%% This is the MATLAB code that will be used for quick introduction to MATLAB
% Code is divided into section so that each can be run separately.
% Recommended way of going through the examples is by selecting and
% clicking F9 (evaluate selection option).

%%  MATLAB Variables
% If you wish to print the line of code results, just ommit the semi colon
% at the end of the code line.

45

pi

eps
P
inf

NaN

i

%% Elementary math functions

% Choose a value for x arbitrairly 
x = 23;

% Assign value to properly named variable
% 
squareRoot = sqrt(x);
exponential = exp(x);
naturalLogarithm = log(x);
logarithTen = log10(x);
sinus = sin(x); %(in radians)

% Choose a value for y arbitrairly 
y = 1.23;

lowerValueRound = fix(y);
higherValueRound = ceil(y);
integerRound = round(y);

%% Creating MATLAB matrices
% We can create a matrix in various ways, take for example matrix:
% 2 5 3
% 6 4 1

%a direct way of creating matrix - by imputing values
A = [2,5,3;6,4,1]

%crating matrix using range-values, the value between colons is a step
%size.
B = [1:1.5:6; 2 3 4 5]

%a purely iterative way of creating a matrix, imputing each cell of a
%2-D matrix in a nested for loop
for i = 1:4
    for j = 1:3
        C(i,j) = i*j;
    end
end
C

%creating a matrix/vector by concatenating
D = [];
D = [D, 5];
D = [D, 6, 7]

%creating a matrix using MATLAB function
E = zeros(4,5)


%creating a multi-dimesional matrices is not that easy. How would you do
%it?

%% Matrix operations

%generating two sample matrices
A = [4,1,1;2,4,2;3,3,4];
B = [9,3,3;4,9,4;4,4,9];

%Addiction:
C = A + B;

%Subtraction:
D = A - B;

%Multiplication
E1 = A * B %(Matrix multiplicaiton)
E2 = A .* B %(Element wise multiplication, A and B are same size)

%Max, Min, Sum
max = max(A);
min = min(A);
sum = sum(sum(A))

%Division:
%Left Division and Right Division
F = A ./ B %(Element wise division)

F1 = A/B 
F2 = A*inv(B)    %(A * inverse of B)

%are F1 and F2 different?
difference = sum(sum(F1-F2));
if difference == 0
    disp('A/B is the same as A*inv(B)');
else
    disp('A/B is the same as A*inv(B)');
end

F3 = A .\ B %(Element wise division)

F4 = A\B 
F5= inv(A)*B      %(inverse of A * B)

%are F4 and F5 different?
difference = sum(sum(F4-F5));
if difference == 0
    disp('A\B is the same as inv(A)*B');
else
    disp('A\B is the same as inv(A)*B');
end

%Transpose:
A
A'
%% Workspace maintenance

%Sometimes workspace get too crowded! It is smart to remove unnecessary variables

clearvars -except A B

%Or you could just clear entire worspace
clear

%If command window is crowded with text, simply clean it with
clc

%% Generating basic matrices

m = 3;
n = 2;

%Matrix with ZEROS:
A = zeros(m, n)

%Matrix with ONES:
B = ones(m, n)

%IDENTITY Matrix:
I = eye(m, n)

%RANDOM Matrix: 
I = rand(m, n)

%MAGIC SQUARE Matrix: 
M = magic(n)

%matrix with each entry ~ U(0,1)
Rand(m,n)

%standard normal distribution
Randn(m,n)


%% Array indexing, obtaining information

% Get the dimensions of a matrix
size(M)

% Get a length of a vector
V = [1:10:100]
length(V)

% Get a second cell
M(2)

% Get a second row
M(2,:)

%% Save/load data

%save the workspace
save sample_workspace.mat;

%save a single variable
save('single_variable.mat','M');
clear M

%load single variable
load('single_variable.mat');

%% MATLAB 2-D plotting, Example 1
% reference: http://www.mathworks.com/matlabcentral/fileexchange/35214-matlab-plot-gallery-line-plot-2d--1-/content/html/Line_Plot_2D_1.html

% Define values for x, y1, and y2
x  = 0: .1 : 2*pi;
y1 = cos(x);
y2 = sin(x);

