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Annotation of rpl/lapack/lapack/dlassq.f, revision 1.18

1.11      bertrand    1: *> \brief \b DLASSQ updates a sum of squares represented in scaled form.
1.8       bertrand    2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
1.15      bertrand    5: * Online html documentation available at
                      6: *            http://www.netlib.org/lapack/explore-html/
1.8       bertrand    7: *
                      8: *> \htmlonly
1.15      bertrand    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">
1.8       bertrand   15: *> [TXT]</a>
1.15      bertrand   16: *> \endhtmlonly
1.8       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
1.15      bertrand   22: *
1.8       bertrand   23: *       .. Scalar Arguments ..
                     24: *       INTEGER            INCX, N
                     25: *       DOUBLE PRECISION   SCALE, SUMSQ
                     26: *       ..
                     27: *       .. Array Arguments ..
                     28: *       DOUBLE PRECISION   X( * )
                     29: *       ..
1.15      bertrand   30: *
1.8       bertrand   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
1.18    ! bertrand   63: *>          X is DOUBLE PRECISION array, dimension (1+(N-1)*INCX)
1.8       bertrand   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: *
1.15      bertrand   94: *> \author Univ. of Tennessee
                     95: *> \author Univ. of California Berkeley
                     96: *> \author Univ. of Colorado Denver
                     97: *> \author NAG Ltd.
1.8       bertrand   98: *
1.15      bertrand   99: *> \date December 2016
1.8       bertrand  100: *
1.15      bertrand  101: *> \ingroup OTHERauxiliary
1.8       bertrand  102: *
                    103: *  =====================================================================
1.1       bertrand  104:       SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
                    105: *
1.15      bertrand  106: *  -- LAPACK auxiliary routine (version 3.7.0) --
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..--
1.15      bertrand  109: *     December 2016
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: *     ..
1.11      bertrand  129: *     .. External Functions ..
                    130:       LOGICAL            DISNAN
                    131:       EXTERNAL           DISNAN
                    132: *     ..
1.1       bertrand  133: *     .. Intrinsic Functions ..
                    134:       INTRINSIC          ABS
                    135: *     ..
                    136: *     .. Executable Statements ..
                    137: *
                    138:       IF( N.GT.0 ) THEN
                    139:          DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX
1.11      bertrand  140:             ABSXI = ABS( X( IX ) )
                    141:             IF( ABSXI.GT.ZERO.OR.DISNAN( ABSXI ) ) THEN
1.1       bertrand  142:                IF( SCALE.LT.ABSXI ) THEN
                    143:                   SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2
                    144:                   SCALE = ABSXI
                    145:                ELSE
                    146:                   SUMSQ = SUMSQ + ( ABSXI / SCALE )**2
                    147:                END IF
                    148:             END IF
                    149:    10    CONTINUE
                    150:       END IF
                    151:       RETURN
                    152: *
                    153: *     End of DLASSQ
                    154: *
                    155:       END