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https://github.com/tgorordo/WignerSymbols.jl.git
synced 2026-06-13 02:02:14 -07:00
use RationalRoots representation
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Jutho Haegeman
parent
80cc592dd3
commit
8ee830e173
6 changed files with 52 additions and 45 deletions
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@ -4,14 +4,15 @@ export δ, Δ, clebschgordan, wigner3j, wigner6j, racahV, racahW, HalfInteger
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using Base.GMP.MPZ
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using HalfIntegers
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using RationalRoots
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const RRBig = RationalRoot{BigInt}
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import RationalRoots: _convert
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include("primefactorization.jl")
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const Wigner3j = Dict{Tuple{UInt,UInt,UInt,Int,Int},Tuple{Rational{BigInt},Rational{BigInt}}}()
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const Wigner6j = Dict{NTuple{6,UInt},Tuple{Rational{BigInt},Rational{BigInt}}}()
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const FASTCUTOFF = convert(BigInt, typemax(Int))
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function __init__()
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global bigone, bigprimetable, Wigner3j, Wigner6j
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bigone[] = big(1)
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@ -44,8 +45,8 @@ as a type `T` floating point number.
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Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but
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throws a `DomainError` if the `jᵢ`s are not (half)integer
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"""
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Δ(j₁, j₂, j₃) = Δ(Float64, j₁, j₂, j₃)
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function Δ(T::Type{<:AbstractFloat}, j₁, j₂, j₃)
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Δ(j₁, j₂, j₃) = Δ(RRBig, j₁, j₂, j₃)
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function Δ(T::Type{<:Real}, j₁, j₂, j₃)
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for jᵢ in (j₁, j₂, j₃)
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(ishalfinteger(jᵢ) && jᵢ >= zero(jᵢ)) || throw(DomainError("invalid jᵢ", jᵢ))
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end
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@ -53,7 +54,7 @@ function Δ(T::Type{<:AbstractFloat}, j₁, j₂, j₃)
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return zero(T)
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end
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n, d = Δ²(j₁, j₂, j₃)
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return sqrt(convert(T, convert(BigInt, n) // convert(BigInt, d)))
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return convert(T, signedroot(RationalRoot{BigInt}, n//d))
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end
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"""
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@ -67,8 +68,8 @@ as a type `T` floating point number. By default, `T = Float64` and `m₃ = -m₁
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Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but
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throws a `DomainError` if the `jᵢ`s and `mᵢ`s are not (half)integer or `abs(mᵢ) > jᵢ`.
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"""
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wigner3j(j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂) = wigner3j(Float64, j₁, j₂, j₃, m₁, m₂, m₃)
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function wigner3j(T::Type{<:AbstractFloat}, j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂)
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wigner3j(j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂) = wigner3j(RRBig, j₁, j₂, j₃, m₁, m₂, m₃)
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function wigner3j(T::Type{<:Real}, j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂)
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# check angular momenta
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for (jᵢ,mᵢ) in ((j₁, m₁), (j₂, m₂), (j₃, m₃))
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ϵ(jᵢ, mᵢ) || throw(DomainError((jᵢ, mᵢ), "invalid combination (jᵢ, mᵢ)"))
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@ -104,13 +105,7 @@ function wigner3j(T::Type{<:AbstractFloat}, j₁, j₂, j₃, m₁, m₂, m₃ =
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s *= compute3jseries(β₁, β₂, β₃, α₁, α₂)
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Wigner3j[(β₁, β₂, β₃, α₁, α₂)] = (r,s)
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end
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if T != BigFloat && all((s.num, s.den, r.num, r.den) .< FASTCUTOFF)
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sn, sd, rn, rd = convert.(T, (s.num, s.den, r.num, r.den))
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return sgn*(sn/sd)*sqrt(rn/rd)
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else
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return convert(T, sgn*s*sqrt(r))
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end
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return _convert(T, sgn*s)*convert(T, signedroot(r))
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end
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"""
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@ -123,11 +118,11 @@ Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisf
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throws a `DomainError` if the `jᵢ`s and `mᵢ`s are not (half)integer or `abs(mᵢ) > jᵢ`.
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"""
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clebschgordan(j₁, m₁, j₂, m₂, j₃, m₃ = m₁+m₂) =
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clebschgordan(Float64, j₁, m₁, j₂, m₂, j₃, m₃)
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function clebschgordan(T::Type{<:AbstractFloat}, j₁, m₁, j₂, m₂, j₃, m₃ = m₁+m₂)
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clebschgordan(RRBig, j₁, m₁, j₂, m₂, j₃, m₃)
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function clebschgordan(T::Type{<:Real}, j₁, m₁, j₂, m₂, j₃, m₃ = m₁+m₂)
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s = wigner3j(T, j₁, j₂, j₃, m₁, m₂, -m₃)
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iszero(s) && return s
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s *= sqrt(convert(T, j₃+j₃+one(j₃)))
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s *= convert(T, signedroot(RRBig, j₃+j₃+one(j₃)))
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return isodd(convert(Int,j₁ - j₂ + m₃)) ? -s : s
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end
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@ -142,8 +137,8 @@ as a type `T` floating point number. By default, `T = Float64` and `m₃ = -m₁
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Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but
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throws a `DomainError` if the `jᵢ`s and `mᵢ`s are not (half)integer or `abs(mᵢ) > jᵢ`.
