//Polynomial Fit
#include<iostream>
#include<iomanip>
#include<cmath>
using namespace std;
int main()
{
int i,j,k,n,N;
cout.precision(4); //set precision
cout.setf(ios::fixed);
cout<<"\nEnter the no. of data pairs to be entered:\n"; //To find the size of arrays that will store x,y, and z values
cin>>N;
double x[N],y[N];
cout<<"\nEnter the x-axis values:\n"; //Input x-values
for (i=0;i<N;i++)
cin>>x[i];
cout<<"\nEnter the y-axis values:\n"; //Input y-values
for (i=0;i<N;i++)
cin>>y[i];
cout<<"\nWhat degree of Polynomial do you want to use for the fit?\n";
cin>>n; // n is the degree of Polynomial
double X[2*n+1]; //Array that will store the values of sigma(xi),sigma(xi^2),sigma(xi^3)....sigma(xi^2n)
for (i=0;i<2*n+1;i++)
{
X[i]=0;
for (j=0;j<N;j++)
X[i]=X[i]+pow(x[j],i); //consecutive positions of the array will store N,sigma(xi),sigma(xi^2),sigma(xi^3)....sigma(xi^2n)
}
double B[n+1][n+2],a[n+1]; //B is the Normal matrix(augmented) that will store the equations, 'a' is for value of the final coefficients
for (i=0;i<=n;i++)
for (j=0;j<=n;j++)
B[i][j]=X[i+j]; //Build the Normal matrix by storing the corresponding coefficients at the right positions except the last column of the matrix
double Y[n+1]; //Array to store the values of sigma(yi),sigma(xi*yi),sigma(xi^2*yi)...sigma(xi^n*yi)
for (i=0;i<n+1;i++)
{
Y[i]=0;
for (j=0;j<N;j++)
Y[i]=Y[i]+pow(x[j],i)*y[j]; //consecutive positions will store sigma(yi),sigma(xi*yi),sigma(xi^2*yi)...sigma(xi^n*yi)
}
for (i=0;i<=n;i++)
B[i][n+1]=Y[i]; //load the values of Y as the last column of B(Normal Matrix but augmented)
n=n+1; //n is made n+1 because the Gaussian Elimination part below was for n equations, but here n is the degree of polynomial and for n degree we get n+1 equations
cout<<"\nThe Normal(Augmented Matrix) is as follows:\n";
for (i=0;i<n;i++) //print the Normal-augmented matrix
{
for (j=0;j<=n;j++)
cout<<B[i][j]<<setw(16);
cout<<"\n";
}
for (i=0;i<n;i++) //From now Gaussian Elimination starts(can be ignored) to solve the set of linear equations (Pivotisation)
for (k=i+1;k<n;k++)
if (B[i][i]<B[k][i])
for (j=0;j<=n;j++)
{
double temp=B[i][j];
B[i][j]=B[k][j];
B[k][j]=temp;
}
for (i=0;i<n-1;i++) //loop to perform the gauss elimination
for (k=i+1;k<n;k++)
{
double t=B[k][i]/B[i][i];
for (j=0;j<=n;j++)
B[k][j]=B[k][j]-t*B[i][j]; //make the elements below the pivot elements equal to zero or elimnate the variables
}
for (i=n-1;i>=0;i--) //back-substitution
{ //x is an array whose values correspond to the values of x,y,z..
a[i]=B[i][n]; //make the variable to be calculated equal to the rhs of the last equation
for (j=0;j<n;j++)
if (j!=i) //then subtract all the lhs values except the coefficient of the variable whose value is being calculated
a[i]=a[i]-B[i][j]*a[j];
a[i]=a[i]/B[i][i]; //now finally divide the rhs by the coefficient of the variable to be calculated
}
cout<<"\nThe values of the coefficients are as follows:\n";
for (i=0;i<n;i++)
cout<<"x^"<<i<<"="<<a[i]<<endl; // Print the values of x^0,x^1,x^2,x^3,....
cout<<"\nHence the fitted Polynomial is given by:\ny=";
for (i=0;i<n;i++)
cout<<" + ("<<a[i]<<")"<<"x^"<<i;
cout<<"\n";
return 0;
}//output attached as .jpg
https://www.bragitoff.com/2015/09/c-program-for-polynomial-fit-least-squares/
C++ Program for Polynomial Fit (Least Squares) - BragitOff.com
//Polynomial Fit #include #include #include using namespace std; int main() { int i,j,k,n,N; cout.precision(4); //set precision cout.setf(ios::fixed); cout<<"\nEnter the no. of data pairs…
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