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<HTML>
<HEAD><TITLE>MB01XD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB01XD">MB01XD</A></H2>
<H3>
Computing U' U or L L', with U and L upper and lower triangular matrices (block algorithm)
</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 the matrix product U' * U or L * L', where U and L are
upper and lower triangular matrices, respectively, stored in the
corresponding upper or lower triangular part of the array A.
If UPLO = 'U' then the upper triangle of the result is stored,
overwriting the matrix U in A.
If UPLO = 'L' then the lower triangle of the result is stored,
overwriting the matrix L in A.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB01XD( UPLO, N, A, LDA, INFO )
C .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, N
C .. Array Arguments ..
DOUBLE PRECISION A( LDA, * )
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
UPLO CHARACTER*1
Specifies which triangle (U or L) is given in the array A,
as follows:
= 'U': the upper triangular part U is given;
= 'L': the lower triangular part L is given.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the triangular matrices U or L. N >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, if UPLO = 'U', the leading N-by-N upper
triangular part of this array must contain the upper
triangular matrix U.
On entry, if UPLO = 'L', the leading N-by-N lower
triangular part of this array must contain the lower
triangular matrix L.
On exit, if UPLO = 'U', the leading N-by-N upper
triangular part of this array contains the upper
triangular part of the product U' * U. The strictly lower
triangular part is not referenced.
On exit, if UPLO = 'L', the leading N-by-N lower
triangular part of this array contains the lower
triangular part of the product L * L'. The strictly upper
triangular part is not referenced.
LDA INTEGER
The leading dimension of array A. LDA >= max(1,N).
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
The matrix product U' * U or L * L' is computed using BLAS 3
operations as much as possible (a block algorithm).
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
This routine is a counterpart of LAPACK Library routine DLAUUM,
which computes the matrix product U * U' or L' * L.
</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>
<HR>
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