--- language: Matlab filename: learnmatlab.mat contributors: - ["mendozao", "http://github.com/mendozao"] - ["jamesscottbrown", "http://jamesscottbrown.com"] - ["Colton Kohnke", "http://github.com/voltnor"] - ["Claudson Martins", "http://github.com/claudsonm"] --- MATLAB stands for MATrix LABoratory. It is a powerful numerical computing language commonly used in engineering and mathematics. If you have any feedback please feel free to reach me at [@the_ozzinator](https://twitter.com/the_ozzinator), or [osvaldo.t.mendoza@gmail.com](mailto:osvaldo.t.mendoza@gmail.com). ```matlab %% Code sections start with two percent signs. Section titles go on the same line. % Comments start with a percent sign. %{ Multi line comments look something like this %} % 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); %% Code sections are also known as code cells or cell mode (not to be confused with cell arrays) % 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 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 % 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 % Calling functions can be done in either of two ways: % Standard function syntax: load('myFile.mat', 'y') % arguments within parentheses, separated by commas % Command syntax: load myFile.mat y % no parentheses, and spaces instead of commas % Note the lack of quote marks in command form: inputs are always passed as % literal text - cannot pass variable values. Also, can't receive output: [V,D] = eig(A); % this has no equivalent in command form [~,D] = eig(A); % if you only want D and not V % 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; % Vectors x = [4 32 53 7 1] x(2) % ans = 32, indices in Matlab start 1, not 0 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 9 A(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 size(A) % ans = 3 3 A(1, :) =[] % Delete the first row of the matrix A(:, 1) =[] % Delete the first column of the matrix transpose(A) % Transpose the matrix, which is the same as: A one ctranspose(A) % Hermitian transpose the matrix % (the transpose, followed by taking complex conjugate of each element) A' % Concise version of complex transpose A.' % Concise version of transpose (without taking complex conjugate) % 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 % 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 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 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 % To use functions or scripts, they must be on your path or current directory path % display current path addpath /path/to/dir % add to path rmpath /path/to/dir % remove from path cd /path/to/move/into % change directory % Variables can be saved to .mat files save('myFileName.mat') % Save the variables in your Workspace load('myFileName.mat') % Load saved variables into Workspace % 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 % You can also have subfunctions and nested functions. % Subfunctions are in the same file as the primary function, and can only be % called by functions in the file. Nested functions are defined within another % functions, and have access to both its workspace and their own workspace. % If you want to create a function without creating a new file you can use an % anonymous function. Useful when quickly defining a function to pass to % another function (eg. plot with fplot, evaluate an indefinite integral % with quad, find roots with fzero, or find minimum with fminsearch). % Example that returns the square of its 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; toc % Connecting to a MySQL Database dbname = 'database_name'; username = 'root'; password = 'root'; driver = 'com.mysql.jdbc.Driver'; dburl = ['jdbc:mysql://localhost:8889/' dbname]; javaclasspath('mysql-connector-java-5.1.xx-bin.jar'); %xx depends on version, download available at http://dev.mysql.com/downloads/connector/j/ conn = database(dbname, username, password, driver, dburl); sql = ['SELECT * from table_name where id = 22'] % Example sql statement a = fetch(conn, sql) %a will contain your data % Common math functions sin(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 % 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 % 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 % Classes % Matlab can support object-oriented programming. % Classes must be put in a file of the class name with a .m extension. % To begin, we create a simple class to store GPS waypoints. % Begin WaypointClass.m classdef WaypointClass % The class name. properties % The properties of the class behave like Structures latitude longitude end methods % This method that has the same name of the class is the constructor. function obj = WaypointClass(lat, lon) obj.latitude = lat; obj.longitude = lon; end % Other functions that use the Waypoint object function r = multiplyLatBy(obj, n) r = n*[obj.latitude]; end % If we want to add two Waypoint objects together without calling % a special function we can overload Matlab's arithmetic like so: function r = plus(o1,o2) r = WaypointClass([o1.latitude] +[o2.latitude], ... [o1.longitude]+[o2.longitude]); end end end % End WaypointClass.m % We can create an object of the class using the constructor a = WaypointClass(45.0, 45.0) % Class properties behave exactly like Matlab Structures. a.latitude = 70.0 a.longitude = 25.0 % Methods can be called in the same way as functions ans = multiplyLatBy(a,3) % The method can also be called using dot notation. In this case, the object % does not need to be passed to the method. ans = a.multiplyLatBy(1/3) % Matlab functions can be overloaded to handle objects. % In the method above, we have overloaded how Matlab handles % the addition of two Waypoint objects. b = WaypointClass(15.0, 32.0) c = a + b ``` ## More on Matlab * [The official website](http://www.mathworks.com/products/matlab/) * [The official MATLAB Answers forum](http://www.mathworks.com/matlabcentral/answers/) * [Loren on the Art of MATLAB](http://blogs.mathworks.com/loren/) * [Cleve's Corner](http://blogs.mathworks.com/cleve/)