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/* monte/vegas.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000 Michael Booth
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* Copyright (C) 2009 Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* Author: MJB */
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/* Modified by: Brian Gough, 12/2000 */
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/* This is an implementation of the adaptive Monte-Carlo algorithm
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of G. P. Lepage, originally described in J. Comp. Phys. 27, 192(1978).
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The current version of the algorithm was described in the Cornell
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preprint CLNS-80/447 of March, 1980.
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This code follows most closely the c version by D.R.Yennie, coded
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in 1984.
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The input coordinates are x[j], with upper and lower limits xu[j]
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and xl[j]. The integration length in the j-th direction is
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delx[j]. Each coordinate x[j] is rescaled to a variable y[j] in
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the range 0 to 1. The range is divided into bins with boundaries
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xi[i][j], where i=0 corresponds to y=0 and i=bins to y=1. The grid
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is refined (ie, bins are adjusted) using d[i][j] which is some
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variation on the squared sum. A third parameter used in defining
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the real coordinate using random numbers is called z. It ranges
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from 0 to bins. Its integer part gives the lower index of the bin
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into which a call is to be placed, and the remainder gives the
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location inside the bin.
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When stratified sampling is used the bins are grouped into boxes,
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and the algorithm allocates an equal number of function calls to
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each box.
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The variable alpha controls how "stiff" the rebinning algorithm is.
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alpha = 0 means never change the grid. Alpha is typically set between
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1 and 2.
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*/
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/* configuration headers */
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#include <config.h>
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/* standard headers */
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#include <math.h>
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#include <stdio.h>
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/* gsl headers */
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_errno.h>
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#include <gsl/gsl_rng.h>
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#include <gsl/gsl_monte_vegas.h>
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/* lib-specific headers */
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#define BINS_MAX 50 /* even integer, will be divided by two */
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/* A separable grid with coordinates and values */
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#define COORD(s,i,j) ((s)->xi[(i)*(s)->dim + (j)])
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#define NEW_COORD(s,i) ((s)->xin[(i)])
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#define VALUE(s,i,j) ((s)->d[(i)*(s)->dim + (j)])
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#define USE_ORIGINAL_CHISQ_FORMULA 0
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/* predeclare functions */
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typedef int coord;
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static void init_grid (gsl_monte_vegas_state * s, double xl[], double xu[],
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size_t dim);
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static void reset_grid_values (gsl_monte_vegas_state * s);
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static void init_box_coord (gsl_monte_vegas_state * s, coord box[]);
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static int change_box_coord (gsl_monte_vegas_state * s, coord box[]);
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static void accumulate_distribution (gsl_monte_vegas_state * s, coord bin[],
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double y);
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static void random_point (double x[], coord bin[], double *bin_vol,
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const coord box[],
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const double xl[], const double xu[],
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gsl_monte_vegas_state * s, gsl_rng * r);
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static void resize_grid (gsl_monte_vegas_state * s, unsigned int bins);
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static void refine_grid (gsl_monte_vegas_state * s);
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static void print_lim (gsl_monte_vegas_state * state,
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double xl[], double xu[], unsigned long dim);
