LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
dlarnv.f
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1 *> \brief \b DLARNV returns a vector of random numbers from a uniform or normal distribution.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DLARNV( IDIST, ISEED, N, X )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER IDIST, N
25 * ..
26 * .. Array Arguments ..
27 * INTEGER ISEED( 4 )
28 * DOUBLE PRECISION X( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> DLARNV returns a vector of n random real numbers from a uniform or
38 *> normal distribution.
39 *> \endverbatim
40 *
41 * Arguments:
42 * ==========
43 *
44 *> \param[in] IDIST
45 *> \verbatim
46 *> IDIST is INTEGER
47 *> Specifies the distribution of the random numbers:
48 *> = 1: uniform (0,1)
49 *> = 2: uniform (-1,1)
50 *> = 3: normal (0,1)
51 *> \endverbatim
52 *>
53 *> \param[in,out] ISEED
54 *> \verbatim
55 *> ISEED is INTEGER array, dimension (4)
56 *> On entry, the seed of the random number generator; the array
57 *> elements must be between 0 and 4095, and ISEED(4) must be
58 *> odd.
59 *> On exit, the seed is updated.
60 *> \endverbatim
61 *>
62 *> \param[in] N
63 *> \verbatim
64 *> N is INTEGER
65 *> The number of random numbers to be generated.
66 *> \endverbatim
67 *>
68 *> \param[out] X
69 *> \verbatim
70 *> X is DOUBLE PRECISION array, dimension (N)
71 *> The generated random numbers.
72 *> \endverbatim
73 *
74 * Authors:
75 * ========
76 *
77 *> \author Univ. of Tennessee
78 *> \author Univ. of California Berkeley
79 *> \author Univ. of Colorado Denver
80 *> \author NAG Ltd.
81 *
82 *> \date September 2012
83 *
84 *> \ingroup auxOTHERauxiliary
85 *
86 *> \par Further Details:
87 * =====================
88 *>
89 *> \verbatim
90 *>
91 *> This routine calls the auxiliary routine DLARUV to generate random
92 *> real numbers from a uniform (0,1) distribution, in batches of up to
93 *> 128 using vectorisable code. The Box-Muller method is used to
94 *> transform numbers from a uniform to a normal distribution.
95 *> \endverbatim
96 *>
97 * =====================================================================
98  SUBROUTINE dlarnv( IDIST, ISEED, N, X )
99 *
100 * -- LAPACK auxiliary routine (version 3.4.2) --
101 * -- LAPACK is a software package provided by Univ. of Tennessee, --
102 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
103 * September 2012
104 *
105 * .. Scalar Arguments ..
106  INTEGER idist, n
107 * ..
108 * .. Array Arguments ..
109  INTEGER iseed( 4 )
110  DOUBLE PRECISION x( * )
111 * ..
112 *
113 * =====================================================================
114 *
115 * .. Parameters ..
116  DOUBLE PRECISION one, two
117  parameter( one = 1.0d+0, two = 2.0d+0 )
118  INTEGER lv
119  parameter( lv = 128 )
120  DOUBLE PRECISION twopi
121  parameter( twopi = 6.2831853071795864769252867663d+0 )
122 * ..
123 * .. Local Scalars ..
124  INTEGER i, il, il2, iv
125 * ..
126 * .. Local Arrays ..
127  DOUBLE PRECISION u( lv )
128 * ..
129 * .. Intrinsic Functions ..
130  INTRINSIC cos, log, min, sqrt
131 * ..
132 * .. External Subroutines ..
133  EXTERNAL dlaruv
134 * ..
135 * .. Executable Statements ..
136 *
137  DO 40 iv = 1, n, lv / 2
138  il = min( lv / 2, n-iv+1 )
139  IF( idist.EQ.3 ) THEN
140  il2 = 2*il
141  ELSE
142  il2 = il
143  END IF
144 *
145 * Call DLARUV to generate IL2 numbers from a uniform (0,1)
146 * distribution (IL2 <= LV)
147 *
148  CALL dlaruv( iseed, il2, u )
149 *
150  IF( idist.EQ.1 ) THEN
151 *
152 * Copy generated numbers
153 *
154  DO 10 i = 1, il
155  x( iv+i-1 ) = u( i )
156  10 continue
157  ELSE IF( idist.EQ.2 ) THEN
158 *
159 * Convert generated numbers to uniform (-1,1) distribution
160 *
161  DO 20 i = 1, il
162  x( iv+i-1 ) = two*u( i ) - one
163  20 continue
164  ELSE IF( idist.EQ.3 ) THEN
165 *
166 * Convert generated numbers to normal (0,1) distribution
167 *
168  DO 30 i = 1, il
169  x( iv+i-1 ) = sqrt( -two*log( u( 2*i-1 ) ) )*
170  \$ cos( twopi*u( 2*i ) )
171  30 continue
172  END IF
173  40 continue
174  return
175 *
176 * End of DLARNV
177 *
178  END