Actual source code: petscdt.h

petsc-3.14.0 2020-09-29
Report Typos and Errors
  1: /*
  2:   Common tools for constructing discretizations
  3: */
  4: #if !defined(PETSCDT_H)
  5: #define PETSCDT_H

  7: #include <petscsys.h>

  9: PETSC_EXTERN PetscClassId PETSCQUADRATURE_CLASSID;

 11: /*S
 12:   PetscQuadrature - Quadrature rule for integration.

 14:   Level: beginner

 16: .seealso:  PetscQuadratureCreate(), PetscQuadratureDestroy()
 17: S*/
 18: typedef struct _p_PetscQuadrature *PetscQuadrature;

 20: /*E
 21:   PetscGaussLobattoLegendreCreateType - algorithm used to compute the Gauss-Lobatto-Legendre nodes and weights

 23:   Level: intermediate

 25: $  PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA - compute the nodes via linear algebra
 26: $  PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON - compute the nodes by solving a nonlinear equation with Newton's method

 28: E*/
 29: typedef enum {PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA,PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON} PetscGaussLobattoLegendreCreateType;

 31: /*E
 32:   PetscDTNodeType - A description of strategies for generating nodes (both
 33:   quadrature nodes and nodes for Lagrange polynomials)

 35:   Level: intermediate

 37: $  PETSCDTNODES_DEFAULT - Nodes chosen by PETSc
 38: $  PETSCDTNODES_GAUSSJACOBI - Nodes at either Gauss-Jacobi or Gauss-Lobatto-Jacobi quadrature points
 39: $  PETSCDTNODES_EQUISPACED - Nodes equispaced either including the endpoints or excluding them
 40: $  PETSCDTNODES_TANHSINH - Nodes at Tanh-Sinh quadrature points

 42:   Note: a PetscDTNodeType can be paired with a PetscBool to indicate whether
 43:   the nodes include endpoints or not, and in the case of PETSCDT_GAUSSJACOBI
 44:   with exponents for the weight function.

 46: E*/
 47: typedef enum {PETSCDTNODES_DEFAULT=-1, PETSCDTNODES_GAUSSJACOBI, PETSCDTNODES_EQUISPACED, PETSCDTNODES_TANHSINH} PetscDTNodeType;

 49: PETSC_EXTERN const char *const PetscDTNodeTypes[];

 51: PETSC_EXTERN PetscErrorCode PetscQuadratureCreate(MPI_Comm, PetscQuadrature *);
 52: PETSC_EXTERN PetscErrorCode PetscQuadratureDuplicate(PetscQuadrature, PetscQuadrature *);
 53: PETSC_EXTERN PetscErrorCode PetscQuadratureGetOrder(PetscQuadrature, PetscInt*);
 54: PETSC_EXTERN PetscErrorCode PetscQuadratureSetOrder(PetscQuadrature, PetscInt);
 55: PETSC_EXTERN PetscErrorCode PetscQuadratureGetNumComponents(PetscQuadrature, PetscInt*);
 56: PETSC_EXTERN PetscErrorCode PetscQuadratureSetNumComponents(PetscQuadrature, PetscInt);
 57: PETSC_EXTERN PetscErrorCode PetscQuadratureGetData(PetscQuadrature, PetscInt*, PetscInt*, PetscInt*, const PetscReal *[], const PetscReal *[]);
 58: PETSC_EXTERN PetscErrorCode PetscQuadratureSetData(PetscQuadrature, PetscInt, PetscInt, PetscInt, const PetscReal [], const PetscReal []);
 59: PETSC_EXTERN PetscErrorCode PetscQuadratureView(PetscQuadrature, PetscViewer);
 60: PETSC_EXTERN PetscErrorCode PetscQuadratureDestroy(PetscQuadrature *);

 62: PETSC_EXTERN PetscErrorCode PetscQuadratureExpandComposite(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], PetscQuadrature *);

 64: PETSC_EXTERN PetscErrorCode PetscQuadraturePushForward(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], const PetscReal[], PetscInt, PetscQuadrature *);

