1 /* 2 Common tools for constructing discretizations 3 */ 4 #ifndef PETSCDT_H 5 #define PETSCDT_H 6 7 #include <petscsys.h> 8 9 /* SUBMANSEC = DT */ 10 11 PETSC_EXTERN PetscClassId PETSCQUADRATURE_CLASSID; 12 13 /*S 14 PetscQuadrature - Quadrature rule for integration. 15 16 Level: beginner 17 18 .seealso: `PetscQuadratureCreate()`, `PetscQuadratureDestroy()` 19 S*/ 20 typedef struct _p_PetscQuadrature *PetscQuadrature; 21 22 /*E 23 PetscGaussLobattoLegendreCreateType - algorithm used to compute the Gauss-Lobatto-Legendre nodes and weights 24 25 Level: intermediate 26 27 $ `PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA` - compute the nodes via linear algebra 28 $ `PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON` - compute the nodes by solving a nonlinear equation with Newton's method 29 30 E*/ 31 typedef enum { 32 PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA, 33 PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON 34 } PetscGaussLobattoLegendreCreateType; 35 36 /*E 37 PetscDTNodeType - A description of strategies for generating nodes (both 38 quadrature nodes and nodes for Lagrange polynomials) 39 40 Level: intermediate 41 42 $ `PETSCDTNODES_DEFAULT` - Nodes chosen by PETSc 43 $ `PETSCDTNODES_GAUSSJACOBI` - Nodes at either Gauss-Jacobi or Gauss-Lobatto-Jacobi quadrature points 44 $ `PETSCDTNODES_EQUISPACED` - Nodes equispaced either including the endpoints or excluding them 45 $ `PETSCDTNODES_TANHSINH` - Nodes at Tanh-Sinh quadrature points 46 47 Note: 48 A `PetscDTNodeType` can be paired with a `PetscBool` to indicate whether 49 the nodes include endpoints or not, and in the case of `PETSCDT_GAUSSJACOBI` 50 with exponents for the weight function. 51 52 E*/ 53 typedef enum { 54 PETSCDTNODES_DEFAULT = -1, 55 PETSCDTNODES_GAUSSJACOBI, 56 PETSCDTNODES_EQUISPACED, 57 PETSCDTNODES_TANHSINH 58 } PetscDTNodeType; 59 60 PETSC_EXTERN const char *const *const PetscDTNodeTypes; 61 62 /*E 63 PetscDTSimplexQuadratureType - A description of classes of quadrature rules for simplices 64 65 Level: intermediate 66 67 $ `PETSCDTSIMPLEXQUAD_DEFAULT` - Quadrature rule chosen by PETSc 68 $ `PETSCDTSIMPLEXQUAD_CONIC` - Quadrature rules constructed as 69 conically-warped tensor products of 1D 70 Gauss-Jacobi quadrature rules. These are 71 explicitly computable in any dimension for any 72 degree, and the tensor-product structure can be 73 exploited by sum-factorization methods, but 74 they are not efficient in terms of nodes per 75 polynomial degree. 76 $ `PETSCDTSIMPLEXQUAD_MINSYM` - Quadrature rules that are fully symmetric 77 (symmetries of the simplex preserve the nodes 78 and weights) with minimal (or near minimal) 79 number of nodes. In dimensions higher than 1 80 these are not simple to compute, so lookup 81 tables are used. 82 83 .seealso: `PetscDTSimplexQuadrature()` 84 E*/ 85 typedef enum { 86 PETSCDTSIMPLEXQUAD_DEFAULT = -1, 87 PETSCDTSIMPLEXQUAD_CONIC = 0, 88 PETSCDTSIMPLEXQUAD_MINSYM 89 } PetscDTSimplexQuadratureType; 90 91 PETSC_EXTERN const char *const *const PetscDTSimplexQuadratureTypes; 92 93 PETSC_EXTERN PetscErrorCode PetscQuadratureCreate(MPI_Comm, PetscQuadrature *); 94 PETSC_EXTERN PetscErrorCode PetscQuadratureDuplicate(PetscQuadrature, PetscQuadrature *); 95 PETSC_EXTERN PetscErrorCode PetscQuadratureGetOrder(PetscQuadrature, PetscInt *); 96 PETSC_EXTERN PetscErrorCode PetscQuadratureSetOrder(PetscQuadrature, PetscInt); 97 PETSC_EXTERN PetscErrorCode PetscQuadratureGetNumComponents(PetscQuadrature, PetscInt *); 98 PETSC_EXTERN PetscErrorCode PetscQuadratureSetNumComponents(PetscQuadrature, PetscInt); 99 PETSC_EXTERN PetscErrorCode PetscQuadratureEqual(PetscQuadrature, PetscQuadrature, PetscBool *); 100 PETSC_EXTERN PetscErrorCode PetscQuadratureGetData(PetscQuadrature, PetscInt *, PetscInt *, PetscInt *, const PetscReal *[], const PetscReal *[]); 101 PETSC_EXTERN PetscErrorCode PetscQuadratureSetData(PetscQuadrature, PetscInt, PetscInt, PetscInt, const PetscReal[], const PetscReal[]); 102 