Refactor substitution methods and add LinearAlgebra dependency

- Add LinearAlgebra dependency in Project.toml
- Introduce type aliases ForwardSubstitution and BackSubstitution
- Modify ForwardSubstitutionProblem constructor to use inner constructor
- Update test runner to include specific substitution test files
- Remove setup.jl script

Author: yangjunjie0320

Makefile

@@ -0,0 +1,21 @@
+jl:=julia
+
+init: 
+	$(jl) -e 'd=pwd(); @assert isdir(d);\
+	using Pkg: activate, instantiate, develop, precompile; \
+	activate(d); instantiate(); activate(joinpath(d, "examples")); \
+	develop(path=d); instantiate(); precompile();'
+	@echo "environment initialized at: $$PWD"
+
+update:
+	$(jl) -e 'd=pwd(); @assert isdir(d);\
+	using Pkg: activate, update, develop, precompile; \
+	activate(d); update(); activate(joinpath(d, "examples")); \
+	update(); precompile();'
+	@echo "environment updated at: $$PWD"
+
+test:
+	@echo "Running tests at: $$PWD"
+	$(jl) -e 'd=pwd(); @assert isdir(d);\
+	using Pkg: activate, test; \
+	activate(d); test();'

Project.toml

@@ -3,7 +3,11 @@ uuid = "555e9691-8231-4cde-a0d7-6dc20204a59a"
 authors = ["Junjie Yang <yangjunjie0320@gmail.com> and contributors"]
 version = "1.0.0-DEV"
 
+[deps]
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
 [compat]
+LinearAlgebra = "1.11.0"
 julia = "1"
 
 [extras]

examples/Manifest.toml

@@ -0,0 +1,39 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.11.3"
+manifest_format = "2.0"
+project_hash = "6bccd7e9beaf72625f8173864188b586b1c437d4"
+
+[[deps.Artifacts]]
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+version = "1.11.0"
+
+[[deps.CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+version = "1.1.1+0"
+
+[[deps.Libdl]]
+uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
+version = "1.11.0"
+
+[[deps.LinearAlgebra]]
+deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
+uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+version = "1.11.0"
+
+[[deps.OpenBLAS_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
+uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
+version = "0.3.27+1"
+
+[[deps.SimpleLinearAlgebra]]
+deps = ["LinearAlgebra"]
+path = "/Users/yangjunjie/.julia/dev/SimpleLinearAlgebra"
+uuid = "555e9691-8231-4cde-a0d7-6dc20204a59a"
+version = "1.0.0-DEV"
+
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+version = "5.11.0+0"

examples/Project.toml

@@ -0,0 +1,2 @@
+[deps]
+SimpleLinearAlgebra = "555e9691-8231-4cde-a0d7-6dc20204a59a"

src/back_substitution.jl

@@ -15,6 +15,8 @@ struct BackSubstitutionSolution <: LinearSystemSolutionMixin
     x::AbstractVector
 end
 
+BackSubstitution = BackSubstitutionProblem
+
 function kernel(prob::BackSubstitutionProblem)
     u = prob.u
     b = copy(prob.b)
@@ -35,4 +37,5 @@ function kernel(prob::BackSubstitutionProblem)
     return BackSubstitutionSolution(x)
 end
 
-export BackSubstitutionProblem, kernel
+
+export BackSubstitution, kernel

src/forward_substitution.jl

@@ -2,15 +2,17 @@ struct ForwardSubstitutionProblem <: LinearSystemProblemMixin
     l::AbstractMatrix
     b::AbstractVector
     tol::Real
-end
 
-function ForwardSubstitutionProblem(l, b, tol)
-    if !istril(l)
-        ArgumentError("Matrix must be lower triangular") |> throw
+    function ForwardSubstitutionProblem(l, b, tol)
+        if !istril(l)
+            ArgumentError("Matrix must be lower triangular") |> throw
+        end
+        return new(l, b, tol)
     end
-    return new(l, b, tol)
 end
 
+ForwardSubstitution = ForwardSubstitutionProblem
+
 struct ForwardSubstitutionSolution <: LinearSystemSolutionMixin
     x::AbstractVector
 end
@@ -32,4 +34,5 @@ function kernel(prob::ForwardSubstitutionProblem)
     return ForwardSubstitutionSolution(x)
 end
 
-export ForwardSubstitutionProblem, kernel
+
+export ForwardSubstitution, kernel

src/setup.jl

@@ -0,0 +1,11 @@
+@testset "backward substitution" begin
+    n = 10
+    tol = 1e-10
+    u = LinearAlgebra.triu(rand(n, n))
+    b = rand(n)
+
+    p = BackSubstitution(u, b, tol)
+    s = kernel(p)
+    x = s.x
+    @test maximum(abs, u * x - b) < tol
+end

test/backward_substitution.jl

@@ -0,0 +1,11 @@
+@testset "forward substitution" begin
+    n = 10
+    tol = 1e-10
+    u = LinearAlgebra.tril(rand(n, n))
+    b = rand(n)
+
+    p = ForwardSubstitution(u, b, tol)
+    s = kernel(p)
+    x = s.x
+    @test maximum(abs, u * x - b) < tol
+end

test/forward_substitution.jl

@@ -1,6 +1,10 @@
 using SimpleLinearAlgebra
-using Test
+using Test, LinearAlgebra
 
-@testset "SimpleLinearAlgebra.jl" begin
-    # Write your tests here.
+@testset "forward substitution" begin
+    include("forward_substitution.jl")
+end
+
+@testset "backward substitution" begin
+    include("backward_substitution.jl")
 end