RooGaussKronrodIntegrator1D.cxx

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/*****************************************************************************
 * Project: RooFit                                                           *
 * Package: RooFitCore                                                       *
 * @(#)root/roofitcore:$Id$
 * Authors:                                                                  *
 *   WV, Wouter Verkerke, UC Santa Barbara, verkerke@slac.stanford.edu       *
 *   DK, David Kirkby,    UC Irvine,         dkirkby@uci.edu                 *
 *                                                                           *
 * Copyright (c) 2000-2005, Regents of the University of California          *
 *                          and Stanford University. All rights reserved.    *
 *                                                                           *
 * Redistribution and use in source and binary forms,                        *
 * with or without modification, are permitted according to the terms        *
 * listed in LICENSE (http://roofit.sourceforge.net/license.txt)             *
 *****************************************************************************/

/**
\file RooGaussKronrodIntegrator1D.cxx
\class RooGaussKronrodIntegrator1D
\ingroup Roofitcore

RooGaussKronrodIntegrator1D implements the Gauss-Kronrod integration algorithm.

An Gaussian quadrature method for numerical integration in which
error is estimation based on evaluation at special points known as
"Kronrod points."  By suitably picking these points, abscissas from
previous iterations can be reused as part of the new set of points,
whereas usual Gaussian quadrature would require recomputation of
all abscissas at each iteration.

This class automatically handles (-inf,+inf) integrals by dividing
the integration in three regions (-inf,-1), (-1,1), (1,inf) and
calculating the 1st and 3rd term using a x -> 1/x coordinate
transformation

This class embeds the Gauss-Kronrod integrator from the GNU
Scientific Library version 1.5 and applies the 10-, 21-, 43- and
87-point rule in succession until the required target precision is
reached
**/



#include "RooFit.h"

#include <assert.h>
#include <math.h>
#include <float.h>
#include "Riostream.h"
#include "TMath.h"
#include "RooGaussKronrodIntegrator1D.h"
#include "RooArgSet.h"
#include "RooRealVar.h"
#include "RooNumber.h"
#include "RooNumIntFactory.h"
#include "RooIntegratorBinding.h"
#include "RooMsgService.h"


using namespace std;

ClassImp(RooGaussKronrodIntegrator1D);
;


// --- From GSL_MATH.h -------------------------------------------
struct gsl_function_struct
{
  double (* function) (double x, void * params);
  void * params;
};
typedef struct gsl_function_struct gsl_function ;
#define GSL_FN_EVAL(F,x) (*((F)->function))(x,(F)->params)
//----From GSL_INTEGRATION.h ---------------------------------------
int gsl_integration_qng (const gsl_function * f,
                         double a, double b,
                         double epsabs, double epsrel,
                         double *result, double *abserr,
                         size_t * neval);
//-------------------------------------------------------------------



////////////////////////////////////////////////////////////////////////////////
/// Register RooGaussKronrodIntegrator1D, its parameters and capabilities with RooNumIntConfig

void RooGaussKronrodIntegrator1D::registerIntegrator(RooNumIntFactory& fact)
{
  fact.storeProtoIntegrator(new RooGaussKronrodIntegrator1D(),RooArgSet()) ;
}



////////////////////////////////////////////////////////////////////////////////
/// coverity[UNINIT_CTOR]
/// Default constructor

RooGaussKronrodIntegrator1D::RooGaussKronrodIntegrator1D() : _x(0)
{
}



////////////////////////////////////////////////////////////////////////////////
/// Construct integral on 'function' using given configuration object. The integration
/// range is taken from the definition in the function binding

RooGaussKronrodIntegrator1D::RooGaussKronrodIntegrator1D(const RooAbsFunc& function, const RooNumIntConfig& config) :
  RooAbsIntegrator(function),
  _epsAbs(config.epsRel()),
  _epsRel(config.epsAbs())
{
  _useIntegrandLimits= kTRUE;
  _valid= initialize();
} 



////////////////////////////////////////////////////////////////////////////////
/// Construct integral on 'function' using given configuration object in the given range

