1 /* 2 Common tools for constructing discretizations 3 */ 4 #ifndef PETSCDT_H 5 #define PETSCDT_H 6 7 #include <petscsys.h> 8 #include <petscdmtypes.h> 9 #include <petscistypes.h> 10 11 /* SUBMANSEC = DT */ 12 13 PETSC_EXTERN PetscClassId PETSCQUADRATURE_CLASSID; 14 15 /*S 16 PetscQuadrature - Quadrature rule for integration. 17 18 Level: beginner 19 20 .seealso: `PetscQuadratureCreate()`, `PetscQuadratureDestroy()` 21 S*/ 22 typedef struct _p_PetscQuadrature *PetscQuadrature; 23 24 /*E 25 PetscGaussLobattoLegendreCreateType - algorithm used to compute the Gauss-Lobatto-Legendre nodes and weights 26 27 Level: intermediate 28 29 $ `PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA` - compute the nodes via linear algebra 30 $ `PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON` - compute the nodes by solving a nonlinear equation with Newton's method 31 32 E*/ 33 typedef enum { 34 PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA, 35 PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON 36 } PetscGaussLobattoLegendreCreateType; 37 38 /*E 39 PetscDTNodeType - A description of strategies for generating nodes (both 40 quadrature nodes and nodes for Lagrange polynomials) 41 42 Level: intermediate 43 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 Note: 50 A `PetscDTNodeType` can be paired with a `PetscBool` to indicate whether 51 the nodes include endpoints or not, and in the case of `PETSCDT_GAUSSJACOBI` 52 with exponents for the weight function. 53 54 E*/ 55 typedef enum { 56 PETSCDTNODES_DEFAULT = -1, 57 PETSCDTNODES_GAUSSJACOBI, 58 PETSCDTNODES_EQUISPACED, 59 PETSCDTNODES_TANHSINH 60 } PetscDTNodeType; 61 62 PETSC_EXTERN const char *const *const PetscDTNodeTypes; 63 64 /*E 65 PetscDTSimplexQuadratureType - A description of classes of quadrature rules for simplices 66 67 Level: intermediate 68 69 $ `PETSCDTSIMPLEXQUAD_DEFAULT` - Quadrature rule chosen by PETSc 70 $ `PETSCDTSIMPLEXQUAD_CONIC` - Quadrature rules constructed as 71 conically-warped tensor products of 1D 72 Gauss-Jacobi quadrature rules. These are 73 explicitly computable in any dimension for any 74 degree, and the tensor-product structure can be 75 exploited by sum-factorization methods, but 76 they are not efficient in terms of nodes per 77 polynomial degree. 78 $ `PETSCDTSIMPLEXQUAD_MINSYM` - Quadrature rules that are fully symmetric 79 (symmetries of the simplex preserve the nodes 80 and weights) with minimal (or near minimal) 81 number of nodes. In dimensions higher than 1 82 these are not simple to compute, so lookup 83 tables are used. 84 85 .seealso: `PetscDTSimplexQuadrature()` 86 E*/ 87 typedef enum { 88 PETSCDTSIMPLEXQUAD_DEFAULT = -1, 89 PETSCDTSIMPLEXQUAD_CONIC = 0, 90 PETSCDTSIMPLEXQUAD_MINSYM 91 } PetscDTSimplexQuadratureType; 92 93 PETSC_EXTERN const char *const *const PetscDTSimplexQuadratureTypes; 94 95 PETSC_EXTERN PetscErrorCode PetscQuadratureCreate(MPI_Comm, PetscQuadrature *); 96 PETSC_EXTERN PetscErrorCode PetscQuadratureDuplicate(PetscQuadrature, PetscQuadrature *); 97 PETSC_EXTERN PetscErrorCode PetscQuadratureGetCellType(PetscQuadrature, DMPolytopeType *); 98 PETSC_EXTERN PetscErrorCode PetscQuadratureSetCellType(PetscQuadrature, DMPolytopeType); 99 PETSC_EXTERN PetscErrorCode PetscQuadratureGetOrder(PetscQuadrature, PetscInt *); 100 PETSC_EXTERN PetscErrorCode PetscQuadratureSetOrder(PetscQuadrature, PetscInt); 101 PETSC_EXTERN PetscErrorCode PetscQuadratureGetNumComponents(PetscQuadrature, PetscInt *); 102 PETSC_EXTERN PetscErrorCode PetscQuadratureSetNumComponents(PetscQuadrature, PetscInt); 103 PETSC_EXTERN PetscErrorCode PetscQuadratureEqual(PetscQuadrature, PetscQuadrature, PetscBool *); 104 PETSC_EXTERN PetscErrorCode PetscQuadratureGetData(PetscQuadrature, PetscInt *, PetscInt *, PetscInt *, const PetscReal *[], const PetscReal *[]); 105 PETSC_EXTERN PetscErrorCode PetscQuadratureSetData(PetscQuadrature, PetscInt, PetscInt, PetscInt, const PetscReal[], const PetscReal[]); 106 PETSC_EXTERN PetscErrorCode PetscQuadratureView(PetscQuadrature, PetscViewer); 107 PETSC_EXTERN PetscErrorCode PetscQuadratureDestroy(PetscQuadrature *); 108 109 PETSC_EXTERN PetscErrorCode PetscDTTensorQuadratureCreate(PetscQuadrature, PetscQuadrature, PetscQuadrature *); 110 PETSC_EXTERN PetscErrorCode PetscQuadratureExpandComposite(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], PetscQuadrature *); 111 PETSC_EXTERN PetscErrorCode PetscQuadratureComputePermutations(PetscQuadrature, PetscInt *, IS *[]); 112 113 PETSC_EXTERN PetscErrorCode PetscQuadraturePushForward(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], const PetscReal[], PetscInt, PetscQuadrature *); 114 115 PETSC_EXTERN PetscErrorCode PetscDTLegendreEval(PetscInt, const PetscReal *, PetscInt, const PetscInt *, PetscReal *, PetscReal *, PetscReal *); 116 PETSC_EXTERN PetscErrorCode PetscDTJacobiNorm(PetscReal, PetscReal, PetscInt, PetscReal *); 117 PETSC_EXTERN PetscErrorCode PetscDTJacobiEval(PetscInt, PetscReal, PetscReal, const PetscReal *, PetscInt, const PetscInt *, PetscReal *, PetscReal *, PetscReal *); 118 PETSC_EXTERN PetscErrorCode PetscDTJacobiEvalJet(PetscReal, PetscReal, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscReal[]); 119 PETSC_EXTERN PetscErrorCode PetscDTPKDEvalJet(PetscInt, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscReal[]); 120 PETSC_EXTERN PetscErrorCode PetscDTPTrimmedSize(PetscInt, PetscInt, PetscInt, PetscInt *); 121 PETSC_EXTERN PetscErrorCode PetscDTPTrimmedEvalJet(PetscInt, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscInt, PetscReal[]); 122 PETSC_EXTERN PetscErrorCode PetscDTGaussQuadrature(PetscInt, PetscReal, PetscReal, PetscReal *, PetscReal *); 123 PETSC_EXTERN PetscErrorCode PetscDTGaussJacobiQuadrature(PetscInt, PetscReal, PetscReal, PetscReal, PetscReal, PetscReal *, PetscReal *); 124 PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoJacobiQuadrature(PetscInt, PetscReal, PetscReal, PetscReal, PetscReal, PetscReal *, PetscReal *); 125 PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoLegendreQuadrature(PetscInt, PetscGaussLobattoLegendreCreateType, PetscReal *, PetscReal *); 126 PETSC_EXTERN PetscErrorCode PetscDTReconstructPoly(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *); 127 PETSC_EXTERN PetscErrorCode PetscDTGaussTensorQuadrature(PetscInt, PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 128 PETSC_EXTERN PetscErrorCode PetscDTStroudConicalQuadrature(PetscInt, PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 129 PETSC_EXTERN PetscErrorCode PetscDTSimplexQuadrature(PetscInt, PetscInt, PetscDTSimplexQuadratureType, PetscQuadrature *); 130 PETSC_EXTERN PetscErrorCode PetscDTCreateDefaultQuadrature(DMPolytopeType, PetscInt, PetscQuadrature *, PetscQuadrature *); 131 132 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhTensorQuadrature(PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 133 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrate(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *); 134 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrateMPFR(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *); 135 136 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreIntegrate(PetscInt, PetscReal *, PetscReal *, const PetscReal *, PetscReal *); 137 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 138 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 139 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); 140 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); 141 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 142 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 