Why does MATLAB not finding a element from my matrix?

x = 0.4:0.01:0.5

x = 1x11

0.4000 0.4100 0.4200 0.4300 0.4400 0.4500 0.4600 0.4700 0.4800 0.4900 0.5000

idx = find(x==0.41)

idx =

  1x0 empty double row vector

[Dyuman Joshi]

Welcome to the world of floating point numbers! Here not all numbers can be represented exactly in binary form.

Stephen has provided an extensive list of material which you can refer to - for detailed information and explainations regarding the same.

Also, see - ismembertol.

[Tshikaya]

Thank you for the tip. My problem was actually the following:

A = zeros(1,100);
x = zeros(1,100);
for i = 1:100
    x(i) = 0.01*randi([38 45],1,1);
    if ismember(0.41,x(i));
        A(i) = 10;
    else
        A(i) = -1;
    end
end

So I was shoked to see that x was sometimes 0.41 but still not picking from the code. I have just changed ismember by ismembertol and now everything is fine.

[Walter Roberson]

Note that the colon operator is handled as repeated addition, so 0.4, 0.4+0.1, 0.4+0.1+0.1, 0.4+0.1+0.1+0.1 and so on. Because double precision numbers operate in binary instead of in decimal, 0.1 cannot be exactly represented, and instead each 0.1 addition adds 0.1000000000000000055511151231257827021181583404541015625

Mathworks could have chosen an impletation of (initial value) + increment * (position in the sequence minus 1), so 0.4 + [0, 1, 2, 3, 4 ...] * 0.1 ... but Mathworks did not chose that (possibly for efficiency reasons.)

Answer 1

[Stephen23]

Testing for exact equivalence of binary floating point numbers should be avoided.

Compare the values, are they actually the same? (hint: no):

x = 0.4:0.01:0.5;
fprintf('%.40f\n', x(2), 0.41)

0.4100000000000000310862446895043831318617
0.4099999999999999755750934582465561106801

The recommended approach is to compare the absolute difference against a tolerance:

tol = 1e-5;
abs(x(2)-0.41)<tol

ans = logical
   1

More information on this topic:

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

[Tshikaya]

Thank you for your answer

[Steven Lord]

If you're using release R2024b or later, you could use the isapprox function to determine if two numbers are approximately equal.