No jump in in if-query even though if-statement is true

In the following Code I want to compare the values of two different variables.

X = 0:0.1:200;
T = [0.1; 0.2; 0.3; 0.5; 0.9; 1.5; 2.6; 4.5; 7.7; 13.2; 22.8; 39.2; 67.5; 116.2; 200];
jump_in = zeros([length(T) 1]);

for t = 1:length(T)
    for x = 1:length(X)
        if X(x) == T(t)
            jump_in(t) = 1;
            break;
        end
    end
end

After running there are no warnings or errors but for the values of 0.3, 13.2 and 116.2 even if the statement is true it does not jump in.

I changed the if-statement into X(x) -T(t) == 0 but this did not work either.

I also changed the values of the Variables X and T into

X = [0.3:0.1:200];
T = [0.3; 0.5; 0.9; 1.5; 2.6; 4.5; 7.7; 13.2; 22.8; 39.2; 67.5; 116.2; 200];

Then it jumps into the if-query for 0.3 but it does not jump in for the vaules of 0.9, 1.5, 13.2 and 116.2.

Does someone has expierence with this problem or a hint?

My Matlab version is R2019a and I did not used any toolboxes or blocksets.

Thank you.

[Stephen23]

"Does someone has expierence with this problem or a hint?"

You are seeing some of the behaviors of floating point numbers, which can only represent approximations of some of those values. These behaviors are quite well documented:

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 worth reading as well:

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

[Stefanie Schwarz]

Thank you, for posting these links. I will read them carefully.

Answer 1

[Rik]

Not all decimal numbers can be stored in binary as an exact value. This float rounding error can lead to situations like this. You can solve this by testing against a tolerance (functions like ismembertol and uniquetol are also useful).

If abs(X(x) -T(t)) <= eps

[Stefanie Schwarz]

I checked your answers and it works fine for ismembertol() and uniquetol().

With the

If abs(X(x)-T(t)) <= eps

it jumps in for 0.3 but not for 13.2 and 116.2.

Thank you

[Rik]

When using ismembertol, don't forget to set 'DataScale',1 because otherwise you might get unexpected results. Refer to the documentation to see if you want to leave the scaling on auto, or if you want to set it to 1.

As a side-note: I personally tend to use 2*eps, although there shouldn't really be a difference.

Glad to be of help.

Answer 2

[Bhaskar R]

I don't know,why are you taking variable jump_in.

From your code we can summarize as

% c- common values(X(x) == T(t))
% iX - indices if vector X
% iT - indices if vector T
[c, iX, iT] = intersect(X,T);
jump_in = ones(1, length(iX));

Correct me if I am wrong

[Stefanie Schwarz]

By reducing my code to the actuall problem I turned the variable X from a 3x2001 size to a 1x2001. This is why jump_in seems useless but in my full code I wanted to also save the data of the other two rows of X in jump_in. So jump_in has an actuall size of 3xlength(T). Thank you for telling me about intersect(), it will come in handy.