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

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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?

Accepted Answer

Ken Atwell
Ken Atwell on 13 Mar 2015
Edited: Ken Atwell on 16 Mar 2015
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.
  1 Comment
James Tursa
James Tursa on 13 Mar 2015
E.g., for this particular example,
>> num2strexact(graph(3:4))
ans =
'0.99834605415192101407484415176440961658954620361328125' '0.93171798264940119960186848402372561395168304443359375'
>> num2strexact(graph(23:24))
ans =
'0.99834605415192101407484415176440961658954620361328125' '0.931717982649401310624170946539379656314849853515625'

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