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Merge pull request #347 from jamesscottbrown/master
[matlab/en] Extend MATLAB article
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@ -20,18 +20,25 @@ something
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like
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this %}
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% commands can span multiple lines, using '...':
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a = 1 + 2 + ...
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+ 4
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% commands can be passed to the operating system
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!ping google.com
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who % Displays all variables in memory
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whos % Displays all variables in memory, with their types
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clear % Erases all your variables from memory
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clear('A') % Erases a aprticualr variable
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clear('A') % Erases a particular variable
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openvar('A') % Open variable in variable editor
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clc % Erases the writing on your Command Window
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diary % Toggle writing Command Window text to file
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ctrl-c % Abort current computation
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edit('myfunction.m') % Open function in editor
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type('myfunction.m') % Print the source of function to Command Window
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edit('myfunction.m') % Open function/script in editor
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type('myfunction.m') % Print the source of function/script to Command Window
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profile viewer % Open profiler
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@ -43,6 +50,7 @@ lookfor command % Searches for a given command
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% Output formatting
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format short % 4 decimals in a floating number
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format long % 15 decimals
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format bank % only two digits after decimal point - for financial calculations
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fprintf
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% Variables & Expressions
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@ -54,6 +62,17 @@ myVariable = 4; % Semi colon suppresses output to the Command Window
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a = 2; b = 3;
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c = exp(a)*sin(pi/2) % c = 7.3891
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% Calling functions can be done in either of two ways:
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% Standard function syntax:
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load('myFile.mat', 'y')
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% Command syntax:
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load myFile.mat y % no parentheses, and spaces instead of commas
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% Note the lack of quote marks in command form: inputs are always passed as
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% literal text - cannot pass variable values. Also, can't receive output:
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[V,D] = eig(A) % this has no equivalent in command form
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% Logicals
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1 > 5 % ans = 0
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10 >= 10 % ans = 1
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@ -63,7 +82,7 @@ c = exp(a)*sin(pi/2) % c = 7.3891
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3 > 1 || 4 > 1 % OR -> ans = 1
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~1 % NOT -> ans = 0
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% Logicals can be applied to matricies:
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% Logicals can be applied to matrices:
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A > 5
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% for each element, if condition is true, that element is 1 in returned matrix
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A[ A > 5 ]
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@ -169,9 +188,18 @@ transpose(A) % Transpose the matrix, without taking complex conjugate
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% Element by Element Arithmetic vs. Matrix Arithmetic
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% On their own, the arithmetic operators act on whole matrices. When preceded
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% by a period, they act on each element instead. For example:
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A * B % Matrix multiplication
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A .* B % Multiple each element in A by its corresponding element in B
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% There are several pairs of functions, where one acts on each element, and
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% the other (whose name ends in m) acts on the whole matrix.
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exp(A) % exponentiate each element
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expm(A) % calculate the matrix exponential
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sqrt(A) % take the square root of each element
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sqrtm(A) % find the matrix whose square is A
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% Plotting
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x = 0:.10:2*pi; % Creates a vector that starts at 0 and ends at 2*pi with increments of .1
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@ -181,9 +209,24 @@ xlabel('x axis')
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ylabel('y axis')
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title('Plot of y = sin(x)')
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axis([0 2*pi -1 1]) % x range from 0 to 2*pi, y range from -1 to 1
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plot(x,y1,'-',x,y2,'--',x,y3,':'') % For multiple functions on one plot
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grid on % Show grid; turn off with 'grid off'
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plot(x,y1,'-',x,y2,'--',x,y3,':') % For multiple functions on one plot
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legend('Line 1 label', 'Line 2 label') % Label curves with a legend
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% Alternative method to plot multiple functions in one plot.
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% while 'hold' is on, commands add to existing graph rather than replacing it
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plot(x, y)
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hold on
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plot(x, z)
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hold off
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loglog(x, y) % A log-log plot
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semilogx(x, y) % A plot with logarithmic x-axis
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semilogy(x, y) % A plot with logarithmic y-axis
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fplot (@(x) x^2, [2,5]) % plot the function x^2 from x=2 to x=5
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grid on % Show grid; turn off with 'grid off'
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axis square % Makes the current axes region square
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axis equal % Set aspect ratio so data units are the same in every direction
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@ -197,11 +240,19 @@ pcolor(A) % Heat-map of matrix: plot as grid of rectangles, coloured by value
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contour(A) % Contour plot of matrix
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mesh(A) % Plot as a mesh surface
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h = figure %C reate new figure object, with handle f
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figure(h) %M akes the figure corresponding to handle h the current figure
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h = figure % Create new figure object, with handle f
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figure(h) % Makes the figure corresponding to handle h the current figure
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close(h) % close figure with handle h
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close all % close all open figure windows
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close % close current figure window
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% Properties can be set and changed through a figure handle
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h = plot(x, y);
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shg % bring an existing graphics window forward, or create new one if needed
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clf clear % clear current figure window, and reset most figure properties
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% Properties can be set and changed through a figure handle.
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% You can save a handle to a figure when you create it.