PETSC_EXTERN PetscErrorCode PetscQuadratureView(PetscQuadrature, PetscViewer); 103 PETSC_EXTERN PetscErrorCode PetscQuadratureDestroy(PetscQuadrature *); 104 105 PETSC_EXTERN PetscErrorCode PetscDTTensorQuadratureCreate(PetscQuadrature, PetscQuadrature, PetscQuadrature *); 106 PETSC_EXTERN PetscErrorCode PetscQuadratureExpandComposite(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], PetscQuadrature *); 107 108 PETSC_EXTERN PetscErrorCode PetscQuadraturePushForward(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], const PetscReal[], PetscInt, PetscQuadrature *); 109 110 PETSC_EXTERN PetscErrorCode PetscDTLegendreEval(PetscInt, const PetscReal *, PetscInt, const PetscInt *, PetscReal *, PetscReal *, PetscReal *); 111 PETSC_EXTERN PetscErrorCode PetscDTJacobiNorm(PetscReal, PetscReal, PetscInt, PetscReal *); 112 PETSC_EXTERN PetscErrorCode PetscDTJacobiEval(PetscInt, PetscReal, PetscReal, const PetscReal *, PetscInt, const PetscInt *, PetscReal *, PetscReal *, PetscReal *); 113 PETSC_EXTERN PetscErrorCode PetscDTJacobiEvalJet(PetscReal, PetscReal, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscReal[]); 114 PETSC_EXTERN PetscErrorCode PetscDTPKDEvalJet(PetscInt, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscReal[]); 115 PETSC_EXTERN PetscErrorCode PetscDTPTrimmedSize(PetscInt, PetscInt, PetscInt, PetscInt *); 116 PETSC_EXTERN PetscErrorCode PetscDTPTrimmedEvalJet(PetscInt, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscInt, PetscReal[]); 117 PETSC_EXTERN PetscErrorCode PetscDTGaussQuadrature(PetscInt, PetscReal, PetscReal, PetscReal *, PetscReal *); 118 PETSC_EXTERN PetscErrorCode PetscDTGaussJacobiQuadrature(PetscInt, PetscReal, PetscReal, PetscReal, PetscReal, PetscReal *, PetscReal *); 119 PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoJacobiQuadrature(PetscInt, PetscReal, PetscReal, PetscReal, PetscReal, PetscReal *, PetscReal *); 120 PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoLegendreQuadrature(PetscInt, PetscGaussLobattoLegendreCreateType, PetscReal *, PetscReal *); 121 PETSC_EXTERN PetscErrorCode PetscDTReconstructPoly(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *); 122 PETSC_EXTERN PetscErrorCode PetscDTGaussTensorQuadrature(PetscInt, PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 123 PETSC_EXTERN PetscErrorCode PetscDTStroudConicalQuadrature(PetscInt, PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 124 PETSC_EXTERN PetscErrorCode PetscDTSimplexQuadrature(PetscInt, PetscInt, PetscDTSimplexQuadratureType, PetscQuadrature *); 125 126 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhTensorQuadrature(PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 127 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrate(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *); 128 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrateMPFR(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *); 129 130 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreIntegrate(PetscInt, PetscReal *, PetscReal *, const PetscReal *, PetscReal *); 131 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 132 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 133 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); 134 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); 135 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 136 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 137 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 138 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 139 140 PETSC_EXTERN PetscErrorCode PetscDTAltVApply(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 141 PETSC_EXTERN PetscErrorCode PetscDTAltVWedge(PetscInt, PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 142 PETSC_EXTERN PetscErrorCode PetscDTAltVWedgeMatrix(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); 143 PETSC_EXTERN PetscErrorCode PetscDTAltVPullback(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *); 144 PETSC_EXTERN PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt, PetscInt, const PetscReal *, PetscInt, PetscReal *); 145 PETSC_EXTERN PetscErrorCode PetscDTAltVInterior(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 146 PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorMatrix(PetscInt, PetscInt, const PetscReal *, PetscReal *); 147 PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorPattern(PetscInt, PetscInt, PetscInt (*)[3]); 148 PETSC_EXTERN PetscErrorCode PetscDTAltVStar(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); 149 150 PETSC_EXTERN PetscErrorCode PetscDTBaryToIndex(PetscInt, PetscInt, const PetscInt[], PetscInt *); 151 PETSC_EXTERN PetscErrorCode PetscDTIndexToBary(PetscInt, PetscInt, PetscInt, PetscInt[]); 152 PETSC_EXTERN PetscErrorCode PetscDTGradedOrderToIndex(PetscInt, const PetscInt[], PetscInt *); 153 PETSC_EXTERN PetscErrorCode PetscDTIndexToGradedOrder(PetscInt, PetscInt, PetscInt[]); 154 155 #if defined(PETSC_USE_64BIT_INDICES) 156 #define PETSC_FACTORIAL_MAX 20 157 #define PETSC_BINOMIAL_MAX 61 158 #else 159 #define PETSC_FACTORIAL_MAX 12 160 #define PETSC_BINOMIAL_MAX 29 161 #endif 162 163 /*MC 164 PetscDTFactorial - Approximate n! as a real number 165 166 Input Parameter: 167 . n - a non-negative integer 168 169 Output Parameter: 170 . factorial - n! 171 172 Level: beginner 173 M*/ 174 static inline PetscErrorCode PetscDTFactorial(PetscInt n, PetscReal *factorial) 175 { 176 PetscReal f = 1.0; 177 178 PetscFunctionBegin; 179 *factorial = -1.0; 180 PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Factorial called with negative number %" PetscInt_FMT, n); 181 for (PetscInt i = 1; i < n + 1; ++i) f *= (PetscReal)i; 182 *factorial = f; 183 PetscFunctionReturn(PETSC_SUCCESS); 184 } 185 186 /*MC 187 PetscDTFactorialInt - Compute n! as an integer 188 189 Input Parameter: 190 . n - a non-negative integer 191 192 Output Parameter: 193 . factorial - n! 194 195 Level: beginner 196 197 Note: this is limited to n such that n! can be represented by PetscInt, which is 12 if PetscInt is a signed 32-bit integer and 20 if PetscInt is a signed 64-bit integer. 198 M*/ 199 static inline PetscErrorCode PetscDTFactorialInt(PetscInt n, PetscInt *factorial) 200 { 201 PetscInt facLookup[13] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600}; 202 203 PetscFunctionBegin; 204 *factorial = -1; 205 PetscCheck(n >= 0 && n <= PETSC_FACTORIAL_MAX, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of elements %" PetscInt_FMT " is not in supported range [0,%d]", n, PETSC_FACTORIAL_MAX); 206 if (n <= 12) { 207 *factorial = facLookup[n]; 208 } else { 209 PetscInt f = facLookup[12]; 210 PetscInt i; 211 212 for (i = 13; i < n + 1; ++i) f *= i; 213 *factorial = f; 214 } 215 PetscFunctionReturn(PETSC_SUCCESS); 216 } 217 218 /*MC 219 PetscDTBinomial - Approximate the binomial coefficient "n choose k" 220 221 Input Parameters: 222 + n - a non-negative integer 223 - k - an integer between 0 and n, inclusive 224 225 Output Parameter: 226 . binomial - approximation of the binomial coefficient n choose k 227 228 Level: beginner 229 M*/ 230 static inline PetscErrorCode PetscDTBinomial(PetscInt n, PetscInt k, PetscReal *binomial) 231 { 232 PetscFunctionBeginHot; 233 *binomial = -1.0; 234 PetscCheck(n >= 0 && k >= 0 && k <= n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Binomial arguments (%" PetscInt_FMT " %" PetscInt_FMT ") must be non-negative, k <= n", n, k); 235 if (n <= 3) { 236 PetscInt binomLookup[4][4] = { 237 {1, 0, 0, 0}, 238 {1, 1, 0, 0}, 239 {1, 2, 1, 0}, 240 {1, 3, 3, 1} 241 }; 242 243 *binomial = (PetscReal)binomLookup[n][k]; 244 } else { 245 PetscReal binom = 1.0; 246 247 k = PetscMin(k, n - k); 248 for (PetscInt i = 0; i < k; i++) binom = (binom * (PetscReal)(n - i)) / (PetscReal)(i + 1); 249 *binomial = binom; 250 } 251 PetscFunctionReturn(PETSC_SUCCESS); 252 } 253 254 /*MC 255 PetscDTBinomialInt - Compute the binomial coefficient "n choose k" 256 257 Input Parameters: 258 + n - a non-negative integer 259 - k - an integer between 0 and n, inclusive 260 261 Output Parameter: 262 . binomial - the binomial coefficient n choose k 263 264 Note: this is limited by integers that can be represented by `PetscInt` 265 266 Level: beginner 267 M*/ 268 static inline PetscErrorCode PetscDTBinomialInt(PetscInt n, PetscInt k, PetscInt *binomial) 269 { 270 PetscInt bin; 271 272 PetscFunctionBegin; 273 *binomial = -1; 274 PetscCheck(n >= 0 && k >= 0 && k <= n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Binomial arguments (%" PetscInt_FMT " %" PetscInt_FMT ") must be non-negative, k <= n", n, k); 275 PetscCheck(n <= PETSC_BINOMIAL_MAX, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Binomial elements %" PetscInt_FMT " is larger than max for PetscInt, %d", n, PETSC_BINOMIAL_MAX); 276 if (n <= 3) { 277 PetscInt binomLookup[4][4] = { 278 {1, 0, 0, 0}, 279 {1, 1, 0, 0}, 280 {1, 2, 1, 0}, 281 {1, 3, 3, 1} 282 }; 283 284 bin = binomLookup[n][k]; 285 } else { 286 PetscInt binom = 1; 287 288 k = PetscMin(k, n - k); 289 for (PetscInt i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1); 290 bin = binom; 291 } 292 *binomial = bin; 293 PetscFunctionReturn(PETSC_SUCCESS); 294 } 295 296 /*MC 297 PetscDTEnumPerm - Get a permutation of n integers from its encoding into the integers [0, n!) as a sequence of swaps. 298 299 A permutation can be described by the operations that convert the lists [0, 1, ..., n-1] into the permutation, 300 by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in 301 some position j >= i. This swap is encoded as the difference (j - i). The difference d_i at step i is less than 302 (n - i). This sequence of n-1 differences [d_0, ..., d_{n-2}] is encoded as the number 303 (n-1)! * d_0 + (n-2)! * d_1 + ... + 1! * d_{n-2}. 304 305 Input Parameters: 306 + n - a non-negative integer (see note about limits below) 307 - k - an integer in [0, n!) 308 309 Output Parameters: 310 + perm - the permuted list of the integers [0, ..., n-1] 311 - isOdd - if not NULL, returns whether the permutation used an even or odd number of swaps. 312 313 Note: 314 Limited to n such that n! can be represented by `PetscInt`, which is 12 if `PetscInt` is a signed 32-bit integer and 20 if `PetscInt` is a signed 64-bit integer. 315 316 Level: beginner 317 M*/ 318 static inline PetscErrorCode PetscDTEnumPerm(PetscInt n, PetscInt k, PetscInt *perm, PetscBool *isOdd) 319 { 320 PetscInt odd = 0; 321 PetscInt i; 322 PetscInt work[PETSC_FACTORIAL_MAX]; 323 PetscInt *w; 324 325 PetscFunctionBegin; 326 if (isOdd) *isOdd = PETSC_FALSE; 327 PetscCheck(n >= 0 && n <= PETSC_FACTORIAL_MAX, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of elements %" PetscInt_FMT " is not in supported range [0,%d]", n, PETSC_FACTORIAL_MAX); 328 w = &work[n - 2]; 329 for (i = 2; i <= n; i++) { 330 *(w--) = k % i; 331 k /= i; 332 } 333 for (i = 0; i < n; i++) perm[i] = i; 334 for (i = 0; i < n - 1; i++) { 335 PetscInt s = work[i]; 336 PetscInt swap = perm[i]; 337 338 perm[i] = perm[i + s]; 339 perm[i + s] = swap; 340 odd ^= (!!s); 341 } 342 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 343 PetscFunctionReturn(PETSC_SUCCESS); 344 } 345 346 /*MC 347 PetscDTPermIndex - Encode a permutation of n into an integer in [0, n!). This inverts `PetscDTEnumPerm`. 348 349 Input Parameters: 350 + n - a non-negative integer (see note about limits below) 351 - perm - the permuted list of the integers [0, ..., n-1] 352 353 Output Parameters: 354 + k - an integer in [0, n!) 355 - isOdd - if not NULL, returns whether the permutation used an even or odd number of swaps. 356 357 Note: 358 Limited to n such that n! can be represented by `PetscInt`, which is 12 if `PetscInt` is a signed 32-bit integer and 20 if `PetscInt` is a signed 64-bit integer. 