gsl_vegas Class Template Reference

Multidimensional integration using Vegas Monte Carlo (GSL). More...

#include <gsl_vegas.h>

Inheritance diagram for gsl_vegas:

mcarlo_inte multi_inte

Detailed Description

template<class param_t, class func_t = multi_funct<param_t>, class rng_t = gsl_rnga, class vec_t = ovector_base, class alloc_vec_t = ovector, class alloc_t = ovector_alloc>
class gsl_vegas< param_t, func_t, rng_t, vec_t, alloc_vec_t, alloc_t >

The output options are a little different than the original GSL routine. The default setting of mcarlo_inte::verbose is 0, which turns off all output. A verbose value of 1 prints summary information about the weighted average and final result, while a value of 2 also displays the grid coordinates. A value of 3 prints information from the rebinning procedure for each iteration.

Some original documentation from GSL:

      The input coordinates are x[j], with upper and lower limits
      xu[j] and xl[j]. The integration length in the j-th direction is
      delx[j]. Each coordinate x[j] is rescaled to a variable y[j] in
      the range 0 to 1. The range is divided into bins with boundaries
      xi[i][j], where i=0 corresponds to y=0 and i=bins to y=1. The
      grid is refined (ie, bins are adjusted) using d[i][j] which is
      some variation on the squared sum. A third parameter used in
      defining the real coordinate using random numbers is called z.
      It ranges from 0 to bins. Its integer part gives the lower index
      of the bin into which a call is to be placed, and the remainder
      gives the location inside the bin.

      When stratified sampling is used the bins are grouped into
      boxes, and the algorithm allocates an equal number of function
      calls to each box.

      The variable alpha controls how "stiff" the rebinning algorithm
      is. alpha = 0 means never change the grid. Alpha is typically
      set between 1 and 2. 
      

Idea for future:
Prettify the verbose output
Idea for future:
Allow the user to get information about the how the sampling was done, possibly by converting the bins and boxes into a structure or class.
Idea for future:
Allow the user to change the maximum number of bins.
Idea for future:
The testing file requires setting err_nonconv to true in the composite_inte section. Fix this.
Based on Lepage78 . The current version of the algorithm was described in the Cornell preprint CLNS-80/447 of March, 1980. The GSL code follows most closely the C version by D. R. Yennie, coded in 1984.

Definition at line 112 of file gsl_vegas.h.


Integration mode (default is mode_importance)

int mode
static const int mode_importance = 1
static const int mode_importance_only = 0
static const int mode_stratified = -1

Public Member Functions

virtual int allocate (size_t ldim)
 Allocate memory.
virtual int free ()
 Free allocated memory.
virtual int vegas_minteg_err (int stage, func_t &func, size_t ndim, const vec_t &xl, const vec_t &xu, param_t &pa, double &res, double &err)
 Integrate function func from x=a to x=b.
virtual int minteg_err (func_t &func, size_t ndim, const vec_t &a, const vec_t &b, param_t &pa, double &res, double &err)
 Integrate function func from x=a to x=b.
virtual double minteg (func_t &func, size_t ndim, const vec_t &a, const vec_t &b, param_t &pa)
 Integrate function func over the hypercube from $ x_i=a_i $ to $ x_i=b_i $ for $ 0<i< $ ndim-1.
virtual const char * type ()
 Return string denoting type ("gsl_vegas").

Data Fields

double result
 Result from last iteration.
double sigma
 Uncertainty from last iteration.
double alpha
 The stiffness of the rebinning algorithm (default 1.5).
unsigned int iterations
 Set the number of iterations (default 5).
double chisq
 The chi-squared per degree of freedom for the weighted estimate of the integral.
std::ostream * outs
 The output stream to send output information (default std::cout).

