1 /* 2 Common tools for constructing discretizations 3 */ 4 #pragma once 5 6 #include <petscsys.h> 7 #include <petscdmtypes.h> 8 #include <petscistypes.h> 9 10 /* SUBMANSEC = DT */ 11 12 PETSC_EXTERN PetscClassId PETSCQUADRATURE_CLASSID; 13 14 /*S 15 PetscQuadrature - Quadrature rule for numerical integration. 16 17 Level: beginner 18 19 .seealso: `PetscQuadratureCreate()`, `PetscQuadratureDestroy()` 20 S*/ 21 typedef struct _p_PetscQuadrature *PetscQuadrature; 22 23 /*E 24 PetscGaussLobattoLegendreCreateType - algorithm used to compute the Gauss-Lobatto-Legendre nodes and weights 25 26 Values: 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 Level: intermediate 31 32 .seealso: `PetscQuadrature` 33 E*/ 34 typedef enum { 35 PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA, 36 PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON 37 } PetscGaussLobattoLegendreCreateType; 38 39 /*E 40 PetscDTNodeType - A description of strategies for generating nodes (both 41 quadrature nodes and nodes for Lagrange polynomials) 42 43 Values: 44 + `PETSCDTNODES_DEFAULT` - Nodes chosen by PETSc 45 . `PETSCDTNODES_GAUSSJACOBI` - Nodes at either Gauss-Jacobi or Gauss-Lobatto-Jacobi quadrature points 46 . `PETSCDTNODES_EQUISPACED` - Nodes equispaced either including the endpoints or excluding them 47 - `PETSCDTNODES_TANHSINH` - Nodes at Tanh-Sinh quadrature points 48 49 Level: intermediate 50 51 Note: 52 A `PetscDTNodeType` can be paired with a `PetscBool` to indicate whether 53 the nodes include endpoints or not, and in the case of `PETSCDT_GAUSSJACOBI` 54 with exponents for the weight function. 55 56 .seealso: `PetscQuadrature` 57 E*/ 58 typedef enum { 59 PETSCDTNODES_DEFAULT = -1, 60 PETSCDTNODES_GAUSSJACOBI, 61 PETSCDTNODES_EQUISPACED, 62 PETSCDTNODES_TANHSINH 63 } PetscDTNodeType; 64 65 PETSC_EXTERN const char *const *const PetscDTNodeTypes; 66 67 /*E 68 PetscDTSimplexQuadratureType - A description of classes of quadrature rules for simplices 69 70 Values: 71 + `PETSCDTSIMPLEXQUAD_DEFAULT` - Quadrature rule chosen by PETSc 72 . `PETSCDTSIMPLEXQUAD_CONIC` - Quadrature rules constructed as 73 conically-warped tensor products of 1D 74 Gauss-Jacobi quadrature rules. These are 75 explicitly computable in any dimension for any 76 degree, and the tensor-product structure can be 77 exploited by sum-factorization methods, but 78 they are not efficient in terms of nodes per 79 polynomial degree. 80 - `PETSCDTSIMPLEXQUAD_MINSYM` - Quadrature rules that are fully symmetric 81 (symmetries of the simplex preserve the nodes 82 and weights) with minimal (or near minimal) 83 number of nodes. In dimensions higher than 1 84 these are not simple to compute, so lookup 85 tables are used. 86 87 Level: intermediate 88 89 .seealso: `PetscQuadrature`, `PetscDTSimplexQuadrature()` 90 E*/ 91 typedef enum { 92 PETSCDTSIMPLEXQUAD_DEFAULT = -1, 93 PETSCDTSIMPLEXQUAD_CONIC = 0, 94 PETSCDTSIMPLEXQUAD_MINSYM 95 } PetscDTSimplexQuadratureType; 96 97 PETSC_EXTERN const char *const *const PetscDTSimplexQuadratureTypes; 98 99 PETSC_EXTERN PetscErrorCode PetscQuadratureCreate(MPI_Comm, PetscQuadrature *); 100 PETSC_EXTERN PetscErrorCode PetscQuadratureDuplicate(PetscQuadrature, PetscQuadrature *); 101 PETSC_EXTERN PetscErrorCode PetscQuadratureGetCellType(PetscQuadrature, DMPolytopeType *); 102 PETSC_EXTERN PetscErrorCode PetscQuadratureSetCellType(PetscQuadrature, DMPolytopeType); 103 PETSC_EXTERN PetscErrorCode PetscQuadratureGetOrder(PetscQuadrature, PetscInt *); 104 PETSC_EXTERN PetscErrorCode PetscQuadratureSetOrder(PetscQuadrature, PetscInt); 105 PETSC_EXTERN PetscErrorCode PetscQuadratureGetNumComponents(PetscQuadrature, PetscInt *); 106 PETSC_EXTERN PetscErrorCode PetscQuadratureSetNumComponents(PetscQuadrature, PetscInt); 107 PETSC_EXTERN PetscErrorCode PetscQuadratureEqual(PetscQuadrature, PetscQuadrature, PetscBool *); 108 PETSC_EXTERN PetscErrorCode PetscQuadratureGetData(PetscQuadrature, PetscInt *, PetscInt *, PetscInt *, const PetscReal *[], const PetscReal *[]); 109 PETSC_EXTERN PetscErrorCode PetscQuadratureSetData(PetscQuadrature, PetscInt, PetscInt, PetscInt, const PetscReal[], const PetscReal[]); 110 PETSC_EXTERN PetscErrorCode PetscQuadratureView(PetscQuadrature, PetscViewer); 111 PETSC_EXTERN PetscErrorCode PetscQuadratureDestroy(PetscQuadrature *); 112 113 PETSC_EXTERN PetscErrorCode PetscDTTensorQuadratureCreate(PetscQuadrature, PetscQuadrature, PetscQuadrature *); 114 PETSC_EXTERN PetscErrorCode PetscQuadratureExpandComposite(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], PetscQuadrature *); 115 PETSC_EXTERN PetscErrorCode PetscQuadratureComputePermutations(PetscQuadrature, PetscInt *, IS *[]); 116 117 PETSC_EXTERN PetscErrorCode PetscQuadraturePushForward(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], const PetscReal[], PetscInt, PetscQuadrature *); 118 119 PETSC_EXTERN PetscErrorCode PetscDTLegendreEval(PetscInt, const PetscReal *, PetscInt, const PetscInt *, PetscReal *, PetscReal *, PetscReal *); 120 PETSC_EXTERN PetscErrorCode PetscDTJacobiNorm(PetscReal, PetscReal, PetscInt, PetscReal *); 121 PETSC_EXTERN PetscErrorCode PetscDTJacobiEval(PetscInt, PetscReal, PetscReal, const PetscReal *, PetscInt, const PetscInt *, PetscReal *, PetscReal *, PetscReal *); 122 PETSC_EXTERN PetscErrorCode PetscDTJacobiEvalJet(PetscReal, PetscReal, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscReal[]); 123 PETSC_EXTERN PetscErrorCode PetscDTPKDEvalJet(PetscInt, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscReal[]); 124 PETSC_EXTERN PetscErrorCode PetscDTPTrimmedSize(PetscInt, PetscInt, PetscInt, PetscInt *); 125 PETSC_EXTERN PetscErrorCode PetscDTPTrimmedEvalJet(PetscInt, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscInt, PetscReal[]); 126 PETSC_EXTERN PetscErrorCode PetscDTGaussQuadrature(PetscInt, PetscReal, PetscReal, PetscReal *, PetscReal *); 127 PETSC_EXTERN PetscErrorCode PetscDTGaussJacobiQuadrature(PetscInt, PetscReal, PetscReal, PetscReal, PetscReal, PetscReal *, PetscReal *); 128 PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoJacobiQuadrature(PetscInt, PetscReal, PetscReal, PetscReal, PetscReal, PetscReal *, PetscReal *); 129 PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoLegendreQuadrature(PetscInt, PetscGaussLobattoLegendreCreateType, PetscReal *, PetscReal *); 130 PETSC_EXTERN PetscErrorCode PetscDTReconstructPoly(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *); 131 PETSC_EXTERN PetscErrorCode PetscDTGaussTensorQuadrature(PetscInt, PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 132 PETSC_EXTERN PetscErrorCode PetscDTStroudConicalQuadrature(PetscInt, PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 133 PETSC_EXTERN PetscErrorCode PetscDTSimplexQuadrature(PetscInt, PetscInt, PetscDTSimplexQuadratureType, PetscQuadrature *); 134 PETSC_EXTERN PetscErrorCode PetscDTCreateDefaultQuadrature(DMPolytopeType, PetscInt, PetscQuadrature *, PetscQuadrature *); 135 136 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhTensorQuadrature(PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 137 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrate(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *); 138 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrateMPFR(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *); 139 140 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreIntegrate(PetscInt, PetscReal *, PetscReal *, const PetscReal *, PetscReal *); 141 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 142 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 143 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); 144 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); 145 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 146 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 147 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 148 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 