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lessons/lesson01/matlab_intro.m
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lessons/lesson01/matlab_intro.m
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%% Lesson 1
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%% Objective
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% After this class, you should be able to:
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%%
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%
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% * Know why you need MATLAB
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% * Manuever around the MATLAB interface
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% * Understand arithmetic and basic functions in MATLAB
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% * Know how to make scalar, vector and matrix variables in MATLAB
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% * Know how to perform matrix operations in MATLAB
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%
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%% MATLAB overview
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% MATLAB (short for MATrix LABoratory) is a commonly used interactive
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% software amongst engineers. As the name suggests, MATLAB organizes its
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% data as matrices and is specially designed for matrix multiplication. In
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% addition, it has a plethora of plugins and functions that engineers can
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% use, such as machine learning, financial analysis, filter design etc.
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%%
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% In Cooper, MATLAB is widely used in electrical and computer engineering
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% classes (signals, comm theory, machine learning, etc.), and is more broadly
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% used for these purposes and others (physics simulations, controls design,
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% etc.) across many engineering and scientific disciplines.
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%
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%% MATLAB Environment
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%%% Command window
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% The command window is sort of the equivalent of a terminal in Linux, or
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% Cygwin in Windows. When you type a command into the command window, an
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% operation performs. You can type a MATLAB command, such as 5+10, and the
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% answer would be printed out. If a variable is not assigned to the
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% command, the result would be stored in the variable ans automatically. If
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% a semicolon is added at the end of the line, the result would be
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% suppressed. You can clear the command window by typing clc. Moreover, you
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% can also type command line commands in the command window, such as ls,
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% pwd etc.
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%%% Command history
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% When you are playing around with different functions in MATLAB, you might
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% want to trace back what functions you played with. At that time, you can
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% press the up arrow, which would show you your command history.
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%%% Workspace
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% The workspace is where all the variables are stored. Each variable is
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% displayed as a name value pair in the workspace. If the variable is a
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% scalar, then the actual value would be shown. If it is a vector or matrix
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% , then depending on the size of the vector / matrix, it would either be
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% shown as its value or simply the size of the vector / array and its type.
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% You can double click on the variables to investigate its actual value in
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% a spreadsheet.
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%%% Current Folder
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% The current folder shows you where you are located at in MATLAB. If you
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% execute the command pwd on the command window, it should show you the
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% location of the current folder. You might find a time where you need to
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% add a folder and link it to your current folder location. At that time,
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% you can right click and select "Add to Path". To change current folder,
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% you can execute the cd command on your command window
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%%% Editor
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% The editor is where you can write a script and execute it. All MATLAB
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% scripts are saved as .m files. To execute a script, press the play button
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% on top in EDITOR tab. When you are executing a script, you can use the
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% semicolon to suppress the output of each line. To display a certain
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% variable at an arbitrary location in your script, you can use disp()
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% function.
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%% Arithmetic and Basic functions
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%% Basic Operations
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5+10; % Addition
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ans; % Prints out previous answer
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25-7; % Subtraction
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24*86; % Multiplication
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123.456*78.90; % Multiplication
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145/123; % Division
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2^5; % Exponential
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log10(1000); % Logarithm base 10
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log(exp(5)); % Natural logarithm
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sqrt(625); % Square root
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sin(pi); % sine function
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asin(0); % arc sine function
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1e5; % e5 multiplies 1 by 10^5
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1e-2; % e-2 multiplies 1 by 10^-2
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%% Complex Numbers
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2+1i; % equivalently, 2+i
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2+1j; % equivalently, 2+j
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(2+2i)*(3+4j);
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%% Special Numbers
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pi;
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exp(2*pi*j);
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inf;
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%% Complex number operations
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conj(2+i); % complex conjugate
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real(2+i); % real part
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imag(2+i); % imaginary part
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abs(2+i); % magnitude/absolute value
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angle(2+i); % angle or phase
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%% Variables
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% In matlab, there are 3 (main) different kinds of variables
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%%
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% * Scalar - A scalar appears as 1-by-1 and it is a single real or complex
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% number
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% * Vector - A vector is 1-by-n or n-by-1, and appears in MATLAB as a row or
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% column of complex numbers
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% * Matrix - A matrix is m-by-n, and appears in MATLAB as, essentially, a
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% matrix. A matrix is a 2-D array
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% If you want to see what variables you've declared, either look in the
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% Workspace section of the MATLAB window, or type:
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who;
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whos;
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%% Scalar Variables
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a = 5;
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b = 10;
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c = a+b;
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z1 = 2+j;
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z2 = 3+4j;
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z = z1*z2;
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%% Vector Variables
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x = [1 2+3j 2.718 pi cos(pi)]; % row vector
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x = [1, 2+3j, 2.718, pi, cos(pi)]; % same thing with commas
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xT = transpose(x); % now you created the column vector
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xT = x.'; % regular tranpose
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xT = x'; % complex tranpose
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y = [1 ; 2.5 ; 3.2 ; 4*pi; cos(pi)]; % column vector
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xlen = length(x); % length of row/col vector
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ylen = length(y); % same value as length(x)!
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%% BE CAREFUL!
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% The following two vectors produces vectors of different sizes, the reason
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% being linspace(x1, x2, n) creates n evenly spaced points between x1 and
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% x2 , with the value of interval (x2-x1)/(n+1), while the colon operator
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% (used in the form of x1:i:x2) creates an array with [x1, x1+i, x1+2i...,
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% x1+mi], where m = (x2-x1)/i. Hence when creating a vector with the colon
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% operator or linspace, make sure you know when to use it. In conclusion,
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% linspace works with number of points, whereas the colon operator works
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% with increments.
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%%
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v1 = linspace(-5,5,10);
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v2 = -5:1:5;
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%% Matrix Variables
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A = [1 2 3; 4 5 6; 7 8 9]; % basic construction of matrix
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B = repmat(A,2,1); % you concatenated A one above the other
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C = [A; A]; % same as above
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C1 = transpose(C); % now you transposed C!
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C2 = C.'; % still transposed! if it is only C' then it is
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% conjugate transpose
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size(C); % Confirm that they are tranposes of each other
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size(C1);
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size(C1,1); % You get the dimension you want!
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eye(3); % Create identity matrix
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speye(30000000); % Create sparse identity matrix
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D = ones(50,60); % D is 50-by-60 ones
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E = zeros(40); % E is 40-by-40 zeros
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%% Matrix Operations
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B+C; % addition
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B-C; % subtraction
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4*B + C/5; % multiplication and division with a constant
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A+ones(size(A)); % elementwise addition with a constant
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B*C'; % matrix multiplication
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B.*C; % elementwise multiplication
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B.^3; % elementwise exponentiation! note: do not use B^3
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2*(eye(3))^3; % only possible with square matrices
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%% Documentation
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% If you don't know how to use a function, look it up using one of the
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% following commands. help opens a textual documentation in the
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% command window (just like Linux's man command), while doc will open a
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% new window with graphical documentation just like their website. The
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% MATLAB documentation website is also a great resource!
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help clc;
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doc size;
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