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/***************************************************/
/* 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;
}
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