MATLAB Programming/Print Version

Chapter 1: A Tutorial Introduction

Chapter 2: Basic MATLAB Concepts

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, thecurrent directory will be .../MATLAB/work. After you start MATLAB, change the current directory by either using the toolbar at the left-hand side of thescreen, 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 hasan 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 whichMATLAB 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, followthe 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 andselect 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 Files

There are many ways to save to files in MATLAB.

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

uisave - includes user interfacehgsave - saves figures to files, *.fig by defaultdiary [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. By default the current directory is.../MATLAB/work.

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 datafrom 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 environmentvariables, 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 ofMATLAB'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 youdeclare 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.

Introduction

MATLAB is interesting in that it is dynamically compiled. In other words, when you're using it, you won't run all your code through a compiler, generatean executable, and then run the executable file to obtain a result. Instead, MATLAB simply goes line by line and performs the calculations without theneed for an executable.

Partly because of this, it is possible to do calculations one line at a time at the command line using the same syntax as would be used in a file. It's evenpossible to write loops and branches at the command line if you want to. Of course this would often lead to a lot of wasted efforts, so doing anythingbeyond very simple calculations, testing to see if a certain function, syntax, etc. works, or calling a function you put into an .m file should be done within an.m file.

Calculator

MATLAB, among other things, can perform the functions of a simple calculator from the command line. Let us try to solve a simple problem: Sam's car'sodometer reading was 3215 when he last filled the fuel tank. Yesterday he checked his odometer and it read 3503. He filled the tank and noticed that ittook 10 gallons to do that. If his car's gas tank holds 15.4 gallons, how long can he drive before he is going to run out of gas, assuming the gas mileage isthe same as before?

First let us compute the distance Sam's car has travelled in between the two gas fillings

>> 3503-3215

ans =

288

Gas mileage of Sam's car is

>> 288/10

ans =

28.8

With this, he can drive

>> 28.8 * 15.4

ans =

443.5200

443.52 miles before he runs out of gas.

Let us do the same example, now by creating named variables

>> distance = 3503-3215

distance =

288

>> mileage = distance/10

mileage =

28.8000

>> projected_distance = mileage * 15.4

projected_distance =

443.5200

To prevent the result from printing out in the command window, use a semicolon after the statement. The result will be stored in memory. You can thenaccess the variable by calling its name. Example:

>>projected_distance = mileage * 15.4;

>>

>>projected_distance

projected_distance =

443.5200

Using the command line to call functions

The command line can be used to call any function that's in a defined path. To call a function, the following general syntax is used:

>> [Output1, Output2, ..] = functionname(input1, input2,..)

MATLAB will look for a file called functionname.m and will execute all of the code inside it until it either encounters an error or finishes the file. In theformer case, it produces a noise and displays an error message in red. In the latter case, MATLAB will relinquish control to you, which you can see whenthe >> symbol is visible on the bottom of the workspace and the text next to "start" button on the bottom-left of the screen says "ready".

Use this in order to call homemade functions as well as those built into MATLAB. MATLAB has a large array of functions, and the help file as well as thiswikibook are good places to look for help on what you need to provide as inputs and what you will get back.

Be careful; the syntax for functions and for indexing arrays is the same. To avoid confusion, just make sure you don't name a variable the same as anyfunction. To ensure this, type the name of the variable you want to define in the command prompt. If it tells you:

Error using ==> (functionname)

Not enough input arguments.

then you'll have a conflict with an existing function. If it tells you:

??? Undefined function or variable '(functionname)'

you'll be OK.

External Resources

ControlTheoryPro.com (http://wikis.controltheorypro.com/index.php?title=Basic_Tutorial)

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.

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

Get a cell array of variables in saved file.

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

Reading and Writing from an Excel spreadsheet

Since 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 thecommand 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 the xlsread function use the syntax:

>>g=xlsread('filename');

This line of code reads filename.xls (from the current directory) and places it in an identical array inside MATLAB called g. You can then manipulate thearray 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) otherwiseyou 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 directoryfrom 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 Ihave 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 insideExcel 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 afile 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 soon).

