add doc

Author: MikaelSlevinsky

src/PaduaTransform.jl

@@ -1,4 +1,4 @@
-"""
+doc"""
 Pre-plan an Inverse Padua Transform.
 """
 # lex indicates if its lexigraphical (i.e., x, y) or reverse (y, x)
@@ -10,6 +10,9 @@ end
 IPaduaTransformPlan{T,lex}(cfsmat::Matrix{T},idctplan,::Type{Val{lex}}) =
     IPaduaTransformPlan{lex,typeof(idctplan),T}(cfsmat,idctplan)
 
+doc"""
+Pre-plan an Inverse Padua Transform.
+"""
 function plan_ipaduatransform!{T}(::Type{T},N::Integer,lex)
     n=Int(cld(-3+sqrt(1+8N),2))
     if N ≠ div((n+1)*(n+2),2)
@@ -20,7 +23,6 @@ end
 
 
 plan_ipaduatransform!{T}(::Type{T},N::Integer) = plan_ipaduatransform!(T,N,Val{true})
-
 plan_ipaduatransform!{T}(v::AbstractVector{T},lex...) = plan_ipaduatransform!(eltype(v),length(v),lex...)
 
 function *{T}(P::IPaduaTransformPlan,v::AbstractVector{T})
@@ -33,12 +35,12 @@ function *{T}(P::IPaduaTransformPlan,v::AbstractVector{T})
 end
 
 ipaduatransform!(v::AbstractVector,lex...) = plan_ipaduatransform!(v,lex...)*v
-"""
+doc"""
 Inverse Padua Transform maps the 2D Chebyshev coefficients to the values of the interpolation polynomial at the Padua points.
 """
 ipaduatransform(v::AbstractVector,lex...) = plan_ipaduatransform!(v,lex...)*copy(v)
 
-"""
+doc"""
 Creates (n+2)x(n+1) Chebyshev coefficient matrix from triangle coefficients.
 """
 function trianglecfsmat(P::IPaduaTransformPlan{true},cfs::AbstractVector)
@@ -79,7 +81,7 @@ function trianglecfsmat(P::IPaduaTransformPlan{false},cfs::AbstractVector)
     return cfsmat
 end
 
-"""
+doc"""
 Vectorizes the function values at the Padua points.
 """
 function paduavec!(v,P::IPaduaTransformPlan,padmat::Matrix)
@@ -98,7 +100,7 @@ function paduavec!(v,P::IPaduaTransformPlan,padmat::Matrix)
     return v
 end
 
-"""
+doc"""
 Pre-plan a Padua Transform.
 """
 immutable PaduaTransformPlan{lex,DCTPLAN,T}
@@ -109,6 +111,9 @@ end
 PaduaTransformPlan{T,lex}(vals::Matrix{T},dctplan,::Type{Val{lex}}) =
     PaduaTransformPlan{lex,typeof(dctplan),T}(vals,dctplan)
 
+doc"""
+Pre-plan a Padua Transform.
+"""
 function plan_paduatransform!{T}(::Type{T},N::Integer,lex)
     n=Int(cld(-3+sqrt(1+8N),2))
     if N ≠ ((n+1)*(n+2))÷2
@@ -135,12 +140,12 @@ function *{T}(P::PaduaTransformPlan,v::AbstractVector{T})
 end
 
 paduatransform!(v::AbstractVector,lex...) = plan_paduatransform!(v,lex...)*v
-"""
+doc"""
 Padua Transform maps from interpolant values at the Padua points to the 2D Chebyshev coefficients.
 """
 paduatransform(v::AbstractVector,lex...) = plan_paduatransform!(v,lex...)*copy(v)
 
-"""
+doc"""
 Creates (n+2)x(n+1) matrix of interpolant values on the tensor grid at the (n+1)(n+2)/2 Padua points.
 """
 function paduavalsmat(P::PaduaTransformPlan,v::AbstractVector)
@@ -160,7 +165,7 @@ function paduavalsmat(P::PaduaTransformPlan,v::AbstractVector)
     return vals
 end
 
