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

1.1     ! bertrand    1:       SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )
        !             2: *
        !             3: *  -- LAPACK auxiliary 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            INCX, INCY, N
        !            10:       DOUBLE PRECISION   SSMIN
        !            11: *     ..
        !            12: *     .. Array Arguments ..
        !            13:       DOUBLE PRECISION   X( * ), Y( * )
        !            14: *     ..
        !            15: *
        !            16: *  Purpose
        !            17: *  =======
        !            18: *
        !            19: *  Given two column vectors X and Y, let
        !            20: *
        !            21: *                       A = ( X Y ).
        !            22: *
        !            23: *  The subroutine first computes the QR factorization of A = Q*R,
        !            24: *  and then computes the SVD of the 2-by-2 upper triangular matrix R.
        !            25: *  The smaller singular value of R is returned in SSMIN, which is used
        !            26: *  as the measurement of the linear dependency of the vectors X and Y.
        !            27: *
        !            28: *  Arguments
        !            29: *  =========
        !            30: *
        !            31: *  N       (input) INTEGER
        !            32: *          The length of the vectors X and Y.
        !            33: *
        !            34: *  X       (input/output) DOUBLE PRECISION array,
        !            35: *                         dimension (1+(N-1)*INCX)
        !            36: *          On entry, X contains the N-vector X.
        !            37: *          On exit, X is overwritten.
        !            38: *
        !            39: *  INCX    (input) INTEGER
        !            40: *          The increment between successive elements of X. INCX > 0.
        !            41: *
        !            42: *  Y       (input/output) DOUBLE PRECISION array,
        !            43: *                         dimension (1+(N-1)*INCY)
        !            44: *          On entry, Y contains the N-vector Y.
        !            45: *          On exit, Y is overwritten.
        !            46: *
        !            47: *  INCY    (input) INTEGER
        !            48: *          The increment between successive elements of Y. INCY > 0.
        !            49: *
        !            50: *  SSMIN   (output) DOUBLE PRECISION
        !            51: *          The smallest singular value of the N-by-2 matrix A = ( X Y ).
        !            52: *
        !            53: *  =====================================================================
        !            54: *
        !            55: *     .. Parameters ..
        !            56:       DOUBLE PRECISION   ZERO, ONE
        !            57:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
        !            58: *     ..
        !            59: *     .. Local Scalars ..
        !            60:       DOUBLE PRECISION   A11, A12, A22, C, SSMAX, TAU
        !            61: *     ..
        !            62: *     .. External Functions ..
        !            63:       DOUBLE PRECISION   DDOT
        !            64:       EXTERNAL           DDOT
        !            65: *     ..
        !            66: *     .. External Subroutines ..
        !            67:       EXTERNAL           DAXPY, DLARFG, DLAS2
        !            68: *     ..
        !            69: *     .. Executable Statements ..
        !            70: *
        !            71: *     Quick return if possible
        !            72: *
        !            73:       IF( N.LE.1 ) THEN
        !            74:          SSMIN = ZERO
        !            75:          RETURN
        !            76:       END IF
        !            77: *
        !            78: *     Compute the QR factorization of the N-by-2 matrix ( X Y )
        !            79: *
        !            80:       CALL DLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
        !            81:       A11 = X( 1 )
        !            82:       X( 1 ) = ONE
        !            83: *
        !            84:       C = -TAU*DDOT( N, X, INCX, Y, INCY )
        !            85:       CALL DAXPY( N, C, X, INCX, Y, INCY )
        !            86: *
        !            87:       CALL DLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU )
        !            88: *
        !            89:       A12 = Y( 1 )
        !            90:       A22 = Y( 1+INCY )
        !            91: *
        !            92: *     Compute the SVD of 2-by-2 Upper triangular matrix.
        !            93: *
        !            94:       CALL DLAS2( A11, A12, A22, SSMIN, SSMAX )
        !            95: *
        !            96:       RETURN
        !            97: *
        !            98: *     End of DLAPLL
        !            99: *
        !           100:       END