# Lagrange Interpolation Polynomial – C PROGRAM

Given a set of $n+1$ data-points $(x_i,y_i)$, the Lagrange Interpolating Polynomial is a polynomial of degree $\leq n$, such that it passes through all the given $n+1$ data-points.

It is given as,

$\boxed{Pn(x) = \sum^n_{i=0} L_i(x)y_i}$

where $(x_0,y_0), (x_1,y_1),.....(x_n,y_n)$ are the $n+1$ data-points.
and,
$\boxed{L_i(x)=\prod^n_{j=0;j \neq i}\frac{x-x_j}{x_i-x_j}}$

### CODE:

/**********************************
******LAGRANGE INTERPOLATION*******
**********************************/
#include<stdio.h>

/*Function to evaluate Li(x)*/

double Li(int i, int n, double x[n+1], double X){
int j;
double prod=1;
for(j=0;j<=n;j++){
if(j!=i)
prod=prod*(X-x[j])/(x[i]-x[j]);
}
return prod;
}

/*Function to evaluate Pn(x) where Pn is the Lagrange interpolating polynomial of degree n*/

double Pn(int n, double x[n+1], double y[n+1], double X){
double sum=0;
int i;
for(i=0;i<=n;i++){
sum=sum+Li(i,n,x,X)*y[i];
}
return sum;
}
main(){
int i,n;  //n is the degree
printf("Enter the number of data-points:\n");
scanf("%d",&n);  //no. of data-points is n+1
n=n-1;
//Arrays to store the (n+1) x and y data-points of size n+1
double x[n+1];
double y[n+1];
printf("Enter the x data-points:\n");
for(i=0;i<n+1;i++){
scanf("%lf",&x[i]);
}

printf("Enter the y data-points:\n");
for(i=0;i<n+1;i++){
scanf("%lf",&y[i]);
}

double X;  //value of x for which interpolated value is required
printf("Enter the value of x for which you want the interpolated value of y(x):\n");
scanf("%lf",&X);
printf("The interpolated value is %lf",Pn(n,x,y,X));
}


f(x)=1/x

f(x)=x^2

### References and Resources:

[wpedon id="7041" align="center"]

## 3 thoughts on “Lagrange Interpolation Polynomial – C PROGRAM”

1. Hello just check the function LI(……) , as per your code i was getting an error while using double x[n+1] , i tried and changed each parameter x[n+1] with x[] and same with y[n+1] with y[] , just check the below code 🙂

8:33: error: use of parameter outside function body before ‘]’ token
8:34: error: expected ‘)’ before ‘,’ token
8:35: error: expected unqualified-id before ‘double’

solution:

/**********************************
******LAGRANGE INTERPOLATION*******
**********************************/
#include

/*Function to evaluate Li(x)*/

double Li(int i,int n,double x[],double X){
int j;
double prod=1;
for(j=0;j

1. Thank you very much for your valuable correction to the above program. I can successfully run a program as per your correction suggestion.