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 PetscQuadratureEqual(PetscQuadrature, PetscQuadrature, PetscBool*); 58 PETSC_EXTERN PetscErrorCode PetscQuadratureGetData(PetscQuadrature, PetscInt*, PetscInt*, PetscInt*, const PetscReal *[], const PetscReal *[]); 59 PETSC_EXTERN PetscErrorCode PetscQuadratureSetData(PetscQuadrature, PetscInt, PetscInt, PetscInt, const PetscReal [], const PetscReal []); 60 PETSC_EXTERN PetscErrorCode PetscQuadratureView(PetscQuadrature, PetscViewer); 61 PETSC_EXTERN PetscErrorCode PetscQuadratureDestroy(PetscQuadrature *); 62 63 PETSC_EXTERN PetscErrorCode PetscDTTensorQuadratureCreate(PetscQuadrature, PetscQuadrature, PetscQuadrature *); 64 PETSC_EXTERN PetscErrorCode PetscQuadratureExpandComposite(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], PetscQuadrature *); 65 66 PETSC_EXTERN PetscErrorCode PetscQuadraturePushForward(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], const PetscReal[], PetscInt, PetscQuadrature *); 67 68 PETSC_EXTERN PetscErrorCode PetscDTLegendreEval(PetscInt,const PetscReal*,PetscInt,const PetscInt*,PetscReal*,PetscReal*,PetscReal*); 69 PETSC_EXTERN PetscErrorCode PetscDTJacobiNorm(PetscReal,PetscReal,PetscInt,PetscReal *); 70 PETSC_EXTERN PetscErrorCode PetscDTJacobiEval(PetscInt,PetscReal,PetscReal,const PetscReal*,PetscInt,const PetscInt*,PetscReal*,PetscReal*,PetscReal*); 71 PETSC_EXTERN PetscErrorCode PetscDTJacobiEvalJet(PetscReal,PetscReal,PetscInt,const PetscReal[],PetscInt,PetscInt,PetscReal[]); 72 PETSC_EXTERN PetscErrorCode PetscDTPKDEvalJet(PetscInt,PetscInt,const PetscReal[],PetscInt,PetscInt,PetscReal[]); 73 PETSC_EXTERN PetscErrorCode PetscDTPTrimmedSize(PetscInt,PetscInt,PetscInt,PetscInt*); 74 PETSC_EXTERN PetscErrorCode PetscDTPTrimmedEvalJet(PetscInt,PetscInt,const PetscReal[],PetscInt,PetscInt,PetscInt,PetscReal[]); 75 PETSC_EXTERN PetscErrorCode PetscDTGaussQuadrature(PetscInt,PetscReal,PetscReal,PetscReal*,PetscReal*); 76 PETSC_EXTERN PetscErrorCode PetscDTGaussJacobiQuadrature(PetscInt,PetscReal,PetscReal,PetscReal,PetscReal,PetscReal*,PetscReal*); 77 PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoJacobiQuadrature(PetscInt,PetscReal,PetscReal,PetscReal,PetscReal,PetscReal*,PetscReal*); 78 PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoLegendreQuadrature(PetscInt,PetscGaussLobattoLegendreCreateType,PetscReal*,PetscReal*); 79 PETSC_EXTERN PetscErrorCode PetscDTReconstructPoly(PetscInt,PetscInt,const PetscReal*,PetscInt,const PetscReal*,PetscReal*); 80 PETSC_EXTERN PetscErrorCode PetscDTGaussTensorQuadrature(PetscInt,PetscInt,PetscInt,PetscReal,PetscReal,PetscQuadrature*); 81 PETSC_EXTERN PetscErrorCode PetscDTStroudConicalQuadrature(PetscInt,PetscInt,PetscInt,PetscReal,PetscReal,PetscQuadrature*); 82 83 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhTensorQuadrature(PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 84 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrate(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *); 85 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrateMPFR(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *); 86 87 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreIntegrate(PetscInt, PetscReal *, PetscReal *, const PetscReal *, PetscReal *); 88 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 89 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 90 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); 91 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); 92 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 93 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 94 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 95 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 96 97 PETSC_EXTERN PetscErrorCode PetscDTAltVApply(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 98 PETSC_EXTERN PetscErrorCode PetscDTAltVWedge(PetscInt, PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 99 PETSC_EXTERN PetscErrorCode PetscDTAltVWedgeMatrix(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); 100 PETSC_EXTERN PetscErrorCode PetscDTAltVPullback(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *); 101 PETSC_EXTERN PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt, PetscInt, const PetscReal *, PetscInt, PetscReal *); 102 PETSC_EXTERN