MatLab Guide Wikibooks

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MATLAB Guide WikiBook


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Contents

Articles

MATLAB Programming 1

Saving and loading a MAT-file 5

Basic Reading and Writing data from a file 7

Boolean and Rational 9

Strings 12

Portable Functions 16

Complex Numbers 17

Arrays 19

Introduction to array operations 21

Struct Arrays 28

Cell Arrays 30

Sparse Matrices 31

Graphics 31

Annotate 33

Scripts 34

Comments 37

Entering data at the command line 38

Loops and Branches 38

Error Messages 39

MATLAB Caveats 47

Debugging M Files 47

Simple matrix manipulation 49

More complicated matrix operations 51

Ordinary Differential Equations 52

Partial Differential Equations 54

Reading and writing from files 55

Writing and Reading to A Serial Port 57

Writing to a USB port 58

Filtering 58

Controls 61

Struct arrays 61

MATlab Classes 63

GNU Octave 63

Differences between Octave and MATLAB 65


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Symbolic Toolbox 71

GUIDE 78

Simulink 79

Psychtoolbox 80

References

Article Sources and Contributors 81

Image Sources, Licenses and Contributors 82

Article Licenses

License 83


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MATLAB Programming

MATLAB is a programming language developed by MathWorks. It started out as a matrix programming language

where linear algebra programming was simple. It can be run both under interactive sessions and as a batch job.

Most MATLAB scripts and functions can be run in the open source programme octave. This is freely available for

most computing platforms.

GNU Octave and LabVIEW MathScript are systems for numerical computations with an m-file script language that

is mostly compatible with MATLAB. Both alternatives can replace MATLAB in many circumstances. While a good

deal of the content of this book will also apply to both Octave and LabVIEW MathScript, it is not guaranteed to

work in exactly the same manner. Differences and comparison between MATLAB and Octave are presented in

Comparing Octave and MATLAB.

Basic MATLAB Concepts

Saving and loading a MAT-file Commands

File Naming conventions

Basic Reading and Writing data from a file

The MATLAB Command Prompt

Calculator

Data Storage and Manipulation

Data Types and Operators on Point Values

Boolean and Rational

Strings

Portable Functions

Complex Numbers

Arrays and Matrices

What is an array?

Introduction to array operations

Vectors and Basic Vector Operations

Mathematics with Vectors and Matrices

Struct Arrays

Cell Arrays

Sparse Matrices
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Graphics

Graphics

Plot

Polar Plot

Mesh Semilogx or Semilogy

Loglog

Bode Plot

Nichols Plot

Nyquist Plot

Handle Graphics

What is a handle?

Figure handles

Axis handles

Other types of handles

Annotating Plots

Inserting Newlines into Plot Labels

M-file Programming

Scripts

Comments

The Input Function

Control Flow

Loops and Branches

Error Messages

MATLAB Caveats

Inserting Newlines into Disp Warn and Error
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Numerical Manipulation

Linear Algebra

It is the Matrix laboratory after all.

Simple matrix manipulation

Operations

Transpose

Systems of linear equations

More complicated matrix operations

Row reduced echelon form

Inverse

Coffactor, minor

Jacobian

Differential Equations Ordinary Differential Equations

Partial Differential Equations

More advanced I/O

Different versions of MATLAB handle this differently. We will focus on versions 6.5 and 7.x, primarily on

MATLAB 7.x since it is the latest. A note will appear when the procedure is different for ver. 6.

Examples

Filtering

Moving Average

Alpha Beta

Kalman

PSD estimation

Entropy

Markov Processes

Queuing Theory

Phase vocoder

See "Phase vocoder and encoder in MATLAB" for an example phase vocoder and the corresponding sound sample

encoder in MATLAB.

Object Oriented Programming

MATLAB as well as Octave have object oriented capabilities. Yet, technically it is not fully an object oriented

language.

An Object Oriented Language(OOL) has three components: 1. Polymorphism 2. Inheritance 3. Encapsulation

Octave can be extended by adding new objects. Those objects can overload the operators like e.g. assignment,slicing, comparison.
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While in MATLAB, this can be done with m-script, in Octave new objects are implemented as C++ classes. A

simple example of how objects can be added to Octave can be found here[1]

.

An alternative to MATLAB: Octave

What is Octave ?A short presentation of Octave and its history.

Differences between Octave and MATLAB

The most important differences between Octave and MATLAB that anyone willing to use Octave instead of

MATLAB should be aware of.

Toolboxes and Extensions

The toolboxes are pretty good if you can afford them. In version 7 there are a lot of toolboxes.

Legacy Toolboxes

GUIDE allows the creation of interactive user interfaces.

Simulink is for modeling, simulating and analysing systems.

Psychtoolbox is a set of tools that aid in vision research.

Distributed computing- The distributed computing toolbox is a set of tools that aid in distributing models over a

cluster.

Optimization- The optimization toolbox includes various algorithms for minimization.

Matlab in medicine

Image Processing in Optical Coherence Tomography using Matlab is a book which will introduce you to subtleties

related to the implementation of selected fragments of algorithms, the notation of some of them in the Matlab

environment has been given. The presented source code is shown only in the form of example of implementable

selected algorithm. The book is addressed to ophthalmologists , IT specialists and students involved in the

development of applications designed for automation of measurements for the needs of medicine.

References

MATLAB documentation[2]

from The MathWorks.

MATLAB programs compilation[3]

from 'Matlab programs for Engineering Students'.

External links

MATLAB at literateprograms.org[4]

ControlTheoryPro.com MATLAB Category[5]

Processing in Optical Coherence Tomography using Matlab[6]

programs compilation for Engineering Students[7]
http://engineering-matlab.blogspot.in/:Matlabhttp://www.octnews.org/articles/2932585/image-processing-in-optical-coherence-tomography-u/:Imagehttp://wikis.controltheorypro.com/index.php?title=Category:MATLABhttp://en.literateprograms.org/Category:Programming_language:Matlabhttp://engineering-matlab.blogspot.in/http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.htmlhttp://en.wikibooks.org/w/index.php?title=File:00%25.svghttp://en.wikibooks.org/w/index.php?title=MATLAB_Programming/Psychtoolboxhttp://en.wikibooks.org/w/index.php?title=File:00%25.svghttp://en.wikibooks.org/w/index.php?title=MATLAB_Programming/Simulinkhttp://en.wikibooks.org/w/index.php?title=File:00%25.svghttp://en.wikibooks.org/w/index.php?title=MATLAB_Programming/GUIDEhttp://en.wikibooks.org/w/index.php?title=MATLAB_Programming/Differences_between_Octave_and_MATLABhttp://en.wikibooks.org/w/index.php?title=MATLAB_Programming/GNU_Octavehttp://en.wikibooks.org/w/index.php?title=MATLAB_Programming/Comparing_Octavehttp://wiki.octave.org/wiki.pl?CodaTypes


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Other Wikibooks

A number of other wikibooks use MATLAB to teach their subjects. The following wikibooks make use of

MATLAB:

Signals and Systems

Control Systems

References

[1] http://wiki.octave.org/wiki.pl?CodaTypes

[2] http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html

[3] http://engineering-matlab.blogspot. in

[4] http://en. literateprograms.org/Category:Programming_language:Matlab

[5] http://wikis.controltheorypro. com/index.php?title=Category:MATLAB

[6] http://www.octnews.org/articles/2932585/image-processing-in-optical-coherence-tomography-u/:Image

[7] http://engineering-matlab.blogspot. in/:Matlab

Saving and loading a MAT-file

The Current Directory and Defined Path

It is necessary to declare a current directory before saving a file, loading a file, or running an M-file. By default,

unless you edit the MATLAB shortcut, the current directory will be .../MATLAB/work. After you start MATLAB,

change the current directory by either using the toolbar at the left-hand side of the screen, or entering the path in the

bar at the top.

