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smoothed Grassmann algebra operations
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@chakravala
chakravala committed Apr 15, 2024
1 parent 2776111 commit ef7b1f5
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184 changes: 91 additions & 93 deletions src/algebra.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -565,8 +565,6 @@ end

### Algebra Constructors

insert_t(x) = Expr(:block,:(t=promote_type(valuetype(a),valuetype(b))),x)

addvec(a,b,s,o) = o ≠ :+ ? subvec(a,b,s) : addvec(a,b,s)
addvec(a,b,s) = isfixed(a,b) ? (:($Sym.:∑),:($Sym.:∑),:svec) : (:+,:+,:mvec)
subvec(a,b,s) = isfixed(a,b) ? (s ? (:($Sym.:-),:($Sym.:∑),:svec) : (:($Sym.:∑),:($Sym.:-),:svec)) : (s ? (:-,:+,:mvec) : (:+,:-,:mvec))
Expand Down Expand Up @@ -613,12 +611,11 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
:(PseudoCouple{V,basis(a)}(Complex(value(a),$bop(value(b)))))
elseif L == G
if binomial(mdims(V),G)<(1<<cache_limit)
$(insert_expr((:N,:ib),:svec)...)
out = zeros(svec(N,G,Any))
setblade!_pre(out,:(value(a,t)),UInt(basis(a)),Val{N}())
setblade!_pre(out,:($bop(value(b,t))),UInt(basis(b)),Val{N}())
return Expr(:block,insert_expr((:t,),VEC)...,
:(Chain{V,L}($(Expr(:call,tvec(N,G,:t),out...)))))
$(insert_expr((:N,:ib,:t),:mvec)...)
out = svec(N,G,Any)(zeros(svec(N,G,t)))
setblade!_pre(out,:(value(a,$t)),UInt(basis(a)),Val{N}())
setblade!_pre(out,:($bop(value(b,$t))),UInt(basis(b)),Val{N}())
return :(Chain{V,L}($(Expr(:call,tvec(N,G,t),out...))))
else return quote
$(insert_expr((:N,:t))...)
out = zeros($VEC(N,L,t))
Expand All @@ -627,55 +624,57 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
return Chain{V,L}(out)
end end
elseif iseven(L) && iseven(G)
if mdims(V)-1<cache_limit
$(insert_expr((:N,),:svecs)...)
t = promote_type(valuetype(a),valuetype(b))
out,ib = zeros(svecs(N,Any)),indexbasis(N)
setspin!_pre(out,:(value(a,t)),UInt(basis(a)),Val{N}())
setspin!_pre(out,:($bop(value(b,t))),UInt(basis(b)),Val{N}())
return Expr(:block,insert_expr((:t,),VEC)...,
:(Spinor{V}($(Expr(:call,tvecs(N,:t),out...)))))
else quote
$(insert_expr((:N,),VEC)...)
t = promote_type(valuetype(a),valuetype(b))
out = zeros(svecs(N,Any))
setspin!(out,value(a,t),UInt(basis(a)),Val{N}())
setspin!(out,$bop(value(b,t)),UInt(basis(b)),Val{N}())
return Spinor{V}(out)
end end
adderspin(a,b,op)
elseif isodd(L) && isodd(G)
if mdims(V)-1<cache_limit
$(insert_expr((:N,),:svecs)...)
t = promote_type(valuetype(a),valuetype(b))
out,ib = zeros(svecs(N,Any)),indexbasis(N)
setanti!_pre(out,:(value(a,t)),UInt(basis(a)),Val{N}())
setanti!_pre(out,:($bop(value(b,t))),UInt(basis(b)),Val{N}())
return Expr(:block,insert_expr((:t,),VEC)...,
:(AntiSpinor{V}($(Expr(:call,tvecs(N,:t),out...)))))
else quote
$(insert_expr((:N,),VEC)...)
t = promote_type(valuetype(a),valuetype(b))
out = zeros(svecs(N,Any))
setanti!(out,value(a,t),UInt(basis(a)),Val{N}())
setanti!(out,$bop(value(b,t)),UInt(basis(b)),Val{N}())
return AntiSpinor{V}(out)
end end
adderanti(a,b,op)
else
adder2(a,b,op)
addermulti(a,b,op)
end
end
@noinline function adder2(a::Type{<:TensorTerm{V,L}},b::Type{<:TensorTerm{V,G}},op) where {V,L,G}
@noinline function adderspin(a::Type{<:TensorTerm{V,L}},b::Type{<:TensorTerm{V,G}},op) where {V,L,G}
(isodd(L) || isodd(G)) && (return :(error("$(basis(a)) and $(basis(b)) are not expressible as Spinor")))
left,bop,VEC = addvec(a,b,false,op)
if mdims(V)-1<cache_limit
$(insert_expr((:N,:t),:mvecs)...)
