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<HTML>
<HEAD><TITLE>MB03CZ - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB03CZ">MB03CZ</A></H2>
<H3>
Exchanging eigenvalues of a complex 2-by-2 upper triangular pencil (factored version)
</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 unitary matrices Q1, Q2, and Q3 for a complex 2-by-2
regular pencil aAB - bD, with A, B, D upper triangular, such that
Q3' A Q2, Q2' B Q1, Q3' D Q1 are still upper triangular, but the
eigenvalues are in reversed order. The matrices Q1, Q2, and Q3 are
represented by
( CO1 SI1 ) ( CO2 SI2 ) ( CO3 SI3 )
Q1 = ( ), Q2 = ( ), Q3 = ( ).
( -SI1' CO1 ) ( -SI2' CO2 ) ( -SI3' CO3 )
The notation M' denotes the conjugate transpose of the matrix M.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB03CZ( A, LDA, B, LDB, D, LDD, CO1, SI1, CO2, SI2,
$ CO3, SI3 )
C .. Scalar Arguments ..
INTEGER LDA, LDB, LDD
DOUBLE PRECISION CO1, CO2, CO3
COMPLEX*16 SI1, SI2, SI3
C .. Array Arguments ..
COMPLEX*16 A( LDA, * ), B( LDB, * ), D( LDD, * )
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
</PRE>
<B>Input/Output Parameters</B>
<PRE>
A (input) COMPLEX*16 array, dimension (LDA, 2)
On entry, the leading 2-by-2 upper triangular part of
this array must contain the matrix A of the pencil.
The (2,1) entry is not referenced.
LDA INTEGER
The leading dimension of the array A. LDA >= 2.
B (input) COMPLEX*16 array, dimension (LDB, 2)
On entry, the leading 2-by-2 upper triangular part of
this array must contain the matrix B of the pencil.
The (2,1) entry is not referenced.
LDB INTEGER
The leading dimension of the array B. LDB >= 2.
D (input) COMPLEX*16 array, dimension (LDD, 2)
On entry, the leading 2-by-2 upper triangular part of
this array must contain the matrix D of the pencil.
The (2,1) entry is not referenced.
LDD INTEGER
The leading dimension of the array D. LDD >= 2.
CO1 (output) DOUBLE PRECISION
The upper left element of the unitary matrix Q1.
SI1 (output) COMPLEX*16
The upper right element of the unitary matrix Q1.
CO2 (output) DOUBLE PRECISION
The upper left element of the unitary matrix Q2.
SI2 (output) COMPLEX*16
The upper right element of the unitary matrix Q2.
CO3 (output) DOUBLE PRECISION
The upper left element of the unitary matrix Q3.
SI3 (output) COMPLEX*16
The upper right element of the unitary matrix Q3.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
The algorithm uses unitary transformations as described on page 37
in [1].
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
[1] Benner, P., Byers, R., Mehrmann, V. and Xu, H.
Numerical Computation of Deflating Subspaces of Embedded
Hamiltonian Pencils.
Tech. Rep. SFB393/99-15, Technical University Chemnitz,
Germany, June 1999.
</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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