`pagesvd`

Singular value decomposition of every page of a 3-D array.

Syntax

S = pagesvd(A)

Returns the singular values of each page A(:,:,k), in descending order.

[U, S, V] = pagesvd(A)

Returns the factors of each page, so that every page satisfies A(:,:,k) = U(:,:,k)*S(:,:,k)*V(:,:,k)'.

[U, S, V] = pagesvd(A, 'econ')

Computes the economy-size factors of each page.

Description

pagesvd applies svd independently to each m-by-n page of an m-by-n-by-p array. It avoids writing a loop over the third dimension and returns the results stacked in the same page order.

With one output the result is a stack of column vectors, which is convenient for comparing the spectra of many matrices at once.

Input arguments

A: Numeric array whose pages (the first two dimensions) are the matrices to decompose.
'econ': Optional flag that drops the singular vectors that do not correspond to a singular value.

Output arguments

S: With one output, an array of size min(m,n)-by-1-by-p holding the singular values of each page. With three outputs, the diagonal matrices of singular values, one per page.
U, V: Orthogonal (unitary) factors of each page.

Example

Singular values of two pages

A = cat(3, [1 2; 3 4], [2 0; 0 1]);
S = pagesvd(A);
disp(S(:,:,1)')
disp(S(:,:,2)')

Output

    5.4650    0.3660
     2     1

pagesvd