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if __name__ == "__main__":
import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
import gamma_approx as ga
import targets
mpl.rcParams.update(
{
"mathtext.fontset": "stix",
"font.family": "serif",
"font.serif": "TeX Gyre Termes",
}
)
N = 200
ns = np.arange(1, 13)
step = 1 / (N - 1)
x = np.linspace(step, 1 - step, N + 1)
bests = targets.find_best_loc(N, ns=ns)
mean_m = np.mean(bests, -1)
intercept, bias = np.polyfit(ns, mean_m, 1)
fig, axs = plt.subplots(
2, num=1, sharex=True, clear=True, constrained_layout=True, figsize=(4.5, 3.6)
)
xl = np.array([ns[0] - 0.5, ns[-1] + 0.5])
axs[0].plot(xl, intercept * xl + bias, label=r"$\hat{m}$")
axs[0].plot(ns, mean_m, "x", label=r"$\overline{m}$")
axs[1].plot(
ns, ((intercept * ns + bias) - mean_m), "-x", label=r"$\hat{m} - \overline{m}$"
)
axs[0].set_xlim(*xl)
axs[0].set_xticks(ns)
axs[0].set_yticks(np.arange(np.floor(mean_m[0]), np.ceil(mean_m[-1]) + 0.1, 2))
# axs[0].set_title("Schätzung von Mittelwert")
# axs[1].set_title("Fehler")
axs[-1].set_xlabel(r"$n$")
for ax in axs:
ax.grid(1)
ax.legend()
# fig.savefig(f"{ga.img_path}/estimates.pgf")
fig.savefig(f"{ga.img_path}/estimates.pdf")
print(f"Intercept={intercept:.6g}, Bias={bias:.6g}")
predicts = np.ceil(intercept * ns[:, None] + bias - np.real(x))
print(f"Error: {np.mean(np.abs(bests - predicts))}")
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