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static void print_head (gsl_monte_vegas_state * state,
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unsigned long num_dim, unsigned long calls,
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unsigned int it_num,
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unsigned int bins, unsigned int boxes);
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static void print_res (gsl_monte_vegas_state * state,
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unsigned int itr, double res, double err,
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double cum_res, double cum_err,
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double chi_sq);
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static void print_dist (gsl_monte_vegas_state * state, unsigned long dim);
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static void print_grid (gsl_monte_vegas_state * state, unsigned long dim);
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int
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gsl_monte_vegas_integrate (gsl_monte_function * f,
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double xl[], double xu[],
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size_t dim, size_t calls,
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gsl_rng * r,
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gsl_monte_vegas_state * state,
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double *result, double *abserr)
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{
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double cum_int, cum_sig;
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size_t i, k, it;
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if (dim != state->dim)
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{
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GSL_ERROR ("number of dimensions must match allocated size", GSL_EINVAL);
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}
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for (i = 0; i < dim; i++)
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{
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if (xu[i] <= xl[i])
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{
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GSL_ERROR ("xu must be greater than xl", GSL_EINVAL);
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}
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if (xu[i] - xl[i] > GSL_DBL_MAX)
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{
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GSL_ERROR ("Range of integration is too large, please rescale",
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GSL_EINVAL);
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}
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}
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if (state->stage == 0)
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{
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init_grid (state, xl, xu, dim);
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if (state->verbose >= 0)
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{
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print_lim (state, xl, xu, dim);
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}
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}
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if (state->stage <= 1)
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{
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state->wtd_int_sum = 0;
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state->sum_wgts = 0;
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state->chi_sum = 0;
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state->it_num = 1;
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state->samples = 0;
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state->chisq = 0;
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}
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if (state->stage <= 2)
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{
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unsigned int bins = state->bins_max;
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unsigned int boxes = 1;
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if (state->mode != GSL_VEGAS_MODE_IMPORTANCE_ONLY)
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{
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/* shooting for 2 calls/box */
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boxes = floor (pow (calls / 2.0, 1.0 / dim));
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state->mode = GSL_VEGAS_MODE_IMPORTANCE;
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if (2 * boxes >= state->bins_max)
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{
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/* if bins/box < 2 */
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int box_per_bin = GSL_MAX (boxes / state->bins_max, 1);
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bins = GSL_MIN(boxes / box_per_bin, state->bins_max);
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boxes = box_per_bin * bins;
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state->mode = GSL_VEGAS_MODE_STRATIFIED;
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}
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}
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{
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double tot_boxes = gsl_pow_int ((double) boxes, dim);
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state->calls_per_box = GSL_MAX (calls / tot_boxes, 2);
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calls = state->calls_per_box * tot_boxes;
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}
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/* total volume of x-space/(avg num of calls/bin) */
