MATLAB

About MATLAB

MATLAB is a numerical computing environment and programming language. Created by The MathWorks, MATLAB allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. Although it specializes in numerical computing, an optional toolbox interfaces with the Maple symbolic engine, making it a full computer algebra system. It is used by more than one million people in industry and academia and runs on most modern operating systems, including Windows, Mac OS, Linux and Unix. The current version is MATLAB 7.1 Service Pack 3. It is available for commercial use for approximately US$2000 and US$100 for an academic license with a limited set of Toolboxes.
— from Wikipedia:MATLAB

For Bioinformatics and Systems Biology, there are useful toolboxes available:

• SBMLToolbox v2.0.2, by the SBML Team download from sourceforge
• SimBiology 1, from Mathworks
• Bioinformatics Toolbox v2.2, from Mathworks

Elementary Tutorial

The following is an unstructured quick bare bones introduction to some of MATLAB's important commands/functions. MATLAB is reasonably easy to use and intuitive to pick up, so go ahead and experiment and learn!

GENERAL COMMANDS

clc

clears the command window

clear

removes all variables from the workspace

clear all

removes all variables, globals, functions and MEX links

ls

Returns listing of the current directory (works on Windows as well)

!ls

Use ! to run shell commands both in windows and linux. In windows, !explorer . maybe a useful command, to browse the current directory

pwd

Shows the present working directory (in Windows too)

help <command name>

gives a brief documentation

doc <command name>

gives the complete documentation

lookfor <text>

looks for the string <text> in the first comment line of the HELP text in all M-files (MATLAB functions/scripts) found on MATLABPATH.

whos

It lists all the variables in the current workspace, together with information about their size, bytes, class, etc.

whos -file <filename.mat>

lists the variables in the specified .MAT file.

type <filename>

'cats' or echoes the file to the screen

ESSENTIAL FUNCTIONS

size

returns the size of the matrix

length

returns the maximum dimension of a matrix

A'

transposes a matrix

1:7:100

Generates numbers upto 100 beginning from 1 in steps of 7.

   >> 1:7:100
   
   ans =
   
        1     8    15    22    29    36    43    50    57    64    71    78    85    92    99
   
   >>   

linspace

linspace(a,b,n) generates n linearly spaced points between a and b

logspace

generates logarithmically spaced points

:

: (colon) is a wildcard (similar to * in shell). e.g. A(:,4:end). This returns all rows of A and columns from 4 onwards. end is a keyword that tells MATLAB to take elements untill the last column is reached.

Entering a vector

x= [1 2 3 4 5]

Entering a matrix

I_4= [1 0 0 0; 0 1 0 0 ; 0 0 1 0; 0 0 0 1] Instead of a semi-colon, line-breaks (Enter) will also work.

A([1 3 5 7],[2 4 6 8])

any submatrix can be addressed; it can even be assigned a value. For example A([1 3 5 7],[2 4 6 8])=0 sets those elements to zero!

prod(size(x))

a simple construct for calculating the number of elements in x.

find(A)

returns the indices of the non-zero elements in a vector. For matrices, it is better to give two outputs: [i,j]=find(A).

sqrt(i)

complex variables are handled seamlessly. i and j are both square roots of -1. Avoid i,j in loops, therefore.

inline

Can create functions like [math]\displaystyle{ f(x,y)=\sin(x^2+y^2+xy) }[/math]. e.g.:

   >> f=inline('sin(x.^2+y.^2+x.*y)')
   
   f =
   
        Inline function:
        f(x,y) = sin(x.^2+y.^2+x.*y)

sparse

Use whenever memory problems are possible due to the usage of large matrices. MATLAB intelligently applies the corresponding algorithms. Typically, just saying A=sparse(A) may cause your code to run 10 times faster, if your matrix is large and sparse.

SPECIAL MATRICES

ones(m,n[,p,..])

Generates a matrix of the corresponding size with all elements 1.

zeros(m,n)

Generates a matrix filled with zeroes; useful for initialisation some times.

rand(n)

gives an n-by-n matrix with random entries, chosen from a uniform distribution on the interval (0.0,1.0).

eye(n)

eye(n) is the n-by-n identity matrix.

eye(m,n)

is an m-by-n matrix with 1's on the diagonal and zeros elsewhere.

Note that a single argument usually creates a square matrix for the above functions.

diag

Can be used to extract the diagonal of a matrix or even create diagonal matrices.

INPUT/OUTPUT RELATED

x=1 vs x=1;

; suppresses the output

   >> x=1
   
   x =
   
        1
   
   >> x=1;
   >> 

disp

Suppresses some of the extra lines...

