cgeqlf.f

          SUBROUTINE CGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, LDA, LWORK, M, N
    *     ..
    *     .. Array Arguments ..
          COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CGEQLF computes a QL factorization of a complex M-by-N matrix A:
    *  A = Q * L.
    *
    *  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 A.
    *          On exit,
    *          if m >= n, the lower triangle of the subarray
    *          A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
    *          if m <= n, the elements on and below the (n-m)-th
    *          superdiagonal contain the M-by-N lower trapezoidal matrix L;
    *          the remaining elements, with the array TAU, represent the
    *          unitary matrix Q as a product of elementary reflectors
    *          (see Further Details).
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,M).
    *
    *  TAU     (output) COMPLEX array, dimension (min(M,N))
    *          The scalar factors of the elementary reflectors (see Further
    *          Details).
    *
    *  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK.  LWORK >= max(1,N).
    *          For optimum performance LWORK >= N*NB, where NB is
    *          the optimal blocksize.
    *
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the optimal size of the WORK array, returns
    *          this value as the first entry of the WORK array, and no error
    *          message related to LWORK is issued by XERBLA.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  Further Details
    *  ===============
    *
    *  The matrix Q is represented as a product of elementary reflectors
    *
    *     Q = H(k) . . . H(2) H(1), where k = min(m,n).
    *
    *  Each H(i) has the form
    *
    *     H(i) = I - tau * v * v'
    *
    *  where tau is a complex scalar, and v is a complex vector with
    *  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
    *  A(1:m-k+i-1,n-k+i), and tau in TAU(i).
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          LOGICAL            LQUERY
          INTEGER            I, IB, IINFO, IWS, K, KI, KK, LDWORK, LWKOPT,
         $                   MU, NB, NBMIN, NU, NX
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CGEQL2, CLARFB, CLARFT, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN
    *     ..
    *     .. External Functions ..
          INTEGER            ILAENV
          EXTERNAL           ILAENV
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          INFO = 0
          LQUERY = ( LWORK.EQ.-1 )
          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.EQ.0 ) THEN
             K = MIN( M, N )
             IF( K.EQ.0 ) THEN
                LWKOPT = 1
             ELSE
                NB = ILAENV( 1, 'CGEQLF', ' ', M, N, -1, -1 )
                LWKOPT = N*NB
             END IF
             WORK( 1 ) = LWKOPT
    *
             IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
                INFO = -7
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CGEQLF', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( K.EQ.0 ) THEN
             RETURN
          END IF
    *
          NBMIN = 2
          NX = 1
          IWS = N
          IF( NB.GT.1 .AND. NB.LT.K ) THEN
    *
    *        Determine when to cross over from blocked to unblocked code.
    *
             NX = MAX( 0, ILAENV( 3, 'CGEQLF', ' ', M, N, -1, -1 ) )
             IF( NX.LT.K ) THEN
    *
    *           Determine if workspace is large enough for blocked code.
    *
                LDWORK = N
                IWS = LDWORK*NB
                IF( LWORK.LT.IWS ) THEN
    *
    *              Not enough workspace to use optimal NB:  reduce NB and
    *              determine the minimum value of NB.
    *
                   NB = LWORK / LDWORK
                   NBMIN = MAX( 2, ILAENV( 2, 'CGEQLF', ' ', M, N, -1,
         $                 -1 ) )
                END IF
             END IF
          END IF
    *
          IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
    *
    *        Use blocked code initially.
    *        The last kk columns are handled by the block method.
    *
             KI = ( ( K-NX-1 ) / NB )*NB
             KK = MIN( K, KI+NB )
    *
             DO 10 I = K - KK + KI + 1, K - KK + 1, -NB
                IB = MIN( K-I+1, NB )
    *
    *           Compute the QL factorization of the current block
    *           A(1:m-k+i+ib-1,n-k+i:n-k+i+ib-1)
    *
                CALL CGEQL2( M-K+I+IB-1, IB, A( 1, N-K+I ), LDA, TAU( I ),
         $                   WORK, IINFO )
                IF( N-K+I.GT.1 ) THEN
    *
    *              Form the triangular factor of the block reflector
    *              H = H(i+ib-1) . . . H(i+1) H(i)
    *
                   CALL CLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
         $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
    *
    *              Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
    *
                   CALL CLARFB( 'Left', 'Conjugate transpose', 'Backward',
         $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
         $                      A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA,
         $                      WORK( IB+1 ), LDWORK )
                END IF
       10    CONTINUE
             MU = M - K + I + NB - 1
             NU = N - K + I + NB - 1
          ELSE
             MU = M
             NU = N
          END IF
    *
    *     Use unblocked code to factor the last or only block
    *
          IF( MU.GT.0 .AND. NU.GT.0 )
         $   CALL CGEQL2( MU, NU, A, LDA, TAU, WORK, IINFO )
    *
          WORK( 1 ) = IWS
          RETURN
    *
    *     End of CGEQLF
    *
          END