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authorJames Scott-Brown <james@jamesscottbrown.com>2013-09-14 22:17:41 +0100
committerJames Scott-Brown <james@jamesscottbrown.com>2013-09-14 22:17:41 +0100
commitf7ef4e6f8fde6ab60473f7ba8fd0f9d656cb87b3 (patch)
treef15620d589ad7f8a283041e8600a4709a80adea3 /matlab.html.markdown
parent1dd0e00f2249526520b047c6852d22a7ee2df7ad (diff)
Extend and improve MATLAB article
Diffstat (limited to 'matlab.html.markdown')
-rw-r--r--matlab.html.markdown198
1 files changed, 144 insertions, 54 deletions
diff --git a/matlab.html.markdown b/matlab.html.markdown
index 3c909153..e72a95ea 100644
--- a/matlab.html.markdown
+++ b/matlab.html.markdown
@@ -2,9 +2,11 @@
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.
+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
@@ -18,13 +20,23 @@ something
like
this %}
+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 aprticualr variable
+openvar('A') % Open variable in variable editor
+
clc % Erases the writing on your Command Window
-who % Displays all variables in memory
-diary % History of session
+diary % Toggle writing Command Window text to file
ctrl-c % Abort current computation
+edit('myfunction.m') % Open function in editor
+type('myfunction.m') % Print the source of function 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
@@ -38,6 +50,7 @@ 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
@@ -50,6 +63,12 @@ c = exp(a)*sin(pi/2) % c = 7.3891
3 > 1 || 4 > 1 % OR -> ans = 1
~1 % NOT -> ans = 0
+% Logicals can be applied to matricies:
+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
@@ -75,7 +94,7 @@ 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 seperated with a semi colon, each element is seperated with space or comma
+% Rows are separated by a semicolon; elements are separated with space or comma
% A =
% 1 2 3
@@ -83,6 +102,10 @@ A = [1 2 3; 4 5 6; 7 8 9]
% 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 =
@@ -108,77 +131,125 @@ A(1,:) % All columns in row 1
% 1 2 3
-A(:, [3 1 2]) %Rearrange the columns of original matrix
+[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
-A(1, :) =[] %Delete the first row of the matrix
-
size(A) % ans = 3 3
-A' % Transpose the matrix
+A(1, :) =[] % Delete the first row of the matrix
-[A ; A] % Concatenation of matrices
-%ans =
+A' % Hermitian transpose the matrix
+% (the transpose, followed by taking complex conjugate of each element)
+transpose(A) % Transpose the matrix, without taking complex conjugate
-% 1 2 3
-% 4 5 42
-% 7 8 9
-% 1 2 3
-% 4 5 42
-% 7 8 9
-%Element by Element Arithmetic VS Matrix Arithmetic
+% Element by Element Arithmetic vs. Matrix Arithmetic
A * B % Matrix multiplication
A .* B % Multiple each element in A by its corresponding element in B
-%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)
+% 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
+plot(x,y1,'-',x,y2,'--',x,y3,':'') % For multiple functions on one plot
+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
-% .mat files
-% Save the variables in your Workspace
+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
-%M-file Scripts
-%A script file is an external file that contains a sequence of statements.
-%Better than typing your code in the Command Window
-%Have .m extensions
+h = figure %C reate new figure object, with handle f
+figure(h) %M akes the figure corresponding to handle h the current figure
+% Properties can be set and changed through a figure handle
+h = plot(x, y);
+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')
-%M-file Functions
-%Programs that accept inputs and return an output
-%Have .m extensions
-% double_input.m - naming your ,m file the same as you call it in the file is required
+
+% 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)
+% double_input.m - .m file name must be same as function name in file
function output = double_input(x)
%double_input(x) returns twice the value of x
output = 2*x;
end
double_input(6) % ans = 12
-%User input
+
+% You can also have subfunctions and nested functions.
+% Subfunctions are in the same file as the primary function, and can only be
+% called from within that function. Nested functions are defined within another
+% functions, and have access to both its workspace and their own workspace.
+
+
+% User input
a = input('Enter the value: ')
-%Reading in data
+% Reading in data
fopen(filename)
-%Output
+% Output
disp(a) % Print out the value of variable a
disp('Hello World') % Print out a string
-fprintf % More control display to Command Window
+fprintf % Print to Command Window with more control
-%Conditional statements
+% Conditional statements
if a > 15
disp('Greater than 15')
elseif a == 23
@@ -187,7 +258,9 @@ else
disp('neither condition met')
end
-%Looping
+% 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
@@ -197,8 +270,13 @@ 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
+% Connecting to a MySQL Database
dbname = 'database_name';
username = 'root';
password = 'root';
@@ -206,7 +284,7 @@ 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
+sql = ['SELECT * from table_name where id = 22'] % Example sql statement
a = fetch(conn, sql) %a will contain your data
@@ -228,14 +306,19 @@ ceil(x)
floor(x)
round(x)
rem(x)
-rand
-randi
+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)
+x=A\b % Solves Ax=b
+x=B/a % Solves xa=B
+
% Common matrix functions
zeros(m,n) % m x n matrix of 0's
ones(m,n) % m x n matrix of 1's
@@ -243,30 +326,37 @@ diag(A) % Extracts the diagonal elements of a matrix
eye(m,n) % Indentity matrix
inv(A) % Inverse of matrix A
det(A) % Determinant of A
-eig(A) %Eigenvalues and eigenvectors 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
+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 the scalar product of the vectors A and B. A and B must be vectors of the same length.
+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
% 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
-median %median value
-mean %mean value
-std %standard deviation
-
+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/)
+