143 // Allocate 2144 CeedCall(CeedMalloc(basis->Q * basis->P, &basis->interp)); 2145 2146 // Initialize 2147 for (CeedInt i = 0; i < basis->Q * basis->P; i++) basis->interp[i] = 1.0; 2148 2149 // Calculate 2150 for (CeedInt d = 0; d < basis->dim; d++) { 2151 for (CeedInt qpt = 0; qpt < basis->Q; qpt++) { 2152 for (CeedInt node = 0; node < basis->P; node++) { 2153 CeedInt p = (node / CeedIntPow(basis->P_1d, d)) % basis->P_1d; 2154 CeedInt q = (qpt / CeedIntPow(basis->Q_1d, d)) % basis->Q_1d; 2155 2156 basis->interp[qpt * (basis->P) + node] *= basis->interp_1d[q * basis->P_1d + p]; 2157 } 2158 } 2159 } 2160 } 2161 *interp = basis->interp; 2162 return CEED_ERROR_SUCCESS; 2163 } 2164 2165 /** 2166 @brief Get 1D interpolation matrix of a tensor product `CeedBasis` 2167 2168 @param[in] basis `CeedBasis` 2169 @param[out] interp_1d Variable to store interpolation matrix 2170 2171 @return An error code: 0 - success, otherwise - failure 2172 2173 @ref Backend 2174 **/ 2175 int CeedBasisGetInterp1D(CeedBasis basis, const CeedScalar **interp_1d) { 2176 bool is_tensor_basis; 2177 2178 CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis)); 2179 CeedCheck(is_tensor_basis, CeedBasisReturnCeed(basis), CEED_ERROR_MINOR, "CeedBasis is not a tensor product CeedBasis"); 2180 *interp_1d = basis->interp_1d; 2181 return CEED_ERROR_SUCCESS; 2182 } 2183 2184 /** 2185 @brief Get gradient matrix of a `CeedBasis` 2186 2187 @param[in] basis `CeedBasis` 2188 @param[out] grad Variable to store gradient matrix 2189 2190 @return An error code: 0 - success, otherwise - failure 2191 2192 @ref Advanced 2193 **/ 2194 int CeedBasisGetGrad(CeedBasis basis, const CeedScalar **grad) { 2195 if (!basis->grad && basis->is_tensor_basis) { 2196 // Allocate 2197 CeedCall(CeedMalloc(basis->dim * basis->Q * basis->P, &basis->grad)); 2198 2199 // Initialize 2200 for (CeedInt i = 0; i < basis->dim * basis->Q * basis->P; i++) basis->grad[i] = 1.0; 2201 2202 // Calculate 2203 for (CeedInt d = 0; d < basis->dim; d++) { 2204 for (CeedInt i = 0; i < basis->dim; i++) { 2205 for (CeedInt qpt = 0; qpt < basis->Q; qpt++) { 2206 for (CeedInt node = 0; node < basis->P; node++) { 2207 CeedInt p = (node / CeedIntPow(basis->P_1d, d)) % basis->P_1d; 2208 CeedInt q = (qpt / CeedIntPow(basis->Q_1d, d)) % basis->Q_1d; 2209 2210 if (i == d) basis->grad[(i * basis->Q + qpt) * (basis->P) + node] *= basis->grad_1d[q * basis->P_1d + p]; 2211 else basis->grad[(i * basis->Q + qpt) * (basis->P) + node] *= basis->interp_1d[q * basis->P_1d + p]; 2212 } 2213 } 2214 } 2215 } 2216 } 2217 *grad = basis->grad; 2218 return CEED_ERROR_SUCCESS; 2219 } 2220 2221 /** 2222 @brief Get 1D gradient matrix of a tensor product `CeedBasis` 2223 2224 @param[in] basis `CeedBasis` 2225 @param[out] grad_1d Variable to store gradient matrix 2226 2227 @return An error code: 0 - success, otherwise - failure 2228 2229 @ref Advanced 2230 **/ 2231 int CeedBasisGetGrad1D(CeedBasis basis, const CeedScalar **grad_1d) { 2232 bool is_tensor_basis; 2233 2234 CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis)); 