Strange output from arange()

[Christopher Barrington-Leigh]

The following code:

from pylab import arange
nSegments=5.0
print arange(0,1.0+1.0/nSegments,1.0/nSegments)
nSegments=6.0
print arange(0,1.0+1.0/nSegments,1.0/nSegments)
nSegments=8.0
print arange(0,1.0+1.0/nSegments,1.0/nSegments)
nSegments=10.0
print arange(0,1.0+1.0/nSegments,1.0/nSegments)

gives an output of:

[ 0. 0.2 0.4 0.6 0.8 1. ]
[ 0. 0.16666667 0.33333333 0.5 0.66666667
0.83333333 1. 1.16666667]
[ 0. 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1. ]
[ 0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. ]

These arrays have lengths, 6, 8, 9, and 11, in stead of 6, 7, 9, and
11.
What is going on for the case of n=6?

 

[Wanderer]

The following code:

    from pylab import arange
    nSegments=5.0
    print arange(0,1.0+1.0/nSegments,1.0/nSegments)
    nSegments=6.0
    print arange(0,1.0+1.0/nSegments,1.0/nSegments)
    nSegments=8.0
    print arange(0,1.0+1.0/nSegments,1.0/nSegments)
    nSegments=10.0
    print arange(0,1.0+1.0/nSegments,1.0/nSegments)

gives an output of:

[ 0.   0.2  0.4  0.6  0.8  1. ]
[ 0.          0.16666667  0.33333333  0.5         0..66666667
0.83333333  1.          1.16666667]
[ 0.     0.125  0.25   0.375  0.5    0.625  0.75   0.875  1.   ]
[ 0.   0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.. ]

These arrays have lengths, 6, 8, 9, and 11, in stead of 6, 7, 9, and
11.
What is going on for the case of n=6?

It's rounding.

See http://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html

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.

The stops are

5 -- 1.2
6 -- 1.1666666666666666666666667
8 -- 1.125
10 -- 1.1

Only 6 has to be rounded up.

 

[Robert Kern]

The following code:

from pylab import arange
nSegments=5.0
print arange(0,1.0+1.0/nSegments,1.0/nSegments)
nSegments=6.0
print arange(0,1.0+1.0/nSegments,1.0/nSegments)
nSegments=8.0
print arange(0,1.0+1.0/nSegments,1.0/nSegments)
nSegments=10.0
print arange(0,1.0+1.0/nSegments,1.0/nSegments)

gives an output of:

[ 0. 0.2 0.4 0.6 0.8 1. ]
[ 0. 0.16666667 0.33333333 0.5 0.66666667
0.83333333 1. 1.16666667]
[ 0. 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1. ]
[ 0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. ]

These arrays have lengths, 6, 8, 9, and 11, in stead of 6, 7, 9, and
11.
What is going on for the case of n=6?

Floating point computations are not always accurate, and when one tries to
compute "the same thing" two different ways, one may get inconsistent results.
This is what is happening with n=6. 1+1./6 happens to be slightly greater than
7*(1./6) while 1+1./5 happens to be slightly less than 6*(1./5), etc. The trick
of using 1.0+1.0/nSegments/2 tends to work better.

Nonetheless, if you want to get exactly nSegments segments with exact endpoints,
you should use numpy.linspace(0.0, 1.0, nSegments+1). That's a much better API
for what you want.

Also, you will want to ask numpy questions on the numpy-discussion mailing list,
not here.

http://www.scipy.org/Mailing_Lists

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco