Singular value decomposition
s = svd(X)
[U,S,V] = svd(X)
[U,S,V] = svd(X,0)
[U,S,V] = svd(X,'econ')
The svd command computes the matrix singularvalue decomposition.
s = svd(X) returns a vectorof singular values.
[U,S,V] = svd(X) producesa diagonal matrix S of the same dimension as X,with nonnegative diagonal elements in decreasing order, and unitarymatrices U and V so that X= U*S*V'.
[U,S,V] = svd(X,0) producesthe "economy size" decomposition. If X ism-by-n with m > n, then svd computes onlythe first n columns of U and S isn-by-n.
[U,S,V] = svd(X,'econ') also produces the"economy size" decomposition. If X ism-by-n with m >= n, it is equivalent to svd(X,0).For m < n, only the first m columns of V arecomputed and S is m-by-m.
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
If the limit of 75 QR step iterations is exhausted while seekinga singular value, this message appears:
Solution will not converge.