Matlab gets basic arithmetic completely wrong!

I just had a Matlab experience that made me question everything.

I have two vectors: v1 and v2. Both are of length 10 000 and in double-precision. If I plot them, they look like this:

Clearly, these two vectors are very different - one contains values as high as 30 while the other one contains mostly zeros and maxes out at around 6.8.

So far so good. But now when I plot the difference between the two vectors ( v1-v2) I get this:

And if I calculate the maximum absolute difference between the two:

max(abs(v1-v2))

I get 4.4409e-15! What is going on here!?

Clearly the maximum absolute difference should be around 30, not in the order of e-15 something. So what am I facing here? Is it:

• My Matlab installation that is broken
• My system that is broken and can’t do arithmetic correctly
• My brain that is broken and the result are correct

This is the code I use to replicate the results, and I’m attaching a .mat file with the v1 and v2 vectors:

% Load v1 and v2
load('TwoStrangeVectors.mat')

% Plot vector 1
subplot(3,1,1)
plot(v1)
title('vector #1'), xlim([1 10000])

% Plot vector 2
subplot(3,1,2)
plot(v2)
title('vector #2'), xlim([1 10000])

% Plot vector 1 minus vector 2
subplot(3,1,3)
plot(v1 - v2)
title('vector #1 - vector #2'), xlim([1 10000])

I’m using Matlab 2018a on Windows 10 using a i7-8700K processor.

Answer 1

[Dimitris Kalogiros]

Vector v1 is corrupted. It contains "NaN" at the most of its values. Matlab subtracts only at positions where v1 contains valid numbers.

Run the following script, to see what I mean:

close all;
clear all

% Load v1 and v2
load('TwoStrangeVectors.mat')

%define an area of interest
t=2000:2030;

% Plot vector 1
subplot(3,1,1)
plot(t,v1(t),'-ro'); zoom on; grid on;
title('a piece of vector #1') % xlim([1 10000])

% Plot vector 2
subplot(3,1,2)
plot(t,v2(t),'-b*'); zoom on; grid on;
title('a piece of  vector #2') %xlim([1 10000])

% Plot vector 1 minus vector 2
subplot(3,1,3)
plot(t, v1(t)-v2(t), '-ms'); zoom on; grid on;
title(' a piece of  vector #1 - vector #2')

[Petter Stefansson]

Oh wow, how did I manage to miss that. That’s embarrassing. Thank you spotting the NaNs!