MATLAB: X = 0:0.1:10… What’s going on, really

accuracyfaqfindfloating pointvectors

Please have a look at the following example:
A = 0:0.1:0.4;
find(A == 0.3)
ans =
   Empty matrix: 1-by-0
find(A == 0.1+0.1+0.1)
ans =
     4
This is in my opinion expected behavior, as 0.1 can't be represented accurately with floating point numbers. What's bugging me is the following:
A = 5.8:0.1:6
A =
    5.8000    5.9000    6.0000
find(A == 5.9)
ans =
     2
%%Found it!
A = 5.8:0.1:6.1
A =
    5.8000    5.9000    6.0000    6.1000
find(A == 5.9)
ans =
   Empty matrix: 1-by-0
%%Didn't find it!
find(A == 5.8+0.1)
ans =
     2
%%Found it again!
For the record, linspace results in the same results.
A = linspace(5.8, 6.0, 3)
A =
    5.8000    5.9000    6.0000
find(A == 5.9)
ans =
     2
A = linspace(5.8, 6.1, 4)
A =
    5.8000    5.9000    6.0000    6.1000
find(A == 5.9)
ans =
   Empty matrix: 1-by-0
find(A == 5.8+0.1)
ans =
     2
Notice that the only difference is that the vectors are going to 6.1 instead of 6.0. So, what's going on? Are the following two actually the same: x = [a:b:c] and y = linspace(a,c,(c-a)/b+1)?
A = 5.8:0.1:6.1
A =
    5.8000    5.9000    6.0000    6.1000
B = linspace(5.8,6.1,4)
B =
    5.8000    5.9000    6.0000    6.1000
A == B
ans =
     1     1     1     1
It might appear that way… But the answer is of course no, they're not the same!
x = -0.1:0.1:0.3
x =
   -0.1000         0    0.1000    0.2000    0.3000
y = linspace(-0.1,0.3,5)
y =
   -0.1000         0    0.1000    0.2000    0.3000
x == y
ans =
     1     1     0     0     1
So, what happens when you do A = 5.8:0.1:6? How are the numbers created? And how can the following be explained?
A = 5.8:0.1:6;
B = 5.8:0.1:6.1;
A(2)-B(2)
ans =
  8.8818e-016
eps(5.9)
ans =
  8.8818e-016

Best Answer

What's going on is explained in the FAQ , along with some workarounds for comparing floating point numbers. http://matlab.wikia.com/wiki/FAQ?title=FAQ&cb=7710#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F
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