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revised grade selection, etc
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@chakravala
chakravala committed Apr 22, 2024
1 parent 6f7f7c3 commit 885b4d9
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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
name = "Grassmann"
uuid = "4df31cd9-4c27-5bea-88d0-e6a7146666d8"
authors = ["Michael Reed"]
version = "0.8.15"
version = "0.8.16"

[deps]
AbstractTensors = "a8e43f4a-99b7-5565-8bf1-0165161caaea"
Expand Down
116 changes: 51 additions & 65 deletions src/algebra.jl
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1257,17 +1257,16 @@ for (op,product) ∈ ((:∧,:exteradd),(:*,:geomadd),
@inbounds for i ∈ 1:bn[g]
if S<:Chain
@inbounds val = :(@inbounds b.v[$(bs[g]+i)])
for j ∈ 1:bn[G+1]
A,B = swapper(ib[j],ia[i],swap)
@inbounds for j ∈ 1:bn[G+1]
@inbounds A,B = swapper(ib[j],ia[i],swap)
X,Y = swapper(:(@inbounds a[$j]),val,swap)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
$preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
end
else
U = UInt(basis(a))
A,B = swapper(U,ia[i],swap)
@inbounds A,B = swapper(UInt(basis(a)),ia[i],swap)
if S<:Single
X,Y = swapper(:(a.v),:(@inbounds b.v[$(bs[g]+i)]),swap)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
$preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,:(@inbounds b.v[$(bs[g]+i)]),false))
end
Expand All @@ -1288,19 +1287,19 @@ for (op,product) ∈ ((:∧,:exteradd),(:*,:geomadd),
A,B = $(swap ? :(@inbounds (ia[i],ib[j])) : :(@inbounds (ib[j],ia[i])))
X,Y = $(swap ? :((val,@inbounds a[j])) : :((@inbounds a[j],val)))
dm = derive_mul(V,A,B,X,Y,$MUL)
if @inbounds $$product!(V,out,A,B,dm)&μ
if $$product!(V,out,A,B,dm)&μ
$(insert_expr((:out,);mv=:out)...)
@inbounds $$product!(V,out,A,B,dm)
$$product!(V,out,A,B,dm)
end
end end
else quote
A,B = $(swap ? :((@inbounds ia[i],$(UInt(basis(a))))) : :(($(UInt(basis(a))),@inbounds ia[i])))
$(if S<:Single; quote
X,Y=$(swap ? :((b.v[bs[g]+1],a.v)) : :((a.v,@inbounds b.v[rs[g]+1])))
dm = derive_mul(V,A,B,X,Y,$MUL)
if @inbounds $$product!(V,out,A,B,dm)&μ
if $$product!(V,out,A,B,dm)&μ
$(insert_expr((:out,);mv=:out)...)
@inbounds $$product!(V,out,A,B,dm)
$$product!(V,out,A,B,dm)
end end
else
:(if @inbounds $$product!(V,out,A,B,derive_mul(V,A,B,b.v[rs[g]+i],false))&μ
Expand Down Expand Up @@ -1338,19 +1337,16 @@ for input ∈ (:Spinor,:AntiSpinor)
@inbounds for i ∈ 1:bn[g]
@inbounds val = par ? :(@inbounds -b.v[$(bs[g]+i)]) : :(@inbounds b.v[$(bs[g]+i)])
if S<:Chain
for j ∈ 1:bn[G+1]
A,B = swapper(ib[j],ia[i],true)
X,Y = swapper(:(@inbounds a[$j]),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
@inbounds for j ∈ 1:bn[G+1]
@inbounds A,B = ia[i],ib[j]
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,:(@inbounds a[$j]),MUL))
end
else
U = UInt(basis(a))
A,B = swapper(U,ia[i],true)
@inbounds A,B = ia[i],UInt(basis(a))
if S<:Single
