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enhanced algebra operators
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@chakravala
chakravala committed Apr 19, 2024
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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 = "0.8.14"
version = "0.8.15"

[deps]
AbstractTensors = "a8e43f4a-99b7-5565-8bf1-0165161caaea"
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162 changes: 119 additions & 43 deletions src/algebra.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -241,30 +241,47 @@ end

export ⊘, sandwich, pseudosandwich

⊘(x::TensorAlgebra{V},y::TensorAlgebra{V}) where V = clifford(y)*x*y
⊘(x::TensorTerm{V},y::TensorTerm{V}) where V = clifford(y)*x*y
⊘(x::TensorGraded{V},y::Couple{V}) where V = x⊘multispin(y)
⊘(x::TensorGraded{V},y::PseudoCouple{V}) where V = x⊘multispin(y)
@generated ⊘(a::TensorGraded{V,G},b::TensorGraded{V,L}) where {V,G,L} = product_sandwich(a,b)
⊘(x::TensorTerm{V},y::TensorTerm{V}) where V = reverse(y)*x*involute(y)
⊘(x::TensorAlgebra{V},y::TensorAlgebra{V}) where V = reverse(y)*x*involute(y)
⊘(x::Couple{V},y::TensorAlgebra{V}) where V = (scalar(x)⊘y)+(imaginary(x)⊘y)
⊘(x::PseudoCouple{V},y::TensorAlgebra{V}) where V = (imaginary(x)⊘y)+(volume(x)⊘y)
@generated ⊘(a::TensorGraded{V,G},b::Spinor{V}) where {V,G} = product_sandwich(a,b)
@generated ⊘(a::TensorGraded{V,G},b::AntiSpinor{V}) where {V,G} = product_sandwich(a,b)
@generated ⊘(a::TensorGraded{V,G},b::Couple{V}) where {V,G} = product_sandwich(a,b)
@generated ⊘(a::TensorGraded{V,G},b::PseudoCouple{V}) where {V,G} = product_sandwich(a,b)
@generated ⊘(a::TensorGraded{V,G},b::TensorGraded{V,L}) where {V,G,L} = product_sandwich(a,b)
#=for t ∈ (:Spinor,:AntiSpinor)
@eval quote
@generated ⊘(a::Spinor{V,G},b::$$t{V}) where {V,G} = product_sandwich(a,b)
@generated ⊘(a::AntiSpinor{V,G},b::$$t{V}) where {V,G} = product_sandwich(a,b)
@generated ⊘(a::Multivector{V,G},b::$$t{V}) where {V,G} = product_sandwich(a,b)
end
end=#

@doc """
⊘(ω::TensorAlgebra,η::TensorAlgebra)
General sandwich product: ω⊘η = clifford(η)⊖ω⊖η
General sandwich product: ω⊘η = reverse(η)⊖ω⊖involute(η)
For normalized even grade η it is ω⊘η = (~η)⊖ω⊖η
""" Grassmann.:⊘

for X ∈ TAG, Y ∈ TAG
@eval >>>(x::$X{V},y::$Y{V}) where V = y⊘clifford(x) # x * y * ~x
end
>>>(y::TensorTerm{V},x::TensorTerm{V}) where V = y*x*clifford(y)
>>>(y::TensorAlgebra{V},x::TensorAlgebra{V}) where V = y*x*clifford(y)
>>>(y::TensorAlgebra{V},x::Couple{V}) where V = (y>>>scalar(x))+(y>>>imaginary(x))
>>>(y::TensorAlgebra{V},x::PseudoCouple{V}) where V = (y>>>imaginary(x))+(y>>>volume(x))
@generated >>>(b::Spinor{V},a::TensorGraded{V,G}) where {V,G} = product_sandwich(a,b,true)
@generated >>>(b::AntiSpinor{V},a::TensorGraded{V,G}) where {V,G} = product_sandwich(a,b,true)
@generated >>>(b::Couple{V},a::TensorGraded{V,G}) where {V,G} = product_sandwich(a,b,true)
@generated >>>(b::PseudoCouple{V},a::TensorGraded{V,G}) where {V,G} = product_sandwich(a,b,true)
@generated >>>(b::TensorGraded{V,L},a::TensorGraded{V,G}) where {V,G,L} = product_sandwich(a,b,true)

