funct::GaussIntegrator Class Reference

#include <NumericalIntegration.h>

Public Member Functions
double	error () const
	GaussIntegrator ()
	GaussIntegrator (double epsilon)
template<typename F >
double	operator() (const F &f, double a, double b) const

Private Attributes
double	aa
double	aconst
double	bb
double	c1
double	c2
double	epsilon_
double	error_
double	f1
double	f2
double	h
unsigned int	i
double	s16
double	s8
double	u
double	xx

Static Private Attributes
static const double	kCST = 5. / 1000
static const double	kHF = 0.5
static const double	w [12]
static const double	x [12]

Detailed Description

Definition at line 65 of file NumericalIntegration.h.

Constructor & Destructor Documentation

GaussIntegrator() [1/2]

funct::GaussIntegrator::GaussIntegrator ( )

inline

Definition at line 67 of file NumericalIntegration.h.

{}

GaussIntegrator() [2/2]

funct::GaussIntegrator::GaussIntegrator ( double  epsilon )

inline

Definition at line 68 of file NumericalIntegration.h.

: epsilon_(epsilon) {}

Member Function Documentation

error()

double funct::GaussIntegrator::error ( ) const

inline

Definition at line 115 of file NumericalIntegration.h.

{ return error_; }

References error_.

Referenced by Page1Parser.Page1Parser::check_for_whole_start_tag().

operator()()

template<typename F >

double funct::GaussIntegrator::operator() ( const F &  f, double  a, double  b  ) const

inline

Definition at line 70 of file NumericalIntegration.h.

                                                            {
      h = 0;
      if (b == a)
        return h;
      aconst = kCST / std::abs(b - a);
      bb = a;
    CASE1:
      aa = bb;
      bb = b;
    CASE2:
      c1 = kHF * (bb + aa);
      c2 = kHF * (bb - aa);
      s8 = 0;
      for (i = 0; i < 4; ++i) {
        u = c2 * x[i];
        xx = c1 + u;
        f1 = f(xx);
        xx = c1 - u;
        f2 = f(xx);
        s8 += w[i] * (f1 + f2);
      }
      s16 = 0;
      for (i = 4; i < 12; ++i) {
        u = c2 * x[i];
        xx = c1 + u;
        f1 = f(xx);
        xx = c1 - u;
        f2 = f(xx);
        s16 += w[i] * (f1 + f2);
      }
      s16 = c2 * s16;
      if (std::abs(s16 - c2 * s8) <= epsilon_ * (1. + std::abs(s16))) {
        h += s16;
        if (bb != b)
          goto CASE1;
      } else {
        bb = c1;
        if (1. + aconst * std::abs(c2) != 1)
          goto CASE2;
        h = s8;
      }
 
      error_ = std::abs(s16 - c2 * s8);
      return h;
    }

References a, aa, funct::abs(), aconst, b, bb, c1, c2, epsilon_, error_, f, f1, f2, h, i, kCST, kHF, s16, s8, u, w, x, and xx.

Member Data Documentation

aa

double funct::GaussIntegrator::aa

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by geometryXMLparser.Alignable::covariance(), and operator()().

aconst

double funct::GaussIntegrator::aconst

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by operator()().

bb

double funct::GaussIntegrator::bb

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by geometryXMLparser.Alignable::covariance(), and operator()().

c1

double funct::GaussIntegrator::c1

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by operator()().

c2

double funct::GaussIntegrator::c2

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by operator()().

epsilon_

double funct::GaussIntegrator::epsilon_

private

Definition at line 119 of file NumericalIntegration.h.

Referenced by operator()().

error_

double funct::GaussIntegrator::error_

mutableprivate

Definition at line 118 of file NumericalIntegration.h.

Referenced by error(), and operator()().

f1

double funct::GaussIntegrator::f1

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by operator()().

f2

double funct::GaussIntegrator::f2

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by operator()().

h

double funct::GaussIntegrator::h

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by operator()().

i

unsigned int funct::GaussIntegrator::i

mutableprivate

Definition at line 124 of file NumericalIntegration.h.

Referenced by operator()().

kCST

const double funct::GaussIntegrator::kCST = 5. / 1000

staticprivate

Definition at line 122 of file NumericalIntegration.h.

Referenced by operator()().

kHF

const double funct::GaussIntegrator::kHF = 0.5

staticprivate

Definition at line 121 of file NumericalIntegration.h.

Referenced by operator()().

s16

double funct::GaussIntegrator::s16

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by operator()().

s8

double funct::GaussIntegrator::s8

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by operator()().

u

double funct::GaussIntegrator::u

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by operator()().

w

const double funct::GaussIntegrator::w

staticprivate

Initial value:

= {0.10122853629037626,
                                              0.22238103445337447,
                                              0.31370664587788729,
                                              0.36268378337836198,
                                              0.02715245941175409,
                                              0.06225352393864789,
                                              0.09515851168249278,
                                              0.12462897125553387,
                                              0.14959598881657673,
                                              0.16915651939500254,
                                              0.18260341504492359,
                                              0.18945061045506850}

Definition at line 120 of file NumericalIntegration.h.

Referenced by operator()().

x

const double funct::GaussIntegrator::x

staticprivate

Initial value:

= {0.96028985649753623,
                                              0.79666647741362674,
                                              0.52553240991632899,
                                              0.18343464249564980,
                                              0.98940093499164993,
                                              0.94457502307323258,
                                              0.86563120238783174,
                                              0.75540440835500303,
                                              0.61787624440264375,
                                              0.45801677765722739,
                                              0.28160355077925891,
                                              0.09501250983763744}

Definition at line 120 of file NumericalIntegration.h.

Referenced by svgfig.Curve.Sample::__repr__(), svgfig.Ellipse::__repr__(), operator()(), geometryXMLparser.Alignable::pos(), ntupleDataFormat._HitObject::r(), and ntupleDataFormat._HitObject::r3D().

xx

double funct::GaussIntegrator::xx

mutableprivate

Definition at line 123 of file NumericalIntegration.h.

Referenced by geometryXMLparser.Alignable::covariance(), and operator()().