Numpy matrix power/exponent with modulo?

Question

Is it possible to use numpy\'s linalg.matrix_power with a modulo so the elements don\'t grow larger than a certain value?

Answer 1

Using the implementation from Numpy:

https://github.com/numpy/numpy/blob/master/numpy/matrixlib/defmatrix.py#L98

I adapted it by adding a modulo term. HOWEVER, there is a bug, in that if an overflow occurs, no OverflowError or any other sort of exception is raised. From that point on, the solution will be wrong. There is a bug report here.

Here is the code. Use with care:

from numpy.core.numeric import concatenate, isscalar, binary_repr, identity, asanyarray, dot
from numpy.core.numerictypes import issubdtype    
def matrix_power(M, n, mod_val):
    # Implementation shadows numpy's matrix_power, but with modulo included
    M = asanyarray(M)
    if len(M.shape) != 2 or M.shape[0] != M.shape[1]:
        raise ValueError("input  must be a square array")
    if not issubdtype(type(n), int):
        raise TypeError("exponent must be an integer")

    from numpy.linalg import inv

    if n==0:
        M = M.copy()
        M[:] = identity(M.shape[0])
        return M
    elif n<0:
        M = inv(M)
        n *= -1

    result = M % mod_val
    if n <= 3:
        for _ in range(n-1):
            result = dot(result, M) % mod_val
        return result

    # binary decompositon to reduce the number of matrix
    # multiplications for n > 3
    beta = binary_repr(n)
    Z, q, t = M, 0, len(beta)
    while beta[t-q-1] == '0':
        Z = dot(Z, Z) % mod_val
        q += 1
    result = Z
    for k in range(q+1, t):
        Z = dot(Z, Z) % mod_val
        if beta[t-k-1] == '1':
            result = dot(result, Z) % mod_val
    return result % mod_val