MATLAB Function Reference 
Syntax
Description
The svd
command computes the matrix singular value decomposition.
s = svd(X)
returns a vector of singular values.
[U,S,V] = svd(X)
produces a diagonal matrix S
of the same dimension as X
, with nonnegative diagonal elements in decreasing order, and unitary matrices U
and V
so that X
=
U*S*V'.
[U,S,V] = svd(X,0)
produces the "economy size" decomposition. If X
is mbyn with m > n, then svd
computes only the first n
columns of U
and S
is nbyn.
[U,S,V] = svd(X,'econ')
also produces the "economy size" decomposition. If X
is mbyn with m >= n, it is equivalent to svd(X,0)
. For m < n, only the first m columns of V
are computed and S
is mbym.
Examples
U = 0.1525 0.8226 0.3945 0.3800 0.3499 0.4214 0.2428 0.8007 0.5474 0.0201 0.6979 0.4614 0.7448 0.3812 0.5462 0.0407 S = 14.2691 0 0 0.6268 0 0 0 0 V = 0.6414 0.7672 0.7672 0.6414
The economy size decomposition generated by
U = 0.1525 0.8226 0.3499 0.4214 0.5474 0.0201 0.7448 0.3812 S = 14.2691 0 0 0.6268 V = 0.6414 0.7672 0.7672 0.6414
Algorithm
svd
uses the LAPACK routines listed in the following table to compute the singular value decomposition.
Real 
Complex 

X double 
DGESVD 
ZGESVD 
X single 
SGESVD 
CGESVD 
Diagnostics
If the limit of 75 QR step iterations is exhausted while seeking a singular value, this message appears:
References
[1] Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK User's Guide (http://www.netlib.org/lapack/lug/lapack_lug.html), Third Edition, SIAM, Philadelphia, 1999.
surfnorm  svds 
© 19942005 The MathWorks, Inc.