<p>可能这个答案对于@Coolcrab来说已经太迟了,但是我想把它留在这里以供将来参考。</p>
<p>可以使用多元高斯公式,如下所示</p>
<p><a href="https://i.stack.imgur.com/rcpmi.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/rcpmi.png" alt="enter image description here"/></a></p>
<p>更改平均元素将更改原点,而更改协方差元素将更改形状(从圆到椭圆)。</p>
<p><a href="https://i.stack.imgur.com/cjWE0.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/cjWE0.png" alt="enter image description here"/></a></p>
<p>代码如下:</p>
<pre><code>import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
# Our 2-dimensional distribution will be over variables X and Y
N = 40
X = np.linspace(-2, 2, N)
Y = np.linspace(-2, 2, N)
X, Y = np.meshgrid(X, Y)
# Mean vector and covariance matrix
mu = np.array([0., 0.])
Sigma = np.array([[ 1. , -0.5], [-0.5, 1.]])
# Pack X and Y into a single 3-dimensional array
pos = np.empty(X.shape + (2,))
pos[:, :, 0] = X
pos[:, :, 1] = Y
def multivariate_gaussian(pos, mu, Sigma):
"""Return the multivariate Gaussian distribution on array pos."""
n = mu.shape[0]
Sigma_det = np.linalg.det(Sigma)
Sigma_inv = np.linalg.inv(Sigma)
N = np.sqrt((2*np.pi)**n * Sigma_det)
# This einsum call calculates (x-mu)T.Sigma-1.(x-mu) in a vectorized
# way across all the input variables.
fac = np.einsum('...k,kl,...l->...', pos-mu, Sigma_inv, pos-mu)
return np.exp(-fac / 2) / N
# The distribution on the variables X, Y packed into pos.
Z = multivariate_gaussian(pos, mu, Sigma)
# plot using subplots
fig = plt.figure()
ax1 = fig.add_subplot(2,1,1,projection='3d')
ax1.plot_surface(X, Y, Z, rstride=3, cstride=3, linewidth=1, antialiased=True,
cmap=cm.viridis)
ax1.view_init(55,-70)
ax1.set_xticks([])
ax1.set_yticks([])
ax1.set_zticks([])
ax1.set_xlabel(r'$x_1$')
ax1.set_ylabel(r'$x_2$')
ax2 = fig.add_subplot(2,1,2,projection='3d')
ax2.contourf(X, Y, Z, zdir='z', offset=0, cmap=cm.viridis)
ax2.view_init(90, 270)
ax2.grid(False)
ax2.set_xticks([])
ax2.set_yticks([])
ax2.set_zticks([])
ax2.set_xlabel(r'$x_1$')
ax2.set_ylabel(r'$x_2$')
plt.show()
</code></pre>