-"""
+doc"""
 Creates length (n+1)(n+2)/2 vector from matrix of triangle Chebyshev coefficients.
 """
 function trianglecfsvec!(v,P::PaduaTransformPlan{true},cfs::Matrix)
@@ -189,7 +194,7 @@ function trianglecfsvec!(v,P::PaduaTransformPlan{false},cfs::Matrix)
     return v
 end
 
-"""
+doc"""
 Returns coordinates of the (n+1)(n+2)/2 Padua points.
 """
 function paduapoints{T}(::Type{T},n::Integer)

src/cjt.jl

@@ -112,23 +112,23 @@ function *(p::FastTransformPlan,c::AbstractMatrix)
 end
 
 
-"""
+doc"""
 Computes the Chebyshev expansion coefficients
 given the Jacobi expansion coefficients ``c`` with parameters ``α`` and ``β``.
 
 See also [`icjt`](#method__icjt.1) and [`jjt`](#method__jjt.1).
 """
 cjt(c,α,β) = plan_cjt(c,α,β)*c
 
-"""
+doc"""
 Computes the Jacobi expansion coefficients with parameters ``α`` and ``β``
 given the Chebyshev expansion coefficients ``c``.
 
 See also [`cjt`](#method__cjt.1) and [`jjt`](#method__jjt.1).
 """
 icjt(c,α,β) = plan_icjt(c,α,β)*c
 
-"""
+doc"""
 Computes the Jacobi expansion coefficients with parameters ``γ`` and ``δ``
 given the Jacobi expansion coefficients ``c`` with parameters ``α`` and ``β``.
 
@@ -143,7 +143,7 @@ function jjt(c,α,β,γ,δ)
 end
 
 
-"""
+doc"""
 Pre-plan optimized DCT-I and DST-I plans and pre-allocate the necessary
 arrays, normalization constants, and recurrence coefficients for a forward Chebyshev—Jacobi transform.
 
@@ -157,7 +157,7 @@ Optionally:
 """
 plan_cjt(c::AbstractVector,α,β;M::Int=7) = α == β ? plan_cjt(c,α+half(α);M=M) : ForwardChebyshevJacobiPlan(c,α,β,M)
 
-"""
+doc"""
 Pre-plan optimized DCT-I and DST-I plans and pre-allocate the necessary
 arrays, normalization constants, and recurrence coefficients for an inverse Chebyshev—Jacobi transform.
 

src/clenshawcurtis.jl

@@ -1,12 +1,12 @@
 clenshawcurtis_plan(μ) = length(μ) > 1 ? FFTW.plan_r2r!(μ, FFTW.REDFT00) : ones(μ)'
 
-"""
+doc"""
 Compute nodes and weights of the Clenshaw—Curtis quadrature rule with a Jacobi weight.
 """
 clenshawcurtis{T<:AbstractFloat}(N::Int,α::T,β::T) = clenshawcurtis(N,α,β,clenshawcurtis_plan(zeros(T,N)))
 clenshawcurtis{T<:AbstractFloat}(N::Int,α::T,β::T,plan) = T[cospi(k/(N-one(T))) for k=0:N-1],clenshawcurtisweights(N,α,β,plan)
 
-"""
+doc"""
 Compute weights of the Clenshaw—Curtis quadrature rule with a Jacobi weight.
 """
 clenshawcurtisweights{T<:AbstractFloat}(N::Int,α::T,β::T) = clenshawcurtisweights(N,α,β,clenshawcurtis_plan(zeros(T,N)))

src/fejer.jl

@@ -1,12 +1,12 @@
 fejer_plan1(μ) = FFTW.plan_r2r!(μ, FFTW.REDFT01)
 fejer_plan2(μ) = FFTW.plan_r2r!(μ, FFTW.RODFT00)
 
-"""
+doc"""
 Compute nodes and weights of Fejer's first quadrature rule with a Jacobi weight.
 """
 fejer1{T<:AbstractFloat}(N::Int,α::T,β::T) = fejer1(N,α,β,fejer_plan1(zeros(T,N)))
 
