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%   Solution to homework 1 of CS 525 (Linear Programming with Matlab)
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% Please follow the instruction on
% "http://pages.cs.wisc.edu/~swright/525/MATLAB.setup" to set up your 
% computer if you use the computer in CS. If not, you can download the data
% file "hwk1.mat" on the course website 
% "http://www.cs.wisc.edu/%7Eswright/525/homeworks/hwk1.mat". Please make  
% sure the data file stays in the same folder as your ".m" file or add the
% path of the folder containing the data file by writing 
% "addpath('thefolderpath');" at the beginning of your code.

% clean the command window
clc;

% if you do not use the CS computer or do not copy the data file to the
% current folder, then run the next line
% addpath('thefolderpath');

% create a new diary or open an existing diary file
diary hwk1.Liu.Ji;

% clear all variable in the workspace
clear all;

% load the data file "hwk1.mat" 
load hwk1;

% list the names of all variables currently in workspace
who;

% calculate F = AB without display. note that ";" can prevent printing the
% result. one can print the result by removing ";" 
F = A*B;

% calculate and print A-2alphaC
A - 2*alpha*C

% print out F. one can also use disp(F) to print the result. the difference
% is that disp(F) would not print the name of this variable.
F

% "./" a very useful operator. "A ./ B" denotes element-by-element
% division. A and B can be vectors, matrices, or tensors. of course, one 
% should make sure the size of A is equal to that of B.
v = 2*x ./ y

% change the 5th component of x into -8
v(5) = -8;

% reorder the entries in x and save it to w
w = x([6, 2, 4, 1, 3, 5])'

% find the minimal entry of x
min(x)

% calculate D = C'A + 2B
D = C'*A + 2*B;

% lu decomposition. one also can use [L, U, P] = lu(D). in that case, D =
% inv(P)*L*U
[L, U] = lu(D);

% max(A) serves to find the maximal value in each column if A is a matrix. If A is
% a vector (no matter a row or column), max(A) returns the maximal entry.
% max(A(:)) is another way to get the maximal entry in the matrice A, where A(:)
% vectorized the matrix A.
max(max(abs(L*U - D)))

% extract the diagonal of the matrix U into d (d is a vector)
d = diag(D)

% set the format of numeric values displayed in the command window
format long;
sum(d)

% recover the default setting
format short;

% close the diary
diary off;