[Numpy-discussion] Tensor contraction

[Pauli Virtanen]

Sat, 12 Jun 2010 23:15:16 +0200, Friedrich Romstedt wrote:
[clip]
> But note that for:
> T[:, I, I]
> the shape is reversed with respect to that of: 
> T[I, :, I]  and T[I, I, :] .
> 
> I think it should be written in the docs how the shape is derived.

It's explained there in detail (although maybe not in the simplest 
possible words):

    http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html#integer

Let "index dimension" be a dimension for which you supply an array  
(rather than the :-slice) as an index. 

Let "broadcast shape of indices" be the shape to which all the index 
arrays are broadcasted to. (= same as "(i1+i2+...+in).shape").

The rule is that

1) if all the index dimensions are next to each other, then the shape of 
the result array is

    (dimensions preceding the index dimensions) 
    + (broadcast shape of indices) 
    + (dimensions after the index dimensions)

2) if the index dimensions are not all next to each other, then the shape 
of the result array is

    (broadcast shape of indices) + (non-index dimensions)

Might be a bit surprising, but at this point it's not going to be changed.

-- 
Pauli Virtanen