布局

主要参数类别：

import matplotlib.pyplot as plt
import numpy as np

# 查看所有默认参数
plt.rcParams  

# 常用参数修改示例
plt.rcParams['figure.figsize'] = (10, 6)  # 图片大小
plt.rcParams['font.size'] = 12             # 字体大小
plt.rcParams['axes.grid'] = True           # 显示网格
plt.rcParams['grid.alpha'] = 0.3           # 网格透明度

from sympy import symbols, exp, lambdify
import numpy as np

x, y = symbols("x, y")

# 定义MATLAB二元函数 peaks()
f_xy = 3*(1-x)**2*exp(-(x**2) - (y+1)**2) \
    - 10*(x/5 - x**3 - y**5)*exp(-x**2-y**2) \
    - 1/3*exp(-(x+1)**2 - y**2)

# 转换为Python函数
f_xy_fcn = lambdify([x,y], f_xy)

# 创建网格
x_vals = np.linspace(-3, 3, 100)
y_vals = np.linspace(-3, 3, 100)
X, Y = np.meshgrid(x_vals, y_vals)
Z = f_xy_fcn(X, Y)

from scipy.stats import norm
import matplotlib.pyplot as plt
import numpy as np

# 创建5x5的子图网格
fig, axs = plt.subplots(nrows=5, ncols=5, figsize=(10, 10))

x_array = np.linspace(-5, 5, 200)
mu_array = [-2, -1, 0, 1, 2]
sigma_array = [0.5, 0.75, 1, 1.5, 2]

# 使用meshgrid生成参数组合
mu_array_, sigma_array_ = np.meshgrid(mu_array, sigma_array)

# 遍历每个子图
for mu_idx, sigma_idx, ax in zip(mu_array_.ravel(), 
                                   sigma_array_.ravel(), 
                                   axs.ravel()):
    # 计算一元高斯分布PDF
    pdf_vals = norm.pdf(x_array, loc=mu_idx, scale=sigma_idx)
    
    # 绘制曲线
    ax.plot(x_array, pdf_vals, 'b-', linewidth=1.5)
    ax.fill_between(x_array, pdf_vals, alpha=0.2)
    
    # 设置标题
    ax.set_title(f'μ={mu_idx}, σ={sigma_idx}', fontsize=8)
    ax.set_xlim(-5, 5)
    ax.set_ylim(0, None)
    
plt.tight_layout()
plt.show()

from scipy.stats import beta

x_array = np.linspace(0, 1, 200)
alpha_array = [0.5, 1, 2, 4, 8]
beta_array = [0.5, 1, 2, 4, 8]

fig, axs = plt.subplots(nrows=5, ncols=5, figsize=(10, 10))

alpha_array_, beta_array_ = np.meshgrid(alpha_array, beta_array)

for alpha_idx, beta_idx, ax in zip(alpha_array_.ravel(), 
                                     beta_array_.ravel(), 
                                     axs.ravel()):
    pdf_vals = beta.pdf(x_array, alpha_idx, beta_idx)
    ax.plot(x_array, pdf_vals, 'r-', linewidth=1.5)
    ax.fill_between(x_array, pdf_vals, alpha=0.2, color='red')
    ax.set_title(f'α={alpha_idx}, β={beta_idx}', fontsize=8)
    ax.set_xlim(0, 1)
    
plt.tight_layout()

import matplotlib.pyplot as plt
import numpy as np

# 生成二元高斯分布随机数
mean = [0, 0]
cov = [[1, 1], [1, 2]]
x, y = np.random.multivariate_normal(mean, cov, 1000).T

# 创建4x4的GridSpec
fig = plt.figure(figsize=(6, 6))
grid = plt.GridSpec(4, 4, hspace=0.3, wspace=0.3)

# 主图占据右上3x3区域
main_ax = fig.add_subplot(grid[:-1, 1:])
# x轴边缘直方图占据底部1x3区域
x_hist = fig.add_subplot(grid[-1, 1:], yticklabels=[])
# y轴边缘直方图占据左侧3x1区域
y_hist = fig.add_subplot(grid[:-1, 0], xticklabels=[])

