numpy: apply operation to multidimensional array

Question

Assume I have a matrix of matrices, which is an order-4 tensor. What's the best way to apply the same operation to all the submatrices, similar to Map in Mathematica?

#!/usr/bin/python3
from pylab import *
t=random( (8,8,4,4) )
#t2=my_map(det,t)
#then shape(t2) becomes (8,8)

EDIT
Sorry for the bad English, since it's not my native one.

I tried numpy.linalg.det, but it doesn't seem to cope well with 3D or 4D tensors:

>>> import numpy as np
>>> a=np.random.rand(8,8,4,4)
>>> np.linalg.det(a)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/usr/lib/python3/dist-packages/numpy/linalg/linalg.py", line 1703, in det
sign, logdet = slogdet(a)
File "/usr/lib/python3/dist-packages/numpy/linalg/linalg.py", line 1645, in slogdet
_assertRank2(a)
File "/usr/lib/python3/dist-packages/numpy/linalg/linalg.py", line 155, in _assertRank2
'two-dimensional' % len(a.shape))
numpy.linalg.linalg.LinAlgError: 4-dimensional array given. Array must be two-dimensional

EDIT2 (Solved) The problem is older numpy version (<1.8) doesn't support inner loop in numpy.linalg.det, updating to numpy 1.8 solves the problem.

HYRY · Accepted Answer · 2014-01-27 01:40:16Z

1

numpy 1.8 has some gufunc that can do this in C loop:

for example, numpy.linalg.det() is a gufunc:

import numpy as np
a = np.random.rand(8,8,4,4)
np.linalg.det(a)

answered Jan 27, 2014 at 1:40

HYRY

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2 Comments

Kh40tiK Over a year ago

Thanks for the answer! But I got error message: numpy.linalg.linalg.LinAlgError: 4-dimensional array given. Array must be two-dimensional

HYRY Over a year ago

Are you using numpy 1.8?

hpaulj · Accepted Answer · 2014-01-27 01:47:24Z

1

First check the documentation for the operation that you intend to use. Many have a way of specifying which axis to operate on (np.sum). Others specify which axes they use (e.g. np.dot).

For np.linalg.det the documentation includes:

a : (..., M, M) array_like Input array to compute determinants for.

So np.linalg.det(t) returns an (8,8) array, having calculated each det using the last 2 dimensions.

While it is possible to iterate on dimensions (the first is the default), it is better to write a function that makes use of numpy operations that use the whole array.

answered Jan 27, 2014 at 1:47

hpaulj

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