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refined some syntax
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@chakravala
chakravala committed Jan 25, 2025
1 parent 45d04f9 commit f5a784f
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Showing 4 changed files with 65 additions and 83 deletions.
8 changes: 0 additions & 8 deletions src/Grassmann.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -562,14 +562,6 @@ function __init__()
Chain(m::StaticArrays.SMatrix{N,N}) where N = Chain{Submanifold(N),1}(m)
Chain{V,G}(m::StaticArrays.SMatrix{N,N}) where {V,G,N} = Chain{V,G}(Chain{V,G}.(getindex.(Ref(m),:,StaticArrays.SVector{N}(1:N))))
Chain{V,G,<:Chain{W,G}}(m::StaticArrays.SMatrix{M,N}) where {V,W,G,M,N} = Chain{V,G}(Chain{W,G}.(getindex.(Ref(m),:,StaticArrays.SVector{N}(1:N))))
#Base.log(A::Chain{V,G,<:Chain{V,G}}) where {V,G} = Chain{V,G}(log(StaticArrays.SMatrix(A)))
LinearAlgebra.eigvals(A::Chain{V,G,<:Chain{V,G}}) where {V,G} = Chain(Values{binomial(mdims(V),G)}(LinearAlgebra.eigvals(StaticArrays.SMatrix(A))))
LinearAlgebra.eigvecs(A::Chain{V,G,<:Chain{V,G}}) where {V,G} = Chain(Chain.(Values{binomial(mdims(A),G)}.(getindex.(Ref(LinearAlgebra.eigvecs(StaticArrays.SMatrix(A))),:,list(1,binomial(mdims(A),G))))))
function LinearAlgebra.eigen(A::Chain{V,G,<:Chain{V,G}}) where {V,G}
E,N = eigen(StaticArrays.SMatrix(A)),binomial(mdims(V),G)
e = Chain(Chain.(Values{N}.(getindex.(Ref(E.vectors),:,list(1,N)))))
Proj(e,Chain(Values{N}(E.values)))
end
end
@require Meshes = "eacbb407-ea5a-433e-ab97-5258b1ca43fa" begin
Meshes.Point(t::Values) = Meshes.Point(Tuple(t.v))
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89 changes: 24 additions & 65 deletions src/composite.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -16,9 +16,7 @@ export exph, log_fast, logh_fast, pseudoexp, pseudolog, pseudometric, pseudodot,
export pseudoabs, pseudoabs2, pseudosqrt, pseudocbrt, pseudoinv, pseudoscalar
export pseudocos, pseudosin, pseudotan, pseudocosh, pseudosinh, pseudotanh
export coabs, coabs2, cosqrt, cocbrt, coinv, coscalar, coexp, colog, cometric, codot, @co
export cocos, cosin, cotan, cocosh, cosinh, cotanh

export vandermonde, volumes, detsimplex, submesh
export cocos, cosin, cotan, cocosh, cosinh, cotanh, vandermonde, volumes, submesh

## exponential & logarithm function

Expand Down Expand Up @@ -740,8 +738,8 @@ end
else
x,y,xy = Grassmann.Cramer(N-1,1)
mid = [:(signscalar(($(x[i])∧(v-x1)∧$(y[end-i]))/d)) for i ∈ list(1,N-2)]
out = Values(:(signscalar((v∧∧(vectors(t,v)))/d)),mid...,:(signscalar(($(x[end])∧(v-x1))/d)))
return Expr(:block,:(T=vectors(t)),:((x1,y1)=@inbounds (t[1],T[end])),xy...,
out = Values(:(signscalar((v∧∧(affineframe(t,v)))/d)),mid...,:(signscalar(($(x[end])∧(v-x1))/d)))
return Expr(:block,:(T=value(affineframe(t))),:((x1,y1)=@inbounds (t[1],T[end])),xy...,
:($(x[end])=$(x[end-1])∧T[end-1];d=$(x[end])∧T[end]),ands(out))
end
end
Expand Down Expand Up @@ -836,19 +834,17 @@ function vandermondeinterp(x,y,V,grid) # grid=384
return coef,xp,yp # coefficients, interpolation
end

