202 lines
8.2 KiB
Julia
202 lines
8.2 KiB
Julia
@doc doc"""
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Tester l'algorithme de Newton local
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# Entrées :
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* afficher : (Bool) affichage ou non des résultats de chaque test
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# Les cas de test (dans l'ordre)
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* fct 1 : x011,x012
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* fct 2 : x021,x022
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"""
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function tester_algo_newton(afficher::Bool, Algorithme_De_Newton::Function)
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max_iter = 100
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Tol_abs = sqrt(eps())
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Tol_rel = 1e-15
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options = [max_iter, Tol_abs, Tol_rel]
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@testset "L'algo de Newton" begin
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# tests sur la fonction fct0
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@testset "Cas test 0 x0 = solution" begin
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# point de départ sol_exacte
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xmin, f_min, flag, nb_iters = Algorithme_De_Newton(fct0, grad_fct0, hess_fct0, sol_exacte_fct0, options)
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if (afficher)
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afficher_resultats("algorithme de Newton", "fct0", "sol_exacte", xmin, f_min, flag, sol_exacte_fct0, nb_iters)
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end
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@testset "solution" begin
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@test isapprox(xmin, sol_exacte_fct0, atol = tol_erreur)
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end
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@testset "itération" begin
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@test nb_iters == 0
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end
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end
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@testset "Cas test 0 x0 = x001" begin
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#point de départ x001
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xmin, f_min, flag, nb_iters = Algorithme_De_Newton(fct0, grad_fct0, hess_fct0, pts1.x001, options)
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if (afficher)
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afficher_resultats("algorithme de Newton", "fct0", "x001", xmin, f_min, flag, sol_exacte_fct0, nb_iters)
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end
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@testset "solution" begin
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@test isapprox(xmin, sol_exacte_fct0, atol = tol_erreur)
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end
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@testset "itération" begin
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@test nb_iters == 3
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end
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end
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@testset "Cas test 0 x0 = x002" begin
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#point de départ x002 = -sol_exacte_fct0
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xmin, f_min, flag, nb_iters = Algorithme_De_Newton(fct0, grad_fct0, hess_fct0, pts1.x002, options)
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if (afficher)
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afficher_resultats("algorithme de Newton", "fct0", "x002", xmin, f_min, flag, sol_exacte_fct0, nb_iters)
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end
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@testset "solution" begin
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@test isapprox(xmin, -sol_exacte_fct0, atol = tol_erreur)
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end
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@testset "itération" begin
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@test nb_iters == 0
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end
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end
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# tests sur la fonction fct1
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@testset "Cas test 1 x0 = solution" begin
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# point de départ sol_exacte
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x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct1, grad_fct1, hess_fct1, sol_exacte_fct1, options)
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if (afficher)
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afficher_resultats("algorithme de Newton", "fct1", "sol_exacte", x_min, fx_min, flag, sol_exacte_fct1, nb_iters)
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end
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@testset "solution" begin
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@test isapprox(x_min, sol_exacte_fct1, atol = tol_erreur)
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end
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@testset "itération" begin
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@test nb_iters == 0
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end
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end
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@testset "Cas test 1 x0 = x011" begin
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#point de départ x011
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x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct1, grad_fct1, hess_fct1, pts1.x011, options)
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if (afficher)
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afficher_resultats("algorithme de Newton", "fct1", "x011", x_min, fx_min, flag, sol_exacte_fct1, nb_iters)
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end
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@testset "solution" begin
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@test isapprox(x_min, sol_exacte_fct1, atol = tol_erreur)
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end
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@testset "itération" begin
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@test nb_iters == 1
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end
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end
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@testset "Cas test 1 x0 = x012" begin
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x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct1, grad_fct1, hess_fct1, pts1.x012, options)
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if (afficher)
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afficher_resultats("algorithme de Newton", "fct1", "x012", x_min, fx_min, flag, sol_exacte_fct1, nb_iters)
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end
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@testset "solution" begin
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@test isapprox(x_min, sol_exacte_fct1, atol = tol_erreur)
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end
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@testset "itération" begin
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@test nb_iters == 1
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end
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end
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# tests sur la fonction fct2
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@testset "Cas test 2 x0 = solution" begin
