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Fundamentals of MATLAB
Main screen of MATLABEdit
When the MATLAB is opened for the first time after installing, you will see the MATLAB main display shown as followed (Note that the version is R2020a, which other versions may look more or less similar):
The main screen of MATLAB will consists of the following (in order from top to bottom):
 Search Bar  Can search the documentations online for any commands / functions / class
 Menu Bar  The shortcut keys on top of the window to access commonly used features such as creating new script, running scripts or launching SIMULINK
 Home Tab  Commonly used features/functions are grouped here
 Plots Tab  The plot charts is shown here. Basic charts (without additional toolbox are shown as follows):
 Line Plots, Bar Plots, Scatter Plots, Pie Chart, Histogram, Polar Plots, Geographic Plots, Contour Plots,3D Surface, Vector Field and Analytic Plots
 Apps Tab  The additional installed toolbox with related functionality are shown here
 Home Tab  Commonly used features/functions are grouped here
 Current Folder Panel — The created files are accessed at this panel
 Command Window Panel — All of the workings are done at this panel, enter commands at the command line, indicated by the prompt (>>).
 Workspace Panel — Explore data that you had created or import the data from files at this panel
Benefits of MATLABEdit
Platform IndependentEdit
MATLAB language is supported by Windows, Linux and Mac. Thus, a program written on one platform can be easily run on other platforms. This is a platform independence feature.
Full Graphics CapabilitiesEdit
MATLAB provides advanced graphics that can help visualize the scientific and engineering data very well. The graphs are highly customizable such: One can change the colors, lines and marker, add annotations, LATEX expressions, legends, the addition of multiple axes etc.
Ease of UseEdit
MATLAB is an interpreted and interactive language. Programs can be easily written and modified by a user with MATLAB, which is a builtin integrated development environment and debugger.
Good Source of HelpEdit
There are many large communities that let you learn MATLAB such as Reddit (46.5k users) , Facebook group (MATLAB Programs/Code (matlabcoding.com). Hence, you might find answers that the people that come before you that might encounter similiar problems too.
ReferencesEdit
^{[1]}
Fundamentals of MATLAB/MATLAB operator
MATLAB OperatorEdit
MATLAB have a few operator types to manipulate shown below
Note: Variable a and b belows represents number
Arithmetic OperationsEdit
Arithmetic Operator is used as mathematical operator that manipulates the number according to the formula requirement. The result is shown as numbers.
Addition  a + b 
Subtraction  a  b 
Multiplication  a * b 
Forward division  a / b 
Backward division  a \ b 
Exponentiation  a ^ b 
Assignment  a = b 
Relational OperationsEdit
Relational Operator is used to check if numbers are having any significant relationship with one or another. The results is usually is shown TRUE or FALSE.
Equal To  a == b 
Not Equal To  a ~= b 
Greater than  a > b 
Greater or equal to  a >= b 
Lesser than  a < b 
Lesser or equal to  a <= b 
Logical OperationsEdit
Logical Operator is used to check if number fulfills the logical conditions, the result is usually shown TRUE or FALSE.
Logical AND  a && b 
Logical OR  a  b 
Logical NOT  a ~ b 
Elementary Mathematics Constants and FunctionsEdit
Besides mathematical formula, there are a few mathematical constant and function that you can use to make your works in Matlab easier. More information about the functions used can be found here:Mathematical_symbols
pi  Returns value of 3.1416 (Note: Ratio of a circle's circumference to its diameter) 
sqrt(a)  Returns square root of a 
exp(1)  Returns value of 2.7183 This is exponential function (Note: it is inverse of natural log, try log(exp(1) and see the result) 
log(a)  This logarithm operator is to find natural number log of a number 
log10(a)  This base10 log operator is common logarithm for base 10 
mod(a,b) or rem(a,b)  This modulo operator returns the remainder after a is divided by b. 
: (Colon)  Generate a sequence 
round(a,b)  This rounding operator round up to the number to the nearest digit "a" by the significant digit "b"

primes(a)  Returns a list of prime numbers less than or equal to number a 
gcd(a,b)  Returns the greatest common divisors of the number of a and b. 
lcm(a,b)  Returns the least common multiples of the number of a and b. 
Trigonometry OperationsEdit
The trigonometry formula are given as followed:
Sin α  a / h
Cos α  b / c
Tan α  a / b
sin(α)  This sine operator returns sine value of argument in radians 
sind(α)  This sine operator returns sine value of argument in degree 
cos(α)  This sine operator returns cosine value of argument in radians 
cosd(α)  This sine operator returns sine value of argument in degree 
tan(α)  This sine operator returns tangent value of argument in radians 
tand(α)  This sine operator returns tangent value of argument in degree 
deg2rad(α)  Convert angle from degrees to radian 
rad2deg(α)  Convert angle from radians to degrees (Note: Try to convert the pi from radian to degrees) 
Matrix OperationsEdit
[ ]  Container for matrix 
,  Matrix row separator 
;  Matrix column separator 
OthersEdit
randi  Random integer 
Fundamentals of MATLAB/Basic MATLAB commands
Basic MATLAB commandEdit
During start to use the program, you may see double "greater than" symbols aka " >> " on the top left of command window.
You can start to type simple or complex mathematic equation to your liking.
Some of the examples are as follows:
>> 6+3  4/2
ans =
7
>> sind(30)
ans =
0.5000
or you may even assign a value to a variable / perform simple algebra equations
>> x = 200
x =
200
>> y = 120
y =
120
>> p = xy
p =
80
Note: You can learn more about MATLAB operator from this page: MATLAB Programming/Fundamentals of MATLAB/MATLAB operator
Basic CommandsEdit
These commands listed below are the commands that you usually will encounter when using MATLAB
clc  Clear command window.
clear  Remove all variable values from workspace
disp  Display the values inside of the variable / matrix
help  Display tooltip help text inside the Command Window. The help displays the help for the functionality specified by NAME, such as a function, operator symbol, method, class, or toolbox.
Hello WorldEdit
For the beginner just starting into MATLAB programming, a tutorial is available to write Hello World.
Once Hello World, which is the simplest of programs, works the beginner can move on to explore the MATLAB workspace available for developing or running Matlab code.
Using the workspace the beginner can then learn to manipulate basic MATLAB Variables. For convenience Matlab allows the workspace to be saved and loaded using *.mat files.
Boolean and Rational
IntroductionEdit
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 nonzero 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.
Note: MATLAB refers to Booleans as "logicals" and does not use the word "Boolean" in code or documentation.
Rational Operators on Single ValuesEdit
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
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 OperatorsEdit
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 =
logical
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 >, <, >=, <= respectively. All of them return a value of true or false. Example:
>>a=3;b=5;
>>a<=b
ans = 1
>>b<a
ans = 0
Boolean Operators on Single ValuesEdit
The boolean operators are & (boolean AND)  (boolean OR) and ~ (boolean NOT /negation). A value of zero means false, any nonzero 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
ReferencesEdit
^{[2]}
Complex Numbers
Complex NumbersEdit
Complex numbers are also used in MATLAB.
It consists of two parts, one is real number and one is imaginary number. It is in the form of or .
i or j returns the basic imaginary unit. i or j is equivalent to square root of 1 where the formula is ( ).
Note: The symbol i and j are interchangeable for one to another, as MATLAB just convert j into i, if equations is using two different notations as shown below.
Declaring a complex number in MATLABEdit
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 as following:
>> compnum = 1 + i
compnum = 1.000 + 1.000i
>>%Note:If you use j MATLAB still displays i on the screen
>> compnum = 1 + j
compnum = 1.000 + 1.000i
Note 1: Even if you use j to indicate complex number , MATLAB will still displays i on the screen.
Note 2: Since i is used as the complex number indicator it is not recommended to use it as a variable, since it will assume i is a variable.
>> i = 1; %bad practise to use i as variable
>> a = 1 + i
a = 2
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 complex 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.
Complex functionsEdit
However, the best practice to declare a complex number is by using function complex.
>>%Best practise to declare complex number in MATLAB
>> complex(2,6)
ans =
2.0000 + 6.0000i
If you want to declare just the imaginary number, just use the square root of negative numbers, such as followed.
>> sqrt(49)
ans =
0.0000 + 7.0000i
To declare multiple complex numbers , create two row vectors with real numbers and another with imaginary numbers. Combine both of them using complex functions
>> %create a vector consiots of real number
>> RE = [1,2,3]
RE =
1 2 3
>> %create a vector consiots of imaginary number
>> IM = [4,5,6]
IM =
4 5 6
>> %create 3 complex number
>> complex(RE,IM)
ans =
1.0000 + 4.0000i 2.0000 + 5.0000i 3.0000 + 6.0000i
Arithmetic operations that create complex numbersEdit
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.
Manipulate complex numbersEdit
Finding real and imaginary numberEdit
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=[complex(2,3),complex(4,0)]
A =
2.0000 + 3.0000i 4.0000 + 0.0000i
>> %returns 1 if complex number does not have an imaginary part and 0 if otherwise.
>> %A denotes the whole vectors
>> isreal(A)
ans =
logical
0
>> %A(2) denotes second complex number in the vector (4+0i)
>> isreal(A(2))
ans =
logical
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.
>>%Extract real number from the complex number vector A
>> real(A)
ans =
2 4
>>%Extract imaginary number from the complex number vector A
>> imag(A)
ans =
3 0
Complex conjugateEdit
To find complex conjugate , we can use conj function. If complex number, Z is , then the conjugate, Ẑ is>> conj(A)
ans =
2.0000  3.0000i 4.0000 + 0.0000i
Phase AngleEdit
To find phase angle , we can use the phase angle in the radian for each element of a complex numbers>> angle(A)
ans =
0.9828 0
ReferencesEdit
^{[3]}
 ↑ https://web.archive.org/web/20210615132903/https://www.educba.com/matlabfree/?source=leftnav
 ↑ https://web.archive.org/web/20210322123642/https://www.maths.unsw.edu.au/sites/default/files/MatlabSelfPaced/lesson8/MatlabLesson8_Logic.html
 ↑ https://web.archive.org/web/20211006102547/https://www.maths.unsw.edu.au/sites/default/files/MatlabSelfPaced/lesson1/MatlabLesson1_Complex.html
Portable Functions
Functions in MATLABEdit
A function is a group of sequential expression statements (a.k.a pseudoalgorithm) that are formed together perform a task. In MATLAB, functions are defined in separate files. The name of the file and of the function MUST be the same. Functions operate on variables within their own workspace, which is also called the local workspace, separate from the workspace you access at the MATLAB command prompt which is called the base workspace.
Functions can accept more than one input arguments and may return more than one output arguments.
The sntax of functions as followed
function [y1,...,yN] = myfunc(x1,...,xM)
where syntax declares a function named myfunc that accepts inputs x1,...,xM and returns outputs y1,...,yN .
This declaration statement must be the first executable line of the function. Valid function names begin with an alphabetic character, and can contain letters, numbers, or underscores.
Create Functions in Separate FilesEdit
To create a new function, at "Home" tab, click on "New" > "Functions" It will create a template looks like the following:
function [outputArg1,outputArg2] = untitled2(inputArg1,inputArg2)
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
outputArg1 = inputArg1;
outputArg2 = inputArg2;
end
Declare a functionEdit
To demonstrate a function usefulness, we are going to take a hypothetical situations ,
Recently, in your class there are some exchange students from America whom are consistently complaining the weather is hot outside, when they check on their weather app, they exclaimed the weather is 100 degrees outside. But as to the people who never uses the imperial units before, you might wonder, what is the temperature outside right now ?
So, to solve the question, it might be a good time to create a custom functions to convert from Fahrenheit to Celsius .
First of all, we must know the conversion formula from Fahrenheit to Celsius which is given as:
At "Home" tab, click on "New" > "Functions"
function [Ce] = convertTemp(Fa)
% Convert from Fahrenheit to Celcius
Ce = (Fa32)*(5/9);
end
Click on save button to save the functions as convertTemp.m file
Note: The filename MUST be same as function name or else it won't work !
Later, on the Current Folder Panel, select the directory where you save the function files just now.
Calling a functionEdit
To call the newly created function, do the following: On the Command Window Panel, type this command as shown
>> convertTemp(100)
ans =
37.7778
Hence, the weather outside is almost 38 Celsius degrees.
Benefits of functionsEdit
Why this is beneficial, you might ask ?
Well, from this exercise , you can see that you can just type function name to execute the calculation especially for repetitive tasks.
Just imagine for example above, it will be a real time saver to just type function convertTemp instead of manually typing formula each tims.
Type of functionsEdit
The type of functions includes such as:
 Anonymous Functions
 Local Functions
 Nested Functions
 Private Functions
 Inline function (Phased out in future version)
Anonymous FunctionsEdit
Anonymous functions allow you to define a function without creating a program file, as long as the function consists of a single statement. A common application of anonymous functions is to define a mathematical expression without creating a separate files.
