Remove eltype assumption from ldiv!(LowerTriangular(SparseMatrixCSC{Tv,Ti), ...) (#40174)

(cherry picked from commit beeb6d7)

Author: palday

stdlib/SparseArrays/src/linalg.jl

@@ -646,7 +646,7 @@ function _ldiv!(L::LowerTriangularPlain, B::StridedVecOrMat)
     for k = 1:ncolB
         for j = 1:nrowB
             i1 = ia[j]
-            i2 = ia[j + 1] - 1
+            i2 = ia[j + 1] - one(eltype(ia))
 
             # find diagonal element
             ii = searchsortedfirst(ja, j, i1, i2, Base.Order.Forward)
@@ -688,7 +688,7 @@ function _ldiv!(U::UpperTriangularPlain, B::StridedVecOrMat)
     for k = 1:ncolB
         for j = nrowB:-1:1
             i1 = ia[j]
-            i2 = ia[j + 1] - 1
+            i2 = ia[j + 1] - one(eltype(ia))
 
             # find diagonal element
             ii = searchsortedlast(ja, j, i1, i2, Base.Order.Forward)

stdlib/SparseArrays/test/sparsevector.jl

@@ -1050,6 +1050,10 @@ end
             @test y == Af'x2f
         end
     end
+    @testset "ldiv with different element types (#40171)" begin
+        sA = sparse(Int16.(1:4), Int16.(1:4), ones(4))
+        @test all(ldiv!(LowerTriangular(sA), ones(4)) .≈ 1.)
+    end
     @testset "ldiv ops with triangular matrices and sparse vecs (#14005)" begin
         m = 10
         sparsefloatvecs = SparseVector[sprand(m, 0.4) for k in 1:3]