104 lines
2.1 KiB
Python
104 lines
2.1 KiB
Python
import numpy as np
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from scipy import optimize
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import matplotlib.pyplot as plt
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x0 = np.array(
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[
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102,
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128,
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143,
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161,
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176,
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191,
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207,
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222,
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237,
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255,
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270,
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]
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)
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y0 = np.array(
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[
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1.5,
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1.3,
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1.1,
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1.3,
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1.5,
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1.6,
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2.3,
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2.9,
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4.2,
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5.9,
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7.7,
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]
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)
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x1 = np.array(
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[
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100,
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120,
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140,
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160,
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180,
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200,
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220,
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240,
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260,
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]
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)
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y1 = np.array(
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[
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1.4,
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1,
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1.4,
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1.5,
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1.7,
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2.9,
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2.8,
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3,
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6.2,
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]
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)
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def get_poly_fit(x, y, remove_first_n=1, remove_last_n=1, n_points=100):
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coeffs = np.polyfit(x, y, 3)
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poly = np.poly1d(coeffs)
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x_start = x[remove_first_n]
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x_end = x[-1-remove_last_n]
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x_poly = np.linspace(x_start, x_end, n_points)
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y_poly = poly(x_poly)
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return x_poly, y_poly
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def get_log_log_threshold(x, y):
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x_log = np.log(x)
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y_log = np.log(y)
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p, e = optimize.curve_fit(piecewise_linear, x_log, y_log, p0=[np.mean(x_log), np.mean(y_log), 0.5, 4.0])
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return np.exp(p[0])
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def piecewise_linear(x, x0, y0, k1, k2):
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return np.piecewise(
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x, [x < x0], [lambda x: k1 * x + y0 - k1 * x0, lambda x: k2 * x + y0 - k2 * x0]
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)
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def main():
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first_x, first_y = get_poly_fit(x0, y0)
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second_x, second_y = get_poly_fit(x1, y1)
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first_lt1 = get_log_log_threshold(first_x, first_y)
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second_lt1 = get_log_log_threshold(second_x, second_y)
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plt.plot(first_x, first_y, color='C0')
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plt.scatter(x0, y0, color='C0')
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plt.plot(second_x, second_y, color='C1')
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plt.scatter(x1, y1, color='C1')
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plt.axvline(first_lt1, color='C0', linestyle='dashed')
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plt.axvline(second_lt1, color='C1', linestyle='dashed')
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plt.grid(True, which='major')
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major_ticks = np.arange(0, 8, 1)
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minor_ticks = np.arange(0, 8, 0.1)
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plt.yticks(major_ticks)
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plt.yticks(minor_ticks, minor=True)
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plt.show()
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if __name__ == '__main__':
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main()
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