Actual source code: petscdt.h
1: /*
2: Common tools for constructing discretizations
3: */
4: #pragma once
6: #include <petscsys.h>
7: #include <petscdmtypes.h>
8: #include <petscistypes.h>
10: /* SUBMANSEC = DT */
12: PETSC_EXTERN PetscClassId PETSCQUADRATURE_CLASSID;
14: /*S
15: PetscQuadrature - Quadrature rule for numerical integration.
17: Level: beginner
19: .seealso: `PetscQuadratureCreate()`, `PetscQuadratureDestroy()`
20: S*/
21: typedef struct _p_PetscQuadrature *PetscQuadrature;
23: /*E
24: PetscGaussLobattoLegendreCreateType - algorithm used to compute the Gauss-Lobatto-Legendre nodes and weights
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
30: Level: intermediate
32: .seealso: `PetscQuadrature`
33: E*/
34: typedef enum {
35: PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA,
36: PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON
37: } PetscGaussLobattoLegendreCreateType;
39: /*E
40: PetscDTNodeType - A description of strategies for generating nodes (both
41: quadrature nodes and nodes for Lagrange polynomials)
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
49: Level: intermediate
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.
56: .seealso: `PetscQuadrature`
57: E*/
58: typedef enum {
59: PETSCDTNODES_DEFAULT = -1,
60: PETSCDTNODES_GAUSSJACOBI,
61: PETSCDTNODES_EQUISPACED,
62: PETSCDTNODES_TANHSINH
63: } PetscDTNodeType;
65: PETSC_EXTERN const char *const *const PetscDTNodeTypes;
67: /*E
68: PetscDTSimplexQuadratureType - A description of classes of quadrature rules for simplices
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.
87: Level: intermediate
89: .seealso: `PetscQuadrature`, `PetscDTSimplexQuadrature()`
90: E*/
91: typedef enum {
92: PETSCDTSIMPLEXQUAD_DEFAULT = -1,
93: PETSCDTSIMPLEXQUAD_CONIC = 0,
94: PETSCDTSIMPLEXQUAD_MINSYM
95: } PetscDTSimplexQuadratureType;
97: PETSC_EXTERN const char *const *const PetscDTSimplexQuadratureTypes;
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 *);
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 *[]);
117: PETSC_EXTERN PetscErrorCode PetscQuadraturePushForward(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], const PetscReal[], PetscInt, PetscQuadrature *);
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 *);
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 *);
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 ***);
150: /*MC
151: PETSC_FORM_DEGREE_UNDEFINED - Indicates that a field does not have
152: a well-defined form degree in exterior calculus.
154: Level: advanced
156: .seealso: `PetscDTAltV`, `PetscDualSpaceGetFormDegree()`
157: M*/
158: #define PETSC_FORM_DEGREE_UNDEFINED PETSC_INT_MIN
160: PETSC_EXTERN PetscErrorCode PetscDTAltVApply(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
161: PETSC_EXTERN PetscErrorCode PetscDTAltVWedge(PetscInt, PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
162: PETSC_EXTERN PetscErrorCode PetscDTAltVWedgeMatrix(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *);
163: PETSC_EXTERN PetscErrorCode PetscDTAltVPullback(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *);
164: PETSC_EXTERN PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt, PetscInt, const PetscReal *, PetscInt, PetscReal *);
165: PETSC_EXTERN PetscErrorCode PetscDTAltVInterior(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
166: PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorMatrix(PetscInt, PetscInt, const PetscReal *, PetscReal *);
167: PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorPattern(PetscInt, PetscInt, PetscInt (*)[3]);
168: PETSC_EXTERN PetscErrorCode PetscDTAltVStar(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *);
170: PETSC_EXTERN PetscErrorCode PetscDTBaryToIndex(PetscInt, PetscInt, const PetscInt[], PetscInt *);
171: PETSC_EXTERN PetscErrorCode PetscDTIndexToBary(PetscInt, PetscInt, PetscInt, PetscInt[]);
172: PETSC_EXTERN PetscErrorCode PetscDTGradedOrderToIndex(PetscInt, const PetscInt[], PetscInt *);
173: PETSC_EXTERN PetscErrorCode PetscDTIndexToGradedOrder(PetscInt, PetscInt, PetscInt[]);
175: #if defined(PETSC_USE_64BIT_INDICES)
176: #define PETSC_FACTORIAL_MAX 20
177: #define PETSC_BINOMIAL_MAX 61
178: #else
179: #define PETSC_FACTORIAL_MAX 12
180: #define PETSC_BINOMIAL_MAX 29
181: #endif
183: /*MC
184: PetscDTFactorial - Approximate n! as a real number
186: Input Parameter:
187: . n - a non-negative integer
189: Output Parameter:
190: . factorial - n!