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state->jac = state->vol * pow ((double) bins, (double) dim) / calls;
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state->boxes = boxes;
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/* If the number of bins changes from the previous invocation, bins
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are expanded or contracted accordingly, while preserving bin
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density */
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if (bins != state->bins)
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{
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resize_grid (state, bins);
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if (state->verbose > 1)
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{
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print_grid (state, dim);
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}
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}
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if (state->verbose >= 0)
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{
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print_head (state,
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dim, calls, state->it_num, state->bins, state->boxes);
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}
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}
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state->it_start = state->it_num;
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cum_int = 0.0;
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cum_sig = 0.0;
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for (it = 0; it < state->iterations; it++)
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{
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double intgrl = 0.0, intgrl_sq = 0.0;
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double tss = 0.0;
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double wgt, var, sig;
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size_t calls_per_box = state->calls_per_box;
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double jacbin = state->jac;
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double *x = state->x;
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coord *bin = state->bin;
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state->it_num = state->it_start + it;
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reset_grid_values (state);
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init_box_coord (state, state->box);
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do
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{
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volatile double m = 0, q = 0;
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double f_sq_sum = 0.0;
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for (k = 0; k < calls_per_box; k++)
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{
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volatile double fval;
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double bin_vol;
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random_point (x, bin, &bin_vol, state->box, xl, xu, state, r);
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fval = jacbin * bin_vol * GSL_MONTE_FN_EVAL (f, x);
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/* recurrence for mean and variance (sum of squares) */
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{
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double d = fval - m;
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m += d / (k + 1.0);
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q += d * d * (k / (k + 1.0));
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}
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if (state->mode != GSL_VEGAS_MODE_STRATIFIED)
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{
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double f_sq = fval * fval;
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accumulate_distribution (state, bin, f_sq);
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}
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}
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intgrl += m * calls_per_box;
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f_sq_sum = q * calls_per_box;
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tss += f_sq_sum;
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if (state->mode == GSL_VEGAS_MODE_STRATIFIED)
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{
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accumulate_distribution (state, bin, f_sq_sum);
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}
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}
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while (change_box_coord (state, state->box));
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/* Compute final results for this iteration */
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var = tss / (calls_per_box - 1.0) ;
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if (var > 0)
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{
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wgt = 1.0 / var;
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}
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else if (state->sum_wgts > 0)
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{
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wgt = state->sum_wgts / state->samples;
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}
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else
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{
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wgt = 0.0;
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}
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intgrl_sq = intgrl * intgrl;
