#include "petscdt.h" PetscErrorCode PetscDTAltVStar(PetscInt N, PetscInt k, PetscInt pow, const PetscReal *w, PetscReal *starw)
| N | - the dimension of the vector space, N >= 0 | |
| k | - the degree k of the k-form w, 0 <= k <= N | |
| pow | - the number of times to apply the Hodge star operator: pow < 0 indicates that the inverse of the Hodge star operator should be applied |pow| times. | |
| w | - a k-form, size [N choose k] |
| starw = (star)^pow w. Each degree of freedom of a k | - form is associated with a subset S of k coordinates of the N dimensional vector space: the Hodge start operator (star) maps that degree of freedom to the degree of freedom associated with S', the complement of S, with a sign change if the permutation of coordinates {S[0], ... S[k-1], S'[0], ... S'[N-k- 1]} is an odd permutation. This implies (star)^2 w = (-1)^{k(N-k)} w, and (star)^4 w = w. |