% Plot y1 vs. x (blue, solid) and y2 vs. x (red, dashed)
figure
plot(x, y1, 'b', x, y2, 'r-.', 'LineWidth', 2)

% Turn on the grid
grid on

% Set the axis limits
axis([0 2*pi -1.5 1.5])

% Add title and axis labels
title('Trigonometric Functions')
xlabel('angle')
ylabel('sin(x) and cos(x)')

%% MATLAB 2-D plotting, example 2
% reference: http://www.mathworks.com/matlabcentral/fileexchange/35259-matlab-plot-gallery-function-plot--1-/content/html/Function_Plot_1.html

% Create the plot using the lemniscate function f(x,y) = (x^2 + y^2)^2 - x^2 + y^2
figure
ezplot('(x^2 + y^2)^2 - x^2 + y^2', [-1.1, 1.1], [-1.1, 1.1])

% Adjust the colormap to plot the function in blue
colormap([0 0 1])

% Add a multi-line title
title({'Lemniscate Function', '(x^2 + y^2)^2 - x^2 + y^2'})

%% MATLAB 2-D plotting, example 3
% reference: http://www.mathworks.com/matlabcentral/fileexchange/35273-matlab-plot-gallery-horizontal-bar-plot/content/html/Horizontal_Bar_Plot.html

% Create the data for the temperatures and months
temperatures = [40.5 48.3 56.2 65.3 73.9 69.9 71.1 59.5 48.7 35.3 31.7 30.0];
months = {'Dec', 'Nov', 'Oct', 'Sep', 'Aug', 'Jul', 'Jun', 'May', 'Apr', 'Mar', 'Feb', 'Jan'};

% Plot the temperatures on a horizontal bar chart
figure
barh(temperatures)

% Set the axis limits
axis([0 80 0 13])

% Add a title
title('Boston Monthly Average Temperature - 2001')

% Change the Y axis tick labels to use the months
set(gca, 'YTick', 1:12)
set(gca, 'YTickLabel', months)

%% MATLAB 2-D plotting, example 4
% reference: http://www.mathworks.com/matlabcentral/fileexchange/35268-matlab-plot-gallery-semilogy-plot/content/html/Semilogy_Plot.html

% Create some data
eb = 0:5;
SER = [0.1447 0.1112 0.0722 0.0438 0.0243 0.0122];
BER = [0.0753 0.0574 0.0370 0.0222 0.0122 0.0061];

% Create a y-axis semilog plot using the semilogy function
% Plot SER data in blue and BER data in red
figure
semilogy(eb, SER, 'bo-')
hold on
semilogy(eb, BER, 'r^-')

% Turn on the grid
grid on

% Add title and axis labels
title('Performance of Baseband QPSK')
xlabel('EbNo (dB)')
ylabel('SER and BER')

%% MATLAB 3-D plotting, example 1

x = [0:10]; 
y = [0:10]; 
z = x'*y; 

figure;
mesh(x,y,z); 
colorbar;
figure; 
surf(x,y,z);
colorbar;

%% MATLAB 3-D plotting, example 2
% reference: http://www.mathworks.com/matlabcentral/fileexchange/35310-matlab-plot-gallery-function-mesh-plot/content/html/Function_Mesh_Plot.html

% Create the mesh plot using the function f(x,y) = y^2 - x^2
figure
ezmesh('y^2 - x^2', [-3 3], [-3 3])

%% MATLAB 3-D plotting, example 3
% reference: http://www.mathworks.com/matlabcentral/fileexchange/35240-matlab-plot-gallery-change-lighting-to-phong/content/html/Lighting_Phong.html

% Create a grid of x and y points
points = linspace(-2, 0, 20);
[X, Y] = meshgrid(points, -points);

% Define the function Z = f(X,Y)
Z = 2./exp((X-.5).^2+Y.^2)-2./exp((X+.5).^2+Y.^2);

% "phong" lighting is good for curved, interpolated surfaces. "gouraud"
% is also good for curved surfaces
surf(X, Y, Z)
view(30, 30)

%for reference what is asimuth and projection use this
[X,map] = imread('http://upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Azimuth-Altitude_schematic.svg/436px-Azimuth-Altitude_schematic.svg.png');
imtool(X,map)

shading interp
light
lighting phong
title('Lighting phong')