Okay, so the following is a code for fitting a polynomial to a given set of data using the Least Squares Approximation Method(Wikipedia).

**Formula Used:**

where and are the data-points entered by the user.

I had written a C++ and C code for this a long time ago, and coincidentally it got very popular for some reason. But then I felt the need to make an Android app that does the same.

So I ported my code to JAVA so that it works in my Android App.

Let’s say you have *x*-axis values and y-axis values in two double arrays called x[] and y[] of size N(no. of data points). You can either have the user enter them or have them imported from a CSV. It’s your call.

Then you need to have the user enter the degree(order) of the polynomial to use to fit the curve.

**Note**: If you have *n* data-points, then an *n-1* degree polynomial will interpolate your data (fit your data perfectly).

The following information is required:

int n; //degree of polynomial to fit the data int N; //no. of data points double[] x=double[]; //array to store x-axis data points double[] y=double[]; //array to store y-axis data points

Once you have all the values for x[], y[], n, and N, the following code will fit a polynomial of nth degree to the given set of data-points and return the coefficients of the polynomial in an array a[], such that a[0] is the coefficient of x^0 , a[1] is the coefficient of x^1,… and so on.

double X[] = new double[2 * n + 1]; for (int i = 0; i < 2 * n + 1; i++) { X[i] = 0; for (int j = 0; j < N; j++) X[i] = X[i] + Math.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[][] = new double[n + 1][n + 2], a[] = new double[n + 1]; //B is the Normal matrix(augmented) that will store the equations, 'a' is for value of the final coefficients for (int i = 0; i <= n; i++) for (int 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[] = new double[n + 1]; //Array to store the values of sigma(yi),sigma(xi*yi),sigma(xi^2*yi)...sigma(xi^n*yi) for (int i = 0; i < n + 1; i++) { Y[i] = 0; for (int j = 0; j < N; j++) Y[i] = Y[i] + Math.pow(x[j], i) * y[j]; //consecutive positions will store sigma(yi),sigma(xi*yi),sigma(xi^2*yi)...sigma(xi^n*yi) } for (int 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; for (int i = 0; i < n; i++) //From now Gaussian Elimination starts(can be ignored) to solve the set of linear equations (Pivotisation) for (int k = i + 1; k < n; k++) if (B[i][i] < B[k][i]) for (int j = 0; j <= n; j++) { double temp = B[i][j]; B[i][j] = B[k][j]; B[k][j] = temp; } for (int i = 0; i < n - 1; i++) //loop to perform the gauss elimination for (int k = i + 1; k < n; k++) { double t = B[k][i] / B[i][i]; for (int 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 (int 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 (int 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 }

Well, that’s it. The array a[] contains the coefficients such that a[i]=coefficient of x^i.

To understand the theory behind this, refer to this link.

Hope you guys find it useful!

If you have any questions/doubts, hit me up in the comments section below.

You can refer to the following links for more info:

Polynomial Fitting – C Program

Polynomial Fitting – C++ Program

Linear Fitting – Lab Write-Up

Linear Fitting – C++ Program

Linear Fitting – Scilab Code

Curve Fit Tools – Android App (using the above code)

Curve Fit Tools – Documentation

Curve Fit Tools – Play Store

Curve Fit Tools – GitHub Repository

Curve Fitters – Scilab Toolbox

I’m a physicist specializing in computational material science with a PhD in Physics from Friedrich-Schiller University Jena, Germany. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT, and Machine Learning related apps and software from time to time. Can code in most of the popular languages. I like to share my knowledge in Physics and applications using this Blog and a YouTube channel.

Thanks. You saved me a lot of time.