DGETC2 - compute an LU factorization with complete pivot
ing of the n-by-n matrix A
SYNOPSIS
SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
INTEGER INFO, LDA, N
INTEGER IPIV( * ), JPIV( * )
DOUBLE PRECISION A( LDA, * )
PURPOSE
DGETC2 computes an LU factorization with 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.
This is the Level 2 BLAS algorithm.
ARGUMENTS
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) DOUBLE PRECISION array, dimension
(LDA, N)
On entry, the n-by-n matrix A to be factored. On
exit, 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, i.e., giving a
nonsingular perturbed system.
LDA (input) 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).
INFO (output) INTEGER
= 0: successful exit
> 0: if INFO = k, U(k, k) is likely to produce
owerflow if we try to solve for x in Ax = b. So U
is perturbed to avoid the overflow.
Based on contributions by
Bo Kagstrom and Peter Poromaa, Department of Computing
Science,
Umea University, S-901 87 Umea, Sweden.
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