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implement left and right complements for ⋅,∨ products #3

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merged 3 commits into from
Feb 20, 2019
Merged

implement left and right complements for ⋅,∨ products #3

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f0f1c35
implemented left and right complements for ⋅,∨ products
chakravala Feb 18, 2019
7abd899
replaced Lengyel's product with Browne's recommendation
chakravala Feb 19, 2019
5bb7fde
revised interior and regressive product cache for high performance
chakravala Feb 20, 2019
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replaced Lengyel's product with Browne's recommendation
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@chakravala
chakravala committed Feb 19, 2019
commit 7abd8997820009ab2ab810e1572b969325d8dbcd
149 changes: 63 additions & 86 deletions src/algebra.jl
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Expand Up @@ -6,7 +6,8 @@ import Base: +, -, *, ^, /, inv
import AbstractLattices: ∧, ∨, dist
import AbstractTensors: ⊗

Field = Number
const Field = Number
const ExprField = Union{Expr,Symbol}

## mutating operations

Expand Down Expand Up @@ -184,22 +185,35 @@ const ⋆ = complementright
import LinearAlgebra: dot, ⋅
export ⋅

dot(a::A,b::B) where {A<:TensorTerm,B<:TensorTerm} = ⋆(complementleft(a)∧b)
dot(a::A,b::B) where {A<:TensorMixed,B<:TensorMixed} = ⋆(complementleft(a)∧b)
dot(a::A,b::B) where {A<:TensorTerm,B<:TensorMixed} = ⋆(complementleft(a)∧b)
dot(a::A,b::B) where {A<:TensorMixed,B<:TensorTerm} = ⋆(complementleft(a)∧b)
dot(a::A,b::B) where {A<:TensorTerm,B<:TensorTerm} = a∨⋆(b)
dot(a::A,b::B) where {A<:TensorMixed,B<:TensorMixed} = a∨⋆(b)
dot(a::A,b::B) where {A<:TensorTerm,B<:TensorMixed} = a∨⋆(b)
dot(a::A,b::B) where {A<:TensorMixed,B<:TensorTerm} = a∨⋆(b)

## regressive product

∨(a::A,b::B) where {A<:TensorTerm,B<:TensorTerm} = ⋆(complementleft(a)∧complementleft(b))
∨(a::A,b::B) where {A<:TensorMixed,B<:TensorMixed} = ⋆(complementleft(a)∧complementleft(b))
∨(a::A,b::B) where {A<:TensorTerm,B<:TensorMixed} = ⋆(complementleft(a)∧complementleft(b))
∨(a::A,b::B) where {A<:TensorMixed,B<:TensorTerm} = ⋆(complementleft(a)∧complementleft(b))
function ∨(a::A,b::B) where {A<:TensorTerm{V},B<:TensorTerm{V}} where V
L = grade(a) + grade(b)
(-1)^(L*(L-ndims(V)))*⋆(⋆(a)∧⋆(b))
end
function ∨(a::A,b::B) where {A<:TensorMixed{V},B<:TensorMixed{V}} where V
L = grade(a) + grade(b)
(-1)^(L*(L-ndims(V)))*⋆(⋆(a)∧⋆(b))
end
function ∨(a::A,b::B) where {A<:TensorTerm{V},B<:TensorMixed{V}} where V
L = grade(a) + grade(b)
(-1)^(L*(L-ndims(V)))*⋆(⋆(a)∧⋆(b))
end
function ∨(a::A,b::B) where {A<:TensorMixed{V},B<:TensorTerm{V}} where V
L = grade(a) + grade(b)
(-1)^(L*(L-ndims(V)))*⋆(⋆(a)∧⋆(b))
end

