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