How can I ignore zeros when I take the median on columns of an array?

六月ゝ 毕业季﹏ 提交于 2021-01-21 04:10:05

问题


I have a simple numpy array.

array([[10,   0,  10,  0],
       [ 1,   1,   0,  0]
       [ 9,   9,   9,  0]
       [ 0,  10,   1,  0]])

I would like to take the median of each column, individually, of this array.

However, there are a few 0 values in various places which I would like to ignore in the calculation of the medians.

To further complicate, I would like to keep the columns with only 0 entries as having the median of 0. In this manner, those columns would serve as a bit of a place holder, keeping the dimensions of the matrix the same.

The numpy documentation doesn't have any argument that would work for what I want (maybe I am spoiled by the many switches we get with R!)

numpy.median(a, axis=None, out=None, overwrite_input=False)[source]

Can someone please shed some light on an effective way to do this, which is in line with the spirit of numpy? I could hack it out but in that case I feel like I've defeated the purpose of using numpy in the first place.

Thanks in advance.


回答1:


Use masked arrays and np.ma.median(axis=0).filled(0) to get the medians of the columns.

In [1]: x = np.array([[10, 0, 10, 0], [1, 1, 0, 0], [9, 9, 9, 0], [0, 10, 1, 0]])
In [2]: y = np.ma.masked_where(x == 0, x)
In [3]: x
Out[3]: 
array([[10,  0, 10, 0],
       [ 1,  1,  0, 0],
       [ 9,  9,  9, 0],
       [ 0, 10,  1, 0]])
In [4]: y
Out[4]: 
masked_array(data =
 [[10 -- 10 --]
 [1 1 -- --]
 [9 9 9 --]
 [-- 10 1 --]],
             mask =
 [[False  True False True]
 [False False  True True]
 [False False False True]
 [ True False False True]],
       fill_value = 999999)
In [6]: np.median(x, axis=0)
Out[6]: array([ 5.,  5.,  5., 0.])
In [7]: np.ma.median(y, axis=0).filled(0)
Out[7]: 
array(data = [ 9.  9.  9., 0.])



回答2:


Masked array is always handy, but slooooooow:

In [14]:

%timeit np.ma.median(y, axis=0).filled(0)
1000 loops, best of 3: 1.73 ms per loop
In [15]:

%%timeit
ans=np.apply_along_axis(lambda v: np.median(v[v!=0]), 0, x)
ans[np.isnan(ans)]=0.
1000 loops, best of 3: 402 µs per loop

In [16]:

ans=np.apply_along_axis(lambda v: np.median(v[v!=0]), 0, x)
ans[np.isnan(ans)]=0.; ans
Out[16]:
array([ 9.,  9.,  9.,  0.])

np.nonzero is even faster:

In [25]:

%%timeit
ans=np.apply_along_axis(lambda v: np.median(v[np.nonzero(v)]), 0, x)
ans[np.isnan(ans)]=0.
1000 loops, best of 3: 384 µs per loop



回答3:


You can use masked arrays.

a = np.array([[10, 0, 10, 0], [1, 1, 0, 0],[9,9,9,0],[0,10,1,0]])
m = np.ma.masked_equal(a, 0)

In [44]: np.median(a)
Out[44]: 1.0

In [45]: np.ma.median(m)
Out[45]: 9.0

In [46]: m
Out[46]:
masked_array(data =
 [[10 -- 10 --]
 [1 1 -- --]
 [9 9 9 --]
 [-- 10 1 --]],
             mask =
 [[False  True False  True]
 [False False  True  True]
 [False False False  True]
 [ True False False  True]],
       fill_value = 0)



回答4:


This may help. Once you get the nonzero array, you can obtain the median directly from a[nonzero(a)]

numpy.nonzero

numpy.nonzero(a)[source]

Return the indices of the elements that are non-zero.

Returns a tuple of arrays, one for each dimension of a, containing the indices of the non-zero elements in that dimension. The corresponding non-zero values can be obtained with:

a[nonzero(a)]

To group the indices by element, rather than dimension, use:

transpose(nonzero(a))

The result of this is always a 2-D array, with a row for each non-zero element.
Parameters :    

a : array_like

    Input array.

Returns :   

tuple_of_arrays : tuple

    Indices of elements that are non-zero.

See also

flatnonzero
    Return indices that are non-zero in the flattened version of the input array.
ndarray.nonzero
    Equivalent ndarray method.
count_nonzero
    Counts the number of non-zero elements in the input array.

Examples

>>> x = np.eye(3)
>>> x
array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]])
>>> np.nonzero(x)
(array([0, 1, 2]), array([0, 1, 2]))

>>> x[np.nonzero(x)]
array([ 1.,  1.,  1.])
>>> np.transpose(np.nonzero(x))
array([[0, 0],
       [1, 1],
       [2, 2]])

A common use for nonzero is to find the indices of an array, where a condition is True. Given an array a, the condition a > 3 is a boolean array and since False is interpreted as 0, np.nonzero(a > 3) yields the indices of the a where the condition is true.

>>> a = np.array([[1,2,3],[4,5,6],[7,8,9]])
>>> a > 3
array([[False, False, False],
       [ True,  True,  True],
       [ True,  True,  True]], dtype=bool)
>>> np.nonzero(a > 3)
(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))

The nonzero method of the boolean array can also be called.

>>> (a > 3).nonzero()
(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))


来源:https://stackoverflow.com/questions/22049140/how-can-i-ignore-zeros-when-i-take-the-median-on-columns-of-an-array

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