%% E5 Matlab Intro
% Erik Cheever - Fall 2009

%% Simple math
%%
% addition
3+5

%%
% multiplication
3*5

%%
% sin()  - note the argument is in radians
sin(pi/4)

%%
% sind() - takes argument in degrees
sind(45)

%%
% sqrt
sqrt(3)

%% 
% power
3^5

%%
3^0.5

%%
3^1/2

%% 
% natural log (ln)
log(10)

%%
% log base 10 
log10(10)

%% 
% pi
pi

%%
% show more digits
format long
pi

%% 
% show fewer digits
format short
pi

%% 
% scientific notation
256*256*256*256


%% Variables - not equivalent to mathematical notation
% variables go on left side.  Read equals sign as "gets": x gets 3
x=3

%%
% display value of variable
x

%%
% note that you can't switch order.
%
% 3=x gives an error

%%
% Whatever is on left gets a new value
y=4

%%
x=y  %This changes the value of x
     %y=x would have changed value of y

%%
% anything following a "%" sign is a comment
%
% if you put a semicolon ";" at the end of a line, the result doesn't
% display.

x=5;

%%
% The above result wasn't displayed.  But we can check the value of x
x


%% Matrices and vectors
%%
% Row vector
a=[1 3 5 -1]

%%
% Column vector
b=[2; 4; 1; 0]

%%
% Get 3rd element of each
a(3)

%%
b(3)

%%
% Try to add
%a+b

%% 
% define another row vector
c=[1 0 3 1]

%%
% now we can add
a+c

%%
% Define a 2x2 (2 rows x 2 colums) matrix.
A=[3 5; 6 -1]

%%
% Access individual elements
A(2,1)  % 2nd row, 1st column

%%
% Retrieve a whole column....
A(:,1)   % 1st column

%%
% or a row...
A(2,:)   % 2nd row

%%
% Another matrix
B=[3 5; 5 2]

%% 
% Add matrices
A+B

%%
% Multiplication
A*B

%%
% Transpose (switch rows and columns)\
A
A'

%% 
% Find inverse
inv(A)

%%
% check inverse
ans*A

%%
% can also define identity matrix
I=eye(2)

%% 
% check
A*I

%% Creating a range of numbers, and plotting
% range of numbers
x=linspace(0,3*pi,12)  %x is linearly spaced with 12 elements

%%
% calculate sin()
y=sin(x)

%%
% plot
plot(x,y)

%%
% Label the plot
title('Sin(x) vs x');
xlabel('x values');
ylabel('sin(x)');

%%
% use more points
x=linspace(0,3*pi,1000);
y=sin(x);
plot(x,y,'r-.','LineWidth',2);

%%
% a circle (radius = 2)
theta=linspace(0,6*pi,1000);
x=2*cos(theta);  y=2*sin(theta);
plot(x,y,'r','LineWidth',2);


%% 
% a spiral (radius=theta)
x=theta.*cos(theta);  y=theta.*sin(theta);
plot(x,y,'r','LineWidth',2);

%%
% a 3-D spiral
plot3(x,y,theta,'r','LineWidth',2);

%% 
% Label the axes
xlabel('x');  ylabel('y');  zlabel('theta');
title('3d Spiral');

%% Patch graphics
%%
% Define a "patch"
clf;  %clear the figure
x=[0 1 1 0];  
y=[0 0 1 1];
myPatch=patch(x,y,[1 0 0]);  %(x, y, color)

%%
% Set axes
axis([-5 5 -5 5]);  %[xmin xmax ymin ymax]
grid

%% 
% move the patch
set(myPatch,'Xdata',x+2);

%%
% change the color
set(myPatch,'FaceColor',[0 0 1]);

%% 
% a 3d patch
x=[0 0; 1 1; 1 1];
y=[0 0; 1 -1; 0 0];
z=[0 0; 1 0.5; 0 0];
tcolor(1,1,1:3) = [1 0 0];
tcolor(1,2,1:3) = [0 1 0];
my3dPatch=patch(x,y,z,tcolor);