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: /* MANSEC = DM */
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 = 0,
62: PETSCDTNODES_EQUISPACED = 1,
63: PETSCDTNODES_TANHSINH = 2
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 = 1
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 *);
136: PETSC_EXTERN PetscErrorCode PetscDTCreateQuadratureByCell(DMPolytopeType, PetscInt, PetscDTSimplexQuadratureType, PetscQuadrature *, PetscQuadrature *);
138: PETSC_EXTERN PetscErrorCode PetscDTTanhSinhTensorQuadrature(PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *);
139: PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrate(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *);
140: PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrateMPFR(void (*)(const PetscReal[], void *, PetscReal *), PetscReal, PetscReal, PetscInt, void *, PetscReal *);
142: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreIntegrate(PetscInt, PetscReal *, PetscReal *, const PetscReal *, PetscReal *);
143: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
144: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
145: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***);
146: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***);
147: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
148: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
149: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
150: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
152: /*MC
153: PETSC_FORM_DEGREE_UNDEFINED - Indicates that a field does not have
154: a well-defined form degree in exterior calculus.
156: Level: advanced
158: .seealso: `PetscDTAltV`, `PetscDualSpaceGetFormDegree()`
159: M*/
160: #define PETSC_FORM_DEGREE_UNDEFINED PETSC_INT_MIN
162: PETSC_EXTERN PetscErrorCode PetscDTAltVApply(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
163: PETSC_EXTERN PetscErrorCode PetscDTAltVWedge(PetscInt, PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
164: PETSC_EXTERN PetscErrorCode PetscDTAltVWedgeMatrix(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *);
165: PETSC_EXTERN PetscErrorCode PetscDTAltVPullback(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *);
166: PETSC_EXTERN PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt, PetscInt, const PetscReal *, PetscInt, PetscReal *);
167: PETSC_EXTERN PetscErrorCode PetscDTAltVInterior(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
168: PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorMatrix(PetscInt, PetscInt, const PetscReal *, PetscReal *);
169: PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorPattern(PetscInt, PetscInt, PetscInt (*)[3]);
170: PETSC_EXTERN PetscErrorCode PetscDTAltVStar(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *);
172: PETSC_EXTERN PetscErrorCode PetscDTBaryToIndex(PetscInt, PetscInt, const PetscInt[], PetscInt *);
173: PETSC_EXTERN PetscErrorCode PetscDTIndexToBary(PetscInt, PetscInt, PetscInt, PetscInt[]);
174: PETSC_EXTERN PetscErrorCode PetscDTGradedOrderToIndex(PetscInt, const PetscInt[], PetscInt *);
175: PETSC_EXTERN PetscErrorCode PetscDTIndexToGradedOrder(PetscInt, PetscInt, PetscInt[]);
177: #if defined(PETSC_USE_64BIT_INDICES)
178: #define PETSC_FACTORIAL_MAX 20
179: #define PETSC_BINOMIAL_MAX 61
180: #else
181: #define PETSC_FACTORIAL_MAX 12
182: #define PETSC_BINOMIAL_MAX 29
183: #endif
185: /*MC
186: PetscDTFactorial - Approximate n! as a real number
188: Input Parameter:
189: . n - a non-negative integer
191: Output Parameter:
192: . factorial - n!
194: Level: beginner
196: .seealso: `PetscDTFactorialInt()`, `PetscDTBinomialInt()`, `PetscDTBinomial()`
197: M*/
198: static inline PetscErrorCode PetscDTFactorial(PetscInt n, PetscReal *factorial)
199: {
200: PetscReal f = 1.0;
202: PetscFunctionBegin;
203: *factorial = -1.0;
204: PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Factorial called with negative number %" PetscInt_FMT, n);
205: for (PetscInt i = 1; i < n + 1; ++i) f *= (PetscReal)i;
206: *factorial = f;
207: PetscFunctionReturn(PETSC_SUCCESS);
208: }
210: /*MC
211: PetscDTFactorialInt - Compute n! as an integer
213: Input Parameter:
214: . n - a non-negative integer
216: Output Parameter:
217: . factorial - n!
219: Level: beginner
221: Note:
222: 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.
