svds (MATLAB Functions)

A few singular values

Syntax

s = svds(A)
s = svds(A,k)
s = svds(A,k,0)
[U,S,V] = svds(A,...)

Description

svds(A) computes the five largest singular values and associated singular vectors of the matrix A.

svds(A,k) computes the k largest singular values and associated singular vectors of the matrix A.

svds(A,k,0) computes the k smallest singular values and associated singular vectors.

With one output argument, s is a vector of singular values. With 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

Algorithm

svds(A,k) uses eigs to find the k largest magnitude eigenvalues and corresponding eigenvectors of B = [0 A; A' 0].

svds(A,k,0) uses eigs to find the 2k smallest magnitude eigenvalues and corresponding eigenvectors of B = [0 A; A' 0], and then selects the k positive eigenvalues and their eigenvectors.

Example

west0479 is a real 479-by-479 sparse matrix. svd calculates all 479 singular values. svds picks out the largest and smallest singular values.

load west0479
s = svd(full(west0479))
sl = svds(west0479,4)
ss = svds(west0479,6,0)

These plots show some of the singular values of west0479 as computed by svd and svds.

The largest singular value of west0479 can be computed a few different ways:

svds(west0479,1) =
 3.189517598808622e+05
max(svd(full(west0479))) =
 3.18951759880862e+05
norm(full(west0479)) =
 3.189517598808623e+05

and estimated:

normest(west0479) =
 3.189385666549991e+05

See Also

svd, eigs

svd switch