== operator says two identical arrays aren't the same

I have an array which I call graph and it is made like this.

graph = sin(1:pi/10:10*pi);

There's a variable called period_two.

period_two = 22;

Then period_two is used to make two arrays out of the first one.

graph(2:period_two-1)
graph(period_two:2*period_two-3)

And the output MatLab gives me is:

graph(2:period_two-1)

ans =

    Columns 1 through 8

      0.9672    0.9983    0.9317    0.7739    0.5403    0.2538   -0.0575   -0.3632

    Columns 9 through 16

     -0.6333   -0.8415   -0.9672   -0.9983   -0.9317   -0.7739   -0.5403   -0.2538

    Columns 17 through 20

      0.0575    0.3632    0.6333    0.8415

and

graph(period_two:2*period_two-3)

ans =

    Columns 1 through 8

      0.9672    0.9983    0.9317    0.7739    0.5403    0.2538   -0.0575   -0.3632

    Columns 9 through 16

     -0.6333   -0.8415   -0.9672   -0.9983   -0.9317   -0.7739   -0.5403   -0.2538

    Columns 17 through 20

      0.0575    0.3632    0.6333    0.8415

But if I use the == operator to check if the two arrays are the same, I get.

graph(2:period_two-1) == graph(period_two:2*period_two-3)

ans =

       1     1     0     0     0     0     0     0     0     0     1     1     0     0     0     0     0     0     0     0

Can you tell me why it says that the most of the values are not the same, when I can see that the two arrays are identical?

Answer 1

[Ken Atwell]

Floating point numbers are not infinitely precise, and you probably have differences too small to be noticed when displaying only 4 digits after the decimal.

Read this topic on determining equality, specifically the discussion about eps.

[James Tursa]

E.g., for this particular example,

>> num2strexact(graph(3:4))
ans = 
    '0.99834605415192101407484415176440961658954620361328125'    '0.93171798264940119960186848402372561395168304443359375'
>> num2strexact(graph(23:24))
ans = 
    '0.99834605415192101407484415176440961658954620361328125'    '0.931717982649401310624170946539379656314849853515625'