224: .seealso: `PetscDTFactorial()`, `PetscDTBinomialInt()`, `PetscDTBinomial()`
225: M*/
226: static inline PetscErrorCode PetscDTFactorialInt(PetscInt n, PetscInt *factorial)
227: {
228: PetscInt facLookup[13] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600};
230: PetscFunctionBegin;
231: *factorial = -1;
232: 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);
233: if (n <= 12) {
234: *factorial = facLookup[n];
235: } else {
236: PetscInt f = facLookup[12];
237: PetscInt i;
239: for (i = 13; i < n + 1; ++i) f *= i;
240: *factorial = f;
241: }
242: PetscFunctionReturn(PETSC_SUCCESS);
243: }
245: /*MC
246: PetscDTBinomial - Approximate the binomial coefficient `n` choose `k`
248: Input Parameters:
249: + n - a non-negative integer
250: - k - an integer between 0 and `n`, inclusive
252: Output Parameter:
253: . binomial - approximation of the binomial coefficient `n` choose `k`
255: Level: beginner
257: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`
258: M*/
259: static inline PetscErrorCode PetscDTBinomial(PetscInt n, PetscInt k, PetscReal *binomial)
260: {
261: PetscFunctionBeginHot;
262: *binomial = -1.0;
263: 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);
264: if (n <= 3) {
265: PetscInt binomLookup[4][4] = {
266: {1, 0, 0, 0},
267: {1, 1, 0, 0},
268: {1, 2, 1, 0},
269: {1, 3, 3, 1}
270: };
272: *binomial = (PetscReal)binomLookup[n][k];
273: } else {
274: PetscReal binom = 1.0;
276: k = PetscMin(k, n - k);
277: for (PetscInt i = 0; i < k; i++) binom = (binom * (PetscReal)(n - i)) / (PetscReal)(i + 1);
278: *binomial = binom;
279: }
280: PetscFunctionReturn(PETSC_SUCCESS);
281: }
283: /*MC
284: PetscDTBinomialInt - Compute the binomial coefficient `n` choose `k`
286: Input Parameters:
287: + n - a non-negative integer
288: - k - an integer between 0 and `n`, inclusive
290: Output Parameter:
291: . binomial - the binomial coefficient `n` choose `k`
293: Level: beginner
295: Note:
296: This is limited by integers that can be represented by `PetscInt`.
298: Use `PetscDTBinomial()` for real number approximations of larger values
300: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTEnumPerm()`
301: M*/
302: static inline PetscErrorCode PetscDTBinomialInt(PetscInt n, PetscInt k, PetscInt *binomial)
303: {
304: PetscInt bin;
306: PetscFunctionBegin;
307: *binomial = -1;
308: 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);
309: 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);
310: if (n <= 3) {
311: PetscInt binomLookup[4][4] = {
312: {1, 0, 0, 0},
313: {1, 1, 0, 0},
314: {1, 2, 1, 0},
315: {1, 3, 3, 1}
316: };
318: bin = binomLookup[n][k];
319: } else {
320: PetscInt binom = 1;
322: k = PetscMin(k, n - k);
323: for (PetscInt i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1);
324: bin = binom;
325: }
326: *binomial = bin;
327: PetscFunctionReturn(PETSC_SUCCESS);
328: }
330: /* the following inline routines should be not be inline routines and then Fortran binding can be built automatically */
331: #define PeOp
333: /*MC
334: PetscDTEnumPerm - Get a permutation of `n` integers from its encoding into the integers [0, n!) as a sequence of swaps.
336: Input Parameters:
337: + n - a non-negative integer (see note about limits below)
338: - k - an integer in [0, n!)
340: Output Parameters:
341: + perm - the permuted list of the integers [0, ..., n-1]
342: - isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps.
344: Level: intermediate
346: Notes:
347: A permutation can be described by the operations that convert the lists [0, 1, ..., n-1] into the permutation,
348: by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in
349: some position j >= i. This swap is encoded as the difference (j - i). The difference d_i at step i is less than
350: (n - i). This sequence of n-1 differences [d_0, ..., d_{n-2}] is encoded as the number
351: (n-1)! * d_0 + (n-2)! * d_1 + ... + 1! * d_{n-2}.
353: 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.
