def calcWignerMatrices(self, rot):
a,b,y = rot
sinb2 = sin(b/2)
cosb2 = cos(b/2)
cosb = cos(b)
sinb = sin(b)
Jmax = self.Jmax
Js, m1s, m2s = self.Js, self.m1s, self.m2s
Ds = np.zeros((Jmax+1, 2*Jmax+1, 2*Jmax+1), np.complex128)
grad = np.zeros((3, Jmax+1, 2*Jmax+1, 2*Jmax+1), np.complex128)
mu = abs(m1s-m2s)
nu = abs(m1s+m2s)
s = Js - (mu + nu)/2
xi = np.ones_like(s)
xi[m2s<m1s] = (-1)**(m1s-m2s)[m2s<m1s]
factor = sqrt(factorial(s)*factorial(s+mu+nu)/
factorial(s+mu)/factorial(s+nu)) * xi
jac = eval_jacobi(s, mu, nu, cosb)
d = (factor * jac * sinb2 ** mu * cosb2 ** nu)
##
gradjac = eval_grad_jacobi(s, mu, nu, cosb) * - sinb
gradd = (factor * gradjac * sinb2 ** mu * cosb2 ** nu +
factor * jac * sinb2 ** (mu-1) * cosb2 ** (nu+1) * mu/2 -
factor * jac * sinb2 ** (mu+1) * cosb2 ** (nu-1) * nu/2)
##
Ds[Js, m1s, m2s] = exp(-1j*m1s*a) * d * exp(-1j*m2s*y)
grad[0,Js, m1s, m2s] = -1j*m1s * Ds[Js, m1s, m2s]
grad[1,Js, m1s, m2s] = exp(-1j*m1s*a) * gradd * exp(-1j*m2s*y)
grad[2,Js, m1s, m2s] = -1j*m2s * Ds[Js, m1s, m2s]
return Ds, grad
def _rnm(self, radialDegree, azimuthalFrequency, rhoArray):
n = radialDegree
m = azimuthalFrequency
rho = rhoArray
if (n - m) % 2 != 0:
raise Exception("n-m must be even. Got %d-%d" % (n, m))
if abs(m) > n:
raise Exception("The following must be true |m|<=n. Got %d, %d" %
(n, m))
mask = np.where(rho <= 1, False, True)
if (n == 0 and m == 0):
return np.ma.masked_array(data=np.ones(rho.shape), mask=mask)
rho = np.where(rho < 0, 0, rho)
Rnm = np.zeros(rho.shape)
S = (n - abs(m)) // 2
for s in range(0, S + 1):
CR = pow(-1, s) * factorial(n - s) / \
(factorial(s) * factorial(-s + (n + abs(m)) / 2) *
factorial(-s + (n - abs(m)) / 2))
p = CR * pow(rho, n - 2 * s)
Rnm = Rnm + p
return np.ma.masked_array(data=Rnm, mask=mask)
def calcWignerMatrices(self):
bw = self.bw
bws = self.bws
beta = self.b
sinb2 = sin(beta / 2)
cosb2 = cos(beta / 2)
cosb = cos(beta)
Js, m1s, m2s = self.Js, self.m1s, self.m2s
Dfull = np.zeros((bw, 2 * bw - 1, 2 * bw - 1, 2 * bw))
mu = abs(m1s - m2s)
nu = abs(m1s + m2s)
s = Js - (mu + nu) / 2
xi = np.ones_like(s)
xi[m2s < m1s] = (-1)**(m1s - m2s)[m2s < m1s]
factor = sqrt(
factorial(s) * factorial(s + mu + nu) / factorial(s + mu) /
factorial(s + nu)) * xi
jac = eval_jacobi(s[:, None], mu[:, None], nu[:, None], cosb[None, :])
Dfull[Js[:, None], m1s[:, None], m2s[:, None],
bws[None, :]] = (((2. * Js[:, None] + 1.) / 2.)**0.5 *
factor[:, None] * jac *
sinb2[None, :]**mu[:, None] *
cosb2[None, :]**nu[:, None])
return Dfull
def norm_harmonicBasis(n, l, r0):
"""
returns the normalisaton constant of the harmonic basis function
"""
return (2 * factorial(n) * r0**(-2 * l - 3) / gamma(1.5 + n + l))**0.5