/* Common tools for constructing discretizations */ #ifndef PETSCDT_H #define PETSCDT_H #include #include #include /* SUBMANSEC = DT */ PETSC_EXTERN PetscClassId PETSCQUADRATURE_CLASSID; /*S PetscQuadrature - Quadrature rule for numerical integration. Level: beginner .seealso: `PetscQuadratureCreate()`, `PetscQuadratureDestroy()` S*/ typedef struct _p_PetscQuadrature *PetscQuadrature; /*E PetscGaussLobattoLegendreCreateType - algorithm used to compute the Gauss-Lobatto-Legendre nodes and weights Values: + `PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA` - compute the nodes via linear algebra - `PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON` - compute the nodes by solving a nonlinear equation with Newton's method Level: intermediate .seealso: `PetscQuadrature` E*/ typedef enum { PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA, PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON } PetscGaussLobattoLegendreCreateType; /*E PetscDTNodeType - A description of strategies for generating nodes (both quadrature nodes and nodes for Lagrange polynomials) Values: + `PETSCDTNODES_DEFAULT` - Nodes chosen by PETSc . `PETSCDTNODES_GAUSSJACOBI` - Nodes at either Gauss-Jacobi or Gauss-Lobatto-Jacobi quadrature points . `PETSCDTNODES_EQUISPACED` - Nodes equispaced either including the endpoints or excluding them - `PETSCDTNODES_TANHSINH` - Nodes at Tanh-Sinh quadrature points Level: intermediate Note: A `PetscDTNodeType` can be paired with a `PetscBool` to indicate whether the nodes include endpoints or not, and in the case of `PETSCDT_GAUSSJACOBI` with exponents for the weight function. .seealso: `PetscQuadrature` E*/ typedef enum { PETSCDTNODES_DEFAULT = -1, PETSCDTNODES_GAUSSJACOBI, PETSCDTNODES_EQUISPACED, PETSCDTNODES_TANHSINH } PetscDTNodeType; PETSC_EXTERN const char *const *const PetscDTNodeTypes; /*E PetscDTSimplexQuadratureType - A description of classes of quadrature rules for simplices Values: + `PETSCDTSIMPLEXQUAD_DEFAULT` - Quadrature rule chosen by PETSc . `PETSCDTSIMPLEXQUAD_CONIC` - Quadrature rules constructed as conically-warped tensor products of 1D Gauss-Jacobi quadrature rules. These are explicitly computable in any dimension for any degree, and the tensor-product structure can be exploited by sum-factorization methods, but they are not efficient in terms of nodes per polynomial degree. - `PETSCDTSIMPLEXQUAD_MINSYM` - Quadrature rules that are fully symmetric (symmetries of the simplex preserve the nodes and weights) with minimal (or near minimal) number of nodes. In dimensions higher than 1 these are not simple to compute, so lookup tables are used. Level: intermediate .seealso: `PetscQuadrature`, `PetscDTSimplexQuadrature()` E*/ typedef enum { PETSCDTSIMPLEXQUAD_DEFAULT = -1, PETSCDTSIMPLEXQUAD_CONIC = 0, PETSCDTSIMPLEXQUAD_MINSYM } PetscDTSimplexQuadratureType; PETSC_EXTERN const char *const *const PetscDTSimplexQuadratureTypes; PETSC_EXTERN PetscErrorCode PetscQuadratureCreate(MPI_Comm, PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscQuadratureDuplicate(PetscQuadrature, PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscQuadratureGetCellType(PetscQuadrature, DMPolytopeType *); PETSC_EXTERN PetscErrorCode PetscQuadratureSetCellType(PetscQuadrature, DMPolytopeType); PETSC_EXTERN PetscErrorCode PetscQuadratureGetOrder(PetscQuadrature, PetscInt *); PETSC_EXTERN PetscErrorCode PetscQuadratureSetOrder(PetscQuadrature, PetscInt); PETSC_EXTERN PetscErrorCode PetscQuadratureGetNumComponents(PetscQuadrature, PetscInt *); PETSC_EXTERN PetscErrorCode PetscQuadratureSetNumComponents(PetscQuadrature, PetscInt); PETSC_EXTERN PetscErrorCode PetscQuadratureEqual(PetscQuadrature, PetscQuadrature, PetscBool *); PETSC_EXTERN PetscErrorCode PetscQuadratureGetData(PetscQuadrature, PetscInt *, PetscInt *, PetscInt *, const PetscReal *[], const PetscReal *[]); PETSC_EXTERN