cgerq2.f

          SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, 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 ..
          COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CGERQ2 computes an RQ factorization of a complex m by n matrix A:
    *  A = R * Q.
    *
    *  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 upper triangle of the subarray
    *          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
    *          if m >= n, the elements on and above the (m-n)-th subdiagonal
    *          contain the m by n upper trapezoidal matrix R; 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) COMPLEX array, dimension (M)
    *
    *  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(1)' H(2)' . . . H(k)', 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
    *  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX            ONE
          PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, K
          COMPLEX            ALPHA
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CLACGV, CLARF, CLARFG, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          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( 'CGERQ2', -INFO )
             RETURN
          END IF
    *
          K = MIN( M, N )
    *
          DO 10 I = K, 1, -1
    *
    *        Generate elementary reflector H(i) to annihilate
    *        A(m-k+i,1:n-k+i-1)
    *
             CALL CLACGV( N-K+I, A( M-K+I, 1 ), LDA )
             ALPHA = A( M-K+I, N-K+I )
             CALL CLARFG( N-K+I, ALPHA, A( M-K+I, 1 ), LDA,
         $                TAU( I ) )
    *
    *        Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
    *
             A( M-K+I, N-K+I ) = ONE
             CALL CLARF( 'Right', M-K+I-1, N-K+I, A( M-K+I, 1 ), LDA,
         $               TAU( I ), A, LDA, WORK )
             A( M-K+I, N-K+I ) = ALPHA
             CALL CLACGV( N-K+I-1, A( M-K+I, 1 ), LDA )
       10 CONTINUE
          RETURN
    *
    *     End of CGERQ2
    *
          END