X,Y = swapper(:(a.v),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,:(a.v),MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
end
end
end
Expand All @@ -1364,11 +1360,11 @@ for input ∈ (:Spinor,:AntiSpinor)
!isnull(val) && for g2 ∈ $(inspin ? :(evens(1,N+1)) : :(evens(2,N+1)))
io = indexbasis(N,g2-1)
par = swap ? parityclifford(g2-1) : false
for j ∈ 1:bn[g2]
@inbounds for j ∈ 1:bn[g2]
val2 = :(b.v[$(bs[g2]+j)])
A,B = swapper(io[j],ia[i],true)
X,Y = swapper(par ? :(@inbounds -$val2) : :(@inbounds $val2),val,true)
$preproduct2!(V,out2,A,B,derive_pre(V,A,B,X,Y,MUL))
@inbounds A,B = ia[i],io[j]
Y = par ? :(@inbounds -$val2) : :(@inbounds $val2)
$preproduct2!(V,out2,A,B,derive_pre(V,A,B,val,Y,MUL))
end
end
end
Expand Down Expand Up @@ -1427,47 +1423,41 @@ for input ∈ (:Chain,)
VECS = isodd(G) ? VEC : string(VEC)*"s"
if mdims(V)<cache_limit
$(insert_expr((:N,:t,:ib,:bn,:μ))...)
il = indexbasis(N,L)
bs = (iseven(L) ? spinsum_set : antisum_set)(N)
out = svecs(N,Any)(zeros(svecs(N,t)))
par = parityclifford(L)
if Q <: Chain
ia = indexbasis(N,L)
@inbounds for i ∈ 1:bn[L+1]
@inbounds val = (swap ? false : par) ? :(@inbounds -b.v[$i]) : :(@inbounds b.v[$i])
if S<:Chain
for j ∈ 1:bn[G+1]
A,B = swapper(ib[j],ia[i],true)
X,Y = swapper(:(@inbounds a[$j]),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
@inbounds for j ∈ 1:bn[G+1]
@inbounds A,B = il[i],ib[j]
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,:(@inbounds a[$j]),MUL))
end
else
U = UInt(basis(a))
A,B = swapper(U,ia[i],true)
@inbounds A,B = il[i],UInt(basis(a))
if S<:Single
X,Y = swapper(:(a.v),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,:(a.v),MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
end
end
end
else
U2 = UInt(basis(b))
@inbounds val = (swap ? false : par) ? :(@inbounds -value(b)) : :(@inbounds value(b))
A = UInt(basis(b))
val = (swap ? false : par) ? :(-value(b)) : :(value(b))
if S<:Chain
for j ∈ 1:bn[G+1]
A,B = swapper(ib[j],U2,true)
X,Y = swapper(:(@inbounds a[$j]),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
@inbounds for j ∈ 1:bn[G+1]
@inbounds B = ib[j]
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,:(@inbounds a[$j]),MUL))
end
else
U = UInt(basis(a))
A,B = swapper(U,U2,true)
B = UInt(basis(a))
if S<:Single
X,Y = swapper(:(a.v),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,:(a.v),MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
end
end
end
Expand All @@ -1478,19 +1468,18 @@ for input ∈ (:Chain,)
@inbounds for i ∈ 1:bn[g]
@inbounds val = out[bs2[g]+i]
!isnull(val) && if Q<:Chain
for j ∈ 1:bn[L+1]
A,B = swapper(ib[j],ia[i],true)
X,Y = swapper((swap ? par : false) ? :(@inbounds -b[$j]) : :(@inbounds b[$j]),val,true)
@inbounds $preproduct2!(V,out2,A,B,derive_pre(V,A,B,X,Y,MUL))
@inbounds for j ∈ 1:bn[L+1]
@inbounds A,B = ia[i],il[j]
Y = (swap ? par : false) ? :(@inbounds -b[$j]) : :(@inbounds b[$j])
