def test_basex_zeros():
n = 21
x = np.zeros((n, n), dtype='float32')
bs = get_bs_basex_cached(n, basis_dir=None, verbose=False)
recon = basex_transform(x, *bs)
assert_allclose(recon, 0)
def test_basex_shape():
n = 21
x = np.ones((n, n), dtype='float32')
bs = get_bs_basex_cached(n, basis_dir=None, verbose=False)
recon = basex_transform(x, *bs)
assert recon.shape == (n, n)
def test_basex_step_ratio():
"""Check a gaussian solution for BASEX"""
n = 51
r_max = 25
ref = GaussianAnalytical(n, r_max, symmetric=True, sigma=10)
tr = np.tile(ref.abel[None, :], (n, 1)) # make a 2D array from 1D
bs = get_bs_basex_cached(n, basis_dir=None, verbose=False)
recon = basex_transform(tr, *bs)
recon1d = recon[n//2 + n%2]
ratio = absolute_ratio_benchmark(ref, recon1d)
assert_allclose( ratio , 1.0, rtol=3e-2, atol=0)
# define a symmetric step function and calculate its analytical Abel transform
st = StepAnalytical(n, r_max, r1, r2, A0)
ax.plot(st.r, st.func, 'b', label='Original signal')
ax.plot(
st.r, st.abel*0.05, 'r',
label='Direct Abel transform x0.05 [analytical]')
center = n//2
right_half = st.abel[center:]
left_half = st.abel[:center+1][::-1]
# BASEX Transform:
# Calculate the inverse abel transform for the centered data
recon_right = basex_transform(
right_half, basis_dir='./', dr=st.dr, verbose=True)
recon_left = basex_transform(
left_half, basis_dir='./', dr=st.dr, verbose=False)
plt.plot(
st.r[center:], recon_right, '--.', c='red',
label='Inverse transform [BASEX]')
plt.plot(st.r[:center+1], recon_left[::-1], '--.', c='red')
ax.legend()
ax.set_xlim(-20, 20)
ax.set_ylim(-5, 20)
ax.set_xlabel('x')
ax.set_ylabel("f(x)")
# define a symmetric step function and calculate its analytical Abel transform
st = StepAnalytical(n, r_max, r1, r2, A0)
ax.plot(st.r, st.func, 'b', label='Original signal')
ax.plot(
st.r, st.abel*0.05, 'r',
label='Direct Abel transform x0.05 [analytical]')
center = n//2
right_half = st.abel[center:]
left_half = st.abel[:center+1][::-1]
# BASEX Transform:
# Calculate the inverse abel transform for the centered data
recon_right = basex_transform(
right_half, basis_dir='bases', dr=st.dr, verbose=True)
recon_left = basex_transform(
left_half, basis_dir='bases', dr=st.dr, verbose=False)
plt.plot(
st.r[center:], recon_right, '--.', c='red',
label='Inverse transform [BASEX]')
plt.plot(st.r[:center+1], recon_left[::-1], '--.', c='red')
ax.legend()
ax.set_xlim(-20, 20)
ax.set_ylim(-5, 20)
ax.set_xlabel('x')
ax.set_ylabel("f(x)")
