recursive subroutine sgetrf2 (M, N, A, LDA, IPIV, INFO)
SGETRF2
SGETRF2
Purpose:
SGETRF2 computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the recursive version of the algorithm. It divides
the matrix into four submatrices:
[ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ] with n1 = min(m,n)/2
[ A21 | A22 ] n2 = n-n1
[ A11 ]
The subroutine calls itself to factor [ --- ],
[ A12 ]
[ A12 ]
do the swaps on [ --- ], solve A12, update A22,
[ A22 ]
then calls itself to factor A22 and do the swaps on A21.
Parameters:
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix to be factored.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
IPIV
IPIV is INTEGER array, dimension (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 115 of file sgetrf2.f.
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