On Fri, Jul 25, 2008 at 1:24 PM, Gideon Simpson <grs2103@columbia.edu> wrote:

How does python (or numpy/scipy) do exponentiation? If I do x**p, where p is some positive integer, will it compute x*x*...*x (p times), or will it use logarithms?

Here are some examples:

...

np.array([[1,2], [3,4]])**2

array([[ 1, 4], [ 9, 16]])

...

np.matrix([[1,2], [3,4]])**2

matrix([[ 7, 10], [15, 22]])

...

np.power(np.matrix([[1,2], [3,4]]), 2)

matrix([[ 1, 4], [ 9, 16]])

Fri, 25 Jul 2008 16:24:35 -0400, Gideon Simpson wrote:

How does python (or numpy/scipy) do exponentiation? If I do x**p, where p is some positive integer, will it compute x*x*...*x (p times), or will it use logarithms?

For floats it will call operating system's pow, which supposedly is optimized. For integer powers |n| < 100 of complex numbers it computes the power by repeated squarings and multiplications using a binary decomposition, and for larger |n| falls back to using a logarithm. For integer powers of integers, it also appears to use repeated squarings and multiplications according to a binary decomposition. -- Pauli Virtanen