r"""
Plot front position for each method.
===========================
This section shows how to use *show_fronts_over_methods* function to plot front position for each methods.

For each case, we will use an initial water depth :math:`h_0 = 20m`. For Mangeney's method, we use a slope of :math:`\theta = 30°`
and a friction angle of :math:`\delta = 25°`. For Stoker's method, we use a domain depth of :math:`h_r = 1m`:

Implementation
-----------------
"""

from tilupy.analytic_sol import Front_result

A = Front_result(h0=20)

# %%
#
# ---------------------------------

# %%
# **Case 1**: computing only for :math:`t = 5s`.
t = 5

A.xf_mangeney(t, delta=25, theta=30)
A.xf_dressler(t)
A.xf_ritter(t)
A.xf_stoker(t, hr=1)
A.xf_chanson(t, f=0.05)

A.show_fronts_over_methods()

# %%
#
# ---------------------------------

# %%
# **Case 2**: computing for :math:`t = {1, 5, 10, 15, 20}s`.
T = [1, 10, 15, 20]  # t = 5 already compute

for t in T:
    A.xf_mangeney(t, delta=25, theta=30)
    A.xf_dressler(t)
    A.xf_ritter(t)
    A.xf_stoker(t, hr=1)
    A.xf_chanson(t, f=0.05)

A.show_fronts_over_methods()