dgetf2.f

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*> \brief \b DGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO )
* 
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, M, N
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       DOUBLE PRECISION   A( LDA, * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix A.  M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,M).
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*>          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).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup doubleGEcomputational
*
*  =====================================================================
      SUBROUTINE dgetf2( M, N, A, LDA, IPIV, INFO )
*
*  -- LAPACK computational routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. 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
*
      END