4303.sagews

%cython

from sage.rings.complex_double cimport ComplexDoubleElement
from sage.rings.complex_double import CDF
cdef ComplexDoubleElement one = CDF(1), zero = CDF(0)
import numpy

cdef class Matrix2:
    cdef complex m00, m01, m10, m11
    def __init__(self, complex a, complex b,complex c,complex d):
        self.m00=a; self.m01=b; 
        self.m10=c; self.m11=d
    def __repr__(self): # TODO: slow
        return repr(self.numpy())
    def numpy(self):   # TODO: slow
        return numpy.array([[self.m00, self.m01], [self.m10, self.m11]])
    def __mul__(Matrix2 self not None, Matrix2 right not None):
        cdef Matrix2 res = PY_NEW(Matrix2)
        res.m00=self.m00*right.m00+self.m01*right.m10
        res.m01=self.m00*right.m01+self.m01*right.m11
        res.m10=self.m10*right.m00+self.m11*right.m10
        res.m11=self.m10*right.m01+self.m11*right.m11
        return res

v = [CDF(a) for a in 1,2,3,4]
a = Matrix2(*v); a2 = Matrix2(*reversed(v))
b = matrix(CDF, 2, v); b2 = matrix(CDF, 2, list(reversed(v)))
c = b.numpy(); c2 = b2.numpy()

a*a2

array([[ 8.+0.j, 5.+0.j], [ 20.+0.j, 13.+0.j]])

b*b2

[ 8.0 5.0] [20.0 13.0]

c.dot(c2)

array([[ 8.+0.j, 5.+0.j], [ 20.+0.j, 13.+0.j]])

timeit('a*a2')

625 loops, best of 3: 138 ns per loop

timeit('b*b2')

625 loops, best of 3: 20.8 µs per loop

timeit('c.dot(c2)')

625 loops, best of 3: 2.44 µs per loop

2.44/.138

17.6811594202899

20.8/.138

150.724637681159