RooGaussKronrodIntegrator1D::RooGaussKronrodIntegrator1D(const RooAbsFunc& function, 
                      Double_t xmin, Double_t xmax, const RooNumIntConfig& config) :
  RooAbsIntegrator(function),
  _epsAbs(config.epsRel()),
  _epsRel(config.epsAbs()),
  _xmin(xmin),
  _xmax(xmax)
{
  _useIntegrandLimits= kFALSE;
  _valid= initialize();
} 



////////////////////////////////////////////////////////////////////////////////
/// Clone integrator with given function and configuration. Needed for RooNumIntFactory

RooAbsIntegrator* RooGaussKronrodIntegrator1D::clone(const RooAbsFunc& function, const RooNumIntConfig& config) const
{
  return new RooGaussKronrodIntegrator1D(function,config) ;
}



////////////////////////////////////////////////////////////////////////////////
/// Perform one-time initialization of integrator

Bool_t RooGaussKronrodIntegrator1D::initialize()
{
  // Allocate coordinate buffer size after number of function dimensions
  _x = new Double_t[_function->getDimension()] ;

  return checkLimits();
}



////////////////////////////////////////////////////////////////////////////////
/// Destructor

RooGaussKronrodIntegrator1D::~RooGaussKronrodIntegrator1D()
{
  if (_x) {
    delete[] _x ;
  }
}



////////////////////////////////////////////////////////////////////////////////
/// Change our integration limits. Return kTRUE if the new limits are
/// ok, or otherwise kFALSE. Always returns kFALSE and does nothing
/// if this object was constructed to always use our integrand's limits.

Bool_t RooGaussKronrodIntegrator1D::setLimits(Double_t* xmin, Double_t* xmax) 
{
  if(_useIntegrandLimits) {
    oocoutE((TObject*)0,Eval) << "RooGaussKronrodIntegrator1D::setLimits: cannot override integrand's limits" << endl;
    return kFALSE;
  }
  _xmin= *xmin;
  _xmax= *xmax;
  return checkLimits();
}



////////////////////////////////////////////////////////////////////////////////
/// Check that our integration range is finite and otherwise return kFALSE.
/// Update the limits from the integrand if requested.

Bool_t RooGaussKronrodIntegrator1D::checkLimits() const 
{
  if(_useIntegrandLimits) {
    assert(0 != integrand() && integrand()->isValid());
    _xmin= integrand()->getMinLimit(0);
    _xmax= integrand()->getMaxLimit(0);
  }
  return kTRUE ;
}



double RooGaussKronrodIntegrator1D_GSL_GlueFunction(double x, void *data) 
{
  RooGaussKronrodIntegrator1D* instance = (RooGaussKronrodIntegrator1D*) data ;
  return instance->integrand(instance->xvec(x)) ;
}



////////////////////////////////////////////////////////////////////////////////
/// Calculate and return integral

Double_t RooGaussKronrodIntegrator1D::integral(const Double_t *yvec) 
{
  assert(isValid());

  // Copy yvec to xvec if provided
  if (yvec) {
    UInt_t i ; for (i=0 ; i<_function->getDimension()-1 ; i++) {
      _x[i+1] = yvec[i] ;
    }
  }

  // Setup glue function
  gsl_function F;
  F.function = &RooGaussKronrodIntegrator1D_GSL_GlueFunction ;
  F.params = this ;

  // Return values
  double result, error;
  size_t neval = 0 ;

  // Call GSL implementation of integeator
  gsl_integration_qng (&F, _xmin, _xmax, _epsAbs, _epsRel, &result, &error, &neval); 

  return result;
}


// ----------------------------------------------------------------------------
// ---------- Code below imported from GSL version 1.5 ------------------------
// ----------------------------------------------------------------------------

/*
 * 
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
 * 
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

#define GSL_SUCCESS 0
#define GSL_EBADTOL 13  /* user specified an invalid tolerance */
#define GSL_ETOL    14  /* failed to reach the specified tolerance */
#define GSL_ERROR(a,b) oocoutE((TObject*)0,Eval) << "RooGaussKronrodIntegrator1D::integral() ERROR: " << a << endl ; return b ;
#define GSL_DBL_MIN        2.2250738585072014e-308
#define GSL_DBL_EPSILON    2.2204460492503131e-16


