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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="PetscDTAltVPullback"><H1>PetscDTAltVPullback</H1></A>
Compute the pullback of a k-form under a linear transformation of the coordinate space
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petscdt.h"
<A HREF="../Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</A> <A HREF="../DT/PetscDTAltVPullback.html#PetscDTAltVPullback">PetscDTAltVPullback</A>(<A HREF="../Sys/PetscInt.html#PetscInt">PetscInt</A> N, <A HREF="../Sys/PetscInt.html#PetscInt">PetscInt</A> M, const <A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> *L, <A HREF="../Sys/PetscInt.html#PetscInt">PetscInt</A> k, const <A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> *w, <A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> *Lstarw)
</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 origin vector space of the linear transformation, M >= 0
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>M </B></TD><TD>- the dimension of the image vector space of the linear transformation, N >= 0
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>L </B></TD><TD>- a linear transformation, an [M x N] matrix in row-major format
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>k </B></TD><TD>- the *signed* degree k of the |k|-form w, -(min(M,N)) <= k <= min(M,N). A negative form degree indicates that the pullback should be conjugated by the Hodge star operator (see note).
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>w </B></TD><TD>- a |k|-form in the image space, size [M 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>Lstarw </B></TD><TD>- the pullback of w to a |k|-form in the origin space, size [N choose |k|]: (Lstarw)(v_1,...v_k) = w(L*v_1,...,L*v_k).
</TD></TR></TABLE>
<P>
<P>
Note: negative form degrees accomodate, e.g., H-div conforming vector fields. An H-div conforming vector field stores its degrees of freedom as (dx, dy, dz), like a 1-form,
but its normal trace is integrated on faces, like a 2-form. The correct pullback then is to apply the Hodge star transformation from (M-2)-form to 2-form, pullback as a 2-form,
then the inverse Hodge star transformation.
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../DT/PetscDTAltV.html#PetscDTAltV">PetscDTAltV</A>, <A HREF="../DT/PetscDTAltVPullbackMatrix.html#PetscDTAltVPullbackMatrix">PetscDTAltVPullbackMatrix</A>(), <A HREF="../DT/PetscDTAltVStar.html#PetscDTAltVStar">PetscDTAltVStar</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#PetscDTAltVPullback">src/dm/dt/interface/dtaltv.c</A>
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