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Christoffel-Darboux recurrence relation for orthogonal polynomials using numpy
# this is a translation of orthpoly.ado from Stata 11. Their license likely applies.
def orthpoly(X, deg, weights=None):
Christoffel-Darboux recurrence relation for orthogonal polynomials.
nobs = len(X)
orth_poly = np.ones((nobs, deg+1))
for i in range(1, deg+1):
t = X*orth_poly[:,i-1]**2
b = np.average(t, weights=weights)
t = X*t
a = np.average(t, weights=weights)
if i > 1:
k = i - 2
t = X*orth_poly[:,i-1]*orth_poly[:,i-2]
c = np.average(t, weights=weights)
k = 0
c = 0
a = 1/np.sqrt(a - b**2 - c**2)
b *= -a
c *= a
orth_poly[:,i] = (a*X + b)*orth_poly[:,i-1] - c * orth_poly[:,k]
return orth_poly[:,1:]

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jseabold commented Apr 13, 2015

A one-liner free of any license issues, but not numerically sound given the Vandermonde expansion.

poly = lambda x, degree : np.linalg.qr(np.vander(x, degree + 1)[:, ::-1])[0][:, 1:]
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