output[0] = y0 ValueError: setting an array element with a sequence - numpy

Question

I have been struggling for a few days with this. I'm trying t estimate the density of a piecewise gaussian function. Could anyone tell me why I'm now getting the error
TypeError: output[0] = y0
ValueError: setting an array element with a sequence.
It happens on this line:
Zero_RG = integrate.romberg(gaussian(q,x,mu,sigma), Q1, Q2).`
Here is the script:
import numpy as np
import sympy as sp
from sympy import *
from scipy import integrate
from sympy import Integral, log, exp, sqrt, pi
import matplotlib.pyplot as plt
from scipy.stats import norm, gaussian_kde
from quantecon import LAE
from sympy import symbols
var('Q1 Q2 x q sigma mu')
#q= symbols('q')
## == Define parameters == #
mu=80
sigma=20
b=0.2
Q=80
Q1=Q*(1-b)
Q2=Q*(1+b)
d = (sigma*np.sqrt(2*np.pi))
phi = norm()
n = 500
def p(x, y):
x, y = np.array(x, dtype=float), np.array(y, dtype=float)
Positive_RG = norm.pdf(x-y+Q1, mu, sigma)
print('Positive_R = ', Positive_RG)
Negative_RG = norm.pdf(x-y+Q2, mu, sigma)
print('Negative_RG = ', Negative_RG)
gaussian = lambda q,x,mu,sigma: 1/(sigma*np.sqrt(2*np.pi))*np.exp(-(x+q-mu)**2 /(2*sigma**2))
wrapped_gaussian = lambda q: gaussian(q, x, mu, sigma)
Zero_RG = integrate.romberg(wrapped_gaussian, Q1, Q2)
print('pdf',gaussian)
#Zero_RG = scipy.integrate.quad(norm.pdf(x + q, mu, sigma))
# Int_zerocase= lambda q: norm.pdf(x + q, u, sigma)
# Zero_RG = scipy.integrate.quad(Int_zerocase, Q1, Q2)
# print(Zero_RG)
if y>0.0 and x -y>=-Q1:
#print('printA', Positive_RG)
return Positive_RG
elif y<0.0 and x -y>=-Q2:
#print('printC', Negative_RG)
return Negative_RG
elif y==0.0 and x >=-Q1:
#print('printB', Zero_RG)
return Zero_RG
return 0.0
Z = phi.rvs(n)
X = np.empty(n)
for t in range(n-1):
X[t+1] = X[t] + Z[t]
#X[t+1] = np.abs(X[t]) + Z[t]
psi_est = LAE(p, X)
k_est = gaussian_kde(X)
fig, ax = plt.subplots(figsize=(10,7))
ys = np.linspace(-200.0, 200.0, 200)
ax.plot(ys, psi_est(ys), 'g-', lw=2, alpha=0.6, label='look ahead estimate')
ax.plot(ys, k_est(ys), 'k-', lw=2, alpha=0.6, label='kernel based estimate')
ax.legend(loc='upper left')
plt.show()

Answer 1

The docs for romberg are pretty clear that the first argument is a function of a single variable that gets integrated.
First, a minor point. Use np.exp in preference to np.e**.
In Python, the expression
gaussian = lambda q,x,mu,sigma: 1/(sigma*np.sqrt(2*np.pi))*np.exp(-(x+q-mu)**2 /(2*sigma**2))
sets gaussian to a function of four arguments. The expression gaussian(q, x, mu, sigma) is just the return value of that function.
There are two ways to pass in the required parameters to the romberg. The easiest way is to use the args parameter to pass in the three additional arguments as a tuple:
Zero_RG = integrate.romberg(gaussian, Q1, Q2, args=(x,mu,sigma))
The other way is to create a wrapper function that will pass the arguments for you:
wrapped_gaussian = lambda q: gaussian(q, x, mu, sigma)
Zero_RG = integrate.romberg(wrapped_gaussian, Q1, Q2)
I would recommend the fist approach because it uses an existing mechanism, as well as being shorter and easier to read.