如何让Python费米-狄拉克分布程序实现交互？排查非交互问题

我修改了一篇动态可视化示例代码，目标是让它能在Jupyter Notebook以外的环境运行，但当前程序仅能生成动画GIF文件，滑块交互功能完全失效，以下是原代码：

#Based on the example here
# https://towardsdatascience.com/intro-to-dynamic-visualization-with-python-animations-and-interactive-plots-f72a7fb69245

# # Import packages
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
import numpy.typing as npt
from matplotlib.animation import FuncAnimation
from matplotlib.widgets import Slider

# Fermi-Dirac Distribution
def fermi(E: npt.NDArray[np.float64], E_f: float, T: float) -> npt.NDArray[np.float64]:
    k_b = 8.617 * (10**-5) # eV/K
    return 1/(np.exp((E - E_f)/(k_b * T)) + 1)

# Animation function
def animate(i):
    x = np.linspace(0, 1, 100)
    y = fermi(x, 0.5, T[i])
    f_d.set_data(x, y)
    f_d.set_color(colors(i))
    temp.set_text(str(int(T[i])) + ' K')
    temp.set_color(colors(i))

# Update values
def update(val):
    Ef = s_Ef.val
    T = s_T.val
    f_d.set_data(x, fermi(x, Ef, T))
    fig.canvas.draw_idle()

# Create sliders
s_Ef = Slider(ax=ax_Ef, label='Fermi Energy ', valmin=0, valmax=1.0,
              valfmt=' %1.1f eV', facecolor='#cc7000')
              
s_T = Slider(ax=ax_T, label='Temperature ', valmin=100, valmax=1000, 
             valinit=100, valfmt='%i K', facecolor='#cc7000')

# General plot parameters
mpl.rcParams['font.size'] = 18

mpl.rcParams['axes.linewidth'] = 2
mpl.rcParams['axes.spines.top'] = False
mpl.rcParams['axes.spines.right'] = False

mpl.rcParams['xtick.major.size'] = 10
mpl.rcParams['xtick.major.width'] = 2
mpl.rcParams['ytick.major.size'] = 10
mpl.rcParams['ytick.major.width'] = 2

# Temperature values
T = np.linspace(100, 1000, 10)

# Get colors
colors = mpl.colormaps['copper'].resampled(8)

# Create figure and add axes
fig = plt.figure(figsize=(6, 4))
ax = fig.add_subplot(111)

# Add legend
labels = ['100 K', '200 K', '300 K', '400 K', '500 K', '600 K', 
          '700 K', '800 K', '900 K', '1000 K']

ax.legend(labels, bbox_to_anchor=(1.05, -0.1), loc='lower left', 
          frameon=False, labelspacing=0.2)

# Create variable reference to plot
f_d, = ax.plot([], [], linewidth=2.5)

# Add text annotation and create variable reference
temp = ax.text(1, 1, '', ha='right', va='top', fontsize=24)

# Create main axis
fig.subplots_adjust(bottom=0.2, top=0.75)

# Create axes for sliders
ax_Ef = fig.add_axes([0.3, 0.85, 0.4, 0.05])
ax_Ef.spines['top'].set_visible(True)
ax_Ef.spines['right'].set_visible(True)

ax_T = fig.add_axes([0.3, 0.92, 0.4, 0.05])
ax_T.spines['top'].set_visible(True)
ax_T.spines['right'].set_visible(True)

# Plot default data
x = np.linspace(0, 1, 100)
Ef_0 = 0.5
T_0 = 100
y = fermi(x, Ef_0, T_0)
f_d, = ax.plot(x, y, linewidth=2.5)

s_Ef.on_changed(update)
s_T.on_changed(update)

# Create animation
ani = FuncAnimation(fig=fig, func=animate, frames=range(len(T)), interval=500, repeat=True)

# Save and show animation
ani.save('AnimatedPlot.gif', writer='pillow', fps=2)

问题根源及修复步骤 #

1. 滑块初始化顺序错误
   原代码在创建滑块轴ax_Ef、ax_T之前就初始化了滑块s_Ef、s_T，导致程序找不到对应轴对象直接崩溃。必须先创建滑块轴，再初始化滑块。

2. 变量名冲突
   全局温度数组T和update函数内的局部变量T = s_T.val重名，覆盖了全局数组，导致动画功能失效。将局部变量重命名为temp_val避免冲突。

