如何求 f(x,y) 沿 x 和 y 的偏导数：del^2 f(x,y)/[del(x)][del (y)] in python

Question

我在 (xx,yy) 网格中定义了一个二维函数 f(x,y)。我想在数值上获得它的偏导数，如下所示。请注意，np.gradient 不执行此操作，因为它 returns 是沿每个轴的矢量场。

我该怎么做？这是我的代码：

import numpy as np
import matplotlib.pyplot as plt

x = np.arange(-5, 5, 0.1)
y = np.arange(-4, 4, 0.1)
xx, yy = np.meshgrid(x, y, sparse=True)
f = np.sin(xx**2 + yy**2) / (xx**2 + yy**2)
h = plt.contourf(x,y,f)
plt.show()

df=np.gradient(f,y,x) #Doesn't do my job
df=np.array(df)
print(df.shape)

# h = plt.contourf(x,y,df)   #This is what I want to plot.
# plt.show()

Answer 1

您需要调用np.gradient两次：

import numpy as np
import matplotlib.pyplot as plt

x = np.arange(-5, 5, 0.1)
y = np.arange(-4, 4, 0.1)
xx, yy = np.meshgrid(x, y, sparse=True)
f = np.sin(xx**2 + yy**2) / (xx**2 + yy**2)
h = plt.contourf(x,y,f)
plt.show()

dfy = np.gradient(f, y, axis=0)
dfxy = np.gradient(dfy, x, axis=1)
print(dfxy.shape)
# (80, 100)

h = plt.contourf(x, y, dfxy)
plt.show()

输出：

如何求 f(x,y) 沿 x 和 y 的偏导数：del^2 f(x,y)/[del(x)][del (y)] in python

How to find Partial derivative of f(x,y) along x and y: del^2 f(x,y)/[del(x)][del (y)] in python

python

calculus