The current directory is the directory MATLAB will look in first for a function you try to call. Therefore if you have

multiple folders and each of them has an M-file of the same name, there will not be a discrepancy if you set the

current directory beforehand. The current directory is also the directory in which MATLAB will first look for a data

file.

If you still want to call a function but it is not part of the current directory, you must define it using MATLAB's 'set

path' utility. To access this utility, follow the path:

file > set path... > add folder...

You could also go to "add folder with subfolders...", if you're adding an entire group ,as you would if you were

installing a toolbox. Then look for and select the folder you want. If you forget to do this and attempt to access a file

that is not part of your defined path list, you will get an 'undefined function' error.

Saving FilesThere are many ways to save to files in MATLAB.

save - saves data to files, *.mat by default

uisave - includes user interface

hgsave - saves figures to files, *.fig by default

diary [filename] - saves all the text input in the command window to a text file.

All of them use the syntax:

save filename.ext

or similar for the other functions. The files are saved in your current directory, as seen on the top of the window. Bydefault the current directory is .../MATLAB/work.
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Saving and loading a MAT-file 6

Loading Files

Likewise, there are many ways to load files into the workspace. One way is to use the "file" menu. To open a .m file

click "open", whereas to import data from a data file select "import data..." and follow the wizard's instructions.

An alternative way to load a saved .mat file (within a function, for example) is to type:

>> load filename.ext

The file must be in a recognized directory (usually your current directory, but at least one for which the path has

been set).

The data in the .mat file is stored with the same name as the variable originally had when it was saved. To get the

name of this and all other environment variables, type "who".

To open an .m file, you can use file -> open, or type

>>open filename.ext

File Naming Constraints

You can name files whatever you want (usually simpler is better though), with a few exceptions:

MATLAB for Windows retains the file naming constraints set by DOS. The following characters cannot be used

in filenames:

" / : * < > | ?

You're not allowed to use the name of a reserved word as the name of a file. For example, while.m is not a valid

file name because while is one of MATLAB's reserved words.

When you declare an m-file function, the m-file must be the same name as the function or MATLAB will not be

able to run it. For example, if you declare a function called 'factorial':

function Y = factorial(X)

You must save it as "factorial.m" in order to use it. MATLAB will name it for you if you save it after typing

the function declaration, but if you :change the name of the function you must change the name of the file

manually, and vice versa.
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Basic Reading and Writing data from a file

Reading and Writing from a file: Command Line

Reading and Writing data from/to a .mat file

The quickest means of saving and retrieving data is through the binary .mat file format MATLAB provides. This is

the native format for MATLAB.

Note: This author has had some problems with certain classes not being saved correctly when saving data using

version 7 for use in version 6. Most data items will work just fine. Of particular interest was an issue with

State-Space objects that were saved using version 7 to a version 6 compatible file. When the file was opend in

MATLAB version 6+ the State-Space objects did not load.Spradlig (talk) 04:52, 31 March 2008 (UTC).

Saving Data

The save command is used to save workspace data to a file.

Save all workspace data to the file mySave.mat in the current directory.

>> save('mySave.mat')

>> save(fullfile(pwd, 'mySave.mat'))

Save just the variables myData1 and myData2 to mySave.mat.

>> save('mySave.mat', 'myData1', 'myData2')

Save all myData variables to mySave.mat.

>> save('mySave.mat', 'myData*')

Save all myData variables to a mySave.mat file compatible with version 6 of MATLAB.

>> save('mySave.mat', 'myData*', '-v6')

Save all myData variables to an ASCII file.

>> save('mySave.txt', 'myData*', '-ASCII')

Append new variables to the data file.

>> save('mySave.mat', 'newData*', '-append')

Loading Data

The load command is used to load data from a file into the current workspace.

Load all variables from the file mySave.mat into the current workspace.

>> load('mySave.mat')

>> load(fullfile(pwd, 'mySave.mat'))

Load just the variables myData1 and myData2.

>> load('mySave.mat', 'myData1', 'myData2')

Load all myData variables.
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>> load('mySave.mat', 'myData*')

Get a cell array of variables in saved file.

>> whos('-file', 'mySave.mat')

Reading and Writing from an Excel spreadsheetSince analyzing data is one of the more common motivations for using input output I will start with reading and

writing from a spreadsheet. I cover the command line first since it is often necessary to import the data while an

m-function is being evaluated.

MATLAB makes it easy to read from an Excel spreadsheet. It has the built in command "xlsread". To use thexlsread

function use the syntax:

>>g=xlsread('filename');

This line of code readsfilename.xls (from the current directory) and places it in an identical array inside MATLAB

called g. You can then manipulate the array g any way you want. Make sure that the file you choose is in the same

directory were you save your M-files (usually the work directory) otherwise you get an error. You can specify the

path to a file but, this can get messy.

To write data to an .xls the procedure is very similar. The xlswrite command below creates a spreadsheet called

filename.xls in the current directory from the variable g:

>> xlswrite('filename',g);

NOTE: if you are using MATLAB 6.5 there is no "xlswrite" command (that I'm aware of). There are several ways to

write to a file. The simplest way I have found is

fid=fopen('newFile.xls', 'w');

fprintf(fid,'%6.3f %6.3f %10.3f\n', g);

fclose(fid);

You can substitute newFile.xls with .txt. Also, there might be some issues with formatting in Excel. The formatting

issues can usually be handled inside Excel but if they can't you might have to play around with the fopen command

parameters. This is pretty similar (if not the same) way you would write to a file in C.

Reading and Writing from and to other text files

If a file is not an excel spreadsheet, it can still be read using "load" function:

>> load newfile.txt

This works only if the text is entirely numerical, without special formatting. Otherwise you get a 'unrecognized

character' error.

The easiest way to write to a non-excel file, or using MATLAB 6.5 or less, is to use the same code as that for writing

excel files but change the extension. Usually there are no formatting difficulties with plain text files.

For reading more general text files, MATLAB does not have a function to do it easily (unless you have excel), but

you can read very general text files (with different delimiters for both cells and text within cells) using the

"textread.m" function in the MATLAB file exchange (do a google search to find it). You can also try to use fscanf if

the formatting is consistent enough (i.e. consistent numbers of spaces, no mixing of strings and numbers in columns,

and so on).


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Reading and Writing from a data file: GUI

MATLAB contains a nice GUI application that will guide you through importing data from any recognized data file

(usually .mat, .txt, or .xls on a Windows system). To use it, go to file > import data, and select the file you want.

Then, choose what column separators are present (by selecting the appropriate radio button). Finally, click "next".

MATLAB saves the variable under a name similar to that of the file, but with modifications to make it conform with

MATLAB syntax. Spaces are omitted, plusses and minuses are turned into other characters. To see the name

MATLAB generated (and probably change it) type "who" in the command prompt.

External Resources

ControlTheoryPro.com[5]

MatlabCodes.Webs.com[1]

References

[1] http://matlabcodes.webs.com?title=Category:MATLAB

Boolean and Rational

Introduction

A large number of MATLAB's functions are operations on two types of numbers: rational numbers and boolean

numbers.

Rational numbers are what we usually think of when we think of what a number is. 1, 3, and -4.5 are all rational

numbers. MATLAB stores rational numbers as doubles by default, which is a measure of the number of decimal

places that are stored in each variable and thus of how accurate the values are. Note that MATLAB represents

irrational numbers such as pi with rational approximations, except when using the symbolic math toolbox. See that

section for details.

Boolean numbers are either "TRUE" or "FALSE", represented in MATLAB by a 1 and a 0 respectively. Boolean

variables in MATLAB are actually interchangable with doubles, in that boolean operators can be performed with

arrays of doubles and vice versa. Any non-zero number in this case is considered "TRUE".

Most of the rational operators also work with complex numbers. Complex numbers, however, cannot be

interchanged with boolean values like the real rationals can. See the complex numbers section for details on how to

use them.

Rational Operators on Single Values

MATLAB has all the standard rational operators. It is important to note, however, that Unless told otherwise, all

rational operations are done on entire arrays, and use the matrix definitions. Thus, even though for now we're only

talking about operations on a single value, when we get into arrays, it will be important to distinguish between

matrix and componentwise multiplication, for example.

