cgetf2.f

          SUBROUTINE CGETF2( M, N, A, LDA, IPIV, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, LDA, M, N
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX            A( LDA, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CGETF2 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) COMPLEX 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 ..
          COMPLEX            ONE, ZERO
          PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),
         $                   ZERO = ( 0.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          REAL               SFMIN
          INTEGER            I, J, JP
    *     ..
    *     .. External Functions ..
          REAL               SLAMCH
          INTEGER            ICAMAX
          EXTERNAL           SLAMCH, ICAMAX
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CGERU, CSCAL, CSWAP, 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( 'CGETF2', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( M.EQ.0 .OR. N.EQ.0 )
         $   RETURN
    *
    *     Compute machine safe minimum
    *
          SFMIN = SLAMCH('S')
    *
          DO 10 J = 1, MIN( M, N )
    *
    *        Find pivot and test for singularity.
    *
             JP = J - 1 + ICAMAX( 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 CSWAP( 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 CSCAL( 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 CGERU( 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 CGETF2
    *
          END