TP-optimisation-numerique-2/test/tester_algo_newton.jl

@doc doc"""
Tester l'algorithme de Newton local

# Entrées :
   * afficher : (Bool) affichage ou non des résultats de chaque test

# Les cas de test (dans l'ordre)
   * fct 1 : x011,x012
   * fct 2 : x021,x022
"""
function tester_algo_newton(afficher::Bool, Algorithme_De_Newton::Function)
    max_iter = 100
    Tol_abs = sqrt(eps())
    Tol_rel = 1e-15
    options = [max_iter, Tol_abs, Tol_rel]
    @testset "L'algo de Newton" begin

        # tests sur la fonction fct0
        @testset "Cas test 0 x0 = solution" begin
            # point de départ sol_exacte
            xmin, f_min, flag, nb_iters = Algorithme_De_Newton(fct0, grad_fct0, hess_fct0, sol_exacte_fct0, options)
            if (afficher)
                afficher_resultats("algorithme de Newton", "fct0", "sol_exacte", xmin, f_min, flag, sol_exacte_fct0, nb_iters)
            end
            @testset "solution" begin
                @test isapprox(xmin, sol_exacte_fct0, atol = tol_erreur)
            end
            @testset "itération" begin
                @test nb_iters == 0
            end
        end
        @testset "Cas test 0 x0 = x001" begin
            #point de départ x001
            xmin, f_min, flag, nb_iters = Algorithme_De_Newton(fct0, grad_fct0, hess_fct0, pts1.x001, options)
            if (afficher)
                afficher_resultats("algorithme de Newton", "fct0", "x001", xmin, f_min, flag, sol_exacte_fct0, nb_iters)
            end
            @testset "solution" begin
                @test isapprox(xmin, sol_exacte_fct0, atol = tol_erreur)
            end
            @testset "itération" begin
                @test nb_iters == 3
            end
        end
        @testset "Cas test 0 x0 = x002" begin
            #point de départ x002 = -sol_exacte_fct0
            xmin, f_min, flag, nb_iters = Algorithme_De_Newton(fct0, grad_fct0, hess_fct0, pts1.x002, options)
            if (afficher)
                afficher_resultats("algorithme de Newton", "fct0", "x002", xmin, f_min, flag, sol_exacte_fct0, nb_iters)
            end
            @testset "solution" begin
                @test isapprox(xmin, -sol_exacte_fct0, atol = tol_erreur)
            end
            @testset "itération" begin
                @test nb_iters == 0
            end
        end

        # tests sur la fonction fct1
        @testset "Cas test 1 x0 = solution" begin
            # point de départ sol_exacte
            x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct1, grad_fct1, hess_fct1, sol_exacte_fct1, options)
            if (afficher)
                afficher_resultats("algorithme de Newton", "fct1", "sol_exacte", x_min, fx_min, flag, sol_exacte_fct1, nb_iters)
            end
            @testset "solution" begin
                @test isapprox(x_min, sol_exacte_fct1, atol = tol_erreur)
            end
            @testset "itération" begin
                @test nb_iters == 0
            end
        end
        @testset "Cas test 1 x0 = x011" begin
            #point de départ x011
            x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct1, grad_fct1, hess_fct1, pts1.x011, options)
            if (afficher)
                afficher_resultats("algorithme de Newton", "fct1", "x011", x_min, fx_min, flag, sol_exacte_fct1, nb_iters)
            end
            @testset "solution" begin
                @test isapprox(x_min, sol_exacte_fct1, atol = tol_erreur)
            end
            @testset "itération" begin
                @test nb_iters == 1
            end
        end
        @testset "Cas test 1 x0 = x012" begin
            x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct1, grad_fct1, hess_fct1, pts1.x012, options)
            if (afficher)
                afficher_resultats("algorithme de Newton", "fct1", "x012", x_min, fx_min, flag, sol_exacte_fct1, nb_iters)
            end
            @testset "solution" begin
                @test isapprox(x_min, sol_exacte_fct1, atol = tol_erreur)
            end
            @testset "itération" begin
                @test nb_iters == 1
            end
        end

        # tests sur la fonction fct2
        @testset "Cas test 2 x0 = solution" begin
            x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct1, grad_fct1, hess_fct1, sol_exacte_fct1, options)
            if (afficher)
                afficher_resultats("algorithme de Newton", "fct1", "sol_exacte", x_min, fx_min, flag, sol_exacte_fct1, nb_iters)
            end
            @testset "solution" begin
                @test isapprox(x_min, sol_exacte_fct1, atol = tol_erreur)
            end
            @testset "itération" begin
                @test nb_iters == 0
            end
        end
        @testset "Cas test 2 x0 = x021" begin
            x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, pts1.x021, options)
            if (afficher)
                afficher_resultats("algorithme de Newton", "fct2", "x021", x_min, fx_min, flag, sol_exacte_fct2, nb_iters)
            end
            @testset "solution" begin
                @test isapprox(x_min, sol_exacte_fct2, atol = tol_erreur)
            end
            @testset "itération" begin
                @test nb_iters == 6
            end
        end
        @testset "Cas test 2 x0 = x022" begin
            x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, pts1.x022, options)
            if (afficher)
                afficher_resultats("algorithme de Newton", "fct2", "x022", x_min, fx_min, flag, sol_exacte_fct2, nb_iters)
            end
            @testset "solution" begin
                @test isapprox(x_min, sol_exacte_fct2, atol = tol_erreur)
            end
            @testset "itération" begin
                @test nb_iters == 5
            end
        end
        @testset "Cas test 2 x0 = x023" begin
            options[1] = 1
            sol = [-4.99999958629818e9, 8.673617379884035e-19]
            x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, pts1.x023, options)
            if (afficher)
                afficher_resultats("algorithme de Newton", "fct2", "x022", x_min, fx_min, flag, sol_exacte_fct2, nb_iters)
            end
            @testset "solution" begin
                @test isapprox(x_min, sol, atol = tol_erreur)
            end
            @testset "exception" begin
                options[1] = 100
                @test_throws SingularException x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, pts1.x023, options)
            end
        end

        # vérification de tous les flags
        @testset "Cas test stagnation x" begin
            max_iter = 1000
            Tol_abs = sqrt(eps())
            Tol_rel = 1e-15
            options = [max_iter, Tol_abs, Tol_rel]
            hess(x) = [
                1e10 0 0
                0 1e10 0
                0 0 1e10
            ]
            grad(x) = [
                10
                10
                10
            ]
            x0 = ones(3) .* 0.9999
            xmin, f_min, flag, nb_iters = Algorithme_De_Newton(fct1, grad, hess, x0, options)
            if (afficher)
                afficher_resultats("stagnation x de Newton", "fct0", x0, xmin, f_min, flag, sol_exacte_fct0, nb_iters)
            end
            @testset "flag" begin
                @test flag == 1
            end
        end
        @testset "Cas test stagnation f(x)" begin
            x0 = ones(2) .* 100
            xmin, f_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, x0, options)
            if (afficher)
                afficher_resultats("stagnation f(x) de Newton", "fct2", x0, xmin, f_min, flag, sol_exacte_fct2, nb_iters)
            end
            @testset "flag" begin
                @test flag == 2
            end
        end
        @testset "Cas test itermax" begin
            options[1] = 2
            x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, pts1.x021, options)
            if (afficher)
                afficher_resultats("itermax de Newton", "fct2", "x021", x_min, fx_min, flag, sol_exacte_fct2, nb_iters)
            end
            @testset "itération" begin
                @test nb_iters == 2
            end
            @testset "flag" begin
                @test flag == 3
            end
        end
    end
end