control_systems_torbox 0.2.1

Control systems toolbox
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<HTML>
<HEAD><TITLE>MB01OS - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>

<H2><A Name="MB01OS">MB01OS</A></H2>
<H3>
Computation of matrix expression P = H X or P = X H, with 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 compute P = H*X or P = X*H, where H is an upper Hessenberg
  matrix and X is a symmetric matrix.

</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
      SUBROUTINE MB01OS( UPLO, TRANS, N, H, LDH, X, LDX, P, LDP, INFO )
C     .. Scalar Arguments ..
      CHARACTER         TRANS, UPLO
      INTEGER           INFO, LDH, LDP, LDX, N
C     .. Array Arguments ..
      DOUBLE PRECISION  H(LDH,*), P(LDP,*), 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 triangle of the symmetric matrix X is
          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':         compute P = H*X;
          = 'T' or 'C':  compute P = X*H.

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

  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).

  P       (output) DOUBLE PRECISION array, dimension (LDP,N)
          On exit, the leading N-by-N part of this array contains
          the computed matrix P.

  LDP     INTEGER
          The leading dimension of the array P.  LDP &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 BLAS routines.
  Let X = U + sL, where U is upper triangular and sL is strictly
  lower triangular. Then, P = H*X = H*U + H*sL = H*U + H*sU', where
  sU is the strictly upper triangular part of X.
  Similarly, P = X*H = L'*H + sL*H, where L is lower triangular, and
  X = L + sL'. Note that H*U and L'*H are both upper Hessenberg.
  However, when UPLO = 'L' and TRANS = 'N', or when UPLO = 'U' and
  TRANS = 'T', then the matrix P is full. The computations are done
  similarly.

</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>
  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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