128 lines
4.3 KiB
Julia
128 lines
4.3 KiB
Julia
@doc doc"""
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Tester l'algorithme du gradient conjugué tronqué
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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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* la quadratique 1
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* la quadratique 2
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* la quadratique 3
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* la quadratique 4
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* la quadratique 5
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* la quadratique 6
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"""
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function tester_gct(afficher::Bool, Gradient_Conjugue_Tronque::Function)
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tol = 1e-7
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max_iter = 100
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# Tolérance utilisé dans les tests
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tol_test = 1e-3
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@testset "Gradient-CT" begin
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# le cas de test 1
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grad = [0; 0]
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Hess = [7 0; 0 2]
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delta = 1
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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sol = [0.0; 0.0]
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if afficher
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afficher_resultats_gct("GCT 1", s, sol)
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end
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@test isapprox(s, sol, atol = tol_test)
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# le cas de test 2 H definie positive
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grad = [6; 2]
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Hess = [7 0; 0 2]
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delta = 0.5 # sol = pas de Cauchy
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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sol = -delta * grad / norm(grad)
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if afficher
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afficher_resultats_gct("GCT 2", s, sol)
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end
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@test isapprox(s, sol, atol = tol_test)
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delta = 1.2 # saturation à la 2ieme itération
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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sol = [-0.8740776099190263, -0.8221850958502244]
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if afficher
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afficher_resultats_gct("GCT 3", s, sol)
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end
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@test isapprox(s, sol, atol = tol_test)
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delta = 3 # sol = min global
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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sol = -Hess \ grad
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if afficher
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afficher_resultats_gct("GCT 4", s, sol)
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end
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@test isapprox(s, sol, atol = tol_test)
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# le cas test 2 bis matrice avec 1 vp < 0 et 1 vp > 0
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grad = [1, 2]
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Hess = [1 0; 0 -1]
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delta = 1.0 # g^T H g < 0 première direction concave
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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sol = -delta * grad / norm(grad)
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if afficher
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afficher_resultats_gct("GCT 5", s, sol)
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end
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@test isapprox(s, sol, atol = tol_test)
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grad = [1, 0]
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delta = 0.5 # g^T H g > 0 sol pas de Cauchy
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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sol = -delta * grad / norm(grad)
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if afficher
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afficher_resultats_gct("GCT 6", s, sol)
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end
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@test isapprox(s, sol, atol = tol_test)
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grad = [2, 1] # g^T H g > 0 sol à l'itération 2, saturation
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delta = 6
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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@test isapprox(s, [0.48997991959774634, 5.979959839195494], atol = tol_test) || isapprox(s, [-4.489979919597747, -3.979959839195493], atol = tol_test)
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# le cas de test 3
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grad = [-2; 1]
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Hess = [-2 0; 0 10]
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delta = 10
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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sol = [9.102342582478453; -4.140937032991381]
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if afficher
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afficher_resultats_gct("GCT 7", s, sol)
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end
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@test isapprox(s, sol, atol = tol_test)
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# le cas de test 4
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grad = [0; 0]
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Hess = [-2 0; 0 10]
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delta = 1
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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sol = [0.0; 0.0]
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if afficher
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afficher_resultats_gct("GCT 8", s, sol)
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end
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@test isapprox(s, sol, atol = tol_test)
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# le cas de test 5
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grad = [2; 3]
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Hess = [4 6; 6 5]
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delta = 3
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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sol = [1.9059020876695578; -2.3167946029410595]
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if afficher
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afficher_resultats_gct("GCT 9", s, sol)
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end
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@test isapprox(s, sol, atol = tol_test)
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# le cas de test 6
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# Le pas de Cauchy conduit à un gradient nul en 1 itération
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grad = [2; 0]
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Hess = [4 0; 0 -15]
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delta = 2
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s = Gradient_Conjugue_Tronque(grad, Hess, [delta; max_iter; tol])
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sol = [-0.5; 0.0]
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if afficher
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afficher_resultats_gct("GCT 10", s, sol)
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end
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@test isapprox(s, sol, atol = tol_test)
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end
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end
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