Based off of Learn X in Y Minutes.
MATLAB stands for MATrix LABoratory. It is a powerful numerical computing language commonly used in engineering and mathematics.
- Basics
- Matrices and Vectors
- Plots
- Functions and Scripts
- Programming Logic
- Math/Engineering
- Vectorization
- Optimization
- Machine Learning
- Simulink
%% Code sections start with two percent signs. Section titles go on the same line.
% Comments start with a percent sign.
%{
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% Two percent signs denote the start of a new code section
% Individual code sections can be run by moving the cursor to the section followed by
% either clicking the "Run Section" button
% or using Ctrl+Shift+Enter (Windows) or Cmd+Shift+Return (OS X)
%% This is the start of a code section
% One way of using sections is to separate expensive but unchanging start-up code like loading data
load myFile.mat y
%% This is another code section
% This section can be edited and run repeatedly on its own, and is helpful for exploratory programming and demos
A = A * 2;
plot(A);
% commands can span multiple lines, using '...':
a = 1 + 2 + ...
+ 4% commands can be passed to the operating system
!ping google.com
who % Displays all variables in memory
whos % Displays all variables in memory, with their types
clear % Erases all your variables from memory
clear('A') % Erases a particular variable
openvar('A') % Open variable in variable editor
clc % Erases the writing on your Command Window
diary % Toggle writing Command Window text to file
ctrl-c % Abort current computation
close all % Closes all figures
edit('myfunction.m') % Open function/script in editor
type('myfunction.m') % Print the source of function/script to Command Window
profile on % turns on the code profiler
profile off % turns off the code profiler
profile viewer % Open profiler
help command % Displays documentation for command in Command Window
doc command % Displays documentation for command in Help Window
lookfor command % Searches for command in the first commented line of all functions
lookfor command -all % searches for command in all functions
% Output formatting
format short % 4 decimals in a floating number
format long % 15 decimals
format bank % only two digits after decimal point - for financial calculations
fprintf('text') % print "text" to the screen
disp('text') % print "text" to the screen
% pressing the up key shows you a history of previous commands% Variables & Expressions
myVariable = 4 % Notice Workspace pane shows newly created variable
myVariable = 4; % Semi colon suppresses output to the Command Window
4 + 6 % ans = 10
8 * myVariable % ans = 32
2 ^ 3 % ans = 8
a = 2; b = 3;
c = exp(a)*sin(pi/2) % c = 7.3891
% Logicals
1 > 5 % ans = 0
10 >= 10 % ans = 1
3 ~= 4 % Not equal to -> ans = 1
3 == 3 % equal to -> ans = 1
3 > 1 && 4 > 1 % AND -> ans = 1
3 > 1 || 4 > 1 % OR -> ans = 1
~1 % NOT -> ans = 0
% Logicals can be applied to matrices:
A > 5
% for each element, if condition is true, that element is 1 in returned matrix
A( A > 5 )
% returns a vector containing the elements in A for which condition is true
% Strings
a = 'MyString'
length(a) % ans = 8
a(2) % ans = y
[a,a] % ans = MyStringMyString
% Cells
a = {'one', 'two', 'three'}
a(1) % ans = 'one' - returns a cell
char(a(1)) % ans = one - returns a string
% Structures
A.b = {'one','two'};
A.c = [1 2];
A.d.e = false;
% Variables can be saved to .mat files
save('myFileName.mat') % Save the variables in your Workspace
load('myFileName.mat') % Load saved variables into WorkspaceIMPORTANT: Indices in Matlab start at 1, not 0
% Vectors
x = [4 32 53 7 1]
x(2) % ans = 32
x(2:3) % ans = 32 53
x(2:end) % ans = 32 53 7 1
x = [4; 32; 53; 7; 1] % Column vector
x = [1:10] % x = 1 2 3 4 5 6 7 8 9 10
x = [1:2:10] % Increment by 2, i.e. x = 1 3 5 7 9
% Matrices
A = [1 2 3; 4 5 6; 7 8 9]
% Rows are separated by a semicolon; elements are separated with space or comma
% A =
% 1 2 3
% 4 5 6
% 7 8 9
A(2,3) % ans = 6, A(row, column)
A(6) % ans = 8
% (implicitly concatenates columns into vector, then indexes into that)
A(2,3) = 42 % Update row 2 col 3 with 42
% A =
% 1 2 3
% 4 5 42
% 7 8 9A(2:3,2:3) % Creates a new matrix from the old one
%ans =
% 5 42
% 8 9
A(:,1) % All rows in column 1