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 aWindows system). To use it, go to file > import data, and select the file you want. Then, choose what column separators are present (by selecting theappropriate 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 areomitted, plusses and minuses are turned into other characters. To see the name MATLAB generated (and probably change it) type "who" in the commandprompt.

External Resources

ControlTheoryPro.com (http://wikis.controltheorypro.com/index.php?title=Category:MATLAB)

MatlabCodes.Webs.com (http://matlabcodes.webs.com?title=Category:MATLAB)

Chapter 3: Data Storage and Manipulation

Data Types and Operations on Point Values

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 rationalnumbers 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 valuesare. Note that MATLAB represents irrational numbers such as pi with rational approximations, except when using the symbolic math toolbox. See thatsection for details.

Boolean numbers are either "TRUE" or "FALSE", represented in MATLAB by a 1 and a 0 respectively. Boolean variables in MATLAB are actuallyinterchangable with doubles, in that boolean operators can be performed with arrays of doubles and vice versa. Any non-zero number in this case isconsidered "TRUE".

Most of the rational operators also work with complex numbers. Complex numbers, however, cannot be interchanged with boolean values like the realrationals 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 onentire 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 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 valueto 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

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 arrayinto 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 toround 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 thanjust its components:

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

Otherwise it returns [].

strrep(string1, replaced, replacement) replaces all instances of replaced in 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 youare 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 fprintf function. Theformat 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 usethe 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

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 allfail if any elements of the provided cell array are the empty array ( [] ) which is somewhat frustrating if the provided text file contains empty cells. Youmust 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 stringswhose 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 ofstrings, 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 amatch to the query is found.

>> strCell = {'Aa', 'AA'}; >> 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 incombination with these two functions to return the index of all the cells in which the query string was found.

>> strCell = {'Aa', 'AA'}; >> idxCell = strfind(strCell, 'a'); >> isFound = ~cellfun('isempty', idxCell); % Returns "0" if idxCell is empty and a "1" otherwise >> 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 usingregular expressions. Regular expressions are a powerful way to match patterns within strings (not just specific strings within strings). Entire books havebeen written about regular expressions, so they cannot be covered in as much detail here. However, some good resources online include regular-expresions.info (http://www.regular-expressions.info/) and the MATLAB documentation for the matlab-specific syntax. Note that MATLAB implementssome, 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 isquite 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 not discard 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 == operatorfor numeric values.

>> strcmp(1,1) ans = 0.

This section discusses anonymous functions and function handles. Both of these are portable in that rather than having to write an equation multiple timesin 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 anequation to another function for direct evaluation as needed. Anonymous functions are useful for command-line evaluation or for multiple evaluations in thesame 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 distributedprogram 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 yourprogram 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). Thefunctionality 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 dothings like solve systems of ODEs rather than only one. Anonymous functions limit you to one equation.

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 werefunctions:

% 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

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. Forexample, 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 thebest 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 theintended results.

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. Itreturns 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 youcan 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 todirectly 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

Arrays and Matrices

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. Asin 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 typedouble 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 getmore 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, thecommas 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 itsmathematical equivalent, requires all its rows and all its columns to be the same size:

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

??? Error using ==> vertcat

All rows in the bracketed expression must have the same

number of columns.

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 datatype, 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 firstnumber 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. Forexample, 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 twoarrays directly. MATLAB automatically separates the elements:

>> 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 toall 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 deeperexplanation of arrays and their operations, see Arrays and matrices.

