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 *);

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: /*MC
152:   PETSC_FORM_DEGREE_UNDEFINED - Indicates that a field does not have
153:   a well-defined form degree in exterior calculus.

155:   Level: advanced

157: .seealso: `PetscDTAltV`, `PetscDualSpaceGetFormDegree()`
158: M*/
159: #define PETSC_FORM_DEGREE_UNDEFINED PETSC_INT_MIN

161: PETSC_EXTERN PetscErrorCode PetscDTAltVApply(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
162: PETSC_EXTERN PetscErrorCode PetscDTAltVWedge(PetscInt, PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
163: PETSC_EXTERN PetscErrorCode PetscDTAltVWedgeMatrix(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *);
164: PETSC_EXTERN PetscErrorCode PetscDTAltVPullback(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *);
165: PETSC_EXTERN PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt, PetscInt, const PetscReal *, PetscInt, PetscReal *);
166: PETSC_EXTERN PetscErrorCode PetscDTAltVInterior(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
167: PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorMatrix(PetscInt, PetscInt, const PetscReal *, PetscReal *);
168: PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorPattern(PetscInt, PetscInt, PetscInt (*)[3]);
169: PETSC_EXTERN PetscErrorCode PetscDTAltVStar(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *);

171: PETSC_EXTERN PetscErrorCode PetscDTBaryToIndex(PetscInt, PetscInt, const PetscInt[], PetscInt *);
172: PETSC_EXTERN PetscErrorCode PetscDTIndexToBary(PetscInt, PetscInt, PetscInt, PetscInt[]);
173: PETSC_EXTERN PetscErrorCode PetscDTGradedOrderToIndex(PetscInt, const PetscInt[], PetscInt *);
174: PETSC_EXTERN PetscErrorCode PetscDTIndexToGradedOrder(PetscInt, PetscInt, PetscInt[]);

176: #if defined(PETSC_USE_64BIT_INDICES)
177:   #define PETSC_FACTORIAL_MAX 20
178:   #define PETSC_BINOMIAL_MAX  61
179: #else
180:   #define PETSC_FACTORIAL_MAX 12
181:   #define PETSC_BINOMIAL_MAX  29
182: #endif

184: /*MC
185:    PetscDTFactorial - Approximate n! as a real number

187:    Input Parameter:
188: .  n - a non-negative integer

190:    Output Parameter:
191: .  factorial - n!

193:    Level: beginner

195: .seealso: `PetscDTFactorialInt()`, `PetscDTBinomialInt()`, `PetscDTBinomial()`
196: M*/
197: static inline PetscErrorCode PetscDTFactorial(PetscInt n, PetscReal *factorial)
198: {
199:   PetscReal f = 1.0;

201:   PetscFunctionBegin;
202:   *factorial = -1.0;
203:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Factorial called with negative number %" PetscInt_FMT, n);
204:   for (PetscInt i = 1; i < n + 1; ++i) f *= (PetscReal)i;
205:   *factorial = f;
206:   PetscFunctionReturn(PETSC_SUCCESS);
207: }

209: /*MC
210:    PetscDTFactorialInt - Compute n! as an integer

212:    Input Parameter:
213: .  n - a non-negative integer

215:    Output Parameter:
216: .  factorial - n!

218:    Level: beginner

220:    Note:
221:    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.

223: .seealso: `PetscDTFactorial()`, `PetscDTBinomialInt()`, `PetscDTBinomial()`
224: M*/
225: static inline PetscErrorCode PetscDTFactorialInt(PetscInt n, PetscInt *factorial)
226: {
227:   PetscInt facLookup[13] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600};

229:   PetscFunctionBegin;
230:   *factorial = -1;
231:   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);
232:   if (n <= 12) {
233:     *factorial = facLookup[n];
234:   } else {
235:     PetscInt f = facLookup[12];
236:     PetscInt i;

238:     for (i = 13; i < n + 1; ++i) f *= i;
239:     *factorial = f;
240:   }
241:   PetscFunctionReturn(PETSC_SUCCESS);
242: }

244: /*MC
245:    PetscDTBinomial - Approximate the binomial coefficient `n` choose `k`

