Python 数据可视化之密度散点图 Density Scatter Plot

import numpy as np
from numpy import polyfit, poly1d
import matplotlib as mpl
from matplotlib import cm
from matplotlib import ticker
from matplotlib import colors
import matplotlib.pyplot as plt
import matplotlib.font_manager as fm
from scipy.stats import gaussian_kde

# 固定 numpy 的随机种子
np.random.seed(2024)

# 构造二维数据 x 和 y
x = np.random.normal(loc=0.0, scale=1.0, size=1000)
y = x + np.random.normal(loc=0.1, scale=1.0, size=1000)

# 核密度估计
x_and_y = np.vstack([x, y])
kde = gaussian_kde(x_and_y)
z = kde(x_and_y)
idx = z.argsort()
x, y, z = x[idx], y[idx], z[idx]

is_cbar = True

# 创建图形和坐标轴
fig, ax = plt.subplots(figsize=(7, 4), dpi=150)

# cmap: bwr、Spectral_r、viridis_r、spring、gist_rainbow_r、RdBu_r
# 可设置的 colormaps - https://matplotlib.org/tutorials/colors/colormaps.html
my_cmap = "bwr"

# 绘制密度散点图
ax.scatter(x, y, c=z, cmap=my_cmap)

# 用 7 次多项式拟合，调用 poly1d 方法得到多项式系数。
y_fit = polyfit(x, y, 7)
y_fit_1d = np.poly1d(y_fit)
y_hat = np.polyval(y_fit, x)

# 计算相关系数和 R^2
print('Correlation coefficients：')
print(np.corrcoef(y_hat, y))
correlation = np.corrcoef(y_hat, y)[0, 1]
R_square = correlation ** 2
print("R^2：", R_square)

xtick = np.linspace(min(x), max(x), 1000)
# 拟合的多项式曲线
plt.plot(xtick, y_fit_1d(xtick), color="#FF0066", lw=2.2)

# 坐标轴刻度的数值使用 Latin Modern Math 字体
labels = ax.get_xticklabels() + ax.get_yticklabels()
[label.set_fontproperties(font_latex2) for label in labels]
[label.set_color('black') for label in labels]

# 设置坐标轴刻度
plt.tick_params(axis='x', direction='out', labelsize=13, length=4.6, width=1.15)
plt.tick_params(axis='y', direction='out', labelsize=13, length=4.6, width=1.15)

# 展示 X 和 Y 轴的子刻度
ax.xaxis.set_minor_locator(ticker.AutoMinorLocator())
ax.yaxis.set_minor_locator(ticker.AutoMinorLocator())

# 颜色条的设置：刻度、字体、字号等
if is_cbar:
    norm = colors.Normalize(vmin=np.min(z), vmax=np.max(z))
    cbar = plt.colorbar(cm.ScalarMappable(norm=norm, cmap=my_cmap), ax=ax)

    cbar.ax.set_ylabel("Density", fontproperties=font_latex2, labelpad=12)
    cbar.ax.tick_params(labelsize=12)

    labels = cbar.ax.get_xticklabels() + cbar.ax.get_yticklabels()
    [label.set_fontproperties(font_latex2) for label in labels]
    [label.set_color('black') for label in labels]
    
    tick_locator = ticker.MaxNLocator(nbins=8)
    cbar.locator = tick_locator
    cbar.update_ticks()

# 设置 X 轴和 Y 轴的刻度值范围
ax.set_xlim(left=-6, right=6.0000001)
ax.set_xticks(np.arange(-6, 6.000001, step=2.0))
ax.set_ylim(bottom=-6, top=6.0000001)
ax.set_yticks(np.arange(-6, 6.000001, step=2.0))

# 画图对象周围的框的加粗一点
lw = 1.25
ax.spines["right"].set_linewidth(lw)
ax.spines["left"].set_linewidth(lw)
ax.spines["top"].set_linewidth(lw)
ax.spines["bottom"].set_linewidth(lw)

# 设置 X 轴和 Y 轴的标签、字体、刻度和刻度标签在内的坐标轴边界框中的间距
plt.xlabel("X Label", fontproperties=font_latex1, labelpad=8)
plt.ylabel("Y Label", fontproperties=font_latex1, labelpad=8)

# 设置标题 字体 大小 以及距绘图对象的距离
plt.title("Python Matplotlib - Density Scatter Plot",
          fontproperties=font_latex2, pad=12
         )

# 文本的位置是根据数据坐标来确定的
ax.text(x=-5, y=4.5, s=r'$\ {R^2} = 0.522$', usetex=True,
        fontsize=14, fontweight="bold"
       )

# 显示网格  虚线和透明度
plt.grid(alpha=0.360, ls="--", which="major", color="#A9A9A9")
# 紧凑布局
plt.tight_layout()

plt.savefig("./Figures/密度散点图.png", dpi=300, bbox_inches="tight")
plt.show()