matlab – a computational methods by rohit khokher department of computer science, sharda...

MATLAB – A Computational Methods

By

Rohit Khokher

Department of Computer Science, Sharda University,

Greater Noida, India



Outline of the Talk


Introduction

• MATLAB is a program for doing numerical computation. It was originally designed for solving linear algebra type problems using matrices. It’s name is derived from MATrix LABoratory.

• MATLAB has since been expanded and now has built-in functions for solving problems requiring data analysis, signal processing, optimization, and several other types of scientific computations. It also contains functions for 2-D and 3-D graphics and animation.


Contd…

MatLab : Matrix Laboratory

Numerical Computations with matrices

• Every number can be represented as matrix

Why Matlab?

• User Friendly (GUI)

• Easy to work with

• Powerful tools for complex mathematics


Contd…

Workspace

Command History

Command Window


Array and Function Files

• MATLAB treats all variables as matrices. For our purposes a matrix can be thought of as an array, in fact, that is how it is stored.

• Vectors are special forms of matrices and contain only one row OR one column.

• Scalars are matrices with only one row AND one column

MATLAB Matrices


Contd…

• A matrix with only one row AND one column is a scalar. A scalar can be created in MATLAB as follows:

» a_value=23

a_value =

23


Contd…

• A matrix with only one row is called a row vector. A row vector can be created in MATLAB as follows (note the commas):

» rowvec = [12 , 14 , 63]

rowvec =

12 14 63


Contd…

• A matrix with only one column is called a column vector. A column vector can be created in MATLAB as follows (note the semicolons):

» colvec = [13 ; 45 ; -2]

colvec =

13

45

-2


Contd…

• A matrix can be created in MATLAB as follows (note the commas AND semicolons):

» matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9]

matrix =

1 2 3 4 5 6 7 8 9


Contd…

• a vector x = [1 2 5 1]

x =1 2 5 1

• transpose y = x.’

y = 12

51

• a matrix x = [1 2 3; 5 1 4; 3 2 -1]

x = 1 2 3 5 1 4 3 2 -1


Contd…

• x(i,j) subscription

• whole row

y=x(2,3)

y =

4

y=x(3,:)

y =

3 2 -1

y=x(:,2)

y =

2

1

2

• whole column


Files

• Use predefined functions or write your own functions

• Reside on the current directory or the search path

– add with File/Set Path

• Use the Editor/Debugger to edit, run

MatLab Files (.m)


Contd…

Reading Data from files

• MATLAB supports reading an entire file and creating a matrix of the data with one statement.

>> load mydata.dat; % loads file into matrix.

% The matrix may be a scalar, a vector, or a

% matrix with multiple rows and columns. The

% matrix will be named mydata.

>> size (mydata) % size will return the number

% of rows and number of

% columns in the matrix

>> length (myvector) % length will return the total

% no. of elements in myvector


Programming in MATLAB

MATLAB Variable Names

• Variable names ARE case sensitive

• Variable names can contain up to 63 characters (as of MATLAB 6.5 and newer)

• Variable names must start with a letter followed by letters, digits, and underscores.


Contd…

To get started, type one of these commands: A simple program

» a=5;» b=a/2

b =

2.5000

»

Computational Methods MATLAB

Contd…

MATLAB symbols

>> prompt

. . . continue statement on next line

, separate statements and data

% start comment which ends at end of line

; (1) suppress output(2) used as a row separator

in a matrix

: specify range


Contd…

MATLAB Math & Assignment Operators

Operator Symbol Syntax Syntax

Power ^ or .^ a^b a.^b

Multiplication * or .* a*b a.*b

Division

or

/ or ./

\ or .\

a/b

b\a

a./b

b.\a

NOTE: 56/8 = 8\56


Contd...

- (unary) + (unary)

Operator Symbol Syntax

Addition + a + b

Subtraction - a - b

Assignment = a = b (assign b to a)


Contd…

MATLAB Relational Operators

• MATLAB supports six relational operators.

