dgetf2()

subroutine dgetf2	(	integer	m,
		integer	n,
		double precision, dimension( lda, * )	a,
		integer	lda,
		integer, dimension( * )	ipiv,
		integer	info )

DGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm).

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Purpose:

!>
!> DGETF2 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 right-looking Level 2 BLAS version of the algorithm.
!> 

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 DOUBLE PRECISION 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 = -k, the k-th argument had an illegal value !> > 0: if INFO = k, U(k,k) 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 105 of file dgetf2.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION   SFMIN
      INTEGER            I, J, JP
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      INTEGER            IDAMAX
      EXTERNAL           dlamch, idamax
*     ..
*     .. External Subroutines ..
      EXTERNAL           dger, dscal, dswap, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -4
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DGETF2', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 )
     $   RETURN
*
*     Compute machine safe minimum
*
      sfmin = dlamch('S')
*
      DO 10 j = 1, min( m, n )
*
*        Find pivot and test for singularity.
*
         jp = j - 1 + idamax( m-j+1, a( j, j ), 1 )
         ipiv( j ) = jp
         IF( a( jp, j ).NE.zero ) THEN
*
*           Apply the interchange to columns 1:N.
*
            IF( jp.NE.j )
     $         CALL dswap( n, a( j, 1 ), lda, a( jp, 1 ), lda )
*
*           Compute elements J+1:M of J-th column.
*
            IF( j.LT.m ) THEN
               IF( abs(a( j, j )) .GE. sfmin ) THEN
                  CALL dscal( m-j, one / a( j, j ), a( j+1, j ), 1 )
               ELSE
                 DO 20 i = 1, m-j
                    a( j+i, j ) = a( j+i, j ) / a( j, j )
   20            CONTINUE
               END IF
            END IF
*
         ELSE IF( info.EQ.0 ) THEN
*
            info = j
         END IF
*
         IF( j.LT.min( m, n ) ) THEN
*
*           Update trailing submatrix.
*
            CALL dger( m-j, n-j, -one, a( j+1, j ), 1, a( j, j+1 ),
     $                 lda,
     $                 a( j+1, j+1 ), lda )
         END IF
   10 CONTINUE
      RETURN
*
*     End of DGETF2
*

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