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* WIP, add SparseVectorPolynomial * add SparseVector container * SparseVectorPolynomial needs zero(T) * NaN poisons, Inf propogates. No good rational, but ...
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src/polynomial-container-types/mutable-sparse-vector-polynomial.jl
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| """ | ||
| MutableSparseVectorPolynomial{B,T,X} | ||
| This polynomial type uses an `SparseVector{T,Int}` to store the coefficients of a polynomial relative to the basis `B` with indeterminate `X`. | ||
| The type `T` should have `zero(T)` defined. | ||
| """ | ||
| struct MutableSparseVectorPolynomial{B,T,X} <: AbstractUnivariatePolynomial{B, T,X} | ||
| coeffs::SparseVector{T, Int} | ||
| function MutableSparseVectorPolynomial{B,T,X}(cs::SparseVector{S,Int}, order::Int=0) where {B,T,S,X} | ||
| new{B,T,Symbol(X)}(cs) | ||
| end | ||
| end | ||
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| MutableSparseVectorPolynomial{B,T,X}(check::Val{:false}, coeffs::SparseVector{Int,S}) where {B,T,S,X} = | ||
| MutableSparseVectorPolynomial{B,T,X}(coeffs) | ||
| MutableSparseVectorPolynomial{B,T,X}(checked::Val{:true}, coeffs::SparseVector{Int,T}) where {B,T,X<:Symbol} = | ||
| MutableSparseVectorPolynomial{B,T,X}(coeffs) | ||
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| # --- | ||
| function MutableSparseVectorPolynomial{B,T}(coeffs::SparseVector{S,Int}, var::SymbolLike=Var(:x)) where {B,T,S} | ||
| MutableSparseVectorPolynomial{B,T,Symbol(var)}(coeffs) | ||
| end | ||
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| function MutableSparseVectorPolynomial{B}(cs::SparseVector{T,Int}, var::SymbolLike=Var(:x)) where {B,T} | ||
| MutableSparseVectorPolynomial{B,T,Symbol(var)}(cs) | ||
| end | ||
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| # From a Dictionary | ||
| function MutableSparseVectorPolynomial{B,X}(cs::AbstractDict{Int, T}) where {B,T,X} | ||
| N = maximum(keys(cs)) + 1 | ||
| v = SparseVector(N, 1 .+ keys(cs), collect(values(cs))) | ||
| MutableSparseVectorPolynomial{B,T,X}(v) | ||
| end | ||
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| function MutableSparseVectorPolynomial{B}(cs::AbstractDict{Int, T}, var::SymbolLike=Var(:x)) where {B,T} | ||
| MutableSparseVectorPolynomial{B,Symbol(var)}(cs) | ||
| end | ||
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| # abstract vector has order/symbol | ||
| function MutableSparseVectorPolynomial{B,T,X}(coeffs::AbstractVector{S}, order::Int=0) where {B,T,S,X} | ||
| if Base.has_offset_axes(coeffs) | ||
| @warn "ignoring the axis offset of the coefficient vector" | ||
| coeffs = parent(coeffs) | ||
| end | ||
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| MutableSparseVectorPolynomial{B,T,X}(convert(SparseVector, coeffs)) | ||
| end | ||
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| # # cs iterable of pairs; ensuring tight value of T | ||
| # function MutableSparseVectorPolynomial{B}(cs::Tuple, var::SymbolLike=:x) where {B} | ||
| # isempty(cs) && throw(ArgumentError("No type attached")) | ||
| # X = Var(var) | ||
| # if length(cs) == 1 | ||
| # c = only(cs) | ||
| # d = Dict(first(c) => last(c)) | ||
| # T = eltype(last(c)) | ||
| # return MutableSparseVectorPolynomial{B,T,X}(d) | ||
| # else | ||
| # c₁, c... = cs | ||
| # T = typeof(last(c₁)) | ||
| # for b ∈ c | ||
| # T = promote_type(T, typeof(b)) | ||
| # end | ||
| # ks = 0:length(cs)-1 | ||
| # vs = cs | ||
| # d = Dict{Int,T}(Base.Generator(=>, ks, vs)) | ||
| # return MutableSparseVectorPolynomial{B,T,X}(d) | ||
| # end | ||
| # end | ||
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| constructorof(::Type{<:MutableSparseVectorPolynomial{B}}) where {B <: AbstractBasis} = MutableSparseVectorPolynomial{B} | ||
| @poly_register MutableSparseVectorPolynomial | ||
