MATLAB ismember() problem

Question

The following command returns 1:

ismember(-0.6, -1:.1:.9)

but this next command returns 0:

ismember(-0.1, -1:.1:.9)

even though -0.1 clearly is in -1:.1:.9.

Does anybody know what's going on?

Answer 1

The problem is that when you start at -1.0 and add 0.1 repeatedly you get a slightly different number than if you specify -0.1 directly. This is because of floating-point error accumulation. Just like 1/3 cannot be represented exactly in decimal (it becomes 0.33333...), many decimal numbers cannot be represented exactly in binary. 0.1 when converted to binary is actually a very close approximation to 0.1. Because there is a slight error when you do arithmetic with this floating point number this small difference accumulates and becomes bigger and bigger.

From http://www.mathworks.com/matlabcentral/newsreader/view_thread/246492:

Ashwini Deshpande wrote:

---

I have a matrix as follows,

a = 0:0.1:1;

when I tried to find whether 0.300 is present in the matrix a, using the following procedure,

>> [tf, loc]=ismember(0.3,a)

I got the following result:

tf =
     0
loc =
     0

But it's suppose to give me, tf = 1 and loc =4.

---

You're getting the correct result, actually. Look what happens:

     v=0:.1:1;
     n=0.3;
     sprintf('%30.20f\n',v(4),n)
%{
     0.30000000000000004000 % <- result from vec
     0.29999999999999999000 % <- result from handwritten number
%}
     format hex;
     [v(4),n,v(4)-n].'
%{
     3fd3333333333334 % <- vec
     3fd3333333333333 % <- num
     3c90000000000000 % <- diff
%}
     format;

Also, peruse http://matlabwiki.mathworks.com/MATLAB_FAQ#Why_is_0.3-0.2-0.1_not_equal_to_zero_.28or_similar.29.3F

Answer 2

Floating point error.

The number 0.1 is REALLY REALLY CLOSE to the value in the vector, but not exactly. Some numbers can not be represented exactly in a binary computer.

What are you trying to do exactly, there are many thresholding techniques that can work here if we know your situation better.