除了超赞三元相图，还有二元相和圆形图例？！这个可视工具有点猛~~

DataCharm

发布于 2022-10-25 10:28:26

7470

发布于 2022-10-25 10:28:26

之前的推文中，小编给出了Python和R关于三元相图的绘制方法(我汇总了所有三元相图(ternary plots)的绘制方法，超实用！！)，最近在查找资料的同时，小编还发现了其他类型的三元图，如三元相多边形图，即使用多边形(Polygon) 展示不同类别数据在三元相坐标体系中的组成，而完成这一操作的可视化库为Python-poisson_approval库，这个库除了绘制三元相图外，还可以绘制二元相图(Binary Plots),此外，还存在许多其他有用的函数和计算方法，更多内容可查看：poisson_approval库官网[1]

本期推文主要介绍其可视化部分~~

poisson_approval库绘制三元相多边形图

poisson_approval库绘制的三元相图主要表现组成占比情况，主要依赖python-ternary库，这里主要介绍其绘制的三元相图类型，如下：

Number of Equilibria

import matplotlib.pyplot as plt
import poisson_approval as pa
from fractions import Fraction

SCALE = 21
simplex_to_profile = pa.SimplexToProfile(
    pa.ProfileNoisyDiscrete,
    right_type='c>a~b',
    top_type=('abc', 0.5, 0.01),
    left_type=('bac', 0.5, 0.01),
    d_type_fixed_share={('abc', 0.1, 0.01): Fraction(1, 10),
                        ('abc', 0.9, 0.01): Fraction(1, 10)}
)
pa.ternary_plot_n_equilibria(
    simplex_to_profile,
    scale=SCALE,
    title='Number of ordinal equilibria')

Number of Equilibria Example01

还可以通过调整meth参数进行图表样式更改：

pa.ternary_plot_n_equilibria(
    simplex_to_profile,
    scale=SCALE,
    title='Number of group equilibria',
    meth='analyzed_strategies_group')

Number of Equilibria Example02

Winners at Equilibrium 这类图表使用了不同填充颜色去表示组成，如下：

pa.ternary_plot_winners_at_equilibrium(
    simplex_to_profile,
    scale=SCALE,
    title='Winners in ordinal equilibria')

Winners at Equilibrium Example02

Winning Frequencies in Fictitious Play or Iterated Voting

使用一种三元图例表示组成占比：

pa.ternary_plot_winning_frequencies(simplex_to_profile, scale=SCALE, n_max_episodes=100)

Example01

通过修改meth、perception_update_ratio等参数进行绘制调整：

pa.ternary_plot_winning_frequencies(
    simplex_to_profile,
    scale=SCALE,
    meth='iterated_voting',
    init='random_tau_undominated',
    samples_per_point=10,
    perception_update_ratio=1,
    ballot_update_ratio=1,
    winning_frequency_update_ratio=pa.one_over_t,
    n_max_episodes=100,
    title='Winning frequencies in iterated voting',
    legend_title='Winners'
)

Example02

以上就是poisson_approval库绘制三元相图的部分案例，可以看出，无论从组成占比和图例设置等都是新的一种三元相图系列。更多样例及设置参数可参考：tutorial_ernary_plots[2]

poisson_approval库绘制二元相图

poisson_approval库绘制二元相图的基本原理和三元相图的绘制相同，这里介绍基本的案例，如下：

Number of Equilibria

pa.binary_plot_n_equilibria(
    xyy_to_profile,
    xscale=XSCALE, yscale=YSCALE,
    title='Number of ordinal equilibria')

Number of Equilibria

Winners at Equilibrium

pa.binary_plot_winners_at_equilibrium(
    xyy_to_profile,
    xscale=XSCALE, yscale=YSCALE,
    title='Winners in ordinal equilibria')

Winners at Equilibrium

Winning Frequencies in Fictitious Play or Iterated Voting

pa.binary_plot_winning_frequencies(
    xyy_to_profile,
    xscale=XSCALE, yscale=YSCALE,
    n_max_episodes=100)

Example

Advanced Intensity Heat Maps

def f(x, y1, y2):
    return (x**2 + y1) / (y2 + 1)
figure, tax = pa.binary_figure(xscale=XSCALE, yscale=YSCALE)
tax.heatmap_intensity(f,
                      x_left_label='x-left',
                      x_right_label='x-right',
                      y_left_label='y-left',
                      y_right_label='y-right')
tax.set_title('An intensity heat map')

Advanced Intensity Heat Maps

Advanced Candidate Heat Maps

def g(x, y1, y2):
    a = x**.5
    b = y1**2
    c = 1 - a - b
    return [a, b, c]
figure, tax = pa.binary_figure(xscale=XSCALE, yscale=YSCALE)
tax.heatmap_candidates(g,
                       x_left_label='x-left',
                       x_right_label='x-right',
                       y_left_label='y-left',
                       y_right_label='y-right',
                       legend_title='Candidates',
                       legend_style='palette')
tax.set_title('A candidate heat map')