为什么使用布尔索引会改变尺寸顺序？

Question

When we have M of shape (a, b, c) , and an indexing array v that we use to index the last array, why does M[i, :, v] result in an array of shape (d, b) (with d the number of true values in v )? As illustrated below:

In [409]: M = zeros((100, 20, 40))

In [410]: val = ones(shape=(40,), dtype="bool")

In [411]: M[0, :, :].shape
Out[411]: (20, 40)  # As expected

In [412]: M[0, :, val].shape
Out[412]: (40, 20)  # Huh?  Why (40, 20), not (20, 40)?

In [413]: M[:, :, val].shape
Out[413]: (100, 20, 40)  # s expected again

Why does M[0, :, val] have shape (40, 20) rather than (20, 40) ?

Answer 1

According the boolean indexing section of the docs http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html#boolean-array-indexing

Combining multiple Boolean indexing arrays or a Boolean with an integer indexing array can best be understood with the obj.nonzero() analogy.

ind = np.nonzero(val)[0]
# array([ 0,  1,  2, ...., 39], dtype=int32)
M[0, :, ind].shape   # (40,20)

So now we go to the section about combining advanced and basic indexing http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html#combining-advanced-and-basic-indexing

This is a case of the form: x[arr1, :, arr2]

in the first case, the dimensions resulting from the advanced indexing operation come first in the result array, and the subspace dimensions after that.

So the 0 and ind part produce a (40,) selection, while the : in the middle produces a (20,) . By putting the : part last, the resulting dimension is (40,20) . Basically it does this because there is an ambiguity in this indexing style, so it consistently opts to put the slice part at the end.

A way of selecting these values and maintain the shape you want (more or less) is to use np.ix_ to generate a tuple of indices.

M[np.ix_([0],np.arange(20),ind)].shape # (1, 20, 40)

You can use np.squeeze to remove the initial 1 dimension.

This use of ix_ is illustrated at the end of the 'purely index array indexing' section http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html#purely-integer-array-indexing