### Product Algebra Constructor

function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CONJ=:conj)
TF = Field ≠ Number ? :Any : :T
EF = Field ≠ Any ? Field : ExprField
for Value ∈ MSV
@eval begin
adjoint(b::$Value{V,G,B,T}) where {V,G,B,T<:$Field} = $Value{dual(V),G,B',$TF}($CONJ(value(b)))
Expand All @@ -209,10 +223,8 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
@eval begin
function adjoint(m::$Blade{T,V,G}) where {T<:$Field,V,G}
if dualtype(V)<0
N = ndims(V)
M = Int(N/2)
ib = indexbasis(N,G)
out = zeros(mvec(N,G,$TF))
$(insert_expr((:N,:M,:ib),VEC)...)
out = zeros($VEC(N,G,$TF))
for i ∈ 1:binomial(N,G)
@inbounds setblade!(out,$CONJ(m.v[i]),dual(V,ib[i],M),Dimension{N}())
end
Expand All @@ -226,14 +238,11 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
@eval begin
function adjoint(m::MultiVector{T,V}) where {T<:$Field,V}
if dualtype(V)<0
N = ndims(V)
M = Int(N/2)
out = zeros(mvec(N,$TF))
bng = binomial_set(N)
bs = binomsum_set(N)
$(insert_expr((:N,:M,:bs,:bn),VEC)...)
out = zeros($VEC(N,$TF))
for g ∈ 1:N+1
ib = indexbasis(N,g-1)
@inbounds for i ∈ 1:bng[g]
@inbounds for i ∈ 1:bn[g]
@inbounds setmulti!(out,$CONJ(m.v[bs[g]+i]),dual(V,ib[i],M))
end
end
Expand Down Expand Up @@ -263,15 +272,15 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
end
end
@eval begin
*(a::F,b::Basis{V}) where {F<:$Field,V} = SValue{V}(a,b)
*(a::Basis{V},b::F) where {F<:$Field,V} = SValue{V}(b,a)
*(a::F,b::MultiVector{T,V}) where {F<:$Field,T<:$Field,V} = MultiVector{promote_type(T,F),V}(broadcast($MUL,a,b.v))
*(a::MultiVector{T,V},b::F) where {F<:$Field,T<:$Field,V} = MultiVector{promote_type(T,F),V}(broadcast($MUL,a.v,b))
*(a::F,b::MultiGrade{V}) where {F<:$Field,V} = MultiGrade{V}(broadcast($MUL,a,b.v))
*(a::MultiGrade{V},b::F) where {F<:$Field,V} = MultiGrade{V}(broadcast($MUL,a.v,b))
*(a::F,b::Basis{V}) where {F<:$EF,V} = SValue{V}(a,b)
*(a::Basis{V},b::F) where {F<:$EF,V} = SValue{V}(b,a)
*(a::F,b::MultiVector{T,V}) where {F<:$EF,T<:$EF,V} = MultiVector{promote_type(T,F),V}(broadcast($MUL,a,b.v))
*(a::MultiVector{T,V},b::F) where {F<:$EF,T<:$EF,V} = MultiVector{promote_type(T,F),V}(broadcast($MUL,a.v,b))
*(a::F,b::MultiGrade{V}) where {F<:$EF,V} = MultiGrade{V}(broadcast($MUL,a,b.v))
*(a::MultiGrade{V},b::F) where {F<:$EF,V} = MultiGrade{V}(broadcast($MUL,a.v,b))
#∧(::$Field,::$Field) = 0
∧(a::F,b::B) where B<:TensorTerm{V,G} where {F<:$Field,V,G} = G≠0 ? SValue{V,G}(a,b) : zero(V)
∧(a::A,b::F) where A<:TensorTerm{V,G} where {F<:$Field,V,G} = G≠0 ? SValue{V,G}(b,a) : zero(V)
∧(a::F,b::B) where B<:TensorTerm{V,G} where {F<:$EF,V,G} = G≠0 ? SValue{V,G}(a,b) : zero(V)
∧(a::A,b::F) where A<:TensorTerm{V,G} where {F<:$EF,V,G} = G≠0 ? SValue{V,G}(b,a) : zero(V)
#=
∧(a::$Field,b::MultiVector{T,V}) where {T<:$Field,V} = MultiVector{T,V}(a.*b.v)
∧(a::MultiVector{T,V},b::$Field) where {T<:$Field,V} = MultiVector{T,V}(a.v.*b)
Expand All @@ -291,9 +300,8 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
for Blade ∈ MSB
@eval begin
function $c(b::$Blade{T,V,G}) where {T<:$Field,V,G}
N = ndims(V)
ib = indexbasis(N,G)
out = zeros(mvec(N,G,T))
$(insert_expr((:N,:ib),VEC)...)
out = zeros($VEC(N,G,T))
for k ∈ 1:binomial(N,G)
@inbounds val = b.v[k]
@inbounds val≠0 && setblade!(out,$p(V,ib[k]) ? $SUB(val) : val,complement(N,ib[k]),Dimension{N}())
Expand All @@ -304,13 +312,11 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
end
@eval begin
