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<HTML>
<HEAD><TITLE>MB05OY - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB05OY">MB05OY</A></H2>
<H3>
Restoring a matrix after balancing transformations (permutations and scalings)
</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 restore a matrix after it has been transformed by applying
balancing transformations (permutations and scalings), as
determined by LAPACK Library routine DGEBAL.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB05OY( JOB, N, LOW, IGH, A, LDA, SCALE, INFO )
C .. Scalar Arguments ..
CHARACTER JOB
INTEGER IGH, INFO, LDA, LOW, N
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), SCALE(*)
</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 backward transformation required,
as follows:
= 'N', do nothing, return immediately;
= 'P', do backward transformation for permutation only;
= 'S', do backward transformation for scaling only;
= 'B', do backward transformations for both permutation
and scaling.
JOB must be the same as the argument JOB supplied
to DGEBAL.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the matrix A. N >= 0.
LOW (input) INTEGER
IGH (input) INTEGER
The integers LOW and IGH determined by DGEBAL.
1 <= LOW <= IGH <= N, if N > 0; LOW=1 and IGH=0, if N=0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading N-by-N part of this array must
contain the matrix to be back-transformed.
On exit, the leading N-by-N part of this array contains
the transformed matrix.
LDA INTEGER
The leading dimension of the array A. LDA >= max(1,N).
SCALE (input) DOUBLE PRECISION array, dimension (N)
Details of the permutation and scaling factors, as
returned by DGEBAL.
</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="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
Let P be a permutation matrix, and D a diagonal matrix of scaling
factors, both of order N. The routine computes
-1
A <-- P D A D P'.
where the permutation and scaling factors are encoded in the
array SCALE.
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
None.
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE> 2
The algorithm requires O(N ) 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>
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