在3D中绘制正态分布
问题描述:
我想绘制两个正态分布变量的comun分布。在3D中绘制正态分布
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()
答
这听起来像你在找什么是Multivariate Normal Distribution。这是在scipy中实现的,如scipy.stats.multivariate_normal。记住你正在向函数传递一个协方差矩阵是很重要的。因此,为了简单起见保持断开对角线元素是0:
[X variance , 0 ]
[ 0 ,Y Variance]
下面是使用该功能,并产生所得到的分布的3D图的例子。我添加了颜色表以使看到曲线更容易,但随时可以将其删除。
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()
编辑
一个简单verision是avalible通过matplotlib.mlab.bivariate_normal 它采用下列参数,所以你不必担心矩阵 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述图形:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.mlab import biivariate_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()
可以定义 'comun' 分配? matplotlib3d有很多例子可以帮助你做你需要的东西 http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html – jm22b