clear all; echo on;clc
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% Matlab Primer
% Author: Paul Dostert
% Description: This is a series of Matlab commands that should hep a new
% user learn many of the basics of Matlab. This script is meant to be run
% once, which will walk the user through each function. It can also be 
% used as a reference by simply reading through this .m file.
%
% This primer is split into 9 parts. This primer simply walks through some
% commands part by part. It is not interactive.
%  1. Basic Matlab Commands
%  2. Basic Calculator Type Commands
%  3. Vector Assignment
%  4. Vector Operations
%  5. Matrix Assignment
%  6. Matrix Operations
%  7. Matrix Functions
%  8. Plotting in 2D
%  9. Plotting in 3D
% Press any key to start with part 1.
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pause; clc;


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%BASIC MATLAB COMMANDS:  "help XXX" on any command displays more
%information about a function (ie "help clear" tells how to use clear).
%"doc" loads up the help menu, or "doc XXX" loads a very detailed
%description of the function XXX.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Obviously, the '%' comments everything that comes on the line after it
% 
% "echo on" makes it so every command in this .m file is displayed when 
%  the file is run. "echo off" does the opposite. 
echo on; 
% Assign a variable:
x = 5;
% The who command displays all variables currently being used
who
% To clear one variable (such as x) do: "clear x". To clear all variables
% type "clear all"
clear x; 
% Show only 5 digits of precision. "format long" shows more if needed
format short;

% An important command to remember (but not use now) is "Ctrl-c". This
% stops any computation or script. If you hit "Ctrl-c" on your keyboard
% right now it will stop this primer.
%
% The pause command stops the script until the user hits a key. The clc
% command clears the screen (it will clear once you hit a key)
pause; clc;

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% BASIC CALCULATOR COMMANDS: Matlab works scalars (real or complex) just
% like a regular calculator, where all your usual commands (+-/*^) work as
% usual. Most everything else on a calculator (sin,cos,abs,etc) works as
% well. Type: "help arith" to find out more about arithmetic commands
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((3+3)-3)*2 / 6
2^3
1-2*i
sin(pi)
abs(-2.4)
% These are exponential and natural log, log base 10 is log10
exp(1)
log(2)
% This is arccosine (same idea for other arcs)
acos(0)
pause; 
clc; 


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% VECTOR ASSIGNMENT: To create vectors we use
%  the square brackets. A comma (or space) between entries indicates a new
%  column, while a semicolon indicates a new row. 
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% Assign v the row vector from 2 to 7. There are two ways to do this:
v = [2, 3, 4, 5, 6, 7]
% This means 'go from 2 by 1 to 7'
v = [2:1:7]
% Assign w the column vector from 10 to 7 (going down)
w = [10 ; 9 ; 8 ; 7]
% This means 'go from 10 by -1 to 7'. This creates a row vector. To make 
% it a column vector, we use the TRANSPOSE operator, which is '
w = [10:-1:7]'
pause; 
clc;

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% VECTOR OPERATIONS: Many usual vector operations are defined such as dot
% (for the dot product), cross (cross product), norm, & scalar mult
% are handled easily. 
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v = [1 0 1]; w = [1 1 1];
dot(v,w) 
cross(v,w)
norm(w)
2*v
pause; 
clc;

