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<HTML>
<HEAD><TITLE>MB03BB - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB03BB">MB03BB</A></H2>
<H3>
Eigenvalues of a 2-by-2 matrix product via a complex single shifted periodic QZ algorithm
</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 the eigenvalues of a general 2-by-2 matrix product via
a complex single shifted periodic QZ algorithm.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB03BB( BASE, LGBAS, ULP, K, AMAP, S, SINV, A, LDA1,
$ LDA2, ALPHAR, ALPHAI, BETA, SCAL, DWORK, INFO )
C .. Scalar Arguments ..
INTEGER INFO, K, LDA1, LDA2, SINV
DOUBLE PRECISION BASE, LGBAS, ULP
C .. Array Arguments ..
DOUBLE PRECISION A(LDA1,LDA2,*), ALPHAI(2), ALPHAR(2), BETA(2),
$ DWORK(*)
INTEGER AMAP(*), S(*), SCAL(2)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
</PRE>
<B>Input/Output Parameters</B>
<PRE>
BASE (input) DOUBLE PRECISION
Machine base.
LGBAS (input) DOUBLE PRECISION
Logarithm of BASE.
ULP (input) DOUBLE PRECISION
Machine precision.
K (input) INTEGER
The number of factors. K >= 1.
AMAP (input) INTEGER array, dimension (K)
The map for accessing the factors, i.e., if AMAP(I) = J,
then the factor A_I is stored at the J-th position in A.
S (input) INTEGER array, dimension (K)
The signature array. Each entry of S must be 1 or -1.
SINV (input) INTEGER
Signature multiplier. Entries of S are virtually
multiplied by SINV.
A (input) DOUBLE PRECISION array, dimension (LDA1,LDA2,K)
On entry, the leading 2-by-2-by-K part of this array must
contain a 2-by-2 product (implicitly represented by its K
factors) in upper Hessenberg-triangular form.
LDA1 INTEGER
The first leading dimension of the array A. LDA1 >= 2.
LDA2 INTEGER
The second leading dimension of the array A. LDA2 >= 2.
ALPHAR (output) DOUBLE PRECISION array, dimension (2)
On exit, this array contains the scaled real part of the
two eigenvalues. If BETA(I) <> 0, then the I-th eigenvalue
(I = 1 : 2) is given by
(ALPHAR(I) + ALPHAI(I)*SQRT(-1) ) * (BASE)**SCAL(I).
ALPHAI (output) DOUBLE PRECISION array, dimension (2)
On exit, this array contains the scaled imaginary part of
the two eigenvalues. ALPHAI(1) >= 0.
BETA (output) DOUBLE PRECISION array, dimension (2)
On exit, this array contains information about infinite
eigenvalues. If BETA(I) = 0, then the I-th eigenvalue is
infinite. Otherwise, BETA(I) = 1.0.
SCAL (output) INTEGER array, dimension (2)
On exit, this array contains the scaling exponents for the
two eigenvalues.
</PRE>
<B>Workspace</B>
<PRE>
DWORK DOUBLE PRECISION array, dimension (8*K)
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
= 1: the periodic QZ algorithm did not converge;
= 2: the computed eigenvalues might be inaccurate.
Both values might be taken as warnings, since
approximations of eigenvalues are returned.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
A complex single shifted periodic QZ iteration is applied.
</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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