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svd Scilab Group Scilab Function svd
NAME
svd - singular value decomposition
CALLING SEQUENCE
s=svd(X)
[U,S,V]=svd(X)
[U,S,V]=svd(X,0)
[U,S,V,rk]=svd(X [,tol])
PARAMETERS
X : a real or complex matrix
s : real vector (singular values)
S : real diagonal matrix (singular values)
U,V : orthogonal or unitary square matrices (singular vectors).
tol : real number
DESCRIPTION
produces a diagonal matrix S , of the same dimension as X and with
nonnegative diagonal elements in decreasing order, and unitary matrices
U and V so that X = U*S*V'.
decomposition. If X is m-by-n with m > n, then only the first n columns
of U are computed and S is n-by-n.
by itself, returns a vector s containing the singular values.
gives in addition rk, the numerical rank of X i.e. the number of
singular values larger than tol.
The default value of tol is the same as in rank.
EXAMPLE
X=rand(4,2)*rand(2,4)
svd(X)
sqrt(spec(X*X'))
SEE ALSO
rank, qr, colcomp, rowcomp, sva, spec
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