MATLAB Central Newsreader - Vectorizing Specific Access to Multidimensional Array

Vectorizing Specific Access to Multidimensional Array

First Last — Sun, 14 Sep 2008 06:08:03 -0400

Let's say I have a NxMxL array X where N = M = L = 2:

X(:,:,1) =

1 3
2 4

X(:,:,2) =

5 7
6 8

For each vector along L ([1 5], [3 7], etc.), I want to pick a random element of it (in this case either the first or second element). One 'dumb' way of doing this is:

z = zeros(2,2,2);

for n = 1:N
     for m = 1:M
          v = floor(1 + 2 * rand(1,1));
          z(n,m,v) = 1;
     end
end

The resulting matrix z will end up looking something like, say:

z(:,:,1) =

1 0
0 1

z(:,:,2) =

0 1
1 0

and X .* z is

(:,:,1) =

1 0
0 4

(:,:,2) =

0 7
6 0

so that sum(X .* z,3) =

1 7
6 4

Is there any way to create a random matrix z directly so that I can avoid those loops?

Better yet, is there a way to read a random matrix R that has the elements

R = floor(1 + 2 * rand(2,2));

which might look like

1 2
2 1

that I could use to directly access elements of X, using R along the dimension L?

I realize this may be very confusing. Of course I'm happy to clarify anything I can. Thanks.

Re: Vectorizing Specific Access to Multidimensional Array

Bruno Luong — Sun, 14 Sep 2008 06:48:02 -0400

"First Last" <nospam@nospamplease.com> wrote in message <gai9o3$fer$1@fred.mathworks.com>...

Not sure if this is what you want. The function that you need is "sub2ind".

% Data
M=3; N=4; L=5;
X=ceil(10*rand(M,N,L));

[i j]=ndgrid(1:M,1:N);
% random pick of index from to L
k = floor(1 + L * rand(size(i)));
k(k>L) = L; % clip incase rand returns "1"

linind = sub2ind(size(X),i(:),j(:),k(:));

% Generate z
z=zeros(size(X));
z(linind)=1;
sum(X.*z,3)

% Access X directly
Y = X(reshape(linind,size(i)))

% Bruno

Re: Vectorizing Specific Access to Multidimensional Array

Bruno Luong — Sun, 14 Sep 2008 07:09:02 -0400

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <gaic32$st9$1@fred.mathworks.com>...

> k = floor(1 + L * rand(size(i)));
> k(k>L) = L; % clip in case RAND returns "1"
>

Note: the clipping statement might not be necessary, as rand never return 1. The floor(L*(1-eps)) always returns L-1 is something I wasn't sure, but this might be right. Someone can confirm?

Bruno

Re: Vectorizing Specific Access to Multidimensional Array

First Last — Sun, 14 Sep 2008 07:46:02 -0400

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <gaic32$st9$1@fred.mathworks.com>...
> "First Last" <nospam@nospamplease.com> wrote in message <gai9o3$fer$1@fred.mathworks.com>...
>
> Not sure if this is what you want. The function that you need is "sub2ind".
>
> % Data
> M=3; N=4; L=5;
> X=ceil(10*rand(M,N,L));
>
> [i j]=ndgrid(1:M,1:N);
> % random pick of index from to L
> k = floor(1 + L * rand(size(i)));
> k(k>L) = L; % clip incase rand returns "1"
>
> linind = sub2ind(size(X),i(:),j(:),k(:));
>
> % Generate z
> z=zeros(size(X));
> z(linind)=1;
> sum(X.*z,3)
>
> % Access X directly
> Y = X(reshape(linind,size(i)))
>
> % Bruno

This solution is perfect. Thanks very much. You have saved my department's electricity bill and my sanity!