149 150 PETSC_EXTERN PetscErrorCode PetscDTAltVApply(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 151 PETSC_EXTERN PetscErrorCode PetscDTAltVWedge(PetscInt, PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 152 PETSC_EXTERN PetscErrorCode PetscDTAltVWedgeMatrix(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); 153 PETSC_EXTERN PetscErrorCode PetscDTAltVPullback(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *); 154 PETSC_EXTERN PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt, PetscInt, const PetscReal *, PetscInt, PetscReal *); 155 PETSC_EXTERN PetscErrorCode PetscDTAltVInterior(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 156 PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorMatrix(PetscInt, PetscInt, const PetscReal *, PetscReal *); 157 PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorPattern(PetscInt, PetscInt, PetscInt (*)[3]); 158 PETSC_EXTERN PetscErrorCode PetscDTAltVStar(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); 159 160 PETSC_EXTERN PetscErrorCode PetscDTBaryToIndex(PetscInt, PetscInt, const PetscInt[], PetscInt *); 161 PETSC_EXTERN PetscErrorCode PetscDTIndexToBary(PetscInt, PetscInt, PetscInt, PetscInt[]); 162 PETSC_EXTERN PetscErrorCode PetscDTGradedOrderToIndex(PetscInt, const PetscInt[], PetscInt *); 163 PETSC_EXTERN PetscErrorCode PetscDTIndexToGradedOrder(PetscInt, PetscInt, PetscInt[]); 164 165 #if defined(PETSC_USE_64BIT_INDICES) 166 #define PETSC_FACTORIAL_MAX 20 167 #define PETSC_BINOMIAL_MAX 61 168 #else 169 #define PETSC_FACTORIAL_MAX 12 170 #define PETSC_BINOMIAL_MAX 29 171 #endif 172 173 /*MC 174 PetscDTFactorial - Approximate n! as a real number 175 176 Input Parameter: 177 . n - a non-negative integer 178 179 Output Parameter: 180 . factorial - n! 181 182 Level: beginner 183 184 .seealso: `PetscDTFactorialInt()`, `PetscDTBinomialInt()`, `PetscDTBinomial()` 185 M*/ 186 static inline PetscErrorCode PetscDTFactorial(PetscInt n, PetscReal *factorial) 187 { 188 PetscReal f = 1.0; 189 190 PetscFunctionBegin; 191 *factorial = -1.0; 192 PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Factorial called with negative number %" PetscInt_FMT, n); 193 for (PetscInt i = 1; i < n + 1; ++i) f *= (PetscReal)i; 194 *factorial = f; 195 PetscFunctionReturn(PETSC_SUCCESS); 196 } 197 198 /*MC 199 PetscDTFactorialInt - Compute n! as an integer 200 201 Input Parameter: 202 . n - a non-negative integer 203 204 Output Parameter: 205 . factorial - n! 206 207 Level: beginner 208 209 Note: 210 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. 211 212 .seealso: `PetscDTFactorial()`, `PetscDTBinomialInt()`, `PetscDTBinomial()` 213 M*/ 214 static inline PetscErrorCode PetscDTFactorialInt(PetscInt n, PetscInt *factorial) 215 { 216 PetscInt facLookup[13] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600}; 217 218 PetscFunctionBegin; 219 *factorial = -1; 220 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); 221 if (n <= 12) { 222 *factorial = facLookup[n]; 223 } else { 224 PetscInt f = facLookup[12]; 225 PetscInt i; 226 227 for (i = 13; i < n + 1; ++i) f *= i; 228 *factorial = f; 229 } 230 PetscFunctionReturn(PETSC_SUCCESS); 231 } 232 233 /*MC 234 PetscDTBinomial - Approximate the binomial coefficient "n choose k" 235 236 Input Parameters: 237 + n - a non-negative integer 238 - k - an integer between 0 and n, inclusive 239 240 Output Parameter: 241 . binomial - approximation of the binomial coefficient n choose k 242 243 Level: beginner 244 245 .