PetscErrorCode PetscDTAltVInterior(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 103 PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorMatrix(PetscInt, PetscInt, const PetscReal *, PetscReal *); 104 PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorPattern(PetscInt, PetscInt, PetscInt (*)[3]); 105 PETSC_EXTERN PetscErrorCode PetscDTAltVStar(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); 106 107 PETSC_EXTERN PetscErrorCode PetscDTBaryToIndex(PetscInt,PetscInt,const PetscInt[],PetscInt*); 108 PETSC_EXTERN PetscErrorCode PetscDTIndexToBary(PetscInt,PetscInt,PetscInt,PetscInt[]); 109 PETSC_EXTERN PetscErrorCode PetscDTGradedOrderToIndex(PetscInt,const PetscInt[],PetscInt*); 110 PETSC_EXTERN PetscErrorCode PetscDTIndexToGradedOrder(PetscInt,PetscInt,PetscInt[]); 111 112 #if defined(PETSC_USE_64BIT_INDICES) 113 #define PETSC_FACTORIAL_MAX 20 114 #define PETSC_BINOMIAL_MAX 61 115 #else 116 #define PETSC_FACTORIAL_MAX 12 117 #define PETSC_BINOMIAL_MAX 29 118 #endif 119 120 /*MC 121 PetscDTFactorial - Approximate n! as a real number 122 123 Input Parameter: 124 . n - a non-negative integer 125 126 Output Parameter: 127 . factorial - n! 128 129 Level: beginner 130 M*/ 131 static inline PetscErrorCode PetscDTFactorial(PetscInt n, PetscReal *factorial) 132 { 133 PetscReal f = 1.0; 134 135 PetscFunctionBegin; 136 *factorial = -1.0; 137 PetscCheck(n >= 0,PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Factorial called with negative number %" PetscInt_FMT, n); 138 for (PetscInt 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 %" PetscInt_FMT " 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 (%" PetscInt_FMT " %" PetscInt_FMT ") 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; 198 199 k = PetscMin(k, n - k); 200 for (PetscInt i = 0; i < k; i++) binom = (binom * (PetscReal)(n - i)) / (PetscReal)(i + 1); 201 *binomial = binom; 202 } 203 PetscFunctionReturn(0); 204 } 205 206 /*MC 207 PetscDTBinomialInt - Compute the binomial coefficient "n choose k" 208 209 Input Parameters: 210 + n - a non-negative integer 211 - k - an integer between 0 and n, inclusive 212 213 Output Parameter: 214 . binomial - the binomial coefficient n choose k 215 216 Note: this is limited by integers that can be represented by PetscInt 217 218 Level: beginner 219 M*/ 220 static inline PetscErrorCode PetscDTBinomialInt(PetscInt n, PetscInt k, PetscInt *binomial) 221 { 222 PetscInt bin; 223 224 PetscFunctionBegin; 225 *binomial = -1; 226 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); 227 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); 228 if (n <= 3) { 229 PetscInt binomLookup[4][4] = {{1, 0, 0, 0}, {1, 1, 0, 0}, {1, 2, 1, 0}, {1, 3, 3, 1}}; 230 231 bin = binomLookup[n][k]; 232 } else { 233 PetscInt binom = 1; 234 235 k = PetscMin(k, n - k); 236 for (PetscInt i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1); 237 bin = binom; 238 } 239 *binomial = bin; 240 PetscFunctionReturn(0); 241 } 242 243 /*MC 244 PetscDTEnumPerm - Get a permutation of n integers from its encoding into the integers [0, n!) as a sequence of swaps. 245 246 A permutation can be described by the operations that convert the lists [0, 1, ..., n-1] into the permutation, 247 by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in 248 some position j >= i. This swap is encoded as the difference (j - i). The difference d_i at step i is less than 249 (n - i). This sequence of n-1 differences [d_0, ..., d_{n-2}] is encoded as the number 250 (n-1)! * d_0 + (n-2)! * d_1 + ... + 1! * d_{n-2}. 251 252 Input Parameters: 253 + n - a non-negative integer (see note about limits below) 254 - k - an integer in [0, n!) 255 256 Output Parameters: 257 + perm - the permuted list of the integers [0, ..., n-1] 258 - isOdd - if not NULL, returns wether the permutation used an even or odd number of swaps. 259 260 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. 