[Numpy-discussion] einsum

[Mark Wiebe]

On Wed, Jan 26, 2011 at 8:29 PM, Joshua Holbrook <josh.holbrook at gmail.com>wrote:

> >>
> >> The only disadvantage I see, is that choosing the axes to operate on
> >> in a program or function requires string manipulation.
> >
> >
> > One possibility would be for the Python exposure to accept lists or
> tuples
> > of integers.  The subscript 'ii' could be [(0,0)], and 'ij,jk->ik' could
> be
> > [(0,1), (1,2), (0,2)].  Internally it would convert this directly to a
> > C-string to pass to the API function.
> > -Mark
> >
>
> What if you made objects i, j, etc. such that i*j = (0, 1) and
> etcetera? Maybe you could generate them with something like (i, j, k)
> = einstein((1, 2, 3)) .
>
> Feel free to disregard me since I haven't really thought too hard
> about things and might not even really understand what the problem is
> *anyway*. I'm just trying to help brainstorm. :)
>

No worries. :)  The problem is that someone will probably want to
dynamically generate the axes to process in a loop, rather than having them
hardcoded beforehand.  For example, generalizing the diag function as
follows.  Within Python, creating lists and tuples is probably more natural.

-Mark

>>> def diagij(x, i, j):
...     ss = ""
...     so = ""
...     # should error check i, j
...     fill = ord('b')
...     for k in range(x.ndim):
...         if k in [i, j]:
...             ss += 'a'
...         else:
...             ss += chr(fill)
...             so += chr(fill)
...             fill += 1
...     ss += '->' + so + 'a'
...     return np.einsum(ss, x)
...
>>> x = np.arange(3*3*3).reshape(3,3,3)
>>> diagij(x, 0, 1)
array([[ 0, 12, 24],
       [ 1, 13, 25],
       [ 2, 14, 26]])

>>> [np.diag(x[:,:,i]) for i in range(3)]
[array([ 0, 12, 24]), array([ 1, 13, 25]), array([ 2, 14, 26])]

>>> diagij(x, 1, 2)
array([[ 0,  4,  8],
       [ 9, 13, 17],
       [18, 22, 26]])
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