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

@doc doc"""
Tester l'algorithme de pas de Cauchy

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

# Les cas de test (dans l'ordre)
   * quadratique 1
   * quadratique 2
   * quadratique 3
"""
function tester_pas_de_cauchy(afficher::Bool, Pas_De_Cauchy::Function)

    tol_erreur = 1e-6

    @testset "Pas de Cauchy" begin
        "# Pour la quadratique 1"

        @testset "g = 0" begin
            g = [0; 0]
            H = [7 0; 0 2]
            delta = 1
            s, e = Pas_De_Cauchy(g, H, delta)
            @test (e == 0) && (isapprox(s, [0; 0], atol = tol_erreur))
        end

        @testset "quad 2, non saturé" begin
            g = [6; 2]
            H = [7 0; 0 2]
            delta = 1
            s, e = Pas_De_Cauchy(g, H, delta)
            sol = -(norm(g)^2 / (g' * H * g)) * g
            @test (e == 1) && (isapprox(s, sol, atol = tol_erreur)) # sol = [-0.9230769230769234; -0.30769230769230776]
        end
        @testset "quad 2, saturé" begin
            g = [6; 2]
            H = [7 0; 0 2]
            delta = 0.9
            s, e = Pas_De_Cauchy(g, H, delta)
            sol = -(delta / norm(g)) * g
            @test (e == -1) && (isapprox(s, sol, atol = tol_erreur)) # sol = [-0.9230769230769234; -0.30769230769230776]
        end
        @testset "quad 3, non saturé" begin
            g = [-2; 1]
            H = [-2 0; 0 10]
            delta = 6
            s, e = Pas_De_Cauchy(g, H, delta)
            sol = -(norm(g)^2 / (g' * H * g)) * g
            println("Cauchy 4 = ", sol)
            @test (e == 1) && (isapprox(s, sol, atol = tol_erreur)) # sol = [-0.9230769230769234; -0.30769230769230776]
        end
        @testset "quad 3, saturé" begin
            g = [-2; 1]
            H = [-2 0; 0 10]
            delta = 5
            s, e = Pas_De_Cauchy(g, H, delta)
            sol = -(delta / norm(g)) * g
            println("Cauchy 5= ", sol)
            @test (e == -1) && (isapprox(s, sol, atol = tol_erreur)) # sol = [-0.9230769230769234; -0.30769230769230776]
        end
        @testset "quad 3, g'*H*g <0 saturé" begin
            g = [3; 1]
            H = [-2 0; 0 10]
            delta = 5
            s, e = Pas_De_Cauchy(g, H, delta)
            sol = -(delta / norm(g)) * g
            println("Cauchy 6= ", sol)
            @test (e == -1) && (isapprox(s, sol, atol = tol_erreur)) # sol = [-0.9230769230769234; -0.30769230769230776]
        end
        @testset "quad 3, g'*H*g = 0 saturé" begin
            g = [1, 2]
            H = [2 -1; 4 -2]
            delta = 5
            s, e = Pas_De_Cauchy(g, H, delta)
            sol = -(delta / norm(g)) * g
            println("Cauchy 6= ", sol)
            @test (e == -1) && (isapprox(s, sol, atol = tol_erreur)) # sol = [-0.9230769230769234; -0.30769230769230776]
        end
    end
end