sorg2l.f

          SUBROUTINE SORG2L( 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 ..
          REAL               A( LDA, * ), TAU( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SORG2L generates an m by n real matrix Q with orthonormal columns,
    *  which is defined as the last n columns of a product of k elementary
    *  reflectors of order m
    *
    *        Q  =  H(k) . . . H(2) H(1)
    *
    *  as returned by SGEQLF.
    *
    *  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. M >= N >= 0.
    *
    *  K       (input) INTEGER
    *          The number of elementary reflectors whose product defines the
    *          matrix Q. N >= K >= 0.
    *
    *  A       (input/output) REAL array, dimension (LDA,N)
    *          On entry, the (n-k+i)-th column must contain the vector which
    *          defines the elementary reflector H(i), for i = 1,2,...,k, as
    *          returned by SGEQLF in the last k columns 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) REAL array, dimension (K)
    *          TAU(i) must contain the scalar factor of the elementary
    *          reflector H(i), as returned by SGEQLF.
    *
    *  WORK    (workspace) REAL array, dimension (N)
    *
    *  INFO    (output) INTEGER
    *          = 0: successful exit
    *          < 0: if INFO = -i, the i-th argument has an illegal value
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ONE, ZERO
          PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, II, J, L
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SLARF, SSCAL, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          INFO = 0
          IF( M.LT.0 ) THEN
             INFO = -1
          ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
             INFO = -2
          ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
             INFO = -3
          ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
             INFO = -5
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SORG2L', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.LE.0 )
         $   RETURN
    *
    *     Initialise columns 1:n-k to columns of the unit matrix
    *
          DO 20 J = 1, N - K
             DO 10 L = 1, M
                A( L, J ) = ZERO
       10    CONTINUE
             A( M-N+J, J ) = ONE
       20 CONTINUE
    *
          DO 40 I = 1, K
             II = N - K + I
    *
    *        Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
    *
             A( M-N+II, II ) = ONE
             CALL SLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
         $               LDA, WORK )
             CALL SSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
             A( M-N+II, II ) = ONE - TAU( I )
    *
    *        Set A(m-k+i+1:m,n-k+i) to zero
    *
             DO 30 L = M - N + II + 1, M
                A( L, II ) = ZERO
       30    CONTINUE
       40 CONTINUE
          RETURN
    *
    *     End of SORG2L
    *
          END