Add, Subtract, multiply, divide, exponent operators:

%addition

a = 1 + 2

%subtraction
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b = 2 - 1

%matrix multiplication

c = a * b

%matrix division (pseudoinverse)

d = a / b

%exponentiation

e = a ^ b

The modulo function returns the remainder when the arguments are divided together, so a modulo b means the

remainder when a is divided by b.

%modulo

remainder = mod(a,b)

All of these functions except for the modulus work for complex numbers as well.

Relational Operators

Equality '==' returns the value "TRUE" (1) if both arguments are equal. This must not be confused with the

assignment operator '=' which assigns a value to a variable.

>>%relational

>>a=5;b=5;

>>a==b

ans = 1

%Assignment

>>a=5;b=3;

>>a=b

a = 3

Note that in the first case, a value of 1 (true) is returned, however for the second case a gets assigned the value of b.

Greater than, less than and greater than or equal to, less than or equal to are given by >, =, >a=3;b=5;

>>a>b


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Boolean Operators on Single Values

The boolean operators are & (boolean AND) | (boolean OR) and ~ (boolean NOT /negation). A value of zero means

false, any non-zero value (usually 1) is considered true.

Here's what they do:

>>%boolean AND

>> y = 1 & 0

y = 0

>> y = 1 & 1

y = 1

>>%boolean OR

>> y = 1 | 0

y = 1

>> y = 1 | 1

y = 1

The negation operation in MATLAB is given by the symbol ~, which turns any FALSE values into TRUE and vice

versa:

>> c = (a == b)

c = 1

>>~c

ans = 0

This is necessary because conditionals (IF/SWITCH/TRY) and loops (FOR/WHILE) always look for statements that

are TRUE, so if you want it to do something only when the statement is FALSE you need to use the negation to

change it into a true statement.

The NOT operator has precedence over the AND and OR operators in MATLAB unless the AND or OR statements

are in parenthesis:

>> y = ~1 & 0

y = 0

>> y = ~(1&0)

y = 1

Terminology

MATLAB refers to Booleans as "logicals" and does not use the word "Boolean" in code or documentation.


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Strings 12

Strings

Declaring Strings

Besides numbers, MATLAB can also manipulate strings. They should be enclosed in single quotes:

>> fstring = 'hello'

fstring =

hello

If you would like to include a single quote this is one way to do it:

>> fstring = ''''

fstring =

'

>> fstring = 'you''re'

fstring =

you're

An important thing to remember about strings is that MATLAB treats them as array of characters. To see this, try

executing the following code:

>> fstring = 'hello';

>> class(fstring)

ans = char

Therefore, many of the array manipulation functions will work the same with these arrays as any other, such as the

'size' function, transpose, and so on. You can also access specific parts of it by using standard indexing syntax.

Attempting to perform arithmetic operations on character arrays converts them into doubles.

>> fstring2 = 'world';

>> fstring + fstring2

ans = 223 212 222 216 211

These numbers come from the standard numbers for each character in the array. These values are obtained by using

the 'double' function to turn the array into an array of doubles.

>> double(fstring)

ans = 104 101 108 108 111

The 'char' function can turn an array of integer-valued doubles back into characters. Attempting to turn a decimal

into a character causes MATLAB to round down:

>> char(104)

ans = h

>> char(104.6)

ans = h

Since the MATLAB strings are treated as character arrays, they have some special functions if you wish to compare

the entire string at once rather than just its components:

findstr(bigstring, smallstring) looks to see if a small string is contained in a bigger string, and if it is returns theindex of where the smaller string starts. Otherwise it returns [].


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Strings 13

strrep(string1, replaced, replacement) replaces all instances ofreplacedin string1 with replacement

Displaying values of string variables

If all you want to do is display the value of a string, you can omit the semicolon as is standard in MATLAB.

If you want to display a string in the command window in combination with other text, one way is to use array

notation combined with either the 'display' or the 'disp' function:

>> fstring = 'hello';

>> display( [ fstring 'world'] )

helloworld

MATLAB doesn't put the space in between the two strings. If you want one there you must put it in yourself.

This syntax is also used to concatenate two or more strings into one variable, which allows insertion of unusual

characters into strings:

>> fstring = ['you' char(39) 're']

fstring = you're

Any other function that returns a string can also be used in the array.

You can also use the "strcat" function to concatenate strings, which does the same thing as above when you use two

strings, but it is especially useful if you are using a cell array of strings because it lets you concatenate the same thing

to all of the strings at once. Unfortunately you can't use it to add white space (strcat discards what MATLAB

considers extraneous whitespace). Here's the syntax for this use.

>> strCell = {'A', 'B'};

>> strcat(strCell, '_');

ans =

A_

B_

Finally, although MATLAB doesn't have a printf function you can do essentially the same thing by using 1 as your

file identifier in the fprintffunction. The format identifiers are essentially the same as they are in C.

>> X = 9.2

>> fprintf(1, '%1.3f\n', X);

9.200

The "9.200" is printed to the screen. fprintf is nice compared to display because you don't have to call num2str on all

of the numbers in a string - just use the appropriate format identifer in the place you want it.

>> X = 9.2

>> fprintf(1, 'The value of X is %1.3f meters per second \n', X);

The value of X is 9.200 meters per second


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Strings 14

Cell arrays of strings

In many applications (particularly those where you are parsing text files, reading excel sheets with text, etc.) you will

encounter cell arrays of strings.

You can use the function "iscellstr" to tell if all of the elements in a given cell array are strings or not.

>> notStrCell = {'AA', []};

>> iscellstr(notStrCell)

ans = 0

This is useful since functions that work with cell arrays of strings will fail if provided with something that's not a cell

array of strings. In particular, they all fail if any elements of the provided cell array are the empty array ( [] ) which is

somewhat frustrating if the provided text file contains empty cells. You must catch this exception before calling

cellstr manipulation functions.

Searching a cell array of strings can be done with the "strmatch", "strfind", and "regexp" functions. Strmatch looks

for a string within a cell array of strings whose first characters exactly match the string you pass to it, and returns the

index of all strings in the array for which it found a match. If you give it the 'exact' option, it will only return the

indexes of elements that are exactly the same as what you passed. For example:

>> strCell = {'Aa', 'AA'};

>> strmatch('A', strCell);

ans = 1, 2

>> strmatch('A', strCell, 'exact');

ans = []

>> strmatch('Aa', strCell, 'exact');

ans = 1

Strfind looks for a specific string within a cell array of strings, but it tries to find it in any part of each string. For

each element x of the given cell array of strings, it will return an empty array if there is no match found in x and the

starting index (remember, strings are arrays of characters) of all matches in x if a match to the query is found.


>> strfind(strCell, 'A');

ans = % answer is a cell array with two elements (same size as

strCell):

1 % Index of the beginning of string "A" in the first cell

1 2 % Index of each instance of the beginning of string "A" in

the second cell

>> strfind(strCell, 'a');

ans =

2

[] % 'a' is not found

The "cellfun" / "isempty" combination is very useful for identifying cases where the string was or was not found.

You can use the find function in combination with these two functions to return the index of all the cells in which the

query string was found.


>> idxCell = strfind(strCell, 'a');

>> isFound = ~cellfun('isempty', idxCell); % Returns "0" if idxCell is

empty and a "1" otherwise


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Strings 15

>> foundIdx = find(isFound)

foundIdx = 2

The strfind function also has some other options, such as the option to only return the index of the first or last match.

See the documentation for details.

The regexp function works the same way as strfind but instead of looking for strings literally, it tries to find matches

within the cell array of strings using regular expressions. Regular expressions are a powerful way to match patterns

within strings (not just specific strings within strings). Entire books have been written about regular expressions, so

they cannot be covered in as much detail here. However, some good resources online include regular-expresions.info[1]

and the MATLAB documentation for the matlab-specific syntax. Note that MATLAB implements some, but not

all, of the extended regular expressions available in other languages such as Perl.