247:    Input Parameters:
248: +  n - a non-negative integer
249: -  k - an integer between 0 and `n`, inclusive

251:    Output Parameter:
252: .  binomial - approximation of the binomial coefficient `n` choose `k`

254:    Level: beginner

256: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`
257: M*/
258: static inline PetscErrorCode PetscDTBinomial(PetscInt n, PetscInt k, PetscReal *binomial)
259: {
260:   PetscFunctionBeginHot;
261:   *binomial = -1.0;
262:   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);
263:   if (n <= 3) {
264:     PetscInt binomLookup[4][4] = {
265:       {1, 0, 0, 0},
266:       {1, 1, 0, 0},
267:       {1, 2, 1, 0},
268:       {1, 3, 3, 1}
269:     };

271:     *binomial = (PetscReal)binomLookup[n][k];
272:   } else {
273:     PetscReal binom = 1.0;

275:     k = PetscMin(k, n - k);
276:     for (PetscInt i = 0; i < k; i++) binom = (binom * (PetscReal)(n - i)) / (PetscReal)(i + 1);
277:     *binomial = binom;
278:   }
279:   PetscFunctionReturn(PETSC_SUCCESS);
280: }

282: /*MC
283:    PetscDTBinomialInt - Compute the binomial coefficient `n` choose `k`

285:    Input Parameters:
286: +  n - a non-negative integer
287: -  k - an integer between 0 and `n`, inclusive

289:    Output Parameter:
290: .  binomial - the binomial coefficient `n` choose `k`

292:    Level: beginner

294:    Note:
295:    This is limited by integers that can be represented by `PetscInt`.

297:    Use `PetscDTBinomial()` for real number approximations of larger values

299: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTEnumPerm()`
300: M*/
301: static inline PetscErrorCode PetscDTBinomialInt(PetscInt n, PetscInt k, PetscInt *binomial)
302: {
303:   PetscInt bin;

305:   PetscFunctionBegin;
306:   *binomial = -1;
307:   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);
308:   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);
309:   if (n <= 3) {
310:     PetscInt binomLookup[4][4] = {
311:       {1, 0, 0, 0},
312:       {1, 1, 0, 0},
313:       {1, 2, 1, 0},
314:       {1, 3, 3, 1}
315:     };

317:     bin = binomLookup[n][k];
318:   } else {
319:     PetscInt binom = 1;

321:     k = PetscMin(k, n - k);
322:     for (PetscInt i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1);
323:     bin = binom;
324:   }
325:   *binomial = bin;
326:   PetscFunctionReturn(PETSC_SUCCESS);
327: }

329: /* the following inline routines should be not be inline routines and then Fortran binding can be built automatically */
330: #define PeOp

332: /*MC
333:    PetscDTEnumPerm - Get a permutation of `n` integers from its encoding into the integers [0, n!) as a sequence of swaps.

335:    Input Parameters:
336: +  n - a non-negative integer (see note about limits below)
337: -  k - an integer in [0, n!)

339:    Output Parameters:
340: +  perm  - the permuted list of the integers [0, ..., n-1]
341: -  isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps.

343:    Level: intermediate

345:    Notes:
346:    A permutation can be described by the operations that convert the lists [0, 1, ..., n-1] into the permutation,
347:    by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in
348:    some position j >= i.  This swap is encoded as the difference (j - i).  The difference d_i at step i is less than
349:    (n - i).  This sequence of n-1 differences [d_0, ..., d_{n-2}] is encoded as the number
350:    (n-1)! * d_0 + (n-2)! * d_1 + ... + 1! * d_{n-2}.

352:    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.

