SGETRF2 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

          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 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

          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.

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Univ. of California Berkeley

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