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<HTML>
<HEAD><TITLE>MB02UV - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB02UV">MB02UV</A></H2>
<H3>
LU factorization with complete pivoting of a general 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 compute an LU factorization, using complete pivoting, of the
N-by-N matrix A. The factorization has the form A = P * L * U * Q,
where P and Q are permutation matrices, L is lower triangular with
unit diagonal elements and U is upper triangular.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB02UV( N, A, LDA, IPIV, JPIV, INFO )
C .. Scalar Arguments ..
INTEGER INFO, LDA, N
C .. Array Arguments ..
INTEGER IPIV( * ), JPIV( * )
DOUBLE PRECISION A( LDA, * )
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the matrix A.
A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
On entry, the leading N-by-N part of this array must
contain the matrix A to be factored.
On exit, the leading N-by-N part of this array contains
the factors L and U from the factorization A = P*L*U*Q;
the unit diagonal elements of L are not stored. If U(k, k)
appears to be less than SMIN, U(k, k) is given the value
of SMIN, giving a nonsingular perturbed system.
LDA INTEGER
The leading dimension of the array A. LDA >= max(1, N).
IPIV (output) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the
matrix has been interchanged with row IPIV(i).
JPIV (output) INTEGER array, dimension (N)
The pivot indices; for 1 <= j <= N, column j of the
matrix has been interchanged with column JPIV(j).
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
= k: U(k, k) is likely to produce owerflow if one tries
to solve for x in Ax = b. So U is perturbed to get
a nonsingular system. This is a warning.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
In the interests of speed, this routine does not check the input
for errors. It should only be used to factorize matrices A of
very small order.
</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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