"""
created matt_dumont
on: 7/3/24
"""
import numpy as np
import matplotlib.pyplot as plt
[docs]
def s_curve(x, s, a, b, c):
"""
S-curve function
:param x: x value
:param s: scale - the maximum value of the curve (if s=1, the maximum value is 1)
:param a: steepness - smoothing parameter as a increases the curve becomes steeper and the inflection point moves to the right
:param b: steepness about the inflection point
:param c: inflection point (if a=1, c is the x value at which y=0.5)
:return:
"""
return s * (1 / (1 + np.exp(-b * (x - c)))) ** a
def a_var():
fig, ax = plt.subplots(figsize=(10, 10))
for a in np.arange(-5, 2, 0.5):
a = 10 ** a
x = np.linspace(-50, 50, 100)
y = s_curve(x, 1, a, 1, 10)
ax.plot(x, y, label=f'a={a}')
ax.legend()
def b_var():
fig, ax = plt.subplots(figsize=(10, 10))
for b in np.arange(-2, 3, 0.5):
b = 10 ** b
x = np.linspace(-50, 50, 100)
y = s_curve(x, 1, 1, b, 10)
ax.plot(x, y, label=f'b={b}')
ax.legend()
def example_feed_scarcity_cost():
x = np.linspace(0, 100, 100)
c = 33
y = s_curve(x, s=5, a=.85, b=0.33, c=c)
fig, ax = plt.subplots(figsize=(10, 10))
ax.plot(x, y)
ax.axvline(14, ls='--', color='b', label='"typical" feed import')
ax.axvline(28, ls=':', color='b', label='2x "typical" feed import')
ax.axhline(0, ls='--', color='r')
ax.legend()
ax.set_xlabel('Feed import (% of annual full production demand)')
ax.set_ylabel('Additional Feed scarcity cost (multiplier of feed cost)')
ax.set_title('Feed scarcity cost as a function of feed import')
fig.tight_layout()
def feed_scarcity_cost_dnz_system3():
x = np.linspace(0, 100, 100)
c = 22
y = s_curve(x, s=10, a=1, b=0.8, c=c)
fig, ax = plt.subplots(figsize=(10, 10))
ax.plot(x, y)
ax.fill_between([1, 10], [0, 0], [1, 1], transform=ax.get_xaxis_transform(), color='r', alpha=0.1, label='fs2')
ax.fill_between([10, 20], [0, 0], [1, 1], transform=ax.get_xaxis_transform(), color='r', alpha=0.2, label='fs3')
ax.fill_between([20, 30], [0, 0], [1, 1], transform=ax.get_xaxis_transform(), color='r', alpha=0.3, label='fs4')
ax.fill_between([30, 100], [0, 0], [1, 1], transform=ax.get_xaxis_transform(), color='r', alpha=0.4, label='fs5')
ax.axvline(14, ls='--', color='b', label='"typical" feed import')
ax.axvline(28, ls=':', color='b', label='2x "typical" feed import')
ax.axhline(0, ls='--', color='r')
ax.legend()
ax.set_xlabel('Feed import (% of annual full production demand)')
ax.set_ylabel('Additional Feed scarcity cost (multiplier of feed cost)')
ax.set_title('Feed scarcity cost as a function of feed import')
fig.tight_layout()
if __name__ == '__main__':
feed_scarcity_cost_dnz_system3()
a_var()
b_var()
plt.show()