143 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 144 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 145 146 PETSC_EXTERN PetscErrorCode PetscDTAltVApply(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 147 PETSC_EXTERN PetscErrorCode PetscDTAltVWedge(PetscInt, PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 148 PETSC_EXTERN PetscErrorCode PetscDTAltVWedgeMatrix(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); 149 PETSC_EXTERN PetscErrorCode PetscDTAltVPullback(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *); 150 PETSC_EXTERN PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt, PetscInt, const PetscReal *, PetscInt, PetscReal *); 151 PETSC_EXTERN PetscErrorCode PetscDTAltVInterior(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 152 PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorMatrix(PetscInt, PetscInt, const PetscReal *, PetscReal *); 153 PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorPattern(PetscInt, PetscInt, PetscInt (*)[3]); 154 PETSC_EXTERN PetscErrorCode PetscDTAltVStar(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); 155 156 PETSC_EXTERN PetscErrorCode PetscDTBaryToIndex(PetscInt, PetscInt, const PetscInt[], PetscInt *); 157 PETSC_EXTERN PetscErrorCode PetscDTIndexToBary(PetscInt, PetscInt, PetscInt, PetscInt[]); 158 PETSC_EXTERN PetscErrorCode PetscDTGradedOrderToIndex(PetscInt, const PetscInt[], PetscInt *); 159 PETSC_EXTERN PetscErrorCode PetscDTIndexToGradedOrder(PetscInt, PetscInt, PetscInt[]); 160 161 #if defined(PETSC_USE_64BIT_INDICES) 162 #define PETSC_FACTORIAL_MAX 20 163 #define PETSC_BINOMIAL_MAX 61 164 #else 165 #define PETSC_FACTORIAL_MAX 12 166 #define PETSC_BINOMIAL_MAX 29 167 #endif 168 169 /*MC 170 PetscDTFactorial - Approximate n! as a real number 171 172 Input Parameter: 173 . n - a non-negative integer 174 175 Output Parameter: 176 . factorial - n! 177 178 Level: beginner 179 M*/ 180 static inline PetscErrorCode PetscDTFactorial(PetscInt n, PetscReal *factorial) 181 { 182 PetscReal f = 1.0; 183 184 PetscFunctionBegin; 185 *factorial = -1.0; 186 PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Factorial called with negative number %" PetscInt_FMT, n); 187 for (PetscInt i = 1; i < n + 1; ++i) f *= (PetscReal)i; 188 *factorial = f; 189 PetscFunctionReturn(PETSC_SUCCESS); 190 } 191 192 /*MC 193 PetscDTFactorialInt - Compute n! as an integer 194 195 Input Parameter: 196 . n - a non-negative integer 197 198 Output Parameter: 199 . factorial - n! 200 201 Level: beginner 202 203 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. 204 M*/ 205 static inline PetscErrorCode PetscDTFactorialInt(PetscInt n, PetscInt *factorial) 206 { 207 PetscInt facLookup[13] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600}; 208 209 PetscFunctionBegin; 210 *factorial = -1; 211 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); 212 if (n <= 12) { 213 *factorial = facLookup[n]; 214 } else { 215 PetscInt f = facLookup[12]; 216 PetscInt i; 217 218 for (i = 13; i < n + 1; ++i) f *= i; 219 *factorial = f; 220 } 221 PetscFunctionReturn(PETSC_SUCCESS); 222 } 223 224 /*MC 225 PetscDTBinomial - Approximate the binomial coefficient "n choose k" 226 227 Input Parameters: 228 + n - a non-negative integer 229 - k - an integer between 0 and n, inclusive 230 231 Output Parameter: 232 . binomial - approximation of the binomial coefficient n choose k 233 234 Level: beginner 235 M*/ 236 static inline PetscErrorCode PetscDTBinomial(PetscInt n, PetscInt k, PetscReal *binomial) 237 { 238 PetscFunctionBeginHot; 239 *binomial = -1.0; 240 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); 241 if (n <= 3) { 242 PetscInt binomLookup[4][4] = { 243 {1, 0, 0, 0}, 244 {1, 1, 0, 0}, 245 {1, 2, 1, 0}, 246 {1, 3, 3, 1} 247 }; 248 249 *binomial = (PetscReal)binomLookup[n][k]; 250 } else { 251 PetscReal binom = 1.0; 252 253 k = PetscMin(k, n - k); 254 for (PetscInt i = 0; i < k; i++) binom = (binom * (PetscReal)(n - i)) / (PetscReal)(i + 1); 255 *binomial = binom; 256 } 257 PetscFunctionReturn(PETSC_SUCCESS); 258 } 259 260 /*MC 261 PetscDTBinomialInt - Compute the binomial coefficient "n choose k" 262 263 Input Parameters: 264 + n - a non-negative integer 265 - k - an integer between 0 and n, inclusive 266 267 Output Parameter: 268 . binomial - the binomial coefficient n choose k 269 270 Note: this is limited by integers that can be represented by `PetscInt` 271 272 Level: beginner 273 M*/ 274 static inline PetscErrorCode PetscDTBinomialInt(PetscInt n, PetscInt k, PetscInt *binomial) 275 { 276 PetscInt bin; 277 278 PetscFunctionBegin; 279 *binomial = -1; 280 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); 281 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); 282 if (n <= 3) { 283 PetscInt binomLookup[4][4] = { 284 {1, 0, 0, 0}, 285 {1, 1, 0, 0}, 286 {1, 2, 1, 0}, 287 {1, 3, 3, 1} 288 }; 289 290 bin = binomLookup[n][k]; 291 } else { 292 PetscInt binom = 1; 293 294 k = PetscMin(k, n - k); 295 for (PetscInt i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1); 296 bin = binom; 297 } 298 *binomial = bin; 299 PetscFunctionReturn(PETSC_SUCCESS); 300 } 301 302 /*MC 303 PetscDTEnumPerm - Get a permutation of n integers from its encoding into the integers [0, n!) as a sequence of swaps. 304 305 A permutation can be described by the operations that convert the lists [0, 1, ..., n-1] into the permutation, 306 by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in 307 some position j >= i. This swap is encoded as the difference (j - i). The difference d_i at step i is less than 308 (n - i). This sequence of n-1 differences [d_0, ..., d_{n-2}] is encoded as the number 309 (n-1)! * d_0 + (n-2)! * d_1 + ... + 1! * d_{n-2}. 310 311 Input Parameters: 312 + n - a non-negative integer (see note about limits below) 313 - k - an integer in [0, n!) 314 315 Output Parameters: 316 + perm - the permuted list of the integers [0, ..., n-1] 317 - isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps. 318 319 Note: 320 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. 321 322 Level: beginner 323 M*/ 324 static inline PetscErrorCode PetscDTEnumPerm(PetscInt n, PetscInt k, PetscInt *perm, PetscBool *isOdd) 325 { 326 PetscInt odd = 0; 327 PetscInt i; 328 PetscInt work[PETSC_FACTORIAL_MAX]; 329 PetscInt *w; 330 331 PetscFunctionBegin; 332 if (isOdd) *isOdd = PETSC_FALSE; 333 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); 334 w = &work[n - 2]; 335 for (i = 2; i <= n; i++) { 336 *(w--) = k % i; 337 k /= i; 338 } 339 for (i = 0; i < n; i++) perm[i] = i; 340 for (i = 0; i < n - 1; i++) { 341 PetscInt s = work[i]; 342 PetscInt swap = perm[i]; 343 344 perm[i] = perm[i + s]; 345 perm[i + s] = swap; 346 odd ^= (!!s); 347 } 348 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 349 PetscFunctionReturn(PETSC_SUCCESS); 350 } 351 352 /*MC 353 PetscDTPermIndex - Encode a permutation of n into an integer in [0, n!). This inverts `PetscDTEnumPerm`. 354 355 Input Parameters: 356 + n - a non-negative integer (see note about limits below) 357 - perm - the permuted list of the integers [0, ..., n-1] 358 359 Output Parameters: 360 + k - an integer in [0, n!) 361 - isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps. 362 363 Note: 364 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. 