54 lines
1.7 KiB
Mathematica
54 lines
1.7 KiB
Mathematica
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donnees;
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n_tests = 500;
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% Estimation de la droite de regression par le maximum de vraisemblance :
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[theta_Dorth_1,rho_Dorth_1] = estimation_3(x_donnees_bruitees,y_donnees_bruitees,n_tests);
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% Affichage de la droite de regression estimee par le maximum de vraisemblance :
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cos_theta_Dorth_1 = cos(theta_Dorth_1);
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sin_theta_Dorth_1 = sin(theta_Dorth_1);
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if abs(cos_theta_Dorth_1)<abs(sin_theta_Dorth_1)
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x_Dorth_1 = x_D;
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y_Dorth_1 = (rho_Dorth_1-x_Dorth_1*cos_theta_Dorth_1)/sin_theta_Dorth_1;
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else
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y_Dorth_1 = y_D;
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x_Dorth_1 = (rho_Dorth_1-y_Dorth_1*sin_theta_Dorth_1)/cos_theta_Dorth_1;
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end
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plot(x_Dorth_1,y_Dorth_1,'b','LineWidth',3);
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axis(bornes);
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lg = legend('~Droite', ...
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'~Donnees bruitees', ...
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'~$D_\perp$ (maximum de vraisemblance)', ...
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'Location','Best');
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set(lg,'Interpreter','Latex');
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% Calcul et affichage de l'ecart angulaire :
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EA_Dorth_1 = abs(theta_Dorth_1-theta_D);
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fprintf('D_perp (maximum de vraisemblance) : ecart angulaire = %.2f degres\n',EA_Dorth_1/pi*180);
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function [theta_Dorth_1,rho_Dorth_1] = estimation_3(x_donnees_bruitees,y_donnees_bruitees,n_tests)
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G = mean( [ x_donnees_bruitees.' y_donnees_bruitees.' ] );
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x_centre = x_donnees_bruitees - G(1);
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y_centre = y_donnees_bruitees - G(2);
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x = repmat(x_centre.', 1, n_tests);
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y = repmat(y_centre.', 1, n_tests);
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theta = rand(1, n_tests)*pi;
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dist = ( bsxfun(@times, x, cos(theta)) + bsxfun(@times, y, sin(theta)) ).^2;
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[min_val, min_index] = min( sum( dist ) );
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theta_Dorth_1 = theta(min_index);
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rho_Dorth_1 = G(1)*cos(theta_Dorth_1) + G(2)*sin(theta_Dorth_1);
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if rho_Dorth_1 < 0
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theta_Dorth_1 = theta_Dorth_1 - pi;
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rho_Dorth_1 = G(1)*cos(theta_Dorth_1) + G(2)*sin(theta_Dorth_1);
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end
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end
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