bs lab_demo

8/12/2019 BS Lab_Demo

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P. Srikanth, Associate Professor, ECE. 1

Basic Simulation Using

MATLAB


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P. Srikanth, Associate Professor,ECE.

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MATLAB Overview

What is MATLAB?

History of MATLAB

Who developed MATLAB Why MATLAB was developed

Who currently maintains MATLAB

Strengths of MATLAB Weaknesses of MATLAB


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What is MATLAB?

MATLAB

MATrix LABoratory

Interactive system

Programming language


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What is MATLAB cont: 2

Considering MATLAB at home

Standard edition

Available for roughly 2 thousand dollars

Student edition

Available for roughly 1 hundred dollars.

Some limitations, such as the allowable size of amatrix


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What is MATLAB? Cont: 3

MATLAB is a tool for doing numerical

computations with matrices and vectors. It is

very powerful and easy to use. It integratescomputation, graphics and programming in the

same environment.


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History of MATLAB

Ancestral software to MATLAB

Fortran subroutines for solving linear

(LINPACK) and eigenvalue (EISPACK)

problems

Developed primarily by Cleve Moler in the

1970s


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History of MATLAB, cont: 2

Later, when teaching courses in

mathematics, Moler wanted his students to

be able to use LINPACK and EISPACK

without requiring knowledge of Fortran

MATLAB developed as an interactive

system to access LINPACK and EISPACK


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MATLAB gained popularity primarily

through word of mouth because it was not

officially distributed

In the 1980s, MATLAB was rewritten in C

with more functionality (such as plotting

routines)


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The Mathworks, Inc. was created in 1984

The Mathworks is now responsible for

development, sale, and support for

MATLAB

The Mathworks is located in Natick, MA


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Strengths of MATLAB

MATLAB is relatively easy to learn

MATLAB code is optimized to be relativelyquick when performing matrix operations

MATLAB may behave like a calculator oras a programming language

MATLAB is interpreted, errors are easier

to fix Although primarily procedural, MATLAB

does have some object-oriented elements


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Weaknesses of MATLAB

MATLAB is NOT a general purpose

programming language

MATLAB is an interpreted language

(making it for the most part slower than a

compiled language such as C++)

MATLAB is designed for scientific

computation and is not suitable for some

things (such as parsing text)


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FORTRAN:

real*8 A(10,10), B(10,10), C(10,10)

do i=1,10do j=1,10

C(i,j) = A(i,j) + B(i,j)

10 continue20 continue

MATLAB:

C = A + B


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Matrix

MATLAB works with essentially only one

kind of objecta rectangular numerical

matrix with possible complex entries.


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Entering a matrix

Matrices can be

Entered manually

Generated by built-in functions


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An example

A = [1, 2, 3; 7, 8, 9]

Use ; to indicate the end of each row

Use comma to separate elements of a row


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Matrix operations

+addition

-subtraction

*multiplication^power

transpose

To make *and ^operate element-by-

element, we write .*and .^


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Example

A= [1, 2; 3, 4]

B = [0.5, 0.6; 1, 1.5]

C = A*B

C = A.*B


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Subscripts

The element in row i and column j of A is

denoted by A(i, j).

Example: A = zeros(2,2);

A(1,1) + A(1,2) + A(2,2)


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The colon operator

The colon :is one of MATLAB s mostimportant operators. It has many uses.

3:-2:-11is a row vector containing integersfrom 3 to -11 with a increment of -2.

Subscript expressions involving colons referto portions of a matrix. A(1:3, 2)is the first tothe third elements of the second column of

A.


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Working with matrices

MATLAB provides four functions thatgenerate basic matrices.

zeros: all zeros. A = zeros(1,3)

ones: all ones. A = ones(2,4)

rand: uniformly distributed random

numbers. A = rand(3,5)randn: normally distributed random

numbers. A = randn(2,2)


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Working with matrices

Concatenation: join small (compatible)

matrices to make bigger ones. B = [A A-2;

A*2 A/4]

Deleting rows and columns. B(:,2) = [ ]


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Functions

MATLAB provides a large range of standardelementary mathematical functions, including abs,sqrt, exp, and sin.

