%=========================================================================
%            Uplny problem pro urceni vlastnich cisel
%=========================================================================

%-------------------------------------------------------------------------
% function [L,U] = lu_rozklad(A);
% LU-rozklad pro ctvercovou matici A
%-------------------------------------------------------------------------

A=[7 1 3 1 2; 2 8 6 1 5; 2 4 8 1 2; 3 4 1 7 1; 2 3 5 1 3];
[L,U] = lu_rozklad(A)
	

%-------------------------------------------------------------------------
% function [lambda, chyba] = lr_transformace(A, epsilon, max_iter);
%
% LR-algoritmus pro vypocet vlastnich cisel matice A
%-------------------------------------------------------------------------

A=[7 1 3 1 2; 2 8 6 1 5; 2 4 8 1 2; 3 4 1 7 1; 2 3 5 1 3];
lr_transformace(A, 0.001, 100);

%-------------------------------------------------------------------------
% function [lambda, chyba] = qr_transformace(A, epsilon, max_iter);
%
% QR-algoritmus pro vypocet vlastnich cisel matice A
%-------------------------------------------------------------------------

A=[7 1 3 1 2; 2 8 6 1 5; 2 4 8 1 2; 3 4 1 7 1; 2 3 5 1 3];
qr_transformace(A, 0.001, 100);

%-------------------------------------------------------------------------
% function [lambda, chyba] = jacobiova_diagonalizace_I(A, epsilon, max_iter);
%
%  Metoda Jacobiovy diagonalizace pro vypocet vlastnich cisel matice A
%            (specialni pripad metody qr-transformace)
%
%                   postupna volba matic rotace
%-------------------------------------------------------------------------

A=[64 51 47 37 39; 51 130 95 56 74; 47 95 89 39 63; 37 56 39 76 33; 39 74 63 33 48];
jacobiova_diagonalizace_I(A, 0.001, 100);


%-------------------------------------------------------------------------
% function [lambda, chyba] = jacobiova_diagonalizace_II(A, epsilon, max_iter);
%
%  Metoda Jacobiovy diagonalizace pro vypocet vlastnich cisel matice A
%            (specialni pripad metody qr-transformace)
%
%  volba maximalniho prvku v absolutni hodnote pro ziskani matice rotace
%-------------------------------------------------------------------------

A=[64 51 47 37 39; 51 130 95 56 74; 47 95 89 39 63; 37 56 39 76 33; 39 74 63 33 48];
jacobiova_diagonalizace_II(A, 0.001, 100);





%=========================================================================
%            Castecny problem pro urceni vlastnich cisel
%=========================================================================

%-------------------------------------------------------------------------
% function [lambda, chyba] = mocninna_metoda(A, y_0, epsilon, max_iter);
%
% Mocninna metoda pro vypocet
% dominantniho vlastniho cisla matice A
%
% y_0      ...  pocatecni aproximace
% epsilon  ...  tolerance pro zastaveni vypoctu
% max_iter ...  maximalni pocet iteraci
%-------------------------------------------------------------------------

A=[2 1 1 0; 1 3 1 1; 1 1 4 1; 0 1 1 5];
y0=[1 1 1 1]';

mocninna_metoda(A, y0, 0.001, 50);
mocninna_metoda_norm(A, y0, 0.001, 50);


%-------------------------------------------------------------------------
function [lambda, chyba] = metoda_rayleighova_podilu(A, y_0, epsilon, max_iter);
%
% Metoda Rayleighova podilu pro vypocet
% dominantniho vlastniho cisla matice A
%-------------------------------------------------------------------------

metoda_rayleighova_podilu(A, y0, 0.001, 50);
metoda_rayleighova_podilu_norm(A, y0, 0.001, 50);



A=[2 0 0; 0 1 0; 0 -2 3];  
y0=[1 1 1]'; 

mocninna_metoda(A, y0, 0.001, 50);
mocninna_metoda_norm(A, y0, 0.001, 50);
metoda_rayleighova_podilu(A, y0, 0.001, 50);
metoda_rayleighova_podilu_norm(A, y0, 0.001, 50);

[Vlastni_vektory,Spektralni_matice] = eig(A)


A=[2 0 0; 0 1 0; 0 -2 3];  
y0=[1 2 1]';  

mocninna_metoda(A, y0, 0.001, 50);
mocninna_metoda_norm(A, y0, 0.001, 50);
metoda_rayleighova_podilu(A, y0, 0.001, 50);
metoda_rayleighova_podilu_norm(A, y0, 0.001, 50);