[Numpy-discussion] tensor ops in dim > 3?
Konrad Hinsen
hinsen at cnrs-orleans.fr
Wed Aug 28 01:03:04 CDT 2002
"Dr. Dmitry Gokhman" <gokhman at sphere.math.utsa.edu> writes:
> I have a rank three n-dim tensor A. For two of the axes I want to perform
> v^t A v (a quadratic form with scalar output, where v is a vector). The
> final output should be a vector. I also need to compute the derivative of
> this with respect to v. This involves symmetrizing and matrix-vector
> multiplication (2 sym(A)v using two axes of A only, which gives a vector)
> with the final result being a matrix.
Whenever dealing with somewhat more complex operations of this time, I think
it's best to go back to the basic NumPy functionality rather then figuring
out if there happens to be a function that magically does it. In this case,
assuming that the first axis of A is the one that is not summed over:
sum( sum(A*v[NewAxis, NewAxis, :], -1) * v[NewAxis, :], -1)
The idea is to align v with one of the dimensions of A, then multiply
elementwise and sum over the common axis. Note that the first (inner)
sum leaves a rank-2 array, so for the second multiplication v gets
extended to rank-2 only.
> PS One more dumb question: I just installed the ScientificPython-2.4.1 rpm
> on my reincarnated Mandrake linux machine running python2.2. Do I need to
> do something to configure it? My scripts aren't finding things (e.g.
> indexing.py).
If you took the binary RPM from my site, they might not work correctly
with Mandrake, as they were made for RedHat. The source RPM should
work with all RPM-based Linux distributions. There is nothing that needs
configuring with an RPM.
Also note that Scientific is a package, so the correct way to import the
indexing module is
import Scientific.indexing
Konrad.
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