LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dlassq()

subroutine dlassq ( integer  N,
double precision, dimension( * )  X,
integer  INCX,
double precision  SCALE,
double precision  SUMSQ 
)

DLASSQ updates a sum of squares represented in scaled form.

Download DLASSQ + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DLASSQ  returns the values  scl  and  smsq  such that

    ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,

 where  x( i ) = X( 1 + ( i - 1 )*INCX ). The value of  sumsq  is
 assumed to be non-negative and  scl  returns the value

    scl = max( scale, abs( x( i ) ) ).

 scale and sumsq must be supplied in SCALE and SUMSQ and
 scl and smsq are overwritten on SCALE and SUMSQ respectively.

 The routine makes only one pass through the vector x.
Parameters
[in]N
          N is INTEGER
          The number of elements to be used from the vector X.
[in]X
          X is DOUBLE PRECISION array, dimension (N)
          The vector for which a scaled sum of squares is computed.
             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
[in]INCX
          INCX is INTEGER
          The increment between successive values of the vector X.
          INCX > 0.
[in,out]SCALE
          SCALE is DOUBLE PRECISION
          On entry, the value  scale  in the equation above.
          On exit, SCALE is overwritten with  scl , the scaling factor
          for the sum of squares.
[in,out]SUMSQ
          SUMSQ is DOUBLE PRECISION
          On entry, the value  sumsq  in the equation above.
          On exit, SUMSQ is overwritten with  smsq , the basic sum of
          squares from which  scl  has been factored out.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 105 of file dlassq.f.

105 *
106 * -- LAPACK auxiliary routine (version 3.7.0) --
107 * -- LAPACK is a software package provided by Univ. of Tennessee, --
108 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
109 * December 2016
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 * .. External Functions ..
130  LOGICAL disnan
131  EXTERNAL disnan
132 * ..
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
140  absxi = abs( x( ix ) )
141  IF( absxi.GT.zero.OR.disnan( absxi ) ) THEN
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 *
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:61
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