三维正态分布图

Question

我试图绘制两个正态分布变量的comun分布。

下面的代码绘制了一个正态分布变量。绘制两个正态分布变量的代码是什么？

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.mlab as mlab
import math

mu = 0
variance = 1
sigma = math.sqrt(variance)
x = np.linspace(-3, 3, 100)
plt.plot(x,mlab.normpdf(x, mu, sigma))

plt.show()

Answer 1

下面对@Ianhi上面的代码进行的调整将返回上面3D绘图的等高线图版本。

import matplotlib.pyplot as plt
from matplotlib import style
style.use('fivethirtyeight')
import numpy as np
from scipy.stats import multivariate_normal




#Parameters to set
mu_x = 0
variance_x = 3

mu_y = 0
variance_y = 15

x = np.linspace(-10,10,500)
y = np.linspace(-10,10,500)
X,Y = np.meshgrid(x,y)

pos = np.array([X.flatten(),Y.flatten()]).T



rv = multivariate_normal([mu_x, mu_y], [[variance_x, 0], [0, variance_y]])


fig = plt.figure(figsize=(10,10))
ax0 = fig.add_subplot(111)
ax0.contour(rv.pdf(pos).reshape(500,500))



plt.show()

Answer 2

听起来你要找的是一个Multivariate Normal Distribution。这在scipy中实现为scipy.stats.multivariate_normal。重要的是要记住，你要传递一个协方差矩阵给函数。所以为了简单起见，将非对角元素保留为零：

[X variance ,     0    ]
[     0     ,Y Variance]

下面是一个使用此函数并生成结果分布的三维绘图的示例。我添加了colormap以使查看曲线更容易，但可以随意删除它。

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import multivariate_normal
from mpl_toolkits.mplot3d import Axes3D

#Parameters to set
mu_x = 0
variance_x = 3

mu_y = 0
variance_y = 15

#Create grid and multivariate normal
x = np.linspace(-10,10,500)
y = np.linspace(-10,10,500)
X, Y = np.meshgrid(x,y)
pos = np.empty(X.shape + (2,))
pos[:, :, 0] = X; pos[:, :, 1] = Y
rv = multivariate_normal([mu_x, mu_y], [[variance_x, 0], [0, variance_y]])

#Make a 3D plot
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(X, Y, rv.pdf(pos),cmap='viridis',linewidth=0)
ax.set_xlabel('X axis')
ax.set_ylabel('Y axis')
ax.set_zlabel('Z axis')
plt.show()

给你这个情节：

Matplotlib v2.2不赞成使用下面的编辑，并将在v3.1中删除

通过matplotlib.mlab.bivariate_normal提供更简单的版本 它接受以下参数，因此不必担心矩阵 matplotlib.mlab.bivariate_normal(X, Y, sigmax=1.0, sigmay=1.0, mux=0.0, muy=0.0, sigmaxy=0.0) 这里X和Y再次是网格网格的结果，因此使用它重新创建上面的绘图：

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

#Parameters to set
mu_x = 0
sigma_x = np.sqrt(3)

mu_y = 0
sigma_y = np.sqrt(15)

#Create grid and multivariate normal
x = np.linspace(-10,10,500)
y = np.linspace(-10,10,500)
X, Y = np.meshgrid(x,y)
Z = bivariate_normal(X,Y,sigma_x,sigma_y,mu_x,mu_y)

#Make a 3D plot
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(X, Y, Z,cmap='viridis',linewidth=0)
ax.set_xlabel('X axis')
ax.set_ylabel('Y axis')
ax.set_zlabel('Z axis')
plt.show()

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