control_systems_torbox 0.2.1

Control systems toolbox
Documentation 
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<HTML>
<HEAD><TITLE>MB01ND - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>

<H2><A Name="MB01ND">MB01ND</A></H2>
<H3>
Rank 2 operation alpha*x*trans(y) - alpha*y*trans(x) + A, with A a skew-symmetric 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 perform the skew-symmetric rank 2 operation

       A := alpha*x*y' - alpha*y*x' + A,

  where alpha is a scalar, x and y are vectors of length n and A is
  an n-by-n skew-symmetric matrix.

  This is a modified version of the vanilla implemented BLAS
  routine DSYR2 written by Jack Dongarra, Jeremy Du Croz,
  Sven Hammarling, and Richard Hanson.

</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
      SUBROUTINE MB01ND( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )
C     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA
      INTEGER            INCX, INCY, LDA, N
      CHARACTER          UPLO
C     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * ), Y( * )

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

<B>Mode Parameters</B>
<PRE>
  UPLO    CHARACTER*1
          Specifies whether the upper or lower triangular part of
          the array A is to be referenced as follows:
          = 'U':  only the strictly upper triangular part of A is to
                  be referenced;
          = 'L':  only the strictly lower triangular part of A is to
                  be referenced.

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

  ALPHA   (input) DOUBLE PRECISION
          The scalar alpha. If alpha is zero X and Y are not
          referenced.

  X       (input) DOUBLE PRECISION array, dimension
          ( 1 + ( N - 1 )*abs( INCX ) ).
          On entry, elements 1, INCX+1, .., ( N - 1 )*INCX + 1 of
          this array must contain the elements of the vector X.

  INCX    (input) INTEGER
          The increment for the elements of X. IF INCX &lt; 0 then the
          elements of X are accessed in reversed order.  INCX &lt;&gt; 0.

  Y       (input) DOUBLE PRECISION array, dimension
          ( 1 + ( N - 1 )*abs( INCY ) ).
          On entry, elements 1, INCY+1, .., ( N - 1 )*INCY + 1 of
          this array must contain the elements of the vector Y.

  INCY    (input) INTEGER
          The increment for the elements of Y. IF INCY &lt; 0 then the
          elements of Y are accessed in reversed order.  INCY &lt;&gt; 0.

  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
          On entry with UPLO = 'U', the leading N-by-N part of this
          array must contain the strictly upper triangular part of
          the matrix A. The lower triangular part of this array is
          not referenced.
          On entry with UPLO = 'L', the leading N-by-N part of this
          array must contain the strictly lower triangular part of
          the matrix A. The upper triangular part of this array is
          not referenced.
          On exit with UPLO = 'U', the leading N-by-N part of this
          array contains the strictly upper triangular part of the
          updated matrix A.
          On exit with UPLO = 'L', the leading N-by-N part of this
          array contains the strictly lower triangular part of the
          updated matrix A.

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

</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
  Though being almost identical with the vanilla implementation
  of the BLAS routine DSYR2 the performance of this routine could
  be significantly lower in the case of vendor supplied, highly
  optimized BLAS.

</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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