Docstrings for orthogonal polynomial transforms (#199)

* Docstrings for orthogonal polynomial transforms

* Update leg2cheb

Co-authored-by: Sheehan Olver <[email protected]>

* Update cheb2leg

* StridedVector -> AbstractVector

---------

Co-authored-by: Sheehan Olver <[email protected]>

Author: jishnub

src/FastTransforms.jl

@@ -134,5 +134,6 @@ end
 #     end
 # end
 
+include("docstrings.jl")
 
 end # module

src/docstrings.jl

@@ -0,0 +1,121 @@
+"""
+	leg2cheb(v::AbstractVector; normleg::Bool=false, normcheb::Bool=false)
+
+Convert the vector of expansions coefficients `v` from a Legendre to a Chebyshev basis.
+The keyword arguments denote whether the bases are normalized.
+"""
+leg2cheb
+
+"""
+	cheb2leg(v::AbstractVector; normcheb::Bool=false, normleg::Bool=false)
+
+Convert the vector of expansions coefficients `v` from a Chebyshev to a Legendre basis.
+The keyword arguments denote whether the bases are normalized.
+"""
+cheb2leg
+
+"""
+	ultra2ultra(v::AbstractVector, λ, μ; norm1::Bool=false, norm2::Bool=false)
+
+Convert the vector of expansions coefficients `v` from an Ultraspherical basis of
+order `λ` to an Ultraspherical basis of order `μ`.
+The keyword arguments denote whether the bases are normalized.
+"""
+ultra2ultra
+
+"""
+	jac2jac(v::AbstractVector, α, β, γ, δ; norm1::Bool=false, norm2::Bool=false)
+
+Convert the vector of expansions coefficients `v` from a Jacobi basis of
+order `(α,β)` to a Jacobi basis of order `(γ,δ)`.
+The keyword arguments denote whether the bases are normalized.
+"""
+jac2jac
+
+"""
+	lag2lag(v::AbstractVector, α, β; norm1::Bool=false, norm2::Bool=false)
+
+Convert the vector of expansions coefficients `v` from a Laguerre basis of
+order `α` to a La basis of order `β`.
+The keyword arguments denote whether the bases are normalized."""
+lag2lag
+
+"""
+	jac2ultra(v::AbstractVector, α, β, λ; normjac::Bool=false, normultra::Bool=false)
+
+Convert the vector of expansions coefficients `v` from a Jacobi basis of
+order `(α,β)` to an Ultraspherical basis of order `λ`.
+The keyword arguments denote whether the bases are normalized."""
+jac2ultra
+
+"""
+	ultra2jac(v::AbstractVector, λ, α, β; normultra::Bool=false, normjac::Bool=false)
+
+Convert the vector of expansions coefficients `v` from an Ultraspherical basis of
+order `λ` to a Jacobi basis of order `(α,β)`.
+The keyword arguments denote whether the bases are normalized.
+"""
+ultra2jac
+
+"""
+	jac2cheb(v::AbstractVector, α, β; normjac::Bool=false, normcheb::Bool=false)
+
+Convert the vector of expansions coefficients `v` from a Jacobi basis of
+order `(α,β)` to a Chebyshev basis.
+The keyword arguments denote whether the bases are normalized.
+"""
+jac2cheb
+
+"""
+	cheb2jac(v::AbstractVector, α, β; normcheb::Bool=false, normjac::Bool=false)
+
+Convert the vector of expansions coefficients `v` from a Chebyshev basis to a
+Jacobi basis of order `(α,β)`.
+The keyword arguments denote whether the bases are normalized.
+"""
+cheb2jac
+
+"""
+	ultra2cheb(v::AbstractVector, λ; normultra::Bool=false, normcheb::Bool=false)
+
+Convert the vector of expansions coefficients `v` from an Ultraspherical basis of
+order `λ` to a Chebyshev basis.
+The keyword arguments denote whether the bases are normalized.
+"""
+ultra2cheb
+
+"""
+	cheb2ultra(v::AbstractVector, λ; normcheb::Bool=false, normultra::Bool=false)
+
+Convert the vector of expansions coefficients `v` from a Chebyshev basis
+to an Ultraspherical basis of order `λ`.
+The keyword arguments denote whether the bases are normalized.
+"""
+cheb2ultra
+
+"""
+	associatedjac2jac(v::AbstractVector, c::Integer, α, β, γ, δ; norm1::Bool=false, norm2::Bool=false)
+
+Convert the vector of expansions coefficients `v` from an associated Jacobi basis
+of orders `(α,β)` to a Jacobi basis of order `(γ,δ)`.
+The keyword arguments denote whether the bases are normalized.
+"""
+associatedjac2jac
+
+"""
+	modifiedjac2jac(v::AbstractVector{T}, α, β, u::Vector{T}; verbose::Bool=false) where {T}
+	modifiedjac2jac(v::AbstractVector{T}, α, β, u::Vector{T}, v::Vector{T}; verbose::Bool=false) where {T}
+"""
+modifiedjac2jac
+
+"""
+	modifiedlag2lag(v::AbstractVector{T}, α, u::Vector{T}; verbose::Bool=false)
+	modifiedlag2lag(v::AbstractVector{T}, α, u::Vector{T}, v::Vector{T}; verbose::Bool=false) where {T}
+"""
+modifiedlag2lag
+
+"""
+	modifiedherm2herm(v::AbstractVector{T}, u::Vector{T}; verbose::Bool=false)
+	modifiedherm2herm(v::AbstractVector{T}, u::Vector{T}, v::Vector{T}; verbose::Bool=false) where {T}
+"""
+modifiedherm2herm