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

@doc doc"""
Tester l'algorithme du gradient conjugué tronqué

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

# Les cas de test (dans l'ordre)
   * la quadratique 1
   * la quadratique 2
   * la quadratique 3
   * la quadratique 4
   * la quadratique 5
   * la quadratique 6
"""
function tester_gct(afficher::Bool, Gradient_Conjugue_Tronque::Function)

    tol = 1e-7
    max_iter = 100
    # Tolérance utilisé dans les tests
    tol_test = 1e-3

    @testset "Gradient-CT" begin
        # le cas de test 1
        grad = [0; 0]
        Hess = [7 0; 0 2]
        delta = 1
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, [0.0; 0.0], atol = tol_test)

        # le cas de test 2 H definie positive
        grad = [6; 2]
        Hess = [7 0; 0 2]
        delta = 0.5       # sol = pas de Cauchy  
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, -delta * grad / norm(grad), atol = tol_test)
        delta = 1.2       # saturation à la 2ieme itération  
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, [-0.8740776099190263, -0.8221850958502244], atol = tol_test)
        delta = 3         # sol = min global  
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, -Hess \ grad, atol = tol_test)

        # le cas test 2 bis matrice avec 1 vp < 0 et 1 vp > 0
        grad = [1, 2]
        Hess = [1 0; 0 -1]
        delta = 1.0       # g^T H g < 0 première direction concave
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, -delta * grad / norm(grad), atol = tol_test)
        grad = [1, 0]
        delta = 0.5       #  g^T H g > 0 sol pas de Cauchy
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, -delta * grad / norm(grad), atol = tol_test)
        grad = [2, 1]        #  g^T H g > 0 sol à l'itération 2, saturation
        delta = 6
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, [0.48997991959774634, 5.979959839195494], atol = tol_test) || isapprox(s, [-4.489979919597747, -3.979959839195493], atol = tol_test)
        # le cas de test 3
        grad = [-2; 1]
        Hess = [-2 0; 0 10]
        delta = 10
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, [9.102342582478453; -4.140937032991381], atol = tol_test)

        # le cas de test 4
        grad = [0; 0]
        Hess = [-2 0; 0 10]
        delta = 1
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, [0.0; 0.0], atol = tol_test)

        # le cas de test 5
        grad = [2; 3]
        Hess = [4 6; 6 5]
        delta = 3
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, [1.9059020876695578; -2.3167946029410595], atol = tol_test)

        # le cas de test 6
        # Le pas de Cauchy conduit à un gradient nul en 1 itération
        grad = [2; 0]
        Hess = [4 0; 0 -15]
        delta = 2
        s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
        @test isapprox(s, [-0.5; 0.0], atol = tol_test)
    end
end