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.TH rowshuff 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
rowshuff - shuffle algorithm
.SH CALLING SEQUENCE
.nf
[Ws,Fs1]=rowshuff(Fs, [alfa])
.fi
.SH PARAMETERS
.TP 5
Fs
: square real pencil \fVFs = s*E-A\fR
.TP
Ws
: polynomial matrix
.TP
Fs1
: square real pencil \fVF1s = s*E1 -A1\fR with \fVE1\fR non-singular
.TP
alfa
: real number (\fValfa = 0\fR is the default value)
.SH DESCRIPTION
Shuffle algorithm: Given the pencil \fVFs=s*E-A \fR, returns Ws=W(s)
(square polynomial matrix) such that:
.LP
\fV Fs1 = s*E1-A1 = W(s)*(s*E-A) \fR is a pencil with non singular \fVE1\fR matrix.
.LP
This is possible iff the pencil \fVFs = s*E-A \fR is regular (i.e. invertible).
The degree of \fVWs\fR is equal to the index of the pencil.
.LP
The poles at infinity of \fVFs\fR are put to \fValfa\fR and the zeros of \fVWs\fR are at \fValfa\fR.
.LP
Note that \fV(s*E-A)^-1 = (s*E1-A1)^-1 * W(s) = (W(s)*(s*E-A))^-1 *W(s)\fR
.SH EXAMPLE
.nf
F=randpencil([],[2],[1,2,3],[]);
F=rand(5,5)*F*rand(5,5); // 5 x 5 regular pencil with 3 evals at 1,2,3
[Ws,F1]=rowshuff(F,-1);
[E1,A1]=pen2ea(F1);
svd(E1) //E1 non singular
roots(det(Ws))
clean(inv(F)-inv(F1)*Ws,1.d-7)
.fi
.SH SEE ALSO
pencan, glever, penlaur
.SH AUTHOR
F. D.
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