359 360 Level: beginner 361 M*/ 362 static inline PetscErrorCode PetscDTPermIndex(PetscInt n, const PetscInt *perm, PetscInt *k, PetscBool *isOdd) 363 { 364 PetscInt odd = 0; 365 PetscInt i, idx; 366 PetscInt work[PETSC_FACTORIAL_MAX]; 367 PetscInt iwork[PETSC_FACTORIAL_MAX]; 368 369 PetscFunctionBeginHot; 370 *k = -1; 371 if (isOdd) *isOdd = PETSC_FALSE; 372 PetscCheck(n >= 0 && n <= PETSC_FACTORIAL_MAX, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of elements %" PetscInt_FMT " is not in supported range [0,%d]", n, PETSC_FACTORIAL_MAX); 373 for (i = 0; i < n; i++) work[i] = i; /* partial permutation */ 374 for (i = 0; i < n; i++) iwork[i] = i; /* partial permutation inverse */ 375 for (idx = 0, i = 0; i < n - 1; i++) { 376 PetscInt j = perm[i]; 377 PetscInt icur = work[i]; 378 PetscInt jloc = iwork[j]; 379 PetscInt diff = jloc - i; 380 381 idx = idx * (n - i) + diff; 382 /* swap (i, jloc) */ 383 work[i] = j; 384 work[jloc] = icur; 385 iwork[j] = i; 386 iwork[icur] = jloc; 387 odd ^= (!!diff); 388 } 389 *k = idx; 390 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 391 PetscFunctionReturn(PETSC_SUCCESS); 392 } 393 394 /*MC 395 PetscDTEnumSubset - Get an ordered subset of the integers [0, ..., n - 1] from its encoding as an integers in [0, n choose k). 396 The encoding is in lexicographic order. 397 398 Input Parameters: 399 + n - a non-negative integer (see note about limits below) 400 . k - an integer in [0, n] 401 - j - an index in [0, n choose k) 402 403 Output Parameter: 404 . subset - the jth subset of size k of the integers [0, ..., n - 1] 405 406 Note: 407 Limited by arguments such that n choose k can be represented by `PetscInt` 408 409 Level: beginner 410 411 .seealso: `PetscDTSubsetIndex()` 412 M*/ 413 static inline PetscErrorCode PetscDTEnumSubset(PetscInt n, PetscInt k, PetscInt j, PetscInt *subset) 414 { 415 PetscInt Nk; 416 417 PetscFunctionBeginHot; 418 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 419 for (PetscInt i = 0, l = 0; i < n && l < k; i++) { 420 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 421 PetscInt Nminusk = Nk - Nminuskminus; 422 423 if (j < Nminuskminus) { 424 subset[l++] = i; 425 Nk = Nminuskminus; 426 } else { 427 j -= Nminuskminus; 428 Nk = Nminusk; 429 } 430 } 431 PetscFunctionReturn(PETSC_SUCCESS); 432 } 433 434 /*MC 435 PetscDTSubsetIndex - Convert an ordered subset of k integers from the set [0, ..., n - 1] to its encoding as an integers in [0, n choose k) in lexicographic order. 436 This is the inverse of `PetscDTEnumSubset`. 437 438 Input Parameters: 439 + n - a non-negative integer (see note about limits below) 440 . k - an integer in [0, n] 441 - subset - an ordered subset of the integers [0, ..., n - 1] 442 443 Output Parameter: 444 . index - the rank of the subset in lexicographic order 445 446 Note: 447 Limited by arguments such that n choose k can be represented by `PetscInt` 448 449 Level: beginner 450 451 .seealso: `PetscDTEnumSubset()` 452 M*/ 453 static inline PetscErrorCode PetscDTSubsetIndex(PetscInt n, PetscInt k, const PetscInt *subset, PetscInt *index) 454 { 455 PetscInt j = 0, Nk; 456 457 PetscFunctionBegin; 458 *index = -1; 459 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 460 for (PetscInt i = 0, l = 0; i < n && l < k; i++) { 461 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 462 PetscInt Nminusk = Nk - Nminuskminus; 463 464 if (subset[l] == i) { 465 l++; 466 Nk = Nminuskminus; 467 } else { 468 j += Nminuskminus; 469 Nk = Nminusk; 470 } 471 } 472 *index = j; 473 PetscFunctionReturn(PETSC_SUCCESS); 474 } 475 476 /*MC 477 PetscDTEnumSubset - Split the integers [0, ..., n - 1] into two complementary ordered subsets, the first subset of size k and being the jth subset of that size in lexicographic order. 478 479 Input Parameters: 480 + n - a non-negative integer (see note about limits below) 481 . k - an integer in [0, n] 482 - j - an index in [0, n choose k) 483 484 Output Parameters: 485 + perm - the jth subset of size k of the integers [0, ..., n - 1], followed by its complementary set. 486 - isOdd - if not NULL, return whether perm is an even or odd permutation. 