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%
% Tutorial.M (Introduction to Matlab)
%
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%
% BEFORE CONTINUING IT IS GOOD TO OPEN ANOTHER .M FILE SO THAT YOU CAN SAVE YOUR
% WORK. LET US CALL THIS FILE 'MY_PROBLEM1.M'
%

%***********************************************************
%    1. Matlab basics
%**********************************************************
% Matlab is an interpreting programming language that supports all
% basic operations and functions like other programming languages
% (e.g. if then else structure, for loop, while loop, case-switch structure, 
% break, try, catch, return, ...)

a=10
if (a==4)
   b=a^2
elseif (a~=10)
   b=a
else
   b=-a
end

% For loop
for i=1:2:10
	i   
end

% While loop
j=13;
while j>0
   j=j-1
end
%
% EXERCISE 1: 
% Modify the previous 'WHILE' loop to list all numbers from j to 20;
% Write down the solution
%

% Examine switch command by typing
help switch

% Matlab supports help system through help window, or through help statement from the
% command prompt (e.g. help case)
% There is also a lookfor statement, when we are not sure what is the exact name of 
% the statement or the function. Lookfor searches for specified word through description 
% of all available Matlab functions
% e.g. "lookfor write" gives all functions that contains the word write in their
% description

%
% familiarize yourself with the Matlab help window. Browse through help topics.
% EXERCISE 2:
% Explain in one-two sentences the functions from matlap/general, matlab/ops, matlab/elfun
% matlab/lang and matlab/elmat folders in help 
%

% In addition, Matlab has integrated powerful functons for elementary matrix 
% manipulation and numerical linear algebra, elementary and specialized math 
% functions, 2D and 3D graphic, interpolation, polynomials, Fourier transforms,
% sparse matrices, .....
% Unlike other languages it DOES NOT make executable code. Insted, it interprets
% comands of functions written in the script or inside the another funstion.


% Function has a specific syntax and should be called.
% It can have more than one input and output arguments.
% Normally, arguments are transfered by value. It is possible to submit arguments 
% by reference (as common attributes for caller and the function), but you'll 
% never need this...

% 'operations' is an example of a matlab function you downloaded
a = 5
b = 4
[sum_ab, product_ab] = operations(a, b)
% Try to put the semicolumn at the end:
[sum_ab, product_ab] = operations(a, b);
% What is the difference?

%
% EXERCISE 3: 
% open the file 'operations.m' and modify it so that its has the third 
% output square_a. Remember, you should save the modified file before you call it
% from the Matlab prompt
%
% write down the solution in your report (you can print out the modified function)
%


%*********************************************************
% 2. Matrix operations
%*********************************************************

A = [1  2  3 
     4  5  6
     7  8  9
     10 11 12]
   
B = [1  3  5
     7  11  13
     17 19  23
     29 31 37]
   
% Another way to represent matrix   
C = [1 2 3 4; 5 6 7 8; 9 10 11 12]

% Some operations
D = A + B
E = A * C
F = C * B
F1 = diag(inv(sqrt(F)))
%
% EXERCISE 4: 
% Explain what does variable F1 represent?
%

G = B./ A	% What did we do?

% Two ways to do the same thing
G_transpose = G'
G_transpose = transpose(G)


% Matlab is very powerful in matrix computation.
% DO NOT USE for loop for computing with matrices. THERE IS ALWAYS 
% FASTER WAY TO WORK WITH VECTORS OR MATRICES

%
% EXERCISE 5: 
% examine the 'size', 'sum', 'mean', and 'std' commands
% Explain them with one sentence 
%

% Example of using 'size'
[num_rows, num_cols] = size(A)
num_rows = size(A,1)
num_cols = size(A,2)

% Example of using 'sum'
sum(A)      % sumation performed by first index (sums of columns!)
sum (A,1)   % The same
sum(A,2)    %sumation performed by the second index (sum of rows)
sum(sum(A)) %sum all elements in the matrix

% It is important to understand the manipulation with vectors and matrices
A1 = A(:,3)		% separate one COLUMN (Attribute)
A2 = A(2,:)		% separate one ROW (Data Example)
A3 = A(:,[1 3])	% separate columns 1 and 3
A4 = A([1 3],1:3)	% WHAT DID WE DO??