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x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct1, grad_fct1, hess_fct1, sol_exacte_fct1, options)
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if (afficher)
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afficher_resultats("algorithme de Newton", "fct1", "sol_exacte", x_min, fx_min, flag, sol_exacte_fct1, nb_iters)
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end
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@testset "solution" begin
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@test isapprox(x_min, sol_exacte_fct1, atol = tol_erreur)
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end
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@testset "itération" begin
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@test nb_iters == 0
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end
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end
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@testset "Cas test 2 x0 = x021" begin
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x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, pts1.x021, options)
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if (afficher)
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afficher_resultats("algorithme de Newton", "fct2", "x021", x_min, fx_min, flag, sol_exacte_fct2, nb_iters)
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end
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@testset "solution" begin
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@test isapprox(x_min, sol_exacte_fct2, atol = tol_erreur)
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end
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@testset "itération" begin
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@test nb_iters == 6
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end
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end
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@testset "Cas test 2 x0 = x022" begin
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x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, pts1.x022, options)
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if (afficher)
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afficher_resultats("algorithme de Newton", "fct2", "x022", x_min, fx_min, flag, sol_exacte_fct2, nb_iters)
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end
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@testset "solution" begin
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@test isapprox(x_min, sol_exacte_fct2, atol = tol_erreur)
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end
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@testset "itération" begin
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@test nb_iters == 5
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end
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end
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@testset "Cas test 2 x0 = x023" begin
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options[1] = 1
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sol = [-4.99999958629818e9, 8.673617379884035e-19]
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x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, pts1.x023, options)
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if (afficher)
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afficher_resultats("algorithme de Newton", "fct2", "x022", x_min, fx_min, flag, sol_exacte_fct2, nb_iters)
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end
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@testset "solution" begin
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@test isapprox(x_min, sol, atol = tol_erreur)
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end
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@testset "exception" begin
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options[1] = 100
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@test_throws SingularException x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, pts1.x023, options)
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end
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end
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# vérification de tous les flags
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@testset "Cas test stagnation x" begin
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max_iter = 1000
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Tol_abs = sqrt(eps())
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Tol_rel = 1e-15
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options = [max_iter, Tol_abs, Tol_rel]
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hess(x) = [
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1e10 0 0
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0 1e10 0
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0 0 1e10
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]
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grad(x) = [
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10
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10
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10
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]
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x0 = ones(3) .* 0.9999
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xmin, f_min, flag, nb_iters = Algorithme_De_Newton(fct1, grad, hess, x0, options)
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if (afficher)
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afficher_resultats("stagnation x de Newton", "fct0", x0, xmin, f_min, flag, sol_exacte_fct1, nb_iters)
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end
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@testset "flag" begin
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@test flag == 1
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end
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end
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@testset "Cas test stagnation f(x)" begin
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x0 = ones(2) .* 100
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xmin, f_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, x0, options)
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if (afficher)
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afficher_resultats("stagnation f(x) de Newton", "fct2", x0, xmin, f_min, flag, sol_exacte_fct2, nb_iters)
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end
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@testset "flag" begin
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@test flag == 2
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end
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end
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@testset "Cas test itermax" begin
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options[1] = 2
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x_min, fx_min, flag, nb_iters = Algorithme_De_Newton(fct2, grad_fct2, hess_fct2, pts1.x021, options)
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if (afficher)
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afficher_resultats("itermax de Newton", "fct2", "x021", x_min, fx_min, flag, sol_exacte_fct2, nb_iters)
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end
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@testset "itération" begin
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@test nb_iters == 2
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end
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@testset "flag" begin
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@test flag == 3
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end
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end
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end
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end
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