Illustrates integration using Simpson’s rule
Contents
Illustrates integration using Simpson’s rule¶
Randall Romero Aguilar, PhD
This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.
Original (Matlab) CompEcon file: demqua08.m
Running this file requires the Python version of CompEcon. This can be installed with pip by running
!pip install compecon --upgrade
Last updated: 2022-Oct-23
Initial tasks¶
from numpy import poly1d,polyfit, linspace
from compecon import qnwsimp
import matplotlib.pyplot as plt
n = 1001
xmin, xmax = -1, 1
xwid = xmax-xmin
x = linspace(xmin, xmax, n)
f = poly1d([2.0, -1.0, 0.5, 5.0])
def fitquad(xi):
newcoef = polyfit(xi, f(xi), 2)
return poly1d(newcoef)
def plot_simp(n):
xi, wi = qnwsimp(n+1, xmin, xmax)
fig, ax = plt.subplots()
ax.plot(x, f(x), linewidth=3)
for k in range(n//2):
xii = xi[(2*k):(2*k+3)]
xiii = linspace(xii[0], xii[2], 125)
p = fitquad(xii)
ax.fill_between(xiii, p(xiii), alpha=0.35, color='LightSkyBlue')
ax.plot(xiii, p(xiii), color='Tab:Orange', linestyle='--')
ax.vlines(xi, 0, f(xi), color='Tab:Orange', linestyle=':')
ax.axhline(0,color='k',linewidth=2)
xtl = [f'$x_{i}$' for i in range(n+1)]
xtl[0] += '=a'
xtl[n] += '=b'
ax.set(xlim=[xmin-0.1, xmax+0.1],
xticks=xi,
xticklabels=xtl,
yticks=[0],
yticklabels=['0'])
plt.legend([r'$f(x)$', f'$\\tilde{{f}}_{n+1}(x)$'])
return fig
figs = [plot_simp(n) for n in [2, 4, 8]]
