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Annotation of rpl/lapack/lapack/zlapll.f, revision 1.8

1.8     ! bertrand    1: *> \brief \b ZLAPLL
        !             2: *
        !             3: *  =========== DOCUMENTATION ===========
        !             4: *
        !             5: * Online html documentation available at 
        !             6: *            http://www.netlib.org/lapack/explore-html/ 
        !             7: *
        !             8: *> \htmlonly
        !             9: *> Download ZLAPLL + dependencies 
        !            10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlapll.f"> 
        !            11: *> [TGZ]</a> 
        !            12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlapll.f"> 
        !            13: *> [ZIP]</a> 
        !            14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlapll.f"> 
        !            15: *> [TXT]</a>
        !            16: *> \endhtmlonly 
        !            17: *
        !            18: *  Definition:
        !            19: *  ===========
        !            20: *
        !            21: *       SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN )
        !            22: * 
        !            23: *       .. Scalar Arguments ..
        !            24: *       INTEGER            INCX, INCY, N
        !            25: *       DOUBLE PRECISION   SSMIN
        !            26: *       ..
        !            27: *       .. Array Arguments ..
        !            28: *       COMPLEX*16         X( * ), Y( * )
        !            29: *       ..
        !            30: *  
        !            31: *
        !            32: *> \par Purpose:
        !            33: *  =============
        !            34: *>
        !            35: *> \verbatim
        !            36: *>
        !            37: *> Given two column vectors X and Y, let
        !            38: *>
        !            39: *>                      A = ( X Y ).
        !            40: *>
        !            41: *> The subroutine first computes the QR factorization of A = Q*R,
        !            42: *> and then computes the SVD of the 2-by-2 upper triangular matrix R.
        !            43: *> The smaller singular value of R is returned in SSMIN, which is used
        !            44: *> as the measurement of the linear dependency of the vectors X and Y.
        !            45: *> \endverbatim
        !            46: *
        !            47: *  Arguments:
        !            48: *  ==========
        !            49: *
        !            50: *> \param[in] N
        !            51: *> \verbatim
        !            52: *>          N is INTEGER
        !            53: *>          The length of the vectors X and Y.
        !            54: *> \endverbatim
        !            55: *>
        !            56: *> \param[in,out] X
        !            57: *> \verbatim
        !            58: *>          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
        !            59: *>          On entry, X contains the N-vector X.
        !            60: *>          On exit, X is overwritten.
        !            61: *> \endverbatim
        !            62: *>
        !            63: *> \param[in] INCX
        !            64: *> \verbatim
        !            65: *>          INCX is INTEGER
        !            66: *>          The increment between successive elements of X. INCX > 0.
        !            67: *> \endverbatim
        !            68: *>
        !            69: *> \param[in,out] Y
        !            70: *> \verbatim
        !            71: *>          Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
        !            72: *>          On entry, Y contains the N-vector Y.
        !            73: *>          On exit, Y is overwritten.
        !            74: *> \endverbatim
        !            75: *>
        !            76: *> \param[in] INCY
        !            77: *> \verbatim
        !            78: *>          INCY is INTEGER
        !            79: *>          The increment between successive elements of Y. INCY > 0.
        !            80: *> \endverbatim
        !            81: *>
        !            82: *> \param[out] SSMIN
        !            83: *> \verbatim
        !            84: *>          SSMIN is DOUBLE PRECISION
        !            85: *>          The smallest singular value of the N-by-2 matrix A = ( X Y ).
        !            86: *> \endverbatim
        !            87: *
        !            88: *  Authors:
        !            89: *  ========
        !            90: *
        !            91: *> \author Univ. of Tennessee 
        !            92: *> \author Univ. of California Berkeley 
        !            93: *> \author Univ. of Colorado Denver 
        !            94: *> \author NAG Ltd. 
        !            95: *
        !            96: *> \date November 2011
        !            97: *
        !            98: *> \ingroup complex16OTHERauxiliary
        !            99: *
        !           100: *  =====================================================================
1.1       bertrand  101:       SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN )
                    102: *
1.8     ! bertrand  103: *  -- LAPACK auxiliary routine (version 3.4.0) --
1.1       bertrand  104: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    105: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8     ! bertrand  106: *     November 2011
1.1       bertrand  107: *
                    108: *     .. Scalar Arguments ..
                    109:       INTEGER            INCX, INCY, N
                    110:       DOUBLE PRECISION   SSMIN
                    111: *     ..
                    112: *     .. Array Arguments ..
                    113:       COMPLEX*16         X( * ), Y( * )
                    114: *     ..
                    115: *
                    116: *  =====================================================================
                    117: *
                    118: *     .. Parameters ..
                    119:       DOUBLE PRECISION   ZERO
                    120:       PARAMETER          ( ZERO = 0.0D+0 )
                    121:       COMPLEX*16         CONE
                    122:       PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
                    123: *     ..
                    124: *     .. Local Scalars ..
                    125:       DOUBLE PRECISION   SSMAX
                    126:       COMPLEX*16         A11, A12, A22, C, TAU
                    127: *     ..
                    128: *     .. Intrinsic Functions ..
                    129:       INTRINSIC          ABS, DCONJG
                    130: *     ..
                    131: *     .. External Functions ..
                    132:       COMPLEX*16         ZDOTC
                    133:       EXTERNAL           ZDOTC
                    134: *     ..
                    135: *     .. External Subroutines ..
                    136:       EXTERNAL           DLAS2, ZAXPY, ZLARFG
                    137: *     ..
                    138: *     .. Executable Statements ..
                    139: *
                    140: *     Quick return if possible
                    141: *
                    142:       IF( N.LE.1 ) THEN
                    143:          SSMIN = ZERO
                    144:          RETURN
                    145:       END IF
                    146: *
                    147: *     Compute the QR factorization of the N-by-2 matrix ( X Y )
                    148: *
                    149:       CALL ZLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
                    150:       A11 = X( 1 )
                    151:       X( 1 ) = CONE
                    152: *
                    153:       C = -DCONJG( TAU )*ZDOTC( N, X, INCX, Y, INCY )
                    154:       CALL ZAXPY( N, C, X, INCX, Y, INCY )
                    155: *
                    156:       CALL ZLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU )
                    157: *
                    158:       A12 = Y( 1 )
                    159:       A22 = Y( 1+INCY )
                    160: *
                    161: *     Compute the SVD of 2-by-2 Upper triangular matrix.
                    162: *
                    163:       CALL DLAS2( ABS( A11 ), ABS( A12 ), ABS( A22 ), SSMIN, SSMAX )
                    164: *
                    165:       RETURN
                    166: *
                    167: *     End of ZLAPLL
                    168: *
                    169:       END