192: Level: beginner
194: .seealso: `PetscDTFactorialInt()`, `PetscDTBinomialInt()`, `PetscDTBinomial()`
195: M*/
196: static inline PetscErrorCode PetscDTFactorial(PetscInt n, PetscReal *factorial)
197: {
198: PetscReal f = 1.0;
200: PetscFunctionBegin;
201: *factorial = -1.0;
202: PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Factorial called with negative number %" PetscInt_FMT, n);
203: for (PetscInt i = 1; i < n + 1; ++i) f *= (PetscReal)i;
204: *factorial = f;
205: PetscFunctionReturn(PETSC_SUCCESS);
206: }
208: /*MC
209: PetscDTFactorialInt - Compute n! as an integer
211: Input Parameter:
212: . n - a non-negative integer
214: Output Parameter:
215: . factorial - n!
217: Level: beginner
219: Note:
220: 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.
222: .seealso: `PetscDTFactorial()`, `PetscDTBinomialInt()`, `PetscDTBinomial()`
223: M*/
224: static inline PetscErrorCode PetscDTFactorialInt(PetscInt n, PetscInt *factorial)
225: {
226: PetscInt facLookup[13] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600};
228: PetscFunctionBegin;
229: *factorial = -1;
230: 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);
231: if (n <= 12) {
232: *factorial = facLookup[n];
233: } else {
234: PetscInt f = facLookup[12];
235: PetscInt i;
237: for (i = 13; i < n + 1; ++i) f *= i;
238: *factorial = f;
239: }
240: PetscFunctionReturn(PETSC_SUCCESS);
241: }
243: /*MC
244: PetscDTBinomial - Approximate the binomial coefficient `n` choose `k`
246: Input Parameters:
247: + n - a non-negative integer
248: - k - an integer between 0 and `n`, inclusive
250: Output Parameter:
251: . binomial - approximation of the binomial coefficient `n` choose `k`
253: Level: beginner
255: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`
256: M*/
257: static inline PetscErrorCode PetscDTBinomial(PetscInt n, PetscInt k, PetscReal *binomial)
258: {
259: PetscFunctionBeginHot;
260: *binomial = -1.0;
261: 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);
262: if (n <= 3) {
263: PetscInt binomLookup[4][4] = {
264: {1, 0, 0, 0},
265: {1, 1, 0, 0},
266: {1, 2, 1, 0},
267: {1, 3, 3, 1}
268: };
270: *binomial = (PetscReal)binomLookup[n][k];
271: } else {
272: PetscReal binom = 1.0;
274: k = PetscMin(k, n - k);
275: for (PetscInt i = 0; i < k; i++) binom = (binom * (PetscReal)(n - i)) / (PetscReal)(i + 1);
276: *binomial = binom;
277: }
278: PetscFunctionReturn(PETSC_SUCCESS);
279: }
281: /*MC
282: PetscDTBinomialInt - Compute the binomial coefficient `n` choose `k`
284: Input Parameters:
285: + n - a non-negative integer
286: - k - an integer between 0 and `n`, inclusive
288: Output Parameter:
289: . binomial - the binomial coefficient `n` choose `k`
291: Level: beginner
293: Note:
294: This is limited by integers that can be represented by `PetscInt`.