354: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTPermIndex()`
355: M*/
356: static inline PetscErrorCode PetscDTEnumPerm(PetscInt n, PetscInt k, PetscInt *perm, PeOp PetscBool *isOdd)
357: {
358:   PetscInt  odd = 0;
359:   PetscInt  i;
360:   PetscInt  work[PETSC_FACTORIAL_MAX];
361:   PetscInt *w;

363:   PetscFunctionBegin;
364:   if (isOdd) *isOdd = PETSC_FALSE;
365:   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);
366:   if (n >= 2) {
367:     w = &work[n - 2];
368:     for (i = 2; i <= n; i++) {
369:       *(w--) = k % i;
370:       k /= i;
371:     }
372:   }
373:   for (i = 0; i < n; i++) perm[i] = i;
374:   for (i = 0; i < n - 1; i++) {
375:     PetscInt s    = work[i];
376:     PetscInt swap = perm[i];

378:     perm[i]     = perm[i + s];
379:     perm[i + s] = swap;
380:     odd ^= (!!s);
381:   }
382:   if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
383:   PetscFunctionReturn(PETSC_SUCCESS);
384: }

386: /*MC
387:    PetscDTPermIndex - Encode a permutation of n into an integer in [0, n!).  This inverts `PetscDTEnumPerm()`.

389:    Input Parameters:
390: +  n    - a non-negative integer (see note about limits below)
391: -  perm - the permuted list of the integers [0, ..., n-1]

393:    Output Parameters:
394: +  k     - an integer in [0, n!)
395: -  isOdd - if not `NULL`, returns whether the permutation used an even or odd number of swaps.

397:    Level: beginner

399:    Note:
400:    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.

402: .seealso: `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`
403: M*/
404: static inline PetscErrorCode PetscDTPermIndex(PetscInt n, const PetscInt *perm, PetscInt *k, PeOp PetscBool *isOdd)
405: {
406:   PetscInt odd = 0;
407:   PetscInt i, idx;
408:   PetscInt work[PETSC_FACTORIAL_MAX];
409:   PetscInt iwork[PETSC_FACTORIAL_MAX];

411:   PetscFunctionBeginHot;
412:   *k = -1;
413:   if (isOdd) *isOdd = PETSC_FALSE;
414:   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);
415:   for (i = 0; i < n; i++) work[i] = i;  /* partial permutation */
416:   for (i = 0; i < n; i++) iwork[i] = i; /* partial permutation inverse */
417:   for (idx = 0, i = 0; i < n - 1; i++) {
418:     PetscInt j    = perm[i];
419:     PetscInt icur = work[i];
420:     PetscInt jloc = iwork[j];
421:     PetscInt diff = jloc - i;

423:     idx = idx * (n - i) + diff;
424:     /* swap (i, jloc) */
425:     work[i]     = j;
426:     work[jloc]  = icur;
427:     iwork[j]    = i;
428:     iwork[icur] = jloc;
429:     odd ^= (!!diff);
430:   }
431:   *k = idx;
432:   if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
433:   PetscFunctionReturn(PETSC_SUCCESS);
434: }

436: /*MC
437:    PetscDTEnumSubset - Get an ordered subset of the integers [0, ..., n - 1] from its encoding as an integers in [0, n choose k).
438:    The encoding is in lexicographic order.

440:    Input Parameters:
441: +  n - a non-negative integer (see note about limits below)
442: .  k - an integer in [0, n]
443: -  j - an index in [0, n choose k)

445:    Output Parameter:
446: .  subset - the jth subset of size k of the integers [0, ..., n - 1]

448:    Level: beginner

450:    Note:
451:    Limited by arguments such that `n` choose `k` can be represented by `PetscInt`

453: .seealso: `PetscDTSubsetIndex()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()`
454: M*/
455: static inline PetscErrorCode PetscDTEnumSubset(PetscInt n, PetscInt k, PetscInt j, PetscInt *subset)
456: {
457:   PetscInt Nk;

459:   PetscFunctionBeginHot;
460:   PetscCall(PetscDTBinomialInt(n, k, &Nk));
461:   for (PetscInt i = 0, l = 0; i < n && l < k; i++) {
462:     PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
463:     PetscInt Nminusk      = Nk - Nminuskminus;

465:     if (j < Nminuskminus) {
466:       subset[l++] = i;
467:       Nk          = Nminuskminus;
468:     } else {
469:       j -= Nminuskminus;
470:       Nk = Nminusk;
471:     }
472:   }
473:   PetscFunctionReturn(PETSC_SUCCESS);
474: }

476: /*MC
477:    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.
478:    This is the inverse of `PetscDTEnumSubset`.

