Add test for sparse cholesky

Author: avik-pal

src/factorization.jl

@@ -242,8 +242,6 @@ end
     function do_factorization(alg::CholeskyFactorization, A, b, u)
         A = convert(AbstractMatrix, A)
         if A isa SparseMatrixCSC
-            # fact = cholesky!(A; shift = alg.shift, check = false, perm = alg.perm)
-            # fact = @time cholesky!(A; check = false)
             fact = cholesky(A; shift = alg.shift, check = false, perm = alg.perm)
         elseif alg.pivot === Val(false) || alg.pivot === NoPivot()
             fact = cholesky!(A, alg.pivot; check = false)
@@ -270,7 +268,6 @@ function init_cacheval(alg::CholeskyFactorization, A, b, u, Pl, Pr,
     maxiters::Int, abstol, reltol, verbose::Bool,
     assumptions::OperatorAssumptions)
     ArrayInterface.cholesky_instance(convert(AbstractMatrix, A), alg.pivot)
-    # cholesky!(similar(A, 1, 1); check=false)
 end
 
 @static if VERSION < v"1.8beta"

test/sparse_vector.jl

@@ -2,7 +2,7 @@ using SparseArrays
 using LinearSolve
 using LinearAlgebra
 
-# Constructing sparse array 
+# Constructing sparse array
 function hess_sparse(x::Vector{T}) where {T}
     return [
         -sin(x[1] + x[2]) + 1,
@@ -37,7 +37,12 @@ n = length(x0)
 hess_mat = sparse(rowval, colval, hess_sparse(x0), n, n)
 grad_vec = sparsevec(gradinds, grad_sparse(x0), n)
 
-# # Converting grad_vec to dense succeeds in solving
+# Converting grad_vec to dense succeeds in solving
 prob = LinearProblem(hess_mat, grad_vec)
-linsolve = init(prob)
+linsolve = init(prob);
 @test solve!(linsolve).u ≈ hess_mat \ Array(grad_vec)
+
+H = hess_mat' * hess_mat
+prob = LinearProblem(H, hess_mat' * grad_vec)
+linsolve = init(prob, CholeskyFactorization())
+@test solve!(linsolve).u ≈ H \ Array(hess_mat' * grad_vec)