petsc-main 2021-04-20
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# PetscDTAltVStar

Apply a power of the Hodge star operator, which maps k-forms to (N-k) forms, to a k-form

### Synopsis

```#include "petscdt.h"
PetscErrorCode PetscDTAltVStar(PetscInt N, PetscInt k, PetscInt pow, const PetscReal *w, PetscReal *starw)
```

### Input Arguments

 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]

### Output Arguments

 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.