Re: Gallery (or circulant matrices)

[James Sherman Jr.]

On Fri, Jun 7, 2013 at 10:15 PM, Jeffrey <address@hidden> wrote:

Thanks, Markus. I'm afraid this didn't work. You can't subtract (1:length(v)) from (1:length(v))'. Did you mean to repmat them, somehow?

On Fri, Jun 7, 2013 at 9:13 PM, Markus Appel [via Octave] <[hidden email]> wrote:

On 06/08/2013 02:26 AM, Jeffrey wrote:

> Converting from Matlab, the "gallery" command to create circulant
> matrices is not implemented. Is there an Octave equivalent to
>
> K=gallery('circul',[4 -1 zeros(1,N-3) -1]);
>
> How does one find octave equivalents to Matlab statements? Thanks.

I can't answer the general question of how to find equivalents, but in
the special case of this matrix (and if i understood the 'circul'
gallery function right) you should be able to substitute

K=gallery('circul',v)

by

K = v( 1 + mod( (1:length(v))' - (1:length(v)), length(v)) )

The _expression_ is basically creating an index matrix with shifted
columns and picking the elements out of your input vector v in the right
order.

Hope it helps,
Markus
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Hi Jeffrey,

In newer versions of Octave (my guess is that you have an older version) there is a thing called broadcasting (http://www.gnu.org/software/octave/doc/interpreter/Broadcasting.html) which is probably why you had a problem and Markus didn't.  I was working on a very unelegant solution myself, but Markus beat me to it.  But here (I think) is another way to implement the circulant matrix that doesn't depend on broadcasting.  (But is far less nice than Markus's one).

function A = circul(v)

n = size(v,2);

A = zeros(n,n);

for index = 0:n-1,

A((0:(n-index-1))*(n+1)+index+1) = v(index+1);

A((0:(index-1))*(n+1)+n*(n-index)+1) = v(index+1);

endfor

endfunction

Or if you want to keep the same syntax as your matlab code, you can make a file called gallery.m put the function code in there, but replace the first line with something like:

function A = gallery(opt, v)

where opt would ostensibly be the string to choose other types of matrices? (I don't know the full behavior of gallery), but would just be ignored in this case.

Hope this helps.

James Sherman