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<HTML>
<HEAD><TITLE>MB04DB - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB04DB">MB04DB</A></H2>
<H3>
Inverse of a balancing transformation for a real skew-Hamiltonian/Hamiltonian pencil
</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 from the left the inverse of a balancing transformation,
computed by the SLICOT Library routine MB04DP, to the matrix
[ V1 ]
[ ],
[ sgn*V2 ]
where sgn is either +1 or -1.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB04DB( JOB, SGN, N, ILO, LSCALE, RSCALE, M, V1, LDV1,
$ V2, LDV2, INFO )
C .. Scalar Arguments ..
CHARACTER JOB, SGN
INTEGER ILO, INFO, LDV1, LDV2, M, N
C .. Array Arguments ..
DOUBLE PRECISION LSCALE(*), RSCALE(*), V1(LDV1,*), V2(LDV2,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
JOB CHARACTER*1
Specifies the type of inverse transformation required:
= 'N': do nothing, return immediately;
= 'P': do inverse transformation for permutation only;
= 'S': do inverse transformation for scaling only;
= 'B': do inverse transformations for both permutation
and scaling.
JOB must be the same as the argument JOB supplied to
MB04DP.
SGN CHARACTER*1
Specifies the sign to use for V2:
= 'P': sgn = +1;
= 'N': sgn = -1.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The number of rows of the matrices V1 and V2. N >= 0.
ILO (input) INTEGER
The integer ILO determined by MB04DP.
1 <= ILO <= N+1.
LSCALE (input) DOUBLE PRECISION array, dimension (N)
Details of the permutation and scaling factors applied
from the left, as returned by MB04DP.
RSCALE (input) DOUBLE PRECISION array, dimension (N)
Details of the permutation and scaling factors applied
from the right, as returned by MB04DP.
M (input) INTEGER
The number of columns of the matrices V1 and V2. M >= 0.
V1 (input/output) DOUBLE PRECISION array, dimension (LDV1,M)
On entry, the leading N-by-M part of this array must
contain the matrix V1.
On exit, the leading N-by-M part of this array is
overwritten by the updated matrix V1 of the transformed
matrix.
LDV1 INTEGER
The leading dimension of the array V1. LDV1 >= max(1,N).
V2 (input/output) DOUBLE PRECISION array, dimension (LDV2,M)
On entry, the leading N-by-M part of this array must
contain the matrix V2.
On exit, the leading N-by-M part of this array is
overwritten by the updated matrix V2 of the transformed
matrix.
LDV2 INTEGER
The leading dimension of the array V2. LDV2 >= max(1,N).
</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="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
[1] Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J.,
Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A.,
Ostrouchov, S., and Sorensen, D.
LAPACK Users' Guide: Second Edition.
SIAM, Philadelphia, 1995.
[2] Benner, P.
Symplectic balancing of Hamiltonian matrices.
SIAM J. Sci. Comput., 22 (5), pp. 1885-1904, 2001.
</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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