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sig = sqrt (var);
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state->result = intgrl;
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state->sigma = sig;
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if (wgt > 0.0)
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{
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double sum_wgts = state->sum_wgts;
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double wtd_int_sum = state->wtd_int_sum;
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double m = (sum_wgts > 0) ? (wtd_int_sum / sum_wgts) : 0;
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double q = intgrl - m;
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state->samples++ ;
|
|
Packit |
67cb25 |
state->sum_wgts += wgt;
|
|
Packit |
67cb25 |
state->wtd_int_sum += intgrl * wgt;
|
|
Packit |
67cb25 |
state->chi_sum += intgrl_sq * wgt;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
cum_int = state->wtd_int_sum / state->sum_wgts;
|
|
Packit |
67cb25 |
cum_sig = sqrt (1 / state->sum_wgts);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
#if USE_ORIGINAL_CHISQ_FORMULA
|
|
Packit |
67cb25 |
/* This is the chisq formula from the original Lepage paper. It
|
|
Packit |
67cb25 |
computes the variance from <x^2> - <x>^2 and can suffer from
|
|
Packit |
67cb25 |
catastrophic cancellations, e.g. returning negative chisq. */
|
|
Packit |
67cb25 |
if (state->samples > 1)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
state->chisq = (state->chi_sum - state->wtd_int_sum * cum_int) /
|
|
Packit |
67cb25 |
(state->samples - 1.0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
#else
|
|
Packit |
67cb25 |
/* The new formula below computes exactly the same quantity as above
|
|
Packit |
67cb25 |
but using a stable recurrence */
|
|
Packit |
67cb25 |
if (state->samples == 1) {
|
|
Packit |
67cb25 |
state->chisq = 0;
|
|
Packit |
67cb25 |
} else {
|
|
Packit |
67cb25 |
state->chisq *= (state->samples - 2.0);
|
|
Packit |
67cb25 |
state->chisq += (wgt / (1 + (wgt / sum_wgts))) * q * q;
|
|
Packit |
67cb25 |
state->chisq /= (state->samples - 1.0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
#endif
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
cum_int += (intgrl - cum_int) / (it + 1.0);
|
|
Packit |
67cb25 |
cum_sig = 0.0;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (state->verbose >= 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
print_res (state,
|
|
Packit |
67cb25 |
state->it_num, intgrl, sig, cum_int, cum_sig,
|
|
Packit |
67cb25 |
state->chisq);
|
|
Packit |
67cb25 |
if (it + 1 == state->iterations && state->verbose > 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
print_grid (state, dim);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (state->verbose > 1)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
print_dist (state, dim);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
refine_grid (state);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (state->verbose > 1)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
print_grid (state, dim);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* By setting stage to 1 further calls will generate independent
|
|
Packit |
67cb25 |
estimates based on the same grid, although it may be rebinned. */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
state->stage = 1;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
*result = cum_int;
|
|
Packit |
67cb25 |
*abserr = cum_sig;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_monte_vegas_state *
|
|
Packit |
67cb25 |
gsl_monte_vegas_alloc (size_t dim)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
gsl_monte_vegas_state *s =
|
|
Packit |
67cb25 |
(gsl_monte_vegas_state *) malloc (sizeof (gsl_monte_vegas_state));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (s == 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
GSL_ERROR_VAL ("failed to allocate space for vegas state struct",
|
|
Packit |
67cb25 |
GSL_ENOMEM, 0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->delx = (double *) malloc (dim * sizeof (double));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (s->delx == 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
free (s);
|
|
Packit |
67cb25 |
GSL_ERROR_VAL ("failed to allocate space for delx", GSL_ENOMEM, 0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->d = (double *) malloc (BINS_MAX * dim * sizeof (double));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (s->d == 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
free (s->delx);
|
|
Packit |
67cb25 |
free (s);
|
|
Packit |
67cb25 |
GSL_ERROR_VAL ("failed to allocate space for d", GSL_ENOMEM, 0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->xi = (double *) malloc ((BINS_MAX + 1) * dim * sizeof (double));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (s->xi == 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
free (s->d);
|
|
Packit |
67cb25 |
free (s->delx);
|
|
Packit |
67cb25 |
free (s);
|
|
Packit |
67cb25 |
GSL_ERROR_VAL ("failed to allocate space for xi", GSL_ENOMEM, 0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->xin = (double *) malloc ((BINS_MAX + 1) * sizeof (double));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (s->xin == 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
free (s->xi);
|
|
Packit |
67cb25 |
free (s->d);
|
|
Packit |
67cb25 |
free (s->delx);
|
|
Packit |
67cb25 |
free (s);
|
|
Packit |
67cb25 |
GSL_ERROR_VAL ("failed to allocate space for xin", GSL_ENOMEM, 0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->weight = (double *) malloc (BINS_MAX * sizeof (double));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (s->weight == 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
free (s->xin);
|
|
Packit |
67cb25 |
free (s->xi);
|
|
Packit |
67cb25 |
free (s->d);
|
|
Packit |
67cb25 |
free (s->delx);
|
|
Packit |
67cb25 |
free (s);
|
|
Packit |
67cb25 |
