绘制3D中的正态分布

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的分布式变量。用于绘制两个正态分布式变量的代码是什么？

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

听起来你正在寻找的是Multivariate Normal Distribution。这在scipy中实现为scipy.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，为了保持简单，请将对角线元素保持为零：

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

以下是使用此功能并生成所得分布的3D图的示例。我添加了色彩图，以便更容易看到曲线，但可以随意将其删除。

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()

给你这个情节：

修改

通过matplotlib.mlab.bivariate_normal可以进行更简单的检查 它需要以下参数，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X和Y再次是meshgrid的结果，所以使用它来重新创建上面的图：

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()

，并提供：

Answer 2

虽然其他答案很好，但我希望获得相似的结果，同时还要用样本的散点图说明分布。

更多详细信息请参见：Python 3d plot of multivariate gaussian distribution

结果如下：

并使用以下代码生成：

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


# Sample parameters
mu = np.array([0, 0])
sigma = np.array([[0.7, 0.2], [0.2, 0.3]])
rv = multivariate_normal(mu, sigma)
sample = rv.rvs(500)

# Bounds parameters
x_abs = 2.5
y_abs = 2.5
x_grid, y_grid = np.mgrid[-x_abs:x_abs:.02, -y_abs:y_abs:.02]

pos = np.empty(x_grid.shape + (2,))
pos[:, :, 0] = x_grid
pos[:, :, 1] = y_grid

levels = np.linspace(0, 1, 40)

fig = plt.figure()
ax = fig.gca(projection='3d')

# Removes the grey panes in 3d plots
ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))

# The heatmap
ax.contourf(x_grid, y_grid, 0.1 * rv.pdf(pos),
            zdir='z', levels=0.1 * levels, alpha=0.9)

# The wireframe
ax.plot_wireframe(x_grid, y_grid, rv.pdf(
    pos), rstride=10, cstride=10, color='k')

# The scatter. Note that the altitude is defined based on the pdf of the
# random variable
ax.scatter(sample[:, 0], sample[:, 1], 1.05 * rv.pdf(sample), c='k')

ax.legend()
ax.set_title("Gaussian sample and pdf")
ax.set_xlim3d(-x_abs, x_abs)
ax.set_ylim3d(-y_abs, y_abs)
ax.set_zlim3d(0, 1)

plt.show()

Answer 3

下面对@Ianhi的代码的以下修改将返回上述3D图的轮廓图版本。

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()