Dekompozycja LU

zadanie3.m

clear;
function [L,U] = LU_dec(A)
	n = length(A(1,:));
	L = eye(n);
	for i=1:n
		for j=i:n %wiersze U
			U(i,j) = A(i,j);
			for k=1:(i-1)
				U(i,j) = U(i,j) - L(i,k)*U(k,j);
			endfor
		endfor
		for j=(i+1):n %kolumny L
			L(j,i) = A(j,i);
			for k=1:(i-1)
				L(j,i) = L(j,i) - L(j,k)*U(k,i);
			endfor
			L(j,i) = L(j,i)/U(i,i);
		endfor
	endfor
endfunction

function X = solve(A,B)
	[L,U] = LU_dec(A);
	Z = inv(L)*B;
	X = inv(U)*Z;
endfunction

A1 = [1 3 2 -1 ; 4 2 5 -1 ; 3 -3 2 -4; -1 2 -3 -5];
B1 = [9;27;19;14];

A2 = [3 1 -1 3 ; 2 1 -2 0 ; 0 3 2 -1 ; 1 1 1 5];
B2 = [4;-1;4;-2];

 
A3 = [2 -2 2 1; 2 -4 1 1; -1 3 -4 1; 2 4 3 1];
B3 = [7;10;-14;1];

disp("1:");
solve(A1,B1)
inv(A1)*B1

disp("2:");
solve(A2,B2)
inv(A2)*B2

disp("3:");
solve(A3,B3)
inv(A3)*B3