296: Use `PetscDTBinomial()` for real number approximations of larger values
298: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTEnumPerm()`
299: M*/
300: static inline PetscErrorCode PetscDTBinomialInt(PetscInt n, PetscInt k, PetscInt *binomial)
301: {
302: PetscInt bin;
304: PetscFunctionBegin;
305: *binomial = -1;
306: 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);
307: 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);
308: if (n <= 3) {
309: PetscInt binomLookup[4][4] = {
310: {1, 0, 0, 0},
311: {1, 1, 0, 0},
312: {1, 2, 1, 0},
313: {1, 3, 3, 1}
314: };
316: bin = binomLookup[n][k];
317: } else {
318: PetscInt binom = 1;
320: k = PetscMin(k, n - k);
321: for (PetscInt i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1);
322: bin = binom;
323: }
324: *binomial = bin;
325: PetscFunctionReturn(PETSC_SUCCESS);
326: }
328: /*MC
329: PetscDTEnumPerm - Get a permutation of `n` integers from its encoding into the integers [0, n!) as a sequence of swaps.
331: Input Parameters:
332: + n - a non-negative integer (see note about limits below)
333: - k - an integer in [0, n!)
335: Output Parameters:
336: + perm - the permuted list of the integers [0, ..., n-1]
337: - isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps.
339: Level: intermediate
341: Notes:
342: A permutation can be described by the operations that convert the lists [0, 1, ..., n-1] into the permutation,
343: by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in
344: some position j >= i. This swap is encoded as the difference (j - i). The difference d_i at step i is less than
345: (n - i). This sequence of n-1 differences [d_0, ..., d_{n-2}] is encoded as the number
346: (n-1)! * d_0 + (n-2)! * d_1 + ... + 1! * d_{n-2}.
348: 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.
350: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTPermIndex()`
351: M*/
352: static inline PetscErrorCode PetscDTEnumPerm(PetscInt n, PetscInt k, PetscInt *perm, PetscBool *isOdd)
353: {
354: PetscInt odd = 0;
355: PetscInt i;
356: PetscInt work[PETSC_FACTORIAL_MAX];
357: PetscInt *w;
359: PetscFunctionBegin;
360: if (isOdd) *isOdd = PETSC_FALSE;
361: 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);
362: w = &work[n - 2];
363: for (i = 2; i <= n; i++) {
364: *(w--) = k % i;
365: k /= i;
366: }
367: for (i = 0; i < n; i++) perm[i] = i;
368: for (i = 0; i < n - 1; i++) {
369: PetscInt s = work[i];
370: PetscInt swap = perm[i];
372: perm[i] = perm[i + s];
373: perm[i + s] = swap;
374: odd ^= (!!s);
375: }
376: if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
377: PetscFunctionReturn(PETSC_SUCCESS);
378: }
380: /*MC
381: PetscDTPermIndex - Encode a permutation of n into an integer in [0, n!). This inverts `PetscDTEnumPerm()`.
383: Input Parameters:
384: + n - a non-negative integer (see note about limits below)
385: - perm - the permuted list of the integers [0, ..., n-1]
387: Output Parameters:
388: + k - an integer in [0, n!)
389: - isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps.
391: Level: beginner
393: Note:
394: 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.