355: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTPermIndex()`
356: M*/
357: static inline PetscErrorCode PetscDTEnumPerm(PetscInt n, PetscInt k, PetscInt *perm, PeOp PetscBool *isOdd)
358: {
359: PetscInt odd = 0;
360: PetscInt i;
361: PetscInt work[PETSC_FACTORIAL_MAX];
362: PetscInt *w;
364: PetscFunctionBegin;
365: if (isOdd) *isOdd = PETSC_FALSE;
366: 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);
367: if (n >= 2) {
368: w = &work[n - 2];
369: for (i = 2; i <= n; i++) {
370: *(w--) = k % i;
371: k /= i;
372: }
373: }
374: for (i = 0; i < n; i++) perm[i] = i;
375: for (i = 0; i < n - 1; i++) {
376: PetscInt s = work[i];
377: PetscInt swap = perm[i];
379: perm[i] = perm[i + s];
380: perm[i + s] = swap;
381: odd ^= (!!s);
382: }
383: if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
384: PetscFunctionReturn(PETSC_SUCCESS);
385: }
387: /*MC
388: PetscDTPermIndex - Encode a permutation of n into an integer in [0, n!). This inverts `PetscDTEnumPerm()`.
390: Input Parameters:
391: + n - a non-negative integer (see note about limits below)
392: - perm - the permuted list of the integers [0, ..., n-1]
394: Output Parameters:
395: + k - an integer in [0, n!)
396: - isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps.
398: Level: beginner
400: Note:
401: 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.
403: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`
404: M*/
405: static inline PetscErrorCode PetscDTPermIndex(PetscInt n, const PetscInt *perm, PetscInt *k, PeOp PetscBool *isOdd)
406: {
407: PetscInt odd = 0;
408: PetscInt i, idx;
409: PetscInt work[PETSC_FACTORIAL_MAX];
410: PetscInt iwork[PETSC_FACTORIAL_MAX];
412: PetscFunctionBeginHot;
413: *k = -1;
414: if (isOdd) *isOdd = PETSC_FALSE;
415: 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);
416: for (i = 0; i < n; i++) work[i] = i; /* partial permutation */
417: for (i = 0; i < n; i++) iwork[i] = i; /* partial permutation inverse */
418: for (idx = 0, i = 0; i < n - 1; i++) {
419: PetscInt j = perm[i];
420: PetscInt icur = work[i];
421: PetscInt jloc = iwork[j];
422: PetscInt diff = jloc - i;
424: idx = idx * (n - i) + diff;
425: /* swap (i, jloc) */
426: work[i] = j;
427: work[jloc] = icur;
428: iwork[j] = i;
429: iwork[icur] = jloc;
430: odd ^= (!!diff);
431: }
432: *k = idx;
433: if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
434: PetscFunctionReturn(PETSC_SUCCESS);
435: }
437: /*MC
438: PetscDTEnumSubset - Get an ordered subset of the integers [0, ..., n - 1] from its encoding as an integers in [0, n choose k).
439: The encoding is in lexicographic order.
441: Input Parameters:
442: + n - a non-negative integer (see note about limits below)
443: . k - an integer in [0, n]
444: - j - an index in [0, n choose k)
446: Output Parameter:
447: . subset - the jth subset of size k of the integers [0, ..., n - 1]
449: Level: beginner
451: Note:
452: Limited by arguments such that `n` choose `k` can be represented by `PetscInt`
454: .seealso: `PetscDTSubsetIndex()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()`
455: M*/
456: static inline PetscErrorCode PetscDTEnumSubset(PetscInt n, PetscInt k, PetscInt j, PetscInt *subset)
457: {
458: PetscInt Nk;
460: PetscFunctionBeginHot;
461: PetscCall(PetscDTBinomialInt(n, k, &Nk));
462: for (PetscInt i = 0, l = 0; i < n && l < k; i++) {
463: PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
464: PetscInt Nminusk = Nk - Nminuskminus;
466: if (j < Nminuskminus) {
467: subset[l++] = i;
468: Nk = Nminuskminus;
469: } else {
470: j -= Nminuskminus;
471: Nk = Nminusk;
472: }
473: }
474: PetscFunctionReturn(PETSC_SUCCESS);
475: }
477: /*MC
478: 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.
