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<div id="version" align=right><b>petsc-3.14.5 2021-03-03</b></div>
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<A NAME="PetscDTAltVStar"><H1>PetscDTAltVStar</H1></A>
Apply a power of the Hodge star operator, which maps k-forms to (N-k) forms, to a k-form
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petscdt.h"
<A HREF="../Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</A> <A HREF="../DT/PetscDTAltVStar.html#PetscDTAltVStar">PetscDTAltVStar</A>(<A HREF="../Sys/PetscInt.html#PetscInt">PetscInt</A> N, <A HREF="../Sys/PetscInt.html#PetscInt">PetscInt</A> k, <A HREF="../Sys/PetscInt.html#PetscInt">PetscInt</A> pow, const <A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> *w, <A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> *starw)
</PRE>
<H3><FONT COLOR="#CC3333">Input Arguments</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>N </B></TD><TD>- the dimension of the vector space, N >= 0
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>k </B></TD><TD>- the degree k of the k-form w, 0 <= k <= N
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>pow </B></TD><TD>- 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.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>w </B></TD><TD>- a k-form, size [N choose k]
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Output Arguments</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>starw = (star)^pow w. Each degree of freedom of a k</B></TD><TD>- 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.
</TD></TR></TABLE>
<P>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../DT/PetscDTAltV.html#PetscDTAltV">PetscDTAltV</A>, <A HREF="../DT/PetscDTAltVPullback.html#PetscDTAltVPullback">PetscDTAltVPullback</A>(), <A HREF="../DT/PetscDTAltVPullbackMatrix.html#PetscDTAltVPullbackMatrix">PetscDTAltVPullbackMatrix</A>()
<BR><P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>intermediate<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/dm/dt/interface/dtaltv.c.html#PetscDTAltVStar">src/dm/dt/interface/dtaltv.c</A>
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