Here is how the anonymous syntax looks like
output = @(arguments) expression
where, output = output to be returned arguments = required inputs to be passed expression = a single formula/logic
Here, we have an examples of converting Fahrenheit to Celsius.
>> convTempF = @(Fa) (Fa32)*(5/9);
>> convTempF(88)
ans =
31.1111
>> convTempF(60)
ans =
15.5556
Another example here is using anonymous function to convert minute to seconds (NOTE: 1 minute is equal to 60 seconds)
>> convert_min_to_s = @(t) t*60;
>> convert_min_to_s(4)
ans =
240
Local functionsEdit
Sometimes in mathematics, you might be encountering an issue where you might find a use case where function that are better to be calculated within it's own function .
Rather than running separate functions to get one output, you just need to run just one function to get the multiple output. This is where local functions comes in.
To clarify further , in a function file, the first function in the file is called the main or parent function.
Additional functions within the file are called local functions, and they can occur in any order after the main function. Local functions are only visible to other functions in the same file. These are equivalent to subroutines in other programming languages, and are sometimes called subfunctions.
The application for this local functions is in a complex function, it would be easier to be broken down to smaller piece of functions and we are certain that the functions are going to be used in same functions and not at other functions.
Examples of local functionsEdit
To illustrate an examples, we will create a function statistik which will take in a series of number and return an output of basic function of statistic such as max , min, average and standard deviation. We will give it just a sting of random numbers and it will produce all the usual statistic results.
First of all, we need to create a function named statistik , follow the instruction here at Create Functions in Separate Files
function [max,min,ave,stdev] = statistik(v) % this is the main function and can call to other local functions
% The function where it takes arguments of series and it will calculate the basic statistic info
% min function selects the smallest number in the series
% max function selects the largest number in the series
% ave function calculate the average of the series
% stdev function calculate the standard deviations
max = maxf(v);
min = minf(v);
ave = avef(v);
stdev = stdevf(v);
end %end of function statistik
function a=maxf(v)
%Sub function selects the largest number in the series
a = max(v);
end %end of function maxf
function b= minf(v)
%Sub function selects the smallest number in the series
b = min(v);
end %end of function minf
function c = avef(v)
%Sub function to calculate the average of the series
c = mean(v);
end %end of function avef
function d = stdevf(v)
%Sub function to calculate the std dev of the series
d = std(v);
end %end of function stdevf
After creating function statistik in a separate file, we generate a random set of number inside the Command Window using randi function
>> V = randi(50,1,10)
V =
25 29 12 23 49 28 27 12 25 32
We call the function statistik as followed inside the Command Window:
[maximun,minimum,average,stdeviation]=statistik(V)
maximun =
49
minimum =
12
average =
26.2000
stdeviation =
10.4435
Although you cannot call a local function from the command line or from functions in other files, you can access its help using the help function.
Specify names of both the file and the local function, separating them with a > character.
>> help statistik>avef
Sub function to calculate the average of the series
Nested FunctionEdit
Nested functions are functions that are nested entirely inside the main functions.
The primary difference between nested functions and local functions is that nested functions can use variables defined in parent functions without explicitly passing those variables as arguments.
Requirements of nested functionsEdit
(a) To nest any function in a program file, all functions in that file must use an end statement.
(b) A nested function can't be defined inside any of the program control statements, such as if/elseif/else, switch/case, for, while, or try/catch.
(c) A nested function either directly by function name , or using a function handle that you created using the @ operator (refer to anonymous function).
(d) All of the variables in nested functions or the functions that contain them must be explicitly defined. That is, you cannot call a function or script that assigns values to variables unless those variables already exist in the function workspace.
Examples of nested functionsEdit
We have a hypothetical situations where we need to estimate the weight of metal ingots which are in cylindrical shape.
First, before we started on figuring out the metal ingots weight, we need to break down the problems into smaller piece.
To figure out the weight of the metal, we need to figure out the density and before figuring out density we need to figure out volume of the metal.
To start off, before we start to know the volume of ingot, we first calculate the surface area of the cylinder base which is circle.
Area of circles is defined as
,r is radius of base circle
We can use the area of circle to calculate the volume of cylinder
,h is height of cylinder.
Lastly, we use the volume and density to calculate the weight
where D is density.
In MATLAB, we formulate the formula such as these.
Note: For the nested functions beside main funtions, we need to indent the functions .
Editor > Indent.
Note:
function[]=ingot_calc()
%This function is to calculate the price of an cylindrical ingot
r = 3 ; % radius of base circle
h = 10; % height of ingot
d = 4.5;% density of the metal
ar = circle_area;
vo = volume;
we = weight;
function a = circle_area
%calculate area of circle for the radius
a=pi*r*r;
at=['Area of circle is ',num2str(a,'%8.2f') , ' cm2'];
disp(at)
end
function v = volume
%calculate volume
v = ar* h;
vt=['Volume of the ingot is ',num2str(v,'%8.2f') , 'cm3'];
disp(vt)
end
function w = weight
%calculate weight
w = vo*d;
wt=['The weight of ingot is ',num2str(w,'%8.2f'), ' g'];
disp(wt)
end
end
When we calling ingot_calc function in the command window, it should display the values
>> ingot_calc
Area of circle is 28.27 cm2
Volume of the ingot is 282.74cm3
The weight of ingot is 1272.35 g
Inline FunctionsEdit
Inline functions are currently being phased out. Anonymous functions should be used instead. Inline functions are included here for information purposes.
>> convert_s_to_ms = inline('x*1000','x'); >> convert_s_to_ms(20) ans = 20000
Function HandlesEdit
Function handles are doubles serving as an abstract reference to the function. Handles allow an equation to be passed to another function for direct evaluation. Anonymous functions are useful for commandline evaluation or for multiple evaluations in the same mfile.
The ampersat returns the handle of a function either built into Matlab or defined in an Mfile.
To illustrate example, we need to build a tent as shown on the picture but we need to figure out what is the amount of tarp that are needed to build the carnival tent.
Therefore, we will create two separate functions which take the radius and slant height of cone (cone) plus radius and height of cylinder (cylinder) .
To refresh the your memory, formula for cone surface (remember we focus slanting area and ignore the base area) is
and cylinder surface (remember that one side of circle of cylinder is not calculated) is
, where the r is the shared radius of cylinder and cone, l is the length of slanting height of cone and finally h is height of cylinder.
Follow steps in Create Functions in Separate Files to start create totalsurftent
function [surfcone,surfcylin] = totalsurftent(r,l,h)
% The function where it takes arguments of r,l,h to calculate surface area of cylinder and cone
% r is radius
% l is slanting lenth of cone
% h is cylinder height
surfcone = sacone(r,l);
surfcylin = sacylin(r,h);
end
function on=sacone(r,l)
%Sub function to calculate face area of cylinder
on = pi*r*l;
end
function yl= sacylin(r,h)
%Sub function to calculate face area of cylinder
yl = (2*pi*r*h)+(pi*r^2);
end
We can know the surface area by typing following commands:
>> %Testing out the custom functions totalsurftent
>> [areacone,areasurfcylin] = totalsurftent(3,3,3)
areafcone =
28.2743
areacylin =
84.8230
Function Handles in mfilesEdit
If you are not familiar with mfiles, then skip this and come back.
A function handle passes an mfile 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 mfile (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 mfile to a function, you must first write the mfile, 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 mfile, thus allowing you to do things 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 handleEdit
Functions can accept function handles. To do this define them as variables in your header, and then call the handles as if they were functions:
% myadd adds two variables together function result = myfunc(func, a, b); result = func(a, b); [in a separate mfile] function sum = myadd(a, b) sum = a+b;
The command you send to myfunc looks like this:
>> result = myfunc(@myadd, 1, 2); result = 3
ReferencesEdit
^{[1]}^{[2]}^{[3]}
Strings
Declaring StringsEdit
Strings are declared using single quotes ( ' ):
>> fstring = 'hello'
fstring =
hello
Including a single quote in a string is done this way:
>> fstring = ''''
fstring =
'
>> fstring = 'you''re'
fstring =
you're
Concatenate StringsEdit
In MATLAB , multiple strings can be concatenated (linked together as a chain) using square brackets.<concatstring>=[<str1>,<str2>,<str3>,...];
>> subject='The quick brown fox ' %sentence beginning
subject =
'The quick brown fox '
>> verb = 'jumps over '
verb =
'jumps over '
>> object='the lazy dog'
object =
'the lazy dog'
>> phrase=[subject,verb,object]
phrase =
'The quick brown fox jumps over the lazy dog'
Inputting stringsEdit
To let user input , we can use input functions>> name=input('Enter your names: ','s')
Enter your names: Matlab_User
name =
'Matlab_User'
String manipulationsEdit
Count the repeating wordsEdit
Consider the following toungetwisterWe would like to know how many times of the word wood appeared in that tounge twister. We can use the count function.How much wood would a woodchuck chuck
if a woodchuck could chuck wood?
He would chuck, he would, as much as he could,
and chuck as much wood as a woodchuck would
if a woodchuck could chuck wood.
>>%Declare woodchuck twister as an characther vectors
>> twister = 'How much wood would a woodchuck chuck if a woodchuck could chuck wood? He would chuck, he would, as much as he could, and chuck as much wood as a woodchuck would if a woodchuck could chuck wood.'
twister =
'How much wood would a woodchuck chuck if a woodchuck could chuck wood? He would chuck, he would, as much as he could, and chuck as much wood as a woodchuck would if a woodchuck could chuck wood.'
>> count(twister,"wood")
ans =
8
Note that the function count are counting occurrences of pattern in strings .
Therefore, it will counting the word "wood" inside the word "woodchuck"
Now, we have have another examples to count the word " the" of the famous proverbs ofalltimeThe quick brown fox jumps over the lazy dog
phrase = 'The quick brown fox jumps over the lazy dog'
%count function is casesensitive by default . It did not count The with capital 'T'
>> count(phrase,'the')
ans =
1
%need to use IgnoreCase to turn off the casesensitive words
>> count(phrase,'the','IgnoreCase',true)
ans =
2
Finding lengths of stringEdit
At times, you might be needing to find the length of words in a sentence, here is the length(string') functions comes to the rescue.>> length(phrase)
ans =
43
Extracting words from StringsEdit
To extracting certain words in the string, need to stringName(indexnumberfirst:indexnumberlast) .
We using the same example phrase as above.
Note that even empty space is consider as a string.
Index Number  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43 
String  T  h  e  q  u  i  c  k  b  r  o  w  n  f  o  x  j  u  m  p  s  o  vv  e  r  t  h  e  l  a  z  y  d  o  g 
Based on this example, if we wanted to extract the word brown fox and lazy dog,
we can see that each word is represented by index number (11:19) and index number (36:43) respectively. In MATLAB , we can type following commands:>> phrase(11:19)
ans =
'brown fox'
>> phrase(36:43)
ans =
'lazy dog'
Lowercase and Uppercase of StringsEdit
For the string manipulations such as converting the strings to upper and lower cases, we can use lower and upper functions. This will make the strings all in lowercase and uppercase characthers respectively.>> upper(phrase)
>> %Convert the string to uppercase
ans =
'THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG'
>> lower(phrase)
>> %Convert the string to lowercase
ans =
'the quick brown fox jumps over the lazy dog'
Reverse StringsEdit
To reverse the string , we can use reverse / flip function. This will make the string reverse from the last index number to first index number and vice versa.>> reverse(phrase)
ans =
'god yzal eht revo spmuj xof nworb kciuq ehT'
Replace Characters in StringsEdit
To replace certain words in the strings, we can use replace functions
The syntax of replace functions are as followed: replace(stringName,oldword,newword)>>% We don't want brown fox, we want to change to orange fox
>> replace(phrase,'brown','orange')
ans =
'The quick orange fox jumps over the lazy dog'
>>%declare vector where the old words are going to be replaced
>> old={'fox','dog'}
old =
1×2 cell array
{'fox'} {'dog'}
>>%declare vector where the new words are going to do the replaing
>> new={'cheetah','sloth'}
new =
1×2 cell array
{'cheetah'} {'sloth'}
>> % Replace old words (fox) and (dog) into (cheetah) and (sloth) . Make sure sequence is in correct order
>> replace(phrase,old,new)
ans =
'The quick brown cheetah jumps over the lazy sloth'
Strings as a Character ArrayEdit
Strings in MATLAB are an array of characters. To see this, executing the following code:
>> fstring = 'hello';
>> class(fstring)
ans = char
Because strings are arrays, many array manipulation functions work including: size, transpose, and so on. Strings may be indexed to access specific elements.
Performing arithmetic operations on character arrays converts them into doubles.
