summaryrefslogtreecommitdiff
path: root/numlib/sobol.c
blob: 40a2c3819bd8f3ed84e01ebfd9248a15626e0307 (plain)
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
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211

/***************************************************/
/* Sobol sub-random vector sequence generator      */
/***************************************************/

/* Code is an expression of the algorithm decsribed in */
/* the SSOBOL.F fortran source file, with additional */
/* guidance from "Numerical Recipes in C", by W.H.Press, B.P.Flannery, */
/* S.A.Teukolsky & W.T.Vetterling. */

/*
 * Copyright 2002 Graeme W. Gill
 * All rights reserved.
 *
 * This material is licenced under the GNU AFFERO GENERAL PUBLIC LICENSE Version 3 :-
 * see the License.txt file for licencing details.
 */

#include "numsup.h"
#include "sobol.h"

/*
 * The array poly gives successive primitive
 * polynomials coded in binary, e.g.
          45 = 100101
 * has bits 5, 2, and 0 set (counting from the
 * right) and therefore represents
        X**5 + X**2 + X**0

 * These polynomials are in the order used by
 * sobol in ussr comput. maths. math. phys. 16 (1977),
 * 236-242. 
 */

static int sobol_poly[SOBOL_MAXDIM] = {
	  1,   3,   7,  11,  13,  19,  25,  37,  59,  47,
	 61,  55,  41,  67,  97,  91, 109, 103, 115, 131,
	193, 137, 145, 143, 241, 157, 185, 167, 229, 171,
	213, 191, 253, 203, 211, 239, 247, 285, 369, 299
};

/*
 * The initialization of the array vinit is from 
 * Sobol and Levitan, the production of points uniformly
 * distributed in a multidimensional cube (in Russian),
 * preprint ipm akad. nauk sssr, no. 40, moscow 1976.
 * For a polynomial of degree m, m initial
 * values are needed : these are the values given here.
 * subsequent values are calculated during initialisation.
 */

static int vinit[8][SOBOL_MAXDIM] = {
	{
		0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
		1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
		1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
		1, 1, 1, 1, 1, 1, 1, 1, 1, 1 
	},
	{
		0, 0, 1, 3, 1, 3, 1, 3, 3, 1,
		3, 1, 3, 1, 3, 1, 1, 3, 1, 3, 
		1, 3, 1, 3, 3, 1, 3, 1, 3, 1, 
		3, 1, 1, 3, 1, 3, 1, 3, 1, 3
	},
	{
		0, 0, 0, 7, 5, 1, 3, 3, 7, 5, 
		5, 7, 7, 1, 3, 3, 7, 5, 1, 1, 
		5, 3, 3, 1, 7, 5, 1, 3, 3, 7, 
		5, 1, 1, 5, 7, 7, 5, 1, 3, 3
	},
	{
		0, 0, 0, 0, 0, 1, 7, 9, 13, 11, 
		1, 3, 7, 9, 5, 13, 13, 11, 3, 15, 
		5, 3, 15, 7, 9, 13, 9, 1, 11, 7, 
		5, 15, 1, 15, 11, 5, 3, 1, 7, 9
	},
	{
		0, 0, 0, 0, 0, 0, 0, 9, 3, 27, 
		15, 29, 21, 23, 19, 11, 25, 7, 13, 17, 
		1, 25, 29, 3, 31, 11, 5, 23, 27, 19, 
		21, 5, 1, 17, 13, 7, 15, 9, 31, 9
	},
	{
		0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
		0, 0, 0, 37, 33, 7, 5, 11, 39, 63, 
		27, 17, 15, 23, 29, 3, 21, 13, 31, 25, 
		9, 49, 33, 19, 29, 11, 19, 27, 15, 25
	},
	{
		0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
		0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 
		33, 115, 41, 79, 17, 29, 119, 75, 73, 105, 
		7, 59, 65, 21, 3, 113, 61, 89, 45, 107
	},
	{
		0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
		0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
		0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
		0, 0, 0, 0, 0, 0, 0, 7, 23, 39
	}
};

/* Get the next sobol vector */
/* return nz if we've run out */
static int next_sobol(sobol *s, double * v)
{
	int i, p;
	unsigned int c;

	s->count++;

	/* Find the position of the right-hand zero in count */
	for (c = s->count, p = 0; (c & 1) == 0; p++, c >>= 1)
		;

	if(p > SOBOL_MAXBIT)
		return 1;	/* Run out */

	for (i = 0; i < s->dim; i++) {
		s->lastq[i] ^= s->dir[p][i];
		v[i] = s->lastq[i] * s->recipd;
	}

	return 0;
}

/* Free up the object */
static void del_sobol(sobol *s) {
	if (s != NULL)
		free(s);
}

/* reset the count */
static void reset_sobol(sobol *s) {
	int i;

	/* Set up first vector and values */
	s->count = 0;
	for (i = 0; i < s->dim; i++)
		s->lastq[i] = 0;
}

/* Return NULL on error */
sobol *new_sobol(int dim) {
	sobol *s = NULL;
	int i, j, p;

	if (dim < 1 || dim > SOBOL_MAXDIM) {
		return NULL;
	}

	if ((s = (sobol *)malloc(sizeof(sobol))) == NULL) {
		return NULL;
	}

	s->dim  = dim;
	s->next  = next_sobol;
	s->reset = reset_sobol;
	s->del   = del_sobol;

	/* Initialize the direction table */
	for (i = 0; i < dim; i++) {

		if (i == 0) {
			for (j = 0; j < SOBOL_MAXBIT; j++)
				s->dir[j][i] = 1;
		} else {
			int m;				/* Degree */
			int pm;				/* Polinomial mask */
	
			/* Find degree of polynomial from binary encoding */
			for (m = 0, pm = sobol_poly[i] >> 1; pm != 0; m++, pm >>= 1)
				; 
	
			/* The leading elements of row i come from vinit[][] */
			for (j = 0; j < m; j++) {
				s->dir[j][i] = vinit[j][i];
			}
	
			/* Calculate remaining elements of row i as explained */
			/* in bratley and fox, section 2 */
			pm = sobol_poly[i];
			for (j = m; j < SOBOL_MAXBIT; j++) {
				int k;
				int newv = s->dir[j-m][i];
				for (k = 0; k < m; k++) {
					if (pm & (1 << (m-k-1))) {
						newv ^= s->dir[j-k-1][i] << (k+1);
					}
				}
				s->dir[j][i] = newv;
			}
		}
	}
	/* Multiply columns of v by appropriate power of 2 */
	for (p = 2, j = SOBOL_MAXBIT-2; j >= 0; j--, p <<= 1) {
		for (i = 0; i < dim; i++)
			s->dir[j][i] *= p;
	}

	/* recipd is 1/(common denominator of the elements in v) */
	s->recipd = 1.0/(1 << SOBOL_MAXBIT);

	/* Set up first vector and values */
	s->count = 0;
	for (i = 0; i < dim; i++)
		s->lastq[i] = 0;

	return s;
}