How to raise a numpy array to a power? (corresponding to repeated matrix multiplications, not elementwise)

Question

I want to raise a 2-dimensional numpy array, let's call it A, to the power of some number n, but I have thus far failed to find the function or operator to do that.

I'm aware that I could cast it to the matrix type and use the fact that then (similar to what would be the behaviour in Matlab), A**n does just what I want, (for array the same expression means elementwise exponentiation). Casting to matrix and back seems like a rather ugly workaround though.

Surely there must be a good way to perform that calculation while keeping the format to array?

Solution

I believe you want numpy.linalg.matrix_power

As a quick example:

import numpy as np
x = np.arange(9).reshape(3,3)
y = np.matrix(x)

a = y**3
b = np.linalg.matrix_power(x, 3)

print a
print b
assert np.all(a==b)

This yields:

In [19]: a
Out[19]: 
matrix([[ 180,  234,  288],
        [ 558,  720,  882],
        [ 936, 1206, 1476]])

In [20]: b
Out[20]: 
array([[ 180,  234,  288],
       [ 558,  720,  882],
       [ 936, 1206, 1476]])

Comments

[dr jimbob]

While its possible as Joe Kingston pointed out, note that arrays and matrices are fundamentally different. An array is a numerical collection of elements in multi-dimensions, where a matrix is an abstract object (represented by an 2-d array)-- the same difference as between a vector and a 1-d array. (It makes sense for an inventory of fruit to be a array of [1,2,3] representing 1 apple, 2 oranges, 3 bananas but no sense for an vector -- apples can't add/multiple/transform into oranges). Thus arrays have element-by-element operations and matrices have matrix multiplications, det(), etc.

[Sven Marnach]

If you like Joe's answer, you should check it as "accepted", to give credit to Joe and to let others know this question is dealt with.

[mirari]

Yes, that is exactly what I needed. Thank you!

[mirari]

I feel somewhat sheepish for not having thought to look explicitly in the linalg module, but particular thanks for pointing out that that's the place as well. Nice quick example; very illustrative.

[Emmanuel Murairi]

the pow function raises each value on the matrix by power n which is different from matrix power which raises the matrix by power n (multiply the matrix by itself n times)