r"""
Interval pumping
================

Another case often discussed in literatur is interval pumping, where
the pumping is just done in a certain time frame.

Unfortunatly the Stehfest algorithm is not suitable for this kind of solution,
which is demonstrated in the following script.
"""

import numpy as np
from matplotlib import pyplot as plt

from anaflow import theis

time = np.linspace(10, 200)
rad = [1, 5]

# Q(t) = Q * characteristic([0, a])
lap_kwargs = {"cond": 3, "cond_kw": {"a": 100}}

head = theis(
    time=time,
    rad=rad,
    storage=1e-4,
    transmissivity=1e-4,
    rate=-1e-4,
    lap_kwargs=lap_kwargs,
)

for i, step in enumerate(rad):
    plt.plot(time, head[:, i], label="Theis(r={})".format(step))

plt.title("The Stehfest algorithm is not suitable for this!")
plt.legend()
plt.tight_layout()
plt.show()