control_systems_torbox 0.2.1

Control systems toolbox
Documentation 
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<HEAD><TITLE>MB05OY - SLICOT Library Routine Documentation</TITLE>
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<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 &gt;= 0.

  LOW     (input) INTEGER
  IGH     (input) INTEGER
          The integers LOW and IGH determined by DGEBAL.
          1 &lt;= LOW &lt;= IGH &lt;= N, if N &gt; 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 &gt;= 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;
          &lt; 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 &lt;-- 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>

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