For help on functions, type

help elfun(elementary mathematical functions)

help specfun(advanced mathematical functions)

help elmat(advanced matrix functions)

help datafun(data analysis functions)


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Suppressing output

If you simply type a statement and pressEnter,MATLAB automatically displays the

results on screen. If you end the line with asemicolon ; MATLAB performs thecomputation but does not display any result.

Example: C = randn(5,1)

C = randn(5,1);


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Programming with MATLAB

Files that contain code in the MATLAB

language are called M-files. You create M-

files using a text editor, then use them as

you would any other MATLAB functions or

command.


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Flow Control

MATLAB has many flow controls. The most

basic are

if statement

for loopswhile loops


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if elseif else end

ifA > B

greater

elseifA < Bless

elseifA = = B

equalend


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for end

fori = 1:m

forj = 1:n

H(i,j) = 1/(i+j)end

end


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while end

i = 0;

while(i


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Graphics

x = 0 : 0.01 : 100;

y = x.^2;

plot(x,y)

Adding plots to an existing graph: hold on

Multiple plots in one figure: subplot


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MATLAB supports many types of graph and surfaceplots:

line plots (x vs. y), filled plots,

bar charts,

pie charts,

parametric plots, polar plots,

contour plots,

density plots,

log axis plots,

surface plots, parametric plots in 3 dimensions and spherical

plots.


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In Windows

systems

MATLAB is

started bydouble-clicking

the mouse on

the appropriateicon.


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MATLABCommand

Window


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File


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Edit


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View


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View


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Web


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Help


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MATLAB includes hundreds

of functions for: Data analysis and visualization,

Numeric and symbolic computation,

Engineering and Scientific graphics,

Modeling, simulation, and prototyping,

Eigenvalue, singular value

MAT AB D


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ECE.

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MATLAB Demos

Demonstrations areinvaluable since they

give an indication of

the MATLAB

capabilities.

A comprehensive set

are available by

typing the command

>>demoin MATLAB

prompt.

Matlab Variables


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A MATLAB variable is essentially a tag that you

assign to a value in memory.

MATLAB does not require any type declarations or

dimension statements.

When MATLAB encounters a new variable name, itautomatically creates the variable and allocates the

appropriate amount of storage.

If the variable already exists, MATLAB changes itscontents.

Variable names consist of a letter, followed by any

number of letters, digits, or underscores.


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Matlab Variables contd..

MATLAB uses only the first 31 characters

of a variable name.

MATLAB is case sensitive; it distinguishes

between uppercase and lowercase letters.

MATLAB stores variables in a part of

memory called workspace.

To view what is stored in a variable type its

name


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Matrix

Solve the following equation:

X+Y=5; 2X+Y=7; %use CAP

Cramers Rule to solve a 2x2 matrix:

A=[1 1;2 1]; C=[5; 7];

Solution [X Y]

inv(A)*C [X Y]=[2 3]


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2. Plotting

Commands covered: plot, xlabel, ylabel, title grid,axis, stem, subplot

xlabel('time (sec)'); ylabel('step response'); title('My

Plot');Eg:To plot more than one graph on the screen, use the

command subplot(mnp) which partitions the screeninto an mxn grid where p determines the position ofthe particular graph counting the upper left corner as

p=1. For example, subplot(211),semilogx(w,magdb);

subplot(212),semilogx(w,phase);


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3D - Plotting example

x=[0:10]; y=[0:10]; z=x*y;

mesh(x,y,z); title(3-D Graph);

M tl b Pl t t i plot(x y s);


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Matlab Plot t ing plot(x,y, s);

s allows to plot : colors, symbols, different lines

b blue . point - solid

g green o circle : dotted

r red x x-mark -. Dashdot

c cyan + plus -- dashed

m magenta * star (none) no line

y yellow s square k black d diamond

plot (x,y,'c+:') plots a cyan dotted line with a plus at each

data point


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%Matlab - Plotting

cleart=0:0.01:10; % time seconds

signalSin=sin(2*pi*t); % signal1 - frequency =1 Hz

signalCos=0.5*cos(2*pi*t); % signal2 - frequency =1 Hz

plot(t,signalSin);

hold onplot(t,signalCos, '-*r');

xlabel('time'); ylabel('signal');

legend('Sin', 'Cos');

title('Two Signals','FontSize',12)

