Introduction to MATLAB

Mithat Konar
2019-04-26

• A high-level, interpreted language and environment targeting scientific computing.
• A freaking huge, feature filled graphing calculator
• Comprehensive
• Expensive

• GNU Octave
  • FOSS (GPL)
  • Mostly syntax compatible
  • 3rd party SaaS available
• Scilab
  • FOSS (GPL compatible CeCILL license)
  • Similar idea, not as compatible
• SciPy
  • FOSS (MIT-like)
  • Python based, very different
  • Increasingly popular
  • Spyder IDE

• Interactive
  • Interact using a command line interface.
• Scripted
  • Run scripts stored in files.
• Same syntax in both

• 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 other types.
• Ending with a semicolon suppresses output to console.

a = 3.14159
b = a + 5
c = sin(a);
foo = 'How''s it?'

• Use the percent sign.

% a single line comment
a = 99; % this works too
 
%{
foo = 'multiple line comments';
baz = 'use curly brackets inside';
qux = 'a pair of percent signs.';
%}

• One dimensional horizontal array.

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

% 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 ...

% plot row vector (index is abscissa)
plot(y)
 
% plot y vs. x (lengths must match)
plot(x, y) 

• x, y variable names are not special.
• Indexing starts at 1!

x = 0.3 + 0.4i;

% separate matrix rows with ';'
 
a = [1 2 3; 4 5 6; 7 8 9];
b = [9 8 7; 6 5 4; 3 2 1];

r = 1.25 * a; % scalar multiplication
r = a * b;    % matrix multiplication
r = a .* b;   % elementwise multiplication
r = a ./ b;   % elementwise division

r = inv(a); % inverse
r = a';     % transpose

• Starts at one.

% 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;

t = 0 : 0.1 : 1;
data = sin(2*pi*t);
z = data' * data;
 
% create a surface plot
surf(z);

% display info about variables in current workspace:
whos

% clear the screen:
clc
 
% clear (delete) variables:
clear varname1 varname2
 
% clear all variables:
clear

help what-you-want-help-with

• 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
• Heaps more: don't reinvent the wheel!

• Scripts containing MATLAB code can be stored as filename.m.
• Run by invoking filename.

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

• With disp().

a = 'hello';
disp(a);
disp([a ' world']); % [] is one way to concatenate strings
c = 42;
disp(c);
disp(['The answer: ' num2str(c)]); % conversion required

• With input()

prompt = 'What is the frequency? ';
x = input(prompt);        % evaluates input
ans = input(prompt, 's'); % doesn't evaluate, 
                          % can get string.

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

• Use commas to do everything on one line.
• Commas not needed for statements ending with a semicolon:

if x > y, disp('Ponies!'); else disp('Rainbows!'); end

switch switch_expr
  case case_expr, 
	statement, ..., statement
  case {case_expr1, case_expr2, case_expr3,...}
	statement, ..., statement
  ...
  otherwise, 
	statement, ..., statement
end

• switch_expr doesn't need to be a number
• case can match multiple values
• No “break” is needed.

while n < 10
  y = y * n;
  n = n + 1;
end

On one line:

while n < 10,  y = y * n;  n = n + 1; end

for n = 0 : 0.5 : 2
  disp(n);
end

On one line:

for n = 0 : 0.5 : 2, disp(n); end

• No problem.

• 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)

• 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

• any(a): true if any element of vector is nonzero
• all(a): true if all elements of vector are nonzero

• 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.

• Minimum syntax:

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

• Minimum syntax:¹⁾

traparea.m

function area = traparea(a, b, h)
  area = 0.5 * (a + b) * h;
end

calc_trap_area.m

% Uses traparea function defined in traparea.m
area1 = traparea(1, 2, 3);
disp(area1);

• First comment block after first line is used to document functions.
• What user sees when they type help function-name.
  • Only with single-function m-files.

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

• 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.

• We've only covered syntax here.
• MATLAB's "Working the the Development Environment" concisely covers the use and features of the IDE.