python - How to check if all values in the columns of a numpy matrix are the same?

Question

I want to check if all values in the columns of a numpy array/matrix are the same. I tried to use reduce of the ufunc equal, but it doesn't seem to work in all cases:

In [55]: a = np.array([[1,1,0],[1,-1,0],[1,0,0],[1,1,0]])

In [56]: a
Out[56]: 
array([[ 1,  1,  0],
       [ 1, -1,  0],
       [ 1,  0,  0],
       [ 1,  1,  0]])

In [57]: np.equal.reduce(a)
Out[57]: array([ True, False,  True], dtype=bool)

In [58]: a = np.array([[1,1,0],[1,0,0],[1,0,0],[1,1,0]])

In [59]: a
Out[59]: 
array([[1, 1, 0],
       [1, 0, 0],
       [1, 0, 0],
       [1, 1, 0]])

In [60]: np.equal.reduce(a)
Out[60]: array([ True,  True,  True], dtype=bool)

Why does the middle column in the second case also evaluate to True, while it should be False?

Thanks for any help!

Answer 1

In [45]: a
Out[45]: 
array([[1, 1, 0],
       [1, 0, 0],
       [1, 0, 0],
       [1, 1, 0]])

Compare each value to the corresponding value in the first row:

In [46]: a == a[0,:]
Out[46]: 
array([[ True,  True,  True],
       [ True, False,  True],
       [ True, False,  True],
       [ True,  True,  True]], dtype=bool)

A column shares a common value if all the values in that column are True:

In [47]: np.all(a == a[0,:], axis = 0)
Out[47]: array([ True, False,  True], dtype=bool)

---

The problem with np.equal.reduce can be seen by micro-analyzing what happens when it is applied to [1, 0, 0, 1]:

In [49]: np.equal.reduce([1, 0, 0, 1])
Out[50]: True

The first two items, 1 and 0 are tested for equality and the result is False:

In [51]: np.equal.reduce([False, 0, 1])
Out[51]: True

Now False and 0 are tested for equality and the result is True:

In [52]: np.equal.reduce([True, 1])
Out[52]: True

But True and 1 are equal, so the total result is True, which is not the desired outcome.

The problem is that reduce tries to accumulate the result "locally", while we want a "global" test like np.all.