88 lines
3.1 KiB
Julia
88 lines
3.1 KiB
Julia
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@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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@test s ≈ [0.0 ; 0.0] 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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@test s ≈ -delta*grad/norm(grad) 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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@test s ≈ [-0.8740776099190263, -0.8221850958502244] 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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@test s ≈ -Hess\grad 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. # 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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@test s ≈ -delta*grad/norm(grad) 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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@test s ≈ -delta*grad/norm(grad) 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 s ≈ [0.48997991959774634, 5.979959839195494] 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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#@test s ≈ [9.102342582478453; -4.140937032991381] 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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#@test s ≈ [0.0 ; 0.0] 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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@test s ≈ [1.9059020876695578 ; -2.3167946029410595] 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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@test s ≈ [-0.5 ; 0.0] atol = tol_test
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end
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end
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