>> fstring2 = 'world';
>> fstring + fstring2
ans = 223 212 222 216 211
These numbers are from the ASCII standard for each character in the array. These values are obtained 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 integervalued 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
Special String FunctionsEdit
Since MATLAB strings are character arrays, some special functions are available for comparing entire strings rather than just its components:
deblankEdit
deblank removes white spaces from the string.
findstrEdit
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 [].
strrepEdit
strrep(string1, replaced, replacement) replaces all instances of replaced in string1 with replacement
strcmpEdit
Strings, unlike rational arrays, do not compare correctly with the relational operator. To compare strings 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 == operator for numeric values.
>> strcmp(1,1)
ans = 0.
num2strEdit
Convert numbers to character . This functions is useful when you want to use function disp values to limit the display of decimal point.
>>%Limit the display of pi value to 9 decimal points
>> num2str(pi,'%1.9f')
ans =
'3.141592654'
Displaying values of string variablesEdit
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 fprintf function. 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
Cell arrays of stringsEdit
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.
>> 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 in combination 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 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 regularexpresions.info and the MATLAB documentation for the matlabspecific 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.
The MATLAB Command Prompt
IntroductionEdit
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, generate an executable, and then run the executable file to obtain a result. Instead, MATLAB simply goes line by line and performs the calculations without the need 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 even possible 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 anything beyond 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.
ExamplesEdit
MATLAB can perform the functions of a simple calculator from the command line. Here is a simple mathematics problem:
Sam's car's odometer 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 it took 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 is the same as before?
% First let us compute the distance Sam's car has travelled in between the two gas fillings >> 35033215 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 = 35033215 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 then access the variable by calling its name. Example:
>>projected_distance = mileage * 15.4; >> >>projected_distance projected_distance = 443.5200
External ResourcesEdit
Basic Reading and Writing data from a file
MATLAB file typesEdit
There are two file types used by MATLAB namely .m and .mat files
 .m / .mat files: Standard MATLAB files (Most functions in .mat can be supported by the older version off MATLAB)
 .mlx files: Live Code File Format. This format were just introduced on MATLAB version R2016a. This type of files storing the live scripts/live functions that uses the Live Code file format.
Import functionsEdit
The function that usually are used to import data into MATLAB : importdata(filename)
importdata(filename) can loads data into array.
% sample script of loading an images >> A = importdata('example1.png'); imread(A)
Loading DataEdit
load(filename) can loads data from filename. The files can be text, images , and even audio files.
% sample script of loading an audio >> B = load('example2.mp3'); audioread(B,single,1.0)
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')
Saving DataEdit
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.mat', 'myData*', 'ASCII')
 Append new variables to the data file.
>> save('mySave.mat', 'newData*', 'append')
Excel Spreadsheets I/OEdit
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 the command line first since it is often necessary to import the data while an mfunction is being evaluated.
Reading Excel SpreadsheetsEdit
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 the array g any way you want. Make sure that the file you choose is in the same directory were you save your Mfiles (usually the work directory) otherwise you get an error. You can specify the path to a file but, this can get messy.
Writing Excel SpreadsheetsEdit
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.
Text files I/OEdit
Reading Text FilesEdit
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 an 'unrecognized character' error.
The easiest way to write to a nonexcel 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).
MATLAB File I/O: from the Graphical User InterfaceEdit
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 ResourcesEdit
File Name Types
There are many types of files that are used in MATLAB. These are some of the few of commonly used files used for MATLAB.
.m
It consists a MATLAB script. This is a platformindependent file, so you can use the same scripts on whatever operating system (Windows, Linux,Mac) you’re working on at any time.
This file also allows you to create a script on one OS and share it with others, even when they use a different OS than you do. MATLAB script files are always written using the MATLAB language.
.mat
It consists of access to any data you saved on workspace.
To save this file, click the "Save Workspace" and to load the data click "Load Data"
.slx
Contains a Simulink model.(Note that SIMULINK is different products from MATLAB)
Simulink is an addon product for MATLAB that provides a block diagram environment for performing simulations.
.fig
Provides access to any plots or other graphics you create. Keep in mind that the file contains all the information required to reconstruct the chart, but does not contain the graphic of chart itself.
This approach means that the chart's plot is accessible on any OS that MATLAB supports.
.mlapp
A MATLAB application created using the MATLAB App Designer.
MATLAB application lets you share your code in a packaged form (like executable files) with other people, and you can create one without having much of programming experience
Vector and Matrices
What is scalar,vector and matrix ?Edit
ScalarEdit
Scalars are the physical quantities that are described by magnitude only. In other words, scalars are those quantities that are represented just by their numerical value, such as 3, 5, 0.368, etc.
VectorEdit
A vector is an array of numbers or a list of scalar values in one dimensional array of numbers (can be in a row or column).
This example vector A below is row vector
This example vector B below is column vector
MatrixEdit
A matrix is an ordered rectangular array arrangement of numbers. They are stored as twodimensional arrays in MATLAB.
A matrix having m rows and n columns is called a matrix of order m × n or simply m × n matrix.
It can be represented by one or more rows (i) AND one or more columns (j).
Back in Introduction chapter , MATLAB was originally designed to carry out operations with matrices, and received the name of MATrix LABoratory that subsequently was reduced to MATLAB.
It is possible to find applications of matrices not only in the mathematics areas, but also in a great deal of applications in engineering, in physics, in finance, in accounting, in chemistry and in biology, perhaps more.
There are many types of matrices with followings as shown
Rectangular Matrix (Where no. of row and column are unequal)  Square Matrix (Where no. of row and column are same)  Row Matrix (Matrix with one row , aka row vector)  Column Matrix (Matrix with one column , aka column vector)  Diagonal Matrix (Square Matrix with nondiagonal elements equal to zero ) 




Scalar in MATLABEdit
Scalar in MATLAB looks like assigning a variable to a number such as followed:
a = 6
Vectors in MATLABEdit
You can type following in MATLAB
For row vector , just type comma "," to separate each number
>> VR = [6,2,5]
VR =
6 2 5
For column vector , just type semicolon ";" to separate each number
>> VC = [9;1;6]
VC =
9
1
6
Matrix in MATLABEdit
In MATLAB, to create matrix (or matrices), there is 3 important operator to be used
(a) Bracket "[" "]" as container for the matrix
(b) Comma , as matrix row separator
(c) Semicolon ; as matrix column separator
For example, we are creating 4X3 matrix in MATLAB using following commands.
>> M = [4,8,9,6;9,6,9,6;3,6,9,6]
M =
4 8 9 6
9 6 9 6
3 6 9 6
Vector and Matrices/Special Matrices
Special MatricesEdit
Matrix of onesEdit
We can create matrix consists using the functions ones with m numbers of rows and n numbers of columns
>> ones(3,3)
ans =
1 1 1
1 1 1
1 1 1
Matrix of zeroesEdit
We can create matrix consists using the functions zeros with m numbers of rows and n numbers of columns
>> zeros(3,3)
ans =
0 0 0
0 0 0
0 0 0
Identity MatricesEdit
An identity matrix is a square matrix in which each of the elements of its diagonal is a 1 and each of the other elements is a 0.
An identity matrix is used for following purposes:
(a) To verify whether any two given matrices are inverses of each other.
A and B in examples below are inverse to one another
>> A=[3,2;1,1]
A =
3 2
1 1
>> B=[1,2;1,3]
B =
1 2
1 3
>> A*B
ans =
1 0
0 1
(b) To find the inverse of a matrix
Note 1: Not every inverse matrix can use have identity matrix
Note 2: Command "eye(n)" can be used to create identity matrix in a flash, n is the size of matrix
>> A=[3,2;4,3]
A =
3 2
4 3
>> eye(2)
ans =
1 0
0 1
>> eye(2)/A
ans =
3 2
4 3
(c) To find the eigenvalues and eigenvectors.
Eigenvalue is defined as a scalar associated with a given linear transformation of a vector space and having the property that there is some nonzero vector which when multiplied by the scalar is equal to the vector obtained by letting the transformation operate on the vector.
Let say we have a matrix A as followed:
To find lambda, we need to know the equation for finding eigenvalue with following formula :
But MATLAB provided a simple way to find eigenvalue using command "eig"
>> A=[1,4;3,2]
A =
1 4
3 2
>> lambda = eig(A)
lambda =
2
5
Magic Square MatricesEdit
A magic square is basically where the sum of the elements in each column and the sum of the elements in each row are the same and there are no repeating numbers. We can create a magic square use this command M=magic(n). The order n must be a scalar greater than or equal to 3 in order to create a valid magic square.
For more info, can refer to this well written Wikibooks on this topic: Puzzles/Luoshu Squares
For example , we can create a magic square with matrices 5 by 5
>> % creating 5X5 matrix magic square
>> c = magic(5)
c =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
Vector and Matrices/Operations on Matrices
Basic Matrix OperationEdit
Addition and subtractionEdit
We can add and subtract the matrices if both of them are of same number of rows and columns.
Examples as follows:
>> a = [7,9,4;6,2,5]
a =
7 9 4
6 2 5
>> b=[2,0,1;4,7,3]
b =
2 0 1
4 7 3
>> % Addition of a and b matrices
a+b
ans =
9 9 5
10 9 8
>> % Subtraction of a and b matrices
ab
ans =
5 9 3
2 5 2
Matrix multiplicationEdit
For matrix multiplications, there are 2 ways to do multiplications.
(i) Matrix multiplications (using symbol * or mtimes)
Requirements is that the number of columns in the first matrix must be same as the number of rows in the second matrix.
As examples shown on the right , matrix A have 3 X 2 and matrix B have 2 X3
Therefore , 2 X 3 <> 3 X 2 , hence, it fulfils the requirements above.
Also, take note that the resulting matrix sizes is based on number of rows of first matrix with number of columns in second matrix.
>> A=[4,2,4;8,3,1]
A =
4 2 4
8 3 1
>> B=[3,5;2,8;7,9]
B =
3 5
2 8
7 9
>> mtimes(A,B)
ans =
44 72
37 73
>> A*B
ans =
44 72
37 73
As shown, the matrix C have 5X4 and matrix D have 3X2
5X 4 <> 3X2, therefore it cannot fulfill the conditions and unable to solve it.>> %Demonstrations what if matrices dimensions are incorrect
>> C=randi(10,5,4)
C =
2 10 10 3
2 10 4 5
3 5 2 1
5 5 8 2
1 4 4 10
>> D=randi(10,3,2)
D =
10 3
6 4
1 9
>> mtimes(C,D)
Error using *
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first
matrix matches the number of rows in the second matrix. To perform elementwise
multiplication, use '.*'.
>> A.*B % want to show dot product unable to solve this multiplication issues
Matrix dimensions must agree.
Creating Random Integer MatrixEdit
To generate random integer matrix, can type the following randi(IMAX,M,N)
Note: IMAX is the maximum integer (starting from 1) and M*N matrix
Examples as followed:
>> randi(50,3,4)
ans =
9 14 42 48
36 3 35 2
2 5 16 22
TransposeEdit
Using the matrices above, we can transpose the matrices. Transpose matrices usually just switch the row to column and columns into rows. The picture shown just demonstrate the transpose operation. One of the application of transpose the matrix is to crytography.
There are two ways to go about it. One is add ' to the end of the matrix that are going to be transpose or function transpose.
Back to the magic square example above, we are going to transpose it. We can see , it is transpose along the diagonal line looks like this : \
>> % transpose matrix c to d
>> d = c'
d =
17 23 4 10 11
24 5 6 12 18
1 7 13 19 25
8 14 20 21 2
15 16 22 3 9
DeterminantEdit
The determinant of matrix is a special number that is defined only for square matrices.
A determinant is used to find the solution of a system of linear equations and determine the inverse of a matrix.
Determinant of 2X2 matrix :
Determinant of 3X3 matrix :
>> A=[6,1,1;4,2,5;2,8,7]
A =
6 1 1
4 2 5
2 8 7
>> det(A)
ans =
306.0000
InverseEdit
Inverse of matrix is reciprocal matrix where the formula is denoted by
, where the adj is representing adjoint of matrix.
Note: Not all matrix have inverse, if their determinant is equal to zero.
>>%matrix inversion using manual method
>> M=[2,1,3;5,3,1;3,2,3]
M =
2 1 3
5 3 1
3 2 3
>> %First we find the matrix determinant
>> DM = det(M)
DM =
1.0000
>>%Since determinant IS NOT equal to 0, we can find the matrix inverses
>> AM = adjoint(M)
AM =
7.0000 9.0000 10.0000
12.0000 15.0000 17.0000
1.0000 1.0000 1.0000
>> (1/DM)*AM
ans =
7.0000 9.0000 10.0000
12.0000 15.0000 17.0000
1.0000 1.0000 1.0000
%shortcut using function inv which should be same as manual calculation above
>> inv(M)
ans =
7.0000 9.0000 10.0000
12.0000 15.0000 17.0000
1.0000 1.0000 1.0000
There are many applications of matrix such as:
Crytography : where it is used to encrypt message codes. Matrices are used by programmers to code or encrypt letters. A message is made up of a series of binary numbers that are solved using coding theory for communication. As a result, the concept of matrices is used to solve such equations.
