cgetrf2()

recursive subroutine cgetrf2	(	integer	m,
		integer	n,
		complex, dimension( lda, * )	a,
		integer	lda,
		integer, dimension( * )	ipiv,
		integer	info )

CGETRF2

Purpose:

!>
!> CGETRF2 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

[in]	M	!> M is INTEGER !> The number of rows of the matrix A. M >= 0. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix A. N >= 0. !>
[in,out]	A	!> A is COMPLEX 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. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[out]	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). !>
[out]	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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.