Introduction to array operations

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 specialoperator 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 matlabeffectively. However, we won't be as precise as in mathematics when using the terms vector and matrix. In MATLAB, both are arrays of doubles (thusbeing a matrix in the real mathematical meaning), and MATLAB considers vectors as a matrices with only one row or only one column. However, thereare 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

>> [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 3

4 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 alwayspoint 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

>> 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 willoverwrite 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 theoperator (), 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

>> 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 firstcolumn, then the 2d column, etc... The column major mode is the same as 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 ofa 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 thesecond 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 =

1

4

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 =

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 find function to find the indices of allnumbers between 2 and 4 in the array, and then 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. Itthen 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

The interesting part is of course applying some operations on those arrays. You can for example use the classic arithmetic operations + and - on any arrayin matlab: this results in the vector addition and subtraction as defined in classic vector vectors spaces , which is simply the addition and subtractionelements wise:

>> [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 thesymbol * in matlab computes the matrix product, which is only defined when the number of columns of the left operand matches the number of rows ofthe right operand:

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

>> a * a

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 squarematrices, 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 usingmatrix 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 andthus 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.

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 squareproblems.

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 elementscomponentwise and returns them in a logical array of the same size as the two arrays being compared. The two arrays must have the same size. Forexample,

>> 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 causeambiguous 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 call any(array) will return true if array contains any nonzero values and false if all values are zero. It does thecomparisons 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 andonly 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

A vector in MATLAB is defined as an array which has only one dimension with a size greater than one. For example, the array [1,2,3] counts as avector. There are several operations you can perform with vectors which don't make a lot of sense with other arrays such as matrices. However, since avector is a special case of a matrix, any matrix functions can also be performed on vectors as well provided that the operation makes sense mathematically(for instance, you can matrix-multiply a vertical and a horizontal vector). This section focuses on the operations that can only be performed with vectors.

Declaring a vector

Declare vectors as if they were normal arrays, all dimensions except for one must have length 1. It does not matter if the array is vertical or horizontal. Forinstance, both of the following are vectors:

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

>> Vert = [4;5;6];

You can use the isvector function to determine in the midst of a program if a variable is a vector or not before attempting to use it for a vector operation.This is useful for error checking.

>> isvector(Horiz)

ans = 1

>> isvector(Vert)

ans = 1

Another way to create a vector is to assign a single row or column of a matrix to another variable:

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

>> Vec = A(1,:)

Vec = 1 2 3

This is a useful way to store multiple vectors and then extract them when you need to use them. For example, gradients can be stored in the form of theJacobian (which is how the symbolic math toolbox will return the derivative of a multiple variable function) and extracted as needed to find the magnitudeof the derivative of a specific function in a system.

Declaring a vector with linear or logarithmic spacing

Suppose you wish to declare a vector which varies linearly between two endpoints. For example, the vector [1,2,3] varies linearly between 1 and 3, andthe vector [1,1.1,1.2,1.3,...,2.9,3] also varies linearly between 1 and 3. To avoid having to type out all those terms, MATLAB comes with a convenientfunction called linspace to declare such vectors automatically:

>> LinVector = linspace(1,3,21)

LinVector = Columns 1 through 9

1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 1.8000

Columns 10 through 18

1.9000 2.0000 2.1000 2.2000 2.3000 2.4000 2.5000 2.6000 2.7000

Columns 19 through 21

2.8000 2.9000 3.0000

Note that linspace produces a row vector, not a column vector. To get a column vector use the transpose operator (') on LinVector.

The third argument to the function is the total size of the vector you want, which will include the first two arguments as endpoints and n - 2 other points inbetween. If you omit the third argument, MATLAB assumes you want the array to have 100 elements.

If, instead, you want the spacing to be logarithmic, use the logspace function. This function, unlike the linspace function, does not find n - 2 pointsbetween the first two arguments a and b. Instead it finds n-2 points between 10^a and 10^b as follows:

>> LogVector = logspace(1,3,21)

LogVector = 1.0e+003 *

Columns 1 through 9

0.0100 0.0126 0.0158 0.0200 0.0251 0.0316 0.0398 0.0501 0.0631

Columns 10 through 18

0.0794 0.1000 0.1259 0.1585 0.1995 0.2512 0.3162 0.3981 0.5012

Columns 19 through 21

0.6310 0.7943 1.0000

Both of these functions are useful for generating points that you wish to evaluate another function at, for plotting purposes on rectangular and logarithmicaxes respectively.

