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.TH equil1 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
equil1 - balancing (nonnegative) pair of matrices
.SH CALLING SEQUENCE
.nf
[T [,siz]]=equil1(P,Q [,tol])
.fi
.SH PARAMETERS
.TP 10
P, Q
: two non-negative symmetric matrices
.TP
T
: nonsingular matrix
.TP
siz
: vector of three integers
.TP
tol
: threshold
.SH DESCRIPTION
\fVequil1\fR computes \fVt\fR such that:
.LP
\fVP1=T*P*T'\fR and \fVQ1=inv(T)'*Q*inv(T)\fR are as follows:
.LP
\fVP1 = diag(S1,S2,0,0)\fR and \fVQ1 = diag(S1,0,S3,0)\fR with
\fVS1,S2,S3\fR positive and diagonal matrices with respective
dimensions \fVsiz=[n1,n2,n3]\fR
.LP
\fVtol\fR is a threshold for rank determination in SVD
.SH EXAMPLE
.nf
S1=rand(2,2);S1=S1*S1';
S2=rand(2,2);S2=S2*S2';
S3=rand(2,2);S3=S3*S3';
P=sysdiag(S1,S2,zeros(4,4));
Q=sysdiag(S1,zeros(2,2),S3,zeros(2,2));
X=rand(8,8);
P=X*P*X';Q=inv(X)'*Q*inv(X);
[T,siz]=equil1(P,Q);
P1=clean(T*P*T')
Q1=clean(inv(T)'*Q*inv(T))
.fi
.SH SEE ALSO
balreal, minreal, equil, hankelsv
.SH AUTHOR
S. Steer 1987
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