added specialized method for 3-argument dot with diagonal matrix (#565)

Author: matbesancon

src/linalg.jl

@@ -650,6 +650,62 @@ function dot(A::AbstractSparseMatrixCSC, B::Union{DenseMatrixUnion,WrapperMatrix
     return conj(dot(B, A))
 end
 
+function dot(x::AbstractSparseVector, D::Diagonal, y::AbstractVector)
+    d = D.diag
+    if length(x) != length(y) || length(y) != length(d)
+        throw(
+            DimensionMismatch("Vectors and matrix have different dimensions, x has a length $(length(x)), y has a length $(length(y)), D has side dimension $(length(d))")
+        )
+    end
+    nzvals = nonzeros(x)
+    nzinds = nonzeroinds(x)
+    s = zero(typeof(dot(first(x), first(D), first(y))))
+    @inbounds for nzidx in eachindex(nzvals)
+        s += dot(nzvals[nzidx], d[nzinds[nzidx]], y[nzinds[nzidx]])
+    end
+    return s
+end
+
+dot(x::AbstractVector, D::Diagonal, y::AbstractSparseVector) = adjoint(dot(y, D', x))
+
+function dot(x::AbstractSparseVector, D::Diagonal, y::AbstractSparseVector)
+    d = D.diag
+    if length(y) != length(x) || length(y) != length(d)
+        throw(
+            DimensionMismatch("Vectors and matrix have different dimensions, x has a length $(length(x)), y has a length $(length(y)), Q has side dimension $(length(d))")
+        )
+    end
+    xnzind = nonzeroinds(x)
+    ynzind = nonzeroinds(y)
+    xnzval = nonzeros(x)
+    ynzval = nonzeros(y)
+    s = zero(typeof(dot(first(x), first(D), first(y))))
+    if isempty(xnzind) || isempty(ynzind)
+        return s
+    end
+
+    x_idx = 1
+    y_idx = 1
+    x_idx_last = length(xnzind)
+    y_idx_last = length(ynzind)
+
+    # go through the nonzero indices of a and b simultaneously
+    @inbounds while x_idx <= x_idx_last && y_idx <= y_idx_last
+        ix = xnzind[x_idx]
+        iy = ynzind[y_idx]
+        if ix == iy
+            s += dot(xnzval[x_idx], d[ix], ynzval[y_idx])
+            x_idx += 1
+            y_idx += 1
+        elseif ix < iy
+            x_idx += 1
+        else
+            y_idx += 1
+        end
+    end
+    return s
+end
+
 ## triangular sparse handling
 ## triangular multiplication
 function LinearAlgebra.generic_trimatmul!(C::StridedVecOrMat, uploc, isunitc, tfun::Function, A::SparseMatrixCSCUnion, B::AbstractVecOrMat)

test/linalg.jl

@@ -850,6 +850,20 @@ end
             @test dot(TA,WB) ≈ dot(Matrix(TA), WB)
             @test dot(TA,WC) ≈ dot(Matrix(TA), WC)
         end
+        for M in (A, B, C)
+            D = Diagonal(M * M')
+            a = spzeros(Complex{Float64}, size(D, 1))
+            a[1:3] = rand(Complex{Float64}, 3)
+            b = spzeros(Complex{Float64}, size(D, 1))
+            b[1:3] = rand(Complex{Float64}, 3)
+            @test dot(a, D, b) ≈ dot(a, sparse(D), b)
+            @test dot(b, D, a) ≈ dot(b, sparse(D), a)
+            @test dot(b, D, a) ≈ dot(b, D, collect(a))
+            @test dot(b, D, a) ≈ dot(collect(b), D, a)
+            @test_throws DimensionMismatch dot(b, D, [a; 1])
+            @test_throws DimensionMismatch dot([b; 1], D, a)
+            @test_throws DimensionMismatch dot([b; 1], D, [a; 1])
+        end
     end
     @test_throws DimensionMismatch dot(sprand(5,5,0.2),sprand(5,6,0.2))
     @test_throws DimensionMismatch dot(rand(5,5),sprand(5,6,0.2))