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Program to implement Linear Extrapolation

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  • Difficulty Level : Basic
  • Last Updated : 23 Jun, 2022

What is Extrapolation? 
Extrapolation is the process in mathematics where the required value is estimated beyond the range the of the given variable range. Extrapolation is often used to estimate the data of some observation below or above the given range. Extrapolation is also referred to as a mathematical prediction to predict values by observing the relationship between the given variables. There are many processes of Extrapolation.Here only Linear Extrapolation will be discussed. This process was first described by Thomas D. Clareson in 1959 in his book of science. He referred to it as a meaningful prediction by understanding the given data. 
How to calculate Linear Exptrapolation?
The method is useful when the linear function is given. It is done by drawing a tangent and extending it beyond the limit. Linear Extrapolation gives a very good result when the point to be predicted is not very far from the rest of the points.
 

Extrapolation formula: y(x) = y_1(x) +\frac {x-x_1} {x_2-x_1} (y_2-y_1)

Here (x_1, y_1)    and (x_2, y_2)    are two given points and x is the point for which we want to predict the value of y.
Examples: 
 

Input: x_1=0.3, y_1=1.8    x_2=0.5, y_2=2.1    , x = 1.2 
Output: y = 3.15 
 

 

 

Implementation: 
 

C++




// C++ code for the implementation
// of Linear extrapolation
 
#include <bits/stdc++.h>
using namespace std;
 
// Consider a structure
// to keep each pair of x and y together
struct Data {
    double x, y;
};
 
// Function to calculate
// the linear extrapolation
double extrapolate(Data d[], double x)
{
    double y;
    y = d[0].y
        + (x - d[0].x)
              / (d[1].x - d[0].x)
              * (d[1].y - d[0].y);
 
    return y;
}
 
// Driver Code
int main()
{
    // Sample dataset
    Data d[] = { { 1.2, 2.7 }, { 1.4, 3.1 } };
 
    // Sample x value
    double x = 2.1;
 
    // Finding the extrapolation
    cout << "Value of y at x = 2.1 : "
         << extrapolate(d, x);
 
    return 0;
}

Java




// Java code for the implementation of
// Linear extrapolation
class GFG
{
     
// Function to calculate the linear
// extrapolation
static double extrapolate(double[][] d, double x)
{
    double y = d[0][1] + (x - d[0][0]) /
                (d[1][0] - d[0][0]) *
                (d[1][1] - d[0][1]);
 
    return y;
}
 
// Driver Code
public static void main (String[] args)
{
     
// Sample dataset
double[][] d = {{ 1.2, 2.7 },{ 1.4, 3.1 }};
 
// Sample x value
double x = 2.1;
 
// Finding the extrapolation
System.out.println("Value of y at x = 2.1 : " +
                    extrapolate(d, x));
}
}
 
// This code is contributed by chandan_jnu

Python3




# Python3 code for the implementation of
# Linear extrapolation
 
# Function to calculate the linear
# extrapolation
def extrapolate(d, x):
    y = (d[0][1] + (x - d[0][0]) /
        (d[1][0] - d[0][0]) *
        (d[1][1] - d[0][1]));
 
    return y;
 
# Driver Code
 
# Sample dataset
d = [[ 1.2, 2.7 ], [1.4, 3.1 ]];
 
# Sample x value
x = 2.1;
 
# Finding the extrapolation
print("Value of y at x = 2.1 :",
             extrapolate(d, x));
 
# This code is contributed by mits

C#




// C# code for the implementation of
// Linear extrapolation
class GFG
{
     
// Function to calculate the linear
// extrapolation
static double extrapolate(double[,] d, double x)
{
    double y = d[0,1] + (x - d[0,0]) /
                (d[1,0] - d[0,0]) *
                (d[1,1] - d[0,1]);
 
    return y;
}
 
// Driver Code
static void Main()
{
     
// Sample dataset
double[,] d = {{ 1.2, 2.7 },{ 1.4, 3.1 }};
 
// Sample x value
double x = 2.1;
 
// Finding the extrapolation
System.Console.WriteLine("Value of y at x = 2.1 : " +
                    extrapolate(d, x));
}
}
 
// This code is contributed by chandan_jnu

PHP




<?php
// PHP code for the implementation of
// Linear extrapolation
 
// Function to calculate the linear
// extrapolation
function extrapolate($d, $x)
{
    $y = $d[0][1] + ($x - $d[0][0]) /
        ($d[1][0] - $d[0][0]) *
        ($d[1][1] - $d[0][1]);
 
    return $y;
}
 
// Driver Code
 
// Sample dataset
$d = array(array( 1.2, 2.7 ),
           array( 1.4, 3.1 ));
 
// Sample x value
$x = 2.1;
 
// Finding the extrapolation
echo "Value of y at x = 2.1 : ",
            extrapolate($d, $x);
 
// This code is contributed by Ryuga
?>

Javascript




<script>
    // Javascript code for the implementation of
    // Linear extrapolation
     
    // Function to calculate the linear
    // extrapolation
    function extrapolate(d, x)
    {
        let y = d[0][1] + (x - d[0][0]) / (d[1][0] - d[0][0]) *
                    (d[1][1] - d[0][1]);
 
        return y;
    }
     
    // Sample dataset
    let d = [[ 1.2, 2.7 ],[ 1.4, 3.1 ]];
 
    // Sample x value
    let x = 2.1;
 
    // Finding the extrapolation
    document.write("Value of y at x = 2.1 : " +
                        extrapolate(d, x));
 
// This code is contributed by mukesh07.
</script>

Output: 

Value of y at x = 2.1 : 4.5

 

Time Complexity: O(1)

Auxiliary Space: O(1)


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