Create a 2D array that is the product of two functions

Question

I am working on a visualization and trying to create a 2D array that is the product of a normalized Gaussian function on the X axis and a normalized exponential function on the Y axis (using Python).

you are not asking for help, you are asking for the code. What have you done? Where do you have problems? StackOverflow is not for others do your homework. — , Aug 12 '15 at 15:19
It's not my homework. I'm a designer working on a visualization. I have defined the problem I am trying to solve but I don't have any experience translating math to code (or much experience with math). — Zachary Russell Heineman, Aug 12 '15 at 15:28

xnx · Answer 1 · 2015-08-12T16:42:58.603

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)

Great. Thank you. Is there an easy implementation without NumPy? — Zachary Russell Heineman, Aug 12 '15 at 16:38
See my edit: it's not too hard to do, but does require some extra work — xnx, Aug 12 '15 at 16:43

score 0 · Answer 2 · answered Aug 12 '15 at 17:05

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]

Create a 2D array that is the product of two functions

2 Answers2