Multidimensional Indexing and Diagonal Symmetries

Question

I have a pretty big numpy array ...

power = ...
print power.shape
>>> (3, 10, 10, 19, 75, 10, 10)

which is symmetrical wrt 10 × 10 parts, i.e. the following 2-d matrices are symmetric.

power[i, :, :, j, k, l, m]
power[i, j, k, l, m, :, :]

for all values ​​of i, j, k, l, m

Can I use this factor of 4? For instance. when saving the matrix to a file (50 mb with savez_compressed)

My attempt:

size = 10
row_idx, col_idx = np.tril_indices(size)
zip_idx = zip(row_idx, col_idx)
print len(zip_idx), zip_idx[:5]
>>> 55 [(0, 0), (1, 0), (1, 1), (2, 0), (2, 1)]
all_idx = [(r0, c0, r1, c1) for (r0, c0) in zip_idx for (r1, c1) in zip_idx]
print len(all_idx), all_idx[:5]
>>> 3025 [(0, 0, 0, 0), (0, 0, 1, 0), (0, 0, 1, 1), (0, 0, 2, 0), (0, 0, 2, 1)]
a, b, c, d = zip(*all_idx)
tril_part = np.transpose(s.power, (0, 3, 4, 1, 2, 5, 6))[:,:,:, a, b, c, d]
print tril_part.shape
>>> (3, 19, 75, 3025)

It seems ugly, but it works ... as soon as I can get back to power from tril_part again ...

I assume this gives two questions:

• Best way to go from power to tril_part?
• How to switch from tril_part to power?

Edit: the comment "size" is clearly valid, but please ignore it :-) IMHO. The indexing part of the question is one. I found that I want to do similar indexing for smaller matrices.

Answer 1

. np.tril_indices, . , / .

( ):

import numpy as np
shape = (3, 10, 10, 19, 75, 10, 10)
p = np.arange(np.prod(shape)).reshape(shape)  # this is not symmetric, but not important

ix, iy = np.tril_indices(10)
# In order to index properly, we need to add axes. This can be done by hand or with this
ix1, ix2 = np.ix_(ix, ix)
iy1, iy2 = np.ix_(iy, iy)

p_ltriag = p[:, ix1, iy1, :, :, ix2, iy2]
print p_ltriag.shape  # yields (55, 55, 3, 19, 75), axis order can be changed if needed

q = np.zeros_like(p)
q[:, ix1, iy1, :, :, ix2, iy2] = p_ltriag  # fills the lower triangles on both sides
q[:, ix1, iy1, :, :, iy2, ix2] = p_ltriag  # fills the lower on left, upper on right
q[:, iy1, ix1, :, :, ix2, iy2] = p_ltriag  # fills the upper on left, lower on right
q[:, iy1, ix1, :, :, iy2, ix2] = p_ltriag  # fills the upper triangles on both sides

q p ( ). , iy ix , .

, 0

ux, uy = np.triu_indices(10)
p[:, ux, uy] = 0
q[:, ux, uy] = 0
p[:, :, :, :, :, ux, uy] = 0
q[:, :, :, :, :, ux, uy] = 0

print ((p - q) ** 2).sum()  # euclidean distance is 0, so p and q are equal

print ((p ** 2).sum(), (q ** 2).sum())  # prove that not all entries are 0 ;) - This has a negative result due to an overflow