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