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"""
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racahV(j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂) = racahV(Float64, j₁, j₂, j₃, m₁, m₂, m₃)
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function racahV(T::Type{<:AbstractFloat}, j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂)
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racahV(j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂) = racahV(RRBig, j₁, j₂, j₃, m₁, m₂, m₃)
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function racahV(T::Type{<:Real}, j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂)
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s = wigner3j(T, j₁, j₂, j₃, m₁, m₂, m₃)
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return isodd(convert(Int, -j₁ + j₂ + j₃)) ? -s : s
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end
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@ -160,8 +155,8 @@ Returns `zero(T)` if any of triangle conditions `δ(j₁, j₂, j₃)`, `δ(j₁
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`δ(j₂, j₄, j₆)`, `δ(j₃, j₄, j₅)` are not satisfied, but throws a `DomainError` if
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the `jᵢ`s are not integer or halfinteger.
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"""
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wigner6j(j₁, j₂, j₃, j₄, j₅, j₆) = wigner6j(Float64, j₁, j₂, j₃, j₄, j₅, j₆)
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function wigner6j(T::Type{<:AbstractFloat}, j₁, j₂, j₃, j₄, j₅, j₆)
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wigner6j(j₁, j₂, j₃, j₄, j₅, j₆) = wigner6j(RRBig, j₁, j₂, j₃, j₄, j₅, j₆)
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function wigner6j(T::Type{<:Real}, j₁, j₂, j₃, j₄, j₅, j₆)
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# check validity of `jᵢ`s
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for jᵢ in (j₁, j₂, j₃, j₄, j₅, j₆)
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(ishalfinteger(jᵢ) && jᵢ >= zero(jᵢ)) || throw(DomainError("invalid jᵢ", jᵢ))
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@ -201,19 +196,15 @@ function wigner6j(T::Type{<:AbstractFloat}, j₁, j₂, j₃, j₄, j₅, j₆)
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snum, rnum = splitsquare(n₁ * n₂ * n₃ * n₄)
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sden, rden = splitsquare(d₁ * d₂ * d₃ * d₄)
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snu, sden = divgcd!(snum, sden)
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rnu, rden = divgcd!(rnum, rden)
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s = convert(BigInt, snum) // convert(BigInt, sden)
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r = convert(BigInt, rnum) // convert(BigInt, rden)
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s *= compute6jseries(β₁, β₂, β₃, α₁, α₂, α₃, α₄)
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Wigner6j[(β₁, β₂, β₃, α₁, α₂, α₃)] = (r, s)
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end
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if T != BigFloat && all((s.num, s.den, r.num, r.den) .< FASTCUTOFF)
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sn, sd, rn, rd = convert.(T, (s.num, s.den, r.num, r.den))
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return (sn/sd)*sqrt(rn/rd)
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else
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return convert(T, s*sqrt(r))
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end
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return _convert(T, s) * convert(T, signedroot(r))
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end
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"""
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@ -227,8 +218,8 @@ Returns `zero(T)` if any of triangle conditions `δ(j₁, j₂, J₁₂)`, `δ(j
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`δ(j₁, J₂₃, J)`, `δ(J₁₂, j₃, J)` are not satisfied, but throws a `DomainError` if
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the `jᵢ`s and `J`s are not integer or halfinteger.
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"""
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racahW(j₁, j₂, J, j₃, J₁₂, J₂₃) = racahW(Float64, j₁, j₂, J, j₃, J₁₂, J₂₃)
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function racahW(T::Type{<:AbstractFloat}, j₁, j₂, J, j₃, J₁₂, J₂₃)
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racahW(j₁, j₂, J, j₃, J₁₂, J₂₃) = racahW(RRBig, j₁, j₂, J, j₃, J₁₂, J₂₃)
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function racahW(T::Type{<:Real}, j₁, j₂, J, j₃, J₁₂, J₂₃)
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s = wigner6j(T, j₁, j₂, J₁₂, j₃, J, J₂₃)
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if !iszero(s) && isodd(convert(Int, j₁ + j₂ + j₃ + J))
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return -s
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@ -116,13 +116,13 @@ Base.promote_rule(P::Type{<:PrimeFactorization},::Type{BigInt}) = BigInt
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Base.convert(P::Type{<:PrimeFactorization}, n::Integer) = convert(P, primefactor(n))
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function Base.convert(::Type{BigInt}, a::PrimeFactorization)
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A = big(a.sign)
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A = one(BigInt)
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for (n, e) in enumerate(a.powers)
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if !iszero(e)
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MPZ.mul!(A, bigprime(n, e))
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end
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end
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return A
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return a.sign < 0 ? MPZ.neg!(A) : A
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end
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Base.convert(::Type{PrimeFactorization{U}}, a::PrimeFactorization{U}) where {U<:Unsigned} =
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a
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