Vector Magnitude

The magnitude of a vector can be found using the norm function:

>> Magnitude = norm(inputvector,2);

For example:

>> magHoriz = norm(Horiz)

magHoriz = 3.7417

>> magVert = norm(Vert)

magVert = 8.7750

The input vector can be either horizontal or vertical.

Dot product

The dot product of two vectors of the same size (vertical or horizontal, it doesn't matter as long as the long axis is the same length) is found using the dotfunction as follows:

>> DP = dot(Horiz, Vert)

DP = 32

The dot product produces a scalar value, which can be used to find the angle if used in combination with the magnitudes of the two vectors as follows:

>> theta = acos(DP/(magHoriz*magVert));

>> theta = 0.2257

Note that this angle is in radians, not degrees.

Cross Product

The cross product of two vectors of size 3 is computed using the 'cross' function:

>> CP = cross(Horiz, Vert)

CP = -3 6 -3

Note that the cross product is a vector. Analogous to the dot product, the angle between two vectors can also be found using the cross product'smagnitude:

>> CPMag = norm(CP);

>> theta = asin(CPMag/(magHoriz*magVert))

theta = 0.2257

The cross product itself is always perpendicular to both of the two initial vectors. If the cross product is zero then the two original vectors were parallel toeach other.

Introduction to Structures

MATLAB provides a means for structure data elements. Structures are created and accessed in a manner familiar for those accustomed to programmingin 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 underscorecharacters. 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 =

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'

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 seenbelow.

>> [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

ControlTheoryPro.com (http://wikis.controltheorypro.com/index.php?title=Structures)

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 thecell_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 stringsin 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 ofthese 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 getused 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 thecommands: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 - resizecell_array(1)=[]; % remove first element - resize... etc.

External Links

ControlTheoryPro.com (http://wikis.controltheorypro.com/index.php?title=Cell_Arrays)MATLAB Programming/Sparce Matrices

Chapter 4: 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 two or more graphs in one figure, 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 makes it easy to see three-dimensional images. It follows the same syntax as the "plot" command. If you searchthe MATLAB help (not at the command prompt. Go to the HELP tab at the top of the main bar and then type plot3 in the search), you will find all theinstruction you need.

Example:

l=[-98.0556 ; 1187.074];

f=[ -33.5448 ; -240.402];

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, change the values and hit the run button in the menu bar to see theeffect.

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 MATLAB offers incomparable control over the way you can add details to your plot. From inserting text at the right positionsto labelling the axes, MATLAB from the command line offers you an easy way to create publication style graphics. With support for EncapsulatedPostScript and Adobe 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 andthe data are encapsulated into the object. A typical figure would contain at least half a dozen objects. These objects are called handles. A very tackyanalogy would be like handles to several different refrigerators with several different contents. To provide an intuitive feel. I have listed out the propertiesfrom a text handle.

Finding a handle

Various 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);

Chapter 5: M File Programming

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 andmanipulate 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 islazy 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 loopvariable).

Functions are wholly contained in themselves. They possess their own workspace keeping workspaces separate. This means that all variables necessaryfor a particular function must be passed or defined in some way. This can get tedious for complex algorithms requiring lots of variables. However, anymanipulations of variables are discarded when the function is exited. Only those output arguments provided by the function are available to the callingworkspace. 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 planningon 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. The function_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 by invoking the m-file name of the function with the necessaryinput 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 thevariable 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 goodpractice 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 encountersan 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 thenit can easily be checked by the calling function for any errors which may not throw a MATLAB error.

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 thatm-file name.

The current path is

the current directory (which can be seen at the top of the MATLAB window or by typing pwd at 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 nargout commands are only valid inside functions since scripts are not passed any arguments. The nargin command returns the numberof passed input arguments. This is useful in conjunction with nargchk

nargchk(min, max, nargin)

where min is the minimum number of arguments necessary for the function to operate and max is the maximum number of valid input arguments.