$preproduct2!(V,out2,A,B,derive_pre(V,A,B,val,Y,MUL))
end
else
U = UInt(basis(b))
A,B = swapper(U,ia[i],true)
@inbounds A,B = ia[i],UInt(basis(b))
if Q<:Single
X,Y = swapper((swap ? par : false) ? :(-value(b)) : :(value(b)),val,true)
@inbounds $preproduct2!(V,out2,A,B,derive_pre(V,A,B,X,Y,MUL))
Y = swapper((swap ? par : false) ? :(-value(b)) : :(value(b)),val,true)
$preproduct2!(V,out2,A,B,derive_pre(V,A,B,val,Y,MUL))
else
@inbounds $preproduct2!(V,out2,A,B,derive_pre(V,A,B,val,false))
$preproduct2!(V,out2,A,B,derive_pre(V,A,B,val,false))
end
end
end
Expand Down Expand Up @@ -1522,21 +1511,18 @@ for input ∈ (:Couple,:PseudoCouple)
if N<cache_limit
$(insert_expr((:t,:ib,:bn,:μ))...)
out = svecs(N,Any)(zeros(svecs(N,t)))
for (U2,val) ∈ ((UInt(BB),(swap ? false : parityclifford(grade(BB))) ? :(-value(imaginary(b))) : :(value(imaginary(b)))),(indexbasis(N,$pg)[1],(swap ? false : parityclifford($pg)) ? :(-value($$calar(b))) : :(value($$calar(b)))))
for (A,val) ∈ ((UInt(BB),(swap ? false : parityclifford(grade(BB))) ? :(-value(imaginary(b))) : :(value(imaginary(b)))),(indexbasis(N,$pg)[1],(swap ? false : parityclifford($pg)) ? :(-value($$calar(b))) : :(value($$calar(b)))))
if S<:Chain
for j ∈ 1:bn[G+1]
A,B = swapper(ib[j],U2,true)
X,Y = swapper(:(@inbounds a[$j]),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
@inbounds for j ∈ 1:bn[G+1]
@inbounds B = ib[j]
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,:(@inbounds a[$j]),MUL))
end
else
U = UInt(basis(a))
A,B = swapper(U,U2,true)
B = UInt(basis(a))
if S<:Single
X,Y = swapper(:(a.v),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,:(a.v),MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
$preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
end
end
end
Expand All @@ -1547,8 +1533,8 @@ for input ∈ (:Couple,:PseudoCouple)
@inbounds for i ∈ 1:bn[g]
@inbounds val = out[bs2[g]+i]
!isnull(val) && for (B,val2) ∈ ((UInt(BB),(swap ? parityclifford(grade(BB)) : false) ? :(-value(imaginary(b))) : :(value(imaginary(b)))),(indexbasis(N,$pg)[1],(swap ? parityclifford($pg) : false) ? :(-value($$calar(b))) : :(value($$calar(b)))))
A = ia[i] #A,B = swapper(U,ia[i],true)
@inbounds $preproduct2!(V,out2,A,B,derive_pre(V,A,B,val,val2,MUL))
@inbounds A = ia[i]
$preproduct2!(V,out2,A,B,derive_pre(V,A,B,val,val2,MUL))
end
end
end
Expand Down
22 changes: 22 additions & 0 deletions src/composite.jl
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1082,3 +1082,25 @@ Base.rand(::AbstractRNG,::SamplerType{PseudoCouple{V}}) where V = rand(PseudoCou
Base.rand(::AbstractRNG,::SamplerType{PseudoCouple{V,B}}) where {V,B} = PseudoCouple{V,B}(rand(Complex{Float64}))
Base.rand(::AbstractRNG,::SamplerType{PseudoCouple{V,B,T}}) where {V,B,T} = PseudoCouple{V,B}(rand(Complex{T}))
Base.rand(::AbstractRNG,::SamplerType{PseudoCouple{V,B,T} where B}) where {V,T} = rand(PseudoCouple{V,Submanifold{V}(UInt(rand(0:(1<<mdims(V)-1)-1))),T})

