Matrix Laboratory

8/6/2019 Matrix Laboratory

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MATrix LABoratory


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Matlab(FAQ) MATLAB was originally developed to be a

"matrix laboratory," written to provide easy

access to matrix software developed by the

LINPACK and EISPACK projects

Matlab is used for both symbolic and

numerical computation and visualization


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Origin MATLAB was invented in the late 1970s by

Cleve Barry Moler, then chairman of the computerscience department at the University of NewMexico

He designed it to give his students access toLINPACK and EISPACK without having to learnFortran. It soon spread to other universities andfound a strong audience within the appliedmathematics community


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MATLAB is an interactive matrix based system for

scientific and engineering numerical computation

simulation and visualization of problems

MATLAB features a set of application specific

solutions called toolboxes Toolboxes-comprehensive collection of Matlab

functions(M files)

Type demo matlab general at the command

prompt to get a feel of the language capabilites


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Toolboxes available


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Matlab Development

Environment(MDE) By double clicking on the shortcut

From the Run dialog

It is a five panel layout with

A) launchpad

B)workspace variables

C)command window

4)command histroy

5)current directory-workspace


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SIMULINK (FAQ) SIMULINK is an interactive system for the

nonlinear simulation of dynamic systems.

A graphical, mouse-driven program that

allows systems to be modeled by drawing a

block diagram on the screen.


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Simulink Simulink is a block library tool formodeling, simulating andanalyzing dynamic systems. It is

developed by The MathWorks andworks with their flagship product,MATLAB

SIMULINK is an interactive systemfor the nonlinear simulation ofdynamic systems.


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Simulink It can handle linear, nonlinear, continuous-time,

discrete-time, multivariable, and multirate systems SIMULINK is fully integrated with MATLAB,

and, together with MATLAB and the ControlSystem Toolbox, forms a complete control system

design and analysis environment Simulink libraries (blockset) can beinvoked from the command prompt bytyping simulink

Type toilet at the matlab commandprompt to run a simulation and feel ofSimulink

Type vibes to see the L shaped logo


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Simulink is widely used in control theory and

digital signal processing for multidomainsimulation and design.

Coupled withReal Time Workshop, another

product from The MathWorks, Simulink can do

automatic code generation for real-timeimplementation of systems.

In addition to being a popular tool for embedded

system design work because of its flexibility and

capacity for quick iteration,it also supports third-

party hardware and software products


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Matlab

MATLAB is the "Matrix Laboratory", and so

provides many convenient ways for creatingarrays of various dimensions.

In the MATLAB vernacular, a vectorrefers to aone dimensional (1NorN1) matrix, commonly

referred to as an array in other programminglanguages. a matrix generally refers to a multi-dimensional matrix, that is, a matrix with morethan one dimension

Unlike languages such as Java and C++, m is notstatically typed, meaning that variables themselvesdo not have types, only the runtime values storedin those variables have types,


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Besides Matlab also houses its compilerwhich converts the M-file into C or C++.

The source code is compiled into object

code using a C/C++ system compiler.

The resulting code is linked with the

corresponding math and graphics libraries

and any application-specific files making itsan application development tool


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Matlab basics


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Matlab programs can be run from the commandline or by use of a GUI

Run from the command line 2.3+4.2

Matlab woks on different types of data objects thatare manipulated

They are scalars ,vectors and matrices A=[1 2 3]

B=[2 2;2 2];

C=2:8


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M files All functions can be combined and run as a

sequential file on disk called M file

Format rat-rationalize

Format compact

Format long

Sqrt(2)


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Matlab datatypes

The MATLAB language works with only a singleobject type: the MATLAB array.

All MATLAB variables, including scalars,vectors, matrices, strings, cell arrays,structures,and objects are stored as MATLABarrays.

In MATLAB, subscripts begin at 1 rather than 0. Every MATLAB data object is an array. The two-

dimensional version of an array is called a matrix.

MATLAB functions are vectorized.


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Trigonometric functions Cos(pi/6)

Tan(pi/2)

9/0

0/0

Nan/Inf IEEE floating point


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Symbolic object Matlab can also do symbolic computation

Syms a b c x

F=sym(a*x^2+b*x+c)

solve(F)

Pretty(F)


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Variable assignment

X=7

X^2+3*x+2

Log(x) Y=5*x

X=x+5

Who-all variables u have created in this session

whos

Save as mat file

Clear

Load mat file


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Matrices Matrices can be entered in different ways

As an explicit list

Inbuilt functions

Loaded from the diskfile for a local editor

Loaded from external data


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

Matlab is case sensitive

Size(a)

A=[1 2 ; 3 4] +i[5 6;7 8]-complex no

Vectors are matrices with a single row/column

B=[1;2;3] W=[1 2 3 4]

Define even spaced matrices-2:5

[3:2:9]

A(3,2)

A(3,:)

A(:,3)


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Command line help Helpwin

Doc

Lookfor

Help followed by function name


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Concatenate-cat

b=[2 2;4 5] A=[1 2 3; 4 5 6]

[A b]

Dot product and cross product A=[1; 4 ;3; 5] B=[ 7;9;5;0]