365 366 Level: beginner 367 M*/ 368 static inline PetscErrorCode PetscDTPermIndex(PetscInt n, const PetscInt *perm, PetscInt *k, PetscBool *isOdd) 369 { 370 PetscInt odd = 0; 371 PetscInt i, idx; 372 PetscInt work[PETSC_FACTORIAL_MAX]; 373 PetscInt iwork[PETSC_FACTORIAL_MAX]; 374 375 PetscFunctionBeginHot; 376 *k = -1; 377 if (isOdd) *isOdd = PETSC_FALSE; 378 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); 379 for (i = 0; i < n; i++) work[i] = i; /* partial permutation */ 380 for (i = 0; i < n; i++) iwork[i] = i; /* partial permutation inverse */ 381 for (idx = 0, i = 0; i < n - 1; i++) { 382 PetscInt j = perm[i]; 383 PetscInt icur = work[i]; 384 PetscInt jloc = iwork[j]; 385 PetscInt diff = jloc - i; 386 387 idx = idx * (n - i) + diff; 388 /* swap (i, jloc) */ 389 work[i] = j; 390 work[jloc] = icur; 391 iwork[j] = i; 392 iwork[icur] = jloc; 393 odd ^= (!!diff); 394 } 395 *k = idx; 396 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 397 PetscFunctionReturn(PETSC_SUCCESS); 398 } 399 400 /*MC 401 PetscDTEnumSubset - Get an ordered subset of the integers [0, ..., n - 1] from its encoding as an integers in [0, n choose k). 402 The encoding is in lexicographic order. 403 404 Input Parameters: 405 + n - a non-negative integer (see note about limits below) 406 . k - an integer in [0, n] 407 - j - an index in [0, n choose k) 408 409 Output Parameter: 410 . subset - the jth subset of size k of the integers [0, ..., n - 1] 411 412 Note: 413 Limited by arguments such that n choose k can be represented by `PetscInt` 414 415 Level: beginner 416 417 .seealso: `PetscDTSubsetIndex()` 418 M*/ 419 static inline PetscErrorCode PetscDTEnumSubset(PetscInt n, PetscInt k, PetscInt j, PetscInt *subset) 420 { 421 PetscInt Nk; 422 423 PetscFunctionBeginHot; 424 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 425 for (PetscInt i = 0, l = 0; i < n && l < k; i++) { 426 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 427 PetscInt Nminusk = Nk - Nminuskminus; 428 429 if (j < Nminuskminus) { 430 subset[l++] = i; 431 Nk = Nminuskminus; 432 } else { 433 j -= Nminuskminus; 434 Nk = Nminusk; 435 } 436 } 437 PetscFunctionReturn(PETSC_SUCCESS); 438 } 439 440 /*MC 441 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. 442 This is the inverse of `PetscDTEnumSubset`. 443 444 Input Parameters: 445 + n - a non-negative integer (see note about limits below) 446 . k - an integer in [0, n] 447 - subset - an ordered subset of the integers [0, ..., n - 1] 448 449 Output Parameter: 450 . index - the rank of the subset in lexicographic order 451 452 Note: 453 Limited by arguments such that n choose k can be represented by `PetscInt` 454 455 Level: beginner 456 457 .seealso: `PetscDTEnumSubset()` 458 M*/ 459 static inline PetscErrorCode PetscDTSubsetIndex(PetscInt n, PetscInt k, const PetscInt *subset, PetscInt *index) 460 { 461 PetscInt j = 0, Nk; 462 463 PetscFunctionBegin; 464 *index = -1; 465 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 466 for (PetscInt i = 0, l = 0; i < n && l < k; i++) { 467 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 468 PetscInt Nminusk = Nk - Nminuskminus; 469 470 if (subset[l] == i) { 471 l++; 472 Nk = Nminuskminus; 473 } else { 474 j += Nminuskminus; 475 Nk = Nminusk; 476 } 477 } 478 *index = j; 479 PetscFunctionReturn(PETSC_SUCCESS); 480 } 481 482 /*MC 483 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. 484 485 Input Parameters: 486 + n - a non-negative integer (see note about limits below) 487 . k - an integer in [0, n] 488 - j - an index in [0, n choose k) 489 490 Output Parameters: 491 + perm - the jth subset of size k of the integers [0, ..., n - 1], followed by its complementary set. 492 - isOdd - if not `NULL`, return whether perm is an even or odd permutation. 