在3D中绘制正态分布 [英] Plot normal distribution in 3D

问题描述

我正在尝试绘制两个正态分布变量的公共分布.

I am trying to plot the comun distribution of two normal distributed variables.

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?

The code below plots one normal distributed variable. What would the code be for plotting two normal distributed variables?

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()

推荐答案

听起来您正在寻找的是 scipy实现. stats.multivariate_normal .重要的是要记住，您正在将协方差矩阵传递给函数.因此，为了简单起见，请将对角线元素设为零:

It sounds like what you're looking for is a Multivariate Normal Distribution. This is implemented in scipy as scipy.stats.multivariate_normal. It's important to remember that you are passing a covariance matrix to the function. So to keep things simple keep the off diagonal elements as zero:

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

这里是使用此功能并生成结果分布的3D图的示例.我添加了颜色图，以使查看曲线更容易，但可以随时将其删除.

Here is an example using this function and generating a 3D plot of the resulting distribution. I add the colormap to make seeing the curves easier but feel free to remove it.

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()

为您提供此情节:

通过 matplotlib.mlab.bivariate_normal 它采用以下参数，因此您无需担心矩阵 matplotlib.mlab.bivariate_normal(X, Y, sigmax=1.0, sigmay=1.0, mux=0.0, muy=0.0, sigmaxy=0.0) 这里的X和Y再次是网状网格的结果，因此使用它来重新创建上面的图:

A simpler version is available through matplotlib.mlab.bivariate_normal It takes the following arguments so you don't need to worry about matrices matplotlib.mlab.bivariate_normal(X, Y, sigmax=1.0, sigmay=1.0, mux=0.0, muy=0.0, sigmaxy=0.0) Here X, and Y are again the result of a meshgrid so using this to recreate the above plot:

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()

提供:

Giving:

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