zgetrf.f

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      SUBROUTINE ZGETRF ( M, N, A, LDA, IPIV, INFO)
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     March 2008
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         A( LDA, * )
*     ..
*
*  Purpose
*  =======
*
*  ZGETRF 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 Crout Level 3 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*16 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 = -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.
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, IINFO, J, JB, NB
*     ..
*     .. External Subroutines ..
      EXTERNAL           ZGEMM, ZGETF2, ZLASWP, ZTRSM, XERBLA
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ILAENV
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN, MOD
*     ..
*     .. 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( 'ZGETRF', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( M.EQ.0 .OR. N.EQ.0 )
     $   RETURN
*
*     Determine the block size for this environment.
*
      NB = ILAENV( 1, 'ZGETRF', ' ', M, N, -1, -1 )
      IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
*
*        Use unblocked code.
*
         CALL ZGETF2( M, N, A, LDA, IPIV, INFO )
      ELSE
*
*        Use blocked code.
*
         DO 20 J = 1, MIN( M, N ), NB
            JB = MIN( MIN( M, N )-J+1, NB )
*
*           Update current block.
*
            CALL ZGEMM( 'No transpose', 'No transpose', 
     $                 M-J+1, JB, J-1, -ONE, 
     $                 A( J, 1 ), LDA, A( 1, J ), LDA, ONE,
     $                 A( J, J ), LDA )
            
*
*           Factor diagonal and subdiagonal blocks and test for exact
*           singularity.
*
            CALL ZGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
*
*           Adjust INFO and the pivot indices.
*
            IF( INFO.EQ.0 .AND. IINFO.GT.0 )
     $         INFO = IINFO + J - 1
            DO 10 I = J, MIN( M, J+JB-1 )
               IPIV( I ) = J - 1 + IPIV( I )
   10       CONTINUE
*            
*           Apply interchanges to column 1:J-1            
*
            CALL ZLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
*
            IF ( J+JB.LE.N ) THEN
*            
*              Apply interchanges to column J+JB:N            
*
               CALL ZLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, 
     $                     IPIV, 1 )
*               
               CALL ZGEMM( 'No transpose', 'No transpose', 
     $                    JB, N-J-JB+1, J-1, -ONE, 
     $                    A( J, 1 ), LDA, A( 1, J+JB ), LDA, ONE,
     $                    A( J, J+JB ), LDA )
*
*              Compute block row of U.
*
               CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
     $                    JB, N-J-JB+1, ONE, A( J, J ), LDA, 
     $                    A( J, J+JB ), LDA )
            END IF

   20    CONTINUE

      END IF
      RETURN
*
*     End of ZGETRF
*
      END