Restructure domain, polar, and index conversions into separate files

This needed organization.

src/Domain.jl

@@ -0,0 +1,35 @@
+macro domain(ex, msg::String, val)
+    esc(:($ex ? nothing : throw(DomainError($val, $msg))))
+end
+
+macro domain(ex, msg::String, vals...)
+    esc(:(@domain($ex, $msg, ($(vals...),))))
+end
+
+macro domain(ex, val)
+    esc(:(@domain($ex, $(string("\nDomain:\n", ex, "\n")), $val)))
+end
+
+macro domain(ex, vals...)
+    esc(:(
+        @domain($ex, join($(string.(vals)) .* " = " .* string.(($(vals...),)), ", "))
+    ))
+end
+
+macro domain_check_mn()
+    quote
+        @domain(n ≥ 0 && μ ≤ n && iseven(n - μ),
+            """
+            \nDomain:
+            n ≥ 0
+            |m| ≤ n
+            n ≡ m (mod 2)
+            """,
+            m, n
+        )
+    end |> esc
+end
+
+macro domain_check_j()
+    esc(:(@domain(j ≥ 0, j)))
+end

src/IndexConversions.jl

@@ -0,0 +1,104 @@
+# normalization constant for Fringe coefficients
+N(j::Vector{Int}) = broadcast(x -> √radicand(x...), get_mn.(j))
+
+struct Standard
+    v::Vector{Float64}
+end
+
+struct Noll
+    v::Vector{Float64}
+end
+
+struct Fringe
+    v::Vector{Float64}
+end
+
+Standard(noll::Noll) = Standard(standardize(noll))
+Standard(fringe::Fringe) = Standard(standardize(fringe))
+
+Noll(fringe::Fringe) = (Noll ∘ Standard ∘ standardize)(fringe)
+
+Fringe(noll::Noll) = (Fringe ∘ Standard ∘ standardize)(noll)
+
+function Noll(s::Standard)
+    sv = s.v
+    j = eachindex(sv) .- 1
+    noll = j_to_noll.(j)
+    v = zeros(maximum(noll))
+    v[noll] = sv
+    return Noll(v)
+end
+
+function Fringe(s::Standard)
+    sv = s.v
+    j = [i for i ∈ 0:length(sv)-1 if i ∈ valid_fringes]
+    fringe = j_to_fringe.(j)
+    v = zeros(maximum(fringe))
+    v[fringe] .= N(j) .* sv[j.+1]
+    return Fringe(v)
+end
+
+function noll_to_j(noll::Int)
+    @domain(noll ≥ 1, noll)
+    n::Int = trunc(√(2noll - 1) + 0.5) - 1
+    n_mod_2 = isodd(n)
+    m::Int = 2((2noll - (n + 1)n + 1 + n_mod_2) ÷ 4) - n_mod_2
+    m = flipsign(m, iseven(noll) ? 1 : -1)
+    get_j(m, n)
+end
+
+function j_to_noll(j::Int)
+    @domain_check_j
+    m, n = get_mn(j)
+    i = n % 4 ∈ 0:1
+    k = m > 0 && i || m < 0 && !i ? 0 : 1
+    (n + 1)n ÷ 2 + abs(m) + k
+end
+
+function fringe_to_j(fringe::Int)
+    @domain(fringe ∈ 1:37, fringe)
+    if fringe == 37
+        return get_j(0, 12)
+    end
+    d = trunc(Int, √(fringe - 1)) + 1
+    d2 = d^2 - fringe
+    m::Int = (d2 + 1) ÷ 2
+    m = flipsign(m, isodd(d2) ? -1 : 1)
+    n::Int = 2(d - 1) - abs(m)
+    get_j(m, n)
+end
+
+function j_to_fringe(j::Int)
+    @domain_check_j
+    mn = get_mn(j)
+    mn == (0, 12) && return 37
+    m, n = mn
+    μ = abs(m)
+    fringe = ((μ + n) ÷ 2 + 1)^2 - 2μ + fld(1 - sign(m), 2)
+    @domain(fringe ∈ 1:36,
+        """
+        \nPolynomial does not have a Fringe representation.
+        See Zernike.valid_fringes for valid polynomial indices.
+        """,
+        j
+    )
+    return fringe
+end
+
+function standardize(noll::Noll)
+    (; v) = noll
+    p = [noll_to_j(i) + 1 for i in eachindex(v)]
+    u = zeros(maximum(p))
+    u[p] = v
+    return u
+end
+
+function standardize(fringe::Fringe)
+    (; v) = fringe
+    j = fringe_to_j.(eachindex(v))
+    n_max = get_n(maximum(j))
+    j_max = get_j(n_max)
+    a = zeros(eltype(v), j_max + 1)
+    a[j.+1] = v ./ N(j)
+    return a
+end

