lagrange interpolation

lagrange.c

#include <stdio.h>
#include <stdlib.h>

#define N 10
#define MIN -5.0
#define MAX 5.0
#define F(x)  (1 / (1 + x * x))

double x_at (int i);
double get_lj (int j, double x);
double Ln (double x);

int main (){
    double x1, x2, x;
    printf("    ui    \t  f(ui)   \t   Ln(x)\n");
    for (int i=0;i<N;++i){
        x1 = x_at(i);
        x2 = x_at(i+1);
        x = (x1 + x2) / 2;
        printf("%10lf\t%10lf\t%10lf\n", x, F(x), Ln(x));
    }
    system("pause");
    return 0;
}

double x_at (int i){
    double step = (MAX - MIN) / N;
    double x = MIN + i * step;
    return x;
}

double get_lj (int j, double x){
    double result = 1.0;
    double xi;
    double xj = x_at(j);
    for (int i=0;i<N+1;++i){
        if (i == j){
            continue;
        }
        xi = x_at(i);
        result = result * ((x - xi) / (xj - xi));
    }
    return result;
}

double Ln(double x){
    double xj, yj, lj;
    double result = 0;
    for (int j=0;j<N+1;++j){
        xj = x_at(j);
        yj = F(xj);
        lj = get_lj(j, x);
        result = result + yj * lj;
    }
    return result;
}