GSL_ERROR_VAL ("failed to allocate space for xin", GSL_ENOMEM, 0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->box = (coord *) malloc (dim * sizeof (coord));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (s->box == 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
free (s->weight);
|
|
Packit |
67cb25 |
free (s->xin);
|
|
Packit |
67cb25 |
free (s->xi);
|
|
Packit |
67cb25 |
free (s->d);
|
|
Packit |
67cb25 |
free (s->delx);
|
|
Packit |
67cb25 |
free (s);
|
|
Packit |
67cb25 |
GSL_ERROR_VAL ("failed to allocate space for box", GSL_ENOMEM, 0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->bin = (coord *) malloc (dim * sizeof (coord));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (s->bin == 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
free (s->box);
|
|
Packit |
67cb25 |
free (s->weight);
|
|
Packit |
67cb25 |
free (s->xin);
|
|
Packit |
67cb25 |
free (s->xi);
|
|
Packit |
67cb25 |
free (s->d);
|
|
Packit |
67cb25 |
free (s->delx);
|
|
Packit |
67cb25 |
free (s);
|
|
Packit |
67cb25 |
GSL_ERROR_VAL ("failed to allocate space for bin", GSL_ENOMEM, 0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->x = (double *) malloc (dim * sizeof (double));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (s->x == 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
free (s->bin);
|
|
Packit |
67cb25 |
free (s->box);
|
|
Packit |
67cb25 |
free (s->weight);
|
|
Packit |
67cb25 |
free (s->xin);
|
|
Packit |
67cb25 |
free (s->xi);
|
|
Packit |
67cb25 |
free (s->d);
|
|
Packit |
67cb25 |
free (s->delx);
|
|
Packit |
67cb25 |
free (s);
|
|
Packit |
67cb25 |
GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->dim = dim;
|
|
Packit |
67cb25 |
s->bins_max = BINS_MAX;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
gsl_monte_vegas_init (s);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return s;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* Set some default values and whatever */
|
|
Packit |
67cb25 |
int
|
|
Packit |
67cb25 |
gsl_monte_vegas_init (gsl_monte_vegas_state * state)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
state->stage = 0;
|
|
Packit |
67cb25 |
state->alpha = 1.5;
|
|
Packit |
67cb25 |
state->verbose = -1;
|
|
Packit |
67cb25 |
state->iterations = 5;
|
|
Packit |
67cb25 |
state->mode = GSL_VEGAS_MODE_IMPORTANCE;
|
|
Packit |
67cb25 |
state->chisq = 0;
|
|
Packit |
67cb25 |
state->bins = state->bins_max;
|
|
Packit |
67cb25 |
state->ostream = stdout;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
void
|
|
Packit |
67cb25 |
gsl_monte_vegas_free (gsl_monte_vegas_state * s)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
RETURN_IF_NULL (s);
|
|
Packit |
67cb25 |
free (s->x);
|
|
Packit |
67cb25 |
free (s->delx);
|
|
Packit |
67cb25 |
free (s->d);
|
|
Packit |
67cb25 |
free (s->xi);
|
|
Packit |
67cb25 |
free (s->xin);
|
|
Packit |
67cb25 |
free (s->weight);
|
|
Packit |
67cb25 |
free (s->box);
|
|
Packit |
67cb25 |
free (s->bin);
|
|
Packit |
67cb25 |
free (s);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
double
|
|
Packit |
67cb25 |
gsl_monte_vegas_chisq (const gsl_monte_vegas_state * s)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
return s->chisq;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
void
|
|
Packit |
67cb25 |
gsl_monte_vegas_runval (const gsl_monte_vegas_state * s, double * result, double * sigma)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
*result = s->result;
|
|
Packit |
67cb25 |
*sigma = s->sigma;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
void
|
|
Packit |
67cb25 |
gsl_monte_vegas_params_get (const gsl_monte_vegas_state * s, gsl_monte_vegas_params * p)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
p->alpha = s->alpha;
|
|
Packit |
67cb25 |
p->iterations = s->iterations;
|
|
Packit |
67cb25 |
p->stage = s->stage;
|
|
Packit |
67cb25 |
p->mode = s->mode;
|
|
Packit |
67cb25 |
p->verbose = s->verbose;
|
|
Packit |
67cb25 |
p->ostream = s->ostream;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
void
|
|
Packit |
67cb25 |
gsl_monte_vegas_params_set (gsl_monte_vegas_state * s, const gsl_monte_vegas_params * p)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
s->alpha = p->alpha;
|
|
Packit |
67cb25 |
s->iterations = p->iterations;
|
|
Packit |
67cb25 |
s->stage = p->stage;
|
|
Packit |
67cb25 |
s->mode = p->mode;
|
|
Packit |
67cb25 |
s->verbose = p->verbose;
|
|
Packit |
67cb25 |
s->ostream = p->ostream;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
init_box_coord (gsl_monte_vegas_state * s, coord box[])
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t i;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
size_t dim = s->dim;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < dim; i++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
box[i] = 0;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* change_box_coord steps through the box coord like
|
|
Packit |
67cb25 |
{0,0}, {0, 1}, {0, 2}, {0, 3}, {1, 0}, {1, 1}, {1, 2}, ...
|
|
Packit |
67cb25 |
*/
|
|
Packit |
67cb25 |
static int
|
|
Packit |
67cb25 |
change_box_coord (gsl_monte_vegas_state * s, coord box[])
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
int j = s->dim - 1;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
int ng = s->boxes;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
while (j >= 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
box[j] = (box[j] + 1) % ng;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (box[j] != 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
return 1;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
j--;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
return 0;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
init_grid (gsl_monte_vegas_state * s, double xl[], double xu[], size_t dim)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t j;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
double vol = 1.0;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->bins = 1;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < dim; j++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double dx = xu[j] - xl[j];
|
|
Packit |
67cb25 |
