Feature Request: Support indices raising and lowering in N-dimensional numpy arrays

[ritzvik]

Indices raising and lowering are a very crucial part of differential geometry and particularly important in relativistic physics.

See https://en.wikipedia.org/wiki/Raising_and_lowering_indices

Example :

• A 4D tensor can have index configuration ulll, and can be changed to lulu with the help of a metric tensor, here u denotes contravariant index and l denotes covariant index.

Reproducing code example:

import numpy as np
T = np.zeros(shape=(4,4,4,4), dtype=float)
# substitute some values in T
M = np.zeros(shape=(4,4), dtype=float)
# substitute some values in M(Metric Tensor)
T_ = np.change_config(T, metric=M, old='ulll', new='lulu')
print(T_)
# Example snippet

[eric-wieser]

If I understand that function, the implementation is:

def change_config(arr, *, metric, old, new):
    for axis, (o, n) in enumerate(zip(old, new)):
        # assumes metric is its own inverse
        if o != n:
            arr = np.moveaxis(np.moveaxis(arr, axis, -1) @ metric), -1, axis)
    return arr

You might find it's better to make an ndarray subclass that keeps track of the lower/upper-ness of the axes

[ritzvik]

Yes moveaxis is required, and it also requires tensorproduct and tensorcontraction which is provided einsum in np, I guess. I couldn't understand the @ metric thing. Sorry for the trouble!

See https://github.com/einsteinpy/einsteinpy/blob/master/src/einsteinpy/symbolic/tensor.py#L29-L63 . And because of change to any arbitrary configuration, it may require a series of tensorproducts and contractions.

[eric-wieser]

@ here is matrix multiplication, which I believe that when combined with moveaxis, subsumes contraction and product for the cases that matter here - assuming that a metric tensor is always 2D, which your links seem to suggest is so.

I'm not sure this is a good fit for numpy - on the one hand, we don't really have a true concept of tensors - but on the other, we do provide einsum and tensordot...