Plot 二维矩阵方程或 3d 使用 matplotlib

Question

I have an equation as followed:

y = x^T * A * x + b^T * x + c

where x, b, c are vectors in n space and A is a nxn matrix.

I can plot a linear equation in matplotlib, but not sure how a matrix equation can be (if possible) shown also in a 3d plot.

I tried with following code, A is given matrix and w, c and b are column vectors. X and Y are mesh and Z is the solution.

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
# if using a Jupyter notebook, include:
%matplotlib inline

fig = plt.figure(figsize=(10,6))
ax1 = fig.add_subplot(111, projection='3d')

n = 50
i = -5.0
j = 5.0

A = np.random.randint(i, j, size=(n, n))
w = np.random.randint(i, j, size=(n, 1))
c = b = np.random.randint(i, j, size=(n, 1))

X,Y = np.meshgrid(n,n)
Z = w.T*A*w + b.T*w + c

mycmap = plt.get_cmap('gist_earth')
surf1 = ax1.plot_surface(X, A, Z, cmap=mycmap)
fig.colorbar(surf1, ax=ax1, shrink=0.5, aspect=10)

plt.show()

The resulting plot does not seem to be a satisfied plot.

Answer 1

There are two problems in your code: 1) meshgrid was being used incorrectly (it needs two arrays, not two ints); 2) in the surface plot, you were using X, A, Z instead of X, Y, Z -- X, A, Z will work, and might make sense, but I'm guessing it wasn't your intention.

Here's a working solution:

fig = plt.figure(figsize=(10,6))
ax1 = fig.add_subplot(111, projection='3d')

n = 10
i = -5.0
j = 5.0

A = np.random.randint(i, j, size=(n, n))
w = np.random.randint(i, j, size=(n, 1))
c = b = np.random.randint(i, j, size=(n, 1))

X,Y = np.meshgrid(np.arange(n),np.arange(n))
Z = w.T*A*w + b.T*w + c

mycmap = plt.get_cmap('gist_earth')
surf1 = ax1.plot_surface(X, Y, Z, cmap=mycmap)
fig.colorbar(surf1, ax=ax1, shrink=0.5, aspect=10)