@doc """
>>>(ω::TensorAlgebra,η::TensorAlgebra)
Sandwich product: ω>>>η = ω⊖η⊖(~ω)
Traditional sandwich product: ω>>>η = ω⊖η⊖clifford(ω)
For normalized even grade η it is ω>>>η = ω⊖η⊖(~ω)
""" Grassmann.:>>>

## veedot
Expand Down Expand Up @@ -1317,20 +1334,20 @@ for input ∈ (:Spinor,:AntiSpinor)
out = svecs(N,Any)(zeros(svecs(N,t)))
for g ∈ $(inspin ? :(evens(1,N+1)) : :(evens(2,N+1)))
ia = indexbasis(N,g-1)
par = parityclifford(g-1)
par = swap ? false : parityclifford(g-1)
@inbounds for i ∈ 1:bn[g]
@inbounds val = par ? :(@inbounds -b.v[$(bs[g]+i)]) : :(@inbounds b.v[$(bs[g]+i)])
if S<:Chain
for j ∈ 1:bn[G+1]
A,B = swapper(ib[j],ia[i],!swap)
X,Y = swapper(:(@inbounds a[$j]),val,!swap)
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))
end
else
U = UInt(basis(a))
A,B = swapper(U,ia[i],!swap)
A,B = swapper(U,ia[i],true)
if S<:Single
X,Y = swapper(:(a.v),val,!swap)
X,Y = swapper(:(a.v),val,true)
@inbounds $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,val,false))
Expand All @@ -1344,11 +1361,13 @@ for input ∈ (:Spinor,:AntiSpinor)
ia = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
@inbounds val = out[bs2[g]+i]
for g2 ∈ $(inspin ? :(evens(1,N+1)) : :(evens(2,N+1)))
!isnull(val) && for g2 ∈ $(inspin ? :(evens(1,N+1)) : :(evens(2,N+1)))
io = indexbasis(N,g2-1)
par = swap ? parityclifford(g2-1) : false
for j ∈ 1:bn[g2]
A,B = swapper(io[j],ia[i],!swap)
X,Y = swapper(:(@inbounds b.v[$(bs[g2]+j)]),val,!swap)
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))
end
end
Expand Down Expand Up @@ -1399,33 +1418,33 @@ for input ∈ (:Spinor,:AntiSpinor)
end