src/Polar.jl

@@ -0,0 +1,30 @@
+function polar((u, v)::NTuple{2, Int})
+    θ = range(0.0, 2π, u)
+    ρ = range(0.0, 1.0, v)
+    return ρ, θ
+end
+
+function polar(ϵ::Int = ϵ_fit)
+    ρ, θ = polar((ϵ, ϵ))
+    return ρ', θ
+end
+
+function polar(m::Int, n::Int; finesse = finesse)
+    m = abs(m)
+    finesse = clamp(finesse, 1, 100)
+    ϵ_n = finesse * (ceil(Int, π * n) + 1)
+    ϵ_n = min(ϵ_n, ϵ_max)
+    ϵ_m = finesse * (2m + 1)
+    ϵ_m = min(ϵ_m, ϵ_max)
+    ρ = range(0.0, 1.0, ϵ_n)
+    θ = range(0.0, 2π, ϵ_m)
+    return ρ, θ
+end
+
+polar(z::Complex) = abs(z), angle(z)
+
+function polar_mat(ρ, θ)
+    ρᵪ = [ρⱼ * cos(θᵢ) for θᵢ ∈ θ, ρⱼ ∈ ρ]
+    ρᵧ = [ρⱼ * sin(θᵢ) for θᵢ ∈ θ, ρⱼ ∈ ρ]
+    return ρᵪ, ρᵧ
+end

src/Zernike.jl

@@ -68,82 +68,9 @@ struct Output
     high_order::Bool
 end
 
-# normalization constant for Fringe coefficients
-N(j::Vector{Int}) = broadcast(x -> √radicand(x...), get_mn.(j))
-
-struct Standard
-    v::Vector{Float64}
-end
-
-struct Noll
-    v::Vector{Float64}
-end
-
-struct Fringe
-    v::Vector{Float64}
-end
-
-Standard(noll::Noll) = Standard(standardize(noll))
-Standard(fringe::Fringe) = Standard(standardize(fringe))
-
-Noll(fringe::Fringe) = (Noll ∘ Standard ∘ standardize)(fringe)
-
-Fringe(noll::Noll) = (Fringe ∘ Standard ∘ standardize)(noll)
-
-function Noll(s::Standard)
-    sv = s.v
-    j = eachindex(sv) .- 1
-    noll = j_to_noll.(j)
-    v = zeros(maximum(noll))
-    v[noll] = sv
-    return Noll(v)
-end
-
-function Fringe(s::Standard)
-    sv = s.v
-    j = [i for i ∈ 0:length(sv)-1 if i ∈ valid_fringes]
-    fringe = j_to_fringe.(j)
-    v = zeros(maximum(fringe))
-    v[fringe] .= N(j) .* sv[j.+1]
-    return Fringe(v)
-end
-
-macro domain(ex, msg::String, val)
-    esc(:($ex ? nothing : throw(DomainError($val, $msg))))
-end
-
-macro domain(ex, msg::String, vals...)
-    esc(:(@domain($ex, $msg, ($(vals...),))))
-end
-
-macro domain(ex, val)
-    esc(:(@domain($ex, $(string("\nDomain:\n", ex, "\n")), $val)))
-end
-
-macro domain(ex, vals...)
-    esc(:(
-        @domain($ex, join($(string.(vals)) .* " = " .* string.(($(vals...),)), ", "))
-    ))
-end
-
-macro domain_check_mn()
-    quote
-        @domain(n ≥ 0 && μ ≤ n && iseven(n - μ),
-            """
-            \nDomain:
-            n ≥ 0
-            |m| ≤ n
-            n ≡ m (mod 2)
-            """,
-            m, n
-        )
-    end |> esc
-end
-
-macro domain_check_j()
-    esc(:(@domain(j ≥ 0, j)))
-end
-
+include("Domain.jl")
+include("IndexConversions.jl")
+include("Polar.jl")
 include("RadialCoefficients.jl")
 include("FormatStrings.jl")
 include("WavefrontError.jl")
@@ -171,37 +98,6 @@ end
 
