Program to find covariance

Given a two set of random variable, find Covariance. Covariance is a measure of how much two random variables vary together. It’s similar to variance, but where variance tells you how a single variable varies, covariance tells you how two variables vary together. Covariance can be calculated by using the formula 

Where x’ and y’ are the means of two given sets.

Examples: 

Input : arr1[] = {65.21, 64.75, 65.26, 65.76, 65.96}
        arr2[] = {67.25, 66.39, 66.12, 65.70, 66.64}
Output : -0.0580511

Input : arr1[] = {5, 20, 40, 80, 100}
        arr2[] = {10, 24, 33, 54, 10}
Output : 187.75

C++

// C++ Program to find covariance of two set.
#include <bits/stdc++.h>
using namespace std;

// Function to find mean.
float mean(float arr[], int n)
{
    float sum = 0;
    for (int i = 0; i < n; i++)
        sum = sum + arr[i];
    return sum / n;
}

// Function to find covariance.
float covariance(float arr1[], float arr2[], int n)
{
    float sum = 0;
    float mean_arr1 = mean(arr1, n);
    float mean_arr2 = mean(arr2, n);
    for (int i = 0; i < n; i++)
        sum = sum + (arr1[i] - mean_arr1) * (arr2[i] - mean_arr2);
    return sum / (n - 1);
}

// Driver function.
int main()
{
    float arr1[] = { 65.21, 64.75, 65.26, 65.76, 65.96 };
    int n = sizeof(arr1) / sizeof(arr1[0]);
    float arr2[] = { 67.25, 66.39, 66.12, 65.70, 66.64 };
    int m = sizeof(arr2) / sizeof(arr2[0]);

    if (m == n)
        cout << covariance(arr1, arr2, m);
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

C

// C Program to find covariance of two set.
#include <stdio.h>

// Function to find mean.
float mean(float arr[], int n)
{
    float sum = 0;
    for (int i = 0; i < n; i++)
        sum = sum + arr[i];
    return sum / n;
}

// Function to find covariance.
float covariance(float arr1[], float arr2[], int n)
{
    float sum = 0;
    float mean_arr1 = mean(arr1, n);
    float mean_arr2 = mean(arr2, n);
    for (int i = 0; i < n; i++)
        sum = sum + (arr1[i] - mean_arr1) * (arr2[i] - mean_arr2);
    return sum / (n - 1);
}

// Driver function.
int main()
{
    float arr1[] = { 65.21, 64.75, 65.26, 65.76, 65.96 };
    int n = sizeof(arr1) / sizeof(arr1[0]);
    float arr2[] = { 67.25, 66.39, 66.12, 65.70, 66.64 };
    int m = sizeof(arr2) / sizeof(arr2[0]);

    if (m == n)
        printf("%f", covariance(arr1, arr2, m));
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

Java

// Java Program to find covariance of two set.
import java.io.*;

class GFG {

    // Function to find mean.
    static float mean(float arr[], int n)
    {
        float sum = 0;
        for (int i = 0; i < n; i++)
            sum = sum + arr[i];
        return sum / n;
    }

    // Function to find covariance.
    static float covariance(float arr1[], float arr2[], int n)
    {
        float sum = 0;
        float mean_arr1 = mean(arr1, n);
        float mean_arr2 = mean(arr2, n);

        for (int i = 0; i < n; i++)
            sum = sum + (arr1[i] - mean_arr1) * (arr2[i] - mean_arr2);
        return sum / (n - 1);
    }

    // Driver code
    public static void main(String[] args)
    {

        float arr1[] = { 65.21f, 64.75f, 65.26f, 65.76f, 65.96f };
        int n = arr1.length;
        float arr2[] = { 67.25f, 66.39f, 66.12f, 65.70f, 66.64f };
        int m = arr2.length;

        if (m == n)
            System.out.println(covariance(arr1, arr2, m));
    }
}

// This code is contributed by Aditya Kumar (adityakumar129)