s->delx[j] = dx;
|
|
Packit |
67cb25 |
vol *= dx;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
COORD (s, 0, j) = 0.0;
|
|
Packit |
67cb25 |
COORD (s, 1, j) = 1.0;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->vol = vol;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
reset_grid_values (gsl_monte_vegas_state * s)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t i, j;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
size_t dim = s->dim;
|
|
Packit |
67cb25 |
size_t bins = s->bins;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < bins; i++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
for (j = 0; j < dim; j++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
VALUE (s, i, j) = 0.0;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
accumulate_distribution (gsl_monte_vegas_state * s, coord bin[], double y)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t j;
|
|
Packit |
67cb25 |
size_t dim = s->dim;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < dim; j++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
int i = bin[j];
|
|
Packit |
67cb25 |
VALUE (s, i, j) += y;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
random_point (double x[], coord bin[], double *bin_vol,
|
|
Packit |
67cb25 |
const coord box[], const double xl[], const double xu[],
|
|
Packit |
67cb25 |
gsl_monte_vegas_state * s, gsl_rng * r)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
/* Use the random number generator r to return a random position x
|
|
Packit |
67cb25 |
in a given box. The value of bin gives the bin location of the
|
|
Packit |
67cb25 |
random position (there may be several bins within a given box) */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
double vol = 1.0;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
size_t j;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
size_t dim = s->dim;
|
|
Packit |
67cb25 |
size_t bins = s->bins;
|
|
Packit |
67cb25 |
size_t boxes = s->boxes;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
DISCARD_POINTER(xu); /* prevent warning about unused parameter */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < dim; ++j)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
/* box[j] + ran gives the position in the box units, while z
|
|
Packit |
67cb25 |
is the position in bin units. */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
double z = ((box[j] + gsl_rng_uniform_pos (r)) / boxes) * bins;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
int k = z;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
double y, bin_width;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
bin[j] = k;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (k == 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
bin_width = COORD (s, 1, j);
|
|
Packit |
67cb25 |
y = z * bin_width;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
else
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
bin_width = COORD (s, k + 1, j) - COORD (s, k, j);
|
|
Packit |
67cb25 |
y = COORD (s, k, j) + (z - k) * bin_width;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
x[j] = xl[j] + y * s->delx[j];
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
vol *= bin_width;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
*bin_vol = vol;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
resize_grid (gsl_monte_vegas_state * s, unsigned int bins)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t j, k;
|
|
Packit |
67cb25 |
size_t dim = s->dim;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* weight is ratio of bin sizes */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
double pts_per_bin = (double) s->bins / (double) bins;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < dim; j++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double xold;
|
|
Packit |
67cb25 |
double xnew = 0;
|
|
Packit |
67cb25 |
double dw = 0;
|
|
Packit |
67cb25 |
int i = 1;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (k = 1; k <= s->bins; k++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
dw += 1.0;
|
|
Packit |
67cb25 |
xold = xnew;
|
|
Packit |
67cb25 |
xnew = COORD (s, k, j);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (; dw > pts_per_bin; i++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
dw -= pts_per_bin;
|
|
Packit |
67cb25 |
NEW_COORD (s, i) = xnew - (xnew - xold) * dw;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (k = 1 ; k < bins; k++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
COORD(s, k, j) = NEW_COORD(s, k);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
COORD (s, bins, j) = 1;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
s->bins = bins;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
refine_grid (gsl_monte_vegas_state * s)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t i, j, k;
|
|
Packit |
67cb25 |
size_t dim = s->dim;
|
|
Packit |
67cb25 |
size_t bins = s->bins;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < dim; j++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double grid_tot_j, tot_weight;
|
|
Packit |
67cb25 |
double * weight = s->weight;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
double oldg = VALUE (s, 0, j);
|
|
Packit |
67cb25 |
double newg = VALUE (s, 1, j);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
VALUE (s, 0, j) = (oldg + newg) / 2;
|
|
Packit |
67cb25 |
grid_tot_j = VALUE (s, 0, j);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* This implements gs[i][j] = (gs[i-1][j]+gs[i][j]+gs[i+1][j])/3 */
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 1; i < bins - 1; i++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double rc = oldg + newg;
|
|
Packit |
67cb25 |
oldg = newg;
|
|
Packit |
67cb25 |
newg = VALUE (s, i + 1, j);
|
|
Packit |
67cb25 |
VALUE (s, i, j) = (rc + newg) / 3;
|
|
Packit |
67cb25 |
grid_tot_j += VALUE (s, i, j);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
VALUE (s, bins - 1, j) = (newg + oldg) / 2;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