493 494 Note: 495 Limited by arguments such that n choose k can be represented by `PetscInt` 496 497 Level: beginner 498 499 .seealso: `PetscDTEnumSubset()`, `PetscDTSubsetIndex()` 500 M*/ 501 static inline PetscErrorCode PetscDTEnumSplit(PetscInt n, PetscInt k, PetscInt j, PetscInt *perm, PetscBool *isOdd) 502 { 503 PetscInt i, l, m, Nk, odd = 0; 504 PetscInt *subcomp = perm + k; 505 506 PetscFunctionBegin; 507 if (isOdd) *isOdd = PETSC_FALSE; 508 PetscCall(PetscDTBinomialInt(n, k, &Nk)); 509 for (i = 0, l = 0, m = 0; i < n && l < k; i++) { 510 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 511 PetscInt Nminusk = Nk - Nminuskminus; 512 513 if (j < Nminuskminus) { 514 perm[l++] = i; 515 Nk = Nminuskminus; 516 } else { 517 subcomp[m++] = i; 518 j -= Nminuskminus; 519 odd ^= ((k - l) & 1); 520 Nk = Nminusk; 521 } 522 } 523 for (; i < n; i++) subcomp[m++] = i; 524 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 525 PetscFunctionReturn(PETSC_SUCCESS); 526 } 527 528 struct _p_PetscTabulation { 529 PetscInt K; /* Indicates a k-jet, namely tabulated derivatives up to order k */ 530 PetscInt Nr; /* The number of tabulation replicas (often 1) */ 531 PetscInt Np; /* The number of tabulation points in a replica */ 532 PetscInt Nb; /* The number of functions tabulated */ 533 PetscInt Nc; /* The number of function components */ 534 PetscInt cdim; /* The coordinate dimension */ 535 PetscReal **T; /* The tabulation T[K] of functions and their derivatives 536 T[0] = B[Nr*Np][Nb][Nc]: The basis function values at quadrature points 537 T[1] = D[Nr*Np][Nb][Nc][cdim]: The basis function derivatives at quadrature points 538 T[2] = H[Nr*Np][Nb][Nc][cdim][cdim]: The basis function second derivatives at quadrature points */ 539 }; 540 typedef struct _p_PetscTabulation *PetscTabulation; 541 542 typedef PetscErrorCode (*PetscProbFunc)(const PetscReal[], const PetscReal[], PetscReal[]); 543 544 typedef enum { 545 DTPROB_DENSITY_CONSTANT, 546 DTPROB_DENSITY_GAUSSIAN, 547 DTPROB_DENSITY_MAXWELL_BOLTZMANN, 548 DTPROB_NUM_DENSITY 549 } DTProbDensityType; 550 PETSC_EXTERN const char *const DTProbDensityTypes[]; 551 552 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]); 553 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]); 554 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]); 555 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]); 556 PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]); 557 PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]); 558 PETSC_EXTERN PetscErrorCode PetscPDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 559 PETSC_EXTERN PetscErrorCode PetscCDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 560 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); 561 PETSC_EXTERN PetscErrorCode PetscPDFGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]); 562 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]); 563 PETSC_EXTERN PetscErrorCode PetscPDFGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]); 564 PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]); 565 PETSC_EXTERN PetscErrorCode PetscPDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 566 PETSC_EXTERN PetscErrorCode PetscCDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 567 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); 568 PETSC_EXTERN PetscErrorCode PetscPDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 569 PETSC_EXTERN PetscErrorCode PetscCDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 570 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); 571 PETSC_EXTERN PetscErrorCode PetscPDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 572 PETSC_EXTERN PetscErrorCode PetscCDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 573 PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); 574 PETSC_EXTERN PetscErrorCode PetscProbCreateFromOptions(PetscInt, const char[], const char[], PetscProbFunc *, PetscProbFunc *, PetscProbFunc *); 575 576 #include <petscvec.h> 577 578 PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatistic(Vec, PetscProbFunc, PetscReal *); 579 580 #endif 581