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% Solutions to the Session 5: Introduction to Matlab  %
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%% First things
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% Initialize and some comments in advance
% To start, we clear the memory, so that the Matlab workspace and the command window are empty

clear all
clc

% Give MATLAB the path, where you want to work. 
% Otherwise, MATLAB doesn't know where to look for, and the only thing it knows are the 'built-in' functions ...
path(path,'C:\Users\pw05v549\Documents\doing15\session5');

% a semicolon after the command means that in your command window the output will be supressed.
% a double %% means that you make a section in your code, double %% with some text behind gives you a title of the section to evaluate
% to evaluate a section you can press CTRL+ENTER, to evaluate a highlighted part, press F9, otherwise you run the entire code.

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%% 1 Matrices
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%a)

% Either you can use A = [1 3 2;5 0 2]; 
% or you specify each entry: A(1,1)= 1; ...
% or what I use below:

A_1 = [1 3 2 ; 5 0 2];

A_2= [1 3 2
      5 0 2];

%b) 

% Matrix of zeros

V=zeros(4,2);

% Matrix of ones

W=ones(3,1);

% Identity matrix 

I= eye(3,3);

% Create a vector Z=[1,2,...100]'

Z=[1:1:100]';

% Saving the output of a MATLAB run:
%
% We want to save the output of our exercise in the directory C:\Users\pw05v549\Documents\doing15\session5, 
% in a fle called Session5.m
%
% We start by creating the following object:

DFILE=['C:\Users\pw05v549\Documents\doing15\session5']; % ==> Output file

%and we save it to the  directory:

save(DFILE);
clear;

% You retrieve the results via the command load:

load 'C:\Users\pw05v549\Documents\doing15\session5';

%c)

% An easy way to do this is:

% Column vector with 10 normally distributed random variables
% RAND([M,N]) returns an M-by-N matrix.

R0 = randn(10,1);

% Generate values from the uniform distribution on the interval [a, b].
%          r = a + (b-a).*rand(100,1);

R10 = 10+randn(1,10);

% Uniform distribution

U = rand(10,1);

% A nicer way is to use (works under Matlab R2014a): 

% R_0 = random('Normal',0,1,10,1); 
% R_10= 10+random('Normal',0,1,1,10);
% U_1 = random('Uniform',0,1,10,1);

% You can find the probability distributions on
% http://www.mathworks.ch/ch/help/stats/random.html

% d)
A = A_1;
A(1,2) = 8;

% e) 

B = A(2,:);

% f)

C = [4 1 2; 1 3 3];
D = C(C<=3);

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%% 2 Basic Manipulations
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clear

%a)

E=[4 1;1 3]
F=[1 1;2 3]

[n,m]=size(E);

E+F  
E-F

%b)
% Matrix multiplication (not element by element):
G=E*F 

% Multiplication element by element:
H=E.*F
% Division element by element:
I=E./F

%c)
K=inv(E)*F
K=E^-1*F    
K=E\F    
% Determinant of a matrix:
det(K)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 3 Basic plotting and statistics
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% Matla stores numbers into ROWS N and COLUMS M 
% x(n rows, m columns) n,m>0

clear

%a)
% x = random('Uniform',0,100,1,100);
% r = a + (b-a).*rand(100,1); 
% with a being the lower bound and b the upper  bound of the distribution
x = 0+ (100-0).*rand(1,100);
%b)
plot(x);

%c)
x1 = x(1,1:50);
x2 = x(1,51:100);

plot([x1 x2])

figure(1);
subplot(211);
plot(x1);
subplot(212);
plot(x2);

%other possibility
figure(2);
subplot(121);
plot(x1);
subplot(122);
plot(x2);

%editing
figure(3);
plot(x,'r:');
title('100 RANDOM DRAWS');
xlabel('number of the draw');
ylabel('drawn number');
legend('random draws');
axis([0 100 0 100]);

%3d
mean_x =mean(x);
std_x  =std(x);
mean_x1=mean(x1);
std_x1 =std(x1);
mean_x2=mean(x2);
std_x2 =std(x2);

%repeating b)
mean_x_vector=zeros(100,1);       
mean_x_vector(1:100,1)=mean_x;
figure(4);
hold on   ;                        
plot(x,'b');
plot(mean_x_vector,'r--');
title('100 RANDOM DRAWS');
xlabel('number of the draw');
ylabel('drawn number');
legend('random draws','Location','SouthOutside')   ;  
axis([0 100 0 100]);
hold off;

% You can find everything for editing plots on
% http://www.mathworks.ch/ch/help/matlab/creating_plots/using-high-level-plotting-functions.html

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 4 Working with the Data
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%a)
load session5_testdata1.txt -ascii;   
%check
x=session5_testdata1;

%b)
y=xlsread ('session5_testdata2.xls') ; 

%c)
who
clear session5_testdata1              
who

%d)
figure (3);
hist(x);
figure (4);
hist(y);
mean_x=mean(x);
mean_y=mean(y);
std_x=std(x);
std_y=std(y) ;               

%e)
corr_xy=corrcoef(x,y) ;  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 6 Preparation for session 9
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%a)
g=[0:0.1:10]'
size(g) %if you are unsure about the size of g

for j=1:101;          
    g(j)=g(j)+0.05;
end
g

%b)

A=2

while A<10;
    A=A+1
end