%ans =
% 1
% 4
% 7
A(1,:) % All columns in row 1
%ans =
% 1 2 3
[A ; A] % Concatenation of matrices (vertically)
%ans =
% 1 2 3
% 4 5 42
% 7 8 9
% 1 2 3
% 4 5 42
% 7 8 9
% this is the same as
vertcat(A,A);
[A , A] % Concatenation of matrices (horizontally)
%ans =
% 1 2 3 1 2 3
% 4 5 42 4 5 42
% 7 8 9 7 8 9
% this is the same as
horzcat(A,A);
A(:, [3 1 2]) % Rearrange the columns of original matrix
%ans =
% 3 1 2
% 42 4 5
% 9 7 8
A(1, :) =[] % Delete the first row of the matrix
A(:, 1) =[] % Delete the first column of the matrix
squeeze(A); % Removes singular dimensions ie. 2x1x3 -> 2x3transpose(A) % Transpose the matrix, which is the same as:
A one
A' % Concise version of complex transpose
A.' % Concise version of transpose (without taking complex conjugate)
size(A) % ans = 3 3
% Element by Element Arithmetic vs. Matrix Arithmetic
% On their own, the arithmetic operators act on whole matrices. When preceded
% by a period, they act on each element instead. For example:
A * B % Matrix multiplication
A .* B % Multiple each element in A by its corresponding element in B
% There are several pairs of functions, where one acts on each element, and
% the other (whose name ends in m) acts on the whole matrix.
exp(A) % exponentiate each element
expm(A) % calculate the matrix exponential
sqrt(A) % take the square root of each element
sqrtm(A) % find the matrix whose square is A
% Solving matrix equations (if no solution, returns a least squares solution)
% The \ and / operators are equivalent to the functions mldivide and mrdivide
x=A\b % Solves Ax=b. Faster and more numerically accurate than using inv(A)*b.
x=b/A % Solves xA=b
inv(A) % calculate the inverse matrix
pinv(A) % calculate the pseudo-inverse
% Common matrix functions
zeros(m,n) % m x n matrix of 0's
ones(m,n) % m x n matrix of 1's
diag(A) % Extracts the diagonal elements of a matrix A
diag(x) % Construct a matrix with diagonal elements listed in x, and zeroes elsewhere
eye(m,n) % Identity matrix
linspace(x1, x2, n) % Return n equally spaced points, with min x1 and max x2
inv(A) % Inverse of matrix A
det(A) % Determinant of A
eig(A) % Eigenvalues and eigenvectors of A
trace(A) % Trace of matrix - equivalent to sum(diag(A))
isempty(A) % Tests if array is empty
all(A) % Tests if all elements are nonzero or true
any(A) % Tests if any elements are nonzero or true
isequal(A, B) % Tests equality of two arrays
numel(A) % Number of elements in matrix
triu(x) % Returns the upper triangular part of x
tril(x) % Returns the lower triangular part of x
cross(A,B) % Returns the cross product of the vectors A and B
dot(A,B) % Returns scalar product of two vectors (must have the same length)
transpose(A) % Returns the transpose of A
fliplr(A) % Flip matrix left to right
flipud(A) % Flip matrix up to down
% Matrix Factorisations
[L, U, P] = lu(A) % LU decomposition: PA = LU,L is lower triangular, U is upper triangular, P is permutation matrix
[P, D] = eig(A) % eigen-decomposition: AP = PD, P's columns are eigenvectors and D's diagonals are eigenvalues
[U,S,V] = svd(X) % SVD: XV = US, U and V are unitary matrices, S has non-negative diagonal elements in decreasing order
[Q, R] = qr(A) % if A is mxn, Q is mxm and R is mxn upper triangular
% Common vector functions
max % largest component
min % smallest component
length % length of a vector
sort % sort in ascending order
sum % sum of elements
prod % product of elements
mode % modal value
median % median value
mean % mean value
std % standard deviation
perms(x) % list all permutations of elements of x
find(x) % Finds all non-zero elements of x and returns their indexes, can use comparison operators,
% i.e. find( x == 3 ) returns indexes of elements that are equal to 3
% i.e. find( x >= 3 ) returns indexes of elements greater than or equal to 3
% Plotting
x = 0:.10:2*pi; % Creates a vector that starts at 0 and ends at 2*pi with increments of .1
y = sin(x);
plot(x,y)
xlabel('x axis')
ylabel('y axis')
title('Plot of y = sin(x)')
axis([0 2*pi -1 1]) % x range from 0 to 2*pi, y range from -1 to 1
plot(x,y1,'-',x,y2,'--',x,y3,':') % For multiple functions on one plot
legend('Line 1 label', 'Line 2 label') % Label curves with a legend
% Alternative method to plot multiple functions in one plot.
