Calculating the error between true point and interpolation

Hi. I have 35 points where x is distance in meters, and z is seismic depth in seconds. I have made a 1d spline and k-nearest interpolation between these points, and I'm now trying to calculate the error. However, I'm having trouble calculating the difference in z between the real (the red dot) and corresponding interpolated point (blue line at the same x-position as the red dot). I've tried the following, but it doesn't work.

Thanks in advance.

clc; close all;
td = load("thicknesses.dat");

x = td(:,1);
z = td(:,3);

n_x = length(x);
end_x = x(end);

x_sample = linspace(x(1),end_x,n_x);

spline_int = interp1(x,z,x_sample,'spline');
k_nearest_int = interp1(x,z,x_sample,'nearest');

figure();
subplot(1,2,1);
plot(x,z,'or');
set(gca, 'YDir','reverse')
hold on;
plot(x_sample, spline_int, '-b');
title('spline', 'FontSize',15)
xlabel('Distance in x-direction (m)','FontSize',10)
ylabel('Thickness (s)','FontSize',10)

subplot(1,2,2);
plot(x,z,'or');
set(gca, 'YDir','reverse')
hold on;
plot(x_sample, k_nearest_int, '-b');
title('k-nearest', 'FontSize',15)
xlabel('Distance in x-direction (m)','FontSize',10)
ylabel('Thickness (s)','FontSize',10)
hold off;


spline_at_x = [];
for i = 1:length(x);
      k(i) = spline_int(i(x_sample == x(i)))
      
      spline_at_x = [spline_at_x k(i)]

         
    end
end

Hope it is clear, thanks in advance.

Answer 1

[Image Analyst]

Unfortunately you forgot to attach "thicknesses.dat" so we can't run your code. Why can't you simply say

differences = spline_at_x - x;

Take the absolute value if you want.

[Christian Mathiesen]

Hi, thanks for your response. I actually ended up using fittype('smoothingspline') to get the residuals instead. Seemed simpler than what I had going on. Thanks for taking the time.