创建一个二维数组，该数组是两个函数的乘积

Question

我正在进行可视化工作，并尝试创建一个二维数组，该数组是X轴上的标准化高斯函数和Y轴上的标准化指数函数（使用Python）的乘积。

Answer 1

I would use NumPy for this. You can use np.meshgrid to create the (X, Y) axes and use NumPy's vectorized functions to create the function on these coordinates. The array f below is your two-dimensional array, here containing the product of exp(-X/4) and exp(-((Y-2)/1.5)**2) . (Substitute your own normalized functions here.)

import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(0,10,100)
y = np.linspace(0,5,100)
X, Y = np.meshgrid(x, y)
f = np.exp(-X/4.) * np.exp(-((Y-2)/1.5)**2)

fig = plt.figure()
ax = fig.add_subplot(111)
ax.imshow(f)
plt.show()

If you can't or don't want to use NumPy, you'll have to loop by hand and use conventional math functions:

import math
dx, dy = 0.1, 0.05
nx, ny = 101, 101
f = [[None]*nx for i in range(ny)]
for ix in range(nx):
    x = xmin + dx*ix
    for iy in range(ny):
        y = ymin + dy*iy
        f[iy][ix] = math.exp(-x/4.) * math.exp(-((y-2)/1.5)**2)

Answer 2

I would use numpy for this, because numpy makes it very simple to do what you want. If you can't use it, then something like the following should work:

import math

def gauss(x, mu=0.0, sigma=1.0):
    return 1.0 / math.sqrt(2.0*math.pi*sigma**2) * math.exp(-0.5*(x-mu)**2/sigma**2)

def exponential(x, lam=1.0):
    return lam * math.exp(-lam * x)

# X values from -10 to 10 with 0.01 step size
xvals = [x * 0.01 for x in range(-1000, 1001)]
# Y values from 0 to 10 with 0.01 step size
yvals = [y * 0.01 for y in range(0, 1001)]
# Calculate your function at the grid points
f = [[gauss(x)*exponential(y) for x in xvals] for y in yvals]