# 绘制散点图
main_ax.plot(x, y, 'ob', markersize=3, alpha=0.2)
main_ax.set_xticks([])
main_ax.set_yticks([])

# 绘制x边缘直方图
x_hist.hist(x, 40, orientation='vertical', color='b',
            edgecolor='white', linewidth=0.5)
x_hist.invert_yaxis()  # 反转y轴，让直方图向下
x_hist.set_xticks([])
x_hist.set_yticks([])

# 绘制y边缘直方图
y_hist.hist(y, 40, orientation='horizontal', color='b',
            edgecolor='white', linewidth=0.5)
y_hist.invert_xaxis()  # 反转x轴，让直方图向左
y_hist.set_xticks([])
y_hist.set_yticks([])

plt.show()

数学关系：

import scipy.stats as stats
import matplotlib.gridspec as gridspec

# Dirichlet参数
alpha_1, alpha_2, alpha_3 = 2, 2, 2
alpha_0 = alpha_1 + alpha_2 + alpha_3

# 创建网格
x1 = np.linspace(0, 1, 201)
x2 = np.linspace(0, 1, 201)
xx1, xx2 = np.meshgrid(x1, x2)
xx3 = 1.0 - xx1 - xx2
xx3 = np.where(xx3 > 0.0, xx3, np.nan)

# 计算Dirichlet PDF
alphas = np.array([alpha_1, alpha_2, alpha_3])
rv = stats.dirichlet(alphas)
PDF_ff = rv.pdf(np.array([xx1.ravel(), xx2.ravel(), xx3.ravel()]))
PDF_ff = np.reshape(PDF_ff, xx1.shape)

# 计算边缘Beta分布
beta_1 = alpha_0 - alpha_1
f_x1 = stats.beta.pdf(x1, alpha_1, beta_1)

beta_2 = alpha_0 - alpha_2
f_x2 = stats.beta.pdf(x2, alpha_2, beta_2)

# 创建2x2 GridSpec布局
fig = plt.figure(figsize=(6, 6))
gs = gridspec.GridSpec(2, 2, 
                       width_ratios=[3, 1], 
                       height_ratios=[3, 1])

# 左上：联合分布等高线
ax1 = plt.subplot(gs[0])
ax1.contour(xx1, xx2, PDF_ff, 20, cmap='RdYlBu_r')
ax1.set_title(f'Dirichlet({alpha_1}, {alpha_2}, {alpha_3})')

# 右上：x₂边缘分布
ax2 = plt.subplot(gs[1])
ax2.plot(f_x2, x2, color='#0070C0')
ax2.fill_between(f_x2, x2, alpha=0.2)
ax2.set_xlabel('PDF')
ax2.invert_xaxis()

# 左下：x₁边缘分布
ax3 = plt.subplot(gs[2])
ax3.plot(x1, f_x1, color='#0070C0')
ax3.fill_between(x1, f_x1, alpha=0.2)
ax3.set_ylabel('PDF')

# 右下：隐藏
ax4 = plt.subplot(gs[3])
ax4.set_visible(False)

import matplotlib.pyplot as plt
import numpy as np

def squiggle_xy(a, b, c, d, i=np.arange(0.0, 2*np.pi, 0.05)):
    """生成参数化曲线"""
    return np.sin(i*a)*np.cos(i*b), np.sin(i*c)*np.cos(i*d)

fig = plt.figure(figsize=(8, 8), constrained_layout=False)

# 创建4x4的外层网格
outer_grid = fig.add_gridspec(4, 4, wspace=0, hspace=0)

# 在每个外层单元格中创建3x3的内层网格
for a in range(4):
    for b in range(4):
        # 嵌套GridSpec
        inner_grid = outer_grid[a, b].subgridspec(3, 3, 
                                                   wspace=0, hspace=0)
        axs = inner_grid.subplots()  # 创建内层所有子图
        
        # 在每个内层子图中绘制参数曲线
        for (c, d), ax in np.ndenumerate(axs):
            ax.plot(*squiggle_xy(a + 1, b + 1, c + 1, d + 1))
            ax.set(xticks=[], yticks=[])

# 只显示最外层边框
for ax in fig.get_axes():
    ss = ax.get_subplotspec()
    ax.spines.top.set_visible(ss.is_first_row())
    ax.spines.bottom.set_visible(ss.is_last_row())
    ax.spines.left.set_visible(ss.is_first_col())
    ax.spines.right.set_visible(ss.is_last_col())

plt.show()