Only return multiplicities from blockdiag (#11)

* Only return multiplicities from blockdiag

* Update README.md

Project.toml

@@ -1,7 +1,7 @@
 name = "NumericalRepresentationTheory"
 uuid = "6b7c1d51-ecee-4149-97a8-50646b514dce"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.3.0"
+version = "0.4.0"
 
 [deps]
 BlockArrays = "8e7c35d0-a365-5155-bbbb-fb81a777f24e"

README.md

@@ -49,7 +49,9 @@ julia> plot(multiplicities(R)) # We can also plot
 
 In addition, one can find an orthogonal transformation that reduces a representation to irreducibles:
 ```julia
-julia> ρ,Q = blockdiagonalize(R); # Q'R(g)*Q ≈ ρ(g) where ρ is a direct sum (block diagonal) of irreducibles.
+julia> λ,Q = blockdiagonalize(R); # Q'R(g)*Q ≈ ρ(g) where ρ = Representation(λ) is a direct sum (block diagonal) of irreducibles encoded by the dictionary λ.
+
+julia> ρ = Representation(λ);
 
 julia> Q'R(g)*Q ≈ ρ(g)
 true

src/NumericalRepresentationTheory.jl

@@ -278,15 +278,46 @@ end
 irrepgenerators(σ::Partition) = [irrepgenerator(σ, i) for i=1:Int(σ)-1]
 
 
+"""
+    Representation([τ₁,…,τₙ])
 
+is a representation of the symmetric group generated by τ₁,…,τₙ.
+"""
 struct Representation{MT}
        generators::Vector{MT}
 end
 
+
+"""
+    Representation(λ₁::Int, …, λₙ::Int)
+    Representation(Partition(λ₁, …, λₙ))
+
+both generate the irreducible representation associated with the given partition.
+"""
 Representation(σ::Int...) = Representation(Partition(σ...))
 Representation(σ::Partition) = Representation(irrepgenerators(σ))
 Representation{MT}(ρ::Representation) where MT = Representation(convert.(MT, ρ.generators))
 
+
+"""
+    Representation(::Dict{Partition,Int})
+
+makes a representation corresponding to a direct sum of the irreducible representations encoded in
+by the partitions. The partitions are sorted for a consistent ordering.
+"""
+function Representation(d::Dict{Partition,Int})
+    kys = sort(collect(keys(d)))
+
+    reps = Representation{SparseMatrixCSC{Float64,Int}}[]
+    for k in kys
+        irrep = Representation(k)
+        for j in 1:d[k]
+            push!(reps, irrep)
+        end
+    end
+    blockdiag(reps...)
+end
+
 kron(A::Representation, B::Representation) = Representation(kron.(A.generators, B.generators))
 
 _blockdiag(A::AbstractSparseMatrixCSC...) = blockdiag(A...)
@@ -513,9 +544,7 @@ function blockdiagonalize(ρ::Representation)
     n = length(ρ.generators)+1
 
     Q̃ = similar(Q)
-    # diagonalised generators
-    ρd = float.(zero.(ρ.generators))
-
+    # diagonalised generators    
     c = contents2partition(Λ)
 
     k = 0
@@ -526,13 +555,10 @@ function blockdiagonalize(ρ::Representation)
         Q̃ⱼ = singlemultreduce_blockdiag(ρⱼ, Representation(pⱼ))
         m = length(j)
         Q̃[:,k+1:k+m] = Qⱼ * Q̃ⱼ
-        irrep = Representation(pⱼ)
-        for ℓ = 1:n-1
-            ρd[ℓ][k+1:k+m,k+1:k+m] = blockdiag(fill(irrep.generators[ℓ], m÷size(irrep,1))...)
-        end
         k += m
     end
-    Representation(ρd), Q̃
+
+    multiplicities(c), Q̃
 end
 
 function contents2partition(part::Vector)

test/runtests.jl

@@ -20,9 +20,9 @@ import NumericalRepresentationTheory: gelfandbasis, canonicalprojection, singlem
 
     ρ = Representation(Partition([3,2])) ⊗ Representation(Partition([2,2,1])) ⊗ Representation(Partition([3,1,1]))
     λ,Q = blockdiagonalize(ρ)
-
-    for k = 1:length(λ.generators)
-        @test Q' * ρ.generators[k] * Q ≈ λ.generators[k]
+    irreps = Representation(λ)
+    for k = 1:length(ρ.generators)
+        @test Q' * ρ.generators[k] * Q ≈ irreps.generators[k]
     end
 
     @testset "Rotate irrep" begin