diff options
Diffstat (limited to '')
| -rw-r--r-- | buch/papers/laguerre/scripts/gamma_approx.py | 36 |
1 files changed, 23 insertions, 13 deletions
diff --git a/buch/papers/laguerre/scripts/gamma_approx.py b/buch/papers/laguerre/scripts/gamma_approx.py index 9c8f3ee..dd50d92 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.py +++ b/buch/papers/laguerre/scripts/gamma_approx.py @@ -39,7 +39,7 @@ def find_shift(z, target): def find_optimal_shift(z, n): mhat = 1.34093 * n + 0.854093 - steps = int(np.ceil(mhat - np.real(z))) - 1 + steps = int(np.floor(mhat - np.real(z))) return steps @@ -136,7 +136,7 @@ ax.set_xlabel(r"$z$") ax.set_ylabel("Relativer Fehler") ax.legend(ncol=3, fontsize="small") ax.grid(1, "both") -# fig.savefig(f"{img_path}/rel_error_simple.pgf") +fig.savefig(f"{img_path}/rel_error_simple.pgf") # Mirrored @@ -162,7 +162,7 @@ ax2.set_xlabel(r"$z$") ax2.set_ylabel("Relativer Fehler") ax2.legend(ncol=1, loc="upper left", fontsize="small") ax2.grid(1, "both") -# fig2.savefig(f"{img_path}/rel_error_mirror.pgf") +fig2.savefig(f"{img_path}/rel_error_mirror.pgf") # Move to target @@ -202,7 +202,7 @@ ax3.set_yticks(np.arange(len(ns))) ax3.set_yticklabels(ns) ax3.set_xlabel(r"$z$") ax3.set_ylabel(r"$n$") -# fig3.savefig(f"{img_path}/targets.pdf") +fig3.savefig(f"{img_path}/targets.pdf") targets = np.mean(bests, -1) intercept, bias = np.polyfit(ns, targets, 1) @@ -211,16 +211,16 @@ fig4, axs4 = plt.subplots( ) xl = np.array([ns[0] - 0.5, ns[-1] + 0.5]) axs4[0].plot(xl, intercept * xl + bias, label=r"$\hat{m}$") -axs4[0].plot(ns, targets, "x", label=r"$\bar{m}$") -axs4[1].plot(ns, ((intercept * ns + bias) - targets), "-x", label=r"$\hat{m} - \bar{m}$") +axs4[0].plot(ns, targets, "x", label=r"$\overline{m}$") +axs4[1].plot(ns, ((intercept * ns + bias) - targets), "-x", label=r"$\hat{m} - \overline{m}$") axs4[0].set_xlim(*xl) # axs4[0].set_title("Schätzung von Mittelwert") # axs4[1].set_title("Fehler") -axs4[-1].set_xlabel(r"$z$") +axs4[-1].set_xlabel(r"$n$") for ax in axs4: ax.grid(1) ax.legend() -# fig4.savefig(f"{img_path}/schaetzung.pgf") +fig4.savefig(f"{img_path}/estimate.pgf") print(f"Intercept={intercept:.6g}, Bias={bias:.6g}") predicts = np.ceil(intercept * ns[:, None] + bias - x) @@ -234,14 +234,14 @@ gamma = scipy.special.gamma(x)[:, None] n = 8 targets = np.arange(10, 14) gamma = scipy.special.gamma(x) -fig5, ax5 = plt.subplots(num=1, clear=True, constrained_layout=True) +fig5, ax5 = plt.subplots(num=5, clear=True, constrained_layout=True) for target in targets: gamma_lag = eval_laguerre_gamma(x, target=target, n=n, func="shifted") rel_error = np.abs(calc_rel_error(gamma, gamma_lag)) - ax5.semilogy(x, rel_error, label=f"$m={target}$") + ax5.semilogy(x, rel_error, label=f"$m={target}$", linewidth=3) gamma_lgo = eval_laguerre_gamma(x, n=n, func="optimal_shifted") rel_error = np.abs(calc_rel_error(gamma, gamma_lgo)) -ax5.semilogy(x, rel_error, label="$m^*$") +ax5.semilogy(x, rel_error, "c", linestyle="dotted", label="$m^*$", linewidth=3) ax5.set_xlim(x[0], x[-1]) ax5.set_ylim(5e-9, 5e-8) ax5.set_xlabel(r"$z$") @@ -254,10 +254,10 @@ x = np.linspace(-5+ EPSILON, 5-EPSILON, N) gamma = scipy.special.gamma(x)[:, None] n = 8 gamma = scipy.special.gamma(x) -fig6, ax6 = plt.subplots(num=1, clear=True, constrained_layout=True) +fig6, ax6 = plt.subplots(num=6, clear=True, constrained_layout=True) gamma_lgo = eval_laguerre_gamma(x, n=n, func="optimal_shifted") rel_error = np.abs(calc_rel_error(gamma, gamma_lgo)) -ax6.semilogy(x, rel_error, label="$m^*$") +ax6.semilogy(x, rel_error, label="$m^*$", linewidth=3) ax6.set_xlim(x[0], x[-1]) ax6.set_ylim(5e-9, 5e-8) ax6.set_xlabel(r"$z$") @@ -265,4 +265,14 @@ ax6.grid(1, "both") ax6.legend() fig6.savefig(f"{img_path}/rel_error_range.pgf") +N = 2001 +x = np.linspace(-5, 5, N) +gamma = scipy.special.gamma(x) +fig7, ax7 = plt.subplots(num=7, clear=True, constrained_layout=True) +ax7.plot(x, gamma) +ax7.set_xlim(x[0], x[-1]) +ax7.set_ylim(-7.5, 25) +ax7.grid(1, "both") +fig7.savefig(f"{img_path}/gamma.pgf") + # plt.show() |