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

1.8     ! bertrand    1: *> \brief \b DLASSQ
        !             2: *
        !             3: *  =========== DOCUMENTATION ===========
        !             4: *
        !             5: * Online html documentation available at 
        !             6: *            http://www.netlib.org/lapack/explore-html/ 
        !             7: *
        !             8: *> \htmlonly
        !             9: *> Download DLASSQ + dependencies 
        !            10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlassq.f"> 
        !            11: *> [TGZ]</a> 
        !            12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlassq.f"> 
        !            13: *> [ZIP]</a> 
        !            14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlassq.f"> 
        !            15: *> [TXT]</a>
        !            16: *> \endhtmlonly 
        !            17: *
        !            18: *  Definition:
        !            19: *  ===========
        !            20: *
        !            21: *       SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
        !            22: * 
        !            23: *       .. Scalar Arguments ..
        !            24: *       INTEGER            INCX, N
        !            25: *       DOUBLE PRECISION   SCALE, SUMSQ
        !            26: *       ..
        !            27: *       .. Array Arguments ..
        !            28: *       DOUBLE PRECISION   X( * )
        !            29: *       ..
        !            30: *  
        !            31: *
        !            32: *> \par Purpose:
        !            33: *  =============
        !            34: *>
        !            35: *> \verbatim
        !            36: *>
        !            37: *> DLASSQ  returns the values  scl  and  smsq  such that
        !            38: *>
        !            39: *>    ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
        !            40: *>
        !            41: *> where  x( i ) = X( 1 + ( i - 1 )*INCX ). The value of  sumsq  is
        !            42: *> assumed to be non-negative and  scl  returns the value
        !            43: *>
        !            44: *>    scl = max( scale, abs( x( i ) ) ).
        !            45: *>
        !            46: *> scale and sumsq must be supplied in SCALE and SUMSQ and
        !            47: *> scl and smsq are overwritten on SCALE and SUMSQ respectively.
        !            48: *>
        !            49: *> The routine makes only one pass through the vector x.
        !            50: *> \endverbatim
        !            51: *
        !            52: *  Arguments:
        !            53: *  ==========
        !            54: *
        !            55: *> \param[in] N
        !            56: *> \verbatim
        !            57: *>          N is INTEGER
        !            58: *>          The number of elements to be used from the vector X.
        !            59: *> \endverbatim
        !            60: *>
        !            61: *> \param[in] X
        !            62: *> \verbatim
        !            63: *>          X is DOUBLE PRECISION array, dimension (N)
        !            64: *>          The vector for which a scaled sum of squares is computed.
        !            65: *>             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
        !            66: *> \endverbatim
        !            67: *>
        !            68: *> \param[in] INCX
        !            69: *> \verbatim
        !            70: *>          INCX is INTEGER
        !            71: *>          The increment between successive values of the vector X.
        !            72: *>          INCX > 0.
        !            73: *> \endverbatim
        !            74: *>
        !            75: *> \param[in,out] SCALE
        !            76: *> \verbatim
        !            77: *>          SCALE is DOUBLE PRECISION
        !            78: *>          On entry, the value  scale  in the equation above.
        !            79: *>          On exit, SCALE is overwritten with  scl , the scaling factor
        !            80: *>          for the sum of squares.
        !            81: *> \endverbatim
        !            82: *>
        !            83: *> \param[in,out] SUMSQ
        !            84: *> \verbatim
        !            85: *>          SUMSQ is DOUBLE PRECISION
        !            86: *>          On entry, the value  sumsq  in the equation above.
        !            87: *>          On exit, SUMSQ is overwritten with  smsq , the basic sum of
        !            88: *>          squares from which  scl  has been factored out.
        !            89: *> \endverbatim
        !            90: *
        !            91: *  Authors:
        !            92: *  ========
        !            93: *
        !            94: *> \author Univ. of Tennessee 
        !            95: *> \author Univ. of California Berkeley 
        !            96: *> \author Univ. of Colorado Denver 
        !            97: *> \author NAG Ltd. 
        !            98: *
        !            99: *> \date November 2011
        !           100: *
        !           101: *> \ingroup auxOTHERauxiliary
        !           102: *
        !           103: *  =====================================================================
1.1       bertrand  104:       SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
                    105: *
1.8     ! bertrand  106: *  -- LAPACK auxiliary routine (version 3.4.0) --
1.1       bertrand  107: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    108: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8     ! bertrand  109: *     November 2011
1.1       bertrand  110: *
                    111: *     .. Scalar Arguments ..
                    112:       INTEGER            INCX, N
                    113:       DOUBLE PRECISION   SCALE, SUMSQ
                    114: *     ..
                    115: *     .. Array Arguments ..
                    116:       DOUBLE PRECISION   X( * )
                    117: *     ..
                    118: *
                    119: * =====================================================================
                    120: *
                    121: *     .. Parameters ..
                    122:       DOUBLE PRECISION   ZERO
                    123:       PARAMETER          ( ZERO = 0.0D+0 )
                    124: *     ..
                    125: *     .. Local Scalars ..
                    126:       INTEGER            IX
                    127:       DOUBLE PRECISION   ABSXI
                    128: *     ..
                    129: *     .. Intrinsic Functions ..
                    130:       INTRINSIC          ABS
                    131: *     ..
                    132: *     .. Executable Statements ..
                    133: *
                    134:       IF( N.GT.0 ) THEN
                    135:          DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX
                    136:             IF( X( IX ).NE.ZERO ) THEN
                    137:                ABSXI = ABS( X( IX ) )
                    138:                IF( SCALE.LT.ABSXI ) THEN
                    139:                   SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2
                    140:                   SCALE = ABSXI
                    141:                ELSE
                    142:                   SUMSQ = SUMSQ + ( ABSXI / SCALE )**2
                    143:                END IF
                    144:             END IF
                    145:    10    CONTINUE
                    146:       END IF
                    147:       RETURN
                    148: *
                    149: *     End of DLASSQ
                    150: *
                    151:       END