Strange behavior of if statement

i have this very simple code that should return 'ans = 1' when run, since the sum of d is 1. However it returns the error message specified in the 'else' section instead, as if d didn't add up to 1. What's going on?

d = [.4 .1 .1 .1 .1 .1 .1];

if sum(d) == 1
    sum(d)
else
    error('d doesnt add up to 1')
end

Answer 1

[Rik]

Welcome to floating point integers.

Matlab stores these numbers in a binary representation with a finite precision. Similar to what would happen if you only store 4 decimals and do this: (1/3)*3=0.3333*3=0.9999.

You should probably compare to a tolerance:

d = [.4 .1 .1 .1 .1 .1 .1];
if abs( sum(d)-1 ) <= 2*eps
    sum(d)
else
    error('d doesnt add up to 1')
end

ans = 1.0000

[martino corrà]

ah I see, thank you soo soo much, i've been trying to figure out what was going on for hours! It seemed like matlab was mocking me! now i understand. Thanks a lot!

Answer 2

[DGM]

It's correct. The sum isn't 1. It's approximately 1.

d = [0.4 0.1 0.1 0.1 0.1 0.1 0.1]; % leading zeros for readability, pls

sum(d) % that sure looks like 1
sum(d)-1 % but you just don't have the display resolution to see the error

gives

ans =
    1.0000
ans =
  -1.1102e-16

Beware simple equality tests when using floating point numbers. Test to within a tolerance.

tol=1E-12;
if abs(sum(d)-1)<tol
    sum(d)
else
    error('d doesnt add up to 1')
end

[martino corrà]

Now i get it, thank you so much!!!