out,ib = svecs(N,Any)(zeros(svecs(N,t))),indexbasis(N)
setspin!_pre(out,:(value(a,$t)),UInt(basis(a)),Val{N}())
setspin!_pre(out,:($bop(value(b,$t))),UInt(basis(b)),Val{N}())
return :(Spinor{V}($(Expr(:call,tvecs(N,t),out...))))
else quote
$(insert_expr((:N,:t),VEC)...)
out = zeros(mvecs(N,t))
setspin!(out,value(a,t),UInt(basis(a)),Val{N}())
setspin!(out,$bop(value(b,t)),UInt(basis(b)),Val{N}())
return Spinor{V}(out)
end end
end
@noinline function adderanti(a::Type{<:TensorTerm{V,L}},b::Type{<:TensorTerm{V,G}},op) where {V,L,G}
(iseven(L) || iseven(G)) && (return :(error("$(basis(a)) and $(basis(b)) are not expressible as AntiSpinor")))
left,bop,VEC = addvec(a,b,false,op)
if mdims(V)-1<cache_limit
$(insert_expr((:N,),:svecs)...)
t = promote_type(valuetype(a),valuetype(b))
out,ib = svecs(N,Any)(zeros(svecs(N,t))),indexbasis(N)
setanti!_pre(out,:(value(a,$t)),UInt(basis(a)),Val{N}())
setanti!_pre(out,:($bop(value(b,$t))),UInt(basis(b)),Val{N}())
return :(AntiSpinor{V}($(Expr(:call,tvecs(N,t),out...))))
else quote
$(insert_expr((:N,:t),VEC)...)
out = zeros(mvecs(N,t))
setanti!(out,value(a,t),UInt(basis(a)),Val{N}())
setanti!(out,$bop(value(b,t)),UInt(basis(b)),Val{N}())
return AntiSpinor{V}(out)
end end
end
@noinline function addermulti(a::Type{<:TensorTerm{V,L}},b::Type{<:TensorTerm{V,G}},op) where {V,L,G}
left,bop,VEC = addvec(a,b,false,op)
if mdims(V)<cache_limit
$(insert_expr((:N,),:svec)...)
out,ib = zeros(svec(N,Any)),indexbasis(N)
setmulti!_pre(out,:(value(a,t)),UInt(basis(a)),Val{N}())
setmulti!_pre(out,:($bop(value(b,t))),UInt(basis(b)),Val{N}())
return Expr(:block,insert_expr((:t,),VEC)...,
:(Multivector{V}($(Expr(:call,tvec(N,:t),out...)))))
$(insert_expr((:N,:t),:mvec)...)
out,ib = svec(N,Any)(zeros(svec(N,t))),indexbasis(N)
setmulti!_pre(out,:(value(a,$t)),UInt(basis(a)),Val{N}())
setmulti!_pre(out,:($bop(value(b,$t))),UInt(basis(b)),Val{N}())
return :(Multivector{V}($(Expr(:call,tvec(N,t),out...))))
else quote
#@warn("sparse MultiGrade{V} objects not properly handled yet")
#return MultiGrade{V}(a,b)
$(insert_expr((:N,:t,:out),VEC)...)
setmulti!(out,value(a,t),UInt(basis(a)),Val{N}())
setmulti!(out,$bop(value(b,t)),UInt(basis(b)),Val{N}())
Expand All @@ -685,9 +684,8 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
@noinline function adder(a::Type{<:TensorTerm{V,G}},b::Type{<:Chain{V,G,T}},op,swap=false) where {V,G,T}
left,right,VEC = addvec(a,b,swap,op)
if binomial(mdims(V),G)<(1<<cache_limit)
$(insert_expr((:N,:ib),:svec)...)
t = promote_type(valuetype(a),valuetype(b))
out = zeros(svec(N,G,Any))
$(insert_expr((:N,:ib,:t),:mvec)...)
out = svec(N,G,Any)(zeros(svec(N,G,t)))
X = UInt(basis(a))
for k ∈ list(1,binomial(N,G))
B = @inbounds ib[k]
Expand Down Expand Up @@ -733,9 +731,8 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
end
elseif iseven(L) && iseven(G)
if mdims(V)-1<cache_limit
$(insert_expr((:N,:ib,:bn),:svecs)...)
