one problem about ismember function

Hi, everyone, when I'm using ismemeber function, something goes wrong:

A=0.2:0.2:20;
B=5:5:20;

for i=1:100
    if ismember(A(i),B)
        disp(i)
    end
end

it should display i = 25,50,75 and 100; but it only display 50,75,and 100;

Can anyone tell me why? Many thanks.

Answer 1

[OCDER]

This isn't an issue with ismember but with floating point math in general. Computers can't always add and subtract floating point number precisely, which introduces some rounding errors. Thus, when using "==" or ismember to compare floating point numbers, you run into issues.

Read the example for "Comparing Floating Point Numbers" at https://www.mathworks.com/help/matlab/ref/eq.html

C = 0.5-0.4-0.1
   %Should be mathematically equal to 0, right? NOPE! returns -2.7756e-17.
C == 0 
   Equality returns false.
ismember(C, 0)
   ismember returns false.

To fix, you have to see if the values are close enough via some sort of tolerance level.

abs(C-0) < 1E-15
   Inequality returns true. C is close enough to 0 to be considered 0.

In your case, don't use ismember. Instead do something like:

A=0.2:0.2:20;
B=5:5:20;
for i=1:100
    if any(abs(A(i)-B) < 1E-15)
        disp(i)
    end
end

[Steven Lord]

Consider using ismembertol instead of ismember.

Answer 2

[Sayyed Ahmad]

That is not a problem of ismember function. The machine accuracy is in matlab eps

 >>eps
  ans= 
  2.2204e-16

to better understand you have to try this

>> 5==5+2*eps

ans =

    logical

     1

>> 5==5-2*eps

ans =

    logical

     1

I IEEE Standard “double precision floating point” is eps ≈ 1.11 × 10−16. In matlab the eps is 2^-52 but as you see +2*eps or less 2*eps deliverd the same resault.

in your case A(25)-5 is equal 4*eps which is numeric precision of calculation for 0.2:0.2:20.

If you use the diffrent of values (A(25)-5)<=4*eps the answer will be logical true.

I hope that is the answer of your quastion.

Cheers

Ahmad