PetscErrorCode PetscQuadratureSetData(PetscQuadrature, PetscInt, PetscInt, PetscInt, const PetscReal[], const PetscReal[]); PETSC_EXTERN PetscErrorCode PetscQuadratureView(PetscQuadrature, PetscViewer); PETSC_EXTERN PetscErrorCode PetscQuadratureDestroy(PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscDTTensorQuadratureCreate(PetscQuadrature, PetscQuadrature, PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscQuadratureExpandComposite(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscQuadratureComputePermutations(PetscQuadrature, PetscInt *, IS *[]); PETSC_EXTERN PetscErrorCode PetscQuadraturePushForward(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], const PetscReal[], PetscInt, PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscDTLegendreEval(PetscInt, const PetscReal *, PetscInt, const PetscInt *, PetscReal *, PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTJacobiNorm(PetscReal, PetscReal, PetscInt, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTJacobiEval(PetscInt, PetscReal, PetscReal, const PetscReal *, PetscInt, const PetscInt *, PetscReal *, PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTJacobiEvalJet(PetscReal, PetscReal, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscReal[]); PETSC_EXTERN PetscErrorCode PetscDTPKDEvalJet(PetscInt, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscReal[]); PETSC_EXTERN PetscErrorCode PetscDTPTrimmedSize(PetscInt, PetscInt, PetscInt, PetscInt *); PETSC_EXTERN PetscErrorCode PetscDTPTrimmedEvalJet(PetscInt, PetscInt, const PetscReal[], PetscInt, PetscInt, PetscInt, PetscReal[]); PETSC_EXTERN PetscErrorCode PetscDTGaussQuadrature(PetscInt, PetscReal, PetscReal, PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTGaussJacobiQuadrature(PetscInt, PetscReal, PetscReal, PetscReal, PetscReal, PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoJacobiQuadrature(PetscInt, PetscReal, PetscReal, PetscReal, PetscReal, PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoLegendreQuadrature(PetscInt, PetscGaussLobattoLegendreCreateType, PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTReconstructPoly(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTGaussTensorQuadrature(PetscInt, PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscDTStroudConicalQuadrature(PetscInt, PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscDTSimplexQuadrature(PetscInt, PetscInt, PetscDTSimplexQuadratureType, PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscDTCreateDefaultQuadrature(DMPolytopeType, PetscInt, PetscQuadrature *, PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscDTTanhSinhTensorQuadrature(PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrate(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrateMPFR(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreIntegrate(PetscInt, PetscReal *, PetscReal *, const PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); PETSC_EXTERN PetscErrorCode PetscDTAltVApply(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTAltVWedge(PetscInt, PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTAltVWedgeMatrix(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTAltVPullback(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt, PetscInt, const PetscReal *, PetscInt, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTAltVInterior(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorMatrix(PetscInt, PetscInt, const PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorPattern(PetscInt, PetscInt, PetscInt (*)[3]); PETSC_EXTERN PetscErrorCode PetscDTAltVStar(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); PETSC_EXTERN PetscErrorCode PetscDTBaryToIndex(PetscInt, PetscInt, const PetscInt[], PetscInt *); PETSC_EXTERN PetscErrorCode PetscDTIndexToBary(PetscInt, PetscInt, PetscInt, PetscInt[]); PETSC_EXTERN PetscErrorCode