Linv()

function out=Linv(in)

Input:

• in: $d=3$ dimensional data stored as an $\prod S_k\,\times\,1$ vector

Global variables:

• gbl_R: lattice vectors R
• gbl_G2: lengths squared of G vectors

Output:

• out: inverse of L operator applied to in, where ${\bf L}=-\left(\mbox{det\,}{\bf R}\right) \left(\mbox{\bf Diag\,}G2\right)$ and, by convention, out(1)$\equiv$0.

Using your software for ``L.m'' as an example, create a file called ``Linv.m'' containing software for a function Linv() of the above specification.

Hint: Do not form the matrix L$^{-1}$ directly. Rather, use the fact that a./b produces a vector of the ratios of the corresponding elements of a and b.

To verify your Linv() operator, execute the following at the octave prompt,

in=randn(prod(S),1); %# Create a random d=3 dimensional column vector
Linv(L(in))./in %# Check ratio of Linv applied to L(in) to in