DEMAPP08¶
Compute function inverse via collocation¶
In [1]:
from demos.setup import np, plt, demo
from compecon import BasisChebyshev, NLP, nodeunif
%matplotlib inline
Approximation structure¶
In [2]:
n, a, b = 31, 1, 5
F = BasisChebyshev(n, a, b) # define basis functions
x = F.nodes # compute standard nodes
Residual function¶
In [3]:
def resid(c):
F.c = c # update basis coefficients
f = F(x) # interpolate at basis nodes x
return f ** -2 + f ** -5 - 2 * x
Compute function inverse¶
In [4]:
c0 = np.zeros(n) # set initial guess for coeffs
c0[0] = 0.2
problem = NLP(resid)
F.c = problem.broyden(c0) # compute coeff by Broyden's method
Plot setup¶
In [5]:
n = 1000
x = nodeunif(n, a, b)
r = resid(F.c)
Plot function inverse¶
In [6]:
demo.figure('Implicit Function', 'x', 'f(x)')
plt.plot(x, F(x))
Out[6]:
Plot residual¶
In [7]:
demo.figure('Functional Equation Residual', 'x', 'Residual')
plt.hlines(0, a, b, 'k', '--')
plt.plot(x, r)
Out[7]:
