sum() missing for certain values

Hello,

I have an issue which i do not understand using the basic function sum(). I have an array with 2 million values consisting of doubles from 0 to 1 with 3 decimals (rounded). I want to display the distribution by counting every possible output except zero and one using the sum function (0.001-0.999). I tried to calculate it with and without a loop but im allways missing the sum for certain values either way. Example code below.

Vector=rand(2000000,1);
Vector=round(Vector,3,"decimals");

numbers=0.001:0.001:0.999;
b=1;
distribution2=double.empty(999,0);

for x=0.001:0.001:0.999
    distribution2(b)=sum(Vector==x);
    b=b+1;
end
figure()
plot(numbers,distribution2)
title('distribution2 (with loop)')

distribution(:)=sum(Vector==numbers);
figure()
plot(numbers,distribution)
title('distribution')

As u can see I get a feedback with different gaps using the calculation methods as shown above. I checked the gaps (e.g. 0.7) by using the sum function inside the command window and got back a positive feedback

>> sum(Vector==0.7)

ans =

        2009

Can someone explain to me why I am having issues calculating the sum for all numbers and why I am getting two different results depending on how I am trying to calculate it?

Thank you and nice Regards

Anton

[Stephen23]

"Can someone explain to me why I am having issues calculating the sum for all numbers and why I am getting two different results depending on how I am trying to calculate it? "

This is due to the nature of working with binary floating point numbers:

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal

http://www.mathworks.com/matlabcentral/answers/102419-how-do-i-determine-if-the-error-in-my-answer-is-the-result-of-round-off-error-or-a-bug

http://www.mathworks.com/matlabcentral/answers/140656-about-numerical-difficulty-of-equality-comparison-operation-between-two-double-real-numbers-in-matlab

This is highly recommended:

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

http://faculty.tarleton.edu/agapie/documents/cs_343_arch/papers/1991_Goldberg_FloatingPoint.pdf

[Anton]

Hello, I'm aware that matlab is not able to display exactly 0.7 due to binary flaoting numbers, but i was not aware that matlab is using different construction for 0.7 inside command window and inside code. Thank you for the explanation.

[Stephen23]

"I'm aware that matlab is not able to display exactly 0.7 due to binary flaoting numbers"

MATLAB certainly can "display exactly 0.7", even binary floating point. Lets try it right now:

format short G
0.7

ans = 
          0.7

"i was not aware that matlab is using different construction for 0.7 inside command window and inside code"

I have never heard that MATLAB uses a "different construction for 0.7 inside command window and inside code", and I strongly doubt that such a "different construction" exists due solely to where the value is defined. I tried it in R2018a:

The two values are exactly the same.

The links I posted earlier introduce floating point number behavior. David Goldberg's article is highly recommended.

[Anton]

Thank you for clarificaton. I'll read the article.

Answer 1

[KSSV]

Don't use

sum(Vector==x)

use

tol = 0.0001 ; % set your acceptable tolerance 
sum(abs(Vector-x)<tol) ; 

[Anton]

Thank you for the recommendation