SRC/zgetrf2.f(3)           Library Functions Manual           SRC/zgetrf2.f(3)

NAME
       SRC/zgetrf2.f

SYNOPSIS
   Functions/Subroutines
       recursive subroutine zgetrf2 (m, n, a, lda, ipiv, info)
           ZGETRF2

Function/Subroutine Documentation
   recursive subroutine zgetrf2 (integer m, integer n, complex*16, dimension(
       lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)
       ZGETRF2

       Purpose:


            ZGETRF2 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

                     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 COMPLEX*16 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 Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 112 of file zgetrf2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                SRC/zgetrf2.f(3)