control_systems_torbox 0.2.1

Control systems toolbox
Documentation 
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<HTML>
<HEAD><TITLE>MB01OC - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>

<H2><A Name="MB01OC">MB01OC</A></H2>
<H3>
Computation of matrix expression alpha R + beta ( op(H) X + X op(H)' ) with R, X symmetric and H upper Hessenberg
</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 perform one of the special symmetric rank 2k operations

     R := alpha*R + beta*H*X + beta*X*H',
  or
     R := alpha*R + beta*H'*X + beta*X*H,

  where alpha and beta are scalars, R and X are N-by-N symmetric
  matrices, and H is an N-by-N upper Hessenberg matrix.

</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
      SUBROUTINE MB01OC( UPLO, TRANS, N, ALPHA, BETA, R, LDR, H, LDH, X,
     $                   LDX, INFO )
C     .. Scalar Arguments ..
      CHARACTER         TRANS, UPLO
      INTEGER           INFO, LDH, LDR, LDX, N
      DOUBLE PRECISION  ALPHA, BETA
C     .. Array Arguments ..
      DOUBLE PRECISION  H(LDH,*), R(LDR,*), X(LDX,*)

</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>

<B>Mode Parameters</B>
<PRE>
  UPLO    CHARACTER*1
          Specifies which triangles of the symmetric matrices R
          and X are given as follows:
          = 'U':  the upper triangular part is given;
          = 'L':  the lower triangular part is given.

  TRANS   CHARACTER*1
          Specifies the operation to be performed as follows:
          = 'N':         R := alpha*R + beta*H*X  + beta*X*H';
          = 'T' or 'C':  R := alpha*R + beta*H'*X + beta*X*H.

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

  ALPHA   (input) DOUBLE PRECISION
          The scalar alpha. When alpha is zero then R need not be
          set before entry, except when R is identified with X in
          the call.

  BETA    (input) DOUBLE PRECISION
          The scalar beta. When beta is zero then H and X are not
          referenced.

  R       (input/output) DOUBLE PRECISION array, dimension (LDR,N)
          On entry with UPLO = 'U', the leading N-by-N upper
          triangular part of this array must contain the upper
          triangular part of the symmetric matrix R.
          On entry with UPLO = 'L', the leading N-by-N lower
          triangular part of this array must contain the lower
          triangular part of the symmetric matrix R.
          In both cases, the other strictly triangular part is not
          referenced.
          On exit, the leading N-by-N upper triangular part (if
          UPLO = 'U'), or lower triangular part (if UPLO = 'L'), of
          this array contains the corresponding triangular part of
          the computed matrix R.

  LDR     INTEGER
          The leading dimension of the array R.  LDR &gt;= MAX(1,N).

  H       (input) DOUBLE PRECISION array, dimension (LDH,N)
          On entry, the leading N-by-N upper Hessenberg part of this
          array must contain the upper Hessenberg matrix H.
          The remaining part of this array is not referenced.

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

  X       (input) DOUBLE PRECISION array, dimension (LDX,N)
          On entry, if UPLO = 'U', the leading N-by-N upper
          triangular part of this array must contain the upper
          triangular part of the symmetric matrix X and the strictly
          lower triangular part of the array is not referenced.
          On entry, if UPLO = 'L', the leading N-by-N lower
          triangular part of this array must contain the lower
          triangular part of the symmetric matrix X and the strictly
          upper triangular part of the array is not referenced.

  LDX     INTEGER
          The leading dimension of the array X.  LDX &gt;= MAX(1,N).

</PRE>
<B>Error Indicator</B>
<PRE>
  INFO    INTEGER
          = 0:  successful exit;
          &lt; 0:  if INFO = -k, the k-th argument had an illegal
                value.

</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
  The matrix expression is efficiently evaluated taking the
  structure into account, and using inline code and BLAS1 routines.

</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
  The algorithm requires approximately N**3/2 operations.

</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
  This routine acts as a specialization of BLAS Library routine
  DSYR2K.

</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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