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Tibeuleu
248
code_ordonnee_boost/functions.cpp
Executable file
248
code_ordonnee_boost/functions.cpp
Executable file
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/* Librairie de fonctions simple utilisées dans plusieurs programmes */
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#include "functions.h"
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#include<math.h>
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#include<stdlib.h>
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#include<time.h>
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#include "boost/math/special_functions/bessel.hpp"
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using namespace std;
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double angle_princ(double theta){
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while(fabs(theta) > 2.*M_PI){
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if(theta > 0)
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theta -= 2.*M_PI;
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else
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theta += 2.*M_PI;
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}
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if(theta < 0)
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theta += 2.*M_PI;
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return theta;
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}
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double sinc(double x){
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if(fabs(x) < 1e-5)
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return 1.;
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return sin(x)/x;
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}
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/*
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* Fonctions de Bessel modifiées
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*/
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// en utilisant les fonctions bessel de la librairie boost, le fit est prefere ensuite
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double Bessel_I(double alpha, double x){ //Simplification de l appel des fonctions pour le code principal
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return boost::math::cyl_bessel_i((double)alpha,(double)x);
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}
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double Bessel_K(double alpha, double x){
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return boost::math::cyl_bessel_k((double)alpha,(double)x);
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}
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double Bessel_K53(double x){
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return Bessel_K(5./3.,x);
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}
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double Bessel_K23(double x){
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return Bessel_K(2./3.,x);
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}
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double Bessel_K13(double x){
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return Bessel_K(1./3.,x);
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}
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double AsymBessel_1(double nu, double x){ //Un fit des fonctions de Bessel modifiees mais qui ne me permet pas de calculer Bessel_K13
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return 0.5*tgamma(nu)*pow(0.5*x,-nu);
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}
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double AsymBessel_2(double nu, double x){
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return sqrt(M_PI/(2.*x))*exp(-x);
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}
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double Fit_Bessel_K53(double x){ //Voir "Analytical Fits to the Synchrotron Functions", de M. Fouka, S. Ouichaoui sur ResearchGate
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int i;
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double d1,d2, h1=0, h2=0;
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double** a = (double**)malloc(2*sizeof(double*));
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a[0] = (double*)malloc(3*sizeof(double));
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a[0][0] = -1.0194198041210243;
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a[0][1] = 0.28011396300530672;
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a[0][2] = -7.71058491739234908e-2;
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a[1] = (double*)malloc(3*sizeof(double));
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a[1][0] = -15.761577796582387;
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a[1][1] = 0.;
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a[1][2] = 0.;
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for(i=0;i<3;i++){
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h1 += a[0][i]*pow(x,1./(i+1.));
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h2 += a[1][i]*pow(x,1./(i+1.));
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}
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free(a[0]); free(a[1]); free(a);
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d1 = exp(h1);
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d2 = 1-exp(h2);
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return d1*AsymBessel_1(5./3.,x)+d2*AsymBessel_2(5./3.,x);
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}
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double Fit_Bessel_K23(double x){
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int i;
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double d1,d2, h1=0, h2=0;
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double** a = (double**)malloc(2*sizeof(double*));
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a[0] = (double*)malloc(4*sizeof(double));
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a[0][0] = -1.0010216415582440;
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a[0][1] = 0.88350305221249859;
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a[0][2] = -3.6240174463901829;
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a[0][3] = 0.57393980442916881;
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a[1] = (double*)malloc(4*sizeof(double));
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a[1][0] = -0.2493940736333186;
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a[1][1] = 0.9122693061687756;
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a[1][2] = 1.2051408667145216;
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a[1][3] = -5.5227048291651126;
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for(i=0;i<4;i++){
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h1 += a[0][i]*pow(x,1./(i+1.));
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h2 += a[1][i]*pow(x,1./(i+1.));
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}
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free(a[0]); free(a[1]); free(a);
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d1 = exp(h1);
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d2 = 1-exp(h2);
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return d1*AsymBessel_1(2./3.,x)+d2*AsymBessel_2(2./3.,x);
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}
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double Fit_Bessel_K13(double x){ //Attention formule valable seulement pour x >> 1
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return Fit_Bessel_K53(x)-4./(3.*x)*Fit_Bessel_K23(x);
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}
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/*
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* Fonctions Synchrotron
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*/
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double F(double x){ //Fonction synchrotron introduite par Westfold and Legg (1959)
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double b = 100;
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int n = 8e4;
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return x*SimpsonIntegration(x,b,n,Fit_Bessel_K53); //Fait ici intervenir une intégration, on preferera le fit trouve dans le meme papier que precedent
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}
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//un fit de la fonction synchrotron
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double AsymF_1(double x){
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double coeff = M_PI*pow(2.,5./3.)/(sqrt(3)*tgamma(1./3.));