479: This is the inverse of `PetscDTEnumSubset`.
481: Input Parameters:
482: + n - a non-negative integer (see note about limits below)
483: . k - an integer in [0, n]
484: - subset - an ordered subset of the integers [0, ..., n - 1]
486: Output Parameter:
487: . index - the rank of the subset in lexicographic order
489: Level: beginner
491: Note:
492: Limited by arguments such that `n` choose `k` can be represented by `PetscInt`
494: .seealso: `PetscDTEnumSubset()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()`
495: M*/
496: static inline PetscErrorCode PetscDTSubsetIndex(PetscInt n, PetscInt k, const PetscInt *subset, PetscInt *index)
497: {
498: PetscInt j = 0, Nk;
500: PetscFunctionBegin;
501: *index = -1;
502: PetscCall(PetscDTBinomialInt(n, k, &Nk));
503: for (PetscInt i = 0, l = 0; i < n && l < k; i++) {
504: PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
505: PetscInt Nminusk = Nk - Nminuskminus;
507: if (subset[l] == i) {
508: l++;
509: Nk = Nminuskminus;
510: } else {
511: j += Nminuskminus;
512: Nk = Nminusk;
513: }
514: }
515: *index = j;
516: PetscFunctionReturn(PETSC_SUCCESS);
517: }
519: /*MC
520: PetscDTEnumSplit - 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.
522: Input Parameters:
523: + n - a non-negative integer (see note about limits below)
524: . k - an integer in [0, n]
525: - j - an index in [0, n choose k)
527: Output Parameters:
528: + perm - the jth subset of size k of the integers [0, ..., n - 1], followed by its complementary set.
529: - isOdd - if not `NULL`, return whether perm is an even or odd permutation.
531: Level: beginner
533: Note:
534: Limited by arguments such that `n` choose `k` can be represented by `PetscInt`
536: .seealso: `PetscDTEnumSubset()`, `PetscDTSubsetIndex()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`,
537: `PetscDTPermIndex()`
538: M*/
539: static inline PetscErrorCode PetscDTEnumSplit(PetscInt n, PetscInt k, PetscInt j, PetscInt *perm, PeOp PetscBool *isOdd)
540: {
541: PetscInt i, l, m, Nk, odd = 0;
542: PetscInt *subcomp = PetscSafePointerPlusOffset(perm, k);
544: PetscFunctionBegin;
545: if (isOdd) *isOdd = PETSC_FALSE;
546: PetscCall(PetscDTBinomialInt(n, k, &Nk));
547: for (i = 0, l = 0, m = 0; i < n && l < k; i++) {
548: PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
549: PetscInt Nminusk = Nk - Nminuskminus;
551: if (j < Nminuskminus) {
552: perm[l++] = i;
553: Nk = Nminuskminus;
554: } else {
555: subcomp[m++] = i;
556: j -= Nminuskminus;
557: odd ^= ((k - l) & 1);
558: Nk = Nminusk;
559: }
560: }
561: for (; i < n; i++) subcomp[m++] = i;
562: if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
563: PetscFunctionReturn(PETSC_SUCCESS);
564: }
566: struct _n_PetscTabulation {
567: PetscInt K; /* Indicates a k-jet, namely tabulated derivatives up to order k */
568: PetscInt Nr; /* The number of tabulation replicas (often 1) */
569: PetscInt Np; /* The number of tabulation points in a replica */
570: PetscInt Nb; /* The number of functions tabulated */
571: PetscInt Nc; /* The number of function components */
572: PetscInt cdim; /* The coordinate dimension */
573: PetscReal **T; /* The tabulation T[K] of functions and their derivatives
574: T[0] = B[Nr*Np][Nb][Nc]: The basis function values at quadrature points
575: T[1] = D[Nr*Np][Nb][Nc][cdim]: The basis function derivatives at quadrature points
576: T[2] = H[Nr*Np][Nb][Nc][cdim][cdim]: The basis function second derivatives at quadrature points */
577: };
579: /*S
580: PetscTabulation - PETSc object that manages tabulations for finite element methods.
582: Level: intermediate
584: Note:
585: This is a pointer to a C struct, hence the data in it may be accessed directly.