// INCLUDED BELOW #include "qng.c"

int gsl_integration_qng (const gsl_function * f,
                         double a, double b,
                         double epsabs, double epsrel,
                         double *result, double *abserr,
                         size_t * neval);



// INCLUDED BELOW #include "err.c"
static double rescale_error (double err, const double result_abs, const double result_asc) ;

static double
rescale_error (double err, const double result_abs, const double result_asc)
{
  err = fabs(err) ;

  if (result_asc != 0 && err != 0)
      {
        double scale = TMath::Power((200 * err / result_asc), 1.5) ;
        
        if (scale < 1)
          {
            err = result_asc * scale ;
          }
        else 
          {
            err = result_asc ;
          }
      }
  if (result_abs > GSL_DBL_MIN / (50 * GSL_DBL_EPSILON))
    {
      double min_err = 50 * GSL_DBL_EPSILON * result_abs ;

      if (min_err > err) 
        {
          err = min_err ;
        }
    }
  
  return err ;
}


// INCLUDED BELOW #include "qng.h"
/* Gauss-Kronrod-Patterson quadrature coefficients for use in
   quadpack routine qng. These coefficients were calculated with
   101 decimal digit arithmetic by L. W. Fullerton, Bell Labs, Nov
   1981. */

/* x1, abscissae common to the 10-, 21-, 43- and 87-point rule */
static const double x1[5] = {
  0.973906528517171720077964012084452,
  0.865063366688984510732096688423493,
  0.679409568299024406234327365114874,
  0.433395394129247190799265943165784,
  0.148874338981631210884826001129720
} ;

/* w10, weights of the 10-point formula */
static const double w10[5] = {
  0.066671344308688137593568809893332,
  0.149451349150580593145776339657697,
  0.219086362515982043995534934228163,
  0.269266719309996355091226921569469,
  0.295524224714752870173892994651338
} ;

/* x2, abscissae common to the 21-, 43- and 87-point rule */
static const double x2[5] = {
  0.995657163025808080735527280689003,
  0.930157491355708226001207180059508,
  0.780817726586416897063717578345042,
  0.562757134668604683339000099272694,
  0.294392862701460198131126603103866
} ;

/* w21a, weights of the 21-point formula for abscissae x1 */
static const double w21a[5] = {
  0.032558162307964727478818972459390,
  0.075039674810919952767043140916190,
  0.109387158802297641899210590325805,
  0.134709217311473325928054001771707,
  0.147739104901338491374841515972068
} ;

/* w21b, weights of the 21-point formula for abscissae x2 */
static const double w21b[6] = {
  0.011694638867371874278064396062192,
  0.054755896574351996031381300244580,
  0.093125454583697605535065465083366,
  0.123491976262065851077958109831074,
  0.142775938577060080797094273138717,
  0.149445554002916905664936468389821
} ;

/* x3, abscissae common to the 43- and 87-point rule */
static const double x3[11] = {
  0.999333360901932081394099323919911,
  0.987433402908088869795961478381209,
  0.954807934814266299257919200290473,
  0.900148695748328293625099494069092,
  0.825198314983114150847066732588520,
  0.732148388989304982612354848755461,
  0.622847970537725238641159120344323,
  0.499479574071056499952214885499755,
  0.364901661346580768043989548502644,
  0.222254919776601296498260928066212,
  0.074650617461383322043914435796506
} ;

/* w43a, weights of the 43-point formula for abscissae x1, x3 */
static const double w43a[10] = {
  0.016296734289666564924281974617663,
  0.037522876120869501461613795898115,
  0.054694902058255442147212685465005,
  0.067355414609478086075553166302174,
  0.073870199632393953432140695251367,
  0.005768556059769796184184327908655,
  0.027371890593248842081276069289151,
  0.046560826910428830743339154433824,
  0.061744995201442564496240336030883,
  0.071387267268693397768559114425516
} ;

/* w43b, weights of the 43-point formula for abscissae x3 */
static const double w43b[12] = {
  0.001844477640212414100389106552965,
  0.010798689585891651740465406741293,
  0.021895363867795428102523123075149,
  0.032597463975345689443882222526137,
  0.042163137935191811847627924327955,
  0.050741939600184577780189020092084,
  0.058379395542619248375475369330206,
  0.064746404951445885544689259517511,
  0.069566197912356484528633315038405,
  0.072824441471833208150939535192842,
  0.074507751014175118273571813842889,
  0.074722147517403005594425168280423
} ;