3. 重复创建绘图对象
   原代码先后两次执行f_d, = ax.plot(...)，第二次创建的对象覆盖了第一次的引用，导致动画的绘图更新失效。只保留一次初始化即可。

4. 缺失交互窗口启动代码
   非Jupyter环境下，必须调用plt.show()启动Matplotlib交互窗口，原代码仅保存GIF未启动窗口，因此看不到交互界面。

5. 颜色映射调用错误
   colors(i)的调用方式错误，Matplotlib colormap需要接收0-1之间的数值，应改为colors(i/len(T))来正确映射颜色梯度。

6. 无效图例设置
   原代码直接添加温度标签作为图例，但没有对应的绘图系列，图例显示为空。可删除该部分，或调整为对应动画的颜色图例。

修复后的完整代码 #

import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy.typing as npt
from matplotlib.animation import FuncAnimation
from matplotlib.widgets import Slider

# Fermi-Dirac Distribution
def fermi(E: npt.NDArray[np.float64], E_f: float, T: float) -> npt.NDArray[np.float64]:
    k_b = 8.617 * (10**-5) # eV/K
    return 1/(np.exp((E - E_f)/(k_b * T)) + 1)

# Animation function
def animate(i):
    x = np.linspace(0, 1, 100)
    y = fermi(x, 0.5, temp_array[i])
    f_d.set_data(x, y)
    color = colors(i/len(temp_array))
    f_d.set_color(color)
    temp.set_text(f"{int(temp_array[i])} K")
    temp.set_color(color)

# Update values
def update(val):
    Ef = s_Ef.val
    temp_val = s_T.val
    y = fermi(x, Ef, temp_val)
    f_d.set_data(x, y)
    # 更新文本显示当前滑块温度
    temp.set_text(f"{int(temp_val)} K")
    fig.canvas.draw_idle()

# General plot parameters
mpl.rcParams['font.size'] = 18
mpl.rcParams['axes.linewidth'] = 2
mpl.rcParams['axes.spines.top'] = False
mpl.rcParams['axes.spines.right'] = False
mpl.rcParams['xtick.major.size'] = 10
mpl.rcParams['xtick.major.width'] = 2
mpl.rcParams['ytick.major.size'] = 10
mpl.rcParams['ytick.major.width'] = 2

# Temperature values (重命名避免冲突)
temp_array = np.linspace(100, 1000, 10)

# Get colors
colors = mpl.colormaps['copper'].resampled(len(temp_array))

# Create figure and add axes
fig = plt.figure(figsize=(6, 4))
ax = fig.add_subplot(111)

# 设置坐标轴范围，避免动画/交互时图形偏移
ax.set_xlim(0, 1)
ax.set_ylim(0, 1.1)
ax.set_xlabel("Energy (eV)")
ax.set_ylabel("Fermi-Dirac Probability")

# Add text annotation and create variable reference
temp = ax.text(1, 1, '', ha='right', va='top', fontsize=24)

# Create main axis layout
fig.subplots_adjust(bottom=0.2, top=0.75)

# Create axes for sliders (先创建轴)
ax_Ef = fig.add_axes([0.3, 0.85, 0.4, 0.05])
ax_Ef.spines['top'].set_visible(True)
ax_Ef.spines['right'].set_visible(True)

ax_T = fig.add_axes([0.3, 0.92, 0.4, 0.05])
ax_T.spines['top'].set_visible(True)
ax_T.spines['right'].set_visible(True)

# Create sliders (后初始化滑块)
s_Ef = Slider(ax=ax_Ef, label='Fermi Energy ', valmin=0, valmax=1.0,
              valinit=0.5, valfmt=' %1.1f eV', facecolor='#cc7000')
              
s_T = Slider(ax=ax_T, label='Temperature ', valmin=100, valmax=1000, 
             valinit=100, valfmt='%i K', facecolor='#cc7000')

# Plot default data and get reference
x = np.linspace(0, 1, 100)
Ef_0 = 0.5
T_0 = 100
y = fermi(x, Ef_0, T_0)
f_d, = ax.plot(x, y, linewidth=2.5)

# Bind slider update events
s_Ef.on_changed(update)
s_T.on_changed(update)

# Create animation
ani = FuncAnimation(fig=fig, func=animate, frames=range(len(temp_array)), interval=500, repeat=True)

# Save animation (可选)
ani.save('AnimatedPlot.gif', writer='pillow', fps=2)

# 启动交互窗口，非Jupyter环境必须调用
plt.show()

内容的提问来源于stack exchange，提问作者user3877654