In physics, the Inverse matrix is used to explore electrical circuits, quantum mechanics, and optics. These matrices are crucial in the measuring of battery power outputs and the conversion of electrical energy into other useable energy by resistors. When applying Kirchhoff’s laws of voltage and current to solve problems, the inverse matrices are extremely significant.
ReferencesEdit
^{[4]}^{[5]}^{[6]}^{[7]}
 ↑ https://blogs.mathworks.com/loren/2008/01/16/nestedfunctionsandvariablescope/
 ↑ https://web.archive.org/web/20220727140850/https://www.geeksforgeeks.org/functionsinmatlab/
 ↑ https://web.archive.org/web/20220730143213/https://www.educba.com/matlabfunctions/
 ↑ https://web.archive.org/web/20220712153202/https://collegedunia.com/exams/applicationsofdeterminantsandmatricesandsolvedexamplesmathematicsarticleid2195
 ↑ https://web.archive.org/web/20220719154910/https://www.embibe.com/exams/inversematrix/
 ↑ https://web.archive.org/web/20220814062118/https://www.theclickreader.com/dotproductsandmatrixmultiplication/
 ↑ https://web.archive.org/web/20220814062138/https://www.theclickreader.com/matrixtransposedeterminantsandinverse/
Vector and Matrices/Operations on Vectors
Operation on VectorsEdit
Constructing VectorsEdit
If a vector's elements is following the sequential additions, we can just use parentheses with the following:
As for example, if we want to have a vector starting with number 1 and ends with number 19 with the incremental values of 3, we can type commnads shown below
>> V = (1:3:19)
V =
1 4 7 10 13 16 19
Accessing VectorEdit
To access the values in vector , you just need to specify the vector and the array index, from 1 to n .
Using example of vector V above, we access single elements of vector V in third elements which we type commands as followed:
>> V(3)
ans =
7
We can access multiple elements by typing the start index and the end index For example, we need to access element no 3 up to element no 6, we type as followed:
>> V(3:6)
ans =
7 10 13 16
Finding LengthEdit
We can also use length function to knows what is the length of the vector ,for example we can know what is the length of V. There are 7 elements in vector V, therefore the answer should be 7
>> length(V)
ans =
7
Sum VectorEdit
We can find the sums of vector using sum function, it get this values by adding all of the numbers inside vector together: For example, 1+4+7+10+13+16+19
>> sum(V)
ans =
70
Finding Max and MinEdit
Respectively we can know which is the biggest and smallest number in a vector which we can use by using min and max functions
>> min(V)
ans =
1
>> max(V)
ans =
19
Finding MeanEdit
The mean function is to find the center/middle value inside the vector
>> mean(V)
ans =
10
Finding AverageEdit
The average function is to find the average of the vector
>> average(V)
ans =
10
>> % Another way of finding average
>> sum(V)/length(V)
ans =
10
Finding Standard DeviationEdit
To find standard deviation , std function is needed
The standard deviation is a measure of the amount of variation or dispersion of a set of values.
A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
>> std(V)
ans =
6.4807
Random PermutationEdit
There are two different ways to create random permutations for vector
a. randperm(N) returns a vector containing a random permutation of the integers 1:N.
>> P=randperm(7)
ans =
1 6 2 3 4 5 7
b. randperm(N,K) returns a row vector containing K unique integers selected randomly from 1:N
>>>> P=randperm(7,5)
P =
5 1 6 2 3
Sorting VectorEdit
You may want to sort the vectors, you can do this MATLAB.
If the vectors are to be sorted in descending manner, use this example as followed. Note, we use the random permutation example b above.
>> % using argument 'descend' to sort from big to small number
>> S=sort(P,'descend')
S =
6 5 3 2 1
>> % using argument 'asscend' to sort from small to big number
>> S=sort(P,'ascend')
S =
1 2 3 5 6
Calculating dot productsEdit
To find dot product,you can use the dot functions
NOTE: The two vectors must have the same length. The answer will usually in the forms of scalar .
The dot product of vector are calculated as followed
>> % creating row vector A and B
>> A = [3 ,7 , 2]
A =
3 7 2
>> B = [1,2,5]
B =
1 2 5
>> dot(A,B)
ans =
27
Calculating cross productsEdit
To find cross product,you can use the cross functions
NOTE: The two vectors must have the same length of 3. The answer will usually in the forms of vector 3 .
TODO: Search a picture that can illustrate the cross product well.
>> cross(A,B)
ans =
31 13 1
Calculating commonly used values in vectorEdit
To find the most duplicated values in the vector, we can use the mode functions.>>%create vectors with random numbers
>> A=randi(50,1,10)
A =
18 42 30 28 46 15 38 38 20 29
>> mode(A)
ans =
38
>>%38 appear twice in that vector
Arrays
Introduction to ArraysEdit
An array is the most fundamental data type in MATLAB. In MATLAB, as in many traditional languages, arrays are a collection of several values of the same type. The string and number data type formerly presented are particular cases of arrays.
A matrix is an array with two dimensions. Most arrays have the same data type; however, a cell array is an array with varying data types. If no data type is specified for numbers, then the default data type is the equivalent to the double precision floating point in the C programming language on the same architecture. For example on x86 and PowerPC a double has 64 bits.
Declaring ArraysEdit
Row and Column ArraysEdit
A row array is created using comma separated values inside brackets:
>> array = [0, 1, 4, 5] array = 0 1 4 5
Sometimes commas are omitted for simple row arrays. Omitting commas is not recommended because in larger more complex arrays whitespaces can be ambiguous. Commas almost always indicate an array is horizontal.
A column array is created using semicolons to separate values:
>> column = [1; 2; 3] column = 1 2 3
Declaring multidimensional arraysEdit
A two dimensional array (or a matrix) is declared with commas separating columns, and semicolons separating rows:
>> matrix = [1, 2, 3; 4, 5, 6] matrix = 1 2 3 4 5 6
Simple matrix manipulation is the basis of many linear algebra computations. To use arrays of more than two dimensions, a matrix has to be extended using indexing.
When declaring arrays in MATLAB all rows and all columns need have same size. If not an error message will be generated:
>> matrix = [1, 2, 3; 4, 5] ??? Error using ==> vertcat All rows in the bracketed expression must have the same number of columns.
Indexing ArraysEdit
Arrays are indexed using integers. To return a single element in a simple array, use a single integer.
>> array = [0, 1, 4, 5]; >> array(3) ans = 4
To return a single element in a two dimensional array one number as a row index and the second as a column index.
>> matrix = [1, 2, 3; 4, 5, 6]; >> matrix(2,2) ans = 5
To return multiple elements in an array an array can be used as an index.
>> array = [0, 1, 4, 5]; >> array([1 3]) ans = 0 4
To return the last element of an array use (end).
>> array = [0, 1, 4, 5]; >> array(end) ans = 5
A range of indexes can be returned using a colon(:)
>> array = [0, 1, 4, 5]; >> array(2:end) ans = 1 4 5
Properties of MATLAB arrays and matricesEdit
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 builtin 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. Monodimensional arrays are actually a special case of multidimensional 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?Edit
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:
>> 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.
Introduction to array operations
Introduction to array operationsEdit
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.
BasicsEdit
Accessing elements of a matrixEdit
Using a Single IndexEdit
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.
Using Multiple IndexesEdit
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
Using A Unique IndexEdit
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 as in Fortran, and the contrary of the order in the C language.
>> a = [1, 2, 3; 4, 5, 6]; >> a(3) ans = 2
Using a Colon (:) for a Block IndexEdit
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 = 1 4 2 5 3 6
Using the end OperatorEdit
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 AddressingEdit
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 all numbers 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 <= 4); >> 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 <= 4) ans = 2.1 3.2
Basic operationsEdit
Rational Operators on ArraysEdit
Addition and SubtractionEdit
The interesting part is of course applying some operations on those arrays. You can for example use the classic arithmetic operations + and  on any array in matlab: this results in the vector addition and subtraction as defined in classic vector vectors spaces , which is simply the addition and subtraction elements wise:
>> [1, 2, 3]  [1, 2, 1] ans = 0 0 2
Multiplication by a ScalarEdit
The multiplication by a scalar also works as expected:
>> 2 * [1, 2, 3] ans = [2, 4, 6]
Multiplying and Dividing ArraysEdit
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 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
Componentwise OperationsEdit
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.
Nonsquare 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.
TransposeEdit
A transpose of a matrix is taken using .'
>> array = [1,2;3,4] array = 1 2 3 4 >> array.' ans = 1 3 2 4
Boolean Operators on ArraysEdit
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 two arrays 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 call any(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.
Concatenating ArraysEdit
Concatenating arrays involves sticking arrays together.
Horizontal ConcatenatingEdit
Horizontal concatenation is done by treating an array as if it were a variable included in a row.
>> a = [1,2;3,4]; >> b = [5,6;7,8]; >> c = [a,b] c = 1 2 5 6 3 4 7 8
Vertical ConcatenatingEdit
Vertical concatenation is done by treating an array as if it were a variable included in a column.
>> a = [1,2;3,4]; >> b = [5,6;7,8]; >> c = [a;b] c = 1 2 3 4 5 6 7 8
Solving Linear SystemsEdit
To solve a linear system in the form Ax = b use the "\" operator.
>>A = [4 5 ; 2 8]; b = [23 28]'; x = A\b x = 2 3
Basic vector operations
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 a vector. 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 a vector 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 matrixmultiply a vertical and a horizontal vector). This section focuses on the operations that can only be performed with vectors.
Declaring a vectorEdit
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. For instance, 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 the Jacobian (which is how the symbolic math toolbox will return the derivative of a multiple variable function) and extracted as needed to find the magnitude of the derivative of a specific function in a system.
Declaring a vector with linear or logarithmic spacingEdit
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, and the 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 convenient function 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 in between. 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 points between the first two arguments a and b. Instead it finds n2 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 logarithmic axes respectively.
Vector MagnitudeEdit
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 productEdit
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 dot function 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 ProductEdit
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's magnitude:
>> 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 to each other.
Vectoring Mathematics
MATLAB is a vector programming language. The most efficient use of MATLAB will involve taking advantage of the builtin capabilities for manipulating data instead of using constructs such as loops.
Basic MathEdit
Most arithmetic operators will work as expected on vectors:
>> a = [2 43 943 78];
>> 5 * a
ans =
10 215 4715 390
>> a / 2
ans =
1.0000 21.5000 471.5000 39.0000
>> 0.2 + a
ans =
2.2000 43.2000 943.2000 78.2000
Likewise, all of these operations can be done with matrices for the expected results.
Most MATLAB functions, such as sin
or log
, will return a vector or matrix of the same dimensions as its input. So to compute the sine of all the integers between 0 and 10, it suffices to run
>> sin(0:10)
and the returned vector will contains ten values.
Per Element OperationsEdit
Operators such as the carrot (^) or multiplication between vectors may not work as expected because MATLAB sees vectors the same as any other matrix, and so performs matrix power and matrix multiplication. All operators can be prefixed by a .
to make it explicit that an operation should be performed on each element of the matrix. For example, to compute the differences of the sine and cosine function squared for all integers between 1 and 4, one can use:
>> (sin(1:4)  cos(1:4)).^2
ans =
0.0907 1.7568 1.2794 0.0106
as opposed to
>> (sin(1:4)  cos(1:4))^2
??? Error using ==> mpower
Matrix must be square.
which results from MATLAB's attempt to square a 1x4 vector using matrix multiplication.
Using .*
or ./
allows one to divide each element of a matrix or vector by the elements of another matrix or vector. To do this, both vectors must be of the same size.
Converting Loops to Vectorbased mathematicsEdit
Since MATLAB is a vector language, an artificial algorithm such as
x = [];
v = [5,2,4,6];
for i=1:4
x(i) = v(i) * ((i+32)/2  sin(pi/2*i));
if(x(i) < 0)
x(i) = x(i) + 3;
end
end
can be done far more efficiently in MATLAB by working with vectors instead of loops:
i = 1:4;
v = [5,2,4,6];
x = v .* ((i+32)/2  sin(pi/2*i));
x(x<0) = x(x<0) + 3;
Internally, MATLAB is of course looping through the vectors, but it is at a lower level then possible in the MATLAB programming language.
Arrays/Struct Arrays
Introduction to StructuresEdit
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 casesensitive. 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 StructuresEdit
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.
>> a.c = 'test' a = c: 'test'
Structures can be declared as needed and so can the fields.
