On Wed, Jan 26, 2011 at 8:29 PM, Joshua Holbrook <josh.holbr...@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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