Add adjoint_coeffs

src/bases.jl

@@ -77,3 +77,28 @@ function coeffs!(res, cfs, source::AbstractBasis, target::AbstractBasis)
     end
     return res
 end
+
+"""
+    adjoint_coeffs(cfs, source, target)
+Return `A' * cfs` where `A` is the linear map applied by
+`coeffs`.
+"""
+function adjoint_coeffs(cfs, source::AbstractBasis, target::AbstractBasis)
+    source === target && return cfs
+    source == target && return cfs
+    res = zero_coeffs(valtype(cfs), source)
+    return adjoint_coeffs!(res, cfs, source, target)
+end
+
+function adjoint_coeffs!(res, cfs, source::AbstractBasis, target::AbstractBasis)
+    MA.operate!(zero, res)
+    for (k, v) in nonzero_pairs(cfs)
+        x = target[k]
+        # If `x` is not in `source` then the corresponding row in `A` is zero
+        # so the column in `A'` is zero hence we can ignore it.
+        if x in source
+            res[source[x]] += v
+        end
+    end
+    return res
+end

src/types.jl

@@ -38,6 +38,9 @@ coeffs(a::AlgebraElement) = a.coeffs
 function coeffs(x::AlgebraElement, b::AbstractBasis)
     return coeffs(coeffs(x), basis(x), b)
 end
+function adjoint_coeffs(a::AlgebraElement, target::AbstractBasis)
+    return adjoint_coeffs(coeffs(a), target, basis(a))
+end
 basis(a::AlgebraElement) = basis(parent(a))
 
 function AlgebraElement(coeffs, A::AbstractStarAlgebra)

test/abstract_coeffs.jl

@@ -13,6 +13,10 @@
         y = AlgebraElement(ACoeffs(coeffs(b, basis(fRG))), fRG)
         x, y
     end
+    @test coeffs(α - β, SA.FixedBasis(basis(RG); n = 2)) == [1, -1]
+    @test_throws KeyError coeffs(α - β, SA.FixedBasis(basis(RG); n = 1))
+    @test SA.adjoint_coeffs(α - β, SA.FixedBasis(basis(RG); n = 2)) == [1, -1]
+    @test SA.adjoint_coeffs(α - β, SA.FixedBasis(basis(RG); n = 1)) == [1]
     @test coeffs(2α) isa ACoeffs{Int}
     @test coeffs(α - β) isa ACoeffs
     @test coeffs(α - β // 3) isa ACoeffs{<:Rational}