Unfortunately, MATLAB does not innately have functions to do common string operations in some other languages

such as string splitting. However, it is quite possible to find many of these functions in a google search.

Comparing strings

Unlike with rational arrays, strings will not be compared correctly with the relational operator, because this will treat

the string as an array of characters. To get the comparison you probably intended, use the strcmp function as follows:

>> string1 = 'a';

>> strcmp(string1, 'a')

ans = 1

>> strcmp(string1, 'A')

ans = 0

Note that MATLAB strings are case sensitive so that 'a' and 'A' are not the same. In addition the strcmp function

does notdiscard whitespace:

>> strcmp(string1, ' a')

ans = 0

The strings must be exactly the same in every respect.

If the inputs are numeric arrays then the strcmp function will return 0 even if the values are the same. Thus it's only

useful for strings. Use the == operator for numeric values.

>> strcmp(1,1)

ans = 0.

References

[1] http://www.regular-expressions.info/
http://www.regular-expressions.info/http://www.regular-expressions.info/


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Portable Functions

This section discusses anonymous functions and function handles. Both of these are portable in that rather than

having to write an equation multiple times in a program, you can just define it once and then call it whenever you

want to use it. In addition, function handles in particular allow you to pass an equation to another function for direct

evaluation as needed. Anonymous functions are useful for command-line evaluation or for multiple evaluations in

the same m-file.

Anonymous functions

An anonymous function can be created at the command or in a script:

>>f = @(x) 2*x^2-3*x+4;

>>f(3)

ans = 13

To make an anonymous function of multiple variables, use a comma-separated list to declare the variables:

>>f = @(x,y) 2*x*y;

>>f(2,2)

ans = 8

It is possible to make an array of anonymous functions in MATLAB 7.1 but this will become outdated soon so using

this construct in a distributed program is not recommended.

To pass anonymous functions to other functions, just use the name of the anonymous function in your call:

>> f = @(t,x) x;

>> ode45(f, [0:15],1)

Function Handles

A function handle passes an m-file function into another function. This of course lets you have more control over

what's passed there, and makes your program more general as it lets you pass any m-file (as long as it meets other

requirements like having the right number of input arguments and so on). The functionality is similar to that of

function pointers in C++.

To pass an m-file to a function, you must first write the m-file, say something like this:

function xprime = f(t,x)

xprime = x;

Save it as myfunc.m. To pass this to another function, say an ODE integrator, use the @ symbol as follows:

>> ode45(@myfunc, [0:15], 1)

One advantage of using function handles over anonymous functions is that you can evaluate more than one equation

in the m-file, thus allowing you to do things like solve systems of ODEs rather than only one. Anonymous functions

limit you to one equation.


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How to write a function that accepts a function handle

You can also write your own functions that accept function handles. Simply define them as variables in your header,

and then call them as if they were functions:

% myadd adds two variables together

function result = myfunc(func, a, b);

result = func(a, b);

[in a separate m-file]

function sum = myadd(a, b)

sum = a+b;

The command you send to myfunc looks like this:

>> result = myfunc(@myadd, 1, 2);

result = 3

Complex Numbers

Declaring a complex number in MATLAB

Complex numbers in MATLAB are doubles with a real part and an imaginary part. The imaginary part is declared by

using the 'i' or 'j' character. For example, to declare a variable as '1 + i' just type:

>> compnum = 1 + i

compnum = 1.000 + 1.000i

>> compnum = 1 + j

compnum = 1.000 + 1.000i

Note that if you use j MATLAB still displays i on the screen.

Since i is used as the complex number indicator it is not recommended to use it as a variable, since it will assume it's

a variable if given a choice.

>> i = 3; %bad idea

>> a = 1 + i

a = 4

However, since implicit multiplication is not normally allowed in MATLAB, it is still possible to declare a complex

number like this:

>> i = 3;

>> a = 1i + 1

a = 1.000 + 1.000i

It's best still not to declare i as a variable, but if you already have a long program with i as a variable and need to use

complex numbers this is probably the best way to get around it.

If you want to do arithmetic operations with complex numbers make sure you put the whole number in parenthesis,

or else it likely will not give the intended results.


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Complex Numbers 18

Arithmetic operations that create complex numbers

There are several operations that create complex numbers in MATLAB. One of them is taking an even root of a

negative number, by definition.

>> (-1)^0.5

ans = 0.000 + 1.000i

>> (-3)^0.25

ans = 0.9306 + 0.9306i

As a consequence of the Euler formula, taking the logarithm of a negative number also results in imaginary answers.

>> log(-1)

ans = 0 + 3.1416i

In addition, the roots of functions found with the 'roots' function (for polynomials) or some other rootfinding

function will often return complex answers.

MATLAB functions to manipulate complex values

First of all, it is helpful to tell whether a given matrix is real or complex when programming, since certain operations

can only be done on real numbers. Since complex numbers don't have their own class, MATLAB comes with

another function called 'isreal' to determine if a given matrix is real or not. It returns 0 if any of the inputs are

complex.

>> A = [1 + i, 3];

>> isreal(A)

ans = 0

>> isreal(A(2))

ans = 1

Notice that it is possible to have real and complex numbers in the same array, since both are of class double. The

function is set up this way so that you can use this as part of a conditional, so that a block only is executed if all

elements of array A are real.

To extract just the real part of a complex variable use the 'real' function. To extract just the complex part use the

'imag' function.

>> real(A)

ans = 1 3

>> imag(A)

ans = 1 0

One thing you may need to do is perform an operation on the real values of an array but not the complex values.

MATLAB does not have a function to directly do this, but the following pair of commands lets you put only the real

values into another array:

>> RealIndex = (imag(A) == 0); %if imaginary part is zero then the number is real)

>> RealOnly = A(RealIndex)

RealOnly = 3


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Arrays 19

Arrays

Introduction to Arrays

Arrays are the fundamental data type of MATLAB. Indeed, the former data types presented here, strings and

number, are particular cases of arrays. As in many traditional languages, arrays in MATLAB are a collection of

several values of the same type (by default, the type is equivalent to the C type double on the same architecture. On

x86 and powerpc, it is a floating point value of 64 bits). They are indexed through the use of a single integer or, to

get more than one value, an array of integers..

Declaring Arrays

Row and Column Arrays

A simple way to create a row array is to give a comma separated list of values inside brackets:

>> array = [0, 1, 4, 5]array =

0 1 4 5

The commas can be omitted for a row array because MATLAB will assume you want a row array if you don't give it

any separators. However, the commas make it easier to read and can help with larger arrays. The commas indicate

that the array will be a horizontal array.

To make a column array you can use semicolons to separate the values.

>> column = [1; 2; 3]

column =

1

2

3

All elements of an array must be the same data type, so for example you cannot put a function handle and a double in

the same array.

Declaring multi-dimensional arrays

Arrays can be multi-dimensional. To create a 2 dimensional array (a matrix in Linear Algebra terms), we have to

give a list of comma separated values, and each row should be separated by a semi colon:

>> matrix = [1, 2, 3; 4, 5, 6]

matrix =

1 2 3

4 5 6

In MATLAB the term array is synonymous with matrix and will more often than not be referred to as a matrix. It

should be noted that a matrix, as its mathematical equivalent, requires all its rows and all its columns to be the same

size:

>> matrix = [1, 2, 3; 4, 5]

??? Error using ==> vertcatAll rows in the bracketed expression must have the same

number of columns.


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Arrays 20

Properties of MATLAB arrays and matrices

Contrary to low level languages such as C, an array in MATLAB is a more high level type of data: it contains

various information about its size, its data type, and so on.