 66: PETSC_EXTERN PetscErrorCode PetscDTLegendreEval(PetscInt,const PetscReal*,PetscInt,const PetscInt*,PetscReal*,PetscReal*,PetscReal*);
 67: PETSC_EXTERN PetscErrorCode PetscDTJacobiNorm(PetscReal,PetscReal,PetscInt,PetscReal *);
 68: PETSC_EXTERN PetscErrorCode PetscDTJacobiEval(PetscInt,PetscReal,PetscReal,const PetscReal*,PetscInt,const PetscInt*,PetscReal*,PetscReal*,PetscReal*);
 69: PETSC_EXTERN PetscErrorCode PetscDTJacobiEvalJet(PetscReal,PetscReal,PetscInt,const PetscReal[],PetscInt,PetscInt,PetscReal[]);
 70: PETSC_EXTERN PetscErrorCode PetscDTPKDEvalJet(PetscInt,PetscInt,const PetscReal[],PetscInt,PetscInt,PetscReal[]);
 71: PETSC_EXTERN PetscErrorCode PetscDTGaussQuadrature(PetscInt,PetscReal,PetscReal,PetscReal*,PetscReal*);
 72: PETSC_EXTERN PetscErrorCode PetscDTGaussJacobiQuadrature(PetscInt,PetscReal,PetscReal,PetscReal,PetscReal,PetscReal*,PetscReal*);
 73: PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoJacobiQuadrature(PetscInt,PetscReal,PetscReal,PetscReal,PetscReal,PetscReal*,PetscReal*);
 74: PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoLegendreQuadrature(PetscInt,PetscGaussLobattoLegendreCreateType,PetscReal*,PetscReal*);
 75: PETSC_EXTERN PetscErrorCode PetscDTReconstructPoly(PetscInt,PetscInt,const PetscReal*,PetscInt,const PetscReal*,PetscReal*);
 76: PETSC_EXTERN PetscErrorCode PetscDTGaussTensorQuadrature(PetscInt,PetscInt,PetscInt,PetscReal,PetscReal,PetscQuadrature*);
 77: PETSC_EXTERN PetscErrorCode PetscDTStroudConicalQuadrature(PetscInt,PetscInt,PetscInt,PetscReal,PetscReal,PetscQuadrature*);

 79: PETSC_EXTERN PetscErrorCode PetscDTTanhSinhTensorQuadrature(PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *);
 80: PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrate(void (*)(PetscReal, PetscReal *), PetscReal, PetscReal, PetscInt, PetscReal *);
 81: PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrateMPFR(void (*)(PetscReal, PetscReal *), PetscReal, PetscReal, PetscInt, PetscReal *);

 83: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreIntegrate(PetscInt, PetscReal *, PetscReal *, const PetscReal *, PetscReal *);
 84: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
 85: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
 86: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***);
 87: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***);
 88: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
 89: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
 90: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***);
 91: PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***);

 93: PETSC_EXTERN PetscErrorCode PetscDTAltVApply(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
 94: PETSC_EXTERN PetscErrorCode PetscDTAltVWedge(PetscInt, PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
 95: PETSC_EXTERN PetscErrorCode PetscDTAltVWedgeMatrix(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *);
 96: PETSC_EXTERN PetscErrorCode PetscDTAltVPullback(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *);
 97: PETSC_EXTERN PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt, PetscInt, const PetscReal *, PetscInt, PetscReal *);
 98: PETSC_EXTERN PetscErrorCode PetscDTAltVInterior(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *);
 99: PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorMatrix(PetscInt, PetscInt, const PetscReal *, PetscReal *);
100: PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorPattern(PetscInt, PetscInt, PetscInt (*)[3]);
101: PETSC_EXTERN PetscErrorCode PetscDTAltVStar(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *);

103: PETSC_EXTERN PetscErrorCode PetscDTBaryToIndex(PetscInt,PetscInt,const PetscInt[],PetscInt*);
104: PETSC_EXTERN PetscErrorCode PetscDTIndexToBary(PetscInt,PetscInt,PetscInt,PetscInt[]);
105: PETSC_EXTERN PetscErrorCode PetscDTGradedOrderToIndex(PetscInt,const PetscInt[],PetscInt*);
106: PETSC_EXTERN PetscErrorCode PetscDTIndexToGradedOrder(PetscInt,PetscInt,PetscInt[]);

108: #if defined(PETSC_USE_64BIT_INDICES)
109: #define PETSC_FACTORIAL_MAX 20
110: #define PETSC_BINOMIAL_MAX  61
111: #else
112: #define PETSC_FACTORIAL_MAX 12
113: #define PETSC_BINOMIAL_MAX  29
114: #endif

116: /*MC
117:    PetscDTFactorial - Approximate n! as a real number

119:    Input Arguments:
120: .  n - a non-negative integer

122:    Output Arguments:
123: .  factorial - n!

