def basis(i,L):
"Gen Laguerre basis function with weight"
from scipy.special.orthogonal import genlaguerre
a = 2*L+2
lan = genlaguerre(i,a)
def f(x): return pow(x,a)*exp(-x)*lan(x)
return f
def __F_n(n):
"""F_n(q) = \chi_n \exp(-q^2 / 2\zeta) P_n(q)
and P_n(q) = q^2 / zeta * L_n^{5/2}(q^2 / zeta)"""
if n == -1:
return np.poly1d([1.0])
else:
a = np.poly1d([1, 0.0, 0.0])
return a * genlaguerre(n, 2.5)(a)
def coeffs_harmonicBasis(n, l, r0):
"""
Calculates the coefficients of the polynomial that defines the
radial harmonic basis function of degree n and angular momentum order l
r0 is the scale of the harmonic basis function
returns \tilde{g}^{nl}_s given the following
r^l L^{l+1/2}_n = \sum_{s=l}^{n+l} \tilde{g}^{nl}_s r^s,
"""
N = norm_harmonicBasis(n, l, r0)
coeffs = np.zeros(2 * n + l + 1)
coeffs[l::2] = genlaguerre(n, l + 0.5).coeffs[::-1]
coeffs *= N
return coeffs
def test_regression(self):
assert_equal(orth.genlaguerre(1, 1, monic=False)(0), 2.)
assert_equal(orth.genlaguerre(1, 1, monic=True)(0), -2.)
assert_equal(orth.genlaguerre(1, 1, monic=False), np.poly1d([-1, 2]))
assert_equal(orth.genlaguerre(1, 1, monic=True), np.poly1d([1, -2]))
def test_regression(self):
assert_equal(orth.genlaguerre(1, 1, monic=False)(0), 2.)
assert_equal(orth.genlaguerre(1, 1, monic=True)(0), -2.)
assert_equal(orth.genlaguerre(1, 1, monic=False), np.poly1d([-1, 2]))
assert_equal(orth.genlaguerre(1, 1, monic=True), np.poly1d([1, -2]))
def radial_function(r, n, zeta):
"Computes the radial part of the SPF basis."
return genlaguerre(n, 0.5)(r**2 / zeta) * \
np.exp(- r**2 / (2 * zeta)) * \
kappa(zeta, n)
def radial_function(r, n, zeta):
"Computes the radial part of the mSPF basis."
return genlaguerre(n, 2.5)(r**2 / zeta) * \
r**2 / zeta * np.exp(- r**2 / (2 * zeta)) * chi(zeta, n)
def radial_function(r, n, zeta):
"Computes the radial part of the SPF basis."
return genlaguerre(n, 0.5)(r**2 / zeta) * \
np.exp(- r**2 / (2 * zeta)) * \
kappa(zeta, n)
