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<HTML>
<HEAD><TITLE>TG01OB - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="TG01OB">TG01OB</A></H2>
<H3>
Unitary equivalence transformation of a complex SISO descriptor system with E upper triangular, so that B becomes parallel to the first unit vector and E keeps its structure
</H3>
<A HREF ="#Specification"><B>[Specification]</B></A>
<A HREF ="#Arguments"><B>[Arguments]</B></A>
<A HREF ="#Method"><B>[Method]</B></A>
<A HREF ="#References"><B>[References]</B></A>
<A HREF ="#Comments"><B>[Comments]</B></A>
<A HREF ="#Example"><B>[Example]</B></A>
<P>
<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
To compute for a single-input single-output descriptor system,
given by the system matrix
[ D C ]
[ B A - s*E ],
with E upper triangular, a transformed system, (Q'*A*Z, Q'*E*Z,
Q'*B, C*Z), via an orthogonal equivalence transformation, so that
Q'*B has only the first element nonzero and Q'*E*Z remains upper
triangular. The matrices have complex elements.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE TG01OB( JOBE, N, DCBA, LDDCBA, E, LDE, INFO )
C .. Scalar Arguments ..
CHARACTER JOBE
INTEGER INFO, LDDCBA, LDE, N
C .. Array Arguments ..
COMPLEX*16 DCBA(LDDCBA,*), E(LDE,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
JOBE CHARACTER*1
Specifies whether E is an upper triangular or an identity
matrix, as follows:
= 'U': The matrix E is an upper triangular matrix;
= 'I': The matrix E is assumed identity and is not given.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The dimension of the descriptor state vector; also the
order of square matrices A and E, the number of rows of
matrix B, and the number of columns of matrix C. N >= 0.
DCBA (input/output) COMPLEX*16 array, dimension (LDDCBA,N+1)
On entry, the leading (N+1)-by-(N+1) part of this array
must contain the original system matrices A, B, C, and D,
stored as follows
[ D C ]
[ B A ].
On exit, the leading (N+1)-by-(N+1) part of this array
contains the transformed matrices C*Z, Q'*B, and Q'*A*Z,
replacing C, B, and A. The scalar D is unchanged.
LDDCBA INTEGER
The leading dimension of the array DCBA.
LDDCBA >= N+1.
E (input/output) COMPLEX*16 array, dimension (LDE,*)
On entry, if JOBE = 'U', the leading N-by-N upper
triangular part of this array must contain the upper
triangular part of the descriptor matrix E. The lower
triangular part under the first subdiagonal is not
referenced.
On exit, if JOBE = 'U', the leading N-by-N upper
triangular part of this array contains the upper
triangular part of the transformed descriptor matrix,
Q'*E*Z.
If JOBE = 'I', this array is not referenced.
LDE INTEGER
The leading dimension of the array E.
LDE >= MAX(1,N), if JOBE = 'U';
LDE >= 1, if JOBE = 'I'.
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
Givens rotations are used to annihilate the last N-1 elements of B
in reverse order, but preserve the form of E.
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
The algorithm is numerically backward stable.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
None
</PRE>
<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
<P>
<B>Program Text</B>
<PRE>
None
</PRE>
<B>Program Data</B>
<PRE>
None
</PRE>
<B>Program Results</B>
<PRE>
None
</PRE>
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