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
|
*> \brief \b DNRM2
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DNRM2 returns the euclidean norm of a vector via the function
*> name, so that
*>
*> DNRM2 := sqrt( x'*x )
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of DX
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2017
*
*> \ingroup double_blas_level1
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> -- This version written on 25-October-1982.
*> Modified on 14-October-1993 to inline the call to DLASSQ.
*> Sven Hammarling, Nag Ltd.
*> \endverbatim
*>
* =====================================================================
DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX)
*
* -- Reference BLAS level1 routine (version 3.8.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2017
*
* .. Scalar Arguments ..
INTEGER INCX,N
* ..
* .. Array Arguments ..
DOUBLE PRECISION X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE,ZERO
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
* ..
* .. Local Scalars ..
DOUBLE PRECISION ABSXI,NORM,SCALE,SSQ
INTEGER IX
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS,SQRT
* ..
IF (N.LT.1 .OR. INCX.LT.1) THEN
NORM = ZERO
ELSE IF (N.EQ.1) THEN
NORM = ABS(X(1))
ELSE
SCALE = ZERO
SSQ = ONE
* The following loop is equivalent to this call to the LAPACK
* auxiliary routine:
* CALL DLASSQ( N, X, INCX, SCALE, SSQ )
*
DO 10 IX = 1,1 + (N-1)*INCX,INCX
IF (X(IX).NE.ZERO) THEN
ABSXI = ABS(X(IX))
IF (SCALE.LT.ABSXI) THEN
SSQ = ONE + SSQ* (SCALE/ABSXI)**2
SCALE = ABSXI
ELSE
SSQ = SSQ + (ABSXI/SCALE)**2
END IF
END IF
10 CONTINUE
NORM = SCALE*SQRT(SSQ)
END IF
*
DNRM2 = NORM
RETURN
*
* End of DNRM2.
*
END
|