 (Z::Output)(ρ, θ) = Z.Z(ρ, θ)
 
-function polar((u, v)::NTuple{2, Int})
-    θ = range(0.0, 2π, u)
-    ρ = range(0.0, 1.0, v)
-    return ρ, θ
-end
-
-function polar(ϵ::Int = ϵ_fit)
-    ρ, θ = polar((ϵ, ϵ))
-    return ρ', θ
-end
-
-function polar(m::Int, n::Int; finesse = finesse)
-    m = abs(m)
-    finesse = clamp(finesse, 1, 100)
-    ϵ_n = finesse * (ceil(Int, π * n) + 1)
-    ϵ_n = min(ϵ_n, ϵ_max)
-    ϵ_m = finesse * (2m + 1)
-    ϵ_m = min(ϵ_m, ϵ_max)
-    ρ = range(0.0, 1.0, ϵ_n)
-    θ = range(0.0, 2π, ϵ_m)
-    return ρ, θ
-end
-
-polar(z::Complex) = abs(z), angle(z)
-
-function polar_mat(ρ, θ)
-    ρᵪ = [ρⱼ * cos(θᵢ) for θᵢ ∈ θ, ρⱼ ∈ ρ]
-    ρᵧ = [ρⱼ * sin(θᵢ) for θᵢ ∈ θ, ρⱼ ∈ ρ]
-    return ρᵪ, ρᵧ
-end
-
 # radial order
 get_n(j::Int) = ceil(Int, (-3 + √(9 + 8j)) / 2)
 
@@ -226,71 +122,6 @@ function get_mn(j::Int)
     return m, n
 end
 
-function noll_to_j(noll::Int)
-    @domain(noll ≥ 1, noll)
-    n::Int = trunc(√(2noll - 1) + 0.5) - 1
-    n_mod_2 = isodd(n)
-    m::Int = 2((2noll - (n + 1)n + 1 + n_mod_2) ÷ 4) - n_mod_2
-    m = flipsign(m, iseven(noll) ? 1 : -1)
-    get_j(m, n)
-end
-
-function j_to_noll(j::Int)
-    @domain_check_j
-    m, n = get_mn(j)
-    i = n % 4 ∈ 0:1
-    k = m > 0 && i || m < 0 && !i ? 0 : 1
-    (n + 1)n ÷ 2 + abs(m) + k
-end
-
-function standardize(noll::Noll)
-    (; v) = noll
-    p = [noll_to_j(i) + 1 for i in eachindex(v)]
-    u = zeros(maximum(p))
-    u[p] = v
-    return u
-end
-
-function fringe_to_j(fringe::Int)
-    @domain(fringe ∈ 1:37, fringe)
-    if fringe == 37
-        return get_j(0, 12)
-    end
-    d = trunc(Int, √(fringe - 1)) + 1
-    d2 = d^2 - fringe
-    m::Int = (d2 + 1) ÷ 2
-    m = flipsign(m, isodd(d2) ? -1 : 1)
-    n::Int = 2(d - 1) - abs(m)
-    get_j(m, n)
-end
-
-function j_to_fringe(j::Int)
-    @domain_check_j
-    mn = get_mn(j)
-    mn == (0, 12) && return 37
-    m, n = mn
-    μ = abs(m)
-    fringe = ((μ + n) ÷ 2 + 1)^2 - 2μ + fld(1 - sign(m), 2)
-    @domain(fringe ∈ 1:36,
-        """
-        \nPolynomial does not have a Fringe representation.
-        See Zernike.valid_fringes for valid polynomial indices.
-        """,
-        j
-    )
-    return fringe
-end
-
-function standardize(fringe::Fringe)
-    (; v) = fringe
-    j = fringe_to_j.(eachindex(v))
-    n_max = get_n(maximum(j))
-    j_max = get_j(n_max)
-    a = zeros(eltype(v), j_max + 1)
-    a[j.+1] = v ./ N(j)
-    return a
-end
-
 function validate_length(v::Vector)
     len = length(v)
     j_max = len - 1