function $c(m::MultiVector{T,V}) where {T<:$Field,V}
N = ndims(V)
$(insert_expr((:N,:bs,:bn),VEC)...)
out = zeros(mvec(N,T))
bng = binomial_set(N)
bs = binomsum_set(N)
for g ∈ 1:N+1
ib = indexbasis(N,g-1)
@inbounds for i ∈ 1:bng[g]
@inbounds for i ∈ 1:bn[g]
@inbounds val = m.v[bs[g]+i]
@inbounds val≠0 && setmulti!(out,$p(V,ib[i]) ? $SUB(val) : val,complement(N,ib[i]),Dimension{N}())
end
Expand All @@ -322,9 +328,7 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
for (op,product!) ∈ ((:*,:geometric_product!),(:∧,:exterior_product!))
@eval begin
function $op(a::MultiVector{T,V},b::Basis{V,G}) where {T<:$Field,V,G}
$(insert_expr((:N,:t,:out),VEC)...)
bs = binomsum_set(N)
bn = binomial_set(N)
$(insert_expr((:N,:t,:out,:bs,:bn),VEC)...)
for g ∈ 1:N+1
ib = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
Expand All @@ -334,9 +338,7 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
return MultiVector{t,V}(out)
end
function $op(a::Basis{V,G},b::MultiVector{T,V}) where {V,G,T<:$Field}
$(insert_expr((:N,:t,:out),VEC)...)
bs = binomsum_set(N)
bn = binomial_set(N)
$(insert_expr((:N,:t,:out,:bs,:bn),VEC)...)
for g ∈ 1:N+1
ib = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
Expand All @@ -349,10 +351,7 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
for Value ∈ MSV
@eval begin
function $op(a::MultiVector{T,V},b::$Value{V,G,B,S}) where {T<:$Field,V,G,B,S<:$Field}
$(insert_expr((:N,:t,:out),VEC)...)
bs = binomsum_set(N)
bn = binomial_set(N)
ib = indexbasis_set(N)
$(insert_expr((:N,:t,:out,:bs,:bn),VEC)...)
for g ∈ 1:N+1
ib = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
Expand All @@ -362,9 +361,7 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
return MultiVector{t,V}(out)
end
function $op(a::$Value{V,G,B,T},b::MultiVector{S,V}) where {V,G,B,T<:$Field,S<:$Field}
$(insert_expr((:N,:t,:out),VEC)...)
bs = binomsum_set(N)
bn = binomial_set(N)
$(insert_expr((:N,:t,:out,:bs,:bn),VEC)...)
for g ∈ 1:N+1
ib = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
Expand Down Expand Up @@ -392,9 +389,7 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
return MultiVector{t,V}(out)
end
function $op(a::MultiVector{T,V},b::$Blade{S,V,G}) where {T<:$Field,V,S<:$Field,G}
$(insert_expr((:N,:t,:out,:bng,:ib),VEC)...)
bs = binomsum_set(N)
bn = binomial_set(N)
$(insert_expr((:N,:t,:out,:bng,:ib,:bs,:bn),VEC)...)
for g ∈ 1:N+1
A = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
Expand All @@ -407,9 +402,7 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
return MultiVector{t,V}(out)
end
function $op(a::$Blade{T,V,G},b::MultiVector{S,V}) where {V,G,S<:$Field,T<:$Field}
$(insert_expr((:N,:t,:out,:bng,:ib),VEC)...)
bs = binomsum_set(N)
bn = binomial_set(N)
$(insert_expr((:N,:t,:out,:bng,:ib,:bs,:bn),VEC)...)
for g ∈ 1:N+1
B = indexbasis(N,g-1)
@inbounds for i ∈ 1:bn[g]
Expand Down Expand Up @@ -470,17 +463,15 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
end
@eval begin
function $op(a::MultiVector{T,V},b::MultiVector{S,V}) where {V,T<:$Field,S<:$Field}
$(insert_expr((:N,:t,:out),VEC)...)
bng = binomial_set(N)
bs = binomsum_set(N)
$(insert_expr((:N,:t,:out,:bs,:bn),VEC)...)
for g ∈ 1:N+1
Y = indexbasis(N,g-1)
@inbounds for i ∈ 1:bng[g]
@inbounds for i ∈ 1:bn[g]
@inbounds val = b.v[bs[g]+i]
val≠0 && for G ∈ 1:N+1
@inbounds R = bs[G]
X = indexbasis(N,G-1)
@inbounds for j ∈ 1:bng[G]
@inbounds for j ∈ 1:bn[G]
@inbounds $product!(V,out,X[j],Y[i],$MUL(a.v[R+j],val))