The nargout command is useful for determining which output arguments to return. Typically, the outputs are the end results of some algorithm and theyare easily calculated. However, in some instances secondary output arguments can be time consuming to calculate or require more input arguments thanthe primary output arguments do. So the function can check the number of output arguments being requested through the nargout command. If the callerisn'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 theseproperties but the user is allowed to override these defaults. This is accomplished through the use of varargin. varargin is a cell array that is usuallyparsed where varargin{i} is a property and varargin{i+1} is the value the user wishes for that property. The parsing is done with a for or while loopand a switch statement.

function [out] = myFunc(in, varargin)

The varargout output argument option allows for a variable number of output arguments just as varargin allows for a variable number of inputarguments. From the MATLAB site(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)

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.

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 makeyour 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.

Nested functions

External Links

Large parts of this page come from the ControlTheoryPro.com page on M-files (http://wikis.controltheorypro.com/index.php?title=M-files), Scripts(http://wikis.controltheorypro.com/index.php?title=MATLAB_Scripts), and Functions (http://wikis.controltheorypro.com/index.php?title=MATLAB_Functions).

Placing comments

Comment lines begin with the character '%', and anything after a '%' character is ignored by the interpreter. The % character itself only tells the interpreterto 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 foradding 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.

MATLAB also supports multi-line comments, akin to /* ... */ in languages like C or C++, via the %{ and %} delimiters. But there is a small and

important difference. In MATLAB it is not allowed that the lines starting with %{ or %} contains any other text (execpt white spaces). Otherwise it would

not work. E.g.

%{ for i = 1:10

disp(i)

end %}

gives an error, but

%{

for i = 1:10

disp(i)

end

%}

works just fine.

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 orotherwise 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 foundat the beginning. Finally, comments can be used to aid in debugging, as explained in Debugging M Files.

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 theinput() 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 >>

Control Flow

IF statement

An IF statement can be used to execute code when the logical test (expression) returns a true value (anything but 0). An "else" statement following an "if"statement is executed if the same expression is false (0).

Syntax:

if expression

statements

elseif expression2

statements

end

SWITCH statement

Switch statements are used to perform one of several possible sets of operations, depending on the value of a single variable. They are intended to replacenested "if" statements depending on the same variable, which can become very cumbersome. The syntax is as follows:

switch variable

case value1

statements(1)

case value2

statements(2)

...

otherwise

statements

end

The end is only necessary after the entire switch block, not after each case. If you terminate the switch statement and follow it with a "case" statement youwill get an error saying the use of the "case" keyword is invalid. If this happens it is probably because you deleted a loop or an "if" statement but forgot todelete the "end" that went with it, thus leaving you with surplus "end"s. Thus MATLAB thinks you ended the switch statement before you intended to.

The otherwise keyword executes a certain block of code (often an error message) for any value of variable other than those specified by the "case"statements.

Programmers who are used to C style languages, often put break statements after each case. In C, C++, and Java, not putting a break statement allowsthe code to fall through in the code above, if value1 is true, then statements(1), statements(2), etc., will execute in C-style languages. However, inMATLAB only statements(1) will execute.

TRY/CATCH statement

The TRY/CATCH statement executes a certain block of code in the "try" block. If it fails with an error or a warning, the execution of this code isterminated and the code in the "catch" block is executed rather than simply reporting an error to the screen and terminating the entire program. This isuseful for debugging and also for filtering out erroneous calculations, like if you accidentally try to find the inverse of a singular matrix, when you don't wishto end the program entirely.

Syntax:

try

statements

catch

statements

end

Note that unlike the other control flow statements, the TRY/CATCH block does not rely on any conditions. Therefore the code in the TRY block willalways be at least partially executed. Not all of the TRY block code will always be executed, since execution of the TRY ends when an error occurs. Inaddition, the statements in the CATCH block will never be executed if the TRY block does not fail.

FOR statement

The FOR statement executes code a specified number of times using an iterator. Syntax:

for iterator = startvalue:increment:endvalue

statements

end

The iterator variable is initialized to startvalue and is increased by the amount in increment every time it goes through the loop, until it reaches the valueendvalue. If increment is omitted, it is assumed to be 1, as in the following code:

for ii = 1:3

statements

end

This would execute statements three times.