@generated function vectors(t,c=columns(t))
v = Expr(:tuple,[:(M.(p[c[$i]]-A)) for i ∈ list(2,mdims(t))]...)
quote
p = points(t)
M,A = ↓(Manifold(p)),p[c[1]]
Chain{M,1}.($(Expr(:.,:Values,v)))
end
end
@pure list(a::Int,b::Int) = Values{max(0,b-a+1),Int}(a:b...)
@pure evens(a::Int,b::Int) = Values{((b-a)÷2)+1,Int}(a:2:b...)
vectors(x::Values{N,<:Chain{V}},y=x[1]) where {N,V} = ↓(V).(x[list(2,N)].-y)
vectors(x::Chain{V,1},y=x[1]) where V = vectors(value(x),y)
#point(x,y=x[1]) = y∧∧(vectors(x))
affineframe(x::Values{1,<:Chain{V,G,T,N}},y=nothing) where {V,G,T,N} = Values{0,Chain{↓(V),G,T,N-1}}()
@generated function affineframe(x::Values{N,<:Chain{V}},y=x[1]) where {N,V}
M = :(V($(list(2,N)...)))
:(TensorOperator(Chain{$M,1}(↓(V).(x[$(list(2,N))].-y))))
end
affineframe(x::Chain{V,1},y=x[1]) where V = affineframe(value(x),y)
export affineframe
const vectors = affineframe
#point(x,y=x[1]) = y∧∧(affineframe(x))

signscalar(x::Submanifold{V,0} where V) = true
signscalar(x::Single{V,0} where V) = !signbit(value(x))
Expand All @@ -858,56 +854,37 @@ signscalar(x::Chain{V,0} where V) = !signbit(@inbounds x[1])
signscalar(x::Multivector) = isscalar(x) && !signbit(value(scalar(x)))
ands(x,i=length(x)-1) = i ≠ 0 ? Expr(:&&,x[end-i],ands(x,i-1)) : x[end-i]

function Base.findfirst(P,t::Vector{<:Chain{V,1,<:Chain}} where V)
function Base.findfirst(P,t::AbstractVector{<:Chain{V,1,<:Chain}} where V)
for i ∈ 1:length(t)
@inbounds P ∈ t[i] && (return i)
end
return 0
end
function Base.findfirst(P,t::ChainBundle)
p = points(t)
for i ∈ 1:length(t)
P ∈ p[t[i]] && (return i)
end
return 0
end
function Base.findlast(P,t::Vector{<:Chain{V,1,<:Chain}} where V)
function Base.findlast(P,t::AbstractVector{<:Chain{V,1,<:Chain}} where V)
for i ∈ length(t):-1:1
@inbounds P ∈ t[i] && (return i)
end
return 0
end
function Base.findlast(P,t::ChainBundle)
p = points(t)
for i ∈ length(t):-1:1
P ∈ p[t[i]] && (return i)
end
return 0
end
Base.findall(P,t) = findall(P .∈ getindex.(points(t),value(t)))
Base.findall(P,t::AbstractVector{<:Chain{V,1,<:Chain}} where V) = findall(P .∈ t)

edgelength(e) = (v=points(e)[value(e)]; Real(abs(v[2]-v[1])))
volumes(m,dets) = Real.(abs.(dets))
volumes(m) = mdims(Manifold(m))≠2 ? Real.(abs.(detsimplex(m))) : edgelength.(value(m))
detsimplex(m::Vector{<:Chain{V}}) where V = det(m)/factorial(mdims(V)-1)
detsimplex(m::ChainBundle) = detsimplex(value(m))
mean(m::T) where T<:AbstractVector{<:Chain} = sum(m)/length(m)
mean(m::T) where T<:Values = sum(m)/length(m)
mean(m::AbstractVector) = sum(m)/length(m)
mean(m::Values{N}) where N = sum(m)/N
mean(m::Chain{V,1,<:Chain} where V) = mean(value(m))
barycenter(m::Values{N,<:Chain}) where N = (s=sum(m);@inbounds s/s[1])
barycenter(m::Vector{<:Chain}) = (s=sum(m);@inbounds s/s[1])
barycenter(m::AbstractVector{<:Chain}) = (s=sum(m);@inbounds s/s[1])
barycenter(m::Chain{V,1,<:Chain} where V) = barycenter(value(m))
curl(m::FixedVector{N,<:Chain{V}} where N) where V = curl(Chain{V,1}(m))
curl(m::Values{N,<:Chain{V}} where N) where V = curl(Chain{V,1}(m))
curl(m::T) where T<:TensorAlgebra = Manifold(m)(∇)×m
LinearAlgebra.det(t::Chain{V,1,<:Chain} where V) = !∧(t)
LinearAlgebra.det(m::Vector{<:Chain{V}}) where V = .!∧(m)
LinearAlgebra.det(m::ChainBundle) = .!∧(m)
∧(m::ChainBundle) = ∧(value(m))
function ∧(m::Vector{<:Chain{V}}) where V
function ∧(m::DenseVector{<:Chain{V}}) where V
p = points(m); pm = p[m]
if mdims(p)>mdims(V)
.∧(vectors.(pm))
.∧(affineframe.(pm))
else
Chain{↓(Manifold(V)),mdims(V)-1}.(value.(.∧(pm)))
end
Expand Down Expand Up @@ -953,31 +930,13 @@ function refinemesh!(::R,p::ChainBundle{W},e,t,η,_=nothing) where {W,R<:Abstrac
end
end

