add embed()

Author: Jollywatt

src/GeometricAlgebra.jl

@@ -24,7 +24,7 @@ export geometric_prod,
 	sandwich_prod
 export reversion, involution
 export flipdual, hodgedual, invhodgedual, ldual, rdual
-export matrix_repr, outermorphism
+export matrix_repr, outermorphism, embed
 export @symbolicga
 export MiniCAS
 

src/MiniCAS/algebra.jl

@@ -10,6 +10,7 @@ const Π = ProductNode
 const Σ = SumNode
 
 Base.copy(a::Union{Π,Σ}) = typeof(a)(copy(a.x))
+Base.broadcastable(a::Union{Π,Σ}) = Ref(a)
 
 (a::Π == b::Π) = a.x == b.x
 (a::Σ == b::Σ) = a.x == b.x

src/algebra.jl

@@ -44,8 +44,8 @@ Base.:isapprox(a::Scalar, b::AbstractMultivector; kwargs...) = isapprox(zero(b)
 scalar_multiply(a::BasisBlade{Sig,K}, b) where {Sig,K} = BasisBlade{Sig,K}(a.coeff*b, a.bits)
 scalar_multiply(a, b::BasisBlade{Sig,K}) where {Sig,K} = BasisBlade{Sig,K}(a*b.coeff, b.bits)
 
-scalar_multiply(a::Multivector, b) = constructor(a)(a.comps*b)
-scalar_multiply(a, b::Multivector) = constructor(b)(a*b.comps)
+scalar_multiply(a::Multivector, b) = constructor(a)(a.comps.*b)
+scalar_multiply(a, b::Multivector) = constructor(b)(a.*b.comps)
 
 Base.:*(a::AbstractMultivector, b::Scalar) = scalar_multiply(a, b)
 Base.:*(a::Scalar, b::AbstractMultivector) = scalar_multiply(a, b)
@@ -633,7 +633,46 @@ function outermorphism(mat::AbstractMatrix, a::AbstractMultivector{Sig}; sig=Sig
 end
 outermorphism(mat, a::Scalar) = a
 
+"""
+	embed(sig, a::Multivector)
+
+Embed a multivector into the algebra of metric signature `sig`, adding or discarding dimensions as necessary.
+
+Basis vectors in the original and new spaces are associated by the order in which they appear.
+Components are dropped if `dimension(sig) < dimension(a)`, and extra zero components are added
+if `dimension(sig) > dimension(a)`.
 
+# Examples
+```jldoctest
+julia> embed(Cl(2,2), Multivector{3,2}([1, 2, 3]))
+6-component Multivector{Cl(2,2), 2, SVector{6, Float64}}:
+ 1.0 v12
+ 2.0 v13
+ 3.0 v23
+ 0.0 v14
+ 0.0 v24
+ 0.0 v34
+
+julia> embed(2, Multivector{3,1}([1,2,3]))
+2-component Multivector{2, 1, SVector{2, Int64}}:
+ 1 v1
+ 2 v2
+```
+"""
+function embed(sig, a::Multivector)
+	T = Multivector{sig,grade(a)}
+	b = zero(T)
+	for k in grade(a)
+		n_orig = ncomponents(signature(a), k)
+		n_new = ncomponents(sig, k)
+		if n_new > n_orig
+			b += Multivector{sig,k}([a[k].comps; zeros(n_new - n_orig)])
+		else
+			b += Multivector{sig,k}(a[k].comps[1:n_new])
+		end
+	end
+	b
+end
 
 unit_pseudoscalar(::Val{Sig}) where {Sig} = let dim = dimension(Sig)
 	BasisBlade{Sig,dim}(1, bits_dual(dim, UInt(0)))

src/generated.jl

@@ -142,7 +142,7 @@ end
 
 @generated function symbolic_multivector_eval(::Val{Sig}, f::Function, args...) where Sig
 	@assert isdefined(f, :instance)
-	1
+	2
 	symbolic_multivector_eval(Expr, Val(Sig), f.instance, args...)
 end
 
@@ -180,11 +180,11 @@ To do this, the metric signatures in `args` are replaced with the equivalent can
 	of the first `AbstractMultivector` argument in `args`.
 	(The actual signature is lost because signatures are converted to canonical tuples.)
 """
-function symbolic_optim(f::Function, args...)
+function symbolic_optim(f::Function, args...; sig::Val=first_signature(args...))
 	# we’re replacing objects’ type parameters, so type stability is a little delicate
 	args′ = map(canonicalize, args)
-	Sig::Val = first_signature(args...) # guess the original (non-canonical) signature of f(args...)
-	result = symbolic_multivector_eval(Sig, f, args′...)
+	# Sig::Val = first_signature(args...) # guess the original (non-canonical) signature of f(args...)
+	result = symbolic_multivector_eval(sig, f, args′...)
 end
 
 """

test/algebra.jl

@@ -274,4 +274,13 @@ end
 		@inferred a∧b
 		@inferred (a⨼b)∧(v12⋅b)*I
 	end
-end
+end
+
+@testset "embed" begin
+	a = Multivector{3,1}(1, 2, 3)
+	@test embed(4, a) == Multivector{4,1}(1, 2, 3, 0)
+	@test embed(2, a) == Multivector{2,1}(1, 2)
+
+	a = randn(Multivector{3,0:3})
+	@test embed(3, embed(Cl(4,1), a)) == a
+end