Arrays of StructuresEdit
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 FieldsEdit
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 ElementsEdit
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'}
Assigning values to a field of each struct array elementEdit
Matlab provides tools to assign values to a field of each array element. Consider the following struct array:
foo = struct('field_a',{1,2,3,4}, 'field_b',{4,8,12,16})
The following command assigns the same value to the field_b field of each array element:
value = 1;
[foo.field_b] = deal(value)
To assign different values to each array element:
value = {4,8,12,16};
[foo.field_b] = value{:}
Subarrays through logical addressingEdit
With Matlab, it's possible to extract a subarray from an array by using logical indexing. Consider the following struct array:
foo = struct('field_a',{1,2,3,4},'field_b',{4,8,12,16})
To obtain a subarray from foo where all foo.field_a values are equal to 2, a boolean array can be used to perform logical indexing. So, a boolean test that returns a boolean array for this purpose would be:
[foo.field_a] == 2
So, by using this boolean array to perform logical indexing, Matlab defines a struct array whose elements consist of those from foo whose field_a value is equal to 2 by doing:
foo([foo.field_a] == 2)
Cell Arrays
Cell Array IntroductionEdit
Cell Arrays can contain differing information in every element. These types of arrays are useful when interacting with spreadsheet software.
Creating Cell ArraysEdit
Cell arrays follow the same conventions as regular arrays except instead of square brackets use curly brackets.
array = [1, 2, 3; 4, 5, 6]; cell_array = {1, 2, 3; 4, 5, 6};
Cell arrays have fewer limitations than regular arrays. The regular array can hold strings; however, the string in each element must be the same length. If one element in a regular array is a string then 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 fewer limitations for the content of a cell array comes complications. While cell arrays are a powerful tool, these arrays work differently because each element can be almost anything.
Dynamic ResizingEdit
Cell arrays can be dynamically resized, which is a key feature in more advanced data structures. For example, a queue data structure using the commands:
cell_array{end+1}='a'; cell_array{end+1}='b';
An element can be popped from the front of the queue using the commands:
cell_array(1)=[]; % remove first element  resize cell_array(1)=[]; % remove first element  resize
UsesEdit
GUI TablesEdit
Cell arrays are used when displaying a table to a figure.
uitable('Data',{'hello',1;2,'there'})
Converting to and from cell arraysEdit
Converting From a Numeric Array into a Cell ArrayEdit
Use num2cell to convert from a numeric into a cell array.
>> cell_array = num2cell(numeric_array);
Converting From a Cell Array into a Numeric ArrayEdit
Use cell2mat to convert from a cell into a numeric array.
>> numeric_array = cell2mat(numeric_cell_array);
External LinksEdit
Plot
IntroductionEdit
The plot command plots 2D data linearly to the current axis on the current figure.
UsageEdit
Here's how a plot can be created.
>> h = figure; % Create new figure and save the handle to h
>> x = [0:0.001:10]; % Create x vector
>> y = sin(x);
>> plot(x, y) % Plot
>> title('Sine wave from 0 to 10') % Set the title of the current axis
>> ylabel('sin(x)') % Set the label for the yaxis
>> xlabel('x') %set the label for the xaxis
% xlabel('alpha')   > alpha
% xalbel('\alpha')  > symbolic alpha
>> grid on % Turn on the grid
Graphs can also be created and saved using the command line interface. For example, the following code will create a graph comparing the speedup of two algorithms. The graph created is shown below.
>> x = [1 2 4 8];
>> y = [1 2 1.95 3.79];
>> z = [1 1.73 2.02 3.84];
>> h = plot(x,y,'');
>> hold on; % Plot next graph on same figure
>> plot(x,z);
>> hold off;
>> xlabel('Number of processors');
>> ylabel('Speedup');
>> saveas(h,'graph.eps',eps);
External LinksEdit
MATLAB category on ControlTheoryPro.com
Polar Plot
IntroductionEdit
The polar command accepts polar coordinates, plots them in a Cartesian plane, and draws the polar grid on the plane.
UsageEdit
Here's how a plot can be created.
>>t = 0:.01:2*pi;
>>polar(t,sin(2*t).*cos(2*t),'r')
>> grid on % Turn on the grid
Semilog
Note that this page is a copy of the ControlTheoryPro.com page on semilogx/y commands.
IntroductionEdit
The semilogx or semilogy commands plot data with 1 axis linear and the other axis log scale. The semilogx command plots the data on the xaxis on a log scale. For controls this is particularly useful when manually creating a bode plot.
Bode PlotsEdit
The MATLAB bode plot is very convenient but when the plot needs to be formatted then the bode command makes this difficult. As a result this author (Gabe 13:30, 20 April 2008 (CDT)) creates bode plots using the following commands
freqVec = logspace(1, 3, 5000);
[mag, phs] = bode(sys, freqVec * (2*pi));
mag = db(mag(:));
phs = phs(:);
figure;
subplot(2, 1, 1)
semilogx(freqVec, mag)
grid on
title('System Bode Plot')
ylabel('Magnitude (dB)')
subplot(2, 1, 2)
semilogx(freqVec, phs)
grid on
ylabel('Phase (deg)')
xlabel('Frequency (Hz)')
External LinksEdit
Loglog
IntroductionEdit
The loglog command plots both x and y data sets on a log scale while the plot command plots both axes on linear scales and the semilogx/y command plots 1 axis on a linear scale and the other axis on a log scale. Other than the scale of the axes, the 3 plotting commands are identical in most ways.
Basic UsageEdit
The basic usage of the plot, semilogx/y, and loglog command are identical. Below is an example of how a PSD would be plotted
>> Fs = 1000; % Sample Rate of 1 kHz
>> t = 0:(1/Fs):1000; % Time vector
>> x = sin(pi*t); % Sine wave based on time vector
>> [Pxx, f] = pwelch(x, [], [], [], Fs);
>> loglog(f, Pxx)
>> grid on
>> xlabel('Frequency (Hz)')
>> ylabel('Magnitude (units^2/Hz)')
>> title('PSD of Sine Wave')
See AlsoEdit
External LinksEdit
Bode Plot
IntroductionEdit
This article is on the topic of creating Bode plots in MATLAB. The quick answer is use the bode command. However, the bode command has several options and the plots generated by the bode command are not easily reformatted. The default formatting of most MATLAB plots is good for analysis but less than ideal for dropping into Word and PowerPoint documents or even this website. As a result this article presents an alternative that requires more lines of code but offers the full formatting flexibility of the generic plot command.
MATLAB's Bode CommandEdit
The basic bode command is as follows
>> bode(LTI_SYS)
where
The bode command will automatically call gcf which will put the bode plot on the current figure. If no figure exists then one is created by gcf.
If you wish to specify the frequency points at which LTI_SYS is plotted then create a frequency vector using logspace or linspace as follows
>> freqVec = logspace(1, 3, 5000); >> bode(LTI_SYS, freqVec * (2*pi))
where
 freqVec is a vector of 5000 frequencies, in Hz, spaced evenly on a log scale from 10^{1} to 10^{3}
 pi is a MATLAB constant equal to the value of and in this case it is used to convert freqVec to rad/sec as it is passed to the bode command
In order to get the magnitude and phase at each frequency point the bode command must be called with output arguments such as
>> [mag, phase] = bode(LTI_SYS);
or
>> [mag, phase] = bode(LTI_SYS, freqVec * (2*pi));
where
 mag is the magnitude (not in dB) at each point in freqVec
 phase is the phase (in degrees) at each point in freqVec
The mag and phase variables must come out as 3D arrays. Assuming LTI_SYS is SISO then the commands below will convert mag and phase into the vectors you would expect
>> mag = mag(:); >> phase = phase(:); >> mag = db(mag); % to get the magnitude in 20log dB
Issues with the bode commandEdit
The main issue with the bode command is reformatting of the plot. The bode command appears to use a normal semilogx plot and then apply patches ro something similar to the figure. This can lead to odd behavior when attempting to create multiline titles, reformat line widths or font sizes, etc. The normal relationship of axes to figure is just not quite present.
External LinksEdit
Nichols Plot
IntroductionEdit
This article is on the topic of creating Nichols plots in MATLAB. The quick answer is use the Nichols command. However, the Nichols command has several options and the plots generated by the Nichols command are not easily reformatted. The default formatting of most MATLAB plots is good for analysis but less than ideal for dropping into Word and PowerPoint documents or even this website. As a result this article presents an alternative that requires more lines of code but offers the full formatting flexibility of the generic plot command.
MATLAB's Nichols CommandEdit
The basic Nichols command is as follows
>> nichols(LTI_SYS)
where
The Nichols command will automatically call gcf which will put the Nichols plot on the current figure. If no figure exists then one is created by gcf.
If you wish to specify the frequency points at which LTI_SYS is plotted then create a frequency vector using logspace or linspace as follows
>> freqVec = logspace(1, 3, 5000); >> nichols(LTI_SYS, freqVec * (2*pi))
where
 freqVec is a vector of 5000 frequencies, in Hz, spaced evenly on a log scale from 10^{1} to 10^{3}
 pi is a MATLAB constant equal to the value of and in this case it is used to convert freqVec to rad/sec as it is passed to the Nichols command
Issues with the nichols commandEdit
The main issue with the nichols command is reformatting of the plot. The nichols command appears to use a normal semilogx plot and then apply patches or something similar to the figure. This can lead to odd behavior when attempting to create multiline titles, reformat line widths or font sizes, etc. The normal relationship of axes to figure is just not quite present.
External LinksEdit
More on the Nichols plot at ControlTheoryPro.com
Nyquist Plot
IntroductionEdit
This article is on the topic of creating Nyquist plots in MATLAB. The quick answer is use the nyquist command. However, the Nyquist command has several options and the plots generated by the nyquist command are not easily reformatted. The default formatting of most MATLAB plots is good for analysis but less than ideal for dropping into Word and PowerPoint documents or even this website. As a result this article presents an alternative that requires more lines of code but offers the full formatting flexibility of the generic plot command.
MATLAB's Nyquist CommandEdit
The basic Nyquist command is as follows
>> nyquist(LTI_SYS)
where
The Nyquist command will automatically call gcf which will put the Nyquist plot on the current figure. If no figure exists then one is created by gcf.
If you wish to specify the frequency points at which LTI_SYS is plotted then create a frequency vector using logspace or linspace as follows
>> freqVec = logspace(1, 3, 5000); >> nyquist(LTI_SYS, freqVec * (2*pi))
where
 freqVec is a vector of 5000 frequencies, in Hz, spaced evenly on a log scale from 10^{1} to 10^{3}
 pi is a MATLAB constant equal to the value of and in this case it is used to convert freqVec to rad/sec as it is passed to the nyquist command
Issues with the nyquist commandEdit
The main issue with the nyquist command is reformatting of the plot. The nyquist command appears to use a normal semilogx plot and then apply patches or something similar to the figure. This can lead to odd behavior when attempting to create multiline titles, reformat line widths or font sizes, etc. The normal relationship of axes to figure is just not quite present.
External LinksEdit
Handle Graphics
This book discusses some ways of manipulating graphics in MATLAB.
What is a handle?Edit
All of the graphics capabilities explained thus far are ways to generate plots without worrying much about the details. However, very often, you will want a plot that looks a very specific way. You can go into the GUI and change all of the settings every time, but this gets very tedious and wastes a lot of time. If you want a way to generate a plot that has the same look all the time, it is time to delve into the realm of handle graphics.
A handle is a floatingpoint scalar that points to a large list of different properties. Each element of a plot has its own properties, and its own handle. Handles are organized into a treestructured hierarchy, starting from the handle for your monitor (named 0) and branching down to separate handles for children like axis labels, text annotations, error bars, and anything else that can go on a plot. Handles at all levels can be controlled interactively or adjusted programmatically, by changing the values of the handle properties using specific functions.
Monitor properties: the 0 handleEdit
Monitor properties are useful to know when designing graphic user interfaces. For example, you may want to check that a figure window fits inside the user's screen. In order to get a list of the properties of the screen, type:
>> get(0)
To get a specific property, type
>> get(0, 'propertyname');
See the documentation for a complete list of property names and what they mean.
Figure handlesEdit
A figure is essentially a window that acts as a container for one or more plots, uicontrols, and so on. It is the second highest level object you can create
To create a figure, use the figure function like so:
>> fhandle = figure;
This creates a new figure window and stores all the figure data in the variable fhandle. You can also tell MATLAB to give the figure any number of properties at the same time as it's created using the syntax:
>> fhandle = figure('Propertyname1', value1, 'Propertyname2', value2, ...);
See the documentation "figure properties" page for a list of valid property names for figures.
You can close a figure and destroy its handle programmatically by using the close function:
>> close(fhandle);
The get and set functionsEdit
MATLAB allows you to get any property of a figure handle (or actually any type of graphics handle, including axes, line objects, text objects, and so on) by using the 'get' function in the following manner:
>> h = figure; >> propvar = get(h, 'Propertyname');
will store the property with name 'Propertyname' in the variable propvar. With the 'get' function you can only get one property at a time.
The set function allows you to set any number of properties of figures and other graphics handles. You can change as many properties as you want by calling the set function like this:
>> set(h, 'Propname1', propval1, 'Propname2', propval2, ...);
You can also modify the same properties to the same values for any number of handles, if you simply create an array of handles first:
>> handlevec(1) = figure; >> handlevec(2) = figure; >> set(handlevec, 'Name', 'Figure window')
will create two new figures and give them both the same title: 'Figure window'.