% while 'hold' is on, commands add to existing graph rather than replacing it
plot(x, y)
hold on
plot(x, z)
hold off
loglog(x, y) % A log-log plot
semilogx(x, y) % A plot with logarithmic x-axis
semilogy(x, y) % A plot with logarithmic y-axis
fplot (@(x) x^2, [2,5]) % plot the function x^2 from x=2 to x=5
% Creates a meshgrid (2D grid) to calculate a function for every point in the grid
[X, Y] = meshgrid(x_min:step:x_max, y_min:step:y_max)
grid on % Show grid; turn off with 'grid off'
axis square % Makes the current axes region square
axis equal % Set aspect ratio so data units are the same in every direction
scatter(x, y); % Scatter-plot
hist(x); % Histogram
stem(x); % Plot values as stems, useful for displaying discrete data
bar(x); % Plot bar graph
z = sin(x);
plot3(x,y,z); % 3D line plot
pcolor(A) % Heat-map of matrix: plot as grid of rectangles, coloured by value
contour(A) % Contour plot of matrix
contourf(A) % Filled contour plot of matrix
mesh(A) % Plot as a mesh surface
h = figure % Create new figure object, with handle h
figure(h) % Makes the figure corresponding to handle h the current figure
close(h) % close figure with handle h
close all % close all open figure windows
close % close current figure window
shg % bring an existing graphics window forward, or create new one if needed
clf clear % clear current figure window, and reset most figure properties
% Properties can be set and changed through a figure handle.
% You can save a handle to a figure when you create it.
% The function get returns a handle to the current figure
h = plot(x, y); % you can save a handle to a figure when you create it
set(h, 'Color', 'r')
% 'y' yellow; 'm' magenta, 'c' cyan, 'r' red, 'g' green, 'b' blue, 'w' white, 'k' black
set(h, 'LineStyle', '--')
% '--' is solid line, '---' dashed, ':' dotted, '-.' dash-dot, 'none' is no line
get(h, 'LineStyle')
% The function gca returns a handle to the axes for the current figure
set(gca, 'XDir', 'reverse'); % reverse the direction of the x-axis
% To create a figure that contains several axes in tiled positions, use subplot
subplot(2,3,1); % select the first position in a 2-by-3 grid of subplots
plot(x1); title('First Plot') % plot something in this position
subplot(2,3,2); % select second position in the grid
plot(x2); title('Second Plot') % plot something there
% Given
x1 = [-3:0.5:3];
x2 = x1;
y = randi(500, length(x1), length(x1));
% Show a 3-D plot
figure
subplot(2,1,1);
surf(x1,x2,y);
xlabel(’x_1’);
ylabel(’x_2’);
% Show contours
subplot(2,1,2);
contour(x1,x2,y);
xlabel(’x_{1}’);
ylabel(’x_{2}’);
axis equal
% Show a colour map
figure
imagesc(x1,x2,y)
xlabel(’x_{1}’);
ylabel(’x_{2}’);% Calling Functions
% Standard function syntax:
load('myFile.mat', 'y')
% Command syntax:
load myFile.mat y % no parentheses, and spaces instead of commas
% Calling a function from a script
% [arguments out] = function_name(arguments in)
[V,D] = eig(A);
[~,D] = eig(A); % if you only want D and not V
% To use functions or scripts, they must be on your path or current directory
path % displays current path
addpath /path/to/dir % add to path
rmpath /path/to/dir % remove from path
cd /path/to/move/into % change directory
% M-file Scripts
% A script file is an external file that contains a sequence of statements.
