%% Basic Matlab Commands
%
% *Wavelets Workshop*
%
% June 2 - 5, 2009
%
% University of South Florida
%
% *Catherine Beneteau*, *Caroline Haddad*, *David Ruch*, *Patrick Van
% Fleet*

% To see the commands and the results in the same window, under File on the
% main menu, select Save and Publish to HTML.

% You can run this m-file - go to the command window and type 
% echodemo BasicCommands.

% To evaluate individual cells, one at a time, place cursor in cell you 
% wish to evaluate, and either type Ctrl-Enter or under Cell on the top 
% menu, select Evaluate Current Cell.

%% Creating Vectors

v=[1 2 3 4]

v=[1 2 3 4]'
v=[1;2;3;4]

A=[1 2; 3 4; 5 6]

%% Individual Elements

v=[1 2 3 4]

v(1)
v(4)

[m]=size(v)

v(1,m)

A=[1 2; 3 4; 5 6]

A(1,1)
A(3,1)
A(2:3,2)  %extracts 2nd and 3elements of 2nd column of A
A(2,:)  % extracts 2nd row of A

%% Format

x=sqrt(2)

format short
x

format long
x

format hex
x

format rat

%% Dimension and size and matrix products

A=[1 2 3;4 5 6]
size(A)
[m,n]=size(A) % m = #rows, n = # columns
numel(A)
B=[1 2; 3 4;-1 -2]
A*B    % product of two matrices
B*A

C=[-1 2;0 3;5 8]
C.*B  % multiplies corresponding components of A and B 
%% Length and norm and dot product

v=[1 2 3 4]
length(v)
max(size(v))
norm(v)
norm(v,2)
norm(v,1)
norm(v,inf)

x=rand(1,10)
y=rand(1,10)
x'*y     % dot product between 2randomly generated vectors x and y

%% Reshape

A=[ 1 2; 3 4 ; 5 6]
n=numel(A) % number of elements
FlattenByRowsA=reshape(A',1,n)
FlattenByColsA=reshape(A,1,n)


%% Reverse

v=[1 2 3 4]
reverse=x(end:-1:1)

%% Sort 

v=[1 5 7 2 -9]
sort(v)
sort(v,'ascend')
sort(v,'descend')
A=[1 -2 7; 5 2 4]
sort(A)
sort(A,1)
sort(A,2)
%% Sum and cumsum, max and min of a matrix

v
sum(v)
A
sum(A)

v
cumsum(v)
A
cumsum(A)

max(max(A))
min(min(A))


%% Listing Matlabs pre-prorammed functions using Matlab help
% Under MATLAB--> FUNCTIONS by alphabetical list will
% list the standard math fuctions, like exp(x), log(x),sin(x), which also
% work or vectors!
% 
% Doing the same in the Discrete Wavelets Toolbox will give a list of all
% functions there and clicking on one will explain what it does, and
% generally give an example.
%% Common functions:  abs, sqrt, sin, cos, exp, log

abs(-3)
sqrt(4)
sin(pi/3)
cos(pi/3)
exp(pi*i)
log(2.718)
log2(256)
log10(1000)

%% sprint and disp

disp('This is how to print out a string')

sprintf('%s','hello')  % %s is for string
%% For
s=0
for i =1:.5:5   % this executes the following command for i = 1,1.5,2,2.5,3,3.5,4,4.5,5  (1 to 5 using an increment of .5)
    s=s+i^2;
end
sprintf('s is %d',s)  %d is for integer

%% Plot and fplot


for i = 1:10
    x(i)=1+(i-1)*.1;
    y(i)=1/x(i)^2;
end
x
y

figure;plot(x,y,'g-');title('y=1/x^2')

clear x y
x=linspace(1,2,10)
y=1./x.^2
figure;plot(x,y,'ro');title('y=1/x^2')

clear x, y;
figure; fplot(@(x)[abs(1/2+(1/2)*exp(i*x))],[-pi, pi]);title('|H(w)| with h=(1/2,1/2)');


%%  Matlab allows you to easily create special commomly used matrices

% eye(n) is the nxn identity matrix
% ones(m,n) is the mxn ones matrix
% zero(m,n) is the mxn zero matrix
% diag(v) creates a square matrix with the entries of vector v on the diagonal
% diag(A) creates a vector with the entries from the diagonal of matrix A
% size(A) gives the size of the matrix
% blkdiag(A, B, ...) creates a block diagonal matrix

% norm(v) is the 2 norm, norm(v,1) is the 1-norm, norm(v,inf) is the infinity norm
% norm(A) will do the induced matrix norms


%% Special Matrices

eye(5)
zeros(3,5)
ones(4,2)
v=6*ones(1,6)
A=diag(v,1)+diag([v/2 1])+diag(v/4,-1)
diag(A)

%%  Useful Image commands

% Note: Do not execute these without entering an actual image file name
% Type is NOT required to be jpeg

A=imread('Photoname.jpg')  % Reads in a jpeg 
figure  % This will open up a new figure
image('image matrix name goes here')   % displays the image
title('Title goes here')
axis('for example, square will make the image square')
Gray=.2989*A(:,:,1)+.5870*A(:,:,2)+.1140*A(:,:,3);   % This converts a color image to grayscale

% To view it:
figure,colormap(gray(256)),image(Gray), axis('square'),title('Title')