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MATLAB

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Introduction to MATLAB


Introduction


What is MATLAB?MATLAB

High Level Languages such as C, PASCAL,

FORTRAN etc.

Assembly Language

MATLAB

1. Is an abbreviation to MATrix

LABoratory.

2. Is compatible with OOPs.

3. Provides easy access to

matrix softwares developed

by LINPACK and EISPACK

projects.


Key Features of MATLAB...

1. It is a high-level language for numerical computation, visualization and

application development.

2. It also provides an interactive environment for iterative exploration,

design and problem solving.

3. It provides built-in graphics for visualizing data and tools for creating

custom plots.


Key Features of MATLAB

4. It provides tools for building applications with custom graphical

interfaces.

5. It provides functions for integrating MATLAB based algorithms with

external applications and languages such as C, Java, .NET and Microsoft

Excel.


Student Edition of MATLAB...

1. The professional and student editions of MATLAB ® are very similar.

2. Student editions are available for Microsoft Windows, Mac OSX, and

Linux operating systems.

3. It can be purchased from college bookstores or online from The

MathWorks at www.mathworks.com.

4. The MathWorks packages its software in groups called releases.

5. New versions are released every 6 months.

http://www.mathworks.com


Student Edition of MATLAB

6. The release number is the same for both the student and professional

edition, but the student version may lag the professional version by

several months.

7. Toolboxes other than those included with the student edition may be

purchased separately.

8. The biggest difference between the professional and student editions is

the command prompt, which is >> in the professional version and EDU>>

in the student edition.


Problem Solving in Engineering and Science

1. State the problem .

2. Describe the input values (knowns) and the required outputs (unknowns).

3. Develop an algorithm to solve the problem. In computer applications, this

can often be accomplished with a hand example .

4. Solve the problem.

5. Test the solution .


Matlab Environment


Introduction

MATLAB environment consists of

following main parts

1. Command Window

2. Command History

3. Workspace

4. Current Folder

5. Editor Window


Command Window

1. Main window in MATLAB.

2. Used to enter variables.

3. Used to run functions and

M-file scripts.

4. All commands are typed after

command prompt “>>”.


Command History

1. Statements entered in

command window are logged

in Command History.

2. View and search previously

run statements.

3. Copy and execute selected

statements.


Workspace...

1. List all variables used as long

as MATLAB has opened.

2. Type “who” in command

window to list all the

commands used.

3. Type “whos” to list all the

commands with current

values, dimensions, etc.


Workspace

4. “clear” command is used to

clear all the variables from

workspace.

5. Save all the variables and data

to text file (.mat file) to use it

for later.


Current Folder

1. Lists all m files, etc. available

in current directory.

2. Set working folder as current

directory or as a part of the

search path so that MATLAB

will find the files easily.


Editor

1. Used to create scripts and

m-files.

2. Click the “New Script” button

in the Toolbar.


“Help” System...

1. Type “help” in command

window to go through various

topics.

2. Type “help elfun” (Elementary

Math Function), and MATLAB

will list all the functions

according to specific

category.


“Help” System...3. “help<function_name>”

command is used to get

specific help about this

function.

4. To open the help window on

the specific topic of interest,

use “doc<topic>” command.


“Help” System

5. help keyword is used to get

help for a specific function,

but lookfor command is used

to search for all functions, etc.

with a specific keyword.

6. Example: >>lookfor plot


Variables


Introduction...

1. Defined with assignment operator, “=”.

2. Can be assigned without declaring their type and their type can

change.

3. Values can come from constants, computation involving values of

other variables, or from the output of a function.

4. Note that MATLAB is case sensitive! The variables x and X are not the

same.


Introduction

5. Semicolon is used to suppress the output of the line that it concludes

and not to terminate commands.


Built-in Commands

Name Description

i , j Used for complex numbers, e.g., z=2+4i

pi

inf ∞, infinity

NaN Not A Number


Naming a variable uniquely...1. To avoid choosing a name for

a new variable that might

conflict with a name already in

use, check for any

occurrences of the name

using the which command.

Format: which -all variable_name


2. The iskeyword command is also

used to list all reserved names.

3. These reserved names can’t be

assigned to any variable(s).

4. If anyone accidentally assign any

of these names, use clear

command to reset it back to

normal.

Naming a variable uniquely


Task: Basic OperationType following commands in command window:

>>y=16;

>>z=3

1. When semicolon is used, no output will be displayed.

2. Some functions display output even if semicolon is used, like

disp, plot, etc


Built-in Functions...

