94 lines
3.7 KiB
Python
94 lines
3.7 KiB
Python
# [Xu] = Journal of computational physics 139, 137–165
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from __future__ import print_function
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def p_q(q, n, nu):
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return n + nu - 2*q
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def qmax(M, n, mu, nu):
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return floor(min(n, nu, (n+nu-abs(M+mu))/2))
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def Qmax(M, n, mu, nu): # [Xu](60)
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return floor(min(n, nu, (n+nu+1-abs(M+mu))/2))
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def gaunta_p(M, n, mu, nu, p): # [Xu](5)
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#print (M,n,mu,nu,p, file=sys.stderr)
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return (-1)**(M+mu) * (2*p +1) * sqrt(
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factorial(n+M) * factorial(nu+mu) * factorial(p-M-mu)
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/ factorial(n-M) / factorial(nu-mu) / factorial(p+M+mu)) * (
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wigner_3j(n, nu, p, 0, 0, 0) * wigner_3j(n, nu, p, M, mu, -M-mu))
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def bCXcoeff(M, n, mu, nu, p): # [Xu](61)
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#print(M,n,mu,nu,p,file=sys.stderr)
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return (-1)**(M+mu) * (2*p + 3) * sqrt(
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factorial(n+M) * factorial(nu+mu) * factorial(p+1-M-mu)
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/ factorial(n-M) / factorial(nu-mu) / factorial(p+1+M+mu)) * (
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wigner_3j(n, nu, p, 0, 0, 0) * wigner_3j(n, nu, p+1, M, mu, -M-mu))
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def ACXcoeff(m, n, mu, nu, q): # [Xu](58)
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p = p_q(q,n,nu)
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return ((-1)**m * (2*nu + 1) * factorial(n+m) * factorial(nu-mu) / (
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2 * n * (n+1) * factorial(n-m) * factorial(nu+mu)) * I**p *
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(n*(n+1) + nu*(nu+1) - p*(p+1)) * gaunta_p(-m,n,mu,nu,p))
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def BCXcoeff(m, n, mu, nu, q): # [Xu](59)
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p = p_q(q,n,nu)
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return ((-1)**(m+1) * (2*nu + 1) * factorial(n+m) * factorial(nu-mu) / (
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2 * n * (n+1) * factorial(n-m) * factorial(nu+mu)) * I**(p+1) *
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sqrt(((p+1)**2-(n-nu)**2) * ((n+nu+1)**2-(p+1)**2))
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* bCXcoeff(-m,n,mu,nu,p))
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def printACXcoeffs(lMax, file=sys.stdout):
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for n in IntegerRange(lMax+1):
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for nu in IntegerRange(lMax+1):
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for m in IntegerRange(-n, n+1):
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for mu in IntegerRange(-nu, nu+1):
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for q in IntegerRange(qmax(-m,n,mu,nu)):
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#print(m, n, mu, nu, q, p_q(q,n,nu), file=sys.stderr)
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coeff= ACXcoeff(m, n, mu, nu, q);
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print(N(coeff, prec=53),
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", // %d, %d, %d, %d, %d," % (m,n,mu,nu,q),
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coeff,
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file=file)
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return
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def printBCXcoeffs(lMax, file=sys.stdout):
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for n in IntegerRange(lMax+1):
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for nu in IntegerRange(lMax+1):
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for m in IntegerRange(-n, n+1):
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for mu in IntegerRange(-nu, nu+1):
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for q in IntegerRange(1, Qmax(-m,n,mu,nu) +1 ):
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#print(m, n, mu, nu, q, p_q(q,n,nu), file=sys.stderr)
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coeff= BCXcoeff(m, n, mu, nu, q);
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print(N(coeff, prec=53),
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", // %d, %d, %d, %d, %d," % (m,n,mu,nu,q),
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coeff,
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file=file)
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return
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sphericalBessels = (None,
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spherical_bessel_J,
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spherical_bessel_Y,
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spherical_hankel1,
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spherical_hankel2
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)
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# N.B. sage's gen_legendre_P _does_ include (-1)**m Condon-Shortley phase
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# whereas formulae in [Xu] do not.
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def trcoeff_ACX(m, n, mu, nu, besseltype, kd, th, fi, csphase=1): # [Xu](58)
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res = 0
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for q in range(qmax(-m,n,mu,nu)+1):
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p = p_q(q,n,nu)
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res += ACXcoeff(m,n,mu,nu,q) * sphericalBessels[besseltype](p,kd) * gen_legendre_P(p, mu-m, cos(th)) * (-csphase)**(mu-m) # compensate for csphase
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res *= exp(I*(mu-m)*fi)
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return res
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def trcoeff_BCX(m, n, mu, nu, besseltype, kd, th, fi, csphase=1): # [Xu](59)
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res = 0
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for q in IntegerRange(1,Qmax(-m,n,mu,nu)+1):
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p = p_q(q,n,nu)
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res += BCXcoeff(m,n,mu,nu,q) * sphericalBessels[besseltype](p+1,kd) * gen_legendre_P(p+1, mu-m, cos(th)) * (-csphase)**(mu-m)
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res *= exp(I*(mu-m)*fi)
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return res
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