`svds`

A few singular values and vectors of a matrix, typically a large sparse one.

Syntax

s = svds(A)

Returns the 6 largest singular values.

s = svds(A, k)

Returns the k largest singular values.

s = svds(A, k, sigma)

Returns k values selected by sigma: 'largest', 'smallest', or the ones closest to a number.

[U, S, V] = svds(___)

Also returns the corresponding singular vectors.

Description

For big matrices a full svd is wasteful when only the dominant part of the spectrum matters. svds computes just the requested subset, which is what low-rank approximation and principal component methods need.

If k is at least min(size(A)) there is no saving, and svd is the better call.

Input arguments

A: Numeric matrix, dense or sparse.
k: Number of singular values wanted. Default 6.
sigma: 'largest' (default), 'smallest', or a scalar target.

Output arguments

s: Column vector of the requested singular values.
U, S, V: Singular vectors (m-by-k, n-by-k) and the diagonal k-by-k matrix of values.

Example

Largest and smallest

A = diag(1:10);
svds(A, 3)
svds(A, 2, 'smallest')

Output

svds