This behavior is a consequence of floating point arithmetic. See this Answers post and the "Avoiding Common Problems with Floating-Point Arithmetic" section of this documentation page for more information. If you are using the == operator to attempt to locate a floating-point number in an array, instead subtract the number you're trying to find from the numbers in the array and locate those positions where the difference is smaller than some tolerance or use the ismembertol function. For example: x = 0:0.1:1
x =
0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000
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It appears that x contains the value 0.3, but it does not contain exactly 0.3.
checkWithExactEquality = x == 0.3
checkWithExactEquality =
0 0 0 0 0 0 0 0 0 0 0
It does contain a value that is extremely close to 0.3, however.
checkWithTolerance = abs(x-0.3) < tolerance
checkWithTolerance =
0 0 0 1 0 0 0 0 0 0 0
whichValueTolerance = x(checkWithTolerance)
whichValueTolerance = 0.3000
How far away from 0.3 is the value we found using a tolerance?
howDifferent = whichValueTolerance - 0.3
howDifferent = 5.5511e-17
To do the same with ismembertol:
checkWithIsmembertol = ismembertol(x, 0.3, tolerance)
checkWithIsmembertol =
0 0 0 1 0 0 0 0 0 0 0
whichValueIsmembertol = x(checkWithIsmembertol)
whichValueIsmembertol = 0.3000
The ismembertol function found the same value that the check with a tolerance did.
Don't confuse how a number is displayed with how it is stored in memory.