587: Fortran Note:
588: Use `PetscTabulationGetData()` and `PetscTabulationRestoreData()` to access the arrays in the tabulation.
590: Developer Note:
591: TODO: put the meaning of the struct fields in this manual page
593: .seealso: `PetscTabulationDestroy()`, `PetscFECreateTabulation()`, `PetscFEGetCellTabulation()`
594: S*/
595: typedef struct _n_PetscTabulation *PetscTabulation;
597: /*S
598: PetscProbFn - A prototype of a PDF or CDF used with PETSc probability operations whose names begin with `PetscProb` such as
599: `PetscProbComputeKSStatistic()`.
601: Calling Sequence:
602: + x - input value
603: . scale - scale factor, I don't know what this is for
604: - result - the value of the PDF or CDF at the input value
606: Level: beginner
608: Developer Note:
609: Why does this take an array argument for `result` when it seems to be able to output a single value?
611: .seealso: `PetscProbComputeKSStatistic()`, `PetscProbComputeKSStatisticWeighted()`, `PetscPDFMaxwellBoltzmann1D()`
612: S*/
613: typedef PetscErrorCode PetscProbFn(const PetscReal x[], const PetscReal scale[], PetscReal result[]);
615: PETSC_EXTERN_TYPEDEF typedef PetscProbFn *PetscProbFunc PETSC_DEPRECATED_TYPEDEF(3, 24, 0, "PetscProbFn*", );
617: typedef enum {
618: DTPROB_DENSITY_CONSTANT,
619: DTPROB_DENSITY_GAUSSIAN,
620: DTPROB_DENSITY_MAXWELL_BOLTZMANN,
621: DTPROB_NUM_DENSITY
622: } DTProbDensityType;
623: PETSC_EXTERN const char *const DTProbDensityTypes[];
625: PETSC_EXTERN PetscProbFn PetscPDFMaxwellBoltzmann1D;
626: PETSC_EXTERN PetscProbFn PetscCDFMaxwellBoltzmann1D;
627: PETSC_EXTERN PetscProbFn PetscPDFMaxwellBoltzmann2D;
628: PETSC_EXTERN PetscProbFn PetscCDFMaxwellBoltzmann2D;
629: PETSC_EXTERN PetscProbFn PetscPDFMaxwellBoltzmann3D;
630: PETSC_EXTERN PetscProbFn PetscCDFMaxwellBoltzmann3D;
631: PETSC_EXTERN PetscProbFn PetscPDFGaussian1D;
632: PETSC_EXTERN PetscProbFn PetscCDFGaussian1D;
633: PETSC_EXTERN PetscProbFn PetscPDFSampleGaussian1D;
634: PETSC_EXTERN PetscProbFn PetscPDFGaussian2D;
635: PETSC_EXTERN PetscProbFn PetscPDFSampleGaussian2D;
636: PETSC_EXTERN PetscProbFn PetscPDFGaussian3D;
637: PETSC_EXTERN PetscProbFn PetscPDFSampleGaussian3D;
638: PETSC_EXTERN PetscProbFn PetscPDFConstant1D;
639: PETSC_EXTERN PetscProbFn PetscCDFConstant1D;
640: PETSC_EXTERN PetscProbFn PetscPDFSampleConstant1D;
641: PETSC_EXTERN PetscProbFn PetscPDFConstant2D;
642: PETSC_EXTERN PetscProbFn PetscCDFConstant2D;
643: PETSC_EXTERN PetscProbFn PetscPDFSampleConstant2D;
644: PETSC_EXTERN PetscProbFn PetscPDFConstant3D;
645: PETSC_EXTERN PetscProbFn PetscCDFConstant3D;
646: PETSC_EXTERN PetscProbFn PetscPDFSampleConstant3D;
647: PETSC_EXTERN PetscErrorCode PetscProbCreateFromOptions(PetscInt, const char[], const char[], PetscProbFn **, PetscProbFn **, PetscProbFn **);
649: #include <petscvec.h>
651: PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatistic(Vec, PetscProbFn *, PetscReal *);
652: PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatisticWeighted(Vec, Vec, PetscProbFn *, PetscReal *);
653: PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatisticMagnitude(Vec, PetscProbFn *, PetscReal *);