-"""
+doc"""
 Compute nodes and weights of Fejer's second quadrature rule with a Jacobi weight.
 """
 fejer2{T<:AbstractFloat}(N::Int,α::T,β::T) = fejer2(N,α,β,fejer_plan2(zeros(T,N)))
@@ -15,12 +15,12 @@ fejer1{T<:AbstractFloat}(N::Int,α::T,β::T,plan) = T[sinpi((N-2k-one(T))/2N) fo
 fejer2{T<:AbstractFloat}(N::Int,α::T,β::T,plan) = T[cospi((k+one(T))/(N+one(T))) for k=0:N-1],fejerweights2(N,α,β,plan)
 
 
-"""
+doc"""
 Compute weights of Fejer's first quadrature rule with a Jacobi weight.
 """
 fejerweights1{T<:AbstractFloat}(N::Int,α::T,β::T) = fejerweights1(N,α,β,fejer_plan1(zeros(T,N)))
 
-"""
+doc"""
 Compute weights of Fejer's second quadrature rule with a Jacobi weight.
 """
 fejerweights2{T<:AbstractFloat}(N::Int,α::T,β::T) = fejerweights2(N,α,β,fejer_plan2(zeros(T,N)))

src/gaunt.jl

@@ -1,4 +1,4 @@
-"""
+doc"""
 Calculates the Gaunt coefficients, defined by:
 
     a(m,n,μ,ν,q) = (2(n+ν-2q)+1)/2 (n+ν-2q-m-μ)!/(n+ν-2q+m+μ)! ∫₋₁⁺¹ P_m^n(x) P_ν^μ(x) P_{n+ν-2q}^{m+μ}(x) dx.
@@ -18,7 +18,7 @@ function gaunt{T}(::Type{T},m::Int,n::Int,μ::Int,ν::Int;normalized::Bool=false
         scale!(normalization(T,m,n,μ,ν),gaunt(T,m,n,μ,ν;normalized=true))
     end
 end
-"""
+doc"""
 Calculates the Gaunt coefficients in 64-bit floating-point arithmetic.
 """
 gaunt(m::Int,n::Int,μ::Int,ν::Int;kwds...) = gaunt(Float64,m,n,μ,ν;kwds...)

src/specialfunctions.jl

@@ -6,21 +6,21 @@ const BACKWARD = false
 const sqrtpi = 1.772453850905516027298
 const edivsqrt2pi = 1.084437551419227546612
 
-"""
+doc"""
 Compute a typed 0.5.
 """
 half(x::Number) = oftype(x,0.5)
 half(x::Integer) = half(float(x))
 half{T<:Number}(::Type{T}) = convert(T,0.5)
 half{T<:Integer}(::Type{T}) = half(AbstractFloat)
 
-"""
+doc"""
 Compute a typed 2.
 """
 two(x::Number) = oftype(x,2)
 two{T<:Number}(::Type{T}) = convert(T,2)
 
-"""
+doc"""
 The Kronecker δ function.
 """
 δ(k::Integer,j::Integer) = k == j ? 1 : 0
@@ -57,7 +57,7 @@ function pochhammer{T<:Real}(x::Number,n::UnitRange{T})
     ret
 end
 
-"""
+doc"""
 Stirling series for Γ(z).
 """
 stirlingseries(z) = gamma(z)*sqrt((z/π)/2)*exp(z)/z^z
@@ -135,11 +135,11 @@ Anαβ{T<:Integer}(n::AbstractVector{T},α::Number,β::Number) = [ Anαβ(n[i],
 Anαβ{T<:Integer}(n::AbstractMatrix{T},α::Number,β::Number) = [ Anαβ(n[i,j],α,β) for i=1:size(n,1), j=1:size(n,2) ]
 
