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diff --git a/matlab.html.markdown b/matlab.html.markdown new file mode 100644 index 00000000..15ff2303 --- /dev/null +++ b/matlab.html.markdown @@ -0,0 +1,452 @@ +--- +language: Matlab +contributors: + - ["mendozao", "http://github.com/mendozao"] + - ["jamesscottbrown", "http://jamesscottbrown.com"] + +--- + +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 +% Comments start with a percent sign. + +%{ Multi line comments look +something +like +this %} + +% 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 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 a given command + + +% 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 + +% 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') +% 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 + + + +% 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 + + +% 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 + +% 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 + +[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 + + + +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' % Hermitian transpose the matrix +% (the transpose, followed by taking complex conjugate of each element) +transpose(A) % Transpose the matrix, 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 + +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 f +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 gcf 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 it's input, assigned to 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) +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 + +% 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 +flipl(A) % Flip matrix left to right + +% 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 + +``` + +## More on Matlab + +* The official website [http://http://www.mathworks.com/products/matlab/](http://www.mathworks.com/products/matlab/) +* The official MATLAB Answers forum: [http://www.mathworks.com/matlabcentral/answers/](http://www.mathworks.com/matlabcentral/answers/) + |