Other commands: xlabel

ylabel

legend, title


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plot plotyy stem subplot


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plot, plotyy, stem, subplot

plot(Y)

plot(X1,Y1,...)

plot(X1,Y1,LineSpec,PropertyName',PropertyValue,...)

plotyy (X1,Y1,X2,Y2)

plots Y1 versus X1 with y-axis labeling on the left and plots Y2versus X2 with y-axis labeling on the right.

stem (X,Y) plots the data sequence Y at the values specified in X.

suplot (m,n,p), breaks the Figure window into an m-by-n matrix of

small axes, selects the p-th axes for for the current plot


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The following table describes different color codes and styles in plotting the wave forms in figure window:

COLOR CODE COLOR NAME

y Yellow

m Magenta

c Cyan

r Red

g Green

b Blue

k Black

w White

LINE TYPE LINE NAME

. Point

o Circle

x x-mark

+ Plus

- Solid

* Star

: Dotted

-. dash dot

-- Dashed

*- star mark on solid+- plus mark on solid

x- x-mark on solid

^- triangle mark on solid

.- dot mark on solid

PROGRAM 1 a: Basic operations on Single Matrix


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PROGRAM 1.a: Basic operations on Single Matrix

%% Program 1.a Basic operations on Single Matrix

clc;

clear all;mat1=[1 1 2 ; 2 1 2 ; 1 3 3]

row2col3=mat1(2,3)

col3=mat1(:,3)

diag_val=diag(mat1)

det_val=det(mat1)

transpose_val=transpose(mat1) %mat1'uppertri_val=triu(mat1)

lowertri_val=tril(mat1)

inverse_val=inv(mat1)

rank_val=rank(mat1)

trace_val=trace(mat1)

eigen_val=eig(mat1)polynomial_val=poly(mat1)

roots_val=roots(polynomial_val)

size_val=size(mat1)

flip_val=fliplr(mat1) %turns the matrix from left to right

% finding sub matrices


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% g _

part_of_matrix=mat1(1:2,2:3) %(1strow to 2nd row,2nd col: 3rdcol)

part_of_matrix1=mat1(1:3,1:2) %(1strow to 3rdrow,1stcol:2ndcol)

part_of_matrix2=mat1([1,3],[1,3]) %([1strow,3rdrow],[1stcol, 3rdcol])

last_row=mat1(end,:) %displays last rowlast_coloumn=mat1(:,end) %displays last column

col1col2=mat1(:,1:2) %displays 1stand 2nd columns of

the matrix

row1row2row3=mat1(1:2,:) %displays 1stand 2nd rows of the

matrix

sel_row=mat1(:,3) %selecting 3rdcolumnsel_col=mat1(2,:) %selecting 2ndrow

mat1(:,3)=[] %deleting 3rdcolumn(now mat1 is

modified)

mat1(2,:)=[] %deleting 2ndrow in the above

mat1% (since mat1 is modified after deleting 3rdcolumn)

% deleting an element from the matrix


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mat2=[1 2 3 ; 4 5 6 ; 7 8 9]

mat2(8)=[] %deletes 8thelement and displays

all the elements as a row vector

mat3=[1 2 3 ; 4 5 6 ; 7 8 9]mat3([4,4])=[] %mat3(4)=[]

% deletes 4th element and displays all the elements as a row vector

mat4=[1 2 3 ; 4 5 6 ; 7 8 9]

mat4([1,2])=[]

% deletes 1st 2ndelements and displays all the elements as a row vector

magic_matrix=magic(3) %sum of all rows and columns is equal

%the no. passing in the magic function argument should be>=3

orthogonal_matrix=orth(4) %A*A'=A'*A=I

identity_matrix=eye(4,4)

zero_matrix=zeros(2,3)one_matrix=ones(2)

random_matrix=rand(3,3)

symmetric_matrix=symdec(3,4) %for skew symmetric matrix---->skewdec

PROGRAM 1.b: Basic operations on Matrices


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p