GETRF2 - 5.2 English - 68552

GETRF2 computes an LU factorization of a general M-by-N matrix A.

Purpose:

 GETRF2 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 – [in]

  M is INTEGER

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

• N – [in]

  N is INTEGER

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

• A – [inout]

  A is REAL 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 – [in]

  LDA is INTEGER

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

• IPIV – [out]

  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 – [out]

  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.