See the documentation for valid property names and values for figure properties.
gcfEdit
Even if you don't assign a figure to a variable, you can still access it by using the internal MATLAB variable gcf. This is mostly for convenience, so you don't have to pass the figure handle from one function to another to make modifications. However, due to the warning below, you must be VERY careful in use of gcf so that you make sure you are modifying the correct figure in the case of multiple figure programs:
The current figure is the last one to be modified, not necessarily the one that's open 
To get a list of the current properties of the current figure, use the syntax:
>> get(gcf)
You can also get or set a specific property by using:
>> get(gcf, 'propertyname'); >> set(gcf, 'propertyname', value);
See the documentation "figure property" page for valid figure property names and the format for their values.
Saving the contents of a figureEdit
To save the entire contents of a figure, use the saveas function:
>> saveas(fhandle, 'X.fig');
will save the contents of the figure with handle fhandle as X.fig. .fig files can be opened and edited manually later if desired, although it is often difficult to open them and reedit them programmatically in a consistent manner.
You can also use the saveas function to save image formats such as .jpg, .tif, .bmp, .png, and so on. The saveas function is essentially a command line version of the "file > save as..." option in the figure window itself, but there are some possible resolution differences. Using either of these two methods of saving a figure to a file, the quality of the resulting image is often insufficient for purposes such as inclusion in publications.
In the event that a high quality version of the figure is necessary, it is possible to use MATLAB's print function to print the figure to a vector format (such as Adobe Illustrator's format, obtained with the dill flag) or to a raster format with a specified resolution (for example, using the two flags dpng and r300 would tell MATLAB to print the figure to a PNG file at 300dpi). See the documentation for that function here for more details on the supported output formats.
As an alternative to MATLAB's print function, SVG files can be obtained from many figures (not just simulink models) using the plot2svg function from MATLAB's contributor central (available here). SVG files can be edited using freeware tools such as Inkscape, and also can be opened in Illustrator.
Axis handlesEdit
See the documentation for a list of valid axis properties and values of those properties.
gcaEdit
Other types of handlesEdit
Text handlesEdit
uicontrolsEdit
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 Adobe Illustrator output. Complex figures with several axes and conveying large amounts of information can be created.
Concept of a handleEdit
Most operations on figures generate objects with a set of properties. Users familiar with objectoriented 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 handleEdit
Various commands provide required handles, for example:
h = gcf; % Get current figure h = gca; % Get current axis
ExamplesEdit
Axis LabelEdit
xlabel labels the xaxis 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 yaxis of the current plot. It works in same way of xlabel, but the output is vertical in 2D plots.
Documenting a Maximum ValueEdit
% 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);
Inserting Newlines into Plot Labels
Cell arrays are the easiest way to generate new lines when using the functions xlabel, ylabel, zlabel, text, title, and gtext. However, cell arrays do not always work (see next section).
When displaying text on plots, "\n" is typically interpreted as '\' followed by 'n' instead of the newline character. To generate multiple lines, use cell arrays. This is done by separating each string line of text with a comma and enclosing all commaseparated strings in curly braces as follows.
>> title({'First line','Second line'})
Sometimes it is nice to put the value of a variable and a newline into the plot title. You can do this like so:
n = 4; x = n:1:n; y = x.^2; plot(x,y) title( [ 'plot of x squared', 10, 'from x = ', num2str(n), ' to x = ', num2str(n) ] )
The 10 outside the single quotes is the ascii value for a newline. You don't have to use the char() function, just the number will work.
The output should look like this:
plot of x squared from x = 4 to x = 4
Advanced Topics/Numerical Manipulation
Numerical ManipulationEdit
Linear AlgebraEdit
It is the Matrix laboratory after all.
 Operations
 Transpose
 Systems of linear equations
 Row reduced echelon form
 Inverse
 Coffactor, minor
 Jacobian
Differential EquationsEdit
Advanced Topics/Advanced IO
More advanced I/OEdit
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.
Reading and writing from filesEdit
Writing and Reading to A Serial PortEdit
Writing to a USB portEdit
Advanced Topics/Object Oriented Programming
Object Oriented ProgrammingEdit
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.
While in MATLAB, this can be done with mscript, in Octave new objects are implemented as C++ classes. A simple example of how objects can be added to Octave can be found here.
Struct arraysEdit
MATLAB classesEdit
Advanced Topics/Applications and Examples
ExamplesEdit
FilteringEdit
 Moving Average
 Alpha Beta
 Kalman
 PSD estimation
 Entropy
 Markov Processes
 Queuing Theory
ControlsEdit
Phase vocoderEdit
See MATLAB Programming/Phase Vocoder and Encoder for an example phase vocoder and the corresponding sound sample encoder in MATLAB.
MATLAB in medicineEdit
„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.
Advanced Topics/Toolboxes and Extensions
Toolboxes and ExtensionsEdit
The toolboxes are pretty good if you can afford them. In version 7 there are a lot of toolboxes.
Symbolic ToolboxEdit
Image Processing ToolboxEdit
MATLAB CompilerEdit
Legacy ToolboxesEdit
 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.
Scripts
MfilesEdit
There are 2 types of mfile
 Scripts
 Functions
Scripts are a type of mfile 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 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 discarded when 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 mfile so long as the necessary variables are present in the mfiles 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 Mfile 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 functionEdit
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 mfile name is function_name.m. Calling the function from the command line or another mfile is done by invoking the mfile 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.
PathEdit
In order to invoke a function, that function's mfile must be in the current path. There is a default path that can be set up 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 first instance of that mfile 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 & nargoutEdit
The nargin and nargout commands 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 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 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 nargout command. If the caller isn't saving the secondary output arguments then they do not need to be calculated.
varargin & varargoutEdit
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 a for or while loop and 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 input arguments. From the MATLAB site
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 guidelinesEdit
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.
Nested functionsEdit
External LinksEdit
Large parts of this page come from the ControlTheoryPro.com page on Mfiles, Scripts, and Functions.
Comments
Placing commentsEdit
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 CtrlR (⌘/ for Mac) to place one '%' symbol at the beginning of each line and CtrlT (⌘T for Mac) to do the opposite.
MATLAB also supports multiline 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 (except 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 usesEdit
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.
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
>>
Control Flow
Control FlowEdit
IF statementEdit
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 statementEdit
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 replace nested "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 you will 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 to delete 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 allows the code to fall through in the code above, if value1 is true, then statements(1), statements(2), etc., will execute in Cstyle languages. However, in MATLAB only statements(1) will execute.
TRY/CATCH statementEdit
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 is terminated, and the code in the "catch" block is executed rather than simply reporting an error to the screen and terminating the entire program. This is useful 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 wish to 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 will always 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. In addition, the statements in the CATCH block will never be executed if the TRY block does not fail.
FOR statementEdit
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 value endvalue. 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 statementEdit
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 RETURNEdit
MATLAB includes the "break" and "continue" keywords to allow tighter loop control. The "break" keyword will cause the program to leave the loop it is currently 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 breaks from 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 to the beginning of the loop it is presently in, and to recheck the condition to see if it should 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 value of 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; end
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 and pass 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 that doWhat=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.
Loops and Branches
Program FlowEdit
The idea of program flow is simple. However, implementing and using flow techniques effectively 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.
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 errorsEdit
Usually these are selfexplanatory. 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 propagating 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 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 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.
Array Indexing errorsEdit
Array indexing is a key component of MATLAB. One feature is that the names of variables and functions are case sensitive, and that one can alias builtin or userwritten functions with variables of the same name. So, if you make an array called abs and you try to call the function abs(1), MATLAB will return the first value in the array abs instead of the value 1. MATLAB will not return an error for this as it is not possible to know for certain that the aliasing of the function wasn't intentional. Hence, never ever name your variables the same as an existing MATLAB function. Unfortunately, there are so many supplied functions in the base product plus installed toolboxes, remembering all of them is impossible so use which proposedname if you have any doubt the name might be in use previously before defining a new array or function. Later versions of MATLAB with the command completion feature will show the short help information after the opening parenthesis or tabcompletion options, using which will aid in avoiding such errors before they arise later in execution by not creating the alias.
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 doesn't 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 arrays are 1based, not 0based and are fixed lower dimension, not variable. MATLAB may be able to tell you which index is not real or logical depending on context.
>> y=3*A(1) Attempted to access A(1); index must be a positive integer or logical.
The latter being an expression is parsed differently and so has the actual array available in the error message.
Also note that if 0 were a logical 0 (false) then the statement A(0) would not be an indexing error but a logical subscripting expression. In this case the return would be the empty [] array as there are no subscripts matching false in the defined set of [1 2] as A has been defined above. A more useful expression would be something like
>> A(A==3)
Attempting to use nonstandard MATLAB syntax in your indexing will often result in the error:
>> A(2::, 2) ??? A(2::, 2)  Error: Unexpected MATLAB operator.
The above 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(2:end, 2) ans = 3
Assignment errorsEdit
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
>> 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 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 points or not (as the third example shows); the dimensions must also be the same, with the exception that if you 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 errorsEdit
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 struct arrays. 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 be done 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 store them 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 as two 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 same name 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. For example, 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 errorsEdit
Parenthesis errorsEdit
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 to follow. 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 incorrectpossibly 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 very carefully 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 keep trying 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 errorsEdit
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), as in
>> 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 to pass a 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 colorcoded 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 colorcoded 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, because strings are 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 results because you transposed something you didn't intend to.
Other miscellaneous errorsEdit
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 mfile with unusual letters for computers. Like in Germany "ä, ü or ö". Be sure to name your mfiles only with usual letters and no capital letters.
Function Calling errorsEdit
It is quite possible to try to call a function that doesn't exist, such as:
>> samplemat = [1 2; 1 4] >> A = eigen(samplemat); ??? Undefined command/function 'eigen'.
This can happen because you do not know the name of the function that performs the operation intended (for example, if you wanted to compute the eigenvalues of matrix "samplemat", you would want to call eig, not eigen). It is often useful to pull up MATLAB's help (go to help > product help or type doc into the command prompt) and do a search for the operation you want.
If you're trying to call a function you created and you get this error, there are several possible reasons:
 The mfile must be in one of the paths listed under file > set path, or must be in your current directory
 The mfile must have the same name as the name in the function declaration. You must be aware of this especially if you change the name of your functions, you must also change the name of the file or MATLAB will not find the right function!
If MATLAB finds the function, it will attempt to run it. However, there are several potential pitfalls to avoid in calling functions. It is necessary to know the nature of the input and output arguments of a given function in order to call it. For MATLAB's builtin functions, this information is found in the documentation, or by typing
>> help functionname
It is a good idea to set up some comments so that the help function can read them in your own code as well, so you can keep track of how all your functions work and what they do at a quick reference. To do this, note that the help function reads only the block of comments directly under the function declaration, so for example, if you write a function like this:
function outvars = myfunc(invars) % function outvars = myfunc(invars) % Outputs outvars % All of this is outputted when you type >> help myfunc
% But this wouldn't be
save the function as "myfunc.m", and type
>> help myfunc
it will output:
>> function outvars = myfunc(invars) Outputs outvars All of this is outputted when you type >> help myfunc
Most functions (not all however) require at least one input argument, and calling it with too few will result in an error:
>> A = ode45() ??? Error using ==> ode45 Not enough input arguments. See ODE45.
You cannot call a function with too many input arguments either:
>> A = plus(1,2,3) ??? Error using ==> plus Too many input arguments.
Input arguments must be in a format expected by the function. This will be very functionspecific, so see the documentation or help for details on what they expect. For example, the first argument to ODE45 and other ODE solvers has to be the function handle; if you pass arguments in the wrong order you will be given an error to that effect.
You can choose how many of the output arguments you want out of those available by using the bracket notation. You can choose to save fewer outputs than the function offers, but you cannot assign more variables than the function can output:
>> A = [1,2;3,4] D = eig(A); %one output argument [V,D] = eig(A); %two output arguments [V,D,Mistake] = eig(A); ??? Error using ==> eig Too many output arguments.
All assigned output arguments must also be of the correct class if you are replacing parts of an array that already exists (see the section on assignment for more on this). If you're creating a new variable with the output, this is not an issue.
Control Flow errorsEdit
The most common one by far is if you forget the 'END', which is an issue in Mfile functions. It will tell you that 'at least one END is missing' and try to tell you where the loop or conditional statement starts.
If you have too many END statements and more than one function in an Mfile, MATLAB may give you a cryptic message about not formatting the functions correctly. This is because all functions in the same Mfile must either end with an END statement or not. It doesn't matter which, but if you have too many END statements in one of the functions, MATLAB will think your function is ending early and will get confused when the next function in line does not have an END statement at the end of it. So if you get this confusing message, look for extra END statements and it should fix your problem. If the message is displayed when publishing, say to an HTML file, the problem may be an erratic hierarchical indentation. Try selecting all and then hitting cntrli for automatic indentation to fix the problem.
