NAME¶

DGETRF - computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges

SYNOPSIS¶

SUBROUTINE DGETRF(

M, N, A, LDA, IPIV, INFO )

INTEGER INFO, LDA, M, N INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * )

PURPOSE¶

DGETRF 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 right-looking Level 3 BLAS version of the algorithm.

ARGUMENTS¶

M (input) INTEGER

The number of rows of the matrix A. M >= 0.

N (input) INTEGER

The number of columns of the matrix A. N >= 0.

A (input/output) DOUBLE PRECISION 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 (input) INTEGER

The leading dimension of the array A. LDA >= max(1,M).

IPIV (output) 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 (output) 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.