dep0 = (None, None, None, None)
ref_mu = FunctionParam("lnsquare2", 3.62, 5.77, None)
ref_sigma = FunctionParam("asymdecrease3", 0, 0.324, 0.404)
dist1 = LognormalDistribution(sigma=ref_sigma, mu=ref_mu)
dep1 = (0, None, 0)
distributions = [dist0, dist1]
dependencies = [dep0, dep1]
mul_dist = MultivariateDistribution(distributions, dependencies)
ref_f = mul_dist.pdf(x.T)
ref_f_expweib = mul_dist.distributions[0].pdf(x[:, 0])
ref_ln = mul_dist.distributions[1]
ref_f_ln = []
for given in my_given:
y = np.stack([np.full_like(x[:, 1], given), x[:, 1]])
ref_f_ln.append(ref_ln.pdf(x[:, 1], y, (0, None, 0)))
ref_f_ln = np.stack(ref_f_ln, axis=1)
ref_isorm = ISormContour(mul_dist, return_period, state_duration)
ref_coordinates = np.stack(ref_isorm.coordinates, axis=1)
trs = [1, 50, 250]
fms = np.empty(shape=(3, 1))
for i, tr in enumerate(trs):
HDC = HighestDensityContour(joint_dist,
return_period=tr,
state_duration=1,
limits=[(0, 20), (0, 0.1)])
fms[i] = HDC.fm
h_step = 0.05
s_step = 0.00025
h_grid, s_grid = np.mgrid[0:18:h_step, 0:0.08:s_step]
f = np.empty_like(h_grid)
for i in range(h_grid.shape[0]):
for j in range(h_grid.shape[1]):
f[i, j] = joint_dist.pdf([h_grid[i, j], s_grid[i, j]])
print('Done with calculating f')
axs[2].scatter(tp, hs, c='black', s=5, alpha=0.5, rasterized=True)
axs[2].spines['right'].set_visible(False)
axs[2].spines['top'].set_visible(False)
axs[2].set_xlabel(tp_label)
axs[2].set_ylabel(hs_label)
colors = ['red', 'blue', 'green']
labels = ['1-yr', '50-yr', '250-yr']
for i, (fm, c, l) in enumerate(zip(fms, colors, labels)):
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]
axs1[i + 2].set_xlabel(var_symbols[i] + ', theoretical quantiles')
for ax in axs1:
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
# Joint model plot to analyze the dependence structure
fig2, axs2 = plt.subplots(1, 3, figsize=(12, 4))
# Constant density lines
v_step = 0.1
h_step = 0.1
vgrid, hgrid = np.mgrid[0:40:v_step, 0:20:h_step]
f = np.empty_like(vgrid)
for i in range(vgrid.shape[0]):
for j in range(vgrid.shape[1]):
f[i, j] = joint_model_4.pdf([vgrid[i, j], hgrid[i, j]])
density_levels = [1E-6, 1E-5, 1E-4, 1E-3, 1E-2, 1E-1]
axs2[0].scatter(u, hs, s=3, c='black', alpha=0.5, zorder=-2, rasterized=True)
from palettable.colorbrewer.diverging import Spectral_6 as mycorder
level_colors = np.array(mycorder.mpl_colors)
CS = axs2[0].contour(vgrid, hgrid, f, density_levels, colors=level_colors)
axs2[0].set_xlim(0, 35)
axs2[0].set_ylim(0, 16)
lines = [
CS.collections[0], CS.collections[1], CS.collections[2], CS.collections[3],
CS.collections[4], CS.collections[5]
]
labels = [
'$10^{-6}$', '$10^{-5}$', '$10^{-4}$', '$10^{-3}$', '$10^{-2}$',