261 262 Level: beginner 263 M*/ 264 static inline PetscErrorCode PetscDTEnumPerm(PetscInt n, PetscInt k, PetscInt *perm, PetscBool *isOdd) 265 { 266 PetscInt odd = 0; 267 PetscInt i; 268 PetscInt work[PETSC_FACTORIAL_MAX]; 269 PetscInt *w; 270 271 PetscFunctionBegin; 272 if (isOdd) *isOdd = PETSC_FALSE; 273 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); 274 w = &work[n - 2]; 275 for (i = 2; i <= n; i++) { 276 *(w--) = k % i; 277 k /= i; 278 } 279 for (i = 0; i < n; i++) perm[i] = i; 280 for (i = 0; i < n - 1; i++) { 281 PetscInt s = work[i]; 282 PetscInt swap = perm[i]; 283 284 perm[i] = perm[i + s]; 285 perm[i + s] = swap; 286 odd ^= (!!s); 287 } 288 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 289 PetscFunctionReturn(0); 290 } 291 292 /*MC 293 PetscDTPermIndex - Encode a permutation of n into an integer in [0, n!). This inverts PetscDTEnumPerm. 294 295 Input Parameters: 296 + n - a non-negative integer (see note about limits below) 297 - perm - the permuted list of the integers [0, ..., n-1] 298 299 Output Parameters: 300 + k - an integer in [0, n!) 301 - isOdd - if not NULL, returns wether the permutation used an even or odd number of swaps. 302 303 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. 304 305 Level: beginner 306 M*/ 307 static inline PetscErrorCode PetscDTPermIndex(PetscInt n, const PetscInt *perm, PetscInt *k, PetscBool *isOdd) 308 { 309 PetscInt odd = 0; 310 PetscInt i, idx; 311 PetscInt work[PETSC_FACTORIAL_MAX]; 312 PetscInt iwork[PETSC_FACTORIAL_MAX]; 313 314 PetscFunctionBeginHot; 315 *k = -1; 316 if (isOdd) *isOdd = PETSC_FALSE; 317 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); 318 for (i = 0; i < n; i++) work[i] = i; /* partial permutation */ 319 for (i = 0; i < n; i++) iwork[i] = i; /* partial permutation inverse */ 320 for (idx = 0, i = 0; i < n - 1; i++) { 321 PetscInt j = perm[i]; 322 PetscInt icur = work[i]; 323 PetscInt jloc = iwork[j]; 324 PetscInt diff = jloc - i; 325 326 idx = idx * (n - i) + diff; 327 /* swap (i, jloc) */ 328 work[i] = j; 329 work[jloc] = icur; 330 iwork[j] = i; 331 iwork[icur] = jloc; 332 odd ^= (!!diff); 333 } 334 *k = idx; 335 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 336 PetscFunctionReturn(0); 337 } 338 339 /*MC 340 PetscDTEnumSubset - Get an ordered subset of the integers [0, ..., n - 1] from its encoding as an integers in [0, n choose k). 341 The encoding is in lexicographic order. 342 343 Input Parameters: 344 + n - a non-negative integer (see note about limits below) 345 . k - an integer in [0, n] 346 - j - an index in [0, n choose k) 347 348 Output Parameter: 349 . subset - the jth subset of size k of the integers [0, ..., n - 1] 350 351 Note: this is limited by arguments such that n choose k can be represented by PetscInt 352 353 Level: beginner 354 355 .seealso: `PetscDTSubsetIndex()` 356 M*/ 357 static inline PetscErrorCode PetscDTEnumSubset(PetscInt n, PetscInt k, PetscInt j, PetscInt *subset) 358 { 359 PetscInt Nk; 360 361 PetscFunctionBeginHot; 362 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 363 for (PetscInt i = 0, l = 0; i < n && l < k; i++) { 364 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 365 PetscInt Nminusk = Nk - Nminuskminus; 366 367 if (j < Nminuskminus) { 368 subset[l++] = i; 369 Nk = Nminuskminus; 370 } else { 371 j -= Nminuskminus; 372 Nk = Nminusk; 373 } 374 } 375 PetscFunctionReturn(0); 376 } 377 378 /*MC 379 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. 380 381 Input Parameters: 382 + n - a non-negative integer (see note about limits below) 383 . k - an integer in [0, n] 384 - subset - an ordered subset of the integers [0, ..., n - 1] 385 386 Output Parameter: 387 . index - the rank of the subset in lexicographic order 388 389 Note: this is limited by arguments such that n choose k can be represented by PetscInt 390 391 Level: beginner 392 393 .seealso: `PetscDTEnumSubset()` 394 M*/ 395 static inline PetscErrorCode PetscDTSubsetIndex(PetscInt n, PetscInt k, const PetscInt *subset, PetscInt *index) 396 { 397 PetscInt j = 0, Nk; 398 399 PetscFunctionBegin; 400 *index = -1; 401 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 402 for (PetscInt i = 0, l = 0; i < n && l < k; i++) { 403 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 404 PetscInt Nminusk = Nk - Nminuskminus; 405 406 if (subset[l] == i) { 407 l++; 408 Nk = Nminuskminus; 409 } else { 410 j += Nminuskminus; 411 Nk = Nminusk; 412 } 413 } 414 *index = j; 415 PetscFunctionReturn(0); 416 } 417 418 /*MC 419 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. 