Function Description Example

help Displays the help information available >>help

help<function> Displays help about a specific function >>help plot

clc Clear the command window >>clc

clear Clear variables and functions from memory >>clear

format Set output format



who, whos Lists all variables in the active workspace >>who>>whos

size Size of arrays, matrices >>x=[1 2 ; 3 4];>>size(x)

length Length of a vector >>x=[1:1:10];>>length (x)

disp Displays text or array >>x=[1 2 ; 3 4];>>disp(x)




plot To create a plot >>x=[1:1:10];>>plot (x)>>y=cos (x);>>plot (x,y)

rand Creates a random number, vector or matrix >>rand>>rand (2,1)

max Find the largest number in a vector >>x=[1:1:10]>>max (x)




min Find the smallest number in a vector >>x=[1:1:10]>>min (x)

mean Average or mean value >>x=[1:1:10]>>mean (x)

std Standard deviation >>x=[1:1:10]>>std (x)

To read more about these functions, use “help<function_name>” command.



Arrays, Vectors & Matrices


Introduction1. These are basic elements in MATLAB as well as in control

design theory.

2. A general matrix A may be written like this:

A= a11 ------ a1m

: ------ : Rnxm

an1------ anm


Forming a matrix

1. In MATLAB, vectors and matrices will be typed as:

A= 1 2

3 4

2. To separate rows, semicolon “;” is used.

3. To separate columns, comma “,” or space “ ” is used.

or


Selecting matrix elements

To get specific part of a

matrix, type as follows:

or

or


Forming matrix from 2 vectors

`A matrix can also be created

from 2 vectors X and Y as:


Colon Notation

It is very useful to create the

vectors as:

x=[xi:dx:xf]

where, xi is starting value,

xf is final value, and

dx is increment.


Delete rows and columns

Rows and columns can be

deleted from a matrix using just a

pair of square brackets [].

A= 0 1

-2 -3


Tips and Tricks


Naming Conversions

While creating variables and

constants, create a name that is

not already exists by using “which”

command.


Large or Small Numbers

To write large or small

numbers, like 2 x 10^5, 7.5 x 10^-8

“e” notation is used as:


Line Continuation

Large arrays,split the row

across several command lines by

using the line continuation

operator “...”.


Multiple commands on same line

Type several commands on

the same line to save space.


Basic operations

Basic matrix operations are:

+ Addition

- Subtraction

* Multiplication

/ Division

^ Power


Array Operations...

In this the basic matrix operations can be modified for

element-by-element operations by preceding the operator with a period.

+ Addition

- Subtraction

.* Multiplication

./ Division

.^ Power


Array Operations...

Given:

A= a11 a12 B= b11 b12

a21 a22 b21 b22

Then

A.*B= a11b11 a12b12

a21b21 a22b22


Array Operations

Example is given as:


Linear Algebra


Introduction

1. It is a branch of mathematics

2. Concerned with the study of matrices, vectors, vector spaces (also

called linear spaces), linear maps (also called linear transformations),

and systems of linear equations.

3. Type “help matfun” (Matrix functions - numerical linear algebra) for

more information or type “help elmat” (Elementary matrices and matrix

manipulation).


Functions for Linear Algebra...


rank Provides an estimate of the number of linearly independent rows or columns of any matrix.

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

det Find determinant of a square matrix >>A=[1 2;3 4]>>det(A)

inv Find inverse of square matrix >>A=[1 2;3 4]>>inv(A)



eig Find eigenvalues of a square matrix >>A=[1 2; 3 4]>>eig(A)

ones Creates an array or matrix with only ones >>ones(2)>>ones(2,1)

eye Creates an identity matrix >>eye(2)

diag Find diagonal elements in a matrix >>A=[1 2;3 4]>>diag(A)

Functions for Linear Algebra


1. Vector x is given as:

x= x1

x2

x3 ϵ Rn

:

xn

2. “Transpose” of vector x is given as:

x’= [ x1 x2 x3 --- xn ] ϵ R1xn

Vectors...


3. The “Length” of vector x:

||x||= √x’x = √x1^2+x2^2+..+xn^2

4. “Orthogonality” is given as:

x’y=0

Vectors


1. Matrix A is given as:

A= a11 ----- a1m

: ------ : ϵ Rnxm

an1 ----- anm

Matrices...


2. “Transpose” of matrix A is given as:

A= a11 ------- an1

: ------ : ϵ Rmxn

a1m ----- anm

Matrices...


3. The Diagonal elements of matrix

A is the vector:

diag(A)= a11

a22 ϵ Rp=min(m,n)

:

app

Matrices...


4. The Diagonal matrix ⋀ is given by:

1 0 ---- 0

⋀= 0 2 --- 0 ϵ Rnxn

: : --- :

0 0 ---- n

Matrices...


