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if __name__ == "__main__":
import matplotlib.pyplot as plt
import numpy as np
import scipy.special
import gamma_approx as ga
# Simple / naive
xmin = -5
xmax = 30
ns = np.arange(2, 12, 2)
ylim = np.array([-11, 6])
x = np.linspace(xmin + ga.EPSILON, xmax - ga.EPSILON, 400)
gamma = scipy.special.gamma(x)
fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2.5))
for n in ns:
gamma_lag = ga.eval_laguerre_gamma(x, n=n)
rel_err = ga.calc_rel_error(gamma, gamma_lag)
ax.semilogy(x, np.abs(rel_err), label=f"$n={n}$")
ax.set_xlim(x[0], x[-1])
ax.set_ylim(*(10.0 ** ylim))
ax.set_xticks(np.arange(xmin, xmax + ga.EPSILON, 5))
ax.set_xticks(np.arange(xmin, xmax), minor=True)
ax.set_yticks(10.0 ** np.arange(*ylim, 2))
ax.set_xlabel(r"$z$")
# ax.set_ylabel("Relativer Fehler")
ax.legend(ncol=3, fontsize=ga.fontsize)
ax.grid(1, "both")
fig.savefig(f"{ga.img_path}/rel_error_simple.pgf")
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