MATLAB Functions | Help Desk |
svd
Singular value decomposition
s = svd(X) [U,S,V] = svd(X) [U,S,V] = svd(X,0)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 m
-by-n
with m
> n
, then svd
computes only the first n
columns of U
and S
is n
-by-n
.
For the matrix
X = 1 2 3 4 5 6 7 8the statement
produces[U,S,V]
=
svd(X)
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 0.6414The economy size decomposition generated by
produces[U,S,V]
=
svd(X,0)
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 0.6414The
svd
command uses the LINPACK routine ZSVDC
.
If the limit of 75 QR step iterations is exhausted while seeking a singular value, this message appears:
Solution will not converge.[1] Dongarra, J.J., J.R. Bunch, C.B. Moler, and G.W. Stewart, LINPACK Users' Guide, SIAM, Philadelphia, 1979.