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.TH svd G "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
svd - singular value decomposition
.SH CALLING SEQUENCE
.nf
s=svd(X)
[U,S,V]=svd(X)
[U,S,V]=svd(X,0)
[U,S,V,rk]=svd(X [,tol])
.fi
.SH PARAMETERS
.TP 10
X
: a real or complex matrix
.TP
s
: real vector (singular values)
.TP
S
: real diagonal matrix (singular values)
.TP
U,V
: orthogonal or unitary square matrices (singular vectors).
.TP
tol
: real number
.SH DESCRIPTION
.Vb [U,S,V] = svd(X)
produces a diagonal matrix \fVS\fR , of the same
dimension as \fVX\fR and with nonnegative diagonal elements in
decreasing order, and unitary matrices \fVU\fR and \fVV\fR so that
\fVX = U*S*V'\fR.
.LP
.Vb [U,S,V] = svd(X,0) produces the "economy size"
decomposition. If \fVX\fR is m-by-n with m > n, then only the
first n columns of \fVU\fR are computed and \fVS\fR is n-by-n.
.LP
.Vb s = svd(X)
by itself, returns a vector \fVs\fR containing the singular values.
.LP
.Vb [U,S,V,rk]=svd(X,tol)
gives in addition \fVrk\fR, the numerical rank of \fVX\fR i.e. the number of
singular values larger than \fVtol\fR.
.LP
The default value of \fVtol\fR is the same as in \fVrank\fR.
.SH EXAMPLE
.nf
X=rand(4,2)*rand(2,4)
svd(X)
sqrt(spec(X*X'))
.fi
.SH SEE ALSO
rank, qr, colcomp, rowcomp, sva, spec
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