dorgl2.f

          SUBROUTINE DORGL2( M, N, K, 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, K, LDA, M, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DORGL2 generates an m by n real matrix Q with orthonormal rows,
    *  which is defined as the first m rows of a product of k elementary
    *  reflectors of order n
    *
    *        Q  =  H(k) . . . H(2) H(1)
    *
    *  as returned by DGELQF.
    *
    *  Arguments
    *  =========
    *
    *  M       (input) INTEGER
    *          The number of rows of the matrix Q. M >= 0.
    *
    *  N       (input) INTEGER
    *          The number of columns of the matrix Q. N >= M.
    *
    *  K       (input) INTEGER
    *          The number of elementary reflectors whose product defines the
    *          matrix Q. M >= K >= 0.
    *
    *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
    *          On entry, the i-th row must contain the vector which defines
    *          the elementary reflector H(i), for i = 1,2,...,k, as returned
    *          by DGELQF in the first k rows of its array argument A.
    *          On exit, the m-by-n matrix Q.
    *
    *  LDA     (input) INTEGER
    *          The first dimension of the array A. LDA >= max(1,M).
    *
    *  TAU     (input) DOUBLE PRECISION array, dimension (K)
    *          TAU(i) must contain the scalar factor of the elementary
    *          reflector H(i), as returned by DGELQF.
    *
    *  WORK    (workspace) DOUBLE PRECISION array, dimension (M)
    *
    *  INFO    (output) INTEGER
    *          = 0: successful exit
    *          < 0: if INFO = -i, the i-th argument has an illegal value
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE, ZERO
          PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, J, L
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DLARF, DSCAL, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          INFO = 0
          IF( M.LT.0 ) THEN
             INFO = -1
          ELSE IF( N.LT.M ) THEN
             INFO = -2
          ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
             INFO = -3
          ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
             INFO = -5
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DORGL2', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( M.LE.0 )
         $   RETURN
    *
          IF( K.LT.M ) THEN
    *
    *        Initialise rows k+1:m to rows of the unit matrix
    *
             DO 20 J = 1, N
                DO 10 L = K + 1, M
                   A( L, J ) = ZERO
       10       CONTINUE
                IF( J.GT.K .AND. J.LE.M )
         $         A( J, J ) = ONE
       20    CONTINUE
          END IF
    *
          DO 40 I = K, 1, -1
    *
    *        Apply H(i) to A(i:m,i:n) from the right
    *
             IF( I.LT.N ) THEN
                IF( I.LT.M ) THEN
                   A( I, I ) = ONE
                   CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
         $                     TAU( I ), A( I+1, I ), LDA, WORK )
                END IF
                CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
             END IF
             A( I, I ) = ONE - TAU( I )
    *
    *        Set A(i,1:i-1) to zero
    *
             DO 30 L = 1, I - 1
                A( I, L ) = ZERO
       30    CONTINUE
       40 CONTINUE
          RETURN
    *
    *     End of DORGL2
    *
          END