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 63 of file NumericalIntegration.h.

Constructor & Destructor Documentation

funct::GaussIntegrator::GaussIntegrator ( )

inline

Definition at line 65 of file NumericalIntegration.h.

{ }

funct::GaussIntegrator::GaussIntegrator ( double  epsilon )

inline

Definition at line 66 of file NumericalIntegration.h.

: epsilon_(epsilon) { }

Member Function Documentation

double funct::GaussIntegrator::error ( ) const

inline

Definition at line 110 of file NumericalIntegration.h.

References error_.

{ return error_; }

template<typename F >

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

inline

Definition at line 68 of file NumericalIntegration.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.

                                                            {
      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;   
    }    

Member Data Documentation

double funct::GaussIntegrator::aa

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::aconst

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::bb

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::c1

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::c2

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::epsilon_

private

Definition at line 113 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::error_

mutableprivate

Definition at line 112 of file NumericalIntegration.h.

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

double funct::GaussIntegrator::f1

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::f2

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::h

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

unsigned int funct::GaussIntegrator::i

mutableprivate

Definition at line 118 of file NumericalIntegration.h.

Referenced by operator()().

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

staticprivate

Definition at line 116 of file NumericalIntegration.h.

Referenced by operator()().

const double funct::GaussIntegrator::kHF = 0.5

staticprivate

Definition at line 115 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::s16

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::s8

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussIntegrator::u

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

Referenced by operator()().

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 114 of file NumericalIntegration.h.

Referenced by operator()().

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 114 of file NumericalIntegration.h.

Referenced by svgfig.Curve.Sample::__repr__(), svgfig.Ellipse::__repr__(), Vispa.Gui.WidgetContainer.WidgetContainer::autosize(), Vispa.Gui.VispaWidget.VispaWidget::boundingRect(), operator()(), geometryXMLparser.Alignable::pos(), and Vispa.Gui.ConnectableWidget.ConnectableWidget::positionizeMenuWidget().

double funct::GaussIntegrator::xx

mutableprivate

Definition at line 117 of file NumericalIntegration.h.

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