5. The Identity matrix I is given as:

1 0 ----- 0

I= 0 1 ----- 0 ϵ Rnxm

: : ----- :

0 0 ----- 1

Matrices


Given matrices A ϵ Rnxm and B ϵ

Rmxp , then

C= AB ϵ Rnxp

where

Cjk=∑ aji bik

Matrix Multiplication...

n

i=1


Note that n [ A ] m [ B ] = n [ C ]

Also

AB = BA

A(BC) = (AB)C

(A+B)C = AC+BC

C(A+B) = CA+CB

m p p

Matrix Multiplication


Given matrices A ϵ Rnxm and B ϵ

Rnxm , then

C= A+B ϵ Rnxm

Matrix Addition


Given a matrix A ϵ Rnxn , then

det(A) =|A|

Given 2x2 matrix:

A= a11 a12 ϵ R2x2

a21 a22

Then det(A) = |A| = a11 a22 - a21 a12

Determinant...


Note that

det (AB) = det(A) det(B)

and

det(A’) = det(A)

Determinant


5. Inverse Matrices: The inverse of quadratic matrix A ϵ Rnxn is

defined by:

A

if

AA = A A = I

Inverse Matrices...

-1

-1 -1


For 2x2 matrix

Inverse Matrices

A= a11 a12 ϵ R2x2

a21 a22

Then A is given by

A = 1 a11 -a12 ϵ R2x2

det (A) -a21 a11

-1

-1


Given A ϵ Rnxn , then eigenvalues

is defined as:

det( I - A) = 0

Eigenvalues


7. Solving linear equations: Given

following equations:

x1 + 2x2 = 5

3x1 + 4x2 = 6

7x1 + 8x2 = 9

To find the solution, backlash

operator “\” is used.

Solving Linear Equations


Introduction to File Input/Output


1. Input to a script will come from a data file that has been created by

another source.

2. It is useful to be able to store output in an external file that can be

manipulated and/or printed later.

3. There are basically three different operations, or modes on files. Files

can be: read from, written to, and appended to.

Introduction...


4. Writing to a file means writing to a file from the beginning. Appending

to a file is also writing, but starting at the end of the file rather than the

beginning.

5. Use the load function to read and the save function to write to files.

Introduction


1. The save command can be

used to write data from a matrix

to a data file, or to append to a

data file. The format is:

save filename matvarname -ascii

The “-ascii” qualifier is used

when creating a text or data file.

Writing Data to a File...


2. The type command can be

used to display the contents of

the file.

3. Note that if the file already

exists, the save command will

overwrite the file.

4. Save always writes from the

beginning of a file.

Writing Data to a File


Once a text file exists, data can

be appended to it.

The format is the same as the

preceding, with the addition of the

qualifier “-append”.

Appending Data to a Data File


1. It is accomplished using load.

Once a file has been created, it

can be read into a matrix

variable.

2. If the file is a data file, the load

command will read from the file

“filename.ext”

Reading from a File...


3. The load command works only if there are the same number of values

in each line so that the data can be stored in a matrix, and the save

command only writes from a matrix to a file.

Reading from a File


M-files


1. Scripts or m-files are text files containing MATLAB code.

2. Editor is used to create a file containing the same statements written at command line.

3. Files are saved under a name ends with “.m”.

4. Both scripts and functions are created using MATLAB Editor.

Introduction


1. A collection of commands

that will be executed in

command window.

2. Used for automate repetitive

tasks.

Scripts...


3. Sequence of MATLAB commands is created in the Editor which will be saved as m-file.

4. Push the “Run” button to run a program.

5. Errors in code are displayed by some color symbols to right in the Editor.

Scripts...


6. An m-file will be opened or

edited by using the open

button in the toolbar.

7. An alternative is to type

“Edit<name of m-file>” from

Command window.

Scripts


1. Operate on information (inputs) fed into them and return outputs.

2. Have a separate workspace and internal variables.

3. User-defined functions work the same as the built-in functions.

4. Function is defined by using following syntax:

function outputs = function_name (inputs)

% documentation

Functions...


5. First line of a function starts with

the keyword function.

6. It gives the function name and

order of arguments.

7. To separate words lowercase is

used, and not spaces.

Functions...


8. Function can also be used as:

Functions...


9. The name of the m-file and of

the function should be the same.

Functions...


10. In order to read the information

of the function type

“help<function name>” in the

command window.

Functions


Plotting


1. It is a very important and powerful feature in MATLAB.

2. Plot functions: some useful functions for creating plots are:

Introduction...


plot Generates a plot. >>x=[0:0.01:1]’>>y=x.*x>>plot(x,y)

figure Create a new figure window. >>figure>>figure(1)


Introduction...


subplot Create subplots in a figure. Subplot (m,n,p) breaks the figure window into mxn matrix of small axis, selects the pth axis for the current plot.

>>subplot(2,2,1)

grid Creates grid lines in a plot. “grid on” adds major grid lines to the current plot and “grid off” removes major and minor grid lines.

>>grid>>grid on>>grid off


Introduction...


axis Control axis scaling and appearance. “axis([xmin xmax ymin ymax])” sets the limits for x and y axis.

