def test_fft_ifft():
assert all(
tf(ls) == ls for tf in (fft, ifft) for ls in ([], [Rational(5, 3)]))
ls = list(range(6))
fls = [
15,
-7 * sqrt(2) / 2 - 4 - sqrt(2) * I / 2 + 2 * I,
2 + 3 * I,
-4 + 7 * sqrt(2) / 2 - 2 * I - sqrt(2) * I / 2,
-3,
-4 + 7 * sqrt(2) / 2 + sqrt(2) * I / 2 + 2 * I,
2 - 3 * I,
-7 * sqrt(2) / 2 - 4 - 2 * I + sqrt(2) * I / 2,
]
assert fft(ls) == fls
assert ifft(fls) == ls + [S.Zero] * 2
ls = [1 + 2 * I, 3 + 4 * I, 5 + 6 * I]
ifls = [
Rational(9, 4) + 3 * I, I * Rational(-7, 4),
Rational(3, 4) + I, -2 - I / 4
]
assert ifft(ls) == ifls
assert fft(ifls) == ls + [S.Zero]
x = Symbol("x", real=True)
raises(TypeError, lambda: fft(x))
raises(ValueError, lambda: ifft([x, 2 * x, 3 * x**2, 4 * x**3]))
def test_fft_ifft():
assert all(tf(ls) == ls for tf in (fft, ifft)
for ls in ([], [S(5)/3]))
ls = list(range(6))
fls = [15, -7*sqrt(2)/2 - 4 - sqrt(2)*I/2 + 2*I, 2 + 3*I,
-4 + 7*sqrt(2)/2 - 2*I - sqrt(2)*I/2, -3,
-4 + 7*sqrt(2)/2 + sqrt(2)*I/2 + 2*I,
2 - 3*I, -7*sqrt(2)/2 - 4 - 2*I + sqrt(2)*I/2]
assert fft(ls) == fls
assert ifft(fls) == ls + [S.Zero]*2
ls = [1 + 2*I, 3 + 4*I, 5 + 6*I]
ifls = [S(9)/4 + 3*I, -7*I/4, S(3)/4 + I, -2 - I/4]
assert ifft(ls) == ifls
assert fft(ifls) == ls + [S.Zero]
x = Symbol('x', real=True)
raises(TypeError, lambda: fft(x))
raises(ValueError, lambda: ifft([x, 2*x, 3*x**2, 4*x**3]))
def test_fft_ifft():
assert all(tf(ls) == ls for tf in (fft, ifft) for ls in ([], [S(5) / 3]))
ls = list(range(6))
fls = [
15, -7 * sqrt(2) / 2 - 4 - sqrt(2) * I / 2 + 2 * I, 2 + 3 * I,
-4 + 7 * sqrt(2) / 2 - 2 * I - sqrt(2) * I / 2, -3,
-4 + 7 * sqrt(2) / 2 + sqrt(2) * I / 2 + 2 * I, 2 - 3 * I,
-7 * sqrt(2) / 2 - 4 - 2 * I + sqrt(2) * I / 2
]
assert fft(ls) == fls
assert ifft(fls) == ls + [S.Zero] * 2
ls = [1 + 2 * I, 3 + 4 * I, 5 + 6 * I]
ifls = [S(9) / 4 + 3 * I, -7 * I / 4, S(3) / 4 + I, -2 - I / 4]
assert ifft(ls) == ifls
assert fft(ifls) == ls + [S.Zero]
x = Symbol('x', real=True)
raises(TypeError, lambda: fft(x))
raises(ValueError, lambda: ifft([x, 2 * x, 3 * x**2, 4 * x**3]))