/* this is the header file for integration routines */

#ifndef int_h
#define int_h

#include <default.h>
#include <matrix.h>


double int_trapzd(double (*func)(double x), double a, double b);
double int_simp(double (*func)(double x), double a, double b);
double trapzd(double (*func)(double x), double a, double b, int n);

void gauss_leg(double x1, double x2, double *x, double *w, int n);
double int_gauss(double (*func)(double), double a, double b, int n );
double int_gauss2(double (*func2)(double), double a, double b, int n );
double int_gauss3(double (*func3)(double), double a, double b, int n );
double int_gauss4(double (*func4)(double), double a, double b, int n );

double int_gauss_infinit(double (*func)(double), double c, int n );
void gauss_leg_infinit(double *q, double *W, double c, int n);

double int1d(double (*func)(double x), double x1, double x2, int n);
double int2d(double (*func)(double x, double y), double x1, double x2,
                                                 double y1, double y2, int n);
double int3d(double (*func)(double x, double y, double z), 
             double x1, double x2, double y1, double y2, 
             double z1, double z2, int n);

double W1 ( double x, double a, double b );
double W2 ( double x, double a, double b );
double W3 ( double x, double a, double b );

void MOMENTS1(int nmax, double a, double b,double x1, double x2, double *ct);
void MOMENTS2(int nmax, double a, double b,double x1, double x2,
              double *ct1, double *ct2);
void MOMENTS3(int nmax, double a, double b, double c, double x1, double x2,
              double *ct3);
void MOMENTS3bis(int nmax, double a, double b, double c, double x1, double x2,
              double *ct3);
void MOMENTS4(int nmax, double a, double b, double c, double x1, double x2,
              double *ct3, double *ct4);

double fact(int n);
double producttermes(int m, int n);

void gl_f3(int m_max, double a, double b, double c, 
           int nb_tranche, double *xmin, double *xmax, double *anu3_se2);
void gl_f4(int m_max, double a, double b, double c, 
           int nb_tranche, double *xmin, double *xmax, double *anu4_se2);

void int_cmn(int nmax, double a, double b, double x1, double x2, 
             int *mmax, double **cmn);
void int_dmn(double a, double b, double c, double x1, double x2, 
             int *mmax, double **dmn);
             
void int_cmn_anal(double a, double b, int *mmax, double **cmn);
void int_dmn_anal(double a, double b, double c, int *mmax, double **dmn);
                
void int_cmn_cp(double a, double b, dcomplex **res, int m_max, int n_max, double epsilon);
void int_dmn_cp(double a, double b, double c, dcomplex **res, int m_max, double epsilon);

void int_cmn_cp_anal(double xmin, double xmax, double a, double b,
                     dcomplex **res, int m_max, int n_max, double epsilon);
void int_dmn_cp_anal(double xmin, double xmax, double a, double b, double c,
                     dcomplex **res, int m_max, int n_max, double epsilon);

#endif