ATOOLS/Math/Gauss_Integrator.H

0001 #ifndef ATOOLS_Math_Gauss_Integrator_H
0002 #define ATOOLS_Math_Gauss_Integrator_H
0003
0004 #include "ATOOLS/Math/Function_Base.H"
0005
0006 namespace ATOOLS {
0007
0008   struct Weight_Module {
0009     int      methode;
0010     int      n;
0011     double * w;
0012     double * x;
0013     Weight_Module * next;
0014   };
0015
0016   class Gauss_Integrator {
0017   protected:
0018     // weights or abscissas already calculated ? available
0019     static int s_ngauleg,s_ngaulag,s_ngauherm,s_ngaujac;
0020     static Weight_Module * s_wlistroot;
0021
0022     // status of one instance of the calculator
0023     int    m_numberabsc;        // number of abscissas
0024     Function_Base * m_func;
0025     Weight_Module * m_wlistact;
0026
0027     void   GauLeg(double * x, double * w, int n);    // mode=1;
0028     void   GauJac(double * x, double * w, int n, double alf = -0.5, double bet= -0.5);  // mode=5;
0029   public:
0030     Gauss_Integrator(Function_Base *a =0);
0031     double Legendre(double x1 , double x2,int n);
0032     double Jacobi(double x1, double x2, int n, double alf, double bet);
0033     double Chebyshev( double a, double b, double prec, int n_max, int &i_err );
0034     double Integrate(double x1, double x2, double prec, int mode=1, int nmax=65536 );
0035   };
0036
0037
0038   /*!
0039     \file
0040     \brief contains the class Gauss_Integrator
0041   */
0042
0043   /*!
0044     \class Gauss_Integrator
0045     \brief This class can be used to evaluate one dimensional integrals numerically.
0046
0047     The Gauss_Integrator can calculate the integral of any given one dimensional
0048     analytical function (Function_Base) numerically.
0049
0050     Several methods are avaliable:
0051      - Gauss - Legendre (default)
0052      - Gauss - Jacobi
0053      - Gauss - Chebyshev
0054     .
0055   */
0056
0057   /*!
0058     \fn Gauss_Integrator::Gauss_Integrator(Function_Base *)
0059     \brief Constructor taking the function to be integrated.
0060   */
0061
0062   /*!
0063     \fn  double Gauss_Integrator::Legendre(double x1 , double x2,int n)
0064     \brief Gauss - Legendre integration
0065
0066     Calculates the integral
0067     \f[
0068        \int_{x_1}^{x_2} dx f(x) = \sum^n w_i f(\xi_i)
0069     \f]
0070     The weights \f$w_i\f$ and abscissas \f$\xi_i\f$ are such, that in case
0071     the function \f$f(x)\f$ is a polynomial of order k < n
0072     the result is exact!
0073   */
0074
0075   /*!
0076     \fn double Gauss_Integrator::Jacobi(double x1, double x2, int n, double alf, double bet)
0077     \brief Gauss-Jacobi integration
0078
0079     This integrator is optimized to integrate function of the Form
0080     \f[
0081       f(x) = (1-x)^\alpha (1+x)^\beta  P(x)
0082     \f]
0083     where \f$P(x)\f$ is a polynominal.
0084   */
0085
0086
0087   /*!
0088     \fn double  Gauss_Integrator::Chebyshev( double a, double b, double prec, int N_Max, int &I_Err )
0089     \brief Gauss-Chebyshev integration
0090
0091     This integrator is optimized to integrate function of the Form
0092     \f[
0093       f(x) = (1-x^2)^{-1/2} P(x)
0094     \f]
0095     where \f$P(x)\f$ is a polynominal.
0096   */
0097
0098   /*!
0099     \fn   double  Gauss_Integrator::Integrate(double x1, double x2, double prec, int mode=1, int nmax=65536 )
0100     \brief Integrates a function between x1 and x2 nummerically up to precission prec.
0101
0102     Calculates the integral
0103     \f[
0104        \int_{x_1}^{x_2} dx f(x)
0105     \f]
0106     utilizing either a Legendre, a Chebyshev or a Jacobi method.
0107   */
0108
0109
0110 }
0111
0112 #endif
0113