Dot[A,B]=dot[B,A]

Length=sqrt(dot(A,A))

Norm

cosU=v.w/(length(v)*length(w))


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U=[1;2;3] V=[7;8;9]

Cross(U,V)

Dot(cross ans and primary vectors is zero)

Matrix operations A+B, 2*A

Matrix building functions

Eye,zeros,ones,diag,Triu,Tril,Rand,Hilb,ma

gic,toeplitz

Eig ,inv,det,rank

Programming Constructs: for ,while, if


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Script- is a sequence of normal matlab statements.scriptsare invoked at the command line by their name

Functions- are scripts with input and output arguments ,eg

open m editor and type function [mean,stdev]=stat(x)

% comment and help

[m,n]=size(x)

If m==1 m=n;

End

Mean=sum(x)/m

Stdev= sqrt(sum(x.^2)/m mean.^2); vectorize Save as stat.m

A command [a,b]=stat(c) will assign mean and standarddeviation to a and b


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PATH PATH setting path and preferences

C:\MATLAB6p1\toolbox\matlab\matfun

Each set of functions in a specific area is

called a toolbox

Each toolbox will contain a contents.m

which is the function summary


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Datafun The data functions in matlab -Data analysis

and Fourier transforms.

Basic operations

Finite differences.

Filtering and convolution.

Fourier transforms


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Matfun directory Matfun directory -

C:\MATLAB6p1\toolbox\matlab\matfun

The matlab functions in matfun

Matrix analysis

Linear equations

Eigenvalues and singular values Matrix functions

Factorization utilities


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Datatypes supported by matlab C:\MATLAB6p1\toolbox\matlab\datatypes

Data types (classes)

Multi-dimensional array functions

Cell array functions

Structure functions

Function handle functions Object oriented programming functions

Overloadable operators


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Stand-Alone Programs In addition to writing M-files, there are three other

ways you can call MATLAB functions:via MEX-

files or via the MATLAB Engine, or by usingeither the MATLAB C or C++ Math Library.

Any M-file, MEX file, or Engine code you write

requires the entire MATLAB environment to run.

However, with the MATLAB C and C++ Mathlibraries, you can write stand-alone (external)

programs.


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Data Storage

All MATLAB data is stored columnwise.

This is how Fortran stores matrices;

MATLAB uses this convention because itwas originally written in Fortran. For

example, given the matrix

a=['house'; 'floor'; 'porch']


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Data Types in MATLAB

Cell Arrays- Cell arrays are a special class of

MATLAB array whose elements consist of cells

that themselves contain MATLAB arrays. Bothstructures and cell arrays provide a hierarchical

storage mechanism for dissimilar kinds of data.

Structures-Structures are collections of different

kinds of data organized by named fields.

Objects-timer ,serial objects


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Cell array You can build a cell array by assigning data

to individual cells, one cell at a time.

MATLAB automatically builds the array asyou go along. There are two ways to assign

data to cells:

Cell indexing Content indexing


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Cell indexing Enclose the cell subscripts in parentheses usingstandard array notation.Enclose the cell contents

on the right side of the assignment statement incurlybraces, "{}.

For example, create a 2-by-2 cell array A A(1,1) = {[1 4 3; 0 5 8; 7 2 9]};

A(1,2) = {'Anne Smith'};

Cell arrays in MATLAB are multidimensional

arrays whose elements are copies of other arrays.A cell array of empty matrices can be created withthe cell function.

A = cell(8,1);


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Content indexing Enclose the cell subscripts in curly braces

using standard array notation. Specify the

cell contents on the right side of theassignment statement.

A{2,1} = 3+7i;

A{8,1} = -pi:pi/10:pi;


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Structure Structures are MATLAB arrays with named "data

containers" called fields

The fields of a structure can contain any kind ofdata.

For example, one field might contain a textstringrepresenting a name, another might contain ascalar representing a billing amount, a third mighthold a matrix of medical test results,

patient.name = 'John Doe'; patient.billing = 127.00;

patient.test = [79 75 73; 180 178 177.5; 220 210205]


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Function Handles You can create a handle to any MATLAB function

and then use that handle as a means of referencingthe function. A function handle is typically passedin an argument list to other functions, which canthen execute, or evaluate, the function using the

handle. Construct a function handle in MATLAB usingthe at sign, @, before the function name.

Evaluate a function handle using the MATLAB

feval function. fhandle=@sqrt;

feval(fhandle,9);

feval(fhandle,25);


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Function handles enable you to do all of

The following: Pass function access information to otherfunctions

Allow wider access to subfunctions and private

functions Ensure reliability when evaluating functions

Reduce the number of files that define yourfunctions

Improve performance in repeated operations Manipulate handles in arrays, structures, and cell

arrays


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A Simple Function Handle handle = @function

F = functions(@disp)

F=figure

Get(F);

Serial object ,s = serial('COM1');


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Specialized functions C:\MATLAB6p1\toolbox\matlab\specfun

Specialized math functions.

