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.TH fullrf 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
fullrf - full rank factorization
.SH CALLING SEQUENCE
.nf
[Q,M,rk]=fullrf(A,[tol])
.fi
.SH PARAMETERS
.TP 4
A
: real or complex matrix
.TP
tol
: real number (threshold for rank determination)
.TP
Q,M
: real or complex matrix
.TP
rk
: integer (rank of \fVA\fR)
.SH DESCRIPTION
Full rank factorization : \fVfullrf\fR returns \fVQ\fR and \fVM\fR such
that \fVA = Q*M\fR
with range(\fVQ\fR)=range(\fVA\fR) and ker(\fVM\fR)=ker(\fVA\fR),
\fVQ\fR full column rank , \fVM\fR full row rank,
\fVrk\fR = rank(\fVA\fR) = #columns(\fVQ\fR) = #rows(\fVM\fR).
.LP
\fVtol\fR is an optional real parameter (default value is \fVsqrt(%eps)\fR).
The rank \fVrk\fR of \fVA\fR is defined as the number of singular values
larger than \fVnorm(A)*tol\fR.
.LP
If A is symmetric, \fVfullrf\fR returns \fVM=Q'\fR.
.SH EXAMPLE
.nf
A=rand(5,2)*rand(2,5);
[Q,M]=fullrf(A);
norm(Q*M-A,1)
[X,d]=rowcomp(A);Y=X';
svd([A,Y(:,1:d),Q]) //span(Q) = span(A) = span(Y(:,1:2))
.fi
.SH SEE ALSO
svd, qr, fullrfk, rowcomp, colcomp
.SH AUTHOR
F.D.
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