t = promote_type(valuetype(a),valuetype(b))
out = zeros(svecs(N,Any))
$(insert_expr((:N,:ib,:bn,:t),:mvecs)...)
out = svecs(N,Any)(zeros(svecs(N,t)))
X = UInt(basis(a))
for k ∈ list(1,binomial(N,G))
B = @inbounds ib[k]
Expand All @@ -759,9 +756,8 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
end end end
elseif isodd(L) && isodd(G)
if mdims(V)-1<cache_limit
$(insert_expr((:N,:ib,:bn),:svecs)...)
t = promote_type(valuetype(a),valuetype(b))
out = zeros(svecs(N,Any))
$(insert_expr((:N,:ib,:bn,:t),:mvecs)...)
out = svecs(N,Any)(zeros(svecs(N,t)))
X = UInt(basis(a))
for k ∈ list(1,binomial(N,G))
B = @inbounds ib[k]
Expand All @@ -785,9 +781,8 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
end end end
else
if mdims(V)<cache_limit
$(insert_expr((:N,:ib,:bn),:svec)...)
t = promote_type(valuetype(a),valuetype(b))
out = zeros(svec(N,Any))
$(insert_expr((:N,:ib,:bn,:t),:mvec)...)
out = svec(N,Any)(zeros(svec(N,t)))
X = UInt(basis(a))
for k ∈ list(1,binomial(N,G))
B = @inbounds ib[k]
Expand All @@ -814,9 +809,8 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
@noinline function adder(a::Type{<:TensorTerm{V,G}},b::Type{<:Multivector{V,T}},op,swap=false) where {V,G,T}
left,right,VEC = addvec(a,b,swap,op)
if mdims(V)<cache_limit
$(insert_expr((:N,:bs,:bn),:svec)...)
t = promote_type(valuetype(a),valuetype(b))
out = zeros(svec(N,Any))
$(insert_expr((:N,:bs,:bn,:t),:mvec)...)
out = svec(N,Any)(zeros(svec(N,t)))
X = UInt(basis(a))
for g ∈ list(1,N+1)
ib = indexbasis(N,g-1)
Expand Down Expand Up @@ -845,9 +839,8 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
VECS = Symbol(string(VEC)*"s")
!iseven(G) && (return swap ? :($op(Multivector(b),a)) : :($op(a,Multivector(b))))
if mdims(V)<cache_limit
$(insert_expr((:N,:rs,:bn),:svec)...)
t = promote_type(valuetype(a),valuetype(b))
out = zeros(svecs(N,Any))
$(insert_expr((:N,:rs,:bn,:t),:mvecs)...)
out = svecs(N,Any)(zeros(svecs(N,t)))
X = UInt(basis(a))
for g ∈ evens(1,N+1)
ib = indexbasis(N,g-1)
Expand Down Expand Up @@ -876,9 +869,8 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
VECS = Symbol(string(VEC)*"s")
!isodd(G) && (return swap ? :($op(Multivector(b),a)) : :($op(a,Multivector(b))))
if mdims(V)<cache_limit
$(insert_expr((:N,:ps,:bn),:svec)...)
t = promote_type(valuetype(a),valuetype(b))
out = zeros(svecs(N,Any))
$(insert_expr((:N,:ps,:bn,:t),:mvecs)...)
out = svecs(N,Any)(zeros(svecs(N,t)))
X = UInt(basis(a))
for g ∈ evens(2,N+1)
ib = indexbasis(N,g-1)
Expand Down Expand Up @@ -916,8 +908,8 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
return swap ? :(b[1]*complementlefthodge(~a)) : S<:Single ? :(value(a)*complementlefthodge(~b)) : S<:Chain ? :(@inbounds a[1]*complementlefthodge(~b)) : :(complementlefthodge(~b))
elseif binomial(mdims(V),G)*(S<:Chain ? binomial(mdims(V),L) : 1)<(1<<cache_limit)
if S<:Chain
$(insert_expr((:N,:t,:bng,:ib,:μ),:svecs)...)
out = zeros(svecs(N,t))
$(insert_expr((:N,:t,:bng,:ib,:μ),:mvecs)...)
out = svecs(N,Any)(zeros(svecs(N,t)))
B = indexbasis(N,L)
for i ∈ list(1,binomial(N,L))
@inbounds v,ibi = :(@inbounds a[$i]),B[i]
Expand All @@ -926,7 +918,8 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
end
end
else
$(insert_expr((:N,:t,:out,:ib,:μ),:svecs)...)