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| function Base.map(fn, p::P, args...) where {B,T,X, P<:MutableSparseVectorPolynomial{B,T,X}} | ||
| xs = map(fn, p.coeffs) | ||
| R = eltype(xs) | ||
| return MutableSparseVectorPolynomial{B, R, X}(xs) | ||
| end | ||
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| function Base.map!(fn, q::Q, p::P, args...) where {B,T,X, P<:MutableSparseVectorPolynomial{B,T,X},S,Q<:MutableSparseVectorPolynomial{B,S,X}} | ||
| map!(fn, p.coeffs, p.coeffs) | ||
| nothing | ||
| end | ||
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| ## --- | ||
| Base.collect(p::MutableSparseVectorPolynomial) = collect(p.coeffs) | ||
| Base.collect(::Type{T}, p::MutableSparseVectorPolynomial) where {T} = collect(T, p.coeffs) | ||
| minimumexponent(::Type{<:MutableSparseVectorPolynomial}) = 0 | ||
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| Base.length(p::MutableSparseVectorPolynomial) = length(p.coeffs) | ||
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| function degree(p::MutableSparseVectorPolynomial) | ||
| idx = findall(!iszero, p.coeffs) | ||
| isempty(idx) && return -1 | ||
| n = maximum(idx) | ||
| n - 1 | ||
| end | ||
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| Base.copy(p::MutableSparseVectorPolynomial{B,T,X}) where {B,T,X} = MutableSparseVectorPolynomial{B,T,X}(copy(p.coeffs)) | ||
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| function Base.convert(::Type{MutableSparseVectorPolynomial{B,T,X}}, p::MutableSparseVectorPolynomial{B,S,X}) where {B,T,S,X} | ||
| cs = convert(SparseVector{T,Int}, p.coeffs) | ||
| MutableSparseVectorPolynomial{B,T,X}(cs) | ||
| end | ||
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| function Base.:(==)(p1::P, p2::P) where {P <: MutableSparseVectorPolynomial} | ||
| iszero(p1) && iszero(p2) && return true | ||
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| ks1 = findall(!iszero, p1.coeffs) | ||
| ks2 = findall(!iszero, p2.coeffs) | ||
| length(ks1) == length(ks2) || return false | ||
| idx = sortperm(ks1) | ||
| for i ∈ idx | ||
| ks1[i] == ks2[i] || return false | ||
| p1.coeffs[ks1[i]] == p2.coeffs[ks2[i]] || return false | ||
| end | ||
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| return true | ||
| # # eachindex(p1) == eachindex(p2) || return false | ||
| # # coeffs(p1) == coeffs(p2), but non-allocating | ||
| # p1val = (p1[i] for i in eachindex(p1)) | ||
| # p2val = (p2[i] for i in eachindex(p2)) | ||
| # all(((a,b),) -> a == b, zip(p1val, p2val)) | ||
| end | ||
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| # --- | ||
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| Base.firstindex(p::MutableSparseVectorPolynomial) = 0 | ||
| function Base.lastindex(p::MutableSparseVectorPolynomial) | ||
| isempty(p.coeffs) && return 0 | ||
| maximum(keys(p.coeffs)) | ||
| end | ||
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| function Base.getindex(p::MutableSparseVectorPolynomial{B,T,X}, i::Int) where {B,T,X} | ||
| get(p.coeffs, i + 1, zero(T)) | ||
| end | ||
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| # errors if extending | ||
| function Base.setindex!(p::MutableSparseVectorPolynomial{B,T,X}, value, i::Int) where {B,T,X} | ||
| p.coeffs[i+1] = value | ||
| end | ||
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| function Base.pairs(p::MutableSparseVectorPolynomial) | ||
| ks, vs = findnz(p.coeffs) | ||
| idx = sortperm(ks) # guarantee order here | ||
| Base.Generator(=>, ks[idx] .- 1, vs) | ||
| end | ||
| Base.keys(p::MutableSparseVectorPolynomial) = Base.Generator(first, pairs(p)) | ||
| Base.values(p::MutableSparseVectorPolynomial) = Base.Generator(last, pairs(p)) | ||
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| basis(P::Type{<:MutableSparseVectorPolynomial{B, T, X}}, i::Int) where {B,T,X} = P(SparseVector(1+i, [i+1], [1])) | ||
