tgorordo/WignerSymbols.jl
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Update function documentation (#10)

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to reflect the use of RationalRoot as default return type.
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w-vdh 2020-02-01 21:22:34 +01:00 • committed by GitHub
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src/WignerSymbols.jl
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@ -36,11 +36,11 @@ Checks the triangle conditions `j₃ <= j₁ + j₂`, `j₁ <= j₂ + j₃` and
# triangle coefficient # triangle coefficient
""" """
Δ(T::Type{<:AbstractFloat} = Float64, j₁, j₂, j₃) -> ::T Δ(T::Type{<:Real} = RationalRoot{BigInt}, j₁, j₂, j₃) -> ::T
Computes the triangle coefficient Computes the triangle coefficient
`Δ(j₁, j₂, j₃) = √((j₁+j₂-j₃)!*(j₁-j₂+j₃)!*(j₂+j₃-j₁)! / (j₁+j₂+j₃+1)!)` `Δ(j₁, j₂, j₃) = √((j₁+j₂-j₃)!*(j₁-j₂+j₃)!*(j₂+j₃-j₁)! / (j₁+j₂+j₃+1)!)`
as a type `T` floating point number. as a type `T` real number.
Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but
throws a `DomainError` if the `jᵢ`s are not (half)integer throws a `DomainError` if the `jᵢ`s are not (half)integer
@ -58,12 +58,12 @@ function Δ(T::Type{<:Real}, j₁, j₂, j₃)
end end
""" """
wigner3j(T::Type{<:AbstractFloat} = Float64, j₁, j₂, j₃, m₁, m₂, m₃ = -m₂-m₁) -> ::T wigner3j(T::Type{<:Real} = RationalRoot{BigInt}, j₁, j₂, j₃, m₁, m₂, m₃ = -m₂-m₁) -> ::T
Compute the value of the Wigner-3j symbol Compute the value of the Wigner-3j symbol
⎛ j₁ j₂ j₃ ⎞ ⎛ j₁ j₂ j₃ ⎞
⎝ m₁ m₂ m₃ ⎠ ⎝ m₁ m₂ m₃ ⎠
as a type `T` floating point number. By default, `T = Float64` and `m₃ = -m₁-m₂`. as a type `T` real number. By default, `T = RationalRoot{BigInt}` and `m₃ = -m₁-m₂`.
Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but
throws a `DomainError` if the `jᵢ`s and `mᵢ`s are not (half)integer or `abs(mᵢ) > jᵢ`. throws a `DomainError` if the `jᵢ`s and `mᵢ`s are not (half)integer or `abs(mᵢ) > jᵢ`.
@ -109,10 +109,10 @@ function wigner3j(T::Type{<:Real}, j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m
end end
""" """
clebschgordan(T::Type{<:AbstractFloat} = Float64, j₁, m₁, j₂, m₂, j₃, m₃ = m₁+m₂) -> ::T clebschgordan(T::Type{<:Real} = RationalRoot{BigInt}, j₁, m₁, j₂, m₂, j₃, m₃ = m₁+m₂) -> ::T
Compute the value of the Clebsch-Gordan coefficient <j₁, m₁; j₂, m₂ | j₃, m₃ > Compute the value of the Clebsch-Gordan coefficient <j₁, m₁; j₂, m₂ | j₃, m₃ >
as a type `T` floating point number. By default, `T = Float64` and `m₃ = m₁+m₂`. as a type `T` real number. By default, `T = RationalRoot{BigInt}` and `m₃ = m₁+m₂`.
Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but
throws a `DomainError` if the `jᵢ`s and `mᵢ`s are not (half)integer or `abs(mᵢ) > jᵢ`. throws a `DomainError` if the `jᵢ`s and `mᵢ`s are not (half)integer or `abs(mᵢ) > jᵢ`.