396: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`
397: M*/
398: static inline PetscErrorCode PetscDTPermIndex(PetscInt n, const PetscInt *perm, PetscInt *k, PetscBool *isOdd)
399: {
400: PetscInt odd = 0;
401: PetscInt i, idx;
402: PetscInt work[PETSC_FACTORIAL_MAX];
403: PetscInt iwork[PETSC_FACTORIAL_MAX];
405: PetscFunctionBeginHot;
406: *k = -1;
407: if (isOdd) *isOdd = PETSC_FALSE;
408: 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);
409: for (i = 0; i < n; i++) work[i] = i; /* partial permutation */
410: for (i = 0; i < n; i++) iwork[i] = i; /* partial permutation inverse */
411: for (idx = 0, i = 0; i < n - 1; i++) {
412: PetscInt j = perm[i];
413: PetscInt icur = work[i];
414: PetscInt jloc = iwork[j];
415: PetscInt diff = jloc - i;
417: idx = idx * (n - i) + diff;
418: /* swap (i, jloc) */
419: work[i] = j;
420: work[jloc] = icur;
421: iwork[j] = i;
422: iwork[icur] = jloc;
423: odd ^= (!!diff);
424: }
425: *k = idx;
426: if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
427: PetscFunctionReturn(PETSC_SUCCESS);
428: }
430: /*MC
431: PetscDTEnumSubset - Get an ordered subset of the integers [0, ..., n - 1] from its encoding as an integers in [0, n choose k).
432: The encoding is in lexicographic order.
434: Input Parameters:
435: + n - a non-negative integer (see note about limits below)
436: . k - an integer in [0, n]
437: - j - an index in [0, n choose k)
439: Output Parameter:
440: . subset - the jth subset of size k of the integers [0, ..., n - 1]
442: Level: beginner
444: Note:
445: Limited by arguments such that `n` choose `k` can be represented by `PetscInt`
447: .seealso: `PetscDTSubsetIndex()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()`
448: M*/
449: static inline PetscErrorCode PetscDTEnumSubset(PetscInt n, PetscInt k, PetscInt j, PetscInt *subset)
450: {
451: PetscInt Nk;
453: PetscFunctionBeginHot;
454: PetscCall(PetscDTBinomialInt(n, k, &Nk));
455: for (PetscInt i = 0, l = 0; i < n && l < k; i++) {
456: PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
457: PetscInt Nminusk = Nk - Nminuskminus;
459: if (j < Nminuskminus) {
460: subset[l++] = i;
461: Nk = Nminuskminus;
462: } else {
463: j -= Nminuskminus;
464: Nk = Nminusk;
465: }
466: }
467: PetscFunctionReturn(PETSC_SUCCESS);
468: }
470: /*MC
471: 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.
472: This is the inverse of `PetscDTEnumSubset`.
474: Input Parameters:
475: + n - a non-negative integer (see note about limits below)
476: . k - an integer in [0, n]
477: - subset - an ordered subset of the integers [0, ..., n - 1]
479: Output Parameter:
480: . index - the rank of the subset in lexicographic order
482: Level: beginner
484: Note:
485: Limited by arguments such that `n` choose `k` can be represented by `PetscInt`
487: .seealso: `PetscDTEnumSubset()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()`
488: M*/
489: static inline PetscErrorCode PetscDTSubsetIndex(PetscInt n, PetscInt k, const PetscInt *subset, PetscInt *index)
490: {
491: PetscInt j = 0, Nk;
493: PetscFunctionBegin;
494: *index = -1;
495: PetscCall(PetscDTBinomialInt(n, k, &Nk));
496: for (PetscInt i = 0, l = 0; i < n && l < k; i++) {
497: PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
498: PetscInt Nminusk = Nk - Nminuskminus;
500: if (subset[l] == i) {
501: l++;
502: Nk = Nminuskminus;
503: } else {
504: j += Nminuskminus;
505: Nk = Nminusk;
506: }
507: }
508: *index = j;
509: PetscFunctionReturn(PETSC_SUCCESS);
510: }
512: /*MC
513: 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.
515: Input Parameters:
516: + n - a non-negative integer (see note about limits below)
517: . k - an integer in [0, n]
518: - j - an index in [0, n choose k)
520: Output Parameters:
521: + perm - the jth subset of size k of the integers [0, ..., n - 1], followed by its complementary set.
522: - isOdd - if not `NULL`, return whether perm is an even or odd permutation.