>>axis([xmin xmax ymin ymax])>>axis off>>axis on

title Add title to current plot >>title (‘This is a title’)

xlabel Add label to x axis >>xlabel (‘time’)

ylabel Add label to y axis >>ylabel (‘temperature’)


Introduction


legend Creates a legend in the corner (or at specified position) of the plot.

>>legend(‘temperature’)

hold Freezes the current plot, so that the additional plots can be overlaid.

>>hold on>>hold off

Type “help graphics” in command window for more information.


Here are some examples to use

the different plot functions.

Example 1:

Plot Functions...


Example 2:

Plot Functions


Plotting multiple data set in one

graph.

Plot Multiple Data Set


Use of “hold” command

Hold


Displaying multiple plots in one

figure- “subplot”

Syntax: subplot (m,n,p)

n

m

Subplot

p=1 p=2

p=3 p=3


Customizing: various functions

can be used to customize the plot,

such as, title, xlabel, ylabel, etc.

Customizing a Plot...


1. Line styles:

Customizing a Plot...

Specifier Line Style

- Solid line (Default)

-- Dashed line

: Dotted line

-. Dash-dot line

2. Colors:

Specifier Color Specifier Color

r Red m Magenta

g Green y Yellow

b Blue k Black

c Cyan w White


3. Marker specifiers:

Customizing a Plot

Specifier Marker Type Specifier Marker Type

+ Plus sign v Downward-pointing triangle

о Circle > Right-pointing triangle

* Asterisk < Left-pointing triangle

. Point s Square

^ Upward-pointing triangle x Cross


Advanced Plotting


1. The loglog uses logarithmic

scales for both the x and y axes.

2. semilogy uses a linear scale for

the x-axis and a logarithmic

scale for the y-axis.

Logarithmic Plots...


3. semilogx uses a logarithmic

scale for the x-axis and a linear

scale for the y-axis.

Logarithmic Plots


1. The bar function draws a bar

chart.

2. barh draws a horizontal bar

chart.

Other Plots...


3. area draws the plot as a

continuous curve and fills in

under the curve that is created.

4. stem draws a stem plot.

Other Plots...


5. For a matrix, the bar and barh

functions will group together the

values in each row.

Other Plots...


6. Note that MATLAB groups

together the values in the first

row and then in the second row.

7. It cycles through colors to

distinguish the bars.

8. The ‘stacked’ option will stack

the values.

Other Plots


1. It is a particular type of bar chart

that shows the frequency of

occurrence of values within a

vector.

2. It uses bins to collect values that

are in given ranges.

3. hist function is used to create a

histogram.

Histogram


pie function is used to create a

pie chart.

Pie Chart


1. comet function is used to

animate a plot.

2. Movie function can also be used

to display recorded movie

frames.

3. The frames are captured in a

loop using function getframe,

and are stored in a matrix.

Animation

or


1. Functions used for 2D plots are

used to create 3D plots with ‘3’

at the end; like, plot3, bar3,

bar3h, pie3, comet3, stem3, etc.

3D Plots...


2. The meshgrid function can be

used to create (x,y) points for

which z=f(x,y); then the x,y, and z

matrices can be passed to mesh

or surf.

3D Plots


1. These are two-dimensional

representations of

three-dimensional surfaces.

2. The contour and surfc

commands are used to create

the plot.

Contour Plots


1. A two-dimensional shaded map

is generated over a grid.

2. A sample function called peaks

that generates the x , y , and z

matrices of an interesting

surface that looks like a

mountain range.

Pseudo Color Plots


Flow Control & Loops


Different loops can be used in MATLAB such as:

If-else statement

Switch and case statement

For loop

While loop

Introduction


1. “if” statement evaluates a logical expression and executes a group of

statements when the expression is true.

2. The optional “elseif” and else keywords provide for the execution of

alternate groups of statements.

3. An “end” keyword, which matches the “if”, terminates the last group of

statements.

4. The groups of statements are delineated by the four keywords- no

braces or brackets are involved.

If-else statement...


The general syntax is as follows:

if expression1

statements1

elseif expression2

statements2

else

statements3

end

If-else statement...


Example :

Note that “if n==5” is used and

not “if n=5”

If A and B are scalars only then

“if A == B, ...” works, but if A and B are

matrices this might not work as

expected.

If-else statement


Operators...

Mathematical Operator Description MATLAB Operator

< Less Than <

≤ Less Than or Equal To <=

> Greater Than >

≥ Greater Than or Equal To >=

= Equal To ==

≠ Not Equal To ~=


Operators

Logical Operator MATLAB Operator

AND &

OR |


1. “switch” statement executes a group of statements based on the value

of a variable or expression.

