control_systems_torbox 0.2.1

Control systems toolbox
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<HEAD><TITLE>MB04PY - SLICOT Library Routine Documentation</TITLE>
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<BODY>

<H2><A Name="MB04PY">MB04PY</A></H2>
<H3>
Applying an elementary reflector (using in-line code for a low order) to a matrix, from either the left or the right
</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 apply a real elementary reflector H to a real m-by-n matrix
  C, from either the left or the right. H is represented in the form
                                     ( 1 )
        H = I - tau * u *u',    u  = (   ),
                                     ( v )
  where tau is a real scalar and v is a real vector.

  If tau = 0, then H is taken to be the unit matrix.

  In-line code is used if H has order &lt; 11.

</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
      SUBROUTINE MB04PY( SIDE, M, N, V, TAU, C, LDC, DWORK )
C     .. Scalar Arguments ..
      CHARACTER          SIDE
      INTEGER            LDC, M, N
      DOUBLE PRECISION   TAU
C     .. Array Arguments ..
      DOUBLE PRECISION   C( LDC, * ), DWORK( * ), V( * )

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

<B>Mode Parameters</B>
<PRE>
  SIDE    CHARACTER*1
          Indicates whether the elementary reflector should be
          applied from the left or from the right, as follows:
          = 'L':  Compute H * C;
          = 'R':  Compute C * H.

</PRE>
<B>Input/Output Parameters</B>
<PRE>
  M       (input) INTEGER
          The number of rows of the matrix C.  M &gt;= 0.

  N       (input) INTEGER
          The number of columns of the matrix C.  N &gt;= 0.

  V       (input) DOUBLE PRECISION array, dimension
          (M-1), if SIDE = 'L', or
          (N-1), if SIDE = 'R'.
          The vector v in the representation of H.

  TAU     (input) DOUBLE PRECISION
          The scalar factor of the elementary reflector H.

  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the leading M-by-N part of this array must
          contain the matrix C.
          On exit, the leading M-by-N part of this array contains
          the matrix H * C, if SIDE = 'L', or C * H, if SIDE = 'R'.

  LDC     INTEGER
          The leading dimension of array C.  LDC &gt;= MAX(1,M).

</PRE>
<B>Workspace</B>
<PRE>
  DWORK   DOUBLE PRECISION array, dimension (N), if SIDE = 'L', or
                                            (M), if SIDE = 'R'.
          DWORK is not referenced if H has order less than 11.

</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
  The routine applies the elementary reflector H, taking its special
  structure into account. The multiplications by the first component
  of u (which is 1) are avoided, to increase the efficiency.

</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
  The algorithm is backward stable.

</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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