control_systems_torbox 0.2.1

Control systems toolbox
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<HTML>
<HEAD><TITLE>MB04OX - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>

<H2><A Name="MB04OX">MB04OX</A></H2>
<H3>
Rank-one update of a Cholesky factorization
</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 QR factorization

     (U ) = Q*(R),
     (x')     (0)

  where U and R are n-by-n upper triangular matrices, x is an
  n element vector and Q is an (n+1)-by-(n+1) orthogonal matrix.

  U must be supplied in the n-by-n upper triangular part of the
  array A and this is overwritten by R.

</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
      SUBROUTINE MB04OX( N, A, LDA, X, INCX )
C     .. Scalar Arguments ..
      INTEGER            INCX, LDA, N
C     .. Array Arguments ..
      DOUBLE PRECISION   A(LDA,*), X(*)

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

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

  A      (input/output) DOUBLE PRECISION array, dimension (LDA,N)
         On entry, the leading N-by-N upper triangular part of this
         array must contain the upper triangular matrix U.
         On exit, the leading N-by-N upper triangular part of this
         array contains the upper triangular matrix R.
         The strict lower triangle of A is not referenced.

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

  X      (input/output) DOUBLE PRECISION array, dimension
         (1+(N-1)*INCX)
         On entry, the incremented array X must contain the
         vector x. On exit, the content of X is changed.

  INCX   (input) INTEGER.
         Specifies the increment for the elements of X.  INCX &gt; 0.

</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
  The matrix Q is formed as a sequence of plane rotations in planes
  (1, n+1), (2, n+1), ..., (n, n+1), the rotation in the (j, n+1)th
  plane, Q(j), being chosen to annihilate the jth element of x.

</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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