for input ∈ (:Chain,)
product! = :((iseven(G) ? isodd : iseven)(G) ? geomaddanti! : geomaddspin!)
preproduct! = :((iseven(G) ? isodd : iseven)(G) ? geomaddanti!_pre : geomaddspin!_pre)
product! = :((iseven(L) ? isodd : iseven)(G) ? geomaddanti! : geomaddspin!)
preproduct! = :((iseven(L) ? isodd : iseven)(G) ? geomaddanti!_pre : geomaddspin!_pre)
product2! = :(isodd(G) ? geomaddanti! : geomaddspin!)
preproduct2! = :(isodd(G) ? geomaddanti!_pre : geomaddspin!_pre)
@eval @noinline function product_sandwich(a::Type{S},b::Type{Q},swap=false) where {S<:TensorGraded{V,G},Q<:TensorGraded{V,L}} where {V,G,L}
MUL,VEC = mulvec(a,b,:*)
VECS = isodd(G) ? VEC : string(VEC)*"s"
if mdims(V)<cache_limit
$(insert_expr((:N,:t,:ib,:bn,:μ))...)
bs = (iseven(G) ? spinsum_set : antisum_set)(N)
bs = (iseven(L) ? spinsum_set : antisum_set)(N)
out = svecs(N,Any)(zeros(svecs(N,t)))
par = parityclifford(L)
if Q <: Chain
ia = indexbasis(N,L)
@inbounds for i ∈ 1:bn[L+1]
@inbounds val = par ? :(@inbounds -b.v[$i]) : :(@inbounds b.v[$i])
@inbounds val = (swap ? false : par) ? :(@inbounds -b.v[$i]) : :(@inbounds b.v[$i])
if S<:Chain
for j ∈ 1:bn[G+1]
A,B = swapper(ib[j],ia[i],!swap)
X,Y = swapper(:(@inbounds a[$j]),val,!swap)
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))
end
else
U = UInt(basis(a))
A,B = swapper(U,ia[i],!swap)
A,B = swapper(U,ia[i],true)
if S<:Single
X,Y = swapper(:(a.v),val,!swap)
X,Y = swapper(:(a.v),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
Expand All @@ -1434,41 +1453,41 @@ for input ∈ (:Chain,)
end
else
U2 = UInt(basis(b))
@inbounds val = par ? :(@inbounds -value(b)) : :(@inbounds value(b))
@inbounds val = (swap ? false : par) ? :(@inbounds -value(b)) : :(@inbounds value(b))
if S<:Chain
for j ∈ 1:bn[G+1]
A,B = swapper(ib[j],U2,!swap)
X,Y = swapper(:(@inbounds a[$j]),val,!swap)
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))
end
else
U = UInt(basis(a))
A,B = swapper(U,U2,!swap)
A,B = swapper(U,U2,true)
if S<:Single
X,Y = swapper(:(a.v),val,!swap)
X,Y = swapper(:(a.v),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
end
end
end
bs2 = ((iseven(G) ? isodd : iseven)(G) ? antisum_set : spinsum_set)(N)
bs2 = ((iseven(L) ? isodd : iseven)(G) ? antisum_set : spinsum_set)(N)
out2 = svecs(N,Any)(zeros(svecs(N,t)))
for g ∈ ((iseven(G) ? isodd : iseven)(G) ? evens(2,N+1) : evens(1,N+1))
for g ∈ ((iseven(L) ? isodd : iseven)(G) ? evens(2,N+1) : evens(1,N+1))
ia = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
@inbounds val = out[bs2[g]+i]
if S<:Chain
!isnull(val) && if Q<:Chain
for j ∈ 1:bn[L+1]
A,B = swapper(ib[j],ia[i],!swap)
X,Y = swapper(:(@inbounds b[$j]),val,!swap)
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))
end
else
U = UInt(basis(a))
A,B = swapper(U,ia[i],!swap)
if S<:Single
X,Y = swapper(:(value(b)),val,!swap)
U = UInt(basis(b))
A,B = swapper(U,ia[i],true)
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))
else
@inbounds $preproduct2!(V,out2,A,B,derive_pre(V,A,B,val,false))
Expand All @@ -1483,6 +1502,63 @@ for input ∈ (:Chain,)
end
end

