The function np.dot multiplies the GF4 field matrices for a very long time-CodePudding

Multiplies large matrices for a very long time. How can this problem be solved. I use the galois library, and numpy, I think it should still work stably. I tried to implement my GF4 arithmetic and multiplied matrices using numpy, but it takes even longer. Thank you for your reply.

When r = 2,3,4,5,6 multiplies quickly, then it takes a long time. As for me, these are not very large sizes of matrices. This is just a code snippet. I get the sizes n, k of matrices of a certain family given r. And I need to multiply the matrices of those obtained parameters.

import numpy as np
import galois


def family_Hamming(q,r):
    n = int((q**r-1)/(q-1))
    k = int((q**r-1)/(q-1)-r)
    res = (n,k)
    return res

q = 4
r = 7

n,k = family_Hamming(q,r)

GF = galois.GF(2**2)

#(5461,5461)
a = GF(np.random.randint(4, size=(k, k)))
#(5454,5461)
b = GF(np.random.randint(4, size=(k, n)))
c = np.dot(a,b)
print(c)

CodePudding user response：

I'm not sure if it is actually faster but np.dot should be used for the dot product of two vectors, for matrix multiplication use A @ B. That's as efficient as you can get with Python as far as I know

CodePudding user response：

Try using jax on a CUDA runtime. For example, you can try it out on Google Colab's free GPU. (Open a notebook -> Runtime -> Change runtime type -> GPU).

import jax.numpy as jnp
from jax import device_put

a = GF(np.random.randint(4, size=(k, k)))
b = GF(np.random.randint(4, size=(k, n)))

a, b = device_put(a), device_put(b)
c = jnp.dot(a, b)

c = np.asarray(c)

Timing test:

%timeit jnp.dot(a, b).block_until_ready()
# 765 ms ± 96.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)