2235 CeedCheck(is_tensor_basis, CeedBasisReturnCeed(basis), CEED_ERROR_MINOR, "CeedBasis is not a tensor product CeedBasis"); 2236 *grad_1d = basis->grad_1d; 2237 return CEED_ERROR_SUCCESS; 2238 } 2239 2240 /** 2241 @brief Get divergence matrix of a `CeedBasis` 2242 2243 @param[in] basis `CeedBasis` 2244 @param[out] div Variable to store divergence matrix 2245 2246 @return An error code: 0 - success, otherwise - failure 2247 2248 @ref Advanced 2249 **/ 2250 int CeedBasisGetDiv(CeedBasis basis, const CeedScalar **div) { 2251 *div = basis->div; 2252 return CEED_ERROR_SUCCESS; 2253 } 2254 2255 /** 2256 @brief Get curl matrix of a `CeedBasis` 2257 2258 @param[in] basis `CeedBasis` 2259 @param[out] curl Variable to store curl matrix 2260 2261 @return An error code: 0 - success, otherwise - failure 2262 2263 @ref Advanced 2264 **/ 2265 int CeedBasisGetCurl(CeedBasis basis, const CeedScalar **curl) { 2266 *curl = basis->curl; 2267 return CEED_ERROR_SUCCESS; 2268 } 2269 2270 /** 2271 @brief Destroy a @ref CeedBasis 2272 2273 @param[in,out] basis `CeedBasis` to destroy 2274 2275 @return An error code: 0 - success, otherwise - failure 2276 2277 @ref User 2278 **/ 2279 int CeedBasisDestroy(CeedBasis *basis) { 2280 if (!*basis || *basis == CEED_BASIS_NONE || --(*basis)->ref_count > 0) { 2281 *basis = NULL; 2282 return CEED_ERROR_SUCCESS; 2283 } 2284 if ((*basis)->Destroy) CeedCall((*basis)->Destroy(*basis)); 2285 CeedCall(CeedTensorContractDestroy(&(*basis)->contract)); 2286 CeedCall(CeedFree(&(*basis)->q_ref_1d)); 2287 CeedCall(CeedFree(&(*basis)->q_weight_1d)); 2288 CeedCall(CeedFree(&(*basis)->interp)); 2289 CeedCall(CeedFree(&(*basis)->interp_1d)); 2290 CeedCall(CeedFree(&(*basis)->grad)); 2291 CeedCall(CeedFree(&(*basis)->grad_1d)); 2292 CeedCall(CeedFree(&(*basis)->div)); 2293 CeedCall(CeedFree(&(*basis)->curl)); 2294 CeedCall(CeedVectorDestroy(&(*basis)->vec_chebyshev)); 2295 CeedCall(CeedBasisDestroy(&(*basis)->basis_chebyshev)); 2296 CeedCall(CeedDestroy(&(*basis)->ceed)); 2297 CeedCall(CeedFree(basis)); 2298 return CEED_ERROR_SUCCESS; 2299 } 2300 2301 /** 2302 @brief Construct a Gauss-Legendre quadrature 2303 2304 @param[in] Q Number of quadrature points (integrates polynomials of degree `2*Q-1` exactly) 2305 @param[out] q_ref_1d Array of length `Q` to hold the abscissa on `[-1, 1]` 2306 @param[out] q_weight_1d Array of length `Q` to hold the weights 2307 2308 @return An error code: 0 - success, otherwise - failure 2309 2310 @ref Utility 2311 **/ 2312 int CeedGaussQuadrature(CeedInt Q, CeedScalar *q_ref_1d, CeedScalar *q_weight_1d) { 2313 CeedScalar P0, P1, P2, dP2, xi, wi, PI = 4.0 * atan(1.0); 2314 2315 // Build q_ref_1d, q_weight_1d 2316 for (CeedInt i = 0; i <= Q / 2; i++) { 2317 // Guess 2318 xi = cos(PI * (CeedScalar)(2 * i + 1) / ((CeedScalar)(2 * Q))); 2319 // Pn(xi) 2320 P0 = 1.0; 2321 P1 = xi; 2322 P2 = 0.0; 2323 for (CeedInt j = 2; j <= Q; j++) { 2324 P2 = (((CeedScalar)(2 * j - 1)) * xi * P1 - ((CeedScalar)(j - 1)) * P0) / ((CeedScalar)(j)); 2325 P0 = P1; 