WHILE statement

The while statement executes code until a certain condition evaluates to false or zero. Example:

while condition

statements

end

Forgetting to change the condition within a while loop is a common cause of infinite loops.

BREAK, CONTINUE, and RETURN

MATLAB includes the "break" and "continue" keywords to allow tighter loop control. The "break" keyword will cause the program to leave the loop it iscurrently in and continue from the next line after the loop ends, regardless of the loop's controlling conditions. If the code is in a nested loop it only breaksfrom the loop it's in, not all of them. The syntax is simply to write the word "break" within the loop where you desire it to break.

In contrast to "break", "continue" causes the program to return back to the beginning of the loop it is presently in, and to recheck the condition to see if itshould continue executing loop code or not. The code in the loop after the "continue" statement is not executed in the same pass.

If you want to exit a function entirely (as opposed to just a loop) before the last line of code, it is possible to do so using the "return" keyword. The valueof any output variables is immediately returned to the calling function. As an example of how this works, consider the following function:

function output = controlTest(doWhat);

switch doWhat

case 1

output = -1;

return;

case 2

output = 3;

end

output = output + 4;

Calling

>> output = controlTest(1)

would return output = -1, because output is defined to -1 and the return statement tells MATLAB to immediately take the current value of output andpass it back to the calling function. However, calling

>> output = controlTest(2)

would return output = 7, because output is initially defined as 3 and then 4 is added to it. Since the return statement is only executed in the case thatdoWhat=1, it is not called and the rest of the function executes.

Beware that if the output variables are not defined before calling the return statement, you will get an error, so use this with some degree of caution.

Program Flow

The idea of program flow is simple. However, implementing and using flow techniques effectivly takes practice. MATLAB flow control is almost identicalto 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 youneed 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.

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 onceyou 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 awarning 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 usingpower 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 of columns in the first matrix to equal the number of rows in the second. Otherwise, you get the message:

??? Error using ==> mtimes

Inner 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 usecomponentwise 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 totake 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 afunction. 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 andyou 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 (althoughMATLAB 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 yourvariables the same as a function. This clears up some indexing problems.

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

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 oftenoccurs 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 logical0 (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 Aafter 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 inthese 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 sameline that the if/while statement is on. The correct syntax is

>> 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];

??? Subscripted assignment dimension mismatch.

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

??? Subscripted assignment dimension mismatch.

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 1x3array 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 theright 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'tmatter if they have the same number of data points or not (as the third example shows); the dimensions must also be the same, with the exception that ifyou have a 1xn array on one side and an nx1 on the other MATLAB will automatically transpose and replace for you:

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

A = 1 2 3

1 2 3

7 8 9

If you do not want this be aware of it!

Struct array errors

Struct arrays are rather complex, and they have a rigid set of rules of what you can and can not do with them. Let us first deal with indexing within structarrays. Suppose you define the variable "cube" and want to store the volume and the length of one side of two different cubes in a struct array. This can bedone as follows:

>> cube(1).side = 1;

>> cube(1).volume = 1;

>> cube(2).side = 2;

>> cube(2).volume = 8;

This seems like a good way of storing data and it is for some purposes. However, suppose you wanted to abstract the volumes from the struct and storethem in one array. You cannot do it this way:

>> volumes = cube.volume

??? Illegal right hand side in assignment. Too many elements.

You'll notice that if you tell MATLAB to display cube.volume, it will display both values, but reassign the variable ans each time, because it is treated astwo separate variables. In order to avoid the error, you must format 'cube.volume' as an array upon assignment.

>> volumes = {cube.volume}

You can also write in a separate assignment for each cube but this is more adaptable to larger numbers of cubes.

Just like extracting data, you must input the data one at a time, even if it is the same for all instances of the root (cube).

>> cube.volForm = @(S) (S^ 3)

??? Incorrect number of right hand side elements in dot name assignment. Missing [] around left hand side is a likely cause.

>> cube(:).volForm = @(S) (S^ 3)

??? Insufficient outputs from right hand side to satisfy comma separated

list expansion on left hand side. Missing [] are the most likely cause.