@ -127,12 +127,12 @@ function clebschgordan(T::Type{<:Real}, j₁, m₁, j₂, m₂, j₃, m₃ = m
end end
""" """
racahV(T::Type{<:AbstractFloat} = Float64, j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂) -> ::T racahV(T::Type{<:Real} = RationalRoot{BigInt}, j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂) -> ::T
Compute the value of Racah's V-symbol Compute the value of Racah's V-symbol
V(j₁, j₂, j₃; m₁, m₂, m₃) = (-1)^(-j₁+j₂+j₃) * ⎛ j₁ j₂ j₃ ⎞ V(j₁, j₂, j₃; m₁, m₂, m₃) = (-1)^(-j₁+j₂+j₃) * ⎛ j₁ j₂ j₃ ⎞
⎝ m₁ m₂ m₃ ⎠ ⎝ m₁ m₂ m₃ ⎠
as a type `T` floating point number. By default, `T = Float64` and `m₃ = -m₁-m₂`. as a type `T` real number. By default, `T = RationalRoot{BigInt}` and `m₃ = -m₁-m₂`.
Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but Returns `zero(T)` if the triangle condition `δ(j₁, j₂, j₃)` is not satisfied, but
throws a `DomainError` if the `jᵢ`s and `mᵢ`s are not (half)integer or `abs(mᵢ) > jᵢ`. throws a `DomainError` if the `jᵢ`s and `mᵢ`s are not (half)integer or `abs(mᵢ) > jᵢ`.
@ -144,12 +144,12 @@ function racahV(T::Type{<:Real}, j₁, j₂, j₃, m₁, m₂, m₃ = -m₁-m₂
end end
""" """
wigner6j(T::Type{<:AbstractFloat} = Float64, j₁, j₂, j₃, j₄, j₅, j₆) -> ::T wigner6j(T::Type{<:Real} = RationalRoot{BigInt}, j₁, j₂, j₃, j₄, j₅, j₆) -> ::T
Compute the value of the Wigner-6j symbol Compute the value of the Wigner-6j symbol
_⎧ j₁ j₂ j₃ ⎫_ _⎧ j₁ j₂ j₃ ⎫_
⎩ j₄ j₅ j₆ ⎭ ⎩ j₄ j₅ j₆ ⎭
as a type `T` floating point number. By default, `T = Float64`. as a type `T` real number. By default, `T = RationalRoot{BigInt}`.
Returns `zero(T)` if any of triangle conditions `δ(j₁, j₂, j₃)`, `δ(j₁, j₆, j₅)`, Returns `zero(T)` if any of triangle conditions `δ(j₁, j₂, j₃)`, `δ(j₁, j₆, j₅)`,
`δ(j₂, j₄, j₆)`, `δ(j₃, j₄, j₅)` are not satisfied, but throws a `DomainError` if `δ(j₂, j₄, j₆)`, `δ(j₃, j₄, j₅)` are not satisfied, but throws a `DomainError` if
@ -208,11 +208,11 @@ function wigner6j(T::Type{<:Real}, j₁, j₂, j₃, j₄, j₅, j₆)
end end
""" """
racahW(T::Type{<:AbstractFloat} = Float64, j₁, j₂, J, j₃, J₁₂, J₂₃) -> ::T racahW(T::Type{<:Real} = RationalRoot{BigInt}, j₁, j₂, J, j₃, J₁₂, J₂₃) -> ::T
Compute the value of Racah's W coefficient Compute the value of Racah's W coefficient
`W(j₁, j₂, J, j₃; J₁₂, J₂₃) = <(j₁,(j₂j₃)J₂₃)J | ((j₁j₂)J₁₂,j₃)J> / sqrt((2J₁₂+1)*(2J₁₃+1))` `W(j₁, j₂, J, j₃; J₁₂, J₂₃) = <(j₁,(j₂j₃)J₂₃)J | ((j₁j₂)J₁₂,j₃)J> / sqrt((2J₁₂+1)*(2J₁₃+1))`
as a type `T` floating point number. By default, `T = Float64`. as a type `T` real number. By default, `T = RationalRoot{BigInt}`.
Returns `zero(T)` if any of triangle conditions `δ(j₁, j₂, J₁₂)`, `δ(j₂, j₃, J₂₃)`, Returns `zero(T)` if any of triangle conditions `δ(j₁, j₂, J₁₂)`, `δ(j₂, j₃, J₂₃)`,
`δ(j₁, J₂₃, J)`, `δ(J₁₂, j₃, J)` are not satisfied, but throws a `DomainError` if `δ(j₁, J₂₃, J)`, `δ(J₁₂, j₃, J)` are not satisfied, but throws a `DomainError` if