/* x4, abscissae of the 87-point rule */
static const double x4[22] = {
  0.999902977262729234490529830591582,
  0.997989895986678745427496322365960,
  0.992175497860687222808523352251425,
  0.981358163572712773571916941623894,
  0.965057623858384619128284110607926,
  0.943167613133670596816416634507426,
  0.915806414685507209591826430720050,
  0.883221657771316501372117548744163,
  0.845710748462415666605902011504855,
  0.803557658035230982788739474980964,
  0.757005730685495558328942793432020,
  0.706273209787321819824094274740840,
  0.651589466501177922534422205016736,
  0.593223374057961088875273770349144,
  0.531493605970831932285268948562671,
  0.466763623042022844871966781659270,
  0.399424847859218804732101665817923,
  0.329874877106188288265053371824597,
  0.258503559202161551802280975429025,
  0.185695396568346652015917141167606,
  0.111842213179907468172398359241362,
  0.037352123394619870814998165437704
} ;

/* w87a, weights of the 87-point formula for abscissae x1, x2, x3 */
static const double w87a[21] = {
  0.008148377384149172900002878448190,
  0.018761438201562822243935059003794,
  0.027347451050052286161582829741283,
  0.033677707311637930046581056957588,
  0.036935099820427907614589586742499,
  0.002884872430211530501334156248695,
  0.013685946022712701888950035273128,
  0.023280413502888311123409291030404,
  0.030872497611713358675466394126442,
  0.035693633639418770719351355457044,
  0.000915283345202241360843392549948,
  0.005399280219300471367738743391053,
  0.010947679601118931134327826856808,
  0.016298731696787335262665703223280,
  0.021081568889203835112433060188190,
  0.025370969769253827243467999831710,
  0.029189697756475752501446154084920,
  0.032373202467202789685788194889595,
  0.034783098950365142750781997949596,
  0.036412220731351787562801163687577,
  0.037253875503047708539592001191226
} ;

/* w87b, weights of the 87-point formula for abscissae x4    */
static const double w87b[23] = {
  0.000274145563762072350016527092881,
  0.001807124155057942948341311753254,
  0.004096869282759164864458070683480,
  0.006758290051847378699816577897424,
  0.009549957672201646536053581325377,
  0.012329447652244853694626639963780,
  0.015010447346388952376697286041943,
  0.017548967986243191099665352925900,
  0.019938037786440888202278192730714,
  0.022194935961012286796332102959499,
  0.024339147126000805470360647041454,
  0.026374505414839207241503786552615,
  0.028286910788771200659968002987960,
  0.030052581128092695322521110347341,
  0.031646751371439929404586051078883,
  0.033050413419978503290785944862689,
  0.034255099704226061787082821046821,
  0.035262412660156681033782717998428,
  0.036076989622888701185500318003895,
  0.036698604498456094498018047441094,
  0.037120549269832576114119958413599,
  0.037334228751935040321235449094698,
  0.037361073762679023410321241766599
} ;


int
gsl_integration_qng (const gsl_function *f,
                     double a, double b,
                     double epsabs, double epsrel,
                     double * result, double * abserr, size_t * neval)
{
  double fv1[5], fv2[5], fv3[5], fv4[5];
  double savfun[21];  /* array of function values which have been computed */
  double res10, res21, res43, res87;    /* 10, 21, 43 and 87 point results */
  double result_kronrod, err ; 
  double resabs; /* approximation to the integral of abs(f) */
  double resasc; /* approximation to the integral of abs(f-i/(b-a)) */

  const double half_length =  0.5 * (b - a);
  const double abs_half_length = fabs (half_length);
  const double center = 0.5 * (b + a);
  const double f_center = GSL_FN_EVAL(f, center);

  int k ;

  if (epsabs <= 0 && (epsrel < 50 * GSL_DBL_EPSILON || epsrel < 0.5e-28))
    {
      * result = 0;
      * abserr = 0;
      * neval = 0;
      GSL_ERROR ("tolerance cannot be acheived with given epsabs and epsrel",
       GSL_EBADTOL);
    };

