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Annotation of rpl/lapack/lapack/dorg2l.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
        !             2: *
        !             3: *  -- LAPACK routine (version 3.2) --
        !             4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             6: *     November 2006
        !             7: *
        !             8: *     .. Scalar Arguments ..
        !             9:       INTEGER            INFO, K, LDA, M, N
        !            10: *     ..
        !            11: *     .. Array Arguments ..
        !            12:       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        !            13: *     ..
        !            14: *
        !            15: *  Purpose
        !            16: *  =======
        !            17: *
        !            18: *  DORG2L generates an m by n real matrix Q with orthonormal columns,
        !            19: *  which is defined as the last n columns of a product of k elementary
        !            20: *  reflectors of order m
        !            21: *
        !            22: *        Q  =  H(k) . . . H(2) H(1)
        !            23: *
        !            24: *  as returned by DGEQLF.
        !            25: *
        !            26: *  Arguments
        !            27: *  =========
        !            28: *
        !            29: *  M       (input) INTEGER
        !            30: *          The number of rows of the matrix Q. M >= 0.
        !            31: *
        !            32: *  N       (input) INTEGER
        !            33: *          The number of columns of the matrix Q. M >= N >= 0.
        !            34: *
        !            35: *  K       (input) INTEGER
        !            36: *          The number of elementary reflectors whose product defines the
        !            37: *          matrix Q. N >= K >= 0.
        !            38: *
        !            39: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
        !            40: *          On entry, the (n-k+i)-th column must contain the vector which
        !            41: *          defines the elementary reflector H(i), for i = 1,2,...,k, as
        !            42: *          returned by DGEQLF in the last k columns of its array
        !            43: *          argument A.
        !            44: *          On exit, the m by n matrix Q.
        !            45: *
        !            46: *  LDA     (input) INTEGER
        !            47: *          The first dimension of the array A. LDA >= max(1,M).
        !            48: *
        !            49: *  TAU     (input) DOUBLE PRECISION array, dimension (K)
        !            50: *          TAU(i) must contain the scalar factor of the elementary
        !            51: *          reflector H(i), as returned by DGEQLF.
        !            52: *
        !            53: *  WORK    (workspace) DOUBLE PRECISION array, dimension (N)
        !            54: *
        !            55: *  INFO    (output) INTEGER
        !            56: *          = 0: successful exit
        !            57: *          < 0: if INFO = -i, the i-th argument has an illegal value
        !            58: *
        !            59: *  =====================================================================
        !            60: *
        !            61: *     .. Parameters ..
        !            62:       DOUBLE PRECISION   ONE, ZERO
        !            63:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
        !            64: *     ..
        !            65: *     .. Local Scalars ..
        !            66:       INTEGER            I, II, J, L
        !            67: *     ..
        !            68: *     .. External Subroutines ..
        !            69:       EXTERNAL           DLARF, DSCAL, XERBLA
        !            70: *     ..
        !            71: *     .. Intrinsic Functions ..
        !            72:       INTRINSIC          MAX
        !            73: *     ..
        !            74: *     .. Executable Statements ..
        !            75: *
        !            76: *     Test the input arguments
        !            77: *
        !            78:       INFO = 0
        !            79:       IF( M.LT.0 ) THEN
        !            80:          INFO = -1
        !            81:       ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
        !            82:          INFO = -2
        !            83:       ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
        !            84:          INFO = -3
        !            85:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
        !            86:          INFO = -5
        !            87:       END IF
        !            88:       IF( INFO.NE.0 ) THEN
        !            89:          CALL XERBLA( 'DORG2L', -INFO )
        !            90:          RETURN
        !            91:       END IF
        !            92: *
        !            93: *     Quick return if possible
        !            94: *
        !            95:       IF( N.LE.0 )
        !            96:      $   RETURN
        !            97: *
        !            98: *     Initialise columns 1:n-k to columns of the unit matrix
        !            99: *
        !           100:       DO 20 J = 1, N - K
        !           101:          DO 10 L = 1, M
        !           102:             A( L, J ) = ZERO
        !           103:    10    CONTINUE
        !           104:          A( M-N+J, J ) = ONE
        !           105:    20 CONTINUE
        !           106: *
        !           107:       DO 40 I = 1, K
        !           108:          II = N - K + I
        !           109: *
        !           110: *        Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
        !           111: *
        !           112:          A( M-N+II, II ) = ONE
        !           113:          CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
        !           114:      $               LDA, WORK )
        !           115:          CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
        !           116:          A( M-N+II, II ) = ONE - TAU( I )
        !           117: *
        !           118: *        Set A(m-k+i+1:m,n-k+i) to zero
        !           119: *
        !           120:          DO 30 L = M - N + II + 1, M
        !           121:             A( L, II ) = ZERO
        !           122:    30    CONTINUE
        !           123:    40 CONTINUE
        !           124:       RETURN
        !           125: *
        !           126: *     End of DORG2L
        !           127: *
        !           128:       END