   >> x
   
   x =
   
        1
   
   >> disp(x)
        1
   
   >> 

sprintf

similar to sprintf of C/++.

fprintf

similar to fprintf of C/C++. Use either this or sprintf to print on stdout (command window).

load

loads files. Simplest file is one with equal number of entries in each row separated by space or tab. MATLAB will crib if number of entries in any row are different from others.

importdata

Useful for loading text files and other files you would usually load using 'File>Import...'

xlsread

Can read Microsoft Excel files directly

save

Without filename, all variables are saved to 'matlab.mat'. With filename, all are saved to the corresponding file. You can even specify what variables to save, even with a regular expression!

format long

Displays many digits of precision (default format shows only 4 decimals)

format rat

Displays output as rational numbers!

format

Resets format

MATRIX FUNCTIONS

MATLAB has a host of matrix-related functions. lookfor should come handy for searches.

inv

Inverse of a matrix.

inv vs \

Inverse of a matrix is expensive to compute and to be avoided. MATLAB supports the beautiful slash operator: Just as for [math]\displaystyle{ ax=b }[/math], [math]\displaystyle{ x=b/a }[/math], even for matrix equations (simulataneous equations), i.e. when [math]\displaystyle{ \mathbf{A}\mathbf{x}=\mathbf{b} }[/math] MATLAB allows, x=A\b (try to see it is a b 'over' A!)

*

Matrix multiplication

.*

Element-wise multiplication

.

. does element-wise operations.

For example: A^5 vs A.^5: A^5 multiplies A with itself 5 times (matrix product; possible only when A is square) whereas A.^5 raises every element of A to the 5th power.

norm

Various norms maybe calculated for a matrix.

expm(A) vs exp(A)

exp(A) does [math]\displaystyle{ e^{a_{ij}}\ \forall \ a_{ij} \in \mathbf{A} }[/math], whereas expm is defined as:

[math]\displaystyle{ e^\mathbf{A}=\mathbf{I}+\mathbf{A}+\frac{\mathbf{A^2}}{2!}+\frac{\mathbf{A^3}}{3!}+\dots \infty }[/math] This is of great use while solving systems of differential equations.

svd

Singular Value Decomposition

eig

Eigenvalue/Eigenvector finding

chol

Cholesky Decomposition

POLYNOMIAL FUNCTIONS

polyval(P,X)

returns the value of a polynomial P evaluated at X. P is a vector of length N+1 whose elements are the coefficients of the polynomial in descending powers. [math]\displaystyle{ Y = P(1)*X^N + P(2)*X^{N-1} + ... + P(N)*X + P(N+1) }[/math]. If X is a matrix or vector, the polynomial is evaluated at all points in X.

compan

Can be used for solving polynomial equations. Beautiful function! The eigenvalues of the companion matrix of a polynomial are the roots of the polynomial!

Example: Calculate the cube roots of unity, i.e. the roots of the equation [math]\displaystyle{ x^3-1=0 }[/math]:

   >> eig(compan([1 0 0  -1]))
   
   ans =
   
     -0.5000 + 0.8660i
     -0.5000 - 0.8660i
      1.0000
   >>

ADVANCED

cell

symbolic

FIGURE RELATED FUNCTIONS

figure

Opens a new figure window

clf

Clears the current figure

close

Closes the curent figure window

close all

Closes all figure windows

hold on

Holds the current plot on the figure window

waitforbuttonpress

Waits on the plot during a script/function, till a button is pressed, before further execution

subplot

Create a grid of plots in a single figure.

plot

Versatile plot function.

ezplot

Can plot anything you imagine! Just try ezplot('sin(x*y)')!

surf

Plots a surface

mesh

Plots a mesh (similar to surf but ~no solid)

title

Titles a figure

xlabel

Add X-Axis title

ylabel

Add Y-Axis title

colormap

Change the colours of plots/images

spy

Sparsity plot of a matrix — puts blue dots wherever entries are non-zero. Shows number of non-zeroes as well.

PROGRAMMING

• function name and file name should be the same
• % comments
• help and comments

help myfun will return the first block of comments in myfun.m

(see the following example as well)

• return is implicit. For example

   % my function to calculate max of two numbers
   % 
   function a=mymax(x,y)
   if (x>y)
       a=x;
   else
       a=y'
   end
   return %optional: whatever a is at the end of the 
          %function file, that value will be returned.  

• programs vs scripts

Scripts don't have a function keyword. They're just 'scripts', which run a series of commands. The variables are all in memory after the execution of the script

• if (x~=1)

This is a significant difference from C/C++: instead of x!=1, use x~=1.

• elseif
• end - ENDs any blocks - for, if, elseif, while etc (roughly equivalent of } in C++; there is no { if (x~=1) itself implies — loosely— if(x!=1){ of C++))
• for k=1:100 (not i!!)
• All addressing is from 1:n
• handling arguments

Multiple arguments can be specified in the function definition

   function [mean,median,mode,variance]=statistics(x)

• for loops is bad programming... there should be vectorisable alternatives!!

BIOINFORMATICS TOOLBOX

clustergram

useful for clustering microarray data etc. Has a lot of options.

SBMLToolBox

• Rougly a libSBML for MATLAB! More on http://sbml.org/software/sbmltoolbox/

External Links

• Loren on the Art of MATLAB
• MATLAB WikiBook