% They let you avoid repeatedly typing the same code in the Command Window
% Have .m extensions
% M-file Functions
% Like scripts, and have the same .m extension
% But can accept input arguments and return an output
% Also, they have their own workspace (ie. different variable scope).
% Function name should match file name (so save this example as double_input.m).
% 'help double_input.m' returns the comments under line beginning function
function output = double_input(x)
%double_input(x) returns twice the value of x
output = 2*x;
end
double_input(6) % ans = 12
% If you want to create a function without creating a new file you can use an
% anonymous function.
% Example that returns the square of it's input, assigned to the handle sqr:
sqr = @(x) x.^2;
sqr(10) % ans = 100
doc function_handle % find out more% User input
a = input('Enter the value: ')
% Stops execution of file and gives control to the keyboard: user can examine
% or change variables. Type 'return' to continue execution, or 'dbquit' to exit
keyboard
% Reading in data (also xlsread/importdata/imread for excel/CSV/image files)
fopen(filename)
% Output
disp(a) % Print out the value of variable a
disp('Hello World') % Print out a string
fprintf % Print to Command Window with more control
% Conditional statements (the parentheses are optional, but good style)
if (a > 15)
disp('Greater than 15')
elseif (a == 23)
disp('a is 23')
else
disp('neither condition met')
end
% Looping
% NB. looping over elements of a vector/matrix is slow!
% Where possible, use functions that act on whole vector/matrix at once
for k = 1:5
disp(k)
end
k = 0;
while (k < 5)
k = k + 1;
end
% Timing code execution: 'toc' prints the time since 'tic' was called
tic
A = rand(1000);
A*A*A*A*A*A*A;
tocsin(x)
cos(x)
tan(x)
asin(x)
acos(x)
atan(x)
exp(x)
sqrt(x)
log(x)
log10(x)
abs(x) %If x is complex, returns magnitude
min(x)
max(x)
ceil(x)
floor(x)
round(x)
rem(x)
rand % Uniformly distributed pseudorandom numbers
randi % Uniformly distributed pseudorandom integers
randn % Normally distributed pseudorandom numbers
%Complex math operations
abs(x) % Magnitude of complex variable x
phase(x) % Phase (or angle) of complex variable x
real(x) % Returns the real part of x (i.e returns a if x = a +jb)
imag(x) % Returns the imaginary part of x (i.e returns b if x = a+jb)
conj(x) % Returns the complex conjugate
% Common constants
pi
NaN
inf
% Given a meshgrid X,Y and a function defined on the meshgrid like Gauss, interpolates the value of the function at the point u1,u2
interp2(X,Y,Gauss,u1,u2)
% Transfer functions
s = tf('s');
G = s^2/(s^3 + 100*s^2 + 30*s + 50);
pole(G); % Returns the location(s) of the pole(s) in rad/s
zero(G); % Returns the location(s) of the zero(s) in rad/s
pzmap(G); % Plots the locations of both the pole(s) and zero(s)
bandwidth(closed_loop_system); % Returns bandwidth of a closed loop transfer function in rad/s
bode(closed_loop_system) % Creates bode plot of system
rlocus(closed_loop_system) % Plots a root locus of the specified system
margin(open_loop_system); % Creates a bode plot, displaying the gain and phase margins of an open loop transfer function
Tips to vectorize your code to get rid of loops and make it run more efficiently.
% fminconsimulink % starts Simulink