# Calculating the error between true point and interpolation

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Christian Mathiesen on 7 Oct 2021
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.
clc; close all;
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.

Image Analyst on 7 Oct 2021
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 on 7 Oct 2021
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.

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