const array_cache = (Array{T,2} where T)[]
array(m::Vector{<:Chain}) = [m[i][j] for i∈1:length(m),j∈list(1,mdims(Manifold(m)))]
function array(m::ChainBundle{V,G,T,B} where {V,G,T}) where B
for k ∈ length(array_cache):B
push!(array_cache,Array{Any,2}(undef,0,0))
end
isempty(array_cache[B]) && (array_cache[B] = array(value(m)))
return array_cache[B]
end
function array!(m::ChainBundle{V,G,T,B} where {V,G,T}) where B
length(array_cache) ≥ B && (array_cache[B] = Array{Any,2}(undef,0,0))
end
array(m::ChainBundle) = array(value(m))
array!(m::ChainBundle) = nothing

const submesh_cache = (Array{T,2} where T)[]
submesh(m) = [m[i][j] for i∈1:length(m),j∈list(2,mdims(Manifold(m)))]
function submesh(m::ChainBundle{V,G,T,B} where {V,G,T}) where B
for k ∈ length(submesh_cache):B
push!(submesh_cache,Array{Any,2}(undef,0,0))
end
isempty(submesh_cache[B]) && (submesh_cache[B] = submesh(value(m)))
return submesh_cache[B]
end
function submesh!(m::ChainBundle{V,G,T,B} where {V,G,T}) where B
length(submesh_cache) ≥ B && (submesh_cache[B] = Array{Any,2}(undef,0,0))
end
submesh(m::ChainBundle) = submesh(value(m))
submesh!(m::ChainBundle) = nothing

for op ∈ (:div,:rem,:mod,:mod1,:fld,:fld1,:cld,:ldexp)
@eval begin
Expand Down
45 changes: 37 additions & 8 deletions src/forms.jl
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Expand Up @@ -527,10 +527,17 @@ struct TensorOperator{V,W,T<:TensorAlgebra{V,<:TensorAlgebra{W}}} <: TensorNeste
TensorOperator{V,W}(t::T) where {V,W,T<:TensorAlgebra{V,<:TensorAlgebra{W}}} = new{V,W,T}(t)
TensorOperator{V}(t::T) where {V,W,T<:TensorAlgebra{V,<:TensorAlgebra{W}}} = new{V,W,T}(t)
TensorOperator(t::T) where {V,W,T<:TensorAlgebra{V,<:TensorAlgebra{W}}} = new{V,W,T}(t)
TensorOperator(t::T) where {V,W,G,T<:Chain{V,G,<:TensorAlgebra{W},1}} = new{V,W,T}(t)
end

const Endomorphism{V,T<:TensorAlgebra{V,<:TensorAlgebra{V}}} = TensorOperator{V,V,T}
Endomorphism(t::TensorAlgebra{V,<:TensorAlgebra{V}}) where V = TensorOperator{V,V}(t)
for op ∈ (:TensorOperator,:Endomorphism)
@eval $op(t::Vararg{Chain{V,G,T,N},N}) where {V,G,T,N} = $op(Chain{V,G}(t...))
for typ ∈ (:Spinor,:CoSpinor,:Multivector)
@eval $op(t::Vararg{$typ{V,T,N},N}) where {V,T,N} = $op($typ{V}(t...))
end
end

(T::TensorOperator{V})(x::TensorAlgebra{V}) where V = contraction(T,x)
function (T::TensorOperator{V,W})(x::TensorAlgebra{V},y::TensorAlgebra{W}) where {V,W}
Expand All @@ -550,6 +557,7 @@ compound(m::TensorOperator,g) = TensorOperator(compound(value(m),g))
compound(m::TensorOperator,g::Integer) = TensorOperator(compound(value(m),g))
getindex(t::TensorOperator,i::Int,j::Int) = value(value(t.v)[j])[i]
getindex(t::TensorOperator,i::Int) = value(t.v)[i]
Base.lastindex(t::TensorOperator) = lastindex(value(t))
Base.transpose(t::TensorOperator) = TensorOperator(transpose(value(t)))
scalar(m::Endomorphism) = tr(m)/length(value(m))
LinearAlgebra.tr(m::Endomorphism) = tr(value(m))
Expand Down Expand Up @@ -582,17 +590,18 @@ TensorOperator(m::AbstractMatrix) = TensorOperator{Submanifold.(size(m))...}(m)
TensorOperator{V,W}(m::AbstractMatrix) where {V,W} = TensorOperator(Chain{V}(Chain{W,1}.(getindex.(Ref(m),:,list(1,mdims(V))))))