2. The keywords case and otherwise delineated the groups.

3. Only the first matching case is executed.

4. There must always be an end to match the switch.

Switch and Case statement...



switch variablecase case_value1

statements1case case_value2

statements2...

otherwisestatements

end

Switch and Case statement...


Example :

Switch and Case statement


1. “For” loop repeats a group of statements a fixed, predetermined number of times.

2. A matching end delineates the statements.


for variable = initval:endvalstatements

...statementsend

For Loop...


Example :

For Loop


1. “While” loop repeats a group of statements an indefinite number of

times under control of a logical condition.

2. A matching end delineates the statements.


while expression

statements

end

While Loop...


Example :

While Loop


1. The break command can be

used to terminate a loop

prematurely (while the

comparison in the first line is still

true).

2. A break statement will cause

termination of the smallest

enclosing while or for loop.

Break and Continue...


3. The continue command is

similar to break ; however,

instead of terminating the loop,

the program just skips to the

next pass.

Break and Continue


1. In these constructs the loop is

entered, calculations are

processed, and a decision is

made at some arbitrary point in

the loop whether or not to exit.

2. Then additional calculations are

processed and the loop repeats.

Midpoint Break Loop


3. This strategy can be used either with a for loop or a while loop.

Midpoint Break Loop


Mathematics


1. There are various Math functions in MATLAB: exp, sqrt, log, etc. 2. Various statistics functions in MATLAB are: mean, max, min, std, etc.3. MATLAB also offers lots of Trigonometric functions e.g., sin, cos, tan, etc.4. Complex numbers are important in modelling and control theory which

is defined as; z = a + ib or z = a + jb where imaginary unit (i/j) is i=√-1.5. MATLAB represents polynomials as row arrays containing coefficients

ordered by descending powers.

Introduction


Creates a function that calculates the following mathematical exp.

z=3x^2+√(x^2+y^2) +ln(x)

Test with different values of x and y.

Simple Math Function


1. MATLAB has built-in functions for many statistics.

2. min and max functions also return the index of the smallest or largest value.

3. If there is more than one occurrence, it returns the first.

Statistics...


4. For matrices, the min and max functions operate columnwise by default.

Statistics...


5. The arithmetic mean of a data set is what is usually called the average of the values.

6. For a matrix, the mean function operates columnwise.

7. To find the mean of each row, the dimension of 2 is passed as the second argument to the function

Statistics...


8. Harmonic Mean: It is calculated by using harmmean function.

9. Geometric Mean: It is calculated by using geomean function.

Statistics...


10. Variance and standard deviation are ways of determining the spread of the data.

11. The built-in function to calculate the variance is called var.

12. The standard deviation can be found either as the sqrt of the variance or using std.

Statistics...


13. The mode of a data set is the value that appears most frequently.

14. The built-in function in MATLAB for this is called mode.

Statistics...


15. The median is defined only for a data set that has been sorted first, meaning that the values are in order.

16. The function in MATLAB is called median.

Statistics


1. These include union, intersect, unique, setdiff, and setxor.

2. All of these functions can be useful when working with data sets.

Set Operations...


3. The function ismember receives two vectors as input arguments, and returns a logical vector that is the same length as the first argument.

4. Contains logical 1 for true if the element in the first vector is also in the second, or logical 0 for false if not.

Set operations...


5. The issorted function will return logical 1 for true if the argument is sorted in ascending order (lowest to highest), or logical 0 for false if not.

Set operations


Create various trigonometric functions and plot them on same figure.

Trigonometric Functions


Complex no. is defined as:

z = a + ib or z = a + jb

The complex conjugate of z is defined as:

z* = a - ib

Complex Numbers


It is expressed as:

p(x)=p1x^n+p2x^(n-1)+---+pn+pn+1

where p1,p2,p3,... are the coefficients of polynomial.

Polynomial, p(x)=-5.45x^4+3.2x^2+8x+5.6 will be written as shown.

Polynomials


MATLAB Functions...


i,j Imaginary unit. As basic imaginary unit SQRT(-1), i and j are used to enter complex numbers.

>>z=2+4i>>z=2+4j

abs The absolute value of elements of x. When x is complex, abs(x) is the complex modulus (magnitude) of the elements of x.

>>z=2+4i>>abs(z)

angle Phase angle, in radians. >>z=2+4i>>angle(z)


MATLAB Functions...


imag Complex imaginary part. >>z=2+4i>>b=imag(z)

real Complex real part. >>z=2+4i>>a=real(z)

conj Complex conjugate >>z=2+4i>>z_con=conj(z)


MATLAB Functions


complex Construct complex result from real and imaginary parts

>>a=2>>b=3>>z=complex(a,b)


Symbolic Mathematics


1. MATLAB’s symbolic capability is based on the MuPad software,

originally produced by SciFace Software.

