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<HTML>
<HEAD><TITLE>MB03BF - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB03BF">MB03BF</A></H2>
<H3>
Applying iterations of a real single shifted periodic QZ algorithm to a 2-by-2 matrix product, with Hessenberg factor the last one
</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 apply at most 20 iterations of a real single shifted
periodic QZ algorithm to the 2-by-2 product of matrices stored
in the array A. The Hessenberg matrix is the last one of the
formal matrix product.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB03BF( K, AMAP, S, SINV, A, LDA1, LDA2, ULP )
C .. Scalar Arguments ..
INTEGER K, LDA1, LDA2, SINV
DOUBLE PRECISION ULP
C .. Array Arguments ..
INTEGER AMAP(*), S(*)
DOUBLE PRECISION A(LDA1,LDA2,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
</PRE>
<B>Input/Output Parameters</B>
<PRE>
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/output) 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 form. The Hessenberg matrix
is the last one of the formal matrix product.
On exit, the leading 2-by-2-by-K part of this array
contains the product after at most 20 iterations of a real
shifted periodic QZ algorithm.
LDA1 INTEGER
The first leading dimension of the array A. LDA1 >= 2.
LDA2 INTEGER
The second leading dimension of the array A. LDA2 >= 2.
ULP INTEGER
The machine relation precision.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
Twenty iterations of a real single shifted periodic QZ algorithm
are applied to the 2-by-2 matrix product A.
</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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