How can I find the coefficients of the 2D interpolated function?

My function is . I used following code to interpolation. How can I find the coefficients of the interpolated function ?

Eta = load('Eta.txt');
t = 0:5:(8.25*60); % time
x = [0,3750,7500,8000]; % distance
[X,T] = meshgrid(x,t);

% interpolation
[xq,tq] = meshgrid(0:2:8000,0:(8.25*60)) ;
Eta_intp = interp2(X,T,eta,xq,tq,'spline');

Answer 1

[Animesh]

Hey @Sajani Perera,

To find the coefficients of the 2-D interpolated function, we can use polynomial fitting on the interpolated data. You can use the "polyfit" function to do so in MATLAB.

https://www.mathworks.com/help/matlab/ref/polyfit.html

Here is something you can try:

1. Flatten the matrices, since "polyfit" works only with vectors.

% Flatten the matrices
xq_flat = xq(:);
tq_flat = tq(:);
E_intp_flat = E_intp(:);

2. Perform polynomial fitting:

% Perform polynomial fitting
% Here, we assume a polynomial of degree 2 in both x and t
degree = 2;
p = polyfitn([xq_flat, tq_flat], E_intp_flat, degree);
disp(p.Coefficients);

[SPerera]

@Animesh Thank you so much. I got it. After this I checked the difference between original data and polynomial data using following code. There is a difference between these two. Without adjusting the Polynomial Degree, how can I reduce this difference?

% Define a function for evaluating the polynomial
eta_poly = @(xq,tq) polyvaln(p,[xq,tq]);

% Evaluate the polynomial at the original grid points
eta_poly_values = arrayfun(@(x_val, t_val) eta_poly(x_val, t_val), X, T);

% Compare the polynomial values with the original eta data
% Calculate the difference
difference = eta_poly_values - eta;