L()

function out=L(in)

Input:

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

Global variables:

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

Output:

• out: L operator applied to in, where ${\bf L}=-\left(\mbox{det\,}{\bf R}\right) \left(\mbox{\bf Diag\,}G2\right)$

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

Hint: Do not form the matrix L directly. Rather, use the fact that, in octave, a.*b produces a vector of the products of the corresponding elements of a and b.

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

in=randn(prod(S),1); %# Create a random d=3 dimensional column vector
out=L(in); %# Apply O to in and store result in out
[out./in, -det(R)*G2] %# Compare ratio of out to in to -det(R)*G2