Make use of fast sparse outer products from Julia (closes #4)

The feature was added to Julia in time for v1.2 in JuliaLang/julia#24980,
so get rid of the custom `outer()` method here and rewrite `quadprod()`
in terms of just standard matrix methods. Julia v1.2 is the
minimum-supported version at this point, so no need to worry about
backporting the functionality.

In the future, this function may yet still go away since the
implementation is nearly trivial at this point, but that can be a
follow-up PR.

src/numerics.jl

@@ -1,100 +1,17 @@
 using SparseArrays
 
-"""
-Computes the outer product between a given column of a sparse matrix and a vector.
-"""
-function outer end
-
-"""
-    outer(A::SparseMatrixCSC, n::Integer, w::AbstractVector)
-
-Performs the equivalent of ``\\vec a_n \\vec w^\\dagger`` where ``\\vec a_n`` is the
-column `A[:,n]`.
-"""
-function outer(A::SparseMatrixCSC{Tv,Ti}, n::Integer, w::AbstractVector{Tv}) where {Tv,Ti}
-    colptrn = nzrange(A, n)
-    rowvalA = rowvals(A)
-    nzvalsA = nonzeros(A)
-
-    nnza = length(colptrn)
-    nnzw = length(w)
-    numnz = nnza * nnzw
-
-    colptr = Vector{Ti}(undef, nnzw+1)
-    rowval = Vector{Ti}(undef, numnz)
-    nzvals = Vector{Tv}(undef, numnz)
-
-    idx = 0
-    @inbounds for jj = 1:nnzw
-        colptr[jj] = idx + 1
-
-        wv = conj(w[jj])
-        iszero(wv) && continue
-
-        for ii = colptrn
-            idx += 1
-            rowval[idx] = rowvalA[ii] # copy row index from A
-            nzvals[idx] = wv * nzvalsA[ii] # outer product values
-        end
-    end
-    @inbounds colptr[nnzw+1] = idx + 1
-    return SparseMatrixCSC(size(A,1), nnzw, colptr, rowval, nzvals)
-end
-
-"""
-    outer(w::AbstractVector, A::SparseMatrixCSC, n::Integer)
-
-Performs the equivalent of ``\\vec w \\vec{a}_n^\\dagger`` where ``\\vec a_n`` is the
-column `A[:,n]`.
-"""
-function outer(w::AbstractVector{Tv}, A::SparseMatrixCSC{Tv,Ti}, n::Integer) where {Tv,Ti}
-    colptrn = nzrange(A, n)
-    rowvalA = rowvals(A)
-    nzvalsA = nonzeros(A)
-
-    nnza = length(colptrn)
-    nnzw = length(w)
-    numnz = nnza * nnzw
-
-    colptr = zeros(Ti, size(A,1)+1)
-    rowval = Vector{Ti}(undef, numnz)
-    nzvals = Vector{Tv}(undef, numnz)
-
-    idx = 0
-    @inbounds colptr[1] = 1 # col 1 always at index 1
-    @inbounds for jj = colptrn
-        av = conj(nzvalsA[jj])
-        rv = rowvalA[jj]
-
-        for ii = 1:nnzw
-            wv = w[ii]
-            iszero(wv) && continue
-
-            idx += 1
-            colptr[rv+1] += 1 # count num of entries in column
-            rowval[idx] = ii
-            nzvals[idx] = w[ii] * av # outer product values
-        end
-    end
-    cumsum!(colptr, colptr) # offsets are sum of all previous
-
-    return SparseMatrixCSC(nnzw, size(A,1), colptr, rowval, nzvals)
-end
-
 """
     quadprod(A, b, n, dir=:col)
 
-Computes the quadratic product ``ABA^T`` efficiently for the case where ``B`` is all zero
+Computes the quadratic product ``ABA^\\top`` efficiently for the case where ``B`` is all zero
 except for the `n`th column or row vector `b`, for `dir = :col` or `dir = :row`,
 respectively.
 """
-function quadprod(A, b, n, dir::Symbol=:col)
+@inline function quadprod(A, b, n, dir::Symbol=:col)
     if dir == :col
-        w = A * b
-        return outer(w, A, n)
+        return (A * sparse(b)) * view(A, :, n)'
     elseif dir == :row
-        w = A * b
-        return outer(A, n, w)
+        return view(A, :, n) * (A * sparse(b))'
     else
         error("Unrecognized direction `dir = $(repr(dir))`.")
     end