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.

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 (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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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