 LAPACK  3.9.1 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.

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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 (1+(N-1)*INCX) 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.```

Definition at line 102 of file dlassq.f.

103 *
104 * -- LAPACK auxiliary routine --
105 * -- LAPACK is a software package provided by Univ. of Tennessee, --
106 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
107 *
108 * .. Scalar Arguments ..
109  INTEGER INCX, N
110  DOUBLE PRECISION SCALE, SUMSQ
111 * ..
112 * .. Array Arguments ..
113  DOUBLE PRECISION X( * )
114 * ..
115 *
116 * =====================================================================
117 *
118 * .. Parameters ..
119  DOUBLE PRECISION ZERO
120  parameter( zero = 0.0d+0 )
121 * ..
122 * .. Local Scalars ..
123  INTEGER IX
124  DOUBLE PRECISION ABSXI
125 * ..
126 * .. External Functions ..
127  LOGICAL DISNAN
128  EXTERNAL disnan
129 * ..
130 * .. Intrinsic Functions ..
131  INTRINSIC abs
132 * ..
133 * .. Executable Statements ..
134 *
135  IF( n.GT.0 ) THEN
136  DO 10 ix = 1, 1 + ( n-1 )*incx, incx
137  absxi = abs( x( ix ) )
138  IF( absxi.GT.zero.OR.disnan( absxi ) ) THEN
139  IF( scale.LT.absxi ) THEN
140  sumsq = 1 + sumsq*( scale / absxi )**2
141  scale = absxi
142  ELSE
143  sumsq = sumsq + ( absxi / scale )**2
144  END IF
145  END IF
146  10 CONTINUE
147  END IF
148  RETURN
149 *
150 * End of DLASSQ
151 *
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
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