def test_forward_unitary_ordinary():
a, b = 0, 2 * np.pi
Fx, freq, grid = fft(fx, L=L, a=a, b=b, ret_cubegrid=True)
Fx_anl_fc = lambda k: (1. / a_squared) * np.exp(-np.pi * k**2 / a_squared)
# Analytic transform
Fx_anl = Fx_anl_fc(grid)
Fx_circ = angular_average(np.abs(Fx), grid, int(N / 2.2))[0]
Fx_anl_circ = angular_average(Fx_anl, grid, int(N / 2.2))[0]
assert np.max(np.abs(Fx_circ - Fx_anl_circ)) < 1e-10
def test_sum():
x = np.linspace(-3, 3, 200)
X, Y = np.meshgrid(x, x)
r2 = X ** 2 + Y ** 2
P = r2 ** -1.
ave, coord = angular_average(P, np.sqrt(r2), bins=20, bin_ave=False, average=False)
assert np.sum(P[r2 < 18.]) == np.sum(ave)
def test_complex_variance():
x = np.linspace(-3, 3, 400)
X, Y = np.meshgrid(x, x)
r2 = X ** 2 + Y ** 2
P = np.ones_like(r2) + np.ones_like(r2)*1j
with pytest.raises(NotImplementedError):
ave, coord, var = angular_average(P, np.sqrt(r2), bins=np.linspace(0, x.max(), 20), get_variance=True)
def test_null_variance_2d():
x = np.linspace(-3, 3, 400)
X, Y = np.meshgrid(x, x)
r2 = X ** 2 + Y ** 2
P = np.ones_like(r2)
ave, coord, var = angular_average(P, np.sqrt(r2), bins=np.linspace(0,x.max(), 20), get_variance=True)
assert np.all(var==0)
def test_bin_edges():
x = np.linspace(-3, 3, 200)
X, Y = np.meshgrid(x, x)
r2 = X**2 + Y**2
P = r2**-1.
bins = np.linspace(0, x.max(), 20)
ave, coord = angular_average(P, np.sqrt(r2), bins=bins, bin_ave=False)
assert np.all(coord == bins)
def test_logbins():
x = np.linspace(-3, 3, 400)
X, Y = np.meshgrid(x, x)
r2 = X ** 2 + Y ** 2
P = np.ones_like(r2)
ave, coord = angular_average(P, np.sqrt(r2), bins=10, bin_ave=False, log_bins=True)
assert np.all(np.isclose(np.diff(coord[1:]/coord[:-1]), 0))
def test_var_trivial_weights():
x = np.linspace(-3, 3, 400)
X, Y = np.meshgrid(x, x)
r2 = X ** 2 + Y ** 2
P = np.ones_like(r2)
P += np.random.normal(scale=1, size=(len(x), len(x)))
ave, coord, var = angular_average(P, np.sqrt(r2), bins=np.linspace(0,x.max(), 20), get_variance=True, weights=np.ones_like(r2))
print(np.diff(var))
assert np.all(np.diff(var)<=0)
def test_against_multirealisation():
x = np.linspace(-3, 3, 1000)
X, Y = np.meshgrid(x, x)
r2 = X ** 2 + Y ** 2
bins = np.linspace(0, x.max(), 20)
# Get the variance from several realisations
ave = [0]*50
for j in range(50):
P = np.ones_like(r2) + np.random.normal(scale=1, size=(len(x), len(x)))
ave[j], coord = angular_average(P, np.sqrt(r2), bins=bins)
var = np.var(np.array(ave), axis=0)
# Get the variance from a single realisation
ave, coord, var2 = angular_average(P, np.sqrt(r2), bins=bins, get_variance=True)
print(var)
print(var2)
assert(np.all(np.isclose(var, var2, 1e-2)))
def test_mixed_unitary_ordinary_unitary_angular_2d_bf():
N = 1000
Lk = 10.
dk = Lk / N
k = np.arange(-Lk / 2, Lk / 2, dk)[:N]
KX, KY = np.meshgrid(k, k)
alpha = np.pi
Fk = np.exp(-alpha * (KX**2 + KY**2))
fx, x = ifft(Fk, Lk=Lk, a=0, b=1)
Fk_, k_, kgrid = fft(fx,
-2 * np.min(x),
a=0,
b=2 * np.pi,
ret_cubegrid=True)
Fk_, bins = angular_average(Fk_, kgrid, 200)
assert np.max(
np.abs(Fk_ - 2 * np.pi * np.exp(-alpha * ((2 * np.pi) * bins)**2)))
def test_mixed_unitary_ordinary_unitary_angular_2d_fb():
N = 1000
L = 10.
dx = L / N
x = np.arange(-L / 2, L / 2, dx)[:N]
X, Y = np.meshgrid(x, x)
a_squared = 1
fx = np.exp(-np.pi * a_squared * (X**2 + Y**2))
Fk, freq = fft(fx, L=L, a=0, b=2 * np.pi)
Lk = -2 * np.min(freq)
fx_, x_, xgrid = ifft(Fk, Lk=Lk, a=0, b=1, ret_cubegrid=True)
fx_, bins = angular_average(fx_, xgrid, 200)
print(
np.max(
np.abs(fx_ - np.exp(-np.pi * (bins / (2 * np.pi))**2) /
(2 * np.pi))))
assert np.max(
np.abs(fx_ - np.exp(-np.pi * (bins / (2 * np.pi))**2) /
(2 * np.pi))) < 1e-4