41 lines
1.0 KiB
Python
41 lines
1.0 KiB
Python
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import numpy as np
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def exponential_function(x, a, b, c):
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return (a-c)*np.exp(-x/b)+c
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def upper_boltzmann(x, f_max, k, x_zero):
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return f_max * np.clip((2 / (1+np.power(np.e, -k*(x - x_zero)))) - 1, 0, None)
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def full_boltzmann(x, f_max, f_min, k, x_zero):
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return (f_max-f_min) * (1 / (1 + np.power(np.e, -k * (x - x_zero)))) + f_min
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def full_boltzmann_straight_slope(f_max, f_min, k, x_zero=0):
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return (f_max-f_min)*k*1/2
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def derivative_full_boltzmann(x, f_max, f_min, k, x_zero):
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return (f_max - f_min) * k * np.power(np.e, -k * (x - x_zero)) / (1 + np.power(np.e, -k * (x - x_zero))**2)
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def inverse_full_boltzmann(x, f_max, f_min, k, x_zero):
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if x < f_min or x > f_max:
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raise ValueError("Value undefined in inverse_full_boltzmann")
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return -(np.log((f_max-f_min) / (x - f_min) - 1) / k) + x_zero
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def clipped_line(x, a, b):
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return np.clip(a+b*x, 0, None)
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def inverse_clipped_line(x, a, b):
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if clipped_line(x, a, b) == 0:
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raise ValueError("Value undefined in inverse_clipped_line.")
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return (x-a)/b
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