Python 2.7.9 (default, Jun 29 2016, 13:08:31)
IPython 5.6.0 -- An enhanced Interactive Python.
In [1]: import numpy as np
In [2]: np.__version__
Out[2]: '1.14.3'
In [3]: np.arange(1.1, 1.12, 0.01)
Out[3]: array([1.1 , 1.11, 1.12])
In [4]: np.arange(1.1, 1.13, 0.01)
Out[4]: array([1.1 , 1.11, 1.12])
In both cases, the array gets to 1.12... how would you explain that?
Because of floating point error, 1.1, 0.01 and 0.12 are not as precise as one might expect, nor are mathematical operations between them. For example:
>>> 1.1 + 0.01 + 0.01 + 0.01
1.1300000000000001
See also:
>>> decimal.Decimal(0.1)
Decimal('0.1000000000000000055511151231257827021181583404541015625')
>>> decimal.Decimal(1.12)
Decimal('1.12000000000000010658141036401502788066864013671875')
If they were precise, np.arange(1.1, 1.12, 0.01) would be array([1.1 , 1.11])
np.arange specification mentions that as well: For the stop argument it writes:
stop : number
End of interval. The interval does not include this value, except in some cases where step is not an integer and floating point round-off affects the length of out.
You can avoid the problem by always specifying an upper limit which is between two steps, rather than exactly on the boundary:
>>> np.arange(1.1, 1.115, 0.01)
array([1.1 , 1.11])
>>> np.arange(1.1, 1.125, 0.01)
array([1.1 , 1.11, 1.12])
>>> np.arange(1.1, 1.135, 0.01)
array([1.1 , 1.11, 1.12, 1.13])