420 421 Input Parameters: 422 + n - a non-negative integer (see note about limits below) 423 . k - an integer in [0, n] 424 - j - an index in [0, n choose k) 425 426 Output Parameters: 427 + perm - the jth subset of size k of the integers [0, ..., n - 1], followed by its complementary set. 428 - isOdd - if not NULL, return whether perm is an even or odd permutation. 429 430 Note: this is limited by arguments such that n choose k can be represented by PetscInt 431 432 Level: beginner 433 434 .seealso: `PetscDTEnumSubset()`, `PetscDTSubsetIndex()` 435 M*/ 436 static inline PetscErrorCode PetscDTEnumSplit(PetscInt n, PetscInt k, PetscInt j, PetscInt *perm, PetscBool *isOdd) 437 { 438 PetscInt i, l, m, Nk, odd = 0; 439 PetscInt *subcomp = perm+k; 440 441 PetscFunctionBegin; 442 if (isOdd) *isOdd = PETSC_FALSE; 443 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 444 for (i = 0, l = 0, m = 0; i < n && l < k; i++) { 445 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 446 PetscInt Nminusk = Nk - Nminuskminus; 447 448 if (j < Nminuskminus) { 449 perm[l++] = i; 450 Nk = Nminuskminus; 451 } else { 452 subcomp[m++] = i; 453 j -= Nminuskminus; 454 odd ^= ((k - l) & 1); 455 Nk = Nminusk; 456 } 457 } 458 for (; i < n; i++) subcomp[m++] = i; 459 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 460 PetscFunctionReturn(0); 461 } 462 463 struct _p_PetscTabulation { 464 PetscInt K; /* Indicates a k-jet, namely tabulated derivatives up to order k */ 465 PetscInt Nr; /* The number of tabulation replicas (often 1) */ 466 PetscInt Np; /* The number of tabulation points in a replica */ 467 PetscInt Nb; /* The number of functions tabulated */ 468 PetscInt Nc; /* The number of function components */ 469 PetscInt cdim; /* The coordinate dimension */ 470 PetscReal **T; /* The tabulation T[K] of functions and their derivatives 471 T[0] = B[Nr*Np][Nb][Nc]: The basis function values at quadrature points 472 T[1] = D[Nr*Np][Nb][Nc][cdim]: The basis function derivatives at quadrature points 473 T[2] = H[Nr*Np][Nb][Nc][cdim][cdim]: The basis function second derivatives at quadrature points */ 474 }; 475 typedef struct _p_PetscTabulation *PetscTabulation; 476 477 typedef PetscErrorCode (*PetscProbFunc)(const PetscReal[], const PetscReal[], PetscReal[]); 478 479 typedef enum {DTPROB_DENSITY_CONSTANT, DTPROB_DENSITY_GAUSSIAN, DTPROB_DENSITY_MAXWELL_BOLTZMANN, DTPROB_NUM_DENSITY} DTProbDensityType; 480 PETSC_EXTERN const char * const DTProbDensityTypes[]; 481 482 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]); 483 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]); 484 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]); 485 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]); 486 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]); 487 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]); 488 PETSC_EXTERN PetscErrorCode PetscPDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 489 PETSC_EXTERN PetscErrorCode PetscCDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 490 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 491 PETSC_EXTERN PetscErrorCode PetscPDFGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]); 492 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]); 493 PETSC_EXTERN PetscErrorCode PetscPDFGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]); 494 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]); 495 PETSC_EXTERN PetscErrorCode PetscPDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 496 PETSC_EXTERN PetscErrorCode PetscCDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 497 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 498 PETSC_EXTERN PetscErrorCode PetscPDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 499 PETSC_EXTERN PetscErrorCode PetscCDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 500 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 501 PETSC_EXTERN PetscErrorCode PetscPDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 502 PETSC_EXTERN PetscErrorCode PetscCDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 503 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 504 PETSC_EXTERN PetscErrorCode PetscProbCreateFromOptions(PetscInt, const char[], const char[], PetscProbFunc *, PetscProbFunc *, PetscProbFunc *); 505 506 #include <petscvec.h> 507 508 PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatistic(Vec, PetscProbFunc, PetscReal *); 509 510 #endif 511