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<HTML>
<HEAD><TITLE>MB04DI - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB04DI">MB04DI</A></H2>
<H3>
Applying the inverse of a balancing transformation for a real Hamiltonian 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 apply the inverse of a balancing transformation, computed by
the SLICOT Library routines MB04DD or MB04DS, to a 2*N-by-M 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 MB04DI( JOB, SGN, N, ILO, SCALE, M, V1, LDV1, V2, LDV2,
$ INFO )
C .. Scalar Arguments ..
CHARACTER JOB, SGN
INTEGER ILO, INFO, LDV1, LDV2, M, N
C .. Array Arguments ..
DOUBLE PRECISION SCALE(*), 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
MB04DD or MB04DS.
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 MB04DD or MB04DS.
1 <= ILO <= N+1.
SCALE (input) DOUBLE PRECISION array, dimension (N)
Details of the permutation and scaling factors, as
returned by MB04DD or MB04DS.
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] 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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