2326 P1 = P2; 2327 } 2328 // First Newton Step 2329 dP2 = (xi * P2 - P0) * (CeedScalar)Q / (xi * xi - 1.0); 2330 xi = xi - P2 / dP2; 2331 // Newton to convergence 2332 for (CeedInt k = 0; k < 100 && fabs(P2) > 10 * CEED_EPSILON; k++) { 2333 P0 = 1.0; 2334 P1 = xi; 2335 for (CeedInt j = 2; j <= Q; j++) { 2336 P2 = (((CeedScalar)(2 * j - 1)) * xi * P1 - ((CeedScalar)(j - 1)) * P0) / ((CeedScalar)(j)); 2337 P0 = P1; 2338 P1 = P2; 2339 } 2340 dP2 = (xi * P2 - P0) * (CeedScalar)Q / (xi * xi - 1.0); 2341 xi = xi - P2 / dP2; 2342 } 2343 // Save xi, wi 2344 wi = 2.0 / ((1.0 - xi * xi) * dP2 * dP2); 2345 q_weight_1d[i] = wi; 2346 q_weight_1d[Q - 1 - i] = wi; 2347 q_ref_1d[i] = -xi; 2348 q_ref_1d[Q - 1 - i] = xi; 2349 } 2350 return CEED_ERROR_SUCCESS; 2351 } 2352 2353 /** 2354 @brief Construct a Gauss-Legendre-Lobatto quadrature 2355 2356 @param[in] Q Number of quadrature points (integrates polynomials of degree `2*Q-3` exactly) 2357 @param[out] q_ref_1d Array of length `Q` to hold the abscissa on `[-1, 1]` 2358 @param[out] q_weight_1d Array of length `Q` to hold the weights 2359 2360 @return An error code: 0 - success, otherwise - failure 2361 2362 @ref Utility 2363 **/ 2364 int CeedLobattoQuadrature(CeedInt Q, CeedScalar *q_ref_1d, CeedScalar *q_weight_1d) { 2365 CeedScalar P0, P1, P2, dP2, d2P2, xi, wi, PI = 4.0 * atan(1.0); 2366 2367 // Build q_ref_1d, q_weight_1d 2368 // Set endpoints 2369 CeedCheck(Q > 1, NULL, CEED_ERROR_DIMENSION, "Cannot create Lobatto quadrature with Q=%" CeedInt_FMT " < 2 points", Q); 2370 wi = 2.0 / ((CeedScalar)(Q * (Q - 1))); 2371 if (q_weight_1d) { 2372 q_weight_1d[0] = wi; 2373 q_weight_1d[Q - 1] = wi; 2374 } 2375 q_ref_1d[0] = -1.0; 2376 q_ref_1d[Q - 1] = 1.0; 2377 // Interior 2378 for (CeedInt i = 1; i <= (Q - 1) / 2; i++) { 2379 // Guess 2380 xi = cos(PI * (CeedScalar)(i) / (CeedScalar)(Q - 1)); 2381 // Pn(xi) 2382 P0 = 1.0; 2383 P1 = xi; 2384 P2 = 0.0; 2385 for (CeedInt j = 2; j < Q; j++) { 2386 P2 = (((CeedScalar)(2 * j - 1)) * xi * P1 - ((CeedScalar)(j - 1)) * P0) / ((CeedScalar)(j)); 2387 P0 = P1; 2388 P1 = P2; 2389 } 2390 // First Newton step 2391 dP2 = (xi * P2 - P0) * (CeedScalar)Q / (xi * xi - 1.0); 2392 d2P2 = (2 * xi * dP2 - (CeedScalar)(Q * (Q - 1)) * P2) / (1.0 - xi * xi); 2393 xi = xi - dP2 / d2P2; 2394 // Newton to convergence 2395 for (CeedInt k = 0; k < 100 && fabs(dP2) > 10 * CEED_EPSILON; k++) { 2396 P0 = 1.0; 2397 P1 = xi; 2398 for (CeedInt j = 2; j < Q; j++) { 2399 P2 = (((CeedScalar)(2 * j - 1)) * xi * P1 - ((CeedScalar)(j - 1)) * P0) / ((CeedScalar)(j)); 2400 P0 = P1; 2401 P1 = P2; 2402 } 2403 dP2 = (xi * P2 - P0) * (CeedScalar)Q / (xi * xi - 1.0); 2404 d2P2 = (2 * xi * dP2 - (CeedScalar)(Q * (Q - 1)) * P2) / (1.0 - xi * xi); 2405 xi = xi - dP2 / d2P2; 2406 } 2407 // Save xi, wi 2408 wi = 2.0 / (((CeedScalar)(Q * (Q - 1))) * P2 * P2); 2409 if (q_weight_1d) { 2410 q_weight_1d[i] = wi; 2411 q_weight_1d[Q - 1 - i] = wi; 2412 } 2413 q_ref_1d[i] = -xi; 2414 q_ref_1d[Q - 1 - i] = xi; 2415 } 2416 return CEED_ERROR_SUCCESS; 2417 } 2418 2419 /// @} 2420