Unfortunately missing [] is not the cause, since adding them causes more errors. The cause is that you cannot assign the same value to all fields of the samename at once, you must do it one at a time, as in the following code:

>> for ii = 1:2

>> cube(ii).volForm = @(S) (S^ 3);

>> end

>> cube

ans = 1x2 struct array with fields:

volume

side

volForm

The same volume formula is then found in both cubes. This problem can be alleviated if you do not split the root, which is highly recommended. Forexample, you can use a struct like this:

>> shapes.cubeVol = @(S) (S^ 3);

>> shapes.cube(1).vol = 1;

>> shapes.cube(2).vol = 8;

This avoids having to use a loop to put in the formula common to all cubes.

Syntax errors

Parenthesis errors

Unlike in C++, you are not required to terminate every line with anything but a line break of some sort. However, there are still syntax rules you have tofollow. In MATLAB you have to be especially careful with where you put your parenthesis so that MATLAB will do what you want it to.

A very common error is illustrated in the following:

>> A(1

??? A(1

|

Error: Expression or statement is incorrect--possibly unbalanced (, {, or [.

This error is simple enough, it means you're missing a parenthesis, or you have too many. Another closely related error is the following:

>> A(1))

??? A(1))

|

Error: Unbalanced or misused parentheses or brackets.

MATLAB tries to tell you where the missing parenthesis should go but it isn't always right. Thus for a complex expression you have to go through it verycarefully to find your typo. A useful trick is to try to set a breakpoint a line after the offending line. It won't turn red until the error is corrected, so keeptrying to correct it and saving the file until that breakpoint turns red. Of course, after this you have to make sure the parenthesis placement makes sense,otherwise you'll probably get another error related to invalid indecies or invalid function calls.

String errors

There are two ways that you can create a string; use the ' string ' syntax, or type two words separated by only whitespace (not including line breaks), asin

>> save file.txt variable

In this line, file.txt and variable are passed to the save function as strings. It is an occasional mistake to forget a parenthesis and accidentally try and passa string to a function that does not accept strings as input:

>> eye 5

??? Error using ==> eye

Only input must be numeric or a valid numeric class name.

These should not be hard to spot because the string is color-coded purple. Things like this occur if you uncomment a line of text and forget to change it.

Forgetting the closing ' in the other syntax for a string results in an obvious error:

>> A = 'hi

??? A = 'hi

|

Error: A MATLAB string constant is not terminated properly.

The unterminated string is color-coded red to let you know that it is not terminated, since it's otherwise easy to forget.

A common mistake with strings is to try to compare them using the '==' operator. This does not work if the strings are not the same length, becuase stringsare arrays of characters, and to compare arrays with '==' they must be the same size. To compare two strings you must use the strcmp function:

>> 'AA' == 'AaA'

??? Error using ==> eq

Matrix dimensions must agree.

>> strcmp('AA', 'AaA')

ans = 0

>> strcmp('A', 'a')

ans = 0

>> strcmp('AA', 'AA')

ans = 1

Note that MATLAB strings are case sensitive, 'A' and 'a' are not the same string.

Also beware that the ' character for beginning and ending strings is the same character indicating transposition. So if you close a string and don't begin it,you will most likely end up with an error about an undefined variable (if you're trying to transpose an undefined variable) or just get really weird resultsbecause you transposed something you didn't intend to.

Other miscellaneous errors

You cannot leave trailing functions, and if you do MATLAB gives you an error that is similar but not exactly the same as that for a missing parenthesis,since it doesn't want to venture a guess:

>> A = 1+3+

??? A = 1+3+

|

Error: Expression or statement is incomplete or incorrect.

These usually are not hard to spot, and often result from forgetting the "..." necessary to split a line.

The double colon is not the only "unexpected MATLAB operator", there is also "..", "....", and several other typos that generate this error.

If you accidentally type the ` character you get the error:

>> ??? `

|

Error: The input character is not valid in MATLAB statements or expressions.

This usually occurs because you intended to put a "1" in the equation but missed the key. Another possibility is that you named your m-fi