PCML's first assignment

exercise1.m

% Exercice 1.1
ident33 = eye(3,3)

diag_inc = diag([1 2 3])

zeros33 = zeros(3,3)

M = rand(4,3)

T = reshape(M,6,2) % it takes them column by column

a = [1; 2; 3]

% Exercice 1.2
b = M*a % 4x1 it's correct because we did a 4x3 * 3x1 => 4x1

e = transpose(b) * b % 1x1, value is a scalar

% Exercice 1.3
A = rand(3,3)

c = A * a

d = inv(A)*c %size is 3x1

% d == a because we did d = A^(-1)*A*a wich is equals to a!

% Exercice 1.4
top_left_inv = inv(M(1:3,1:3))

% Exercice 1.5
A = [1, 2; 3, 4]

k = 3.1

B = A + k - k

C = A - B % YOu can add a threshold for the approximation

% Exercice 1.6

c = 5;
A = rand(3,3);
B = rand(3,3);
C = A * B;

equ1 = mat_equ(inv(inv(A)), A)

equ2 = mat_equ(inv(c * A), inv(c) * inv(A))

equ3 = mat_equ(inv(transpose(A)), transpose(inv(A)))

equ4a = mat_equ(B, inv(A)*A*B)
equ4b = mat_equ(inv(A)*A*B, inv(A)*C)

equ5a = mat_equ(C, A*B)
equ5b = mat_equ(A*B, (C*inv(B))*(inv(A)*C))
equ5c = mat_equ((C*inv(B))*(inv(A)*C), C*inv(B)*inv(A)*C)

equ6 = mat_equ(C*inv(B)*inv(A), eye(3))

equ7a = mat_equ(inv(C), inv(B)*inv(A))
equ7b = mat_equ(inv(B)*inv(A), inv(A*B))

% Exercice 1.7
x = [-10:10];
%%uncomment to display because plot are annoying!
%plot(x, 100*cos(x).^2 + x.^3,'r')

%%uncomment to display because plot are annoying!
%plot(x, 100*cos(x).^2 + x.^3,'.') % we only see discrete dots

% Exercice 1.8
data = rand(100,1);

%%uncomment to display because plot are annoying!
%hist(data,6) 

% it looks mess with the default number of bins, it should be
% a uniform distribution
% the less bin the more equals they are.


% Exercice 1.9

data = 10 + 2*randn(100,1);

%%uncomment to display because plot are annoying!
%hist(data, 8)


% Intro EDA

clearvars;
load('height_weight_gender.mat')
whos
amnt_male = sum(gender)
amnt_female = length(gender) - amnt_male

height = height * 0.025;
weight = weight * 0.454;

% Exercice 1.10
height_male = mean(height(gender));
height_female = mean(height(~gender));

weight_male = mean(weight(gender));
weight_female = mean(weight(~gender));

% They do make sense to me! Males are bigger and taller than women!

avg_w_fem = mean(weight(~gender & height < 1.7 & height > 1.6));


% Exercice 1.11
x_dim = 3;
y_dim = 2;
figure
subplot(x_dim,y_dim,1)
hist(weight)
axis([0 150 0 2200])

subplot(x_dim,y_dim,2)
hist(males_w)
axis([0 150 0 2200])

subplot(x_dim,y_dim,3)
hist(females_w)
axis([0 150 0 2200])

subplot(x_dim,y_dim,4)
hist(height)
axis([1.2 2.1 0 2500])

subplot(x_dim,y_dim,5)
hist(males_h)
axis([1.2 2.1 0 2500])

subplot(x_dim,y_dim,6)
hist(females_h)
axis([1.2 2.1 0 2500])

% Yes, they do look as expected!


% Exercice 1.12
figure
plot(height, weight, '.')

% 1. Quite well, We can see that most point form a line
% which shows correlation between the two data even
% if that doesn't mean relation.

% 2. Not very well, there's a lot of overlap between the two genders.

% 3. Task 2 is a lot harder in my opinion.

function [ res ] = mat_are_equ( lhs, rhs )
  %COMP_FLOAT_MAT Summary of this function goes here
  %   Detailed explanation goes here
  res = all(abs(lhs(:) - rhs(:)) < .001);
end

You'll need this function in a file named mat_equ.m to run my code