524: Level: beginner
526: Note:
527: Limited by arguments such that `n` choose `k` can be represented by `PetscInt`
529: .seealso: `PetscDTEnumSubset()`, `PetscDTSubsetIndex()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`,
530: `PetscDTPermIndex()`
531: M*/
532: static inline PetscErrorCode PetscDTEnumSplit(PetscInt n, PetscInt k, PetscInt j, PetscInt *perm, PetscBool *isOdd)
533: {
534: PetscInt i, l, m, Nk, odd = 0;
535: PetscInt *subcomp = perm + k;
537: PetscFunctionBegin;
538: if (isOdd) *isOdd = PETSC_FALSE;
539: PetscCall(PetscDTBinomialInt(n, k, &Nk));
540: for (i = 0, l = 0, m = 0; i < n && l < k; i++) {
541: PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
542: PetscInt Nminusk = Nk - Nminuskminus;
544: if (j < Nminuskminus) {
545: perm[l++] = i;
546: Nk = Nminuskminus;
547: } else {
548: subcomp[m++] = i;
549: j -= Nminuskminus;
550: odd ^= ((k - l) & 1);
551: Nk = Nminusk;
552: }
553: }
554: for (; i < n; i++) subcomp[m++] = i;
555: if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
556: PetscFunctionReturn(PETSC_SUCCESS);
557: }
559: struct _p_PetscTabulation {
560: PetscInt K; /* Indicates a k-jet, namely tabulated derivatives up to order k */
561: PetscInt Nr; /* The number of tabulation replicas (often 1) */
562: PetscInt Np; /* The number of tabulation points in a replica */
563: PetscInt Nb; /* The number of functions tabulated */
564: PetscInt Nc; /* The number of function components */
565: PetscInt cdim; /* The coordinate dimension */
566: PetscReal **T; /* The tabulation T[K] of functions and their derivatives
567: T[0] = B[Nr*Np][Nb][Nc]: The basis function values at quadrature points
568: T[1] = D[Nr*Np][Nb][Nc][cdim]: The basis function derivatives at quadrature points
569: T[2] = H[Nr*Np][Nb][Nc][cdim][cdim]: The basis function second derivatives at quadrature points */
570: };
571: typedef struct _p_PetscTabulation *PetscTabulation;
573: typedef PetscErrorCode (*PetscProbFunc)(const PetscReal[], const PetscReal[], PetscReal[]);
575: typedef enum {
576: DTPROB_DENSITY_CONSTANT,
577: DTPROB_DENSITY_GAUSSIAN,
578: DTPROB_DENSITY_MAXWELL_BOLTZMANN,
579: DTPROB_NUM_DENSITY
580: } DTProbDensityType;
581: PETSC_EXTERN const char *const DTProbDensityTypes[];
583: PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]);
584: PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]);
585: PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]);
586: PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]);
587: PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]);
588: PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]);
589: PETSC_EXTERN PetscErrorCode PetscPDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]);
590: PETSC_EXTERN PetscErrorCode PetscCDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]);
591: PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]);
592: PETSC_EXTERN PetscErrorCode PetscPDFGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]);
593: PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]);
594: PETSC_EXTERN PetscErrorCode PetscPDFGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]);
595: PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]);
596: PETSC_EXTERN PetscErrorCode PetscPDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]);
597: PETSC_EXTERN PetscErrorCode PetscCDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]);
598: PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant1D(const PetscReal[], const PetscReal[], PetscReal[]);
599: PETSC_EXTERN PetscErrorCode PetscPDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]);
600: PETSC_EXTERN PetscErrorCode PetscCDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]);
601: PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant2D(const PetscReal[], const PetscReal[], PetscReal[]);
602: PETSC_EXTERN PetscErrorCode PetscPDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]);
603: PETSC_EXTERN PetscErrorCode PetscCDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]);
604: PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant3D(const PetscReal[], const PetscReal[], PetscReal[]);
605: PETSC_EXTERN PetscErrorCode PetscProbCreateFromOptions(PetscInt, const char[], const char[], PetscProbFunc *, PetscProbFunc *, PetscProbFunc *);
607: #include <petscvec.h>
609: PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatistic(Vec, PetscProbFunc, PetscReal *);