1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
|
*> \brief \b DLASSQ updates a sum of squares represented in scaled form.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASSQ + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlassq.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlassq.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlassq.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
*
* .. Scalar Arguments ..
* INTEGER INCX, N
* DOUBLE PRECISION SCALE, SUMSQ
* ..
* .. Array Arguments ..
* DOUBLE PRECISION X( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of elements to be used from the vector X.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> The increment between successive values of the vector X.
*> INCX > 0.
*> \endverbatim
*>
*> \param[in,out] SCALE
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in,out] SUMSQ
*> \verbatim
*> 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup OTHERauxiliary
*
* =====================================================================
SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER INCX, N
DOUBLE PRECISION SCALE, SUMSQ
* ..
* .. Array Arguments ..
DOUBLE PRECISION X( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER IX
DOUBLE PRECISION ABSXI
* ..
* .. External Functions ..
LOGICAL DISNAN
EXTERNAL DISNAN
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS
* ..
* .. Executable Statements ..
*
IF( N.GT.0 ) THEN
DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX
ABSXI = ABS( X( IX ) )
IF( ABSXI.GT.ZERO.OR.DISNAN( ABSXI ) ) THEN
IF( SCALE.LT.ABSXI ) THEN
SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2
SCALE = ABSXI
ELSE
SUMSQ = SUMSQ + ( ABSXI / SCALE )**2
END IF
END IF
10 CONTINUE
END IF
RETURN
*
* End of DLASSQ
*
END
|