>> array = [0,1,4,5];

>> length(array)

ans = 4

>> class(array)

ans = double

The number of rows and columns of the matrix can be known through the built-in size function. Following the

standard mathematical convention, the first number is the number of rows and the second is the number of columns:

>> matrix = [1, 2, 3; 4, 5, 6];

>> size(matrix)

ans =

2 3

The goal of MATLAB arrays is to have a type similar to mathematical vectors and matrices. As such, row and

column arrays are not equivalent. Mono-dimensional arrays are actually a special case of multi-dimensional arrays,

and the 'size' function can be used for them as well.

>> size(array)

ans =

1 4

Row and column do not have the same size, so they are not equivalent:

>> size(column)

ans =

3 1

>> size(row)

ans =

1 3

Why Use Arrays?

A major advantage of using arrays and matrices is that it lets you avoid using loops to perform the same operation on

multiple elements of the array. For example, suppose you wanted to add 3 to each element of the array [1,2,3]. If

MATLAB didn't use arrays you would have to do this using a FOR loop:

>> array = [1,2,3];

>> for ii = 1:3

array(ii) = array(ii) + 3;

>> end

>> array

array = [4,5,6]

Doing this is not efficient in MATLAB, and it will make your programs run very slowly. Instead, you can create

another array of 3s and add the two arrays directly. MATLAB automatically separates the elements:


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Arrays 21

>> array = [1,2,3];

>> arrayofthrees = [3,3,3];

>> array = array + arrayofthrees

array = [4,5,6];

If all you are doing is adding a constant, you can also omit the declaration of 'arrayofthrees', as MATLAB will

assume that the constant will be added to all elements of the array. This is very useful, for example if you use an

array with variable size:

>> array = [1,2,3];

>> array + 3

ans = [4,5,6]

The same rule applies to scalar multiplication.

See Introduction to array operations for more information on the operations MATLAB can perform on arrays.

Arrays are a fundamental principle of MATLAB, and almost everything in MATLAB is done through a massive use

of arrays. To have a deeper explanation of arrays and their operations, see Arrays and matrices.



As arrays are the basic data structure in MATLAB, it is important to understand how to use them effectively. See the

previous section for that.

Arrays in MATLAB obey the same rule as their mathematical counterpart: by default, the matrix definitions of

operations are used, unless a special operator called the dot operator is applied.Because arrays operations are so similar to the equivalent mathematical operations, a basic knowledge of linear

algebra is mandatory to use matlab effectively. However, we won't be as precise as in mathematics when using the

terms vector and matrix. In MATLAB, both are arrays of doubles (thus being a matrix in the real mathematical

meaning), and MATLAB considers vectors as a matrices with only one row or only one column. However, there are

special functions just for vectors; see the vector module for an explanation of how to use these.

Basics

How to input an array

The common way to input an array from the matlab command line is to put the input figures into list into square

brackets:

>> [1, 2, 3]

ans =

1 2 3

Comma is used to separate columns elements, and semicolon is used to separate rows. So [1, 2, 3] is a row vector,

and [1; 2; 3] is a column vector


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>> [1; 2; 3]

ans =

1

2

3

If a blankspace is used to separate elements, the default separator is comma, thus making the vector a row vector.

Logically, inputting a matrix is done by using a comma separated list of column vectors, or a semicolon separated

list of row vectors:

>> [1, 2, 3; 4, 5, 6]

ans =

1 2 34 5 6

Variable assignment

To reuse an array in subsequent operations, one should assign the array to a variable. Variable assignment is done

through the equal symbol:

>> a = [1, 2, 3]

a =

1 2 3

Notice that instead of ans =, the name of the variable is displayed by matlab. If you forget to assign the last statement

to a variable, the variable ans always point to the last non assigned:

>> [1, 2, 3]

ans =

1 2 3

>> a = ans

a =

1 2 3

But:

>> [1, 2, 3]

ans =

1 2 3


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>> b = [4, 5, 6]

b =

4 5 6

>> a = ans

a =

1 2 3

I.e. ans is really the last non assigned result, and not the result of the last statement.

As it is the case for most interpreted languages, you do not need to declare a variable before using it, and reusing a

variable name in an assignment will overwrite the previous content.

To avoid cluttering the command line of matlab, you can postfix any command with a semicolon:

>> a = [1, 2, 3];

Accessing elements of a matrix

Now that you know how to define a simple array, you should know how to access its elements. Accessing the

content of an array is done through the operator (), with the index inside the parenthesis; the indexing of the first

element is 1:

>> a = [1, 2, 3];

>> a(1)

ans =

1

>> a(3)

ans =

3

Accessing an element outside the bounds will result in an error:

>> a(5)

??? Index exceeds matrix dimensions.

To access a single matrix element, you can use the (i,j) subscript, where i is the index in the row, and j in the column:

>> a= [1, 2; 3, 4];

>> a(1, 2)

ans =

2


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>> a(2, 1)

ans =

3

You can also access a matrix element through a unique index; in this case, the order is column major, meaning you

first go through all elements of the first column, then the 2d column, etc... The column major mode is the same than

in Fortran, and the contrary of the order in the C language.

>> a = [1, 2, 3; 4, 5, 6];

>> a(3)

ans =

2

It is also possible to access blocks of matrices using the colon (:) operator. This operator is like a wildcard; it tells

MATLAB that you want all elements of a given dimension or with indices between two given values. For example,

say you want to access the entire first row of matrix a above, but not the second row. Then you can write:

>> a = [1, 2, 3; 4, 5, 6];

>> a(1,:) %row 1, every column

ans =

1 2 3

Now say you only want the first two elements in the first row. To do this, use the following syntax:

>> a = [1, 2, 3; 4, 5, 6];

>> a(1, 1:2)

ans =

1 2

The syntax a(:) changes a into a column vector (column major):

>> a = [1, 2, 3; 4, 5, 6]

>> a(:)

ans =

14

2

5

3

6

Finally, if you do not know the size of an array but wish to access all elements from a certain index until the end of

the array, use the end operator, as in

>> a = [1, 2, 3; 4, 5, 6]

>> a(1, 2:end) %row 1, columns from 2 until end of the array

ans =


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2 3

Logical Addressing

In addition to index addressing, you can also access only elements of an array that satisfy some logical criterion. For

example, suppose a = [1.1, 2.1, 3.2, 4.5] and you only want the values between 2 and 4. Then you can achieve this in

two ways. The first is to use the findfunction to find the indices of all numbers between 2 and 4 in the array, andthen address the array with those indices:

>> a = [1.1, 2.1, 3.2, 4.5];

>> INDICES = find(a >= 2 & a > a(INDICES)

ans =

2.1 3.2

This does not work in Matlab 2006b

The second method is to use logical addressing, which first changes a into a logical array, with value 1 if the logical

expression is true and 0 if it is false. It then finds and returns all values in the a which are true. The syntax for this is

as follows:

>> a = [1.1, 2.1, 3.2, 4.5];

>> a(a >= 2 & a > [1, 2, 3] - [1, 2, 1]

ans =

0 0 2

The multiplication by a scalar also works as expected:

>> 2 * [1, 2, 3]

ans =

[2, 4, 6]

Multiplication and division are more problematic: multiplying two vectors in does not make sense. It makes

sense only in the matrix context. Using the symbol * in matlab computes the matrix product, which is only defined

when the number of columns of the left operand matches the number of rows of the right operand:

>> a = [1, 2; 3, 4];

>> a * a


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ans =

7 10

15 22

>> a = [1, 2, 3]; b = [1; 2; 3];>> a * a

??? Error using ==> *

Inner matrix dimensions must agree.

>> a * b

ans =

14

Using the division symbol / has even more constraints, as it imposes the right operand to be invertible (see

Wikipedia:Invertible matrix). For square matrices, is equivalent to . For example :

>> a = [1, 2; 3, 4]; b = [1, 2; 1, 2]

>> b / a

ans =

1 0

1 0

>> a / b

Warning: Matrix is singular to working precision.

ans =

Inf Inf

Inf Inf

If you desire to multiply or divide two matrices or vectors componentwise, or to raise all components of one matrix

to the same power, rather than using matrix definitions of these operators, you can use the dot (.) operator. The two

matrices must have the same dimensions. For example, for multiplication,

>> a = [1, 2, 3];

>> b = [0, 1, 2];

>> a .* b

ans =

0 2 6

The other two componentwise operators are ./ and .^.