# Dyadic

export operator, gradedoperator

@generated function operator(t::TensorAlgebra{V},::Val{G}=Val(1)) where {V,G}
N = mdims(V)
r,b = binomsum(N,G),binomial(N,G)
bas = Λ(V).b[list(r+1,r+b)]
:(Chain{V,G}($bas .⊘ Ref(t)))
end
operator(t::TensorAlgebra,G::Int) = operator(t,Val(G))
gradedoperator(t::TensorAlgebra{V}) where V = Multivector{V}(Λ(V).b .⊘ Ref(t))

@generated function operator(fun,V,::Val{G}=Val(1)) where G
N = mdims(V)
r,b = binomsum(N,G),binomial(N,G)
bas = Λ(V()).b[list(r+1,r+b)]
:(Chain{V,G}(fun.($bas)))
end
operator(fun,V,G::Int) = operator(fun,V,Val(G))
gradedoperator(fun,V) = Multivector{V}(fun.(Λ(V).b))
36 changes: 34 additions & 2 deletions src/multivectors.jl
View file
Original file line number Diff line number Diff line change
Expand Up @@ -85,6 +85,14 @@ Chain(v::Chain{V,G,𝕂}) where {V,G,𝕂} = v
DyadicProduct{V,W,G,T,N} = Chain{V,G,Chain{W,G,T,N},N}
DyadicChain{V,G,T,N} = DyadicProduct{V,V,G,T,N}

Base.Matrix(m::Chain{V,G,<:Chain{W,G}}) where {V,W,G} = hcat(value.(value(m))...)
DyadicChain(m::Matrix) = Chain{Submanifold(size(m)[1]),1}(m)
function Chain{V,G}(m::Matrix) where {V,G}
N = size(m)[2]
Chain{V,G,Chain{N≠mdims(V) ? Submanifold(N) : V,G}}(m)
end
Chain{V,G,Chain{W,G}}(m::Matrix) where {V,W,G} = Chain{V,G}(Chain{W,G}.(getindex.(Ref(m),:,list(1,size(m)[2]))))

export Chain, DyadicProduct, DyadicChain
getindex(m::Chain,i::Int) = m.v[i]
getindex(m::Chain,i::UnitRange{Int}) = m.v[i]
Expand Down Expand Up @@ -310,6 +318,16 @@ Multivector(val::NTuple{N,T}) where {N,T} = Multivector{log2sub(N)}(Values{N,T}(
Multivector(val::NTuple{N,Any}) where N = Multivector{log2sub(N)}(Values{N}(val))
@inline (::Type{T})(x...) where {T<:Multivector} = T(x)

DyadicMultivector{V,T,N} = Multivector{V,Multivector{V,T,N},N}

Base.Matrix(m::Multivector{V,<:Multivector{W}}) where {V,W} = hcat(value.(value(m))...)
DyadicMultivector(m::Matrix) = Multivector{log2sub(size(m)[1]),1}(m)
function Multivector{V}(m::Matrix) where V
N = size(m)[2]
Multivector{V,Multivector{Int(log2(N))≠mdims(V) ? log2sub(N) : V}}(m)
end
Multivector{V,Chain{W}}(m::Matrix) where {V,W} = Multivector{V}(Multivector{W}.(getindex.(Ref(m),:,list(1,size(m)[2]))))

function grade_src_chain(N,G,r=binomsum(N,G),is=isempty,T=Int)
:(Chain{V,$G,T}($(grade_src(N,G,r,is,T))))
end
Expand All @@ -326,7 +344,7 @@ end
for fun ∈ (:grade_src,:grade_src_chain)
nex = Symbol(fun,:_next)
@eval function $nex(N,G,r=binomsum,is=isempty,T=Int)
Expr(:elseif,:(G==$(N-G)),($fun(N,N-G,r(N,G),is,T),G-1≥0 ? $nex(N,G-1,r,is,T) : nothing)...)
Expr(:elseif,:(G==$(N-G)),($fun(N,N-G,r(N,N-G),is,T),G-1≥0 ? $nex(N,G-1,r,is,T) : nothing)...)
end
end

