Fix non-square sparse matrix preallocations for defaults

Part 2 of fixes SciML/NonlinearSolve.jl#599

Author: ChrisRackauckas

ext/LinearSolveSparseArraysExt.jl

@@ -83,10 +83,14 @@ function LinearSolve.init_cacheval(
         maxiters::Int, abstol,
         reltol,
         verbose::Bool, assumptions::OperatorAssumptions)
-    A = convert(AbstractMatrix, A)
-    zerobased = SparseArrays.getcolptr(A)[1] == 0
-    return SparseArrays.UMFPACK.UmfpackLU(SparseMatrixCSC(size(A)..., getcolptr(A),
-        rowvals(A), nonzeros(A)))
+    if size(A,1) == size(A,2)
+        A = convert(AbstractMatrix, A)
+        zerobased = SparseArrays.getcolptr(A)[1] == 0
+        return SparseArrays.UMFPACK.UmfpackLU(SparseMatrixCSC(size(A)..., getcolptr(A),
+            rowvals(A), nonzeros(A)))
+    else
+        PREALLOCATED_UMFPACK
+    end
 end
 
 function SciMLBase.solve!(
@@ -141,9 +145,13 @@ function LinearSolve.init_cacheval(
         maxiters::Int, abstol,
         reltol,
         verbose::Bool, assumptions::OperatorAssumptions)
-    A = convert(AbstractMatrix, A)
-    return KLU.KLUFactorization(SparseMatrixCSC(size(A)..., getcolptr(A), rowvals(A),
-        nonzeros(A)))
+    if size(A,1) == size(A,2)
+        A = convert(AbstractMatrix, A)
+        return KLU.KLUFactorization(SparseMatrixCSC(size(A)..., getcolptr(A), rowvals(A),
+            nonzeros(A)))
+    else
+        PREALLOCATED_KLU
+    end
 end
 
 # TODO: guard this against errors

test/default_algs.jl

@@ -144,3 +144,18 @@ cache.A = [2.0 1.0
 sol = solve!(cache)
 
 @test !SciMLBase.successful_retcode(sol.retcode)
+
+## Non-square Sparse Defaults 
+# https://github.com/SciML/NonlinearSolve.jl/issues/599
+
+A = SparseMatrixCSC{Float64, Int32}([
+    1.0 0.0
+    1.0 1.0
+])
+b = ones(2)
+A2 = hcat(A,A)
+prob = LinearProblem(A, b)
+@test SciMLBase.successful_retcode(solve(prob))
+
+prob2 = LinearProblem(A2, b)
+@test SciMLBase.successful_retcode(solve(prob2))