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<HTML>
<HEAD><TITLE>MB02RZ - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB02RZ">MB02RZ</A></H2>
<H3>
Solution of a system of linear equations with complex upper Hessenberg matrix
</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 solve a system of linear equations
H * X = B, H' * X = B or H**H * X = B
with a complex upper Hessenberg N-by-N matrix H using the LU
factorization computed by MB02SZ.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB02RZ( TRANS, N, NRHS, H, LDH, IPIV, B, LDB, INFO )
C .. Scalar Arguments ..
CHARACTER TRANS
INTEGER INFO, LDB, LDH, N, NRHS
C .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX*16 B( LDB, * ), H( LDH, * )
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
TRANS CHARACTER*1
Specifies the form of the system of equations:
= 'N': H * X = B (No transpose)
= 'T': H'* X = B (Transpose)
= 'C': H**H * X = B (Conjugate transpose)
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the matrix H. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of
columns of the matrix B. NRHS >= 0.
H (input) COMPLEX*16 array, dimension (LDH,N)
The factors L and U from the factorization H = P*L*U
as computed by MB02SZ.
LDH INTEGER
The leading dimension of the array H. LDH >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indices from MB02SZ; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).
B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) 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>
The routine uses the factorization
H = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (and one nonzero subdiagonal), and U is upper
triangular.
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
-
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE> 2
The algorithm requires 0( N x NRHS ) complex operations.
</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>
<HR>
<p>
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