Initializing matrix randomly and by sample

Hi

I have a matrix X with size m x n and a matrix U with size m x k where k >> n.

Now first I want to fill the columns of matrix U with random columns of matrix X. How can I do that efficiently? Just make a permutation of the columns of X is not possible because there are much more columns in U than in X.

Second I want fill the columns of U with random unit length vectors. How can I do this efficiently? I think just looping over all columns in U and creating a random vector is inefficient.

Answer 1

[Image Analyst]

Try this:

% Create sample data.
x = randi(4, [3,4]);
u = zeros([3,20]);
% Get the two sizes.
[rowsx, colsx] = size(x)
[rowsu, colsu] = size(u)
% Get list of random columns of x to transfer to u.
xColsToUse = randi(colsx, [colsu, 1])
% Transfer columns of x to u
u(:, 1:colsu) = x(:, xColsToUse)

Answer 2

[the cyclist]

First one:

If you have the Statistics Toolbox, you can use

U = X(:,randsample(m,k,'true'))

If not, you can use the randi() function to accomplish the same thing.

Answer 3

[Roger Stafford]

For the first question use 'randi'

 p = randi(n,1,k);
 U = X(:,p);

For the second, very different, question do:

 U = randn(m,k);
 U = bsxfun(@rdivide,U,sqrt(sum(U.^2,1)));