DGETRF (3lapack)

compute 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.