% Special matrix functions
diagonal_matrix=diag([1 2 3 4])
all_zeros=zeros(3,4)
all_ones=ones(4,2)
identity_matrix=eye(4)

% Very useful command
whos

% BASIC STATISTIC
mean_A_column = mean(A)        % Mean for columns
mean_A_row    = mean(A,2)      % Mean for rows
std_A_column  = std(A)         % Standard devaition of columns 
std_A_row     = std(A,[],2)    % Standard deviation of rows ([] MUST be here)

% EXERCISE 6: 
% explain the result of the following three lines:
A1=mean(A(:,2))
A2=mean(A(1,:))
A3=mean(A')'

% Generate a matrix of random numbers between 0 and 1
R = rand(4,3)

%
% EXERCISE 7: Write the code that solves the following:
%
% Generate a matrix R1 of random numbers of dimension 20x5.
% Calculate the mean of column 3. Calculate the mean of row 6.
% Calculate the mean of the first 15 elements of column 4.
%


%*********************************************************
% 3. Input/output
%*********************************************************

% How top read number form keybord
x=input('Input for computation');
y=x^2; %This will not be printed
z=x^3  %this WILL be printed

% How top read strings form keybord
new_string=input('Input a string','s');
latest_string=['You entered ', new_string]


% How to save results. LOOK WHAT HAPPENS IN YOUR FOLDER

% To save specified variables into specified file in ascii form
save file_E.txt E -ASCII 
% ADVICE: BEST IF USED TO SAVE ONLY ONE VARIABLE
% Check what happens when saving more then one

save file_EAB.txt E A B -ASCII 

%'To save specified variables into specified file in binary (matlab-specific) form'
% Default extension is .mat
save file_ABC A B C

% To save ALL variables, write only a file name. All variables in scope 
% will be saved
save file_all

% How to clear variable A
clear A
whos 
% there is no variable A now

clear all  % delete all variables in scope. 
whos
% everything is deleted

% How to load files

% From .mat file
load  file_all
whos

% From ASCII file.
clear	all	% clear all first
load file_E.txt
% CHECK WHAT HAPPENED by typing 'whos'!!

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% 4. Graphic
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% Example:
t=0:0.1:5;
x=sin(pi*t)+0.1*t;
y=cos(pi*t)-0.2*t;

% Examine the resulting figures
f(1)=figure	% WHAT DID WE DO?? EXAMINE THE COMMAND 'figure'
plot(x)
f(2) = figure
plot(t,x)
f(3)=figure
plot(t(1:20),x(1:20),'.')
f(4) = figure
plot(x,y);
% Close all figures
close(f)

% How to put more plots on one figure:
plot(x,y)
hold on
plot(x,y, 'r*');     % plots blue stars instead of line
%pause

figure;
z=2*t;
plot3(x,y,z,'m-d');  % shows magenta diamonds in addition to line


% Plotting x and y axes as well as graph title and legend
A=[1 2 3 4 5 7 9];
B=[12 13 14 14 11 10 8];

plot(A,B); %both arguments are vectors of the same length
pause
C=B-4;
hold on; %retained old graph, new graph is added
plot(A,C,'*-r'); %this line is read and has stars and lines
pause
xlabel('Month')
ylabel('Power consumption')
title('This is demo graph') %title
legend('New York','Philadelphia') %label of the graph

% Method for plotting matrices
figure; %opens new plot
C=eye(10,10);
imagesc(C);
title('The way to plot matrices')

% Other nice graphic functions imagesc, surf, meshgrid, ..... 
% TRY HELP for these commands
[X Y]=meshgrid(-pi:pi/10:pi,-pi:pi/10:pi); %grid to compute function in even intervals
Z=sin(2*X).*cos(3*Y);
surf(X,Y,Z); %Plots 3D function
pause
imagesc(Z);colorbar

% EXERCISE 8:
% type 'demo' and go through matrics and visualization parts
% Explain what you learned in demo in few sentences 


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%   5. Some useful functions
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a = rand(10,5)

a1 = sort(a)      % SORT each colun separately
a2 = sort(a,2)    % SORT each row separately

% VERY USEFUL FUNCTION: 'find'
% FIND all rows (examples) where the values in
% second columen are greater than 5
q = find(a(:,2) > 0.5)

% Use histogram:
b = rand(50,1);
hist(b,20);   % Histogram in 20 bins
% histogram is expected to be fairly flat
b = rand(5000,1); 	% generate more data
figure
hist(b,20);   % Histogram in 20 bins
% CAN YOU CONCLUDE WHAT IS THE DIFFERENCE IN THE SHAPE OF THE TWO HISTOGRAMS??

% EXERCISE 9: WHAT IS THE NAME OF COMMAND THAT
% a) lists all current variables in the workspace
% b) deletes all variables in the workspace
% c) randomly generates normally distributed numbers

return;

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