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author | JODBaer <55744603+JODBaer@users.noreply.github.com> | 2022-05-15 15:38:10 +0200 |
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committer | GitHub <noreply@github.com> | 2022-05-15 15:38:10 +0200 |
commit | f176135c17eacc124e6ad3ed84ca805323bcbee7 (patch) | |
tree | 9a496cb9f67b42f566e4c05a7be5d0024beb9358 /buch/papers/laguerre/scripts/laguerre_plot.py | |
parent | Merge branch 'AndreasFMueller:master' into master (diff) | |
parent | typos (diff) | |
download | SeminarSpezielleFunktionen-f176135c17eacc124e6ad3ed84ca805323bcbee7.tar.gz SeminarSpezielleFunktionen-f176135c17eacc124e6ad3ed84ca805323bcbee7.zip |
Merge branch 'AndreasFMueller:master' into master
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-rw-r--r-- | buch/papers/laguerre/scripts/laguerre_plot.py | 100 |
1 files changed, 100 insertions, 0 deletions
diff --git a/buch/papers/laguerre/scripts/laguerre_plot.py b/buch/papers/laguerre/scripts/laguerre_plot.py new file mode 100644 index 0000000..b9088d0 --- /dev/null +++ b/buch/papers/laguerre/scripts/laguerre_plot.py @@ -0,0 +1,100 @@ +#!/usr/bin/env python3 +# -*- coding:utf-8 -*- +"""Some plots for Laguerre Polynomials.""" + +import os +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np +import scipy.special as ss + + +def get_ticks(start, end, step=1): + ticks = np.arange(start, end, step) + return ticks[ticks != 0] + + +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(np.arange(-ylim, ylim), minor=True) +ax.set_yticks(np.arange(-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_polynomes.pdf") |