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return coeff*pow(x,1./3.);
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}
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double AsymF_2(double x){
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double coeff = sqrt(0.5*M_PI);
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return coeff*sqrt(x)*exp(-x);
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}
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double Fit_F(double x){
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int i;
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double d1,d2, h1=0, h2=0;
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double** a = (double**)malloc(2*sizeof(double*));
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a[0] = (double*)malloc(3*sizeof(double));
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a[0][0] = -0.97947838884478688;
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a[0][1] = -0.83333239129525072;
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a[0][2] = 0.15541796026816246;
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a[1] = (double*)malloc(3*sizeof(double));
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a[1][0] = -4.69247165562628882e-2;
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a[1][1] = -0.70055018056462881;
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a[1][2] = 1.03876297841949544e-2;
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for(i=0;i<3;i++){
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h1 += a[0][i]*pow(x,1./(i+1.));
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h2 += a[1][i]*pow(x,1./(i+1.));
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}
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free(a[0]); free(a[1]); free(a);
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d1 = exp(h1);
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d2 = 1-exp(h2);
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return d1*AsymF_1(x)+d2*AsymF_2(x);
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}
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double G(double x){ //Deuxieme fonction synchrotron
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return x*Bessel_K23(x);
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}
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/*
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* Fonctions définies sur les fonctions de Bessel pour les calculs des paramètres de Stokes de l'émission synchrotron
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*/
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double WL_L(double n){
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if(n<=2./3.)
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return 0;
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else
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return pow(2,n-2)*tgamma(0.5*n-1./3.)*tgamma(0.5*n+1./3.);
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}
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double WL_J(double n){
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if(n<=2./3.)
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return 0;
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else
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return (2./3.+n)/n*WL_L(n);
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}
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double WL_R(double n){
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if(n<=1./3.)
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return 0;
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else
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return pow(2,n-2)*tgamma(0.5*n-1./6.)*tgamma(0.5*n+1./6.);
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}
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/*
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* Methodes d'intégration
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*/
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double SimpsonIntegration(double a, double b, int n, double(*f)(double)){
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double h = (b-a)/n, I = 0, x1, x2;
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int k;
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for(k=0;k<n;k++){
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x1 = a + k*h;
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x2 = a + (k+1)*h;
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I += (x2-x1)/6.0*(f(x1)+4.0*f(0.5*(x1+x2))+f(x2));
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}
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return I;
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}
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double SimpsonIntegration2(double a, double b, int n, double(*f)(double*,double), double* fix){ //Pour les fonctions de plusieurs variables on stocke celle sur lesquels on integre pas dans le pointeur 'fix'
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double h = (b-a)/n, I = 0, x1, x2;
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int k;
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for(k=0;k<n;k++){
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x1 = a + k*h;
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x2 = a + (k+1)*h;
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I += (x2-x1)/6.0*(f(fix,x1)+4.0*f(fix,0.5*(x1+x2))+f(fix,x2));
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}
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return I;
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}
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double TrapezeIntegration(double a, double b, int n, double(*f)(double)){
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double h = (b-a)/n, I = 0, x1, x2;
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int k;
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for(k=0;k<n;k++){
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x1 = a+k*h;
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x2 = a+(k+1)*h;
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I += 0.5*(x2-x1)*(f(x1)+f(x2));
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}
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return I;
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}
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double TrapezeIntegration2(double a, double b, int n, double(*f)(double*,double), double* fix){
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double h = (b-a)/n, I = 0, x1, x2;
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int k;
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for(k=0;k<n;k++){
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x1 = a+k*h;
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x2 = a+(k+1)*h;
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I += 0.5*(x2-x1)*(f(fix,x1)+f(fix,x2));
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}
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return I;
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}
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double GaussIntegration(double a, double b, int n, double(*f)(double)){
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double h = (b-a)/n, I = 0, x1, xl, xr;
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int k;
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for(k=0;k<n;k++){
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x1 = a+k*h;
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xl = x1+(0.5-sqrt(3.)/6.)*h;
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xr = x1+(0.5+sqrt(3.)/6.)*h;
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I += f(xl)+f(xr);
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}
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return 0.5*h*I;
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}
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double GaussIntegration2(double a, double b, int n, double(*f)(double*,double), double* fix){
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double h = (b-a)/n, I = 0, x1, xl, xr;
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int k;
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for(k=0;k<n;k++){
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x1 = a+k*h;
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xl = x1+(0.5-sqrt(3.)/6.)*h;
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xr = x1+(0.5+sqrt(3.)/6.)*h;
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I += f(fix,xl)+f(fix,xr);
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}
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return 0.5*h*I;
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}
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