control_systems_torbox 0.2.1

Control systems toolbox
Documentation
<HTML>
<HEAD><TITLE>MB02RD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>

<H2><A Name="MB02RD">MB02RD</A></H2>
<H3>
Solution of a system of linear equations with 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  or  H' * X = B
  with an upper Hessenberg N-by-N matrix H using the LU
  factorization computed by MB02SD.

</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
      SUBROUTINE MB02RD( 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( * )
      DOUBLE PRECISION   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'* X = B  (Conjugate transpose = Transpose)

</PRE>
<B>Input/Output Parameters</B>
<PRE>
  N       (input) INTEGER
          The order of the matrix H.  N &gt;= 0.

  NRHS    (input) INTEGER
          The number of right hand sides, i.e., the number of
          columns of the matrix B.  NRHS &gt;= 0.

  H       (input) DOUBLE PRECISION array, dimension (LDH,N)
          The factors L and U from the factorization H = P*L*U
          as computed by MB02SD.

  LDH     INTEGER
          The leading dimension of the array H.  LDH &gt;= max(1,N).

  IPIV    (input) INTEGER array, dimension (N)
          The pivot indices from MB02SD; for 1&lt;=i&lt;=N, row i of the
          matrix was interchanged with row IPIV(i).

  B       (input/output) DOUBLE PRECISION 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 &gt;= max(1,N).

</PRE>
<B>Error Indicator</B>
<PRE>
  INFO    (output) 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>
  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 ) 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>
<A HREF=..\libindex.html><B>Return to index</B></A></BODY>
</HTML>