SpectralOperator(t::Endomorphism) = eigen(t)
@generated function DiagonalOperator(t::Endomorphism{V,<:Chain{V,G}}) where {V,G}
Expr(:call,:DiagonalOperator,Expr(:call,:(Chain{V,G}),[:(t[$i,$i]) for i ∈ list(1,binomial(mdims(V),G))]...))
DiagonalOperator(t::Endomorphism) = DiagonalOperator(LinearAlgebra.diag(t))
@generated function LinearAlgebra.diag(t::Endomorphism{V,<:Chain{V,G}}) where {V,G}
Expr(:call,:(Chain{V,G}),[:(t[$i,$i]) for i ∈ list(1,binomial(mdims(V),G))]...)
end
@generated function DiagonalOperator(t::Endomorphism{V,<:Spinor{V}}) where V
Expr(:call,:DiagonalOperator,Expr(:call,:(Spinor{V}),[:(t[$i,$i]) for i ∈ list(1,binomial(mdims(V),G))]...))
@generated function LinearAlgebra.diag(t::Endomorphism{V,<:Spinor{V}}) where V
Expr(:call,:(Spinor{V}),[:(t[$i,$i]) for i ∈ list(1,binomial(mdims(V),G))]...)
end
@generated function DiagonalOperator(t::Endomorphism{V,<:AntiSpinor{V}}) where V
Expr(:call,:DiagonalOperator,Expr(:call,:(AntiSpinor{V}),[:(t[$i,$i]) for i ∈ list(1,binomial(mdims(V),G))]...))
@generated function LinearAlgebra.diag(t::Endomorphism{V,<:AntiSpinor{V}}) where V
Expr(:call,:(AntiSpinor{V}),[:(t[$i,$i]) for i ∈ list(1,binomial(mdims(V),G))]...)
end
@generated function DiagonalOperator(t::Endomorphism{V,<:Multivector{V}}) where V
Expr(:call,:DiagonalOperator,Expr(:call,:(Multivector{V}),[:(t[$i,$i]) for i ∈ list(1,1<<mdims(V))]...))
@generated function LinearAlgebra.diag(t::Endomorphism{V,<:Multivector{V}}) where V
Expr(:call,:(Multivector{V}),[:(t[$i,$i]) for i ∈ list(1,1<<mdims(V))]...)
end

_axes(t::TensorOperator) = (Base.OneTo(length(t.v)),Base.OneTo(length(t.v)))
Expand Down Expand Up @@ -1494,3 +1503,23 @@ isinduced(::Type{<:InducedMetric}) = true
@inline Base.log(t::Real,g::InducedMetric) = Base.log(t)
@inline Base.log(t::Complex,g::InducedMetric) = Base.log(t)

# other

affineframe(x::TensorOperator,y=x[1]) = affineframe(value(value(x)),y)
mean(m::TensorOperator) = mean(value(value(m)))
barycenter(m::TensorOperator) = barycenter(value(value(m)))
curl(m::TensorAlgebra) = Manifold(m)(∇)×m
Base.findall(P,t::AbstractVector{<:TensorOperator}) = findall(P .∈ t)
function Base.findfirst(P,t::AbstractVector{<:TensorOperator})
for i ∈ 1:length(t)
@inbounds P ∈ value(t[i]) && (return i)
end
return 0
end
function Base.findlast(P,t::AbstractVector{<:TensorOperator})
for i ∈ length(t):-1:1
@inbounds P ∈ value(t[i]) && (return i)
end
return 0
end

6 changes: 4 additions & 2 deletions src/multivectors.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -227,13 +227,15 @@ end

@pure Manifold(::ChainBundle{V}) where V = V
@pure Manifold(::Type{<:ChainBundle{V}}) where V = V
@pure Manifold(::Vector{<:Chain{V}}) where V = V
@pure Manifold(::AbstractVector{<:Chain{V}}) where V = V
@pure Manifold(::Type{<:AbstractVector{<:Chain{V}}}) where V = V
@pure LinearAlgebra.rank(M::ChainBundle{V,G} where V) where G = G
@pure grade(::ChainBundle{V}) where V = grade(V)
@pure antigrade(::ChainBundle{V}) where V = antigrade(V)
@pure AbstractTensors.mdims(::ChainBundle{V}) where V = mdims(V)
@pure AbstractTensors.mdims(::Type{T}) where T<:ChainBundle{V} where V = mdims(V)
@pure AbstractTensors.mdims(::Vector{<:Chain{V}}) where V = mdims(V)
@pure AbstractTensors.mdims(::AbstractVector{<:Chain{V}}) where V = mdims(V)
@pure AbstractTensors.mdims(::Type{<:AbstractVector{<:Chain{V}}}) where V = mdims(V)
@pure Base.parent(::ChainBundle{V}) where V = isbundle(V) ? parent(V) : V
@pure Base.parent(::Vector{<:Chain{V}}) where V = isbundle(V) ? parent(V) : V
@pure DirectSum.supermanifold(m::ChainBundle{V}) where V = V
Expand Down

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Registration pull request created: JuliaRegistries/General/123707

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## Breaking changes

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