$(insert_expr((:N,:t,:ib,:μ),:mvecs)...)
out = svecs(N,Any)(zeros(svecs(N,t)))
U = UInt(basis(a))
for i ∈ list(1,binomial(N,G))
A,B = swap ? (@inbounds ib[i],U) : (U,@inbounds ib[i])
Expand All @@ -937,7 +930,7 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
end
end
end
return insert_t(:($type{V}($(Expr(:call,tvecs(N,μ),out...)))))
return :($type{V}($(Expr(:call,tvecs(N,t),out...))))
elseif S<:Chain; return quote
$(insert_expr((:N,:t,:bng,:ib,:μ),VEC)...)
out = zeros($VEC(N,t))
Expand Down Expand Up @@ -981,11 +974,11 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
GL = swap ? G-L : L-G
if binomial(mdims(V),G)*(S<:Chain ? binomial(mdims(V),L) : 1)<(1<<cache_limit)
if S<:Chain
$(insert_expr((:N,:t,:bng,:bnl),:svec)...)
$(insert_expr((:N,:t,:bng,:bnl),:mvec)...)
μ = istangent(V)|hasconformal(V)
ia = indexbasis(N,L)
ib = indexbasis(N,G)
out = zeros(μ ? svec(N,Any) : svec(N,GL,Any))
out = (μ ? svec(N,Any) : svec(N,GL,Any))(zeros(μ ? svec(N,t) : svec(N,GL,t)))
for i ∈ list(1,bnl)
@inbounds v,iai = :(@inbounds a[$i]),ia[i]
for j ∈ list(1,bng)
Expand All @@ -997,8 +990,8 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
end
end
else
$(insert_expr((:N,:t,:ib,:bng,:μ),:svec)...)
out = zeros(μ ? svec(N,Any) : svec(N,GL,Any))
$(insert_expr((:N,:t,:ib,:bng,:μ),:mvec)...)
out = (μ ? svec(N,Any) : svec(N,GL,Any))(zeros(μ ? svec(N,t) : svec(N,GL,t)))
U = UInt(basis(a))
for i ∈ list(1,bng)
A,B = swap ? (@inbounds ib[i],U) : (U,@inbounds ib[i])
Expand All @@ -1019,9 +1012,9 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
end
#return :(value_diff(Single{V,0,$(getbasis(V,0))}($(value(mv)))))
return if μ
insert_t(:(Multivector{$V}($(Expr(:call,istangent(V) ? tvec(N) : tvec(N,:t),out...)))))
:(Multivector{$V}($(Expr(:call,istangent(V) ? tvec(N) : tvec(N,t),out...))))
else
insert_t(:(value_diff(Chain{$V,$GL}($(Expr(:call,tvec(N,GL,:t),out...))))))
:(value_diff(Chain{$V,$GL}($(Expr(:call,tvec(N,GL,t),out...)))))
end
elseif S<:Chain; return quote
$(insert_expr((:N,:t,:bng,:bnl,:μ),VEC)...)
Expand Down Expand Up @@ -1087,10 +1080,11 @@ for (op,po,GL,grass) ∈ ((:∧,:>,:(G+L),:exter),(:∨,:<,:(G+L-mdims(V)),:meet
end
if binomial(mdims(W),L)*(S<:Chain ? binomial(mdims(w),G) : 1)<(1<<cache_limit)
if S<:Chain
$(insert_expr((:N,:t,:μ),:mvec,:T,:S)...)
$(insert_expr((:N,:μ),:mvec,:T,:S)...)
t = promote_type(valuetype(a),valuetype(b))
ia = indexbasis(mdims(w),G)
ib = indexbasis(mdims(W),L)
out = zeros(μ ? svec(N,Any) : svec(N,$GL,Any))
out = (μ ? svec(N,Any) : svec(N,$GL,Any))(zeros(μ ? svec(N,t) : svec(N,$GL,t)))
CA,CB = isdual(w),isdual(W)
for i ∈ list(1,binomial(mdims(w),G))
@inbounds v,iai = :(@inbounds a[$i]),ia[i]
Expand All @@ -1105,9 +1099,10 @@ for (op,po,GL,grass) ∈ ((:∧,:>,:(G+L),:exter),(:∨,:<,:(G+L-mdims(V)),:meet
end
end
else
$(insert_expr((:N,:t,:μ),:mvec,Int,:T)...)
