OS: Win 7 64bit. Matlab: 2014a, 2015a
When I create a vector as follows:
a = 0.2:0.2:1
I get:
a = 0.2000 0.4000 0.6000 0.8000 1.0000
which is expected. Now when I want to see whether 0.6 exists in my vector I type:
a == 0.6
and I get: 0 0 0 0 0
find(a == 0.6) also return an Empty matrix: 1-by-0
These are unexpected. It is able to find all the other values, but for 0.6 there is a problem. I think although 0.6 is created it is actually 0.600000000000000001 or something similar, which is a problem. You can see that this is the case by a > 0.6 and will get 0 0 1 1 1.
1-First of all why is this happening?
2-Second are we able to see the whole value of a number in Matlab, if so what is the function or setting for that?
I created the same vector using linspace, but that also did not help. I have found a solution to this by typing : a = roundn(a, -10). However, I think that such a solution should not even be needed at the first place.
3-Is there a better way to order Matlab to yield exact values?
Thank you all for your help.
First, read the MATLAB documentation on Floating Point values, paying special attention to the section on floating point error and precision: MATLAB Floating Point
You are encountering a incredibly common issue with floating-point precision. It is important to recognize you are not in fact comparing:
>> a = 0.6;
>> b = 0.6;
>> a == b
ans = 1
Instead, you are effectively comparing:
>> a = 0.6;
>> b = 0.2 + 0.2 + 0.2;
>> a == b
ans = 0
The reason for the apparent logical fallacy here is that the arithmetic is not in fact equal. The values 0.6 and 0.2 are both represented in double-precision floating-point to the CLOSEST possible value, the difference known as "floating point error".
Observing the error is straightforward:
>> a = 0.6;
>> b = 0.2 + 0.2 + 0.2;
>> a - b
ans = -1.110223024625157e-16
The simplest solution is to use round() on your scalar and vector to the same precision, then perform the comparison:
>> a = 0.6;
>> b = [ 0.2 : 0.2 : 1 ];
>> roundn ( a , -10) == roundn ( b , -10 )
ans = 0 0 1 0 0