As matlab is a numerical computing language, you should keep in mind that a matrix which is theoretically invertible

may lead to precision problems and thus giving imprecise results or even totally wrong results. The message above

"matrix is singular to working precision" should appear in those cases, meaning the results cannot be trusted.
http://en.wikipedia.org/wiki/Invertible_matrix


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Non-square matrices can also be used as the right operand of /; in this case, it computes the pseudoinverse. This is

especially useful in least square problems.

Boolean Operators on Arrays

The same boolean operators that can be used for point values can also be used to compare arrays. To do this,

MATLAB compares the elements componentwise and returns them in a logical array of the same size as the twoarrays being compared. The two arrays must have the same size. For example,

>> A = [2,4], B = [1,5];

>> A < B

ans =

[0 1]

You must be careful when using comparisons between arrays as loop conditions, since they clearly do not return

single values and therefore can cause ambiguous results. The loop condition should be reducable to a single boolean

value, T or F, not an array. Two common ways of doing this are the "any" and the "all" functions. A function callany(array) will return true if array contains any nonzero values and false if all values are zero. It does the

comparisons in one direction first then the other, so to reduce a matrix you must call the any function twice. The

function all, similarly, returns true if and only if all elements in a given row or column are nonzero.

Solving Linear Systems

To solve a linear system in the form Ax = b use the "\" operator.

Example:

>>A = [4 5 ; 2 8];

b = [23 28]';

x = A\b

x =

2

3
http://en.wikipedia.org/wiki/Pseudoinverse


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Struct Arrays 28

Struct Arrays

Introduction to Structures

MATLAB provides a means for structure data elements. Structures are created and accessed in a manner familiar for

those accustomed to programming in C.

MATLAB has multiple ways of defining and accessing structure fields. See Declaring Structures for more details.

Note: Structure field names must begin with a letter, and are case-sensitive. The rest of the name may contain letters,

numerals, and underscore characters. Use the namelengthmax function to determine the maximum length of a field

name.

Declaring Structures

Structures can be declared using the struct command.

>> a = struct('b', 0, 'c', 'test')

a =

b: 0

c: 'test'

In MATLAB, variables do not require explicit declaration before their use. As a result structures can be declared

with the '.' operator.

>> b.c = 'test'

b =

b: 0

c: 'test'

Structures can be declared as needed and so can the fields.

Arrays of Structures

Structures can also be arrays. Below is an example

>> a = struct('b', 0, 'c', 'test'); % Create structure

>> a(2).b = 1; % Turn it into an array by creating another element

>> a(2).c = 'testing'

a =

1x2 struct array with fields:

b

c

>> a(1) % Initial structure

ans =

b: 0

c: 'test'

>> a(2) % The second element

ans =

b: 1

c: 'testing'


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Struct Arrays 29

Accessing Fields

When the field name is known the field value can be accessed directly.

>> a.c

ans =

test

ans =

testing

In some cases you may need to access the field dynamically which can be done as follows.

>> str = 'c';

>> a(1).(str)

ans =

test

>> a(1).c

ans =

test

Accessing Array Elements

Any given element in a structure array can be accessed through an array index like this

>> a(1).c

ans =

test

To access all elements in a structure array use the syntax {structure.field}. In order to get all values in a vector or

array use square brackets ([]) as seen below.

>> [a.('c')]

ans =

testtesting

>> [a.('b')]

ans =

0 1

Or you can put them all into a cell array (rather than concatenating them) like this:

>> {a.('c')}

ans = {'test', 'testing'}

External Resources


References

[1] http://wikis.controltheorypro. com/index.php?title=Structures
http://wikis.controltheorypro.com/index.php?title=Structureshttp://wikis.controltheorypro.com/index.php?title=Structures


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Cell Arrays 30

Cell Arrays

Introduction

Cell arrays are created just like regular arrays except that curly brackets are used instead of square brackets.

array = [1, 2, 3; 4, 5, 6];

cell_array = {1, 2, 3; 4, 5, 6};

The array variable is 1 array with 2 rows and 3 columns. Each element is a scalar. The cell_array variable is

essentially an array of arrays. In this case the cell_array variable is made up of 6 arrays with 1 scalar element in each

of the 6 arrays.

Cell arrays have fewer limitations than regular arrays. The regular array, defined by the square brackets, can hold

numbers or strings but if it holds strings in each element all the strings must be the same length. Also, if 1 element of

an array is a string all elements must be a string. Cell arrays have neither of these limitations.

cell_array = {1, 2, 'a', 'abc'; rand(3, 2), magic(3), eye(3), 'junk'}cell_array =

[ 1] [ 2] 'a' 'abc'

[3x2 double] [3x3 double] [3x3 double] 'junk'

With the lack of limitations/rules for the content of a cell array comes complications. These cell arrays are very

powerful tools but take a lot of time to get used to because each element can be almost anything.

Cell arrays can also be dynamically resized--a key feature in more advanced data structures. For example, one can

create a queue data structure using the commands:

cell_array{end+1}='a';

cell_array{end+1}='b';

... etc.

Once can pop an element from the front of the queue using the commands:

cell_array(1)=[]; % remove first element - resize

cell_array(1)=[]; % remove first element - resize

... etc.

External Links


References

[1] http://wikis.controltheorypro. com/index.php?title=Cell_Arrays
http://wikis.controltheorypro.com/index.php?title=Cell_Arrayshttp://wikis.controltheorypro.com/index.php?title=Cell_Arrays


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Sparse Matrices 31

Sparse Matrices

A Sparse Matrix is a matrix that mostly contains zeros. In Matlab, sparse matrices contrast regular ones in the way

they are stored, such that memory is used more efficiently for matrices that are sparse.

A regular matrix can be converted to a sparse matrix using

>> S = sparse(A); % Create sparse representation of A

Sparse matrices are very common in engineering purposes. This is useful for manipulation as most of the matrix has

a value of 0.

Graphics

2D Graphics

Plot

Plots a function in Cartesian Coordinates, x and y.

Example:

x=0:0.1:2; % creates a line vector from 0 to 2

fx=(x+2)./x.^2; % creates fx

plot(x,fx,'-ok') % plots 2d graphics of the function fx

To plot 2 or more graphs in one Figure, then simply append the second (x,y) pair to the first:

>>>x1 = [1,2,3,4]

>>>y1 = [1,2,3,4]

>>>y2 = [4,3,2,1]

>>>plot(x1,y1,x1,y2)

This will plot y1 and y2 on the same x-axis in the output.

Polar Plot

Plots a function using and r()

t = 0:.01:2*pi;

polar(t,sin(2*t).^2)

3D Graphics

plot3

The "plot3" command is very helpful and easy to see three dimensional images. It follows the same syntax as the

"plot" command. If you search the MATlab help (not at the command prompt. Go to the HELP tab at the top of the

main bar then type plot3 in the search) you will find all the instruction you need.

Example:

l=[-98.0556 ; 1187.074];

f=[ -33.5448 ; -240.402];


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Graphics 32

d=[ 1298 ; 1305.5]

plot3(l,f,d); grid on;

This example plots a line in 3d. I created this code in an M-file. If you do the same you change the values and hit the

run button in the menu bar to see the effect.

Mesh

Creates a 3D plot using vectors x and y, and a matrix z. If x is n elements long, and y is m elements long, z must be

an m by n matrix.

Example:

x=[0:pi/90:2*pi]';

y=x';

z=sin(x*y);

mesh(x,y,z);

Contour

Creates a 2D plot of a 3D projection, using vectors x and y, and a matrix z. If x is n elements long, and y is m

elements long, z must be an m by n matrix.