2. SciFace was purchased by the Mathworks in2008.

3. The MuPad engine is part of the symbolic toolbox.

4. A MuPad notebook is created by typing mupad at command prompt.

Introduction


1. Symbolic mathematics is used regularly in math, engineering, and

science classes.

2. It is often preferable to manipulate equations symbolically before

substituting values for variables.

3. Before solving any equation(s), there is a need to create some symbolic

variables.

4. Simple symbolic variables can be created in two ways.

Creating Symbolic Variables...


5. To create the symbolic variable x, type either

x = sym (‘x’)

Or

syms x

Both techniques set the character 'x' equal to the symbolic variable x .



6. Note that in the workspace

window both x and y are listed

as symbolic variables and the

array size for each is 1 x 1.



7. The syms command is

particularly convenient, because

it can be used to create multiple

symbolic variables at the same

time.

8. The sym function can also be

used to create either an entire

expression or an entire equation.

Creating Symbolic Variables


1. The Ezplot function: The

symbolic toolbox includes a

group of functions that allow

you to plot symbolic functions.

The most basic is ezplot.

Symbolic Plotting...


2. Other plots: The 3D surface

plotting functions (ezmesh,

ezmeshc, ezsurf, and ezsurfc)

are used that mirror the

functions used in numeric

plotting options.

Symbolic Plotting


A function called diff is used to

find the derivative of a symbolic

expression.

Differentiation


A function called int is used to

find the integral of a symbolic

expression.

Integration


1. Differential equations contain

both the dependent variable and

its derivative with respect to the

independent variable.

2. The symbolic toolbox includes a

function called dsolve that

solves differential equations,

that is, it solves for y in terms of

t.

Differential Equation


The matlab-Function function

converts a symbolic expression into

an anonymous function.

Convert Expressions to Functions


Numerical Techniques


Linear interpolation can be

performed with the interp1 function.

Linear Interpolation


A smoother curve can be

created by using the cubic spline

interpolation technique, included in

the interp1 function.

Cubic Spline Interpolation


1. The simplest way to model a set of data is as a straight line.

2. To plot the data, draw a straight line through the data points to get a

rough model of the data’s behavior.

3. This process is sometimes called “eyeballing it”—meaning that no

calculations were done, but it looks like a good fit.

4. It is seen that several of the points appear to fall exactly on the line, but

others are off by varying amounts.

Linear Regression...


5. In order to compare the quality

of the fit of this line to other

possible estimates, the

difference between the actual

y-value and the value calculated

from the estimate has found.

6. This difference is called the

residual.



7. The linear regression technique

uses an approach called least

squares fit to compare how well

different equations model the

behavior of the data.

8. It is accomplished with the

polyfit function.



1. It is used to get the best fit by

minimizing the sum of the

squares of the deviations of the

calculated values from the data.

2. The polyfit function allows to do

this easily.

Polynomial Regression


1. The polyval function requires

two inputs.

2. The first is a coefficient array,

such as that created by polyfit.

3. The second is an array of input

values for which output values

are calculated.

Polyval Function


1. To activate the curve-fitting

tools, select Tools : Basic Fitting

from the menu bar in the figure.

2. The basic fitting window opens

on top of the plot.

3. By checking linear, cubic, and

show equations, the plot is

generated.

Basic Fitting Tools


To open the curve-fitting

toolbox, type cftool in the command

window.

Curve Fitting Toolbox


String Manipulations


1. A string in MATLAB consists of any number of characters and is contained in a single quotes.

2. Strings are vectors in which every element is a single character.3. MATLAB also has built-in functions that are written specifically to

manipulate strings.

Introduction


1. A string consists of any number of characters (including, possibly, none). The following are examples of strings:

' ''X''Cat''Hello there''123'

2. A substring is a subset or part of a string. For example, ‘there’ is a substring within the string ‘Hello there’.

Creating String Variables...


3. Characters include letters of the alphabet, digits, punctuation marks, white space, and control characters.

4. Control characters are characters that cannot be printed, but accomplish a task.

5. White space characters include the space, tab, newline, and carriage return.

6. Leading blanks are blank spaces at the beginning of a string.7. Trailing blanks are blank spaces at the end of a string.

Creating String Variables...


8. There are several ways that string variables can be created.

9. By using an assignment statement.

10. By using ‘input’ function.

Creating String Variables


1. Strings are treated as vectors of characters.

2. The number of characters in a string can be found by using the length function.

Strings as Vectors...


3. Expressions can refer to an individual element (a character within the string), or a subset of a string, or a transpose of a string.

4. A blank space in a string is a valid character within the string.



5. A character matrix can be created that consists of strings in every row.

6. The following is created as a column vector of strings, but the end result is that it is a matrix in which every element is a character.



7. With a character matrix one can refer to an individual element (a single character) or an individual row (one of the strings).

8. As rows within a matrix must always be the same length, the shorter strings must be padded with blanks so that all strings have the same length; otherwise, an error will occur.