end
end
Expand Down Expand Up @@ -598,10 +589,8 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
for (A,B) ∈ [(A,B) for A ∈ MSB, B ∈ MSB]
@eval begin
function $op(a::$A{T,V,G},b::$B{S,V,L}) where {T<:$Field,V,G,S<:$Field,L}
$(insert_expr((:N,:t,:out),VEC)...)
ra = binomsum(N,G)
Ra = binomial(N,G)
@inbounds out[ra+1:ra+Ra] = value(a,MVector{Ra,t})
$(insert_expr((:N,:t,:out,:r,:bng),VEC)...)
@inbounds out[r+1:r+bng] = value(a,MVector{bng,t})
rb = binomsum(N,L)
Rb = binomial(N,L)
@inbounds out[rb+1:rb+Rb] = $bop(value(b,MVector{Rb,t}))
Expand Down Expand Up @@ -633,18 +622,14 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
return MBlade{t,V,G}(out)
end
function $op(a::$Blade{T,V,G},b::$Value{V,L,B,S} where B) where {T<:$Field,V,G,L,S<:$Field}
$(insert_expr((:N,:t,:out),VEC)...)
r = binomsum(N,G)
R = binomial(N,G)
@inbounds out[r+1:r+R] = value(a,MVector{R,t})
$(insert_expr((:N,:t,:out,:r,:bng),VEC)...)
@inbounds out[r+1:r+bng] = value(a,MVector{bng,t})
addmulti!(out,$bop(value(b,t)),bits(basis(b)),Dimension{N}())
return MultiVector{t,V}(out)
end
function $op(a::$Value{V,L,A,S} where A,b::$Blade{T,V,G}) where {T<:$Field,V,G,L,S<:$Field}
$(insert_expr((:N,:t,:out),VEC)...)
r = binomsum(N,G)
R = binomial(N,G)
@inbounds out[r+1:r+R] = $bop(value(b,MVector{R,t}))
$(insert_expr((:N,:t,:out,:r,:bng),VEC)...)
@inbounds out[r+1:r+bng] = $bop(value(b,MVector{bng,t}))
addmulti!(out,value(a,t),bits(basis(a)),Dimension{N}())
return MultiVector{t,V}(out)
end
Expand All @@ -665,35 +650,27 @@ function generate_product_algebra(Field=Field,MUL=:*,ADD=:+,SUB=:-,VEC=:mvec,CON
return MBlade{t,V,G}(out)
end
function $op(a::$Blade{T,V,G},b::Basis{V,L}) where {T<:$Field,V,G,L}
$(insert_expr((:N,:t,:out),VEC)...)
r = binomsum(N,G)
R = binomial(N,G)
@inbounds out[r+1:r+R] = value(a,MVector{R,t})
$(insert_expr((:N,:t,:out,:r,:bng),VEC)...)
@inbounds out[r+1:r+bng] = value(a,MVector{bng,t})
addmulti!(out,$bop(value(b,t)),bits(basis(b)),Dimension{N}())
return MultiVector{t,V}(out)
end
function $op(a::Basis{V,L},b::$Blade{T,V,G}) where {T<:$Field,V,G,L}
$(insert_expr((:N,:t,:out),VEC)...)
r = binomsum(N,G)
R = binomial(N,G)
@inbounds out[r+1:r+R] = $bop(value(b,MVector{R,t}))
$(insert_expr((:N,:t,:out,:r,:bng),VEC)...)
@inbounds out[r+1:r+bng] = $bop(value(b,MVector{bng,t}))
addmulti!(out,value(a,t),bits(basis(a)),Dimension{N}())
return MultiVector{t,V}(out)
end
function $op(a::$Blade{T,V,G},b::MultiVector{S,V}) where {T<:$Field,V,G,S}
$(insert_expr((:N,:t),VEC)...)
r = binomsum(N,G)
R = binomial(N,G)
$(insert_expr((:N,:t,:r,:bng),VEC)...)
out = $bop(value(b,$VEC(N,t)))
@inbounds out[r+1:r+R] += value(b,MVector{R,t})
@inbounds out[r+1:r+bng] += value(b,MVector{bng,t})
return MultiVector{t,V}(out)
end
function $op(a::MultiVector{T,V},b::$Blade{S,V,G}) where {T<:$Field,V,G,S}
$(insert_expr((:N,:t),VEC)...)
r = binomsum(N,G)
R = binomial(N,G)
$(insert_expr((:N,:t,:r,:bng),VEC)...)
out = copy(value(a,$VEC(N,t)))
@inbounds $(Expr(eop,:(out[r+1:r+R]),:(value(b,MVector{R,t}))))
@inbounds $(Expr(eop,:(out[r+1:r+bng]),:(value(b,MVector{bng,t}))))
return MultiVector{t,V}(out)
end
end
Expand Down
3 changes: 3 additions & 0 deletions src/multivectors.jl
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Expand Up @@ -60,6 +60,9 @@ end
==(a::Basis{V,G} where V,b::Basis{W,L} where W) where {G,L} = false
==(a::Basis{V,G},b::Basis{W,G}) where {V,W,G} = throw(error("not implemented yet"))