487 488 Note: 489 Limited by arguments such that n choose k can be represented by `PetscInt` 490 491 Level: beginner 492 493 .seealso: `PetscDTEnumSubset()`, `PetscDTSubsetIndex()` 494 M*/ 495 static inline PetscErrorCode PetscDTEnumSplit(PetscInt n, PetscInt k, PetscInt j, PetscInt *perm, PetscBool *isOdd) 496 { 497 PetscInt i, l, m, Nk, odd = 0; 498 PetscInt *subcomp = perm + k; 499 500 PetscFunctionBegin; 501 if (isOdd) *isOdd = PETSC_FALSE; 502 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 503 for (i = 0, l = 0, m = 0; i < n && l < k; i++) { 504 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 505 PetscInt Nminusk = Nk - Nminuskminus; 506 507 if (j < Nminuskminus) { 508 perm[l++] = i; 509 Nk = Nminuskminus; 510 } else { 511 subcomp[m++] = i; 512 j -= Nminuskminus; 513 odd ^= ((k - l) & 1); 514 Nk = Nminusk; 515 } 516 } 517 for (; i < n; i++) subcomp[m++] = i; 518 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 519 PetscFunctionReturn(PETSC_SUCCESS); 520 } 521 522 struct _p_PetscTabulation { 523 PetscInt K; /* Indicates a k-jet, namely tabulated derivatives up to order k */ 524 PetscInt Nr; /* The number of tabulation replicas (often 1) */ 525 PetscInt Np; /* The number of tabulation points in a replica */ 526 PetscInt Nb; /* The number of functions tabulated */ 527 PetscInt Nc; /* The number of function components */ 528 PetscInt cdim; /* The coordinate dimension */ 529 PetscReal **T; /* The tabulation T[K] of functions and their derivatives 530 T[0] = B[Nr*Np][Nb][Nc]: The basis function values at quadrature points 531 T[1] = D[Nr*Np][Nb][Nc][cdim]: The basis function derivatives at quadrature points 532 T[2] = H[Nr*Np][Nb][Nc][cdim][cdim]: The basis function second derivatives at quadrature points */ 533 }; 534 typedef struct _p_PetscTabulation *PetscTabulation; 535 536 typedef PetscErrorCode (*PetscProbFunc)(const PetscReal[], const PetscReal[], PetscReal[]); 537 538 typedef enum { 539 DTPROB_DENSITY_CONSTANT, 540 DTPROB_DENSITY_GAUSSIAN, 541 DTPROB_DENSITY_MAXWELL_BOLTZMANN, 542 DTPROB_NUM_DENSITY 543 } DTProbDensityType; 544 PETSC_EXTERN const char *const DTProbDensityTypes[]; 545 546 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]); 547 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]); 548 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]); 549 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]); 550 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]); 551 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]); 552 PETSC_EXTERN PetscErrorCode PetscPDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 553 PETSC_EXTERN PetscErrorCode PetscCDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 554 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 555 PETSC_EXTERN PetscErrorCode PetscPDFGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]); 556 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]); 557 PETSC_EXTERN PetscErrorCode PetscPDFGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]); 558 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]); 559 PETSC_EXTERN PetscErrorCode PetscPDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 560 PETSC_EXTERN PetscErrorCode PetscCDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 561 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 562 PETSC_EXTERN PetscErrorCode PetscPDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 563 PETSC_EXTERN PetscErrorCode PetscCDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 564 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 565 PETSC_EXTERN PetscErrorCode PetscPDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 566 PETSC_EXTERN PetscErrorCode PetscCDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 567 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 568 PETSC_EXTERN PetscErrorCode PetscProbCreateFromOptions(PetscInt, const char[], const char[], PetscProbFunc *, PetscProbFunc *, PetscProbFunc *); 569 570 #include <petscvec.h> 571 572 PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatistic(Vec, PetscProbFunc, PetscReal *); 573 574 #endif 575