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ICS/hw3/assignment3.m

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%% Assignment 2
% Name: Claudio Maggioni
%
% Date: 19/3/2019
%
% This is a template file for the first assignment to get started with running
% and publishing code in Matlab. Each problem has its own section (delineated
% by |%%|) and can be run in isolation by clicking into the particular section
% and pressing |Ctrl| + |Enter| (evaluate current section).
%
% To generate a pdf for submission in your current directory, use the following
% three lines of code at the command window:
%
% >> options.format = 'pdf'; options.outputDir = pwd; publish('assignment2.m', options)
%
%% Problem 3
format rational
A = [4 3 2 1; 8 8 5 2; 16 12 10 5; 32 24 20 11];
[L,U,P] = pivotedOuterProductLU(A)
function [L,U,P] = pivotedOuterProductLU(A)
dimensions = size(A);
n = dimensions(1);
p = 1:n;
L = zeros(n);
U = zeros(n);
for i = 1:n
values = A(:,i);
values(values == 0) = -Inf;
[~, p_k] = max(values);
k = find(p == p_k);
p(k) = p(i);
p(i) = p_k;
L(:,i) = A(:,i) / A(p(i),i);
U(i,:) = A(p(i),:);
A = A - L(:,i) * U(i,:);
end
I = eye(n);
P = zeros(n);
for i = 1:n
P(:,i) = I(:,p(i));
end
P = transpose(P);
L
L = P * L;
end