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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 >= 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 >= 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 > 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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