Python3

# Python3 Program to find
# covariance of two set.
import math

# Function to find mean.


def mean(arr, n):

    sum = 0
    for i in range(0, n):
        sum = sum + arr[i]

    return sum / n

# Function to find covariance.


def covariance(arr1, arr2, n):

    sum = 0
    mean_arr1 = mean(arr1, n)
    mean_arr2 = mean(arr2, n)
    for i in range(0, n):
        sum = (sum + (arr1[i] - mean_arr1) * (arr2[i] - mean_arr2))

    return sum / (n - 1)


# Driver method
arr1 = [65.21, 64.75, 65.26, 65.76, 65.96]
n = len(arr1)
arr2 = [67.25, 66.39, 66.12, 65.70, 66.64]
m = len(arr2)

if (m == n):
    print(covariance(arr1, arr2, m))

# This code is contributed by Aditya Kumar (adityakumar129)

C#

// C# Program to find
// covariance of two set.
using System;

class GFG {

    // Function to find mean.
    static float mean(float []arr, int n)
    {
        float sum = 0;

        for(int i = 0; i < n; i++)
            sum = sum + arr[i];

        return sum / n;
    }

    // Function to find covariance.
    static float covariance(float []arr1,
                        float []arr2, int n)
    {
        float sum = 0;
          float mean_arr1 = mean(arr1,n);
          float mean_arr2 = mean(arr2,n);
        for(int i = 0; i < n; i++)
            sum = sum + (arr1[i] - mean_arr1) *
                            (arr2[i] - mean_arr2);
        return sum / (n - 1);
    }

    // Driver code
    public static void Main () {

        float []arr1 = {65.21f, 64.75f,
                65.26f, 65.76f, 65.96f};
        int n = arr1.Length;

        float []arr2 = {67.25f, 66.39f,
                    66.12f, 65.70f, 66.64f};

        int m = arr2.Length;

        if (m == n)

        Console.WriteLine(covariance(arr1, arr2, m));

    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP Program to find
// covariance of two set.

// Function to find mean.
function mean( $arr, $n)
{
    $sum = 0;
    for( $i = 0; $i < $n; $i++)
        $sum = $sum + $arr[$i];
    return $sum / $n;
}

// Function to find covariance.
function covariance( $arr1, $arr2, $n)
{
    $sum = 0;
    $mean_arr1 = mean($arr1,$n);
      $mean_arr2 = mean($arr2,$n);
    for( $i = 0; $i < $n; $i++)
        $sum = $sum + ($arr1[$i] -
                 $mean_arr1) *
                      ($arr2[$i] -
                  $mean_arr2);
    return $sum / ($n - 1);
}

// Driver function.
$arr1 = array(65.21, 64.75, 65.26,
                        65.76, 65.96);
$n = count($arr1);

$arr2 = array(67.25, 66.39, 66.12,
                        65.70, 66.64);
$m =count($arr2);

if ($m == $n)
    echo covariance($arr1, $arr2, $m);

// This code is contributed by anuj_67.
?>

Javascript

<script>

// Javascript program to find
// covariance of two set.

// Function to find mean.
function mean(arr, n)
{
    let sum = 0;
    for(let i = 0; i < n; i++)
        sum = sum + arr[i];

    return sum / n;
}

// Function to find covariance.
function covariance(arr1, arr2, n)
{
    let sum = 0;
     let mean_arr1 = mean(arr1, n);
    let mean_arr2 = mean(arr2, n);
    for(let i = 0; i < n; i++)
        sum = sum + (arr1[i] - mean_arr1) *
                    (arr2[i] - mean_arr2);

    return sum / (n - 1);
}

// Driver code
let arr1 = [ 65.21, 64.75, 65.26, 65.76, 65.96 ];
let n = arr1.length;

let arr2 = [ 67.25, 66.39, 66.12, 65.70, 66.64 ];
let m = arr2.length;

if (m == n)
    document.write(covariance(arr1, arr2, m));

// This code is contributed by souravmahato348

</script>

Output: 

-0.0580511

Time Complexity: O(N)
Auxiliary Space: O(1)