import numpy as np def get_ticks(start, end, step=1): ticks = np.arange(start, end, step) return ticks[ticks != 0] if __name__ == "__main__": import os from pathlib import Path import matplotlib as mpl import matplotlib.pyplot as plt import scipy.special as ss mpl.rcParams.update( { "mathtext.fontset": "stix", "font.family": "serif", "font.serif": "TeX Gyre Termes", } ) N = 1000 step = 5 t = np.linspace(-1.05, 10.5, N)[:, None] root = str(Path(__file__).parent) img_path = f"{root}/../images" os.makedirs(img_path, exist_ok=True) # fig = plt.figure(num=1, clear=True, tight_layout=True, figsize=(5.5, 3.7)) # ax = fig.add_subplot(axes_class=AxesZero) fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(6, 4)) for n in np.arange(0, 8): k = np.arange(0, n + 1)[None] L = np.sum((-1) ** k * ss.binom(n, k) / ss.factorial(k) * t ** k, -1) ax.plot(t, L, label=f"$n={n}$") ax.set_xticks(get_ticks(int(t[0]), t[-1]), minor=True) ax.set_xticks(get_ticks(0, t[-1], step)) ax.set_xlim(t[0], t[-1] + 0.1 * (t[1] - t[0])) ax.set_xlabel(r"$x$", x=1.0, labelpad=-10, rotation=0, fontsize="large") ylim = 13 ax.set_yticks(get_ticks(-ylim, ylim), minor=True) ax.set_yticks(get_ticks(-step * (ylim // step), ylim, step)) ax.set_ylim(-ylim, ylim) ax.set_ylabel(r"$y$", y=0.95, labelpad=-18, rotation=0, fontsize="large") ax.legend(ncol=2, loc=(0.125, 0.01), fontsize="large") # set the x-spine ax.spines[["left", "bottom"]].set_position("zero") ax.spines[["right", "top"]].set_visible(False) ax.xaxis.set_ticks_position("bottom") hlx = 0.4 dx = t[-1, 0] - t[0, 0] dy = 2 * ylim hly = dy / dx * hlx dps = fig.dpi_scale_trans.inverted() bbox = ax.get_window_extent().transformed(dps) width, height = bbox.width, bbox.height # manual arrowhead width and length hw = 1.0 / 60.0 * dy hl = 1.0 / 30.0 * dx lw = 0.5 # axis line width ohg = 0.0 # arrow overhang # compute matching arrowhead length and width yhw = hw / dy * dx * height / width yhl = hl / dx * dy * width / height # draw x and y axis ax.arrow( t[-1, 0] - hl, 0, hl, 0.0, fc="k", ec="k", lw=lw, head_width=hw, head_length=hl, overhang=ohg, length_includes_head=True, clip_on=False, ) ax.arrow( 0, ylim - yhl, 0.0, yhl, fc="k", ec="k", lw=lw, head_width=yhw, head_length=yhl, overhang=ohg, length_includes_head=True, clip_on=False, ) # fig.savefig(f"{img_path}/laguerre_poly.pgf") fig.savefig(f"{img_path}/laguerre_poly.pdf") # plt.show()