125:    Level: beginner
126: M*/
127: PETSC_STATIC_INLINE PetscErrorCode PetscDTFactorial(PetscInt n, PetscReal *factorial)
128: {
129:   PetscReal f = 1.0;
130:   PetscInt  i;

133:   *factorial = -1.0;
134:   if (n < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Factorial called with negative number %D\n", n);
135:   for (i = 1; i < n+1; ++i) f *= (PetscReal)i;
136:   *factorial = f;
137:   return(0);
138: }

140: /*MC
141:    PetscDTFactorialInt - Compute n! as an integer

143:    Input Arguments:
144: .  n - a non-negative integer

146:    Output Arguments:
147: .  factorial - n!

149:    Level: beginner

151:    Note: this is limited to n such that n! can be represented by PetscInt, which is 12 if PetscInt is a signed 32-bit integer and 20 if PetscInt is a signed 64-bit integer.
152: M*/
153: PETSC_STATIC_INLINE PetscErrorCode PetscDTFactorialInt(PetscInt n, PetscInt *factorial)
154: {
155:   PetscInt facLookup[13] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600};

158:   *factorial = -1;
159:   if (n < 0 || n > PETSC_FACTORIAL_MAX) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of elements %D is not in supported range [0,%D]\n",n,PETSC_FACTORIAL_MAX);
160:   if (n <= 12) {
161:     *factorial = facLookup[n];
162:   } else {
163:     PetscInt f = facLookup[12];
164:     PetscInt i;

166:     for (i = 13; i < n+1; ++i) f *= i;
167:     *factorial = f;
168:   }
169:   return(0);
170: }

172: /*MC
173:    PetscDTBinomial - Approximate the binomial coefficient "n choose k"

175:    Input Arguments:
176: +  n - a non-negative integer
177: -  k - an integer between 0 and n, inclusive

179:    Output Arguments:
180: .  binomial - approximation of the binomial coefficient n choose k

182:    Level: beginner
183: M*/
184: PETSC_STATIC_INLINE PetscErrorCode PetscDTBinomial(PetscInt n, PetscInt k, PetscReal *binomial)
185: {
187:   *binomial = -1.0;
188:   if (n < 0 || k < 0 || k > n) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Binomial arguments (%D %D) must be non-negative, k <= n\n", n, k);
189:   if (n <= 3) {
190:     PetscInt binomLookup[4][4] = {{1, 0, 0, 0}, {1, 1, 0, 0}, {1, 2, 1, 0}, {1, 3, 3, 1}};

192:     *binomial = (PetscReal)binomLookup[n][k];
193:   } else {
194:     PetscReal binom = 1.0;
195:     PetscInt  i;

197:     k = PetscMin(k, n - k);
198:     for (i = 0; i < k; i++) binom = (binom * (PetscReal)(n - i)) / (PetscReal)(i + 1);
199:     *binomial = binom;
200:   }
201:   return(0);
202: }

204: /*MC
205:    PetscDTBinomialInt - Compute the binomial coefficient "n choose k"

207:    Input Arguments:
208: +  n - a non-negative integer
209: -  k - an integer between 0 and n, inclusive

211:    Output Arguments:
212: .  binomial - the binomial coefficient n choose k

214:    Note: this is limited by integers that can be represented by PetscInt

216:    Level: beginner
217: M*/
218: PETSC_STATIC_INLINE PetscErrorCode PetscDTBinomialInt(PetscInt n, PetscInt k, PetscInt *binomial)
219: {
220:   PetscInt bin;

223:   *binomial = -1;
224:   if (n < 0 || k < 0 || k > n) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Binomial arguments (%D %D) must be non-negative, k <= n\n", n, k);
225:   if (n > PETSC_BINOMIAL_MAX) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Binomial elements %D is larger than max for PetscInt, %D\n", n, PETSC_BINOMIAL_MAX);
226:   if (n <= 3) {
227:     PetscInt binomLookup[4][4] = {{1, 0, 0, 0}, {1, 1, 0, 0}, {1, 2, 1, 0}, {1, 3, 3, 1}};

229:     bin = binomLookup[n][k];
230:   } else {
231:     PetscInt  binom = 1;
232:     PetscInt  i;

234:     k = PetscMin(k, n - k);
235:     for (i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1);
236:     bin = binom;
237:   }
238:   *binomial = bin;
239:   return(0);
240: }

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

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

251:    Input Arguments:
252: +  n - a non-negative integer (see note about limits below)
253: -  k - an integer in [0, n!)

