# [Numpy-discussion] Implementation of tensor product and tensor contraction?

Yuxiang Wang yw5aj at virginia.edu
Tue Nov 25 23:06:57 EST 2014

```Dear all,

I have been doing tensor algebra recently (for continuum mechanics)
and was looking into two common operations: tensor product & tensor
contraction.

1. Tensor product

One common usage is:
a[i1, i2, i3, ..., iN, j1, j2, j3, ..., jM] = b[i1, i2, i3, ..., iN] *
c[j1, j2, j3, ..., jM]

I looked into the current np.outer(), and the only difference is that
it always flattens the input array. So actually, the function for
tensor product is simply

np.outer(a, b, out=out).reshape(a.shape+b.shape)  <-- I think I got
this right but please do correct me if I am wrong

Would anyone think it helpful or harmful to add such a function,
np.tensorprod()? it will simply be like
def tensorprod(a, b, out=None):
return outer(a, b, out=out).reshape(a.shape+b.shape)

2. Tensor contraction

It is currently the np.tensordot(a, b) and it will do np.tensordot(a,
b, axes=2) by default. I think this is all great, but it would be even
better if we specify in the doc, that:
i) say explicitly that by default it will be the double-dot or
contraction operator, and
ii) explain that in cases where axes is an integer-like scalar,
which axes were selected from the two array and in what order. Like:
if axes is an integer-like scalar, it is the number axes to sum over,
equivalent to axes=(list(range(-axes, 0)), list(range(0, axes)))   (or
something like this)

It'd be great to hear what you would think about it,

Shawn

--
Yuxiang "Shawn" Wang
Gerling Research Lab
University of Virginia
yw5aj at virginia.edu
+1 (434) 284-0836