Mithat Konar (the wiki)

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====== Introduction to MATLAB ======
Mithat Konar\\
2019-04-26

===== What is it? =====
  * A //high-level//, //interpreted// language and environment targeting scientific computing.
  * A freaking huge, feature filled graphing calculator
  * Comprehensive
  * Expensive

===== Alternatives =====

  * [[https://www.gnu.org/software/octave/|GNU Octave]]
    * FOSS (GPL)
    * Mostly syntax compatible
    * 3rd party [[http://octave-online.net/|SaaS]] available
  * [[http://www.scilab.org/|Scilab]]
    * FOSS (GPL compatible CeCILL license)
    * Similar idea, not as compatible
  * [[https://www.scipy.org/|SciPy]]
    * FOSS (MIT-like)
    * Python based, very different
    * Increasingly popular
    * [[https://github.com/spyder-ide/spyder|Spyder IDE]]

===== Two Modes =====
  * Interactive
    * Interact using a command line interface.
  * Scripted
    * Run scripts stored in files.
  * Same syntax in both

===== Variables =====
  * Numbers are double precision floats by default.
  * Strings exist too.
    * Use single quotes.
    * For a literal single quote in a string, use two single quotes.
  * Lots of [[https://www.mathworks.com/help/matlab/data-types_data-types.html|other types]].
  * Ending with a semicolon suppresses output to console.
<code matlab>
a = 3.14159
b = a + 5
c = sin(a);
foo = 'How''s it?'
</code>

===== Comments =====
  * Use the percent sign.
<code matlab>
% a single line comment
a = 99; % this works too

%{
foo = 'multiple line comments';
baz = 'use curly brackets inside';
qux = 'a pair of percent signs.';
%}
</code>
===== Row vectors =====

  * One dimensional horizontal array.
<code matlab>
a = [5 4 2 1]
b = 1 : 10         % [1, 2, ... , 10]
t = 0 : 0.1 : 1    % 0 to 1 in 0.1 steps
x = 0 : 0.1 : 2*pi % 0 to 2π in 0.1 steps
</code>

===== Vector functions =====

<code matlab>
% x is a row vector
x = 0 : 0.1 : 2*pi

% compute sin(x) from 0 to 2π
y = sin(x)

% how big is a variable?
size(y)

% many, many more ...
</code>

===== 2D Plotting =====

<code matlab>
% plot row vector (index is abscissa)
plot(y)

% plot y vs. x (lengths must match)
plot(x, y) 
</code>

  * x, y variable names are not special.
  * //Indexing starts at 1!//
===== Complex numbers =====

<code matlab>
x = 0.3 + 0.4i;
</code>

===== Higher dimensions =====

<code matlab>
% separate matrix rows with ';'

a = [1 2 3; 4 5 6; 7 8 9];
b = [9 8 7; 6 5 4; 3 2 1];
</code>

===== Matrix operations =====

<code matlab>
r = 1.25 * a; % scalar multiplication
r = a * b;    % matrix multiplication
r = a .* b;   % elementwise multiplication
r = a ./ b;   % elementwise division
</code>

===== Matrix inverse and transpose =====

<code matlab>
r = inv(a); % inverse
r = a';     % transpose
</code>

===== Indexing =====

  * Starts at one.
<code matlab>
% individual element (row, col)
a(3, 2);

% submatrix (row range, col range)
bigMatrix(1:3, 10:end);

% set values of submatrix, all cols
bigMatrix(1:3, :) = -1;
</code>

===== 3D plots =====

<code matlab>
t = 0 : 0.1 : 1;
data = sin(2*pi*t);
z = data' * data;

% create a surface plot
surf(z);
</code>

===== What variables? =====
<code matlab>
% display info about variables in current workspace:
whos
</code>

===== Clearing =====
<code matlab>
% clear the screen:
clc

% clear (delete) variables:
clear varname1 varname2

% clear all variables:
clear
</code>

===== Help! =====

<code matlab>
help what-you-want-help-with
</code>

===== Some useful functions =====

  * ''sqrt(x)'': square root
  * ''mod(a, b)'': modulus after division
  * ''ones(m, n)'', ''zeros(m, n)'': matrix of all ones or zeros
  * ''rand(m, n)'': matrix of random numbers
  * ''linspace(x1, x2, n)'': n linear points between x1 and x2
    * n defaults to 100
  * [[https://www.mathworks.com/help/matlab/functionlist.html|Heaps more]]: don't reinvent the wheel!
===== MATLAB scripts =====

  * Scripts containing MATLAB code can be stored as ''//filename//.m''.
  * Run by invoking ''//filename//''.
<file matlab plot_sinc.m>
% Plot sin(x)/x for x = -4*pi to 4*pi.

x = linspace(-4*pi, 4*pi, 1000);
y = sin(x) ./ x;

plot(x, y); % will skip NaN points
</file>

===== Console output =====
  * With ''disp()''.
<code matlab>
a = 'hello';
disp(a);
disp([a ' world']); % [] is one way to concatenate strings
c = 42;
disp(c);
disp(['The answer: ' num2str(c)]); % conversion required
</code>