for input ∈ (:Couple,:PseudoCouple)
product! = :((inspin ? isodd : iseven)(G) ? geomaddanti! : geomaddspin!)
preproduct! = :((inspin ? isodd : iseven)(G) ? geomaddanti!_pre : geomaddspin!_pre)
product2! = :(isodd(G) ? geomaddanti! : geomaddspin!)
preproduct2! = :(isodd(G) ? geomaddanti!_pre : geomaddspin!_pre)
calar = input == :Couple ? :scalar : :volume
pg = input == :Couple ? 0 : :N
@eval @noinline function product_sandwich(a::Type{S},b::Type{Q},swap=false) where {S<:TensorGraded{V,G},Q<:$input{V,BB}} where {V,G,BB}
MUL,VEC = mulvec(a,b,:*)
N = mdims(V)
$(if input == :Couple
:(isodd(grade(BB)) && return :(a⊘multispin(b)))
else
:(isodd(grade(BB))≠isodd(N) && return :(a⊘multispin(b)))
end)
inspin = iseven(grade(BB))
VECS = isodd(G) ? VEC : string(VEC)*"s"
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)))))
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))
end
else
U = UInt(basis(a))
A,B = swapper(U,U2,true)
if S<:Single
X,Y = swapper(:(a.v),val,true)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
end
end
end
bs2 = ((inspin ? isodd : iseven)(G) ? antisum_set : spinsum_set)(N)
out2 = svecs(N,Any)(zeros(svecs(N,t)))
for g ∈ ((inspin ? isodd : iseven)(G) ? evens(2,N+1) : evens(1,N+1))
ia = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
@inbounds val = out[bs2[g]+i]
!isnull(val) && for (B,val2) ∈ ((UInt(BB),(swap ? parityclifford(grade(BB)) : false) ? :(-value(imaginary(b))) : :(value(imaginary(b)))),(indexbasis(N,$pg)[1],(swap ? parityclifford($pg) : false) ? :(-value($$calar(b))) : :(value($$calar(b)))))
A = ia[i] #A,B = swapper(U,ia[i],true)
@inbounds $preproduct2!(V,out2,A,B,derive_pre(V,A,B,val,val2,MUL))
end
end
end
bs3 = (isodd(G) ? antisum : spinsum)(N,G)
return :(Chain{V,G}($(Expr(:call,tvec(N,G,t),out2[bs3+1:bs3+binomial(N,G)]...))))
#=else return quote
end=# end
end
end

outsym(com) = com ∈ (:spinor,:anti) ? :tvecs : :tvec
function leftrightsym(com)
ls = com ∈ (:spinor,:spin_multi,:s_m,:s_a)
Expand Down Expand Up @@ -1543,12 +1619,12 @@ for com ∈ (:spinor,:s_m,:m_s,:anti,:a_m,:m_a,:multivector,:s_a,:a_s)
end
(:N,:t,:out), :(out = $(Expr(:call,$(outspin ? :tvecs : :tvec)(N,t),out...)))
else
(:N,:t,:out,br...,:bn,:μ), quote
for g ∈ $leftspin
(:N,:t,:out,$br...,:bn,:μ), quote
for g ∈ $$leftspin
X = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
@inbounds val = $(nothing≠d ? :(@inbounds $a[$left[g]+i]/$d) : :(@inbounds $a[$left[g]+i]))
val≠0 && for G ∈ $rightspin
val≠0 && for G ∈ $$rightspin
@inbounds R = $right[G]
Y = indexbasis(N,G-1)
@inbounds for j ∈ 1:bn[G]
Expand Down
6 changes: 3 additions & 3 deletions src/multivectors.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -1057,9 +1057,9 @@ quatvalues(q::AntiQuaternion{V,T}) where {V,T} = Values{4,T}(q.v[4],q.v[3],q.v[2
@pure valuetype(::Type{<:Multivector{V,T} where V}) where T = T
@pure valuetype(::Type{<:Spinor{V,T} where V}) where T = T
@pure valuetype(::Type{<:AntiSpinor{V,T} where V}) where T = T
@pure valuetype(::Type{Couple{V,B,T} where {V,B}}) where T = T
@pure valuetype(::Type{PseudoCouple{V,B,T} where {V,B}}) where T = T
@pure valuetype(::Type{Phasor{V,B,T} where {V,B}}) where T = T
@pure valuetype(::Type{<:Couple{V,B,T} where {V,B}}) where T = T
@pure valuetype(::Type{<:PseudoCouple{V,B,T} where {V,B}}) where T = T
@pure valuetype(::Type{<:Phasor{V,B,T} where {V,B}}) where T = T

@inline value(m::Chain,T=valuetype(m)) = T∉(valuetype(m),Any) ? convert(T,m.v) : m.v
@inline value(m::Multivector,T=valuetype(m)) = T∉(valuetype(m),Any) ? convert(T,m.v) : m.v
Expand Down

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Registration pull request created: JuliaRegistries/General/105256

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Release notes:

## Breaking changes

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To add them here just re-invoke and the PR will be updated.

Tagging

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