Question

I have a simple piece of code which doesn’t run as expected.

from numpy import *
from numpy.linalg import *
from sets import Set

W = matrix('1, 1, 1, 1; 1, 1, -1, -1; 1, -1, 2, -2; 1, -1, -2, 2')
E = matrix('1, 1, 1, 1; 1, 1, -1, -1; 1, -1, 2, -2; 1, -1, -2, 2')

matrices = Set([])
matrices.add(W)
matrices.add(E)
matrices

The matrices are identical, however they both appear seperately when I print the contents of the set. However, if I assign it like below, then the duplicate does not appear.

W = matrix('1, 1, 1, 1; 1, 1, -1, -1; 1, -1, 2, -2; 1, -1, -2, 2')
E = W

Any idea what is happening? I need a way of avoiding duplicate matrices in a program I am writing, which generates a tonne of matrices.

EDIT: I want the following output

set([matrix([[ 1,  1,  1,  1],
        [ 1,  1, -1, -1],
        [ 1, -1,  2, -2],
        [ 1, -1, -2,  2]])])

but instead get the following:

set([matrix([[ 1,  1,  1,  1],
        [ 1,  1, -1, -1],
        [ 1, -1,  2, -2],
        [ 1, -1, -2,  2]]), matrix([[ 1,  1,  1,  1],
        [ 1,  1, -1, -1],
        [ 1, -1,  2, -2],
        [ 1, -1, -2,  2]])])

Answer 1

You’re running into issues with how python implements checking for similarity between objects internally. Specifically, how objects considered “hashable” are compared.

The way that the python set constructor decides if two objects are the same is based on calling a magic method called __hash__ (and another called __eq__). Two objects are considered the same if the result of calling __hash__ on them returns the same value (and caling __eq__ on them returns True). If calling __hash__ on the two objects gives different values, set assumes they cannot be considered the same.

It is also worth noting that sets can only contain objects that are considered “hashable”, that is, those objects which implement the __hash__ method.

Lets see how this works:

In [73]: a = "one"
In [74]: b = "one"
In [75]: c = "two"

In [76]: a.__hash__()
Out[76]: -261223665

In [77]: b.__hash__()
Out[77]: -261223665

In [78]: c.__hash__()
Out[78]: 323309869

In [79]: set([a,b,c])
Out[79]: set(['two', 'one'])

Now, lets import numpy, and see what the hash values are for your matrices.

In [81]: import numpy as np
In [82]: W = np.matrix('1, 1, 1, 1; 1, 1, -1, -1; 1, -1, 2, -2; 1, -1, -2, 2')
In [83]: E = np.matrix('1, 1, 1, 1; 1, 1, -1, -1; 1, -1, 2, -2; 1, -1, -2, 2')

In [84]: W.__hash__()
Out[84]: 4879307

In [85]: E.__hash__()
Out[85]: 4879135

Notice that the hashes are different for E and W even though they seem to contain the same thing. Since their hashes are different, they’re going to show up as different objects in the set. When you do assignment like W = E, then the names W and E are actually referring to the same object.

If you need a workaround for this, you could store the strings you’re using to build the matrices:

In [86]: set(['1, 1, 1, 1; 1, 1, -1, -1; 1, -1, 2, -2; 1, -1, -2, 2',
              '1, 1, 1, 1; 1, 1, -1, -1; 1, -1, 2, -2; 1, -1, -2, 2'])
Out[86]: set(['1, 1, 1, 1; 1, 1, -1, -1; 1, -1, 2, -2; 1, -1, -2, 2'])