cubic spline in matlab

To use cubic spline interpolation in MATLAB, you can use the built-in function 'spline'. The 'spline' function forms piecewise cubic interpolants based on given combinations of points and function values. Here's a basic template for using 'spline' function in MATLAB:

main.m
% define data points
x = [1, 2, 4, 7];   % x-values of data points
y = [3, 1, 2, 4];   % corresponding y-values

% create spline interpolation object
spline_obj = spline(x, [y(1), y, y(end)]); % cubic spline object

% evaluate spline interpolant over higher resolution set of x-values
x_vals_interp = linspace(min(x), max(x), 100);   % higher resolution set of x-values
y_vals_interp = ppval(spline_obj, x_vals_interp); % use spline object to evaluate y-values on interp x-values

% plot original data points and spline interpolant
figure;
plot(x, y, 'o', x_vals_interp, y_vals_interp);
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In the above code, x and y are the data points to be interpolated. The spline function is used to form a piecewise cubic interpolant from these data points, and this spline object is stored in spline_obj. The ppval function is then used to evaluate the spline interpolant over a higher resolution set of x-values generated using linspace. Finally, the original data points and the spline interpolant are plotted together using the plot function.

Note that the above code assumes that the x-values in x are arranged in increasing order. If this is not the case, you should sort x and y accordingly before calling the spline function.