Example:

x=[0:pi/90:2*pi]';

y=x';

z=sin(x*y);

contour(x,y,z);

Contourf

Same as contour, but fills color between contour lines

Surface

Basically the same as mesh


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Annotate 33

Annotate

MATLAB offers incomparable control over the way you can add details to your plot. From inserting text at the right

positions to labelling the axes, MATLAB from the command line offers you an easy way to create publication style

graphics. With support for Encapsulated postscript and Illustrator output. Complex figures with several axes and

conveying large amounts of information can be created.

Concept of a handle

Most operations on figures generate objects with a set of properties. Users familiar with Object oriented

programming would realize that the functions and the data are encapsulated into the object. A typical figure would

contain at least half a dozen objects. These objects are called handles. A very tacky analogy would be like handles to

several different refrigerators with several different contents. To provide an intuitive feel. I have listed out the

properties from a text handle.

Finding a handleVarious commands provide required handles, for example:

h = gcf; % Get current figure

h = gca; % Get current axis

Examples

Axis Label

xlabel labels the x-axis of the current plot

>>xlabel('string')

You can display text on two lines or insert the value of variables

>>xlabel({['First Line or line n ',int2str(a)],['Second Line or line n',int2str(b)]})

ylabel labels the y-axis of the current plot. It works in same way of xlabel but the output is vertical in 2D plots.

Documenting a Maximum Value

% Previous code set the x value of the peak data point into x_peak

plot(lags(1:1000:end),abs_cs(1:1000:end));

ptitle = 'UUT and Source Correlation Score Magnitude';

xlabel('Lag');

ylabel('Correlation Magnitude');

title(ptitle);

yloc = max(get(gca,'YLim')); % Put at top of plot

text(lags(x_peak),yloc,[' \leftarrow ' num2str(x_peak) 'ns']);

lstr{1} = sprintf(' Test %d', TESTNUM);

lstr{2} = sprintf(' Unit %d%s', UNITNUM, comparestr);

text(lags(1),mean(get(gca,'YLim')),lstr);


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Scripts 34

Scripts

M-files

There are 2 types of m-file

Scripts

Functions

Scripts are a type of m-file that runs in the current workspace. So if you call a script from the command line (base

workspace) the script will use and manipulate the variables of the base workspace. This can get very messy and lead

to all sorts of strange errors when loops are involved and the coder is lazy about about naming their loop variables

(i.e. for i = 1:10, if every loop uses i, j, or k then it's likely that any script called from a loop will alter the loop

variable).

Functions are wholly contained in themselves. They possess their own workspace keeping workspaces separate. This

means that all variables necessary for a particular function must be passed or defined in some way. This can get

tedious for complex algorithms requiring lots of variables. However, any manipulations of variables are discardedwhen the function is exited. Only those output arguments provided by the function are available to the calling

workspace. This means that loops can use i, j, or k all they want because the function's workspace and the calling

workspace do not mix.

Any command valid at the command line is valid in any m-file so long as the necessary variables are present in the

m-files operating workspace.

Using functions properly any change can be affected to any algorithm or plotting tool. This allows for automation of

repetitive tasks.

It is optional to end the M-file with 'end'; doing so, however, can lead to complications if you have conditionals or

loops in your code, or if you're planning on using multiple functions in the same file (see nested functions for details

on this).

Requirements for a function

Custom functions follow this syntax in their most basic form:

function [output1, output2, ...]= function_name(input_arg1,input_arg2)

statements

return;

In current versions of MATLAB the return; line is not required. Thefunction_name can be anything you like but it is

best if the m-file name isfunction_name.m. Calling the function from the command line or another m-file is done byinvoking the m-file name of the function with the necessary input and output arguments.

Within the function itself, there must be a statement that defines each of the output arguments (output1, output2,

etc.). Without some declaration the variable for the output argument doesn't exist in the function's workspace. This

will cause an error about "one or more output arguments". It is good practice to initialize the output arguments at the

beginning of the function.

Typically output arguments are initialized to empty ([]) or 0 or -1 or something equivalent for other data types. The

reason is that if the function encounters an error you've anticipated then the function can return (via the return

command) with those default values. If the initialization value is an invalid value then it can easily be checked by the

calling function for any errors which may not throw a MATLAB error.


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Scripts 35

Path

In order to invoke a function that function's m-file must be in the current path. There is a default path that can be

setup through the File menu or the addpath command. The order of the path is important as MATLAB searches the

path in order and stops searching after it finds the 1st

instance of that m-file name.

The current path is

the current directory (which can be seen at the top of the MATLAB window or by typingpwdat the command

prompt

the default path

Note that MATLAB will always search the current directory before searching any of the rest of the path.

nargin & nargout

The nargin and nargoutcommands are only valid inside functions since scripts are not passed any arguments. The

nargin command returns the number of passed input arguments. This is useful in conjunction with nargchk

nargchk(min, max, nargin)

where min is the minimum number of arguments necesary for the function to operate and max is the maximum

number of valid input arguments.

The nargoutcommand is useful for determining which output arguments to return. Typically, the outputs are the end

results of some algorithm and they are easily calculated. However, in some instances secondary output arguments

can be time consuming to calculate or require more input arguments than the primary output arguments do. So the

function can check the number of output arguments being requested through the nargoutcommand. If the caller isn't

saving the secondary output arguments then they do not need to be calculated.

varargin & varargout

When using MATLAB objects and functions they often allow the user to set properties. The functions and objects

come with default values for these properties but the user is allowed to override these defaults. This is accomplished

through the use of varargin. varargin is a cell array that is usually parsed where varargin{i} is a property and

varargin{i+1} is the value the user wishes for that property. The parsing is done with aforor while loop and a switch

statement.

function [out] = myFunc(in, varargin)

The varargoutoutput argument option allows for a variable number of output arguments just as varargin allows for

a variable number of input arguments. From the MATLAB site[1]

function [s,varargout] = mysize(x)nout = max(nargout,1)-1;

s = size(x);

for k=1:nout, varargout(k) = {s(k)}; end

returns the size vector and, optionally, individual sizes. So

[s,rows,cols] = mysize(rand(4,5));

returns s = [4 5], rows = 4, cols = 5.
http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/varargout.html&http://www.google.com/search?sourceid=navclient&ie=UTF-8&rlz=1T4GFRD_enUS257US258&q=varargout+MATLAB


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Scripts 36

Useful syntax guidelines

Placing the semicolon symbol after every line tells the compiler not to place that line of code in the command

prompt and then execute. This can make your programs run a lot faster. Also, placing a semicolon after every line

helps with the debugging process.

syms x y z;

w=[x y z];

e=[1 2 3];

t=jacobian(e,w);

Placing comments in your code can help other people (and yourself) understand your code as it gets more complex.

syms x y z; %syms command makes x y and z symbolic

w=[x y z];

e=[1 2 3];

t=jacobian(e,w);

Comments can also Identify who wrote the code and when they wrote it.

%Some code writer

%mm/dd/yyyy

See the 'comments' section for more details on this.

External Links

Large parts of this page come from the ControlTheoryPro.com page on M-files[2]

, Scripts[3]

, and Functions[4]

.

References[1] http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/varargout. html&http://

www.google.com/search?sourceid=navclient&ie=UTF-8&rlz=1T4GFRD_enUS257US258&q=varargout+ MATLAB

[2] http://wikis.controltheorypro. com/index.php?title=M-files

[3] http://wikis.controltheorypro. com/index.php?title=MATLAB_Scripts

[4] http://wikis.controltheorypro. com/index.php?title=MATLAB_Functions
http://wikis.controltheorypro.com/index.php?title=MATLAB_Functionshttp://wikis.controltheorypro.com/index.php?title=MATLAB_Scriptshttp://wikis.controltheorypro.com/index.php?title=M-fileshttp://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/varargout.html&http://www.google.com/search?sourceid=navclient&ie=UTF-8&rlz=1T4GFRD_enUS257US258&q=varargout+MATLABhttp://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/varargout.html&http://www.google.com/search?sourceid=navclient&ie=UTF-8&rlz=1T4GFRD_enUS257US258&q=varargout+MATLABhttp://wikis.controltheorypro.com/index.php?title=MATLAB_Functionshttp://wikis.controltheorypro.com/index.php?title=MATLAB_Scriptshttp://wikis.controltheorypro.com/index.php?title=M-files


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Comments 37

Comments

Placing comments

Comment lines begin with the character '%', and anything after a '%' character is ignored by the interpreter. The %

character itself only tells the interpreter to ignore the remainder of the same line.