Operator Symbol

Less Than <

Less Than or Equal <=

Greater Than >

Greater Than or Equal >=

Equal To ==

Not Equal To ~=


Contd…

MATLAB Logical Operators

• MATLAB supports three logical operators.

Operator Symbol Precedence

not ~ % highest precedence

and & % equal precedence with or

or | % equal precedence with and


Contd…

• A for loop in MATLAB for i = 1:1:100

temp(1,i)=0; end

• A while loop in MATLAB while x <= 10

% execute these commands end


Contd…

Scalar - Matrix Addition

» a=3;

» b=[1, 2, 3;4, 5, 6]

b =

1 2 3

4 5 6

» c= b+a % Add a to each element of b

c =

4 5 6

7 8 9


Contd…

Scalar - Matrix Multiplication

» a=3;

» b=[1, 2, 3; 4, 5, 6]

b =

1 2 3

4 5 6

» c = a * b % Multiply each element of b by a

c =

3 6 9

12 15 18


Importing and Exporting Data

• Importing Data into the Workspace

The first step in analyzing data is to import it into the MATLAB workspace. See the topics under Importing Data for detailed information about supported data formats and the functions.

When you work with time series data, use the Time Series Tools GUI (tstool) to import the data and create timeseries objects. The Time Series Tools Import Wizard makes it easy to import or define a time vector for your data.

http://www.mathworks.com/help/techdoc/import_export/br5s7ig.html

http://www.mathworks.com/help/techdoc/ref/tstool.html


Contd…

• Exporting Data from the Workspace

When you analyze your data, you might create new variables or modified imported variables. You can export variables from the MATLAB workspace to various file formats, both character-based and binary. You can, for example, create HDF and Excel files containing your data,


Plots

• A plot is any graphic display you can create within a figure window. Plots can display tabular data, geometric objects, surface and image objects, and annotations such as titles, legends, and colorbars. Figures can contain any number of plots. Each plot is created within a 2-D or a 3-D data space called an axes.


Contd…

Plotting with MATLAB

• There are commands in MATLAB to "annotate" a plot to put on axis labels, titles, and legends. For example:

>> % To put a label on the axes we would use:

>> xlabel ('X-axis label')

>> ylabel ('Y-axis label')

>> % To put a title on the plot, we would use:

>> title ('Title of my plot')


Contd…

x = 0:pi/100:2*pi;

y = sin(x);

plot(x,y)

xlabel('x = 0:2\pi')

ylabel('Sine of x')

title('Plot of the Sine Function')


Contd…

Types of 2-D Graphs

• Line Graphs

• Bar Graphs

• Area Graphs

• Direction Graphs

• Radial Graphs

• Scatter Graphs


Contd…

3-D Plots Here are some examples of surface plots in MATLAB.

Mesh Plot of Peaks

z=peaks(25);mesh(z);

Colormap(hsv)

Surface Plot of Peaksz=peaks(25);

surf(z); colormap(jet);

Contour Plot of Peaksz=peaks(25);

contour(z,16); colormap(hsv)


Applications of Matlab

Linear Algebra Solving a linear system Gaussian elimination finding eigenvalues and eigenvectors Matrix factorization

Curve Fitting and Interpolation Polynomial curve fitting on the fly Least squares curve fitting Interpolation

Data Analysis and Statistics

Numerical Integration

Ordinary Differential Equations

Nonlinear Algebraic Equations

Graphs ( 2 D and 3 D)


Contd…

3-D Plots Here are some examples of surface plots in MATLAB.

Mesh Plot of Peaks

z=peaks(25);mesh(z);

Colormap(hsv)

Surface Plot of Peaksz=peaks(25);

surf(z); colormap(jet);

Contour Plot of Peaksz=peaks(25);

contour(z,16); colormap(hsv)


THANK YOU!!!

For any queries contact:[email protected]

matlab – a computational methods by rohit khokher department of computer science, sharda...

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