%% Assignment 1 
% Name: Claudio Maggioni
%
% Date: 21/2/2019
%
% 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('assignment1.m', options)
% 
%% Problem 1
% a)
x = 5
% b)
y = 4.2 * 10 ^ (-2)
% c)
r = sqrt(pi)
% d)
rate = 0.01
t = 6
T = 12
money = 1000
interest = money * (exp(rate * t / T) - 1)
% e)
a = 1 + i
b = i
i = 2
e = exp(i * pi)
d = exp(b * pi)
% \texttt{i} is interpreted as the imaginary unit when assigning to a and b
% until it is defined to 2. In the subsequent expressions \textit{i} is
% interpreted as 2.
c = exp(1i * pi)
% Here \textit{1i} is interpreted as the imaginary unit, making $c = 1$

%% Problem 2 
A = [1 -2 0 ; -2 1 -2; 0 -2 1]
Z = zeros(9,9)
B = ones(9,9) * 3
C = (eye(9) - 1) * -1
D = diag([1:5,4:-1:1])
E = repmat(transpose(1:9), 1, 5)

%% Problem 3 
A = fliplr(A)
B(2, :) = repmat(1, 1, 9) 
C(1, :) = []
F = E(1:2, 1:2)
E(:, 1) = flipud(E(:, 1))

%% Problem 4
geteps
getxmin
getxmax

function myeps = geteps
    y = 1;
    x = 2 * y;
    while 1 + y ~= 1
        x = y;
        y = y / 2;
    end
    myeps = x;
end

function xmin = getxmin
    y = 1;
    x = 2 * y;
    while y ~= 0
        x = y;
        y = y / 2;
    end
    xmin = x;
end

function xmax = getxmax
    y = 1;
    x = y;
    while y ~= +inf
        x = y;
        y = y * 2;
    end
    xmax = typecast(bitor(typecast(x, 'uint64'), 0x000FFFFFFFFFFFFF), ...
        'double');
end
% geteps does not differ from eps, as getxmax does not differ from realmax.
% However, getxmin returns the nearest positive floating point value to 0
% including denormalized numbers, while realmin returns the smallest
% (ignoring sign) non denormalized floating point number.