In the MATLAB Editor, commented areas are printed in green by default, so they should be easy to identify. There

are two useful keyboard shortcuts for adding and removing chunks of comments. Select the code you wish to

comment or uncomment, and then press Ctrl-R to ( -/ for Mac) place one '%' symbol at the beginning of each line

and Ctrl-T ( -T for Mac) to do the opposite.

Common uses

Comments are useful for explaining what function a certain piece of code performs especially if the code relies on

implicit or subtle assumptions or otherwise perform subtle actions. Doing this is a good idea both for yourself and

for others who try to read your code. For example,

% Calculate average velocity, assuming acceleration is constant

% and a frictionless environment.

force = mass * acceleration

It is common and highly recommended to include as the first lines of text a block of comments explaining what an M

file does and how to use it. MATLAB will output the comments leading up to the function definition or the first

block of comments inside a function definition when you type:

>> help functionname

All of MATLAB's own functions written in MATLAB are documented this way as well.

Comments can also be used to identify authors, references, licenses, and so on. Such text is often found at the end of

an M file though also can be found at the beginning. Finally, comments can be used to aid in debugging, as

explained in Debugging M Files.
http://en.wikibooks.org/w/index.php?title=MATLAB_Programming/Debugging_M_Files


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Entering data at the command line 38

Entering data at the command line

The input() function lets your scripts process data entered at the command line. All input is converted into a

numerical value or array. The argument for the input() function is the message or prompt you want it to display.

Inputting strings require an additional 's' argument. Example:

%test.m

%let's ask a user for x

x = input('Please enter a value for x:')

Then running the script would produce the output:

Please enter a value for x:3

x = 3

>>

Loops and Branches

Program Flow

The idea of program flow is simple. However, implementing and using flow techniques effectivly takes practice.

MATLAB flow control is almost identical to flow control in C. There is a tremendous amount of text on the subject

of flow in C. If you do a little homework in about an hour you can know all you need to from one of numerous C

tutorials. To be good at flow control all you have to do is practice.

Here are a few concepts that you can practice using flow control to implement:

Calculate compounding interest using a while loop (don't cheat by using the algebraic form).

Create a moving average filter using a for loop

Make a counter that keeps track of keystrokes:How many times a typist hits a certain letter.


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Error Messages 39

Error Messages

As far as I've seen there is little help out there to help people decipher MATLAB's error messages. Most of the

syntax errors are not difficult to fix once you know what is causing them so this is intended to be a guide to

identifying and fixing errors in MATLAB code.

Warnings are also shown here as these often lead to errors later.

Arithmetic errors

Usually these are self-explanatory. As a reminder, here are some common functions that cannot be performed and

what MATLAB returns (along with a warning for each one):

a/0 = Inf if a > 0, -Inf if a < 0, and NaN if a = 0.

log(0) = -Inf

MATLAB defines 0^0 to be 1.

NaN will very often result in errors or useless results unless measures are taken to avoid propogating them.

???Error using ==> minus

Matrix dimensions must agree.

So check the dimensions of all the terms in your expression. Often it is an indexing mistake that causes the terms to

be of different size. If you are using power function you might add a single dot after the parameter. i.e. y=x.^2

instead of y=x^2

Matrix multiplication requires the number ofcolumns in the first matrix to equal the number ofrows in the second.

Otherwise, you get the message:

??? Error using ==> mtimesInner matrix dimensions must agree.

Note the difference between this error and the previous one. This error often occurs because of indexing issues OR

because you meant to use componentwise multiplication but forgot the dot.

Attempting to take the inverse of a singular matrix will result in a warning and a matrix of Infs. It is wise to calculate

the determinant before attempting to take the inverse or, better, to use a method that does not require you to take the

inverse since its not numerically stable.

Attempting to take a power of a nonsquare matrix results in the error

??? Error using ==> mpower

Matrix must be square.

This is usually because you meant to use componentwise exponentiation and forgot the dot.

Indexing errors

Indexing is a pain in MATLAB, it is probably one of the hardest things to get down, especially since the syntax for

an index is the same as the syntax for a function. One annoying fact is that the names of variables are case sensitive,

but the names of functions are NOT. So if you make an array called Abs and you try to index abs(1), it will return 1

no matter what the first value in the array Abs is. Unfortunately, MATLAB will not return an error for this (although

MATLAB v2008+ or so will return a warning saying that this will be changed in a later version), so a good rule of

thumb is never ever name your variables the same as a function. This clears up some indexing problems.

Some things are rather obvious but take some practice in avoiding:


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Error Messages 40

You cannot try to access part of an array that does not exist yet.

>> A = [1,3];

>> A(3)

??? Index exceeds matrix dimensions.

Unfortunately, MATLAB doesnt tell you which variable you exceeded the dimensions on if there's more than one so

you'll have to check that. This often occurs if, for example, you are using a loop to change which part of an array is

accessed, but the loop doesn't stop before you reach the end of the array. This also happens if you end up with an

empty matrix as a result of some operation and then try to access an element inside it.

You cannot try to access a negative, complex, noninteger, or zero part of an array; if you do you get this message:

>> A(-1)

>> A(i)

>> A(1.5)

>> A(0)

??? Subscript indices must either be real positive integers or logicals.

Note that MATLAB starts counting at 1, not 0 like C++. And again, it doesn't tell you which index is not real or

logical. Also note that if 0 was a logical 0 (false) then the statement A(0) would be valid and would return all 0

values in the array.

Attempting to use non-standard MATLAB syntax in your indexing will often result in the error:

>> A(1::, 2)

??? A(1::, 2)

|

Error: Unexpected MATLAB operator.

The "operator" :: is one of several possible operators that MATLAB does not accept. This could be an example of

someone trying to access all rows of A after the first one and the second column, in which case you should use the

"end" syntax, as in:

>> A(1:end, 2)

ans = 3

Make sure you are careful when using the colon operator, because it does many different things depending on where

you put it and misuse often results in these errors. Try putting in one piece of your code at a time and see what it is

doing, it may surpise you.

Assignment errors

Ah, assignment, that is using the = sign to give a variable, or certain elements of an array, a particular value.

Let's start with a classic mistake:

>> a = 2;

>> if a = 3

??? if a = 3

|

Error: The expression to the left of the equals sign is not a valid target for an assignment.

This error occurs because you meant to see if "a" equaled 3, but instead you told MATLAB to assign "a" a value of

3. You cannot do that on the same line that the if/while statement is on. The correct syntax is


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Error Messages 41

>> if a == 3

>> end

This creates no errors (and you can put anything inside the conditional you want).

You cannot have a normal array with two different classes of data inside it. For example,

>> A = @(T) (1+T)A =

@(T) (1+T)

>> A(2) = 3

??? Conversion to function_handle from double is not possible.

For such a purpose you should use cell arrays or struct arrays.

Here's the tricky one. Take a look at the following code:

>> A = [1,2,3;4,5,6;7,8,9];

>> A(2,:) = [3,5];

??? Subscripted assignment dimension mismatch.

>> A(2,:) = [1,4,5,6];


>> A(1:2, 1:2) = [1,2,3,4];


What is happening here? In all three cases, take a look at the dimensions of the left and the right hand sides. In the

first example, the left hand side is a 1x3 array but the right side is a 1x2 array. In the second, the left hand side is 1x3

while the right is 1x4. Finally, in the third, the left hand side is 2x2 while the right is 1x4. In all three cases, the

dimensions do not match. They must match if you want to replace a specific portion of an existing variable. It

doesn't matter if they have the same number of data

Documents

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