Examples2
tekijä: elkalesk
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tiistai 12. elokuuta 2014, 14.53
Examples2_Introduction.m — Objective-C source code, 2 KB (2051 bytes)
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% Jyvaskyl Summer School 2014 % Aku Seppanen % University of Eastern Finland, Kuopio % Department of Applied Physics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Example 2.1: pair of linear equations % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% a = 1e-6; f_true = [1 1]'; % True parameter values K = [0 1; a 1]; g_true = K*f_true; var_n = 1e-6; % variance of the observation noise % 100 noise realizations for j = 1:100 n = sqrt(var_n)*randn(2,1); g_noisy = g_true + n; g_noisy_all(:,j) = g_noisy; f_est = inv(K)*g_noisy; f_est_all(:,j) = f_est; end figure(1), clf, plot(f_true(1),f_true(2),'bo'), hold on plot(f_est_all(1,:),f_est_all(2,:),'r+') xlabel('f_1'); ylabel('f_2'); legend('f_{true}','estimates') title('Estimates for f corresponding to 100 noise realizations') axis equal figure(2), clf, plot(g_true(1),g_true(2),'bo'), hold on plot(g_noisy_all(1,:),g_noisy_all(2,:),'r+') xlabel('g_1'); ylabel('g_2'); legend('g_{true}','g^{\delta}') title('Noisy data, 100 realizations') %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Example 2.2: modeling error % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% a = 1e-6; f_true = [1 1]'; % True parameter values K_accurate = [0 .999; a 1]; K_approximate = [0 1; a 1]; g_true = K_accurate*f_true; var_n = 1e-10; % variance of the observation noise % Note: the noise level is extremely low % 100 noise realizations for j = 1:100 n = sqrt(var_n)*randn(2,1); g_noisy = g_true + n; g_noisy_all(:,j) = g_noisy; f_est = inv(K_approximate)*g_noisy; f_est_all(:,j) = f_est; end figure(1), clf, plot(f_true(1),f_true(2),'bo'), hold on plot(f_est_all(1,:),f_est_all(2,:),'r+') xlabel('f_1'); ylabel('f_2'); legend('f_{true}','estimates') title('Estimates for f corresponding to 100 noise realizations') axis equal figure(2), clf, plot(g_true(1),g_true(2),'bo'), hold on plot(g_noisy_all(1,:),g_noisy_all(2,:),'r+') xlabel('g_1'); ylabel('g_2'); legend('g_{true}','g^{\delta}') title('Noisy data, 100 realizations')