a=0.02:0.02:2;b=0:0.01:5;ismember(a(6),b)ans = logical 0But it is clear that all elements in a belong to b, so where is the problem?
MATLAB: Issue about ismember wrong output
floating pointismemberMATLAB
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"Does anyone have any idea why this is happening?"
Yes, the behaviors of floating point numbers are quite well documented, and often discussed on this forum.
"It's pretty disturbing to think about the ramifications of this kind of error."
Only if you write your code believing that floating point error does not exist. Experienced programmers understand that calculations on floating point numbers can accumulate floating point errors (like your example does), and do not expect floating point mathematics to be equivalent to the symbolic maths that they learned in high school (i.e. arithmetic operations on floating point values are not associative), so they write their code accordingly to allow for this.
You need to learn about the limits of floating point numbers. Start by reading these:
This is worth reading as well:
0.3 - 0-2 - 0.1 returns -2.7756e-17.
As is mentioned frequently in the newsgroup, some floating point numbers can not be represented exactly in binary form. So that's why you see the very small but not zero result. See EPS.
The difference is that 0:0.1:0.4 increments by a number very close to but not exactly 0.1 for the reasons mentioned below. So after a few steps it will be off whereas [0 0.1 0.2 0.3 0.4] is forcing the the numbers to their proper value, as accurately as they can be represented anyway.
a = [0 0.1 0.2 0.3 0.4]; b = 0:.1:.4; as = sprintf('%20.18f\n',a)>> as = 0.000000000000000000 % ==
0.100000000000000010 % == 0.200000000000000010 % == 0.299999999999999990 % ~= bs !
0.400000000000000020 % == bs = sprintf('%20.18f\n',b)>> bs = 0.000000000000000000 % == 0.100000000000000010 % == 0.200000000000000010 % == 0.300000000000000040 % ~= as !
0.400000000000000020 % ==and:
format hex; hd = [a.',b.']>> hd = 0000000000000000 0000000000000000 % == 3fb999999999999a 3fb999999999999a % == 3fc999999999999a 3fc999999999999a % == 3fd3333333333333 3fd3333333333334 % ~= !
3fd999999999999a 3fd999999999999a % ==If you're trying to compare two floating-point numbers, be very careful about using == to do so. An alternate comparison method is to check if the two numbers you're comparing are "close enough" (as expressed by a tolerance) to one another:
% instead of a == b
% use:
areEssentiallyEqual = abs(a-b) < tol% for some small value of tol relative to a and b
% perhaps defined using eps(a) and/or eps(b)
You can see this same sort of behavior outside MATLAB. Using pencil and paper (or a chalkboard, or a whiteboard, etc.) compute x = 1/3 to as many decimal places as you want. The number of decimal places must be finite, however. Now compute y = 3*x. In exact arithmetic, y would be exactly 1; however, since x is not exactly one third but is a rounded approximation to one third, y will not be exactly 1.
For a readable introduction to floating point arithmetic, look at Cleve's Corner article from 1996: Floating Points (PDF) http://www.mathworks.com/company/newsletters/news_notes/pdf/Fall96Cleve.pdf
For more rigorous and detailed information on floating point arithmetic, read the following paper: What Every Computer Scientist Should Know About Floating Point Arithmetic http://docs.sun.com/source/806-3568/ncg_goldberg.html
Another resource is Technical Note 1108 http://www.mathworks.com/support/tech-notes/1100/1108.html on the Support section of The MathWorks website.
This answer is copied and slightly modifed from matlab.wikia.com/wiki/FAQ: Why_is_0.3-0.2-0.1_not_equal_to_zero
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