 
-"""
+doc"""
 The Lambda function Λ(z) = Γ(z+½)/Γ(z+1) for the ratio of gamma functions.
 """
 Λ(z::Number) = exp(lgamma(z+half(z))-lgamma(z+one(z)))
-"""
+doc"""
 For 64-bit floating-point arithmetic, the Lambda function uses the asymptotic series for τ in Appendix B of
 
     I. Bogaert and B. Michiels and J. Fostier, 𝒪(1) computation of Legendre polynomials and Gauss–Legendre nodes and weights for parallel computing, SIAM J. Sci. Comput., 34:C83–C101, 2012.
@@ -154,7 +154,7 @@ function Λ(x::Float64)
 end
 
 
-"""
+doc"""
 The Lambda function Λ(z,λ₁,λ₂) = Γ(z+λ₁)/Γ(z+λ₂) for the ratio of gamma functions.
 """
 Λ(z::Number,λ₁::Number,λ₂::Number) = exp(lgamma(z+λ₁)-lgamma(z+λ₂))
@@ -390,7 +390,7 @@ function init_c₁c₂!(c₁::Vector,c₂::Vector,u::Vector,v::Vector,c::Vector,
 end
 
 
-"""
+doc"""
 Modified Chebyshev moments of the first kind with respect to the Jacobi weight:
 
     ∫₋₁⁺¹ T_n(x) (1-x)^α(1+x)^β dx.
@@ -408,7 +408,7 @@ function chebyshevjacobimoments1{T<:AbstractFloat}(N::Int,α::T,β::T)
     μ
 end
 
-"""
+doc"""
 Modified Chebyshev moments of the second kind with respect to the Jacobi weight:
 
     ∫₋₁⁺¹ U_n(x) (1-x)^α(1+x)^β dx.
@@ -426,7 +426,7 @@ function chebyshevjacobimoments2{T<:AbstractFloat}(N::Int,α::T,β::T)
     μ
 end
 
-"""
+doc"""
 Compute Jacobi expansion coefficients in Pₙ^(α+1,β) given Jacobi expansion coefficients in Pₙ^(α,β) in-place.
 """
 function incrementα!(c::AbstractVector,α,β)
@@ -437,7 +437,7 @@ function incrementα!(c::AbstractVector,α,β)
     c
 end
 
-"""
+doc"""
 Compute Jacobi expansion coefficients in Pₙ^(α,β+1) given Jacobi expansion coefficients in Pₙ^(α,β) in-place.
 """
 function incrementβ!(c::AbstractVector,α,β)
@@ -448,7 +448,7 @@ function incrementβ!(c::AbstractVector,α,β)
     c
 end
 
-"""
+doc"""
 Compute Jacobi expansion coefficients in Pₙ^(α+1,α+1) given Jacobi expansion coefficients in Pₙ^(α,α) in-place.
 """
 function incrementαβ!(c::AbstractVector,α,β)
@@ -461,7 +461,7 @@ function incrementαβ!(c::AbstractVector,α,β)
     c
 end
 
-"""
+doc"""
 Compute Jacobi expansion coefficients in Pₙ^(α-1,β) given Jacobi expansion coefficients in Pₙ^(α,β) in-place.
 """
 function decrementα!(c::AbstractVector,α,β)
@@ -472,7 +472,7 @@ function decrementα!(c::AbstractVector,α,β)
     c
 end
 
-"""
+doc"""
 Compute Jacobi expansion coefficients in Pₙ^(α,β-1) given Jacobi expansion coefficients in Pₙ^(α,β) in-place.
 """
 function decrementβ!(c::AbstractVector,α,β)
@@ -483,7 +483,7 @@ function decrementβ!(c::AbstractVector,α,β)
     c
 end
 
-"""
+doc"""
 Compute Jacobi expansion coefficients in Pₙ^(α-1,α-1) given Jacobi expansion coefficients in Pₙ^(α,α) in-place.
 """
 function decrementαβ!(c::AbstractVector,α,β)

src/toeplitzhankel.jl

@@ -1,4 +1,4 @@
-"""
+doc"""
 Store a diagonally-scaled Toeplitz∘Hankel matrix:
 
     DL(T∘H)DR