def test_models(doctest_namespace):
cz_model = CzjzekDistribution(0.5)
doctest_namespace["cz_model"] = cz_model
S0 = {"Cq": 1e6, "eta": 0.3}
ext_cz_model = ExtCzjzekDistribution(S0, eps=0.35)
doctest_namespace["ext_cz_model"] = ext_cz_model
def test_czjzek_distribution():
sigma = 0.5
# numerical Czjzek distribution
count_ = COUNT
zeta, eta = CzjzekDistribution(sigma).rvs(size=count_)
# eta projection
e_hist, ran_e = np.histogram(eta, bins=15, range=[0, 1])
e_vector = e_hist / count_
e_range = (ran_e[1:] + ran_e[:-1]) / 2
# zeta projection
z_hist, ran_z = np.histogram(zeta, bins=20, range=[-20, 20])
z_vector = z_hist / count_
z_range = (ran_z[1:] + ran_z[:-1]) / 2
# czjzek distribution from analytical formula
sigma_ = 2 * sigma
V, e = np.meshgrid(z_range, e_range)
denom = (2 * np.pi) ** 0.5 * sigma_**5
res = (V**4 * e) * (1 - e**2 / 9) / denom
res *= np.exp(-(V**2 * (1 + (e**2 / 3))) / (2 * sigma_**2))
res /= res.sum()
eta_pro = res.sum(axis=1)
zeta_pro = res.sum(axis=0)
# eta test
message = "failed to compare eta projection for Czjzek distribution"
np.testing.assert_almost_equal(e_vector, eta_pro, decimal=2, err_msg=message)
# zeta test
message = "failed to compare zeta projection for Czjzek distribution"
np.testing.assert_almost_equal(z_vector, zeta_pro, decimal=2, err_msg=message)
def test_czjzek_pdf():
sigma = 0.5
z_range = np.arange(100) * 30 / 100 - 15
e_range = np.arange(21) / 20
# czjzek distribution from analytical formula
sigma_ = 2 * sigma
V, e = np.meshgrid(z_range, e_range)
denom = (2 * np.pi) ** 0.5 * sigma_**5
res = (V**4 * e) * (1 - e**2 / 9) / denom
res *= np.exp(-(V**2 * (1 + (e**2 / 3))) / (2 * sigma_**2))
res /= res.sum()
_, _, amp = CzjzekDistribution(sigma).pdf([z_range, e_range])
error = "Czjzek analytical is not equal to numerical"
np.testing.assert_almost_equal(res, amp, decimal=2, err_msg=error)
# %% # Generate probability distribution # --------------------------------- # The range of isotropic chemical shifts, the quadrupolar coupling constant, and # asymmetry parameters used in generating a 3D grid. iso_r = np.arange(101) / 1.5 + 30 # in ppm Cq_r = np.arange(100) / 4 # in MHz eta_r = np.arange(10) / 9 # The 3D mesh grid over which the distribution amplitudes are evaluated. iso, Cq, eta = np.meshgrid(iso_r, Cq_r, eta_r, indexing="ij") # The 2D amplitude grid of Cq and eta is sampled from the Czjzek distribution model. Cq_dist, e_dist, amp = CzjzekDistribution(sigma=1).pdf(pos=[Cq_r, eta_r]) # The 1D amplitude grid of isotropic chemical shifts is sampled from a Gaussian model. iso_amp = multivariate_normal(mean=58, cov=[4]).pdf(iso_r) # The 3D amplitude grid is generated as an uncorrelated distribution of the above two # distribution, which is the product of the two distributions. pdf = np.repeat(amp, iso_r.size).reshape(eta_r.size, Cq_r.size, iso_r.size) pdf *= iso_amp pdf = pdf.T # %% # The two-dimensional projections from this three-dimensional distribution are shown # below. _, ax = plt.subplots(1, 3, figsize=(9, 3))
def test_czjzek_polar():
x, y = CzjzekDistribution(sigma=0.5, polar=True).rvs(size=COUNT)
x1, y1 = x_y_from_zeta_eta(*x_y_to_zeta_eta(x, y))
np.testing.assert_almost_equal(x, x1)
np.testing.assert_almost_equal(y, y1)
# sphinx_gallery_thumbnail_number = 4
# %%
# Symmetric shielding tensor
# --------------------------
#
# Create the Czjzek distribution
# ''''''''''''''''''''''''''''''
#
# First, create a distribution of the zeta and eta parameters of the shielding tensors
# using the :ref:`czjzek_distribution` model as follows.
# The range of zeta and eta coordinates over which the distribution is sampled.
z_range = np.arange(100) - 50 # in ppm
e_range = np.arange(21) / 20
z_dist, e_dist, amp = CzjzekDistribution(sigma=3.1415).pdf(
pos=[z_range, e_range])
# %%
# Here ``z_range`` and ``e_range`` are the coordinates along the :math:`\zeta` and
# :math:`\eta` dimensions that form a two-dimensional :math:`\zeta`-:math:`\eta` grid.
# The argument `sigma` of the CzjzekDistribution class is the standard deviation of the
# second-rank tensor parameters used in generating the distribution, and `pos` hold the
# one-dimensional arrays of :math:`\zeta` and :math:`\eta` coordinates, respectively.
#
# The following is the contour plot of the Czjzek distribution.
plt.figure(figsize=(4.25, 3.0))
plt.contourf(z_dist, e_dist, amp, levels=10)
plt.xlabel(r"$\zeta$ / ppm")
plt.ylabel(r"$\eta$")
plt.tight_layout()
plt.show()