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()` 246 M*/ 247 static inline PetscErrorCode PetscDTBinomial(PetscInt n, PetscInt k, PetscReal *binomial) 248 { 249 PetscFunctionBeginHot; 250 *binomial = -1.0; 251 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); 252 if (n <= 3) { 253 PetscInt binomLookup[4][4] = { 254 {1, 0, 0, 0}, 255 {1, 1, 0, 0}, 256 {1, 2, 1, 0}, 257 {1, 3, 3, 1} 258 }; 259 260 *binomial = (PetscReal)binomLookup[n][k]; 261 } else { 262 PetscReal binom = 1.0; 263 264 k = PetscMin(k, n - k); 265 for (PetscInt i = 0; i < k; i++) binom = (binom * (PetscReal)(n - i)) / (PetscReal)(i + 1); 266 *binomial = binom; 267 } 268 PetscFunctionReturn(PETSC_SUCCESS); 269 } 270 271 /*MC 272 PetscDTBinomialInt - Compute the binomial coefficient "n choose k" 273 274 Input Parameters: 275 + n - a non-negative integer 276 - k - an integer between 0 and n, inclusive 277 278 Output Parameter: 279 . binomial - the binomial coefficient n choose k 280 281 Level: beginner 282 283 Note: 284 This is limited by integers that can be represented by `PetscInt`. 285 286 Use `PetscDTBinomial()` for real number approximations of larger values 287 288 .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTEnumPerm()` 289 M*/ 290 static inline PetscErrorCode PetscDTBinomialInt(PetscInt n, PetscInt k, PetscInt *binomial) 291 { 292 PetscInt bin; 293 294 PetscFunctionBegin; 295 *binomial = -1; 296 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); 297 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); 298 if (n <= 3) { 299 PetscInt binomLookup[4][4] = { 300 {1, 0, 0, 0}, 301 {1, 1, 0, 0}, 302 {1, 2, 1, 0}, 303 {1, 3, 3, 1} 304 }; 305 306 bin = binomLookup[n][k]; 307 } else { 308 PetscInt binom = 1; 309 310 k = PetscMin(k, n - k); 311 for (PetscInt i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1); 312 bin = binom; 313 } 314 *binomial = bin; 315 PetscFunctionReturn(PETSC_SUCCESS); 316 } 317 318 /*MC 319 PetscDTEnumPerm - Get a permutation of `n` integers from its encoding into the integers [0, n!) as a sequence of swaps. 320 321 Input Parameters: 322 + n - a non-negative integer (see note about limits below) 323 - k - an integer in [0, n!) 324 325 Output Parameters: 326 + perm - the permuted list of the integers [0, ..., n-1] 327 - isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps. 328 329 Level: intermediate 330 331 Notes: 332 A permutation can be described by the operations that convert the lists [0, 1, ..., n-1] into the permutation, 333 by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in 334 some position j >= i. This swap is encoded as the difference (j - i). The difference d_i at step i is less than 335 (n - i). This sequence of n-1 differences [d_0, ..., d_{n-2}] is encoded as the number 336 (n-1)! * d_0 + (n-2)! * d_1 + ... + 1! * d_{n-2}. 337 338 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. 339 340 .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTPermIndex()` 341 M*/ 342 static inline PetscErrorCode PetscDTEnumPerm(PetscInt n, PetscInt k, PetscInt *perm, PetscBool *isOdd) 343 { 344 PetscInt odd = 0; 345 PetscInt i; 346 PetscInt work[PETSC_FACTORIAL_MAX]; 347 PetscInt *w; 348 349 PetscFunctionBegin; 350 if (isOdd) *isOdd = PETSC_FALSE; 351 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); 352 w = &work[n - 2]; 353 for (i = 2; i <= n; i++) { 354 *(w--) = k % i; 355 k /= i; 356 } 357 for (i = 0; i < n; i++) perm[i] = i; 358 for (i = 0; i < n - 1; i++) { 359 PetscInt s = work[i]; 360 PetscInt swap = perm[i]; 361 362 perm[i] = perm[i + s]; 363 perm[i + s] = swap; 364 odd ^= (!!s); 365 } 366 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 367 PetscFunctionReturn(PETSC_SUCCESS); 368 } 369 370 /*MC 371 PetscDTPermIndex - Encode a permutation of n into an integer in [0, n!). This inverts `PetscDTEnumPerm()`. 372 373 Input Parameters: 374 + n - a non-negative integer (see note about limits below) 375 - perm - the permuted list of the integers [0, ..., n-1] 376 377 Output Parameters: 378 + k - an integer in [0, n!) 379 - isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps. 380 381 Level: beginner 382 383 Note: 384 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. 385 386 .