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