Having an extra END in a 'switch' statement gives a message that you used the 'case' keyword illegally, because MATLAB thinks you ended the switch statement early, and 'case' has no meaning outside a 'switch' statement.
Other errorsEdit
There are numerous types of errors that do not generate errors from the MATLAB compiler, which have to do with calling the wrong function, using the wrong operation, using the wrong variable, introducing an infinite loop, and so on. These will be the hardest to fix, but with the help of the MATLAB debugger, they will be easier to find. See Debugging M Files for details on how to use the debugger.
Detecting or planning an errorEdit
No matter how accurate the programming is, errors might happen. Using debug techniques are to great help, but planning an error or expecting an error could prove to be just as valuable. This includes making a possibly unneeded if block to decide what to do. I.e. if x < 5 do this and x > 5 do something else. Also inside the big loops add an if block with modulo, like: if not ( mod ( ii , 5 ) ) % do something; end. Now the loop only does a test for every ii counter which can be divided by 5 without any remainder after the division. Some syntax errors or logical errors inside a loop happens after looping for a long time, if an error happens then the error message is displayed, explaining where it happened but not necessarily why it happened. I.e. vector x is one element shorter than element y, and x .* y could not happen. This mistake often happens on the last element in the shortest vector, and is quite difficult to discover unless measures are taken. try % do something; catch me me.getReport; then a breakpoint and even disp(me.getReport) will help in this situation. If the error is not fatal the code may even continue, but instead displaying the error as a message or it could be converted to a warning.
Included Matlab tools / functions: warning, lastwarn, disp, try catch, dbstack, rethrow, throwAsCaller and Matlab help on the above functions to discover pros and cons for each method.
MATLAB Caveats
 In MATlab 6.x (not sure exactly which builds this problem occurs in) the random number generator will generate the same sequence the first time you execute the command.
 In all versions, when operating on a network, do not edit the same file under two different paths, e.g. a mapped drive path and a UNC path (Y:\myfile.m and \\server\folder\myfile.m). You may experience strange behavior (e.g. breakpoints stop working) or other issues depending on which path MATLAB takes to execute the script vs which path it uses for the breakpoints. This same caveat most likely applies to Linux and Windows hard links under different names. Obvious, and bad practice, but hard to find if you have many files opened in the editor and happen to be accessing files using both modes.
Inserting Newlines into Disp Warn and Error
The functions warning, error, sprintf and fprintf will interpret '\n' as a newline character. For example
>> error('This error\nhas a newline.') ??? This error has a newline.
Though previous versions of this wiki claimed this functionality was introduced in MATLAB 6.5 (R13), it doesn't work in 7.4.0 (2007a). The explanation that this change happened when formatted error strings were introduced in the Release Notes for that release was unhelpful.
To add a newline character in versions where the above example doesn't work, use SPRINTF or CHAR(10):
>> error(sprintf('This error\nhas a newline.')) ??? This error has a newline.
disp(['abcd' char(10) 'efgh']) abcd efgh
This works as well:
disp(['abcd', 10, 'efgh']) abcd efgh
In MATLAB versions 2016b and newer the function NEWLINE is recommended instead, for code clarity
disp(['abcd' newline 'efgh']) abcd efgh
Debugging M Files
This section explains things you can do if you fix all the syntax errors (the ones that give you actual error messages), the program runs... but it gives you some result you don't want. Maybe it goes into an infinite loop, maybe it goe through the loop one too few or one too many times, maybe one of your "if" statements doesn't work, maybe the program is giving you "infinity" or "NaN" as an answer (which usually isn't very useful!)... there's as many things that can go wrong as there are lines in the code. Thankfully there are techniques for both fixing and improving on working MATLAB code.
Using MATLAB's Debugging toolEdit
Using the Debugging Tool will let you stop your program in midexecution to examine the contents of variables and other things which can help you find mistakes in your program.
Mfile programs are stopped at "breakpoints". To create a breakpoint, simply press F12 and a red dot will appear next to the line where your cursor is. You can also click on the dash next to the line number on the left side of the Mfile window to achieve the same result.
Then press F5 or Debug>Run from the menu to run the program. It will stop at the breakpoint with a green arrow next to it. You can then examine the contents of variables in the workspace, step, continue or stop your program using the Debug menu. To examine contents of a variable, simply type its name into the workspace, but be warned: you can only look at the values of variables in the file you stop in, so this means that you'll probably need multiple breakpoints to find the source of your problem.
There are several different ways you can move through the program from a breakpoint. One way is to go through the whole program, line by line, entering every function that is called. This is effective if you don't know where the problem is, but since it enters every function (including MATLAB functions like ode45), you may not desire to use it all the time. Thankfully, there's also a way to simply step through the function you're currently stopped in, one line at a time, and instead of going through the child functions line by line MATLAB will simply give you the results of those functions.
Finally, note that you cannot set a breakpoint until you save the Mfile. If you change something, you must save before the breakpoint "notices" your changes. This situation is depicted in MATLAB by changing the dots from red to gray. Sometimes, you'll save but the dots will still be gray; this occurs when you have more than one breakpoint in multiple files. To get around this (which is really annoying), you have to keep going to "exit debug mode" until it turns gray. Once you're completely out of debug mode, your file will save and you'll be ready to start another round of debugging.
Using comments to help you debug codeEdit
If you want to test the effects of leaving out certain lines of code (to see, for example, if the program still returns Inf if you take them out), you can comment out the code. To do this, highlight it and then go to:
Text > Comment
Or press CTRL+R. This will simply put a '%' in front of every line; if the line is already commented out it will put another '%' there so when you uncomment them the pattern of comment lines will not change. Commented lines will be ignored by the compiler, so the effect will be that the program is run without them.
To uncomment a line go to
Text > Uncomment
Or press CTRL+T.
Another use of commenting is to test the difference between two different possible sets of code to do something (for example, you may want to test the effect of using ODE113 as opposed to ODE45 to solve a differential equation, so you'd have one line calling each). You can test the difference by commenting one out and running the program, then uncommenting that one and commenting the other one out, and calling the program again.
How to escape infinite loopsEdit
If your program is doing nothing for a long time, it may just be slow (MATLAB creates a lot of overhead and if you don't use arrays wisely it will go very, very slow) but if you are testing a small module, it is more likely that you have an infinite loop. Though MATLAB can't directly tell you you have an infinite loop, it does attempt to give you some hints. The first comes when you terminate the program. Terminate it by pressing CTRL+C and MATLAB will give you a message telling you exactly what line you stopped on. If your program is running a long time, it is likely the line you stopped in is in the middle of an infinite loop (though be warned, if the loop calls a subfunction, it is likely that you will stop in the subfunction and not the parent. Nevertheless, MATLAB also will tell you the lines of the parents too so you can track down the loop easily enough).
However, sometimes MATLAB won't even let you return to the main window to press CTRLC. In this case you probably have to kill the whole MATLAB process. After this, add a "pause (0.001)" or a similarly small value in the loop you suspect to be the infinite one. Whenever MATLAB passes this instruction you will be able to interact with MATLAB for a (very) short time, e.g. go to the main window and press CTRLC with MATLAB being able to respond to your command.
Other debugging tipsEdit
When inside a function, a loop or just anywhere in the script use a special comment syntax. The %% is the Cellmode commenting. By adding a %% on the line above the interesting code and another %% below the code a cell is created. Now this cell may be executed and modified in memory without the requirement to save the code, script or function. By adding some text after the %% a heading for this cell section is created. I.e. %% Start debugging infinite loop
Another method is to enter the breakpoint, selecting the interesting part and copy this to a new file. Now the code may be changed within this new file and tested. When the modified code is working as expected the debug session may be ended. The code from the temporary file may be copied back and replace the debugged code. This method lets the user run this code snippet multiple times include the %% if the code should be run in cell mode.
Instead of using the IDE to run the code, debug the code or selecting breakpoints, command line functions may be used. Just enter db and press the TABkey to choose the functions. The functions dbstatus and dbstack are two usable functions. Experiment with the functions and use help functon name or select the function name and press the F1key
The last debugging tips in is to add possible code inside the comments I.e. % plot(x,y); % This debug plot function plots the value vector y with input x Now select the plot(x,y) with or without the ; and press F9 (run the selected code). Use help and preferences to find and modify keyboard shortcuts if needed. CTRL+D on the selected y variable opens it inside the variable editor, not to forget hovering the mouse over any variable will display it contents if possible. Even the plot command itself is a great debugging tool, when it comes to visualize the variables.
The final tips is actually a summary. Experiment with the above methods and even combine them such that the debugged code is both run efficiently, has valuable comments and have means to be debugged if necessary. Make plans for coding mistakes by adding comments and helper functions. Make small functions which does what it is designed to do, then implement this function in the complete program or script. Inside the functions use try, catch me and me.getReport; And if there are recurring mistakes, expect them to happen and program accordingly. Infinite loops are very common mistakes so by adding functionality to discover this mistake is a great time saver. Another tips could be unit testing.
GUI/Get File or Directory
uigetfileEdit
The uigetfile command is used to open a window which retrieves a specific file name.
[File,Path] = uigetfile('*.*','Select the file');
This is particular useful to give a user an alternate file from the default file.
[File,Path] = uigetfile('*.*','Select the file','c:\default_dir\default_file.ext');
Alternatives to MATLAB
GNU Octave and LabVIEW MathScript are systems for numerical computations with an mfile 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. Julia language was also made to replace MATLAB, with similar syntax/semantics, while having some deep differences (e.g. generics/multiple dispatch). See also Julia for MATLAB Users.
An alternative to MATLAB: OctaveEdit
What is Octave ?Edit
A short presentation of Octave and its history.
Differences between Octave and MATLAB
Octave has been mainly built with MATLAB compatibility in mind. It has a lot of features in common with MATLAB:
 Matrices as fundamental data type.
 Builtin support for complex numbers.
 Powerful builtin math functions and extensive function libraries.
 Extensibility in the form of userdefined functions.
Some of the differences that do exist between Octave and MATLAB can be worked around using "user preference variables."
GNU Octave is mostly compatible with MATLAB. However, Octave's parser allows some (often very useful) syntax that MATLAB's does not, so programs written for Octave might not run in MATLAB. For example, Octave supports the use of both single and double quotes, whereas older versions of MATLAB only supported single quotes, which meant parsing errors occurred if you tried to use double quotes (e.g. in an Octave script when run on MATLAB). More recent versions of MATLAB introduced double quotes, but with different functionality to single quotes (albeit with some overlap in functionality). Octave and MATLAB users who must collaborate with each other need to take note of these issues and program accordingly.
 Note: Octave can be run in "traditional mode" (by including the traditional flag when starting Octave) which makes it give an error when certain Octaveonly syntax is used.
This chapter documents instances where MATLAB's parser will fail to run code that will run in Octave, and instances where Octave's parser will fail to run code that will run in MATLAB. This page also contains notes on differences between things that are different between Octave (in traditional mode) and MATLAB.
CStyle Autoincrement and Assignment operatorsEdit
Octave supports Cstyle autoincrement and assignment operators:
i++; ++i; i+=1; etc.
MatLab does not.
Product of booleansEdit
MATLAB (R2011b) and Octave (3.6.4) respond differently when computing the product of boolean values:
X = ones(2,2) ; prod(size(X)==1) MATLAB: PROD is only supported for floating point input. Octave: ans = 0
They both produce the same result (ans=0) in MATLAB (R2015a) and above
narginEdit
Nargin returns the number of input arguments of a function. MATLAB (R2011b) will not allow the following; Octave will.
function myfun = testfun(c)
if (nargin == 1)
nargin = 2;
else
nargin = 3
end
startup.mEdit
MATLAB will execute a file named 'startup.m' in the directory it was called from on the command line. Old versions of Octave do not. Starting with Octave 4.2.0 it behaves the same as Matlab. For older versions of Octave, it will execute a file named '.octaverc' which can be edited to execute existing startup files. This means that '.octaverc' can be edited to look for and execute a 'startup.m' file.
if ( exist ('startup.m', 'file') )
source ('startup.m') # load startup.m like MATLAB
endif
Character Strings and ArraysEdit
MATLAB differentiates between character strings and character arrays, while Octave does not. In Octave:
>> ["foo" "bar"] ans = foobar >> ['foo' 'bar'] ans = foobar
In MATLAB:
>> ["foo" "bar"] ans = 1×2 string array "foo" "bar"
>> ['foo' 'bar'] ans = 'foobar'
Solution: Use strcat() for character string concatenation.
['abc ';'abc']Edit
['abc ';'abc'] is now allowed in both Octave and MATLAB; (MATLAB previously would return: ?? Error using ==> vertcat)
In Octave and MATLAB the result will be a 2 by 3 matrix.
