dgetf2.f

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      SUBROUTINE dgetf2( M, N, A, LDA, IPIV, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1992
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * )
*     ..
*
*  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.
*
*  Arguments
*  =========
*
*  M       (input) INTEGER
*          The number of rows of the matrix A.  M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix A.  N >= 0.
*
*  A       (input/output) 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.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,M).
*
*  IPIV    (output) 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    (output) 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.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J, JP
*     ..
*     .. External Functions ..
      INTEGER            IDAMAX
      EXTERNAL           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
*
      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 )
     $         CALL dscal( m-j, one / a( j, j ), a( j+1, j ), 1 )
*
         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