==(a::Number,b::TensorTerm{V,G} where V) where G = G==0 && a == value(b)
==(a::TensorTerm{V,G} where V,b::Number) where G = G==0 && value(a) == b

@inline show(io::IO, e::Basis{V}) where V = printindices(io,V,bits(e))

## S/MValue{N}
Expand Down
1 change: 0 additions & 1 deletion src/symbolic.jl
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Expand Up @@ -4,7 +4,6 @@

const Sym = :(Reduce.Algebra)
const SymField = Any
const ExprField = Union{Expr,Symbol}

set_val(set,expr) = Expr(:(=),expr,set≠:(=) ? Expr(:call,:($Sym.:+),expr,:val) : :val)

Expand Down
3 changes: 3 additions & 0 deletions src/utilities.jl
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Expand Up @@ -108,12 +108,15 @@ Base.@pure promote_type(t...) = Base.promote_type(t...)
@pure function insert_expr(e,vec=:mvec,T=:(valuetype(a)),S=:(valuetype(b)),L=:(2^N))
x = Any[] # Any[:(sigcheck(sig(a),sig(b)))]
assign_expr!(e,x,:N,:(ndims(V)))
assign_expr!(e,x,:M,:(Int(N/2)))
assign_expr!(e,x,:t,vec≠:mvec ? :Any : :(promote_type($T,$S)))
assign_expr!(e,x,:out,:(zeros($vec(N,t))))
assign_expr!(e,x,:r,:(binomsum(N,G)))
assign_expr!(e,x,:bng,:(binomial(N,G)))
assign_expr!(e,x,:bnl,:(binomial(N,L)))
assign_expr!(e,x,:ib,:(indexbasis(N,G)))
assign_expr!(e,x,:bs,:(binomsum_set(N)))
assign_expr!(e,x,:bn,:(binomial_set(N)))
return x
end

Expand Down
2 changes: 2 additions & 0 deletions test/runtests.jl
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Expand Up @@ -5,4 +5,6 @@ using Test
@test (@basis "++++" s e; e124 * e23 == e134)
@test [Λ(3).v32^2,Λ(3).v13^2,Λ(3).v21^2] == [-1Λ(3).v for j∈1:3]
@test ((Λ(2).v1+2Λ(2).v2)∧(3Λ(2).w1+4Λ(2).w2))(2)(Λ(2).v1+Λ(2).v2) == 7Λ(2).v1+14Λ(2).v2+0Λ(2).w1
@test (@basis "++++"; ((v1*v1,v1⋅v1,v1∧v1) == (1,1,0)) && ((v2*v2,v2⋅v2,v2∧v2) == (1,1,0)))
@test (@basis "-+++"; ((v1*v1,v1⋅v1,v1∧v1)==(-1,-1,0)) && ((v2*v2,v2⋅v2,v2∧v2) == (1,1,0)))
@test Algebra.:+((:a*Λ(2).v1 + :b*Λ(2).v2) ∧ (:c*Λ(2).v1 + :d*Λ(2).v2),Λ(2).v) == Λ(2).v+:(a*d-b*c)*Λ(2).v12