CODEWITHSUNDEEP
matlablinear-algebra
user1956609
user1956609

Reputation: 2202

svds not working for some matrices - wrong result

Here is my testing function:

            function diff = svdtester()

            y = rand(500,20);
            [U,S,V] = svd(y);

            %{
            y = sprand(500,20,.1);
            [U,S,V] = svds(y);
            %}

            diff_mat = y - U*S*V';
            diff = mean(abs(diff_mat(:)));

            end

There are two very similar parts: one finds the SVD of a random matrix, the other finds the SVD of a random sparse matrix. Regardless of which one you choose to comment (right now the second one is commented-out), we compute the difference between the original matrix and the product of its SVD components and return that average absolute difference.

When using rand/svd, the typical return (mean error) value is around 8.8e-16, basically zero. When using sprand/svds, the typical return values is around 0.07, which is fairly terrible considering the sparse matrix is 90% 0's to start with.

Am I misunderstanding how SVD should work for sparse matrices, or is something wrong with these functions?

Upvotes: 1

Views: 1513

Answers (1)

vharavy
vharavy

Reputation: 4991

Yes, the behavior of svds is a little bit different from svd. According to MATLAB's documentation:

[U,S,V] = svds(A,...) returns three output arguments, and if A is m-by-n:

U is m-by-k with orthonormal columns

S is k-by-k diagonal

V is n-by-k with orthonormal columns

U*S*V' is the closest rank k approximation to A

In fact, usually k will be somethings about 6, so you will get rather "rude" approximation. To get more exact approximation specify k to be min(size(y)):

[U, S, V] = svds(y, min(size(y)))

and you will get error of the same order of magnitude as in case of svd.

P.S. Also, MATLAB's documentations says:

Note svds is best used to find a few singular values of a large, sparse matrix. To find all the singular values of such a matrix, svd(full(A)) will usually perform better than svds(A,min(size(A))).

Upvotes: 8

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