Expand Down Expand Up @@ -450,6 +468,7 @@ abstract type AbstractSpinor{V} <: TensorMixed{V} end
@pure log2sub2(N) = log2sub(2N)

for pinor ∈ (:Spinor,:AntiSpinor)
dpinor = Symbol(:Dyadic,pinor)
@eval begin
@computed struct $pinor{V,𝕂} <: AbstractSpinor{V}
v::Values{1<<(mdims(V)-1),𝕂}
Expand Down Expand Up @@ -482,6 +501,14 @@ for pinor ∈ (:Spinor,:AntiSpinor)
equal(a::Multivector{V,T},b::$pinor{V,S}) where {V,T,S} = equal(a,Multivector(b))
equal(a::Chain{V,G,T},b::$pinor{V,S}) where {V,S,G,T} = b == a
equal(a::T,b::$pinor{V,S} where S) where T<:TensorTerm{V} where V = b==a
$dpinor{V,T,N} = $pinor{V,$pinor{V,T,N},N}
Base.Matrix(m::$pinor{V,<:$pinor{W}}) where {V,W} = hcat(value.(value(m))...)
$pinor(m::Matrix) = $pinor{log2sub(size(m)[1]),1}(m)
function $pinor{V}(m::Matrix) where V
N = size(m)[2]
$pinor{V,$pinor{Int(log2(N))≠mdims(V) ? log2sub(N) : V}}(m)
end
$pinor{V,$pinor{W}}(m::Matrix) where {V,W} = $pinor{V}($pinor{W}.(getindex.(Ref(m),:,list(1,size(m)[2]))))
end
end

Expand Down Expand Up @@ -724,6 +751,11 @@ Spinor{V,𝕂}(z::PseudoCouple{V,B,𝕂}) where {V,B,𝕂} = Spinor{V}(imaginary
AntiSpinor{V}(val::PseudoCouple{V,B,𝕂}) where {V,B,𝕂} = AntiSpinor{V,𝕂}(val)
AntiSpinor{V,𝕂}(z::PseudoCouple{V,B,𝕂}) where {V,B,𝕂} = AntiSpinor{V}(imaginary(z),volume(z))

(t::Couple{V,B})(G::Int) where {V,B} = grade(B) == G ? imaginary(t) : iszero(G) ? scalar(t) : Zero(V)
(t::PseudoCouple{V,B})(G::Int) where {V,B} = grade(B) == G ? imaginary(t) : iszero(G) ? volume(t) : Zero(V)
(t::Couple{V,B})(::Val{G}) where {V,B,G} = grade(B) == G ? imaginary(t) : iszero(G) ? scalar(t) : Zero(V)
(t::PseudoCouple{V,B})(::Val{G}) where {V,B,G} = grade(B) == G ? imaginary(t) : iszero(G) ? volume(t) : Zero(V)

@pure function Base.getproperty(a::Couple{V,B,T},v::Symbol) where {V,B,T}
return if v == :v
getfield(a,:v)
Expand Down Expand Up @@ -984,7 +1016,7 @@ import AbstractTensors: antiabs, antiabs2, geomabs, unit, unitize, unitnorm
import AbstractTensors: value, valuetype, scalar, isscalar, involute, even, odd
import AbstractTensors: vector, isvector, bivector, isbivector, volume, isvolume, ⋆
import LinearAlgebra: rank, norm
export gdims, betti, χ
export gdims, betti, χ, unit
export basis, grade, pseudograde, antigrade, hasinf, hasorigin, scalar, norm, unitnorm
export valuetype, scalar, isscalar, vector, isvector, indices, imaginary, unitize, geomabs
export bivector, isbivector, trivector, istrivector, volume, isvolume, antiabs, antiabs2
Expand Down

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Registration pull request created: JuliaRegistries/General/105384

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