python数据可视化--使用matplotlib绘制二元高斯分布的3D图像

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均值为（0，0），变量之间相互独立时，根据官网给出的教程

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D

X = np.arange(-5, 5, 0.25)
Y = np.arange(-5, 5, 0.25)
X, Y = np.meshgrid(X, Y)
R = np.exp((-0.5)*((X*X)+(Y*Y)))
Z = R

fig = plt.figure()
ax = Axes3D(fig)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, alpha=0.5, cmap=cm.coolwarm)

plt.show()

如图：

当均值为（0,0）,变量之间不是相互独立时：

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d 
from matplotlib import cm
import matplotlib as mpl
import math
num = 200
l = np.linspace(-5,5,num)
X,Y = np.meshgrid(l,l)

u = np.array([0,0])                                                       #均值
o = np.array([[1,0.5],[0.5,1]])                                           #协方差矩阵

pos = np.concatenate((np.expand_dims(X,axis=2),np.expand_dims(Y,axis=2)),axis=2)  #定义坐标点

a = np.dot((pos-u),np.linalg.inv(o))  #o的逆矩阵
b = np.expand_dims(pos-u,axis=3)
# Z = np.dot(a.reshape(200*200,2),(pos-u).reshape(200*200,2).T)
Z = np.zeros((num,num),dtype=np.float32)                
for i in range(num):
    Z[i] = [np.dot(a[i,j],b[i,j]) for j in range(num)]                         #计算指数部分

Z = np.exp(Z*(-0.5))/(2*np.pi*math.sqrt(np.linalg.det(o)))

fig = plt.figure()                                                              #绘制图像
ax = fig.add_subplot(111,projection='3d')
ax.plot_surface(X,Y,Z,rstride=2,cstride=2,alpha=0.6,cmap=cm.coolwarm)

cset = ax.contour(X,Y,Z,10,zdir='z',offset=0,cmap=cm.coolwarm)                     #绘制xy面投影
cset = ax.contour(X,Y,Z,zdir = 'x',offset=-4,cmap = mpl.cm.winter)                 #绘制zy面投影
cset = ax.contour(X,Y,Z,zdir = 'y',offset= 4,cmap =mpl.cm.winter)                  #绘制zx面投影

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')

plt.show()

结果如下：