PetscDTGradedOrderToIndex(PetscInt, const PetscInt[], PetscInt *); PETSC_EXTERN PetscErrorCode PetscDTIndexToGradedOrder(PetscInt, PetscInt, PetscInt[]); #if defined(PETSC_USE_64BIT_INDICES) #define PETSC_FACTORIAL_MAX 20 #define PETSC_BINOMIAL_MAX 61 #else #define PETSC_FACTORIAL_MAX 12 #define PETSC_BINOMIAL_MAX 29 #endif /*MC PetscDTFactorial - Approximate n! as a real number Input Parameter: . n - a non-negative integer Output Parameter: . factorial - n! Level: beginner .seealso: `PetscDTFactorialInt()`, `PetscDTBinomialInt()`, `PetscDTBinomial()` M*/ static inline PetscErrorCode PetscDTFactorial(PetscInt n, PetscReal *factorial) { PetscReal f = 1.0; PetscFunctionBegin; *factorial = -1.0; PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Factorial called with negative number %" PetscInt_FMT, n); for (PetscInt i = 1; i < n + 1; ++i) f *= (PetscReal)i; *factorial = f; PetscFunctionReturn(PETSC_SUCCESS); } /*MC PetscDTFactorialInt - Compute n! as an integer Input Parameter: . n - a non-negative integer Output Parameter: . factorial - n! Level: beginner 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. .seealso: `PetscDTFactorial()`, `PetscDTBinomialInt()`, `PetscDTBinomial()` M*/ static inline PetscErrorCode PetscDTFactorialInt(PetscInt n, PetscInt *factorial) { PetscInt facLookup[13] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600}; PetscFunctionBegin; *factorial = -1; 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); if (n <= 12) { *factorial = facLookup[n]; } else { PetscInt f = facLookup[12]; PetscInt i; for (i = 13; i < n + 1; ++i) f *= i; *factorial = f; } PetscFunctionReturn(PETSC_SUCCESS); } /*MC PetscDTBinomial - Approximate the binomial coefficient "n choose k" Input Parameters: + n - a non-negative integer - k - an integer between 0 and n, inclusive Output Parameter: . binomial - approximation of the binomial coefficient n choose k Level: beginner .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()` M*/ static inline PetscErrorCode PetscDTBinomial(PetscInt n, PetscInt k, PetscReal *binomial) { PetscFunctionBeginHot; *binomial = -1.0; 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); if (n <= 3) { PetscInt binomLookup[4][4] = { {1, 0, 0, 0}, {1, 1, 0, 0}, {1, 2, 1, 0}, {1, 3, 3, 1} }; *binomial = (PetscReal)binomLookup[n][k]; } else { PetscReal binom = 1.0; k = PetscMin(k, n - k); for (PetscInt i = 0; i < k; i++) binom = (binom * (PetscReal)(n - i)) / (PetscReal)(i + 1); *binomial = binom; } PetscFunctionReturn(PETSC_SUCCESS); } /*MC PetscDTBinomialInt - Compute the binomial coefficient "n choose k" Input Parameters: + n - a non-negative integer - k - an integer between 0 and n, inclusive Output Parameter: . binomial - the binomial coefficient n choose k Level: beginner Note: This is limited by integers that can be represented by `PetscInt`. Use `PetscDTBinomial()` for real number approximations of larger values .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTEnumPerm()` M*/ static inline PetscErrorCode PetscDTBinomialInt(PetscInt n, PetscInt k, PetscInt *binomial) { PetscInt bin; PetscFunctionBegin; *binomial = -1; 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); 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); if (n <= 3) { PetscInt binomLookup[4][4] = { {1, 0, 0, 0}, {1, 1, 0, 0}, {1, 2, 1, 0}, {1, 3, 3, 1} }; bin = binomLookup[n][k]; } else { PetscInt binom = 1; k = PetscMin(k, n - k); for (PetscInt i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1); bin = binom; } *binomial = bin; PetscFunctionReturn(PETSC_SUCCESS); } /*MC PetscDTEnumPerm - Get a permutation of `n` integers from its encoding into the integers [0, n!) as a sequence of swaps. Input Parameters: + n - a non-negative integer (see note about limits below) - k - an integer in [0, n!) Output Parameters: + perm - the permuted list of the integers [0, ..., n-1] - isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps. Level: intermediate Notes: A permutation can be described by the operations that convert the lists [0, 1, ..., n-1] into the permutation, by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in some position j >= i. This swap is encoded as the difference (j - i). The difference d_i at step i is less than (n - i). This sequence of n-1 differences [d_0, ..., d_{n-2}] is encoded as the number (n-1)! * d_0 + (n-2)! * d_1 + ... + 1! * d_{n-2}. 