On 8/26/06, Sven Schreiber <[EMAIL PROTECTED]> wrote:
In [7]: (arange(100)*.5).round()
Out[7]:
array([ 0., 0., 1., 2., 2., 2., 3., 4., 4., 4., 5.,
6., 6., 6., 7., 8., 8., 8., 9., 10., 10., 10.,
11., 12., 12., 12., 13., 14., 14., 14., 15., 16., 16.,
16., 17., 18., 18., 18., 19., 20., 20., 20., 21., 22.,
22., 22., 23., 24., 24., 24., 25., 26., 26., 26., 27.,
28., 28., 28., 29., 30., 30., 30., 31., 32., 32., 32.,
33., 34., 34., 34., 35., 36., 36., 36., 37., 38., 38.,
38., 39., 40., 40., 40., 41., 42., 42., 42., 43., 44.,
44., 44., 45., 46., 46., 46., 47., 48., 48., 48., 49.,
50.])
It looks like numpy does round to even. Knuth has a discussion of rounding that is worth reading, although he prefers round to odd. The basic idea is to avoid the systematic bias that comes from always rounding in one direction. Another thing to bear in mind is that floating point isn't always what it seems due to the conversion between decimal and binary representation:
In [8]: print '%25.18f'%.075
0.074999999999999997
Throw in multiplication, different precisions in the internal computations of the fpu, rounding in the print routine, and other complications, and it is tough to know precisely what should happen. For instance:
In [15]: '%25.18f'%(mat(0.575)*100)
Out[15]: ' 57.499999999999992895 '
In [16]: '%25.18f'%(around(mat(0.575)*100))
Out[16]: ' 57.000000000000000000'
In [17]: '%25.18f'%(around(mat(0.575)*100)/100)
Out[17]: ' 0.569999999999999951'
And you can see that .575 after conversion to IEEE floating point and scaling was properly rounded down and showed up as .57 after the default print precision is taken into account.
Python, on the other hand, always rounds up:
In [12]: for i in range(10) : print '%25.18f'%round(i*.5)
....:
0.000000000000000000
1.000000000000000000
1.000000000000000000
2.000000000000000000
2.000000000000000000
3.000000000000000000
3.000000000000000000
4.000000000000000000
4.000000000000000000
5.000000000000000000
Chuck
Hi,
is this normal behavior?:
>>> import numpy as n; print n.mat(0.075).round(2); print
n.mat(0.575).round(2)
[[ 0.08]]
[[ 0.57]]
In [7]: (arange(100)*.5).round()
Out[7]:
array([ 0., 0., 1., 2., 2., 2., 3., 4., 4., 4., 5.,
6., 6., 6., 7., 8., 8., 8., 9., 10., 10., 10.,
11., 12., 12., 12., 13., 14., 14., 14., 15., 16., 16.,
16., 17., 18., 18., 18., 19., 20., 20., 20., 21., 22.,
22., 22., 23., 24., 24., 24., 25., 26., 26., 26., 27.,
28., 28., 28., 29., 30., 30., 30., 31., 32., 32., 32.,
33., 34., 34., 34., 35., 36., 36., 36., 37., 38., 38.,
38., 39., 40., 40., 40., 41., 42., 42., 42., 43., 44.,
44., 44., 45., 46., 46., 46., 47., 48., 48., 48., 49.,
50.])
It looks like numpy does round to even. Knuth has a discussion of rounding that is worth reading, although he prefers round to odd. The basic idea is to avoid the systematic bias that comes from always rounding in one direction. Another thing to bear in mind is that floating point isn't always what it seems due to the conversion between decimal and binary representation:
In [8]: print '%25.18f'%.075
0.074999999999999997
Throw in multiplication, different precisions in the internal computations of the fpu, rounding in the print routine, and other complications, and it is tough to know precisely what should happen. For instance:
In [15]: '%25.18f'%(mat(0.575)*100)
Out[15]: ' 57.499999999999992895 '
In [16]: '%25.18f'%(around(mat(0.575)*100))
Out[16]: ' 57.000000000000000000'
In [17]: '%25.18f'%(around(mat(0.575)*100)/100)
Out[17]: ' 0.569999999999999951'
And you can see that .575 after conversion to IEEE floating point and scaling was properly rounded down and showed up as .57 after the default print precision is taken into account.
Python, on the other hand, always rounds up:
In [12]: for i in range(10) : print '%25.18f'%round(i*.5)
....:
0.000000000000000000
1.000000000000000000
1.000000000000000000
2.000000000000000000
2.000000000000000000
3.000000000000000000
3.000000000000000000
4.000000000000000000
4.000000000000000000
5.000000000000000000
Chuck
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