grid_tot_j += VALUE (s, bins - 1, j);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
tot_weight = 0;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (i = 0; i < bins; i++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
weight[i] = 0;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
if (VALUE (s, i, j) > 0)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
oldg = grid_tot_j / VALUE (s, i, j);
|
|
Packit |
67cb25 |
/* damped change */
|
|
Packit |
67cb25 |
weight[i] = pow (((oldg - 1) / oldg / log (oldg)), s->alpha);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
tot_weight += weight[i];
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
#ifdef DEBUG
|
|
Packit |
67cb25 |
printf("weight[%d] = %g\n", i, weight[i]);
|
|
Packit |
67cb25 |
#endif
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
double pts_per_bin = tot_weight / bins;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
double xold;
|
|
Packit |
67cb25 |
double xnew = 0;
|
|
Packit |
67cb25 |
double dw = 0;
|
|
Packit |
67cb25 |
i = 1;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (k = 0; k < bins; k++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
dw += weight[k];
|
|
Packit |
67cb25 |
xold = xnew;
|
|
Packit |
67cb25 |
xnew = COORD (s, k + 1, j);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (; dw > pts_per_bin; i++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
dw -= pts_per_bin;
|
|
Packit |
67cb25 |
NEW_COORD (s, i) = xnew - (xnew - xold) * dw / weight[k];
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (k = 1 ; k < bins ; k++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
COORD(s, k, j) = NEW_COORD(s, k);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
COORD (s, bins, j) = 1;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
print_lim (gsl_monte_vegas_state * state,
|
|
Packit |
67cb25 |
double xl[], double xu[], unsigned long dim)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
unsigned long j;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
fprintf (state->ostream, "The limits of integration are:\n");
|
|
Packit |
67cb25 |
for (j = 0; j < dim; ++j)
|
|
Packit |
67cb25 |
fprintf (state->ostream, "\nxl[%lu]=%f xu[%lu]=%f", j, xl[j], j, xu[j]);
|
|
Packit |
67cb25 |
fprintf (state->ostream, "\n");
|
|
Packit |
67cb25 |
fflush (state->ostream);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
print_head (gsl_monte_vegas_state * state,
|
|
Packit |
67cb25 |
unsigned long num_dim, unsigned long calls,
|
|
Packit |
67cb25 |
unsigned int it_num, unsigned int bins, unsigned int boxes)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
fprintf (state->ostream,
|
|
Packit |
67cb25 |
"\nnum_dim=%lu, calls=%lu, it_num=%d, max_it_num=%d ",
|
|
Packit |
67cb25 |
num_dim, calls, it_num, state->iterations);
|
|
Packit |
67cb25 |
fprintf (state->ostream,
|
|
Packit |
67cb25 |
"verb=%d, alph=%.2f,\nmode=%d, bins=%d, boxes=%d\n",
|
|
Packit |
67cb25 |
state->verbose, state->alpha, state->mode, bins, boxes);
|
|
Packit |
67cb25 |
fprintf (state->ostream,
|
|
Packit |
67cb25 |
"\n single.......iteration ");
|
|
Packit |
67cb25 |
fprintf (state->ostream, "accumulated......results \n");
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
fprintf (state->ostream,
|
|
Packit |
67cb25 |
"iteration integral sigma integral ");
|
|
Packit |
67cb25 |
fprintf (state->ostream, " sigma chi-sq/it\n\n");
|
|
Packit |
67cb25 |
fflush (state->ostream);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
print_res (gsl_monte_vegas_state * state,
|
|
Packit |
67cb25 |
unsigned int itr,
|
|
Packit |
67cb25 |
double res, double err,
|
|
Packit |
67cb25 |
double cum_res, double cum_err,
|
|
Packit |
67cb25 |
double chi_sq)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
fprintf (state->ostream,
|
|
Packit |
67cb25 |
"%4d %6.4e %10.2e %6.4e %8.2e %10.2e\n",
|
|
Packit |
67cb25 |
itr, res, err, cum_res, cum_err, chi_sq);
|
|
Packit |
67cb25 |
fflush (state->ostream);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
print_dist (gsl_monte_vegas_state * state, unsigned long dim)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
unsigned long i, j;
|
|
Packit |
67cb25 |
int p = state->verbose;
|
|
Packit |
67cb25 |
if (p < 1)
|
|
Packit |
67cb25 |
return;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < dim; ++j)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
fprintf (state->ostream, "\n axis %lu \n", j);
|
|
Packit |
67cb25 |
fprintf (state->ostream, " x g\n");
|
|
Packit |
67cb25 |
for (i = 0; i < state->bins; i++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
fprintf (state->ostream, "weight [%11.2e , %11.2e] = ",
|
|
Packit |
67cb25 |
COORD (state, i, j), COORD(state,i+1,j));
|
|
Packit |
67cb25 |
fprintf (state->ostream, " %11.2e\n", VALUE (state, i, j));
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
fprintf (state->ostream, "\n");
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
fprintf (state->ostream, "\n");
|
|
Packit |
67cb25 |
fflush (state->ostream);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
print_grid (gsl_monte_vegas_state * state, unsigned long dim)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
unsigned long i, j;
|
|
Packit |
67cb25 |
int p = state->verbose;
|
|
Packit |
67cb25 |
if (p < 1)
|
|
Packit |
67cb25 |
return;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
for (j = 0; j < dim; ++j)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
fprintf (state->ostream, "\n axis %lu \n", j);
|
|
Packit |
67cb25 |
fprintf (state->ostream, " x \n");
|
|
Packit |
67cb25 |
for (i = 0; i <= state->bins; i++)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
fprintf (state->ostream, "%11.2e", COORD (state, i, j));
|
|
Packit |
67cb25 |
if (i % 5 == 4)
|
|
Packit |
67cb25 |
fprintf (state->ostream, "\n");
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
fprintf (state->ostream, "\n");
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
fprintf (state->ostream, "\n");
|
|
Packit |
67cb25 |
fflush (state->ostream);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|