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| # return coeffs as a vector | ||
| function coeffs(p::MutableSparseVectorPolynomial{B,T}) where {B,T} | ||
| d = degree(p) | ||
| ps = p.coeffs | ||
| [ps[i] for i ∈ 1:(d+1)] | ||
| end | ||
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| hasnan(p::MutableSparseVectorPolynomial) = any(hasnan, values(p.coeffs))::Bool | ||
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| offset(p::MutableSparseVectorPolynomial) = 1 | ||
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| function keys_union(p::MutableSparseVectorPolynomial, q::MutableSparseVectorPolynomial) | ||
| # IterTools.distinct(Base.Iterators.flatten((keys(p), keys(q)))) may allocate less | ||
| unique(Base.Iterators.flatten((keys(p), keys(q)))) | ||
| end | ||
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| ## --- | ||
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| chop_exact_zeros!(d::SparseVector{T, Int}) where {T} = d | ||
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| function _truncate!(v::SparseVector{T,X}; | ||
| rtol::Real = Base.rtoldefault(real(T)), | ||
| atol::Real = 0) where {T,X} | ||
| isempty(v) && return v | ||
| δ = something(rtol,0) | ||
| ϵ = something(atol,0) | ||
| τ = max(ϵ, norm(values(v),2) * δ) | ||
| for (i,pᵢ) ∈ pairs(v) | ||
| abs(pᵢ) ≤ τ && (v[i] = zero(T)) | ||
| end | ||
| v | ||
| end | ||
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| chop!(p::MutableSparseVectorPolynomial; kwargs...) = (chop!(p.coeffs; kwargs...); p) | ||
| function chop!(d::SparseVector{T, Int}; atol=nothing, rtol=nothing) where {T} | ||
| isempty(d) && return d | ||
| δ = something(rtol,0) | ||
| ϵ = something(atol,0) | ||
| τ = max(ϵ, norm(values(d),2) * δ) | ||
| for (i, pᵢ) ∈ Base.Iterators.reverse(pairs(d)) | ||
| abs(pᵢ) ≥ τ && break | ||
| d[i] = zero(T) | ||
| end | ||
| d | ||
| end | ||
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| ## --- | ||
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| _zeros(::Type{MutableSparseVectorPolynomial{B,T,X}}, z::S, N) where {B,T,X,S} = zeros(T, N) | ||
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| Base.zero(::Type{MutableSparseVectorPolynomial{B,T,X}}) where {B,T,X} = MutableSparseVectorPolynomial{B,T,X}(spzeros(T,0)) | ||
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| ## --- | ||
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| function isconstant(p::MutableSparseVectorPolynomial) | ||
| degree(p) <= 0 | ||
| end | ||
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| Base.:+(p::MutableSparseVectorPolynomial{B,T,X}, q::MutableSparseVectorPolynomial{B,S,X}) where{B,X,T,S} = | ||
| _sparse_vector_combine(+, p, q) | ||
| Base.:-(p::MutableSparseVectorPolynomial{B,T,X}, q::MutableSparseVectorPolynomial{B,S,X}) where{B,X,T,S} = | ||
| _sparse_vector_combine(-, p, q) | ||
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| # embed into bigger vector | ||
| function _embed(v::SparseVector{T, Int}, l) where {T} | ||
| l == length(v) && return v | ||
| ks,vs = findnz(v) | ||
| SparseVector(l, ks, vs) | ||
| end | ||
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| function _sparse_vector_combine(op, p::MutableSparseVectorPolynomial{B,T,X}, q::MutableSparseVectorPolynomial{B,S,X}) where{B,X,T,S} | ||
| R = promote_type(T,S) | ||
| ps, qs = p.coeffs, q.coeffs | ||
| m = max(length(ps), length(qs)) | ||
| ps′, qs′ = _embed(ps, m), _embed(qs, m) | ||
| cs = op(ps′, qs′) | ||
| MutableSparseVectorPolynomial{B,R,X}(cs) | ||
| end |
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@JuliaRegistrator register
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Registration pull request created: JuliaRegistries/General/91087
After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.
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