  /* Compute the integral using the 10- and 21-point formula. */

  res10 = 0;
  res21 = w21b[5] * f_center;
  resabs = w21b[5] * fabs (f_center);

  for (k = 0; k < 5; k++)
    {
      const double abscissa = half_length * x1[k];
      const double fval1 = GSL_FN_EVAL(f, center + abscissa);
      const double fval2 = GSL_FN_EVAL(f, center - abscissa);
      const double fval = fval1 + fval2;
      res10 += w10[k] * fval;
      res21 += w21a[k] * fval;
      resabs += w21a[k] * (fabs (fval1) + fabs (fval2));
      savfun[k] = fval;
      fv1[k] = fval1;
      fv2[k] = fval2;
    }

  for (k = 0; k < 5; k++)
    {
      const double abscissa = half_length * x2[k];
      const double fval1 = GSL_FN_EVAL(f, center + abscissa);
      const double fval2 = GSL_FN_EVAL(f, center - abscissa);
      const double fval = fval1 + fval2;
      res21 += w21b[k] * fval;
      resabs += w21b[k] * (fabs (fval1) + fabs (fval2));
      savfun[k + 5] = fval;
      fv3[k] = fval1;
      fv4[k] = fval2;
    }

  resabs *= abs_half_length ;

  { 
    const double mean = 0.5 * res21;
  
    resasc = w21b[5] * fabs (f_center - mean);
    
    for (k = 0; k < 5; k++)
      {
        resasc +=
          (w21a[k] * (fabs (fv1[k] - mean) + fabs (fv2[k] - mean))
          + w21b[k] * (fabs (fv3[k] - mean) + fabs (fv4[k] - mean)));
      }
    resasc *= abs_half_length ;
  }

  result_kronrod = res21 * half_length;
  
  err = rescale_error ((res21 - res10) * half_length, resabs, resasc) ;

  /*   test for convergence. */

  if (err < epsabs || err < epsrel * fabs (result_kronrod))
    {
      * result = result_kronrod ;
      * abserr = err ;
      * neval = 21;
      return GSL_SUCCESS;
    }

  /* compute the integral using the 43-point formula. */

  res43 = w43b[11] * f_center;

  for (k = 0; k < 10; k++)
    {
      res43 += savfun[k] * w43a[k];
    }

  for (k = 0; k < 11; k++)
    {
      const double abscissa = half_length * x3[k];
      const double fval = (GSL_FN_EVAL(f, center + abscissa) 
                           + GSL_FN_EVAL(f, center - abscissa));
      res43 += fval * w43b[k];
      savfun[k + 10] = fval;
    }

  /*  test for convergence */

  result_kronrod = res43 * half_length;
  err = rescale_error ((res43 - res21) * half_length, resabs, resasc);

  if (err < epsabs || err < epsrel * fabs (result_kronrod))
    {
      * result = result_kronrod ;
      * abserr = err ;
      * neval = 43;
      return GSL_SUCCESS;
    }

  /* compute the integral using the 87-point formula. */

  res87 = w87b[22] * f_center;

  for (k = 0; k < 21; k++)
    {
      res87 += savfun[k] * w87a[k];
    }

  for (k = 0; k < 22; k++)
    {
      const double abscissa = half_length * x4[k];
      res87 += w87b[k] * (GSL_FN_EVAL(f, center + abscissa) 
                          + GSL_FN_EVAL(f, center - abscissa));
    }

  /*  test for convergence */

  result_kronrod = res87 * half_length ;
  
  err = rescale_error ((res87 - res43) * half_length, resabs, resasc);
  
  if (err < epsabs || err < epsrel * fabs (result_kronrod))
    {
      * result = result_kronrod ;
      * abserr = err ;
      * neval = 87;
      return GSL_SUCCESS;
    }

  /* failed to converge */

  * result = result_kronrod ;
  * abserr = err ;
  * neval = 87;

  // GSL_ERROR("failed to reach tolerance with highest-order rule", GSL_ETOL) ;
  return GSL_ETOL ;
}