dist1 = LognormalDistribution(sigma=ref_sigma, mu=ref_mu)
dep1 = (0, None, 0)
distributions = [dist0, dist1]
dependencies = [dep0, dep1]
mul_dist = MultivariateDistribution(distributions, dependencies)
ref_marg_f0 = mul_dist.marginal_pdf(np.squeeze(x), dim=0)
ref_marg_f1 = mul_dist.marginal_pdf(np.squeeze(x), dim=1)
ref_marg_F0 = mul_dist.marginal_cdf(np.squeeze(x), dim=0)
ref_marg_F1 = mul_dist.marginal_cdf(np.squeeze(x), dim=1)
ref_marg_x0 = mul_dist.marginal_icdf(p, dim=0)
ref_marg_x1 = mul_dist.marginal_icdf(p, dim=1)
# %%
plt.close("all")
plt.figure()
plt.plot(x, my_marg_f0, label="my marginal pdf dim=0")
plt.plot(x, ref_marg_f0, label="ref marginal pdf dim=0")
plt.legend()
plt.figure()
plt.plot(x, my_marg_f1, label="my marginal pdf dim=1")
plt.plot(x, ref_marg_f1, label="ref marginal pdf dim=1")
plt.legend()
plt.figure()
plt.plot(x, my_marg_F0, label="my marginal cdf dim=0")
CS = axs[0].contour(h_grid, s_grid, f, [fm], colors=c, label=[l])
# Now transform the contour to tp
hs_s_contour = CS.allsegs[0][0]
hs_contour = hs_s_contour[:, 0]
s_contour = hs_s_contour[:, 1]
tp_contour = np.sqrt((2 * math.pi * hs_contour) / (g * s_contour))
axs[2].plot(tp_contour, hs_contour, c=c)
sorted_s = np.sort(steepness)
sorted_s = sorted_s[0::100]
n = sorted_s.size
i = np.array(range(n)) + 1
pi = np.divide((i - 0.5), n)
steepness_dist = joint_dist.distributions[1]
#theoretical_quantiles = steepness_dist.i_cdf(pi)
theoretical_quantiles = joint_dist.marginal_icdf(pi, dim=1)
color_sample = 'k'
marker_sample = 'x'
marker_size = 10
color_fit = 'b'
axs[1].scatter(theoretical_quantiles,
sorted_s,
c=color_sample,
s=marker_size,
marker=marker_sample,
linewidths=1,
alpha=0.5,
rasterized=True)
axs[1].plot([0, max(theoretical_quantiles)], [0, max(theoretical_quantiles)],
c=color_fit)
mc_hs = mc_sample[1]
# Probability - Quantile plot
for i, x in enumerate(variable_list):
x_ordered, F = ecdf(x)
alpha = 1 - F
tr = 1 / (alpha * 365.25 * 24)
tr_threshold = 0.0001
axs1[i].plot(tr[tr >= tr_threshold],
x_ordered[tr >= tr_threshold],
'ok',
markerfacecolor='none',
ms=3,
rasterized=True)
if i == 0:
model_ordered = joint_model_4.marginal_icdf(F, i)
else:
model_ordered, F = ecdf(mc_hs)
alpha = 1 - F
tr = 1 / (alpha * 365.25 * 24)
# Highest F would be 1, which would lead to x_model = inf for unbounded models --> exclude highest value
mask = (tr >= tr_threshold) & (tr < 50)
axs1[i].plot(tr[mask], model_ordered[mask], rasterized=True)
axs1[i].set_xscale('log')
axs1[i].set_ylabel(var_labels[i].capitalize())
axs1[i].set_xlabel('Return period (years)')
axs1[0].legend(['Empirical', 'Model'],
loc='upper left',
ncol=1,