zgetrf2.f - Man Page



recursive subroutine zgetrf2 (M, N, A, LDA, IPIV, INFO)

Function/Subroutine Documentation

recursive subroutine zgetrf2 (integer M, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, integer INFO)



 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.


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


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


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


          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 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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


June 2016

Definition at line 115 of file zgetrf2.f.


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Referenced By

The man page zgetrf2(3) is an alias of zgetrf2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK