Example of using IndexedBase in order to do for loops in Sympy for memory conservation

SympyGaussians.py

import sympy as sp
import matplotlib.pyplot as plt
import numpy as np

def Gaussian(x, a, xc, sigma):
    return a*sp.exp(-((x-xc)**2)/(2*sigma**2))

x, i, n = sp.symbols('x i n') # x is our main independent variable. i and n are indices
a, xc, sigma = sp.symbols('A xc sigma', cls=sp.IndexedBase) # parameters that are held in arrays
symbols = (x, a, xc, sigma, n)

Gauss = Gaussian(x, a[i], xc[i], sigma[i])
model = sp.Sum(Gauss, (i, 0, n-1)) # Sum over the parameters from (i=0 to i=n)
func = sp.lambdify(symbols, model, modules = 'numpy')

X = np.arange(100)
N = 10
A, XC, SIGMA = np.random.random((3, N))*100
y = func(X, A, XC, SIGMA, N)

plt.figure()
plt.plot(y)