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. .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTPermIndex()` M*/ static inline PetscErrorCode PetscDTEnumPerm(PetscInt n, PetscInt k, PetscInt *perm, PetscBool *isOdd) { PetscInt odd = 0; PetscInt i; PetscInt work[PETSC_FACTORIAL_MAX]; PetscInt *w; PetscFunctionBegin; if (isOdd) *isOdd = PETSC_FALSE; 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); w = &work[n - 2]; for (i = 2; i <= n; i++) { *(w--) = k % i; k /= i; } for (i = 0; i < n; i++) perm[i] = i; for (i = 0; i < n - 1; i++) { PetscInt s = work[i]; PetscInt swap = perm[i]; perm[i] = perm[i + s]; perm[i + s] = swap; odd ^= (!!s); } if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; PetscFunctionReturn(PETSC_SUCCESS); } /*MC PetscDTPermIndex - Encode a permutation of n into an integer in [0, n!). This inverts `PetscDTEnumPerm()`. Input Parameters: + n - a non-negative integer (see note about limits below) - perm - the permuted list of the integers [0, ..., n-1] Output Parameters: + k - an integer in [0, n!) - isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps. Level: beginner Note: 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. .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()` M*/ static inline PetscErrorCode PetscDTPermIndex(PetscInt n, const PetscInt *perm, PetscInt *k, PetscBool *isOdd) { PetscInt odd = 0; PetscInt i, idx; PetscInt work[PETSC_FACTORIAL_MAX]; PetscInt iwork[PETSC_FACTORIAL_MAX]; PetscFunctionBeginHot; *k = -1; if (isOdd) *isOdd = PETSC_FALSE; 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); for (i = 0; i < n; i++) work[i] = i; /* partial permutation */ for (i = 0; i < n; i++) iwork[i] = i; /* partial permutation inverse */ for (idx = 0, i = 0; i < n - 1; i++) { PetscInt j = perm[i]; PetscInt icur = work[i]; PetscInt jloc = iwork[j]; PetscInt diff = jloc - i; idx = idx * (n - i) + diff; /* swap (i, jloc) */ work[i] = j; work[jloc] = icur; iwork[j] = i; iwork[icur] = jloc; odd ^= (!!diff); } *k = idx; if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; PetscFunctionReturn(PETSC_SUCCESS); } /*MC PetscDTEnumSubset - Get an ordered subset of the integers [0, ..., n - 1] from its encoding as an integers in [0, n choose k). The encoding is in lexicographic order. Input Parameters: + n - a non-negative integer (see note about limits below) . k - an integer in [0, n] - j - an index in [0, n choose k) Output Parameter: . subset - the jth subset of size k of the integers [0, ..., n - 1] Level: beginner Note: Limited by arguments such that `n` choose `k` can be represented by `PetscInt` .seealso: `PetscDTSubsetIndex()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()` M*/ static inline PetscErrorCode PetscDTEnumSubset(PetscInt n, PetscInt k, PetscInt j, PetscInt *subset) { PetscInt Nk; PetscFunctionBeginHot; PetscCall(PetscDTBinomialInt(n, k, &Nk)); for (PetscInt i = 0, l = 0; i < n && l < k; i++) { PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); PetscInt Nminusk = Nk - Nminuskminus; if (j < Nminuskminus) { subset[l++] = i; Nk = Nminuskminus; } else { j -= Nminuskminus; Nk = Nminusk; } } PetscFunctionReturn(PETSC_SUCCESS); } /*MC 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`. Input Parameters: + n - a non-negative integer (see note about limits below) . k - an integer in [0, n] - subset - an ordered subset