255:    Output Arguments:
256: +  perm - the permuted list of the integers [0, ..., n-1]
257: -  isOdd - if not NULL, returns wether the permutation used an even or odd number of swaps.

259:    Note: this is limited to n such that n! can be represented by PetscInt, which is 12 if PetscInt is a signed 32-bit integer and 20 if PetscInt is a signed 64-bit integer.

261:    Level: beginner
262: M*/
263: PETSC_STATIC_INLINE PetscErrorCode PetscDTEnumPerm(PetscInt n, PetscInt k, PetscInt *perm, PetscBool *isOdd)
264: {
265:   PetscInt  odd = 0;
266:   PetscInt  i;
267:   PetscInt  work[PETSC_FACTORIAL_MAX];
268:   PetscInt *w;

271:   if (isOdd) *isOdd = PETSC_FALSE;
272:   if (n < 0 || n > PETSC_FACTORIAL_MAX) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of elements %D is not in supported range [0,%D]\n",n,PETSC_FACTORIAL_MAX);
273:   w = &work[n - 2];
274:   for (i = 2; i <= n; i++) {
275:     *(w--) = k % i;
276:     k /= i;
277:   }
278:   for (i = 0; i < n; i++) perm[i] = i;
279:   for (i = 0; i < n - 1; i++) {
280:     PetscInt s = work[i];
281:     PetscInt swap = perm[i];

283:     perm[i] = perm[i + s];
284:     perm[i + s] = swap;
285:     odd ^= (!!s);
286:   }
287:   if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
288:   return(0);
289: }

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

294:    Input Arguments:
295: +  n - a non-negative integer (see note about limits below)
296: -  perm - the permuted list of the integers [0, ..., n-1]

298:    Output Arguments:
299: +  k - an integer in [0, n!)
300: -  isOdd - if not NULL, returns wether the permutation used an even or odd number of swaps.

302:    Note: this is limited to n such that n! can be represented by PetscInt, which is 12 if PetscInt is a signed 32-bit integer and 20 if PetscInt is a signed 64-bit integer.

304:    Level: beginner
305: M*/
306: PETSC_STATIC_INLINE PetscErrorCode PetscDTPermIndex(PetscInt n, const PetscInt *perm, PetscInt *k, PetscBool *isOdd)
307: {
308:   PetscInt  odd = 0;
309:   PetscInt  i, idx;
310:   PetscInt  work[PETSC_FACTORIAL_MAX];
311:   PetscInt  iwork[PETSC_FACTORIAL_MAX];

314:   *k = -1;
315:   if (isOdd) *isOdd = PETSC_FALSE;
316:   if (n < 0 || n > PETSC_FACTORIAL_MAX) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of elements %D is not in supported range [0,%D]\n",n,PETSC_FACTORIAL_MAX);
317:   for (i = 0; i < n; i++) work[i] = i;  /* partial permutation */
318:   for (i = 0; i < n; i++) iwork[i] = i; /* partial permutation inverse */
319:   for (idx = 0, i = 0; i < n - 1; i++) {
320:     PetscInt j = perm[i];
321:     PetscInt icur = work[i];
322:     PetscInt jloc = iwork[j];
323:     PetscInt diff = jloc - i;

325:     idx = idx * (n - i) + diff;
326:     /* swap (i, jloc) */
327:     work[i] = j;
328:     work[jloc] = icur;
329:     iwork[j] = i;
330:     iwork[icur] = jloc;
331:     odd ^= (!!diff);
332:   }
333:   *k = idx;
334:   if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
335:   return(0);
336: }

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

342:    Input Arguments:
343: +  n - a non-negative integer (see note about limits below)
344: .  k - an integer in [0, n]
345: -  j - an index in [0, n choose k)

347:    Output Arguments:
348: .  subset - the jth subset of size k of the integers [0, ..., n - 1]

350:    Note: this is limited by arguments such that n choose k can be represented by PetscInt

352:    Level: beginner

354: .seealso: PetscDTSubsetIndex()
355: M*/
356: PETSC_STATIC_INLINE PetscErrorCode PetscDTEnumSubset(PetscInt n, PetscInt k, PetscInt j, PetscInt *subset)
357: {
358:   PetscInt       Nk, i, l;

362:   PetscDTBinomialInt(n, k, &Nk);
363:   for (i = 0, l = 0; i < n && l < k; i++) {
364:     PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
365:     PetscInt Nminusk = Nk - Nminuskminus;

367:     if (j < Nminuskminus) {
368:       subset[l++] = i;
369:       Nk = Nminuskminus;
370:     } else {
371:       j -= Nminuskminus;
372:       Nk = Nminusk;
373:     }
374:   }
375:   return(0);
376: }

378: /*MC
379:    PetscDTSubsetIndex - Convert an ordered subset of k integers from the set [0, ..., n - 1] to its encoding as an integers in [0, n choose k) in lexicographic order.  This is the inverse of PetscDTEnumSubset.