===== Console input =====
  * With ''input()''
<code matlab>
prompt = 'What is the frequency? ';
x = input(prompt);        % evaluates input
ans = input(prompt, 's'); % doesn't evaluate, 
                          % can get string.
</code>

===== Control structures =====

===== if, if/else =====
<code matlab> 
if x > y
  disp('Ponies!');
elseif x == y
  disp('Skittles!');
  disp('... don''t eat them all at once.');
else
  disp('Rainbows!');
end
</code>

  * Use commas to do everything on one line.
  * Commas not needed for statements ending with a semicolon:
<code matlab> 
if x > y, disp('Ponies!'); else disp('Rainbows!'); end
</code>


===== switch =====
<code matlab>
switch switch_expr
  case case_expr, 
	statement, ..., statement
  case {case_expr1, case_expr2, case_expr3,...}
	statement, ..., statement
  ...
  otherwise, 
	statement, ..., statement
end
</code>

  * ''switch_expr'' doesn't need to be a number
  * ''case'' can match multiple values
  * No "break" is needed.

===== while =====
<code matlab>
while n < 10
  y = y * n;
  n = n + 1;
end
</code>

On one line:
<code matlab>
while n < 10,  y = y * n;  n = n + 1; end
</code>

===== for =====
<code matlab>
for n = 0 : 0.5 : 2
  disp(n);
end
</code>

On one line:
<code matlab>
for n = 0 : 0.5 : 2, disp(n); end
</code>

===== Nesting control structures =====
  * No problem.

===== Relational operators =====
  * ''a < b'', ''lt(a, b)''
  * ''a > b'', ''gt(a, b)''
  * ''%%a <= b%%'', ''le(a, b)''
  * ''%%a >= b%%'', ''ge(a, b)''
  * ''a == b'', ''eq(a, b)''
  * ''a ~= b'', ''ne(a, b)''
===== Logical operators =====
  * ''a && b'': short-circuit logical AND (scalars only)
  * ''a || b'': short-circuit logical OR (scalars only)
  * ''a & b'', ''and(a, b)'': element-wise logical AND (scalars or vectors)
  * ''a | b'', ''or(a, b)'': element-wise logical OR (scalars or vectors)
  * ''~a '', ''not(a)'': logical NOT
  * ''xor(a, b)'': logical EXCLUSIVE OR

===== More logical operators =====
  * ''any(a)'': true if any element of vector is nonzero
  * ''all(a)'': true if all elements of vector are nonzero 

===== User functions =====
  * Functions can be defined in a ''.m'' file with a ''main'' function.
    * Several functions in one file.
    * Functions aren't shared.
  * Functions can be defined in files that also end in ''.m''
    * One function per file.
    * File name must match function name.
    * Functions can be called by any other ''.m'' file or interactively.


===== With "main" function =====
  * Minimum syntax:
<file matlab main.m>
function main()
  area1 = traparea(1, 2, 3);
  disp(area1);
end

function area = traparea(a, b, h)
  area = 0.5 * (a + b) * h;
end
</file>

===== Stand alone function =====
  * Minimum syntax:((Recktenwald, Gerald. "MATLAB Functions -- Basic Features." MATLAB Functions -- Basic Features. Accessed April 30, 2016. http://web.cecs.pdx.edu/~gerry/MATLAB/programming/basics.html.\\
All examples in in the "User functions" section are from Recktenwald.))
<file matlab traparea.m>
function area = traparea(a, b, h)
  area = 0.5 * (a + b) * h;
end
</file>

<file matlab calc_trap_area.m>
% Uses traparea function defined in traparea.m
area1 = traparea(1, 2, 3);
disp(area1);
</file>

===== Documenting functions =====
  * First comment block after first line is used to [[https://www.mathworks.com/help/matlab/matlab_prog/add-help-for-your-program.html|document functions]].
  * What user sees when they type ''help //function-name//''.
    * Only with single-function m-files.
<file matlab traparea.m>
function area = traparea(a, b, h)
% traparea(a, b, h)   Computes the area of a trapezoid given
%                     the dimensions a, b and h, where a and b
%                     are the lengths of the parallel sides and
%                     h is the distance between these sides.

area = 0.5 * (a + b) * h;
end
</file>
===== Which path? =====
  * ''userpath'': list the directories where MATLAB looks for m-files.
  * ''addpath'': add additional directories where MATLAB looks for m-files.
  * ''savepath'': make changes permanent.
  * ''pathtool'': launch a GUI to manage paths.

===== MATLAB's IDE =====
  * We've only covered syntax here.
  * MATLAB's [[https://www.mathworks.com/videos/working-in-the-development-environment-69021.html|"Working the the Development Environment"]] concisely covers the use and features of the IDE.