of the integers [0, ..., n - 1] Output Parameter: . index - the rank of the subset in lexicographic order Level: beginner Note: Limited by arguments such that `n` choose `k` can be represented by `PetscInt` .seealso: `PetscDTEnumSubset()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()` M*/ static inline PetscErrorCode PetscDTSubsetIndex(PetscInt n, PetscInt k, const PetscInt *subset, PetscInt *index) { PetscInt j = 0, Nk; PetscFunctionBegin; *index = -1; PetscCall(PetscDTBinomialInt(n, k, &Nk)); for (PetscInt i = 0, l = 0; i < n && l < k; i++) { PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); PetscInt Nminusk = Nk - Nminuskminus; if (subset[l] == i) { l++; Nk = Nminuskminus; } else { j += Nminuskminus; Nk = Nminusk; } } *index = j; PetscFunctionReturn(PETSC_SUCCESS); } /*MC 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. Input Parameters: + n - a non-negative integer (see note about limits below) . k - an integer in [0, n] - j - an index in [0, n choose k) Output Parameters: + perm - the jth subset of size k of the integers [0, ..., n - 1], followed by its complementary set. - isOdd - if not `NULL`, return whether perm is an even or odd permutation. Level: beginner Note: Limited by arguments such that `n` choose `k` can be represented by `PetscInt` .seealso: `PetscDTEnumSubset()`, `PetscDTSubsetIndex()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()` M*/ static inline PetscErrorCode PetscDTEnumSplit(PetscInt n, PetscInt k, PetscInt j, PetscInt *perm, PetscBool *isOdd) { PetscInt i, l, m, Nk, odd = 0; PetscInt *subcomp = perm + k; PetscFunctionBegin; if (isOdd) *isOdd = PETSC_FALSE; PetscCall(PetscDTBinomialInt(n, k, &Nk)); for (i = 0, l = 0, m = 0; i < n && l < k; i++) { PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); PetscInt Nminusk = Nk - Nminuskminus; if (j < Nminuskminus) { perm[l++] = i; Nk = Nminuskminus; } else { subcomp[m++] = i; j -= Nminuskminus; odd ^= ((k - l) & 1); Nk = Nminusk; } } for (; i < n; i++) subcomp[m++] = i; if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; PetscFunctionReturn(PETSC_SUCCESS); } struct _p_PetscTabulation { PetscInt K; /* Indicates a k-jet, namely tabulated derivatives up to order k */ PetscInt Nr; /* The number of tabulation replicas (often 1) */ PetscInt Np; /* The number of tabulation points in a replica */ PetscInt Nb; /* The number of functions tabulated */ PetscInt Nc; /* The number of function components */ PetscInt cdim; /* The coordinate dimension */ PetscReal **T; /* The tabulation T[K] of functions and their derivatives T[0] = B[Nr*Np][Nb][Nc]: The basis function values at quadrature points T[1] = D[Nr*Np][Nb][Nc][cdim]: The basis function derivatives at quadrature points T[2] = H[Nr*Np][Nb][Nc][cdim][cdim]: The basis function second derivatives at quadrature points */ }; typedef struct _p_PetscTabulation *PetscTabulation; typedef PetscErrorCode (*PetscProbFunc)(const PetscReal[], const PetscReal[], PetscReal[]); typedef enum { DTPROB_DENSITY_CONSTANT, DTPROB_DENSITY_GAUSSIAN, DTPROB_DENSITY_MAXWELL_BOLTZMANN, DTPROB_NUM_DENSITY } DTProbDensityType; PETSC_EXTERN const char *const DTProbDensityTypes[]; PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscCDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscCDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant1D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscCDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant2D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscCDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant3D(const PetscReal[], const PetscReal[], PetscReal[]); PETSC_EXTERN PetscErrorCode PetscProbCreateFromOptions(PetscInt, const char[], const char[], PetscProbFunc *, PetscProbFunc *, PetscProbFunc *); #include PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatistic(Vec, PetscProbFunc, PetscReal *); #endif