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% MATRIX ASSIGNMENT: Just like vector assignment, but you have
% rows/cols. There are a handful of nice commands to create new matrices
% with standard entries
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% Create a 2x3 matrix:
A = [2 3 4; 5 6 7]
% Create a 4x2 matrix:
B = [2 3; 4 5; 6 7; 8 9]
% Create a random 2 x 2 matrix, and a random 3x4 matrix (rand chooses
% values between 0 and 1 randomly)
A = rand(2); B = rand(3,4)
% Create a 2x2 matrix of all ones, then all zeros, then the 2x2 identity
A1 = ones(2)
A2 = zeros(2)
A3 = eye(2)
pause; 
clc;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MATRIX OPERATIONS: Matrix operations behave just as expected. Here is an
% interesting quirk to Matlab. You can have Matrix-Matrix (or
% Matrix-Vector) operations, or you can have element-wise operations.
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A = [1 2; 2 1]; B = [ 1 1; -1 -1];
% AB (A times B, using standard Matrix-Matrix multiplication)
A*B
% A.*B (This take each element of A and multiplies it by the corresponding
% element of B). Note that these are NOT the same.
A.*B
% Scalar multiplication
3*A
% Change ONE element of A
A(1,2) = 9;
A
% Reference only the 1st row of the new A
A(1,:)
% Matrix-Vector multiplication (we need x to be a column vector)
x = [1,2];
A*x' 
% Matrix solve( the \ command, such as x=A\b means "solve Ax=b")
b = [3; 1];
x = A\b
pause; 
clc;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MATRIX FUNCTIONS: There are MANY matrix functions. Some are inv (inverse
% of a matrix), norm (norm of a matrix), det (determinant of a matrix)
% eig (eigenvalues/eigenvectors), size (matrix size), rank (matrix rank) 
% and ' (matrix transpose).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A = [1 2; 3 4];
% Assign "Ainv" the inverse of A. If no inverse exists, this returns infs
Ainv = inv(A) 
% By default, this uses the L2 norm (norm(A,N) uses the "N-norm");
norm(A) 
% Determinant of a matrix
det(A) 
% The cols of V are evecs, the diagonal of D are the evals
[V,D] = eig(A) 
% Assigns n to be the number of rows of A and m the number of cols of A
[n,m] = size(A) 
% Returns the approx rank of A (This is not 100% accurate for each case)
rank(A)
% This returns the transpose of A
A'
pause; 
clc;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PLOTTING IN 2D: There is really no such thing as plotting a function
% "y=f(x)" for some unknown (x,y) in Matlab (unless you use some special
% packages which not everyone has). The idea for doing any type of plotting
% is that you want to plot "y=f(x)" as a set of points (x,f(x)).
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% First, we set up points for "x". The "linspace" command will create a
% vector containing 100 points from the starting to the ending value. So
% the following sets x to be values from 0 to 1 by 1/99 (ie, 0,1/99,...,1)
% You can also specify exactly how many points you want to use. For
% example, x=linspace(0,1,1000) creates 1000 points.
x = linspace(0,1);

% Now, we plot two functions. y=2*x and y=x^2. Recall that x is a vector, so
% x^2 doesn't really make any sense. What we want is x.^2 since we want to
% square each value of x.
% This command means plot x vs 2*x in blue (it uses a solid line by
% default). THEN also plot x vs x.^2 in red, with a dotted line (the :)
plot(x,2*x,'b--',x,x.^2,'r:')

% These commands label the x and y axis, and create a title on the previous
% plot:
xlabel('x'); ylabel('y'); title('Plot of 2x and x^2');
% Note that we could also have done:
y1 = 2*x;
y2 = x.^2;
plot(x,y1,'b--',x,y2,'r:');

pause; 
clc;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PLOTTING IN 3D: This is a bit trickier than 2D, but the same idea
% applies. We want to plot points in 2D, but now what we want to do is
% create a mesh in 2D, then determine where these points on the mesh are in
% 3D. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% We set up points to begin with. This makes x and y go from 0 to 1.
x = linspace(0,1); y=x;

% Now we set up a mesh of points from 0 to 1 in 2D (each combination of x,y
% in 2d)
[X Y] = meshgrid(x,y);

% If we want to plot a surface that is given Z=F(X,Y), we can now. We have
% many options. We can use the "mesh" command, which makes a 3d Mesh plot.
% We can use the "surf" command, which is similar but sometimes gives
% more detail. We can use the "contour" plot, which gives a 2D plot with
% contour lines. We'll use all three to plot Z=X.^2 + Y.^2;
mesh(X,Y,X.^2+Y.^2); 
title('Mesh Plot'); xlabel('x'); ylabel('y'); zlabel('z'); pause(2);

surf(X,Y,X.^2+Y.^2); 
title('Surf Plot'); xlabel('x'); ylabel('y'); zlabel('z'); pause(2);

contour(X,Y,X.^2+Y.^2); colorbar;
title('Contour Plot'); xlabel('x'); ylabel('y'); zlabel('z'); pause(2);

pause; 
clc;

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% MORE HELP: To find any more information, the best way to do this is to
% type "doc". The use the "search" tab to find the functions you're 
% looking for
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