def dft2(points):
complex_list = [Complex(p[0], p[1]) for p in points]
N = len(complex_list)
X = []
for k in range(N):
x = Complex(0, 0)
for n in range(N):
t = 2 * math.pi * k * n / N
c = Complex(math.cos(t), -math.sin(t))
x += c * complex_list[n]
x.re = x.re / N
x.im = x.im / N
radius = x.length()
phase = x.angle()
if radius > 1:
X.append((radius, k, phase))
return X
def test_complex(): x, y = Complex(2, 1), Complex(5, 6) su, sub, mul, div, mod_x, mod_y, x_angle, y_angle, x_conjugate, y_conjugate, x_log, y_log = x+y, x-y, x*y, x/y, x.mod(), y.mod(), x.angle(), y.angle(), x.conjugate(), y.conjugate(), x.log(), y.log() assert su.__str__() == '7.00+7.00i' assert sub.__str__() == '-3.00-5.00i' assert mul.__str__() == '4.00+17.00i' assert div.__str__() == '0.26-0.11i' assert mod_x.__str__() == '2.24+0.00i' assert mod_y.__str__() == '7.81+0.00i' assert x_angle.__str__() == '0.4636476090008061' assert y_angle.__str__() == '0.8760580505981934' assert x_conjugate.__str__() == '2.00-1.00i' assert y_conjugate.__str__() == '5.00-6.00i' assert x_log.__str__() == '0.80+0.46i' assert y_log.__str__() == '2.06+0.88i'
