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Diffstat (limited to 'gsl-1.9/qrng/sobol.c')
| -rw-r--r-- | gsl-1.9/qrng/sobol.c | 231 |
1 files changed, 231 insertions, 0 deletions
diff --git a/gsl-1.9/qrng/sobol.c b/gsl-1.9/qrng/sobol.c new file mode 100644 index 0000000..51c9baa --- /dev/null +++ b/gsl-1.9/qrng/sobol.c @@ -0,0 +1,231 @@ +/* Author: G. Jungman + */ +/* Implementation for Sobol generator. + * See + * [Bratley+Fox, TOMS 14, 88 (1988)] + * [Antonov+Saleev, USSR Comput. Maths. Math. Phys. 19, 252 (1980)] + */ +#include <config.h> +#include <gsl/gsl_qrng.h> + + +/* maximum allowed space dimension */ +#define SOBOL_MAX_DIMENSION 40 + +/* bit count; assumes sizeof(int) >= 32-bit */ +#define SOBOL_BIT_COUNT 30 + +/* prototypes for generator type functions */ +static size_t sobol_state_size(unsigned int dimension); +static int sobol_init(void * state, unsigned int dimension); +static int sobol_get(void * state, unsigned int dimension, double * v); + +/* global Sobol generator type object */ +static const gsl_qrng_type sobol_type = +{ + "sobol", + SOBOL_MAX_DIMENSION, + sobol_state_size, + sobol_init, + sobol_get +}; +const gsl_qrng_type * gsl_qrng_sobol = &sobol_type; + + +/* primitive polynomials in binary encoding + */ +static const int primitive_polynomials[SOBOL_MAX_DIMENSION] = +{ + 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 +}; + +/* degrees of the primitive polynomials */ +static const int degree_table[SOBOL_MAX_DIMENSION] = +{ + 0, 1, 2, 3, 3, 4, 4, 5, 5, 5, + 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, + 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, + 7, 7, 7, 7, 7, 7, 7, 8, 8, 8 +}; + + +/* initial values for direction tables, following + * Bratley+Fox, taken from [Sobol+Levitan, preprint 1976] + */ +static const int v_init[8][SOBOL_MAX_DIMENSION] = +{ + { + 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 + } +}; + + +/* Sobol generator state. + * sequence_count = number of calls with this generator + * last_numerator_vec = last generated numerator vector + * last_denominator_inv = 1/denominator for last numerator vector + * v_direction = direction number table + */ +typedef struct +{ + unsigned int sequence_count; + double last_denominator_inv; + int last_numerator_vec[SOBOL_MAX_DIMENSION]; + int v_direction[SOBOL_BIT_COUNT][SOBOL_MAX_DIMENSION]; +} sobol_state_t; + +/* NOTE: I fixed the size for the preliminary implementation. + This could/should be relaxed, as an optimization. + */ + +static size_t sobol_state_size(unsigned int dimension) +{ + return sizeof(sobol_state_t); +} + + +static int sobol_init(void * state, unsigned int dimension) +{ + sobol_state_t * s_state = (sobol_state_t *) state; + unsigned int i_dim; + int j, k; + int ell; + + if(dimension < 1 || dimension > SOBOL_MAX_DIMENSION) { + return GSL_EINVAL; + } + + /* Initialize direction table in dimension 0. */ + for(k=0; k<SOBOL_BIT_COUNT; k++) s_state->v_direction[k][0] = 1; + + /* Initialize in remaining dimensions. */ + for(i_dim=1; i_dim<dimension; i_dim++) { + + const int poly_index = i_dim; + const int degree_i = degree_table[poly_index]; + int includ[8]; + + /* Expand the polynomial bit pattern to separate + * components of the logical array includ[]. + */ + int p_i = primitive_polynomials[poly_index]; + for(k = degree_i-1; k >= 0; k--) { + includ[k] = ((p_i % 2) == 1); + p_i /= 2; + } + + /* Leading elements for dimension i come from v_init[][]. */ + for(j=0; j<degree_i; j++) s_state->v_direction[j][i_dim] = v_init[j][i_dim]; + + /* Calculate remaining elements for this dimension, + * as explained in Bratley+Fox, section 2. + */ + for(j=degree_i; j<SOBOL_BIT_COUNT; j++) { + int newv = s_state->v_direction[j-degree_i][i_dim]; + ell = 1; + for(k=0; k<degree_i; k++) { + ell *= 2; + if(includ[k]) newv ^= (ell * s_state->v_direction[j-k-1][i_dim]); + } + s_state->v_direction[j][i_dim] = newv; + } + } + + /* Multiply columns of v by appropriate power of 2. */ + ell = 1; + for(j=SOBOL_BIT_COUNT-1-1; j>=0; j--) { + ell *= 2; + for(i_dim=0; i_dim<dimension; i_dim++) { + s_state->v_direction[j][i_dim] *= ell; + } + } + + /* 1/(common denominator of the elements in v_direction) */ + s_state->last_denominator_inv = 1.0 /(2.0 * ell); + + /* final setup */ + s_state->sequence_count = 0; + for(i_dim=0; i_dim<dimension; i_dim++) s_state->last_numerator_vec[i_dim] = 0; + + return GSL_SUCCESS; +} + + +static int sobol_get(void * state, unsigned int dimension, double * v) +{ + sobol_state_t * s_state = (sobol_state_t *) state; + + unsigned int i_dimension; + + /* Find the position of the least-significant zero in count. */ + int ell = 0; + int c = s_state->sequence_count; + while(1) { + ++ell; + if((c % 2) == 1) c /= 2; + else break; + } + + /* Check for exhaustion. */ + if(ell > SOBOL_BIT_COUNT) return GSL_EFAILED; /* FIXME: good return code here */ + + for(i_dimension=0; i_dimension<dimension; i_dimension++) { + const int direction_i = s_state->v_direction[ell-1][i_dimension]; + const int old_numerator_i = s_state->last_numerator_vec[i_dimension]; + const int new_numerator_i = old_numerator_i ^ direction_i; + s_state->last_numerator_vec[i_dimension] = new_numerator_i; + v[i_dimension] = new_numerator_i * s_state->last_denominator_inv; + } + + s_state->sequence_count++; + + return GSL_SUCCESS; +} |