Strings as Vectors


1. It means to join strings together. 2. Note that the variable names (or

strings) must be separated by a blank space in the brackets, but there is no space in between the strings when they are concatenated.

Concatenation...


3. The method of using the square brackets will concatenate all of the characters in the strings, including all leading and trailing blanks.

4. The strcat function, however, will remove trailing blanks (but not leading blanks) from strings before concatenating.

Concatenation


1. The blanks function will create a string consisting of n blank characters.

2. It is usually most useful to use this function when a number of blank spaces is desired in between.

Customizing String...


3. The sprintf function will create a string in which the output is not suppressed so the value of the string variable is shown.

Customizing String


1. The deblank function will remove blank spaces (only trailing blanks) from the end of a string.

Removing White Space Characters...


2. The strtrim function will remove both leading and trailing blanks from a string, but not blanks in the middle of the string.

Removing White Space Characters


MATLAB has two functions that convert strings to all uppercase letters, or lowercase, called upper and lower.

Changing Case


1. The function strcmp compares strings, character by character.

2. Note that for strings these functions are used to determine whether strings are equal to each other or not, not the equality operator ==.

Comparing String...


3. The function strncmp compares only the first n characters in strings and ignores the rest.

4. The first two arguments are the strings to compare, and the third argument is the number of characters to compare (the value of n).

Comparing String


1. The function strfind receives two strings as input arguments.

2. The general form is

strfind(string, substring)

3. If there are no occurrences, the empty vector is returned.

Finding Strings


1. The function strrep finds all occurrences of a substring within a string and replaces them with a new substring.

2. The format is:

strrep(string, oldsubstring, newsubstring)

Replacing Strings


1. The strtok function breaks a string into two pieces.

2. The format is:

[token, rest] = strtok(string)

3. Alternate delimiters can be defined. The format

[token, rest] = strtok(string, delimeters)

Separating Strings


The function eval is used to evaluate a string.

Evaluating a String...


Example:

Evaluating a String


1. The function “isspace” returns logical true for every character that is a whitespace character.

2. The “ischar” function will return logical true if the vector argument is a character vector, or logical false if not.

The “is” Function


1. To convert numbers to strings there are two functions int2str for integers and num2str for real numbers (which also works with integers).

Conversion between String and Number...


2. The function str2num does the reverse; it takes a string in which a number is stored and converts it to the type double.

Conversion between String and Number


1. The sscanf function reads data from a string.2. The strjust function justifies a string.3. The mat2str function converts a matrix to a string.4. The isstrprop function examines string properties.

Other Features


Data Structures


1. Data structures are variables that store more than one value.2. An array is a data structure in which all of the values are logically

related.3. A cell array is a kind of data structure that stores values of different

types.4. Cell arrays can be vectors or matrices; the different values are referred

to as the elements of the array.5. Structures are data structures that group together values that are

logically related, but are not the same thing and not necessarily the same type.

Introduction


1. To create cell arrays curly braces are used instead of square brackets.

2. To create a row vector cell array, the values are separated by commas.

3. To create a column vector cell array, the values are instead separated by semicolons.

Creating cell arrays...


4. The type of cell arrays is cell.5. Another method of creating a

cell array is to simply assign values to specific array elements and build it up element by element.

Creating cell arrays


1. Using curly braces for the subscripts will reference the contents of a cell; called content indexing.

Referring to and display elements...


2. Using parentheses for the subscripts references the cells; this is called cell indexing.



3. The celldisp function displays the contents of all elements of the cell array.



4. To delete an element from a vector cell array or to delete an entire row or column, cell indexing is used.

Referring to and display elements


1. As cell arrays can store different types of values, strings of different lengths can be stored in the elements.

2. The length of each string can be displayed using a for loop to loop through the elements of the cell array.

Storing strings in cell arrays...


3. The function cellstr converts from a character array padded with blanks to a cell array in which the trailing blanks have been removed.

Storing strings in cell arrays...


4. The char function can convert from a cell array to a character matrix.

5. The function iscellstr will return logical true if a cell array is a cell array of all strings or logical false if not.

Storing strings in cell arrays


1. Creating structure variables can be accomplished by using the struct function.

Create and Modify Structure Variables...


2. An alternative method of creating structures is by using the dot operator to refer to the fields within the structure.



3. The disp function will display either the entire structure or an individual field.

4. By using fprintf, only individual fields can be printed.



5. The function rmfield removes a field from a structure.

Create and Modify Structure Variables


Example:

Passing Structures to Functions


1. The function isstruct will return logical 1 for true if the variable argument is a structure variable or 0 if not.

2. The isfield function returns logical true if a field name is a field in the structure argument or logical false if not.

Related structure functions...


