在matlab中沿第3轴复制2d矩阵多次

Question

I'm looking to duplication a 784x784 matrix in matlab along a 3rd axis. The following code seems to work:

mat = reshape(repmat(mat, 1,10000),784,784,10000);

Unfortunately, it takes so long to run it's worthless (changing the 10,000s to 1000 makes it take a few minutes, and using 10,000 makes my whole machine freeze up practically). is there a faster way to do this?

For reference, I'm looking to use mvnpdf on 10,000 vectors each of length 784, using the same covariance matrix for each. So my final call looks like

mvnpdf(X,mu,mat)  

%size(X) = (10000,784), size(mu) = (10000,784), size(mat) = 784,784,10000

If there's a way to do this that's not repeating the covariance matrix 10,000 times, that'd be helpful too. Thanks!

Answer 1

对于超过2个维度的复制，您需要将复制计数作为数组提供：

out = repmat(mat,[1,1,10000])

Answer 2

Creating a 784x784 matrix 10,000 times isn't going to take advantage of the vectorization in MATLAB, which is going to be more useful for small arrays. Avoiding a for loop also won't help too much, given the following:

The main speedup you can gain here is by computing the inverse of the covariance matrix once, and then computing the pdf yourself. The inverse of sigma takes O(n^3), and you are needlessly doing that 10,000 times. (Also, the square root determinant can be precomputed.) For reference, the PDF of the multivariate normal distribution is computed as follows:

http://en.wikipedia.org/wiki/Multivariate_normal_distribution#Properties

Better to just compute the inverse once, and then compute z = x - mu for each value, then doing z'Sz for each pdf value, and applying a simple function and a constant. But wait! You can vectorize that, too.

I don't have MATLAB in front of me, but this is basically what you need to do, and it'll run in an instant.

s = inv(sigma);
c = -0.5*log(det(s)) - (k/2)*log(2*pi);
z = x - mu;                   % 10000 x 784 matrix
ans = exp( c - 0.5 .* dot(z*s, z, 2) ); % 10000 x 1 vector