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()` 387 M*/ 388 static inline PetscErrorCode PetscDTPermIndex(PetscInt n, const PetscInt *perm, PetscInt *k, PetscBool *isOdd) 389 { 390 PetscInt odd = 0; 391 PetscInt i, idx; 392 PetscInt work[PETSC_FACTORIAL_MAX]; 393 PetscInt iwork[PETSC_FACTORIAL_MAX]; 394 395 PetscFunctionBeginHot; 396 *k = -1; 397 if (isOdd) *isOdd = PETSC_FALSE; 398 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); 399 for (i = 0; i < n; i++) work[i] = i; /* partial permutation */ 400 for (i = 0; i < n; i++) iwork[i] = i; /* partial permutation inverse */ 401 for (idx = 0, i = 0; i < n - 1; i++) { 402 PetscInt j = perm[i]; 403 PetscInt icur = work[i]; 404 PetscInt jloc = iwork[j]; 405 PetscInt diff = jloc - i; 406 407 idx = idx * (n - i) + diff; 408 /* swap (i, jloc) */ 409 work[i] = j; 410 work[jloc] = icur; 411 iwork[j] = i; 412 iwork[icur] = jloc; 413 odd ^= (!!diff); 414 } 415 *k = idx; 416 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 417 PetscFunctionReturn(PETSC_SUCCESS); 418 } 419 420 /*MC 421 PetscDTEnumSubset - Get an ordered subset of the integers [0, ..., n - 1] from its encoding as an integers in [0, n choose k). 422 The encoding is in lexicographic order. 423 424 Input Parameters: 425 + n - a non-negative integer (see note about limits below) 426 . k - an integer in [0, n] 427 - j - an index in [0, n choose k) 428 429 Output Parameter: 430 . subset - the jth subset of size k of the integers [0, ..., n - 1] 431 432 Level: beginner 433 434 Note: 435 Limited by arguments such that `n` choose `k` can be represented by `PetscInt` 436 437 .seealso: `PetscDTSubsetIndex()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()` 438 M*/ 439 static inline PetscErrorCode PetscDTEnumSubset(PetscInt n, PetscInt k, PetscInt j, PetscInt *subset) 440 { 441 PetscInt Nk; 442 443 PetscFunctionBeginHot; 444 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 445 for (PetscInt i = 0, l = 0; i < n && l < k; i++) { 446 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 447 PetscInt Nminusk = Nk - Nminuskminus; 448 449 if (j < Nminuskminus) { 450 subset[l++] = i; 451 Nk = Nminuskminus; 452 } else { 453 j -= Nminuskminus; 454 Nk = Nminusk; 455 } 456 } 457 PetscFunctionReturn(PETSC_SUCCESS); 458 } 459 460 /*MC 461 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. 462 This is the inverse of `PetscDTEnumSubset`. 463 464 Input Parameters: 465 + n - a non-negative integer (see note about limits below) 466 . k - an integer in [0, n] 467 - subset - an ordered subset of the integers [0, ..., n - 1] 468 469 Output Parameter: 470 . index - the rank of the subset in lexicographic order 471 472 Level: beginner 473 474 Note: 475 Limited by arguments such that `n` choose `k` can be represented by `PetscInt` 476 477 .seealso: `PetscDTEnumSubset()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()` 478 M*/ 479 static inline PetscErrorCode PetscDTSubsetIndex(PetscInt n, PetscInt k, const PetscInt *subset, PetscInt *index) 480 { 481 PetscInt j = 0, Nk; 482 483 PetscFunctionBegin; 484 *index = -1; 485 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 486 for (PetscInt i = 0, l = 0; i < n && l < k; i++) { 487 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 488 PetscInt Nminusk = Nk - Nminuskminus; 489 490 if (subset[l] == i) { 491 l++; 492 Nk = Nminuskminus; 493 } else { 494 j += Nminuskminus; 495 Nk = Nminusk; 496 } 497 } 498 *index = j; 499 PetscFunctionReturn(PETSC_SUCCESS); 500 } 501 502 /*MC 503 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. 504 505 Input Parameters: 506 + n - a non-negative integer (see note about limits below) 507 . k - an integer in [0, n] 508 - j - an index in [0, n choose k) 509 510 Output Parameters: 511 + perm - the jth subset of size k of the integers [0, ..., n - 1], followed by its complementary set. 512 - isOdd - if not `NULL`, return whether perm is an even or odd permutation. 