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% The function gcf returns a handle to the current figure
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h = plot(x, y); % you can save a handle to a figure when you create it
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set(h, 'Color', 'r')
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% 'y' yellow; 'm' magenta, 'c' cyan, 'r' red, 'g' green, 'b' blue, 'w' white, 'k' black
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set(h, 'LineStyle', '--')
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@ -209,22 +260,38 @@ set(h, 'LineStyle', '--')
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get(h, 'LineStyle')
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% The function gca returns a handle to the axes for the current figure
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set(gca, 'XDir', 'reverse'); % reverse the direction of the x-axis
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% To create a figure that contains several axes in tiled positions, use subplot
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subplot(2,3,1); % select the first position in a 2-by-3 grid of subplots
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plot(x1); title('First Plot') % plot something in this position
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subplot(2,3,2); % select second position in the grid
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plot(x2); title('Second Plot') % plot something there
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% To use functions or scripts, they must be on your path or current directory
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path % display current path
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addpath /path/to/dir % add to path
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rmpath /path/to/dir % remove from path
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cd /path/to/move/into % change directory
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% Variables can be saved to .mat files
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save('myFileName.mat') % Save the variables in your Workspace
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load('myFileName.mat') % Load saved variables into Workspace
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% M-file Scripts
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% A script file is an external file that contains a sequence of statements.
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% They let you avoid repeatedly typing the same code in the Command Window
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% Have .m extensions
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% M-file Functions
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% Like scripts, and have the same .m extension
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% But can accept input arguments and return an output
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% Also, they have their own workspace (ie. different variable scope)
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% double_input.m - .m file name must be same as function name in file
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% Also, they have their own workspace (ie. different variable scope).
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% Function name should match file name (so save this example as double_input.m).
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% 'help double_input.m' returns the comments under line beginning function
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function output = double_input(x)
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%double_input(x) returns twice the value of x
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output = 2*x;
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@ -234,14 +301,26 @@ double_input(6) % ans = 12
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% You can also have subfunctions and nested functions.
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% Subfunctions are in the same file as the primary function, and can only be
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% called from within that function. Nested functions are defined within another
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% called by functions in the file. Nested functions are defined within another
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% functions, and have access to both its workspace and their own workspace.
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% If you want to create a function without creating a new file you can use an
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% anonymous function. Useful when quickly defining a function to pass to
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% another function (eg. plot with fplot, evaluate an indefinite integral
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% with quad, find roots with fzero, or find minimum with fminsearch).
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% Example that returns the square of it's input, assigned to to the handle sqr:
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sqr = @(x) x.^2;
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sqr(10) % ans = 100
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doc function_handle % find out more
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% User input
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a = input('Enter the value: ')
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% Reading in data
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% Stops execution of file and gives control to the keyboard: user can examine
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% or change variables. Type 'return' to continue execution, or 'dbquit' to exit
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keyboard
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% Reading in data (also xlsread/importdata/imread for excel/CSV/image files)
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fopen(filename)
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% Output
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@ -249,10 +328,10 @@ disp(a) % Print out the value of variable a
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disp('Hello World') % Print out a string
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fprintf % Print to Command Window with more control
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% Conditional statements
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if a > 15
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% Conditional statements (the parentheses are optional, but good style)
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if (a > 15)
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disp('Greater than 15')
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elseif a == 23
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elseif (a == 23)
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disp('a is 23')
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else
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disp('neither condition met')
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@ -316,14 +395,20 @@ NaN
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inf
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% Solving matrix equations (if no solution, returns a least squares solution)
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x=A\b % Solves Ax=b
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x=B/a % Solves xa=B
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% The \ and / operators are equivalent to the functions mldivide and mrdivide
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x=A\b % Solves Ax=b. Faster and more numerically accurate than using inv(A)*b.
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x=b/A % Solves xA=b
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inv(A) % calculate the inverse matrix
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pinv(A) % calculate the pseudo-inverse
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% Common matrix functions
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zeros(m,n) % m x n matrix of 0's
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ones(m,n) % m x n matrix of 1's
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diag(A) % Extracts the diagonal elements of a matrix
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eye(m,n) % Indentity matrix
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diag(A) % Extracts the diagonal elements of a matrix A
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diag(x) % Construct a matrix with diagonal elements listed in x, and zeroes elsewhere
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eye(m,n) % Identity matrix
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linspace(x1, x2, n) % Return n equally spaced points, with min x1 and max x2
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inv(A) % Inverse of matrix A
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det(A) % Determinant of A
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eig(A) % Eigenvalues and eigenvectors of A
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@ -331,7 +416,7 @@ trace(A) % Trace of matrix - equivalent to sum(diag(A))
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isempty(A) % Tests if array is empty
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all(A) % Tests if all elements are nonzero or true
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any(A) % Tests if any elements are nonzero or true
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isequal(A, B) %Tests equality of two arrays
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isequal(A, B) % Tests equality of two arrays
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numel(A) % Number of elements in matrix
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triu(x) % Returns the upper triangular part of x
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tril(x) % Returns the lower triangular part of x
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@ -340,6 +425,11 @@ dot(A,B) % Returns scalar product of two vectors (must have the same length)
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transpose(A) % Returns the transpose of A
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flipl(A) % Flip matrix left to right
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% Matrix Factorisations
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[L, U, P] = lu(A) % LU decomposition: PA = LU,L is lower triangular, U is upper triangular, P is permutation matrix
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[P, D] = eig(A) % eigen-decomposition: AP = PD, P's columns are eigenvectors and D's diagonals are eigenvalues
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[U,S,V] = svd(X) % SVD: XV = US, U and V are unitary matrices, S has non-negative diagonal elements in decreasing order
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% Common vector functions
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max % largest component
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min % smallest component
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