$(insert_expr((:N,:μ),:mvec,Int,:T)...)
t = promote_type(valuetype(a),valuetype(b))
ib = indexbasis(mdims(R),L)
out = zeros(μ ? svec(N,Any) : svec(N,$GL,Any))
out = (μ ? svec(N,Any) : svec(N,$GL,Any))(zeros(μ ? svec(N,t) : svec(N,$GL,t)))
C,x = isdual(R),isdual(Q) ? dual(V,UInt(basis(a))) : UInt(basis(a))
for i ∈ list(1,binomial(mdims(W),L))
X = @inbounds C ? dual(V,ib[i]) : ib[i]
Expand All @@ -1128,9 +1123,9 @@ for (op,po,GL,grass) ∈ ((:∧,:>,:(G+L),:exter),(:∨,:<,:(G+L-mdims(V)),:meet
end
end
return if μ
insert_t(:(Multivector{$V}($(Expr(:call,istangent(V) ? tvec(N) : tvec(N,:t),out...)))))
:(Multivector{$V}($(Expr(:call,istangent(V) ? tvec(N) : tvec(N,t),out...))))
else
insert_t(:(Chain{$V,$$GL}($(Expr(:call,tvec(N,$GL,:t),out...)))))
:(Chain{$V,$$GL}($(Expr(:call,tvec(N,$GL,t),out...))))
end
elseif S<:Chain; return quote
V = $V
Expand Down Expand Up @@ -1234,7 +1229,7 @@ for (op,product) ∈ ((:∧,:exteradd),(:*,:geomadd),
if mdims(V)<cache_limit
$(insert_expr((:N,:t,:ib,:bn,:μ))...)
bs = $(inspin ? :spinsum_set : inanti ? :antisum_set : :binomsum_set)(N)
out = zeros($(outmulti ? :svec : :svecs)(N,Any))
out = $(outmulti ? :svec : :svecs)(N,Any)(zeros($(outmulti ? :svec : :svecs)(N,t)))
for g ∈ $(inspin ? :(evens(1,N+1)) : inanti ? :(evens(2,N+1)) : :(list(1,N+1)))
ia = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
Expand All @@ -1257,9 +1252,10 @@ for (op,product) ∈ ((:∧,:exteradd),(:*,:geomadd),
end
end
end
return insert_t(:($$outype{V}($(Expr(:call,$(outmulti ? :tvec : :tvecs)(N,μ),out...)))))
return :($$outype{V}($(Expr(:call,$(outmulti ? :tvec : :tvecs)(N,t),out...))))
else return quote
$(insert_expr((:N,:t,:out,:ib,:bn,:μ),VECS)...)
$(insert_expr((:N,:t,:ib,:bn,:μ),VECS)...)
out = zeros($(outmulti ? :svec : :svecs)(N,t)) # VECS
bs = $(inspin ? :spinsum_set : inanti ? :antisum_set : :binomsum_set)(N)
for g ∈ $(inspin ? :(1:2:N+1) : inanti ? :(2:2:N+1) : :(1:N+1))
ia = indexbasis(N,g-1)
Expand Down Expand Up @@ -1338,10 +1334,12 @@ end
for com ∈ (:spinor,:s_m,:m_s,:anti,:a_m,:m_a,:multivector,:s_a,:a_s)
outspin = com ∈ (:spinor,:anti,:s_a,:a_s)
left,leftspin,right,rightspin,br = leftrightsym(com)
VEC = outspin ? :svecs : :svec
genloop = Symbol(:generate_loop_,com)
@eval @noinline function $genloop(V,a,b,MUL,product!,preproduct!,d=nothing)
@eval @noinline function $genloop(V,a,b,t,MUL,product!,preproduct!,d=nothing)
if mdims(V)<cache_limit/2
$(insert_expr((:N,:t,:out,br...,:bn),outspin ? :svecs : :svec)...)
$(insert_expr((:N,br...,:bn),:mvec)...)
out = $VEC(N,Any)(zeros($VEC(N,t)))
for g ∈ $leftspin
X = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
Expand All @@ -1355,7 +1353,7 @@ for com ∈ (:spinor,:s_m,:m_s,:anti,:a_m,:m_a,:multivector,:s_a,:a_s)
end
end
end
(:N,:t,:out), :(out = $(Expr(:call,$(outspin ? :tvecs : :tvec)(N,:t),out...)))
(:N,:t,:out), :(out = $(Expr(:call,$(outspin ? :tvecs : :tvec)(N,t),out...)))
else
(:N,:t,:out,br...,:bn,:μ), quote
for g ∈ $leftspin
Expand Down
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Registration pull request created: JuliaRegistries/General/104958

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