piecewise interpolation

piecewise interpolation.c

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

#define N 10
#define MIN -5.0
#define MAX 5.0
#define F(x)  (1.0 / (1.0 + x * x))

double x_at(int i);
double get_L(int k, double x);
double Lh(int k, double x);

int main(){
    double x1, x2, x, y;
    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;
        y = F(x);
        printf("%10lf\t%10lf\t%10lf\n", x, F(x), Lh(i, x));
    }
    system("pause");
    return 0;
}

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

double get_L(int k, double x){
    double xk, xk_plus_one, yk, yk_plus_one, L_value;
    xk = x_at(k);
    xk_plus_one = x_at(k + 1);
    yk = F(xk);
    yk_plus_one = F(xk_plus_one);
    L_value = (yk * (x - xk_plus_one) / (xk - xk_plus_one) +
               yk_plus_one * (x - xk) / (xk_plus_one - xk));
    return L_value;
}

double Lh(int k, double x){
    if (x < x_at(k)){
        return get_L(k, 0);
    }
    else if(x > x_at(N)){
        return get_L(k, N);
    }
    else{
        return get_L(k, x);
    }
}