Conjugating a complex number appears to be about 30 times faster if the type() of the complex number is complex rather than numpy.complex128, see the minimal example below. However, the absolute value takes about the same time. Taking the real and the imaginary part is only about 3 times faster.
Why is the conjugate slower by that much? When I take a from a large complex-valued array, it seems I should cast it to complex first (the complex conjugation is part of a larger code which has many (> 10^6) iterations).
import numpy as np np.random.seed(100) a = (np.random.rand(1) + 1j*np.random.rand(1))[0] b = complex(a) %timeit a.conjugate() # 2.95 µs ± 24 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each) %timeit a.conj() # 2.86 µs ± 14.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each) %timeit b.conjugate() # 82.8 ns ± 1.28 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each) %timeit abs(a) # 112 ns ± 1.7 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each) %timeit abs(b) # 99.6 ns ± 0.623 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each) %timeit a.real # 145 ns ± 0.259 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each) %timeit b.real # 54.8 ns ± 0.121 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each) %timeit a.imag # 144 ns ± 0.771 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each) %timeit b.imag # 55.4 ns ± 0.297 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each) 1 Answer
Calling NumPy routines always comes at a fixed cost, which in this case is more expensive than cost of the Python-native routine.
As soon as you start processing more than one number (possibly millions) at once NumPy will be much faster:
import numpy as np N = 10 a = np.random.rand(N) + 1j*np.random.rand(N) b = [complex(x) for x in a] %timeit a.conjugate() # 481 ns ± 1.39 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each) %timeit [x.conjugate() for x in b] # 605 ns ± 6.11 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each) 
