Skip to content

Commit

Permalink
refined algebra operators
Browse files Browse the repository at this point in the history
  • Loading branch information
@chakravala
chakravala committed Apr 17, 2024
1 parent f6f26cf commit 25b928e
Show file tree
Hide file tree
Showing 2 changed files with 199 additions and 17 deletions.
205 changes: 193 additions & 12 deletions src/algebra.jl
View file
Original file line number Diff line number Diff line change
Expand Up @@ -239,28 +239,26 @@ end

## sandwich product

export ⊘
export ⊘, sandwich, pseudosandwich

#=for X ∈ TAG, Y ∈ TAG
@eval ⊘(x::X,y::Y) where {X<:$X{V},Y<:$Y{V}} where V = diffvars(V)≠0 ? conj(y)*x*y : y\x*involute(y)
end=#
for Y ∈ TAG
@eval ⊘(x::TensorGraded{V,1},y::Y) where Y<:$Y{V} where V = diffvars(V)≠0 ? conj(y)*x*involute(y) : y\x*involute(y)
end
#=for Z ∈ TAG
@eval ⊘(x::Chain{V,G},y::T) where {V,G,T<:$Z} = diffvars(V)≠0 ? conj(y)*x*y : ((~y)*x*involute(y))(Val(G))/abs2(y)
end=#
⊘(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)
@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)

@doc """
⊘(ω::TensorAlgebra,η::TensorAlgebra)
General sandwich product: ω⊘η = involute(η)\\ω⊖η
General sandwich product: ω⊘η = clifford(η)⊖ω⊖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 = x * y * ~x
@eval >>>(x::$X{V},y::$Y{V}) where V = y⊘clifford(x) # x * y * ~x
end

@doc """
Expand Down Expand Up @@ -1302,6 +1300,189 @@ for (op,product) ∈ ((:∧,:exteradd),(:*,:geomadd),
end
end

for input ∈ (:Spinor,:AntiSpinor)
inspin = input==:Spinor
outype = :($(inspin ? :isodd : :iseven)(G) ? AntiSpinor : Spinor)
product! = :($(inspin ? :isodd : :iseven)(G) ? geomaddanti! : geomaddspin!)
preproduct! = :($(inspin ? :isodd : :iseven)(G) ? geomaddanti!_pre : geomaddspin!_pre)
product2! = :(isodd(G) ? geomaddanti! : geomaddspin!)
preproduct2! = :(isodd(G) ? geomaddanti!_pre : geomaddspin!_pre)
input≠:Spinor && @eval product_sandwich(a,b,swap=false) = product_sandwich(typeof(a),typeof(b),swap)
@eval @noinline function product_sandwich(a::Type{S},b::Type{<:$input{V,T}},swap=false) where S<:TensorGraded{V,G} where {V,G,T}
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 = $(inspin ? :spinsum_set : :antisum_set)(N)
out = svecs(N,Any)(zeros(svecs(N,t)))
for g ∈ $(inspin ? :(evens(1,N+1)) : :(evens(2,N+1)))
ia = indexbasis(N,g-1)
par = parityclifford(g-1)
@inbounds for i ∈ 1:bn[g]
@inbounds val = par ? :(@inbounds -b.v[$(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)
@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)
if S<:Single
X,Y = swapper(:(a.v),val,!swap)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
end
end
end
end
bs2 = ($(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]
for g2 ∈ $(inspin ? :(evens(1,N+1)) : :(evens(2,N+1)))
io = indexbasis(N,g2-1)
for j ∈ 1:bn[g2]
A,B = swapper(io[j],ia[i],!swap)
X,Y = swapper(:(@inbounds b.v[$(bs[g2]+j)]),val,!swap)
$preproduct2!(V,out2,A,B,derive_pre(V,A,B,X,Y,MUL))
end
end
end
end
bs3 = (isodd(G) ? antisum : spinsum)(N,G)
return :(Chain{V,G}($(Expr(:call,tvec(N,G,t),out2[bs3+1:bs3+binomial(N,G)]...))))
#=else return quote
$(insert_expr((:N,:t,:ib,:bn,:μ),VECS)...)
out = zeros(svecs(N,t)) # VECS
bs = $(inspin ? :spinsum_set : :antisum_set)(N)
for g ∈ $(inspin ? :(1:2:N+1) : :(2:2:N+1))
ia = indexbasis(N,g-1)
par = parityclifford(g-1)
@inbounds for i ∈ 1:bn[g]
$(if S<:Chain; quote
@inbounds val = par ? -b.v[bs[g]+i] : b.v[bs[g]+i]
val≠0 && for j ∈ 1:bn[G+1]
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 $$product!(V,out,A,B,dm)&μ
$(insert_expr((:out,);mv=:out)...)
@inbounds $$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 $$product!(V,out,A,B,dm)&μ
$(insert_expr((:out,);mv=:out)...)
@inbounds $$product!(V,out,A,B,dm)
end end
else
:(if @inbounds $$product!(V,out,A,B,derive_mul(V,A,B,b.v[rs[g]+i],false))&μ
$(insert_expr((:out,);mv=:out)...)
@inbounds $$product!(V,out,A,B,derive_mul(V,A,B,b.v[rs[g]+i],false))
end)
end) end
end)
end
end
return $$outype{V}(out)
end=# end
end
end

for input ∈ (:Chain,)
product! = :((iseven(G) ? isodd : iseven)(G) ? geomaddanti! : geomaddspin!)
preproduct! = :((iseven(G) ? 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
$(insert_expr((:N,:t,:ib,:bn,:μ))...)
bs = (iseven(G) ? spinsum_set : antisum_set)(N)
out = svecs(N,Any)(zeros(svecs(N,t)))
par = parityclifford(L)
if Q <: Chain
ia = indexbasis(N,L)
@inbounds for i ∈ 1:bn[L+1]
@inbounds val = par ? :(@inbounds -b.v[$i]) : :(@inbounds b.v[$i])
if S<:Chain
for j ∈ 1:bn[G+1]
A,B = swapper(ib[j],ia[i],!swap)
X,Y = swapper(:(@inbounds a[$j]),val,!swap)
@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)
if S<:Single
X,Y = swapper(:(a.v),val,!swap)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
end
end
end
else
U2 = UInt(basis(b))
@inbounds val = par ? :(@inbounds -value(b)) : :(@inbounds value(b))
if S<:Chain
for j ∈ 1:bn[G+1]
A,B = swapper(ib[j],U2,!swap)
X,Y = swapper(:(@inbounds a[$j]),val,!swap)
@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)
if S<:Single
X,Y = swapper(:(a.v),val,!swap)
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,X,Y,MUL))
else
@inbounds $preproduct!(V,out,A,B,derive_pre(V,A,B,val,false))
end
end
end
bs2 = ((iseven(G) ? isodd : iseven)(G) ? antisum_set : spinsum_set)(N)
out2 = svecs(N,Any)(zeros(svecs(N,t)))
for g ∈ ((iseven(G) ? isodd : iseven)(G) ? evens(2,N+1) : evens(1,N+1))
ia = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
@inbounds val = out[bs2[g]+i]
if S<:Chain
for j ∈ 1:bn[L+1]
A,B = swapper(ib[j],ia[i],!swap)
X,Y = swapper(:(@inbounds b[$j]),val,!swap)
@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)
@inbounds $preproduct2!(V,out2,A,B,derive_pre(V,A,B,X,Y,MUL))
else
@inbounds $preproduct2!(V,out2,A,B,derive_pre(V,A,B,val,false))
end
end
end
end
bs3 = (isodd(G) ? antisum : spinsum)(N,G)
return :(Chain{V,G}($(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
11 changes: 6 additions & 5 deletions src/multivectors.jl
View file
Original file line number Diff line number Diff line change
Expand Up @@ -310,10 +310,10 @@ 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)

function grade_src_chain(N,G,r=binomsum(N,G),is=isdir,T=Int)
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
function grade_src(N,G,r=binomsum(N,G),is=isdir,T=Int)
function grade_src(N,G,r=binomsum(N,G),is=isempty,T=Int)
b = binomial(N,G)
return if is(G)
zeros(Values{b,T})
Expand All @@ -325,7 +325,7 @@ function grade_src(N,G,r=binomsum(N,G),is=isdir,T=Int)
end
for fun ∈ (:grade_src,:grade_src_chain)
nex = Symbol(fun,:_next)
@eval function $nex(N,G,r=binomsum,is=isdir,T=Int)
@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)...)
end
end
Expand Down Expand Up @@ -535,13 +535,13 @@ end
@generated function (t::Spinor{V,T})(G::Int) where {V,T}
N = mdims(V)
Expr(:block,:(0 <= G <= $N || throw(BoundsError(t, G))),
:(isodd(G) && return Zero(V)),
#:(isodd(G) && return Zero(V)),
Expr(:if,:(G==0),grade_src_chain(N,0,0),grade_src_chain_next(N,N-1,spinsum,isodd,T)))
end
@generated function (t::AntiSpinor{V,T})(G::Int) where {V,T}
N = mdims(V)
Expr(:block,:(0 <= G <= $N || throw(BoundsError(t, G))),
:(iseven(G) && return Zero(V)),
#:(iseven(G) && return Zero(V)),
Expr(:if,:(G==0),grade_src_chain(N,0,0,iseven),grade_src_chain_next(N,N-1,antisum,iseven,T)))
end
@generated function getindex(t::Spinor{V,T},G::Int) where {V,T}
Expand Down Expand Up @@ -1042,6 +1042,7 @@ quaternion(s,ijk::Values{3}) = quaternion(Submanifold(3),s,ijk...)
quaternion(s::T=0,i=zero(T),j=zero(T),k=zero(T)) where T = quaternion(Submanifold(3),Values(s,i,j,k))
quaternion(V::Submanifold,s::T,i=zero(T),j=zero(T),k=zero(T)) where T = quaternion(V,Values(s,i,-j,k))
quaternion(V,sijk::Values{4}) = Quaternion{V}(sijk)
quatvalues(q::TensorAlgebra) = quatvalues(Spinor(even(q)))
quatvalues(q::Quaternion{V,T}) where {V,T} = Values{4,T}(q.v[1],q.v[2],-q.v[3],q.v[4])
quatvalues(q::AntiQuaternion{V,T}) where {V,T} = Values{4,T}(q.v[4],q.v[3],q.v[2],q.v[1])

Expand Down

2 comments on commit 25b928e

@chakravala
Copy link
Owner Author

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

@JuliaRegistrator register()

@JuliaRegistrator
Copy link

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Registration pull request created: JuliaRegistries/General/105082

Tip: Release Notes

Did you know you can add release notes too? Just add markdown formatted text underneath the comment after the text
"Release notes:" and it will be added to the registry PR, and if TagBot is installed it will also be added to the
release that TagBot creates. i.e.

@JuliaRegistrator register

Release notes:

## Breaking changes

- blah

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

Tagging

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

This will be done automatically if the Julia TagBot GitHub Action is installed, or can be done manually through the github interface, or via:

git tag -a v0.8.14 -m "<description of version>" 25b928ed3b5c1f4b219896f0b533d5bb54ed03c0
git push origin v0.8.14

Please sign in to comment.