480:    Input Parameters:
481: +  n      - a non-negative integer (see note about limits below)
482: .  k      - an integer in [0, n]
483: -  subset - an ordered subset of the integers [0, ..., n - 1]

485:    Output Parameter:
486: .  index - the rank of the subset in lexicographic order

488:    Level: beginner

490:    Note:
491:    Limited by arguments such that `n` choose `k` can be represented by `PetscInt`

493: .seealso: `PetscDTEnumSubset()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`, `PetscDTPermIndex()`
494: M*/
495: static inline PetscErrorCode PetscDTSubsetIndex(PetscInt n, PetscInt k, const PetscInt *subset, PetscInt *index)
496: {
497:   PetscInt j = 0, Nk;

499:   PetscFunctionBegin;
500:   *index = -1;
501:   PetscCall(PetscDTBinomialInt(n, k, &Nk));
502:   for (PetscInt i = 0, l = 0; i < n && l < k; i++) {
503:     PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
504:     PetscInt Nminusk      = Nk - Nminuskminus;

506:     if (subset[l] == i) {
507:       l++;
508:       Nk = Nminuskminus;
509:     } else {
510:       j += Nminuskminus;
511:       Nk = Nminusk;
512:     }
513:   }
514:   *index = j;
515:   PetscFunctionReturn(PETSC_SUCCESS);
516: }

518: /*MC
519:    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.

521:    Input Parameters:
522: +  n - a non-negative integer (see note about limits below)
523: .  k - an integer in [0, n]
524: -  j - an index in [0, n choose k)

526:    Output Parameters:
527: +  perm  - the jth subset of size k of the integers [0, ..., n - 1], followed by its complementary set.
528: -  isOdd - if not `NULL`, return whether perm is an even or odd permutation.

530:    Level: beginner

532:    Note:
533:    Limited by arguments such that `n` choose `k` can be represented by `PetscInt`

535: .seealso: `PetscDTEnumSubset()`, `PetscDTSubsetIndex()`, `PetscDTFactorial()`, `PetscDTFactorialInt()`, `PetscDTBinomial()`, `PetscDTBinomialInt()`, `PetscDTEnumPerm()`,
536:           `PetscDTPermIndex()`
537: M*/
538: static inline PetscErrorCode PetscDTEnumSplit(PetscInt n, PetscInt k, PetscInt j, PetscInt *perm, PeOp PetscBool *isOdd)
539: {
540:   PetscInt  i, l, m, Nk, odd = 0;
541:   PetscInt *subcomp = PetscSafePointerPlusOffset(perm, k);

543:   PetscFunctionBegin;
544:   if (isOdd) *isOdd = PETSC_FALSE;
545:   PetscCall(PetscDTBinomialInt(n, k, &Nk));
546:   for (i = 0, l = 0, m = 0; i < n && l < k; i++) {
547:     PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
548:     PetscInt Nminusk      = Nk - Nminuskminus;

550:     if (j < Nminuskminus) {
551:       perm[l++] = i;
552:       Nk        = Nminuskminus;
553:     } else {
554:       subcomp[m++] = i;
555:       j -= Nminuskminus;
556:       odd ^= ((k - l) & 1);
557:       Nk = Nminusk;
558:     }
559:   }
560:   for (; i < n; i++) subcomp[m++] = i;
561:   if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
562:   PetscFunctionReturn(PETSC_SUCCESS);
563: }

565: struct _n_PetscTabulation {
566:   PetscInt    K;    /* Indicates a k-jet, namely tabulated derivatives up to order k */
567:   PetscInt    Nr;   /* The number of tabulation replicas (often 1) */
568:   PetscInt    Np;   /* The number of tabulation points in a replica */
569:   PetscInt    Nb;   /* The number of functions tabulated */
570:   PetscInt    Nc;   /* The number of function components */
571:   PetscInt    cdim; /* The coordinate dimension */
572:   PetscReal **T;    /* The tabulation T[K] of functions and their derivatives
573:                        T[0] = B[Nr*Np][Nb][Nc]:             The basis function values at quadrature points
574:                        T[1] = D[Nr*Np][Nb][Nc][cdim]:       The basis function derivatives at quadrature points
575:                        T[2] = H[Nr*Np][Nb][Nc][cdim][cdim]: The basis function second derivatives at quadrature points */
576: };

578: /*S
579:    PetscTabulation - PETSc object that manages tabulations for finite element methods.