513 514 Level: beginner 515 516 Note: 517 Limited by arguments such that `n` choose `k` can be represented by `PetscInt` 518 519 .seealso: `PetscDTEnumSubset()`, `PetscDTSubsetIndex()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, 520 `PetscDTPermIndex()` 521 M*/ 522 static inline PetscErrorCode PetscDTEnumSplit(PetscInt n, PetscInt k, PetscInt j, PetscInt *perm, PetscBool *isOdd) 523 { 524 PetscInt i, l, m, Nk, odd = 0; 525 PetscInt *subcomp = perm + k; 526 527 PetscFunctionBegin; 528 if (isOdd) *isOdd = PETSC_FALSE; 529 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 530 for (i = 0, l = 0, m = 0; i < n && l < k; i++) { 531 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 532 PetscInt Nminusk = Nk - Nminuskminus; 533 534 if (j < Nminuskminus) { 535 perm[l++] = i; 536 Nk = Nminuskminus; 537 } else { 538 subcomp[m++] = i; 539 j -= Nminuskminus; 540 odd ^= ((k - l) & 1); 541 Nk = Nminusk; 542 } 543 } 544 for (; i < n; i++) subcomp[m++] = i; 545 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 546 PetscFunctionReturn(PETSC_SUCCESS); 547 } 548 549 struct _p_PetscTabulation { 550 PetscInt K; /* Indicates a k-jet, namely tabulated derivatives up to order k */ 551 PetscInt Nr; /* The number of tabulation replicas (often 1) */ 552 PetscInt Np; /* The number of tabulation points in a replica */ 553 PetscInt Nb; /* The number of functions tabulated */ 554 PetscInt Nc; /* The number of function components */ 555 PetscInt cdim; /* The coordinate dimension */ 556 PetscReal **T; /* The tabulation T[K] of functions and their derivatives 557 T[0] = B[Nr*Np][Nb][Nc]: The basis function values at quadrature points 558 T[1] = D[Nr*Np][Nb][Nc][cdim]: The basis function derivatives at quadrature points 559 T[2] = H[Nr*Np][Nb][Nc][cdim][cdim]: The basis function second derivatives at quadrature points */ 560 }; 561 typedef struct _p_PetscTabulation *PetscTabulation; 562 563 typedef PetscErrorCode (*PetscProbFunc)(const PetscReal[], const PetscReal[], PetscReal[]); 564 565 typedef enum { 566 DTPROB_DENSITY_CONSTANT, 567 DTPROB_DENSITY_GAUSSIAN, 568 DTPROB_DENSITY_MAXWELL_BOLTZMANN, 569 DTPROB_NUM_DENSITY 570 } DTProbDensityType; 571 PETSC_EXTERN const char *const DTProbDensityTypes[]; 572 573 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]); 574 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]); 575 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]); 576 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]); 577 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]); 578 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]); 579 PETSC_EXTERN PetscErrorCode PetscPDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 580 PETSC_EXTERN PetscErrorCode PetscCDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 581 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 582 PETSC_EXTERN PetscErrorCode PetscPDFGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]); 583 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]); 584 PETSC_EXTERN PetscErrorCode PetscPDFGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]); 585 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]); 586 PETSC_EXTERN PetscErrorCode PetscPDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 587 PETSC_EXTERN PetscErrorCode PetscCDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 588 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 589 PETSC_EXTERN PetscErrorCode PetscPDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 590 PETSC_EXTERN PetscErrorCode PetscCDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 591 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 592 PETSC_EXTERN PetscErrorCode PetscPDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 593 PETSC_EXTERN PetscErrorCode PetscCDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 594 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 595 PETSC_EXTERN PetscErrorCode PetscProbCreateFromOptions(PetscInt, const char[], const char[], PetscProbFunc *, PetscProbFunc *, PetscProbFunc *); 596 597 #include <petscvec.h> 598 599 PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatistic(Vec, PetscProbFunc, PetscReal *); 600