Number theoretic functions

Coordinate transforms

Others


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Matfun directory PATH

:C:\MATLAB6p1\toolbox\matlab\matfun

Each set of functions in a specific area is

called a toolbox

Each toolbox will contain a contents.m

which is the function summary


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General purpose C:\MATLAB6p1\toolbox\matlab\general-Generalpurpose commands

General information

Managing the workspace Managing commands and functions

Managing the search path

Controlling the command window

Operating system commands

Debugging M-files and profiling M-files.

Obsolete functions

O

thers and GUI utilities


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Elementary math functions C:\MATLAB6p1\toolbox\matlab\elfun

Trigonometric

Exponential

Complex

Rounding and remainder


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Elementary matrix functions C:\MATLAB6p1\toolbox\matlab\elmat

Elementary matrices

Basic array information

Matrix manipulation

Special variables and constants

Specialized matrices and obsolete functions


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Function functions and ODE

solvers. C:\MATLAB6p1\toolbox\matlab\funfun Optimization and root finding

Optimization Option handling

Numerical integration (quadrature)

Plotting and Inline function object

Differential equation solvers Boundary value problem solver forODEs.


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File input/output C:\MATLAB6p1\toolbox\matlab\iofun File import/export functions.

Image file import/export

Audio file andVideo file import/export Formatted file I/O

String conversion

File opening and closing.

Serial port support

Command window I/O

FIG file support for plotedit and printframes


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Programming language

constructs C:\MATLAB6p1\toolbox\matlab\lang

Control flow.

Evaluation and execution

Scripts, functions, and variables.

Argument handling

Message display

Interactive input


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Operators and special characters

C:\MATLAB6p1\toolbox\matlab\ops

Arithmetic operators

Relational operators

Logical operators

Special characters

Bitwise operators

Set operators and Additional help files.


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Sparse matrices.

C:\MATLAB6p1\toolbox\matlab\sparfun

Elementary sparse matrices

Linear algebra.and Linear Equations

(iterative methods)

Operations on graphs (trees)


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String functions-Character strings

C:\MATLAB6p1\toolbox\matlab\strfun

General

String tests

String operations


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Time and dates.

C:\MATLAB6p1\toolbox\matlab\timefun

Basic functions

Date functions and Timing functions


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C:\MATLAB6p1\toolbox\matlab\

winfun Windows Operating System Interface Files

(DDE/ActiveX)

ActiveX Client Functions.

DDE Client Functions


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Handle Graphics

C:\MATLAB6p1\toolbox\matlab\graphics

Figure window creation and control.

Axis creation and control

Handle Graphics objects and operations

Hardcopy and printing

Printing and I/O utilities


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2d graphs

C:\MATLAB6p1\toolbox\matlab\graph2d

Elementary X-Y graphs

Axis control

Scribe utilites


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Three dimensional graphs.

C:\MATLAB6p1\toolbox\matlab\graph3d

Elementary 3-D plots

Color control and lighting

Colormaps

Axis control

Viewpoint control Camera control

Graph notation and printing utility


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Graphical user interface tools

C:\MATLAB6p1\toolbox\matlab\uitools

GUI functions

GUI design tools

Dialog boxes

Menu utilities

Preferences and Miscellaneous utilities

Helper and obsolete functions


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Version control

C:\MATLAB6p1\toolbox\matlab\verctrl

Version control commands

Specific version control

Demos-

C:\MATLAB6p1\toolbox\matlab\demos


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Some Toolboxes.. Symbolic Math Toolbox Control System Toolbox

Neural Network Toolbox

Instrument Control Toolbox

Data Acquisition Toolbox

Mapping Toolbox

Model Predictive Control Toolbox.

Signal Processing Toolbox Partial Differential Equation Toolbox

MATLAB Report Generator


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Sparse matrices.

A=[2 3 4;7 0 8;6 0 0]

B=sparse(A)

Its a different datatype


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String functions-Character strings

C:\MATLAB6p1\toolbox\matlab\strfun

General

String tests

String operations

Character array

name = 'Thomas R. Lee'; title = ' Sr. Developer';

strcat(name,',',title)


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Text string

Assign variable to character array

S=this is a string

Disp(this is a print display)

User prompt-input(enter the variable)

Error(error message)


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MATLAB provides several functions for

searching and replacing characters in a

string.

label = 'Sample 1, 10/28/95';

newlabel = strrep(label,'28','30')

position = findstr('amp',label)

S i /N i C i


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String/Numeric Conversion

MATLAB's string/numeric conversion functions

change numeric values into character strings. Youcan store numeric values as digit-by-digit stringrepresentations, or convert a value into ahexadecimal or binary string.

x=5317 By default, MATLAB stores the number x as a 1-

by-1 double array containing the value 5317.

y = int2str(x);

The int2str (integer to string) function breaks thisscalar into a 1-by-4 vector containing the string'5317'.

p = num2str(pi,9)


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Creating Multidimensional

Arrays One way to create a multidimensional array

is to create a two-dimensional array and

extend it.

A = [5 7 8; 0 1 9; 4 3 6];

A(:,:,2) = [1 0 4; 3 5 6; 9 8 7]


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Command /function duality

Clear

Save junk x y z

Whos are commands

While

Sin(x),Plot(x,y) are functions

Both are duals

axis off and axis(off)

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