581:    Level: intermediate

583:    Note:
584:    This is a pointer to a C struct, hence the data in it may be accessed directly.

586:    Fortran Note:
587:    Use `PetscTabulationGetData()` and `PetscTabulationRestoreData()` to access the arrays in the tabulation.

589:    Developer Note:
590:    TODO: put the meaning of the struct fields in this manual page

592: .seealso: `PetscTabulationDestroy()`, `PetscFECreateTabulation()`, `PetscFEGetCellTabulation()`
593: S*/
594: typedef struct _n_PetscTabulation *PetscTabulation;

596: typedef PetscErrorCode (*PetscProbFunc)(const PetscReal[], const PetscReal[], PetscReal[]);

598: typedef enum {
599:   DTPROB_DENSITY_CONSTANT,
600:   DTPROB_DENSITY_GAUSSIAN,
601:   DTPROB_DENSITY_MAXWELL_BOLTZMANN,
602:   DTPROB_NUM_DENSITY
603: } DTProbDensityType;
604: PETSC_EXTERN const char *const DTProbDensityTypes[];

606: PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]);
607: PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann1D(const PetscReal[], const PetscReal[], PetscReal[]);
608: PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]);
609: PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann2D(const PetscReal[], const PetscReal[], PetscReal[]);
610: PETSC_EXTERN PetscErrorCode PetscPDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]);
611: PETSC_EXTERN PetscErrorCode PetscCDFMaxwellBoltzmann3D(const PetscReal[], const PetscReal[], PetscReal[]);
612: PETSC_EXTERN PetscErrorCode PetscPDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]);
613: PETSC_EXTERN PetscErrorCode PetscCDFGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]);
614: PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian1D(const PetscReal[], const PetscReal[], PetscReal[]);
615: PETSC_EXTERN PetscErrorCode PetscPDFGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]);
616: PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian2D(const PetscReal[], const PetscReal[], PetscReal[]);
617: PETSC_EXTERN PetscErrorCode PetscPDFGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]);
618: PETSC_EXTERN PetscErrorCode PetscPDFSampleGaussian3D(const PetscReal[], const PetscReal[], PetscReal[]);
619: PETSC_EXTERN PetscErrorCode PetscPDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]);
620: PETSC_EXTERN PetscErrorCode PetscCDFConstant1D(const PetscReal[], const PetscReal[], PetscReal[]);
621: PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant1D(const PetscReal[], const PetscReal[], PetscReal[]);
622: PETSC_EXTERN PetscErrorCode PetscPDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]);
623: PETSC_EXTERN PetscErrorCode PetscCDFConstant2D(const PetscReal[], const PetscReal[], PetscReal[]);
624: PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant2D(const PetscReal[], const PetscReal[], PetscReal[]);
625: PETSC_EXTERN PetscErrorCode PetscPDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]);
626: PETSC_EXTERN PetscErrorCode PetscCDFConstant3D(const PetscReal[], const PetscReal[], PetscReal[]);
627: PETSC_EXTERN PetscErrorCode PetscPDFSampleConstant3D(const PetscReal[], const PetscReal[], PetscReal[]);
628: PETSC_EXTERN PetscErrorCode PetscProbCreateFromOptions(PetscInt, const char[], const char[], PetscProbFunc *, PetscProbFunc *, PetscProbFunc *);

630: #include <petscvec.h>

632: PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatistic(Vec, PetscProbFunc, PetscReal *);
633: PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatisticWeighted(Vec, Vec, PetscProbFunc, PetscReal *);
634: PETSC_EXTERN PetscErrorCode PetscProbComputeKSStatisticMagnitude(Vec, PetscProbFunc, PetscReal *);