Calling ShellsEdit
the "! STRING" syntax calls a shell with command STRING in MATLAB. Octave does not recognize ! as system call, since it is used in logical operations. Always use 'system (STRING)' for compatibility.
If you really miss the onecharacter shortcut, for convenience on the command line you can create a similar shortcut by defining the following in your '.octaverc' file:
function S(a), system(a); end
Now "S STRING" will evaluate the string in the shell.
Attempting to load empty filesEdit
MATLAB lets you load empty files, OCTAVE does not.
system('touch emptyfile'); A = load('emptyfile')
MATLAB R2011b : A=[] Octave 4.2.0 : error: load: unable to determine file format of 'emptyfile'
fprintf and printfEdit
Octave supports both printf
and fprintf
as a command for printing to the screen. MATLAB requires fprintf
:
foo = 5; printf ('My result is: %d\n', foo) % Prints to STDOUT. Octave only
fprintf
covers writing both to the screen and to a file by omitting the optional filehandle argument:
foo = 5; fprintf('My result is: %d\n', foo) % Prints to STDOUT. Octave and MATLAB
WhitespaceEdit
MATLAB does not allow whitespace before the transpose operator but Octave does (it is just an operator like others).
[0 1]' % works in MATLAB and Octave [0 1] ' % works only in Octave
Line continuationEdit
MATLAB always requires ...
for line continuation.
rand (1, ... 2)
while Octave also supports
rand (1, 2)
For both programs, a line break without '...' within an array shifts to the next row
>> R=[1 2 3 7 8 9]
R = 1 2 3 7 8 9
AssignmentEdit
Octave supports
z = y = x + 3
MATLAB requires
y = x + 3 z = y
Octave allows
global isOctave = (exist('OCTAVE_VERSION') > 0);
while MATLAB requires
global isOctave; isOctave = (exist('OCTAVE_VERSION') > 0);
This example also shows how to detect the interpreter at runtime.
Logical operator NOTEdit
Octave allows users to use both ~ and ! with boolean values. The first is for MATLAB compatibility, while ! will be more familiar to C/Java/etc programmers. If you use the latter, however, you'll be writing code that MATLAB will not accept:
 For notequal comparison, Octave can use both '~=' or '!='. MATLAB requires '~='.
GNU Octave Control PackageEdit
Both MATLAB and Octave have toolboxes intended to control system design. In Octave, the toolbox is called the Octave Control Package. The package can be downloaded, compiled and installed with the command pkg install control
from the Octave prompt. Users of Debian and its derivatives can install it by installing the package "octavecontrol", if it is not installed by default.
For more information about functions' syntax, type help <name of function>. For more information about the Control Package, view the PDF manual in the package's "doc" folder.
Small differences exist  an example is c2d. Here are the two formats for the bilinear transformation with an analog model C:
* discrete = c2d(C,0.5,'tustin'); % Matlab
* discrete = c2d(C,0.5,'bi'); % GNU Octave
Some other differencesEdit
 MATLAB uses the percent sign '%' to begin a comment. Octave uses both the hash symbol
#
and the percent sign%
interchangeably.  For exponentiation, Octave can use
^
or**
; MATLAB requires^
.  To end blocks, Octave can use
end
or specify the block withendif, endfor, ...
; MATLAB requiresend
.  Octave supports Cstyle hexadecimal notation (e.g. "0xF0"); MATLAB requires the
hex2dec
function (e.g. "hex2dec('F0')").  If something (like Netlab) needs a function named fcnchk, create a file named fcnchk.m with the contents shown below and put it where Octave can find it:
function f=fcnchk(x, n)
f = x;
end
 The main difference used to be the lack of GUI for Octave. With version 4.0 Octave has a GUI as its default interface.
Notes about specific functionsEdit
 For "dbstep, in" use "dbstep"; for "dbstep", use "dbnext"
 For "eig(A,B)" use "qz(A,B)"
 The fputs() function is not available in MATLAB. Use fprintf() instead.
 The strftime() function is not available in MATLAB. Use datestr() instead.
 The time() function is not available in MATLAB. Use now() instead.
 As of 4.2.1, Octave does not print outputs to the console until it has completed all waiting commands, unlike MATLAB. This behavior is controlled by the boolean variable
page_output_immediately
(default:0
), and it is not ameliorated intraditional
.  The functions strread() and textscan() in Octave 3.4.0 are not fully compatible with their implementations in MATLAB 2009b (and probably later versions as well). For instance, the N=1 option (repeat reading format until end of string) is not implemented in Octave 3.4.0 . Using a value of N=a positive integer (read format N times) does work the same as in MATLAB.
 The textscan() function is not included in Octave versions prior to 3.4.0. Use fscanf() instead.
 For the linprog() function, MATLAB is more permissive by allowing the "a" and "b" inputs to be either row or column vectors. Octave requires that they be column vectors.
 In Octave, one can specify data labels (or legends) with the plot() function, while in MATLAB one can only use the legend() function.
Octave: plot(x, y, ';label;') MATLAB/Octave: plot(x, y); legend('label')
 The error(msg) function in MATLAB is a noop if the message is empty. In Octave, it results in an error.
 The contains() function is not available in Octave. Use ~isempty(strfind()) instead.
ReferencesEdit
See alsoEdit
MATLAB Easter Eggs
MATLAB is one of the very few professional software in the market now that included Easter Eggs in their products.
Here are the few known undocumented demo functions: Just type these commands and have a look for yourself:
All of this Easter Eggs were tested on MATLAB R2020a ( in not alphabetical order)
Have fun playing with the known Easter Eggs~ Note: To view the source code, use edit function followed by command name
Working Easter EggsEdit
Command  Description  Picture/Examples 

cruller  Construct a cruller by revolving the eccentric ellipse defined by the function XYCRULL.  
date  Returns date as in ddmmmyyyy format  08Aug2022 
sldemo_fuelsys  Simulations of FaultTolerant Fuel Control System Dashboard  
funtool  A interactive graphing calculator that manipulates functions of a single variable.  
sf_aircraft  Simulate the fuel injection system in aircraft  
sf_newtons_cradle  Simulate Newton's cradle  
teapotdemo 
A demo that uses the famous Newell teapot to demonstrate MATLAB graphics features.  
teapotGeometry  Data generates vertices, faces, and colors that represent the surface of the infamous Utah teapot.  
graf3d  Demonstrate Handle Graphics for surface plots in MATLAB.  
earthmap  Globe to represent the Earth's topography  
soma  Precomputed solutions to Piet Hein's soma cube  
somasols .  Generate complete solutions to the soma cube  
clock  Returns a six element date vector containing the current time and date in decimal form:
[year month day hour minute seconds] 
1.0e+03 *
2.0220 0.0080 0.0070 0.0230 0.0360 0.0192 
taxDemo(income)  Calculate the tax on income.  
logo  Plot the Lshaped membrane logo with MATLAB(R) lighting.  
membrane  Plot a 3D colored surface of MATLAB(R) logos  
spy  This function is actually to use to visualize sparsity pattern.
When no input of argument is given, it will generate a image of the dogs. If typed in version prior to Matlab R2011a, it will show character White Spy from comics Spy vs. Spy 

life  This is MATLAB's simulations of Conway's Game of Life.
Whether cells stay alive, die, or generate new cells depends upon how many of their eight possible neighbors are alive. By using sparse matrices, the calculations required become astonishingly simple. 

truss  Animation of a bending bridge truss. This demo animates 12 natural bending modes of a twodimensional truss.  
vibes  This demonstration solves the wave equation for the vibrations of an Lshaped membrane.  
makevase  Generate and plot a surface of revolution. The bodyofrevolution corresponding to that line is plotted using the SURFL command.  
sf_cdplayer  Simulink model simulate the CD player.  
xpbombs  Shows a game of Minesweeper , There are 13 bombs hidden in the mine field.  
lorenz  Plot the orbit around the Lorenz chaotic attractor.  
travel  This demo animates the solution of the "Traveling Salesman" problem. (Limited to cities inside USA)
The problem is to form a closed circuit of a number of cities while traveling the shortest total distance along the way. 

fifteen  Shows a game of fifteen game puzzles
A sliding puzzle of fifteen squares and sixteen slots. Solve the puzzle by sequentially lining all fifteen squares up, leaving the last square empty. 

bucky  Connectivity graph of the Buckminster Fuller geodesic dome. (shows 60 coordinates)  
sf_spectrum_analyzer  Simulation of measuring the Frequency Response of a System  
census  Shows the extrapolated predicted populations in the United States  
sf_angle_events  Simulate cranking and power output  
ex_guide_timergui  Execute graphic updates at regular intervals  
quivdemo  Superimpose QUIVER on top of a PCOLOR plot with interpolated shading.  
sf_elevator  Simulations of elevators inside 9 storey buildings.  
penny  Shows 3D render of a USA penny  
matlab.ui.internal.toolstrip.Icon.showStandardIcons  Shows allstandard icons  
knot  Compute the parametric representation of tubelike surfaces and displays the tube with SURF.  
spharm2  This example shows how spherical harmonics, which are spherical versions
of Fourier series, can be used to model the free oscillations of the Earth. 

eml_asteroids  Play a game of Asteroids  
eml_fire  Simulations of burning fire  
sf_tetris2  'j', 'l'  move left and right
'i', 'k'  rotate left and right SPACE  drop 'p'  pause 'q'  quit 

ballode  Simulate a demo of a bouncing ball.  
batonode  Simulate the motion of a thrown baton.  
sf_semantics_hotel_checkin  Simulate Hotel Checkins  
sf_traffic_light  Simulating traffic lights at intersections  
sf_fitness  Simulate the smartwatch  
klein1  This example shows how to generate a Klein bottle.
A Klein bottle is a nonorientable surface in fourdimensional space. It is formed by attaching two Mobius strips along their common boundary. 

xpklein  This example shows how to display a selfintersecting Klein bottle.
A Klein bottle is a nonorientable surface in fourdimensional space. It is formed by attaching two Mobius strips along their common boundary. 

brussode  Surface plots of brusselator  
why  Randomly generated answers to life , universe and everything  
iburgersode / burgersode  Burgers' equation solved as implicit ODE system  
sf_stickslip  Stick  slip friction simulations  
sfediticon  Simulink icons that enable to create basic 16 * 16 icon editor  
amp1dae  Stiff differentialalgebraic equation (DAE) from electrical circuits  
taylortool  A Taylor Series Approximation calculator  
sf_climate_control  Simulate an environmental climate control (Temp and humidity) for a chamber  
tori4  This example shows how to generate four linked unknotted tori by rotating four offcenter circles.  
ardemo  Interactive axes properties demonstration  
rlc_gui  Interactive GUI showing the relationship between the physical parameters of common RLC circuits and the time and frequency responses of those circuits.
* Lowpass RLC network * Highpass RLC network * Bandpass RLC network * Bandstop RLC network 

sf_security  Demonstrations of security system of door, window and mention sensor in a home  
sf_server  Display random numbers to serve the assigned clients  
step  Shows a randomly generated stable Transfer Function Model  
imagesc  Shows the images of a boy.
To correct it , into correct orientation , type imagesc
colormap(gray(32));
axis ij image off;


wernerboy  This example shows how to create Boy's surface  
transpdemo  This example shows how to modify the transparency value for graphics objects to reveal structure that is obscured with opaque objects.  
sf_car  Simulate car braking and throttle  
sf_yoyo  Simulate yoyo up and down and the energy  
sf_boiler  Simulation of temperature controller of boiler  
eml_aero_radar  Radar demo to estimate aircraft position using Kalman Filters 
Untested Easter EggsEdit
sf_gui
sf_mandelbrot_fixpt
eomfun  Old
eigshow  Old
imagesAndVideo  Shows an moving images of rocket flying to the space
imagesc(hot) / imagesc(cool) / imagesc(hsv)  ???
old_sf_car
eml_clock
uitabledemo  ???
 ???
sf_tictacflow  SIMULINK project to simulate a game of Tic Tac Toe against AI

wrldtrv  Show great circle flight routes around the globe
xpquad  ???
xpsound  ???
Not working
sfbus_demo
sf_moore_traffic_light
sf_bidder
sf_power_window
NOTE: If there are any readers who knows what is the ??? easter eggs represent, you may kindly add in.
ReferencesEdit
^{[1]}^{[2]}^{[3]}^{[4]}^{[5]}
 ↑ https://blogs.mathworks.com/steve/2006/10/17/thestorybehindthematlabdefaultimage/
 ↑ https://web.archive.org/web/20210615225906/https://undocumentedmatlab.com/articles/imageeasteregg
 ↑ https://web.archive.org/web/20210803075033/https://undocumentedmatlab.com/articles/spyeastereggtake2
 ↑ https://web.archive.org/web/20210123224206/https://ashanpeiris.blogspot.com/2014/12/matlabeastereggs.html
 ↑ https://www.testingdocs.com/inbuiltgraphicaldemosinmatlab/