381:    Input Arguments:
382: +  n - a non-negative integer (see note about limits below)
383: .  k - an integer in [0, n]
384: -  subset - an ordered subset of the integers [0, ..., n - 1]

386:    Output Arguments:
387: .  index - the rank of the subset in lexicographic order

389:    Note: this is limited by arguments such that n choose k can be represented by PetscInt

391:    Level: beginner

393: .seealso: PetscDTEnumSubset()
394: M*/
395: PETSC_STATIC_INLINE PetscErrorCode PetscDTSubsetIndex(PetscInt n, PetscInt k, const PetscInt *subset, PetscInt *index)
396: {
397:   PetscInt       i, j = 0, l, Nk;

401:   *index = -1;
402:   PetscDTBinomialInt(n, k, &Nk);
403:   for (i = 0, l = 0; i < n && l < k; i++) {
404:     PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
405:     PetscInt Nminusk = Nk - Nminuskminus;

407:     if (subset[l] == i) {
408:       l++;
409:       Nk = Nminuskminus;
410:     } else {
411:       j += Nminuskminus;
412:       Nk = Nminusk;
413:     }
414:   }
415:   *index = j;
416:   return(0);
417: }

419: /*MC
420:    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.

422:    Input Arguments:
423: +  n - a non-negative integer (see note about limits below)
424: .  k - an integer in [0, n]
425: -  j - an index in [0, n choose k)

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

431:    Note: this is limited by arguments such that n choose k can be represented by PetscInt

433:    Level: beginner

435: .seealso: PetscDTEnumSubset(), PetscDTSubsetIndex()
436: M*/
437: PETSC_STATIC_INLINE PetscErrorCode PetscDTEnumSplit(PetscInt n, PetscInt k, PetscInt j, PetscInt *perm, PetscBool *isOdd)
438: {
439:   PetscInt       i, l, m, *subcomp, Nk;
440:   PetscInt       odd;

444:   if (isOdd) *isOdd = PETSC_FALSE;
445:   PetscDTBinomialInt(n, k, &Nk);
446:   odd = 0;
447:   subcomp = &perm[k];
448:   for (i = 0, l = 0, m = 0; i < n && l < k; i++) {
449:     PetscInt Nminuskminus = (Nk * (k - l)) / (n - i);
450:     PetscInt Nminusk = Nk - Nminuskminus;

452:     if (j < Nminuskminus) {
453:       perm[l++] = i;
454:       Nk = Nminuskminus;
455:     } else {
456:       subcomp[m++] = i;
457:       j -= Nminuskminus;
458:       odd ^= ((k - l) & 1);
459:       Nk = Nminusk;
460:     }
461:   }
462:   for (; i < n; i++) {
463:     subcomp[m++] = i;
464:   }
465:   if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE;
466:   return(0);
467: }

469: struct _p_PetscTabulation {
470:   PetscInt    K;    /* Indicates a k-jet, namely tabulated derviatives up to order k */
471:   PetscInt    Nr;   /* The number of tabulation replicas (often 1) */
472:   PetscInt    Np;   /* The number of tabulation points in a replica */
473:   PetscInt    Nb;   /* The number of functions tabulated */
474:   PetscInt    Nc;   /* The number of function components */
475:   PetscInt    cdim; /* The coordinate dimension */
476:   PetscReal **T;    /* The tabulation T[K] of functions and their derivatives
477:                        T[0] = B[Nr*Np][Nb][Nc]:             The basis function values at quadrature points
478:                        T[1] = D[Nr*Np][Nb][Nc][cdim]:       The basis function derivatives at quadrature points
479:                        T[2] = H[Nr*Np][Nb][Nc][cdim][cdim]: The basis function second derivatives at quadrature points */
480: };
481: typedef struct _p_PetscTabulation *PetscTabulation;

483: #endif