Protected Member Functions

virtual void init_box_coord (int boxt[])
 Initialize box coordinates.
int change_box_coord (int boxt[])
 Change box coordinates.
virtual void init_grid (const vec_t &xl, const vec_t &xu, size_t ldim)
 Initialize grid.
virtual void reset_grid_values ()
 Reset grid values.
void accumulate_distribution (int lbin[], double y)
 Add the most recently generated result to the distribution.
void random_point (vec_t &lx, int lbin[], double *bin_vol, const int lbox[], const vec_t &xl, const vec_t &xu)
 Generate a random position in a given box.
virtual void resize_grid (unsigned int lbins)
 Resize the grid.
virtual void refine_grid ()
 Refine the grid.
virtual void print_lim (const vec_t &xl, const vec_t &xu, unsigned long ldim)
 Print limits of integration.
virtual void print_head (unsigned long num_dim, unsigned long calls, unsigned int lit_num, unsigned int lbins, unsigned int lboxes)
 Print header.
virtual void print_res (unsigned int itr, double res, double err, double cum_res, double cum_err, double chi_sq)
 Print results.
virtual void print_dist (unsigned long ldim)
 Print distribution.
virtual void print_grid (unsigned long ldim)
 Print grid.

Protected Attributes

size_t dim
 Number of dimensions.
unsigned int bins
 Number of bins.
unsigned int boxes
 Number of boxes.
double * xi
 Boundaries for each bin.
double * xin
 Storage for grid refinement.
double * delx
 The iteration length in each direction.
double * weight
 The weight for each bin.
double vol
 The volume of the current bin.
int * bin
 The bins for each direction.
int * box
 The boxes for each direction.
double * d
 Distribution.
unsigned int it_start
 The starting iteration number.
unsigned int it_num
 The total number of iterations.
unsigned int samples
 Number of samples for computing chi squared.
unsigned int calls_per_box
 Number of function calls per box.
alloc_t ao
 Memory allocation object.
alloc_vec_t x
 Point for function evaluation.
Scratch variables preserved between calls to
double jac
double wtd_int_sum
double sum_wgts
double chi_sum

Static Protected Attributes

static const size_t bins_max = 50
 Maximum number of bins.

Member Function Documentation

void accumulate_distribution ( int  lbin[],
double  y 
) [inline, protected]

This is among the member functions that is not virtual because it is part of the innermost loop.

Definition at line 280 of file gsl_vegas.h.

int change_box_coord ( int  boxt[]  )  [inline, protected]

Steps through the box coordinates, e.g.

       {0,0}, {0,1}, {0,2}, {0,3}, {1,0}, {1,1}, {1,2}, ...
       

This is among the member functions that is not virtual because it is part of the innermost loop.

Definition at line 227 of file gsl_vegas.h.

void random_point ( vec_t &  lx,
int  lbin[],
double *  bin_vol,
const int  lbox[],
const vec_t &  xl,
const vec_t &  xu 
) [inline, protected]

Use the random number generator mcarlo_inte::def_rng to return a random position x in a given box. The value of bin gives the bin location of the random position (there may be several bins within a given box)

This is among the member functions that is not virtual because it is part of the innermost loop.

Definition at line 301 of file gsl_vegas.h.

virtual int vegas_minteg_err ( int  stage,
func_t &  func,
size_t  ndim,
const vec_t &  xl,
const vec_t &  xu,
param_t &  pa,
double &  res,
double &  err 
) [inline, virtual]

Original documentation from GSL:

Normally, stage = 0 which begins with a new uniform grid and empty weighted average. Calling vegas with stage = 1 retains the grid from the previous run but discards the weighted average, so that one can "tune" the grid using a relatively small number of points and then do a large run with stage = 1 on the optimized grid. Setting stage = 2 keeps the grid and the weighted average from the previous run, but may increase (or decrease) the number of histogram bins in the grid depending on the number of calls available. Choosing stage = 3 enters at the main loop, so that nothing is changed, and is equivalent to performing additional iterations in a previous call.

Definition at line 667 of file gsl_vegas.h.


Field Documentation

double alpha

This usual range is between 1 and 2.

Definition at line 136 of file gsl_vegas.h.

double chisq

After an integration, this should be close to 1. If it is not, then this indicates that the values of the integral from different iterations are inconsistent, and the error may be underestimated. Further iterations of the algorithm may enable one to obtain more reliable results.

Definition at line 151 of file gsl_vegas.h.


The documentation for this class was generated from the following file:

Documentation generated with Doxygen and provided under the GNU Free Documentation License. See License Information for details.

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