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Extend and improve MATLAB article
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James Scott-Brown
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@ -2,9 +2,11 @@
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language: Matlab
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contributors:
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- ["mendozao", "http://github.com/mendozao"]
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- ["jamesscottbrown", "http://jamesscottbrown.com"]
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---
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Matlab stands for Matrix Laboratory. It is a powerful numerical computing language commonly used in engineering and mathematics.
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MATLAB stands for MATrix LABoratory. It is a powerful numerical computing language commonly used in engineering and mathematics.
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If you have any feedback please feel free to reach me at
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[@the_ozzinator](https://twitter.com/the_ozzinator), or
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@ -18,13 +20,23 @@ something
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like
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this %}
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clear % Erases all your variables from memory
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clc % Erases the writing on your Command Window
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who % Displays all variables in memory
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diary % History of session
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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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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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profile viewer % Open profiler
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help command % Displays documentation for command in Command Window
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doc command % Displays documentation for command in Help Window
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lookfor command % Searches for a given command
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@ -38,6 +50,7 @@ myVariable = 4 % Notice Workspace pane shows newly created variable
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myVariable = 4; % Semi colon suppresses output to the Command Window
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4 + 6 % ans = 10
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8 * myVariable % ans = 32
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2 ^ 3 % ans = 8
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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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@ -50,6 +63,12 @@ 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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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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% returns a vector containing the elements in A for which condition is true
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% Strings
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a = 'MyString'
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length(a) % ans = 8
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@ -75,7 +94,7 @@ x = [1:10] % x = 1 2 3 4 5 6 7 8 9 10
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% Matrices
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A = [1 2 3; 4 5 6; 7 8 9]
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% Rows are seperated with a semi colon, each element is seperated with space or comma
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% Rows are separated by a semicolon; elements are separated with space or comma
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% A =
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% 1 2 3
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@ -83,6 +102,10 @@ A = [1 2 3; 4 5 6; 7 8 9]
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% 7 8 9
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A(2,3) % ans = 6, A(row, column)
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A(6) % ans = 8
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% (implicitly concatenates columns into vector, then indexes into that)
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A(2,3) = 42 % Update row 2 col 3 with 42
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% A =
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@ -108,77 +131,125 @@ A(1,:) % All columns in row 1
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% 1 2 3
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A(:, [3 1 2]) %Rearrange the columns of original matrix
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[A ; A] % Concatenation of matrices (vertically)
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%ans =
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% 1 2 3
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% 4 5 42
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% 7 8 9
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% 1 2 3
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% 4 5 42
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% 7 8 9
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[A , A] % Concatenation of matrices (horizontally)
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%ans =
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% 1 2 3 1 2 3
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% 4 5 42 4 5 42
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% 7 8 9 7 8 9
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A(:, [3 1 2]) % Rearrange the columns of original matrix
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%ans =
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% 3 1 2
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% 42 4 5
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% 9 7 8
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A(1, :) =[] %Delete the first row of the matrix
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size(A) % ans = 3 3
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A' % Transpose the matrix
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A(1, :) =[] % Delete the first row of the matrix
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[A ; A] % Concatenation of matrices
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%ans =
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% 1 2 3
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% 4 5 42
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% 7 8 9
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% 1 2 3
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% 4 5 42
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% 7 8 9
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A' % Hermitian transpose the matrix
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% (the transpose, followed by taking complex conjugate of each element)
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transpose(A) % Transpose the matrix, without taking complex conjugate
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%Element by Element Arithmetic VS Matrix Arithmetic
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% Element by Element Arithmetic vs. Matrix Arithmetic
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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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%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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y = sin(x)
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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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y = sin(x);
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plot(x,y)
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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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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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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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scatter(x, y); % Scatter-plot
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hist(x); % Histogram
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z = sin(x);
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plot3(x,y,z); % 3D line plot
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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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% Properties can be set and changed through a figure handle
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h = plot(x, y);
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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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% '--' is solid line, '---' dashed, ':' dotted, '-.' dash-dot, 'none' is no line
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get(h, 'LineStyle')
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% .mat files
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% Save the variables in your 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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%Better than typing your code in the Command Window
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%Have .m extensions
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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 Functions
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%Programs that accept inputs and return an output
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%Have .m extensions
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% double_input.m - naming your ,m file the same as you call it in the file is required
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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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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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end
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double_input(6) % ans = 12
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%User input
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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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% functions, and have access to both its workspace and their own workspace.
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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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% Reading in data
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fopen(filename)
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%Output
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% Output
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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 % More control display to Command Window
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fprintf % Print to Command Window with more control
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%Conditional statements
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% Conditional statements
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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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@ -187,7 +258,9 @@ else
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disp('neither condition met')
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end
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%Looping
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% Looping
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% NB. looping over elements of a vector/matrix is slow!
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% Where possible, use functions that act on whole vector/matrix at once
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for k = 1:5
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disp(k)
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end
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k = k + 1;
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end
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% Timing code execution: 'toc' prints the time since 'tic' was called
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tic
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A = rand(1000);
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A*A*A*A*A*A*A;
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toc
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%Connecting to a MySQL Database
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% Connecting to a MySQL Database
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dbname = 'database_name';
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username = 'root';
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password = 'root';
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dburl = ['jdbc:mysql://localhost:8889/' dbname];
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javaclasspath('mysql-connector-java-5.1.xx-bin.jar'); %xx depends on version, download available at http://dev.mysql.com/downloads/connector/j/
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conn = database(dbname, username, password, driver, dburl);
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sql = ['SELECT * from table_name where id = 22'] %Example sql statement
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sql = ['SELECT * from table_name where id = 22'] % Example sql statement
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a = fetch(conn, sql) %a will contain your data
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@ -228,14 +306,19 @@ ceil(x)
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floor(x)
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round(x)
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rem(x)
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rand
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randi
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rand % Uniformly distributed pseudorandom numbers
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randi % Uniformly distributed pseudorandom integers
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randn % Normally distributed pseudorandom numbers
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% Common constants
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pi
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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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% 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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@ -243,30 +326,37 @@ diag(A) % Extracts the diagonal elements of a matrix
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eye(m,n) % Indentity matrix
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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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eig(A) % Eigenvalues and eigenvectors of A
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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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numel(A) %Number of elements in matrix
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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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cross(A,B) % Returns the cross product of the vectors A and B
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dot(A,B) % Returns the scalar product of the vectors A and B. A and B must be vectors of the same length.
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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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% Common vector functions
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max %largest component
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min %smallest component
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length %length of a vector
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sort %sort in ascending order
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sum %sum of elements
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prod %product of elements
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median %median value
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mean %mean value
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std %standard deviation
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max % largest component
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min % smallest component
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length % length of a vector
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sort % sort in ascending order
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sum % sum of elements
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prod % product of elements
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mode % modal value
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median % median value
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mean % mean value
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std % standard deviation
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perms(x) % list all permutations of elements of x
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```
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## More on Matlab
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* The official website [http://http://www.mathworks.com/products/matlab/](http://www.mathworks.com/products/matlab/)
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* The official MATLAB Answers forum: [http://www.mathworks.com/matlabcentral/answers/](http://www.mathworks.com/matlabcentral/answers/)
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