3. The fieldnames function will return the names of the fields that are contained in a structure variable.

Related structure functions


1. In many applications, including database applications, information would normally be stored in a vector of structures, rather than in individual structure variables.

Vectors of Structures...


2. For loop can also be used to display each element in the packages vector.

Vectors of Structures


A Simple GUI with One User Interaction


1. To get started, select the guide icon from the toolbar, or type guide at the

command line.

2. The GUIDE Quick Start window will open.

3. To start a new project, simply select the Blank GUI template, located in the

list on the left-hand side of the window.

4. After that a new figure window—called the GUIDE layout editor—will open,

Creating a layout...


5. To create a layout of buttons,

textboxes, and graphics

windows, use the icons on the

left-hand side of the window in

the “component palette.”

Creating a Layout...


6. To change the palette of tools

to a list of the item names

select

File ➞ Preferences ➞ GUIDE

then check “Show names in

component palette.”



7. The Property Inspector is used

to modify the design

elements.

8. The Property Inspector can be

accessed from the menu bar

by selecting

View ➞ Property Inspector



9. The Property Inspector lists a

wide range of properties for

the selected object in the

GUIDE window.

10. One can change the font of

the message displayed,

change the color of the text

box etc.



11. Use the same process to

modify the properties of the

“edit text” box.

12. The GUIDE window can be

saved and run by selecting

the Save and Run icon from

the window toolbar.

Creating a Layout


1. The m-file is organized as a function, with multiple sub-functions.

2. Some of the subfunctions create the graphics in the saved window.

3. Others are reserved for adding the code that will cause an action when

a user interacts with the GUI.

4. To see a list of the functions in the saved file, select the Show Functions

icon on the toolbar.

Adding Code to M-File...


5. The only functions a user should modify are labeled as:

gui_name_OpeningFcn

graphics_object_name_Callback

Adding Code to M-File


1. It allows the user to interact with the GUI.

2. Clicking on the function of interest will shows the corresponding

section of code.

3. An alternative approach to find the appropriate sub-function to

modify is to use the layout editor.

4. Right click on the graphics object, select View Callbacks, then

select Callback.

Callbacks


1. When a user types in a textbox, the contents are stored as the

string property.

2. To retrieve the information and use it in m-file, use the get

function.

get Function


1. To run GUI, select the Save and

Run icon from the m-file window

or from the Guide layout editor.

2. To run the GUI, type a value into

the edit window, and hit enter.

Run GUI...


3. The opening function is the only

other sub-function to be

modified in this file.

4. It executes when the GUI first

runs, and can be used to control

how the figure window appears

before the user starts adding

data.

Run GUI


Simulink-a Brief Introduction


1. It is an interactive, graphics-based program that allows you to

solve problems by creating models using a set of built-in

“blocks.”

2. It is part of the MATLAB software suite, and requires MATLAB to

run.

Introduction


1. Designed to provide a convenient method for analyzing dynamic

systems, i.e., systems that change with time.

2. It found early acceptance in the signal processing community, and is

reminiscent of the approach used to program analog computers .

3. One way to think of Simulink is as a virtual analog computer.

4. Its strength is its ability to model dynamic systems—which are

modeled mathematically as differential equations .

Applications


To start Simulink, open MATLAB

and type simulink into the command

window or select the Simulink icon

from the Shortcut toolbar

Getting Started...


The Simulink Library Browser

opens, showing the available

libraries of blocks used to create a

Simulink model.

To view the blocks, either select

the library from the left-hand pane

or double click on the icons in the

right-hand pane.

Getting Started...


To create a new model, select

File ➞ New ➞ Model

from the browser window.

Getting Started...


First model will simply add two

numbers.

From the library, click and drag

the constant block into the model

window.

Repeat the process, so that

there are two copies of constant

block in the model.

Model 1


Now drag the sum block into

the model.

Draw connections between the

constants and sum block by clicking

and dragging between the ports.

To add a display, select and

drag display block to model and

connect it to output port of sum

block.

Model 1


The last thing we need to do

before running the model is to

adjust the simulation time, from the

box on the menu bar.

Run the simulation by selecting

the run button on the toolbar or by

selecting Simulation ➞ Start from

the menu bar.

Model 1


Save this model in the usual

way, by selecting File ➞ Save and

adding an appropriate name.

The files are stored with the

extension, .mdl.

Model 1


To solve differential equations with Simulink, create a model by dragging

the appropriate blocks onto the model window, and connect them.

The blocks include; a clock, to generate times (Source library), a math

function block, modified in the parameter window to square the block

input (Math Operations library), a sum block (Commonly Used Blocks library),

an integrator block (Continuous library), and a scope block (Sink library).

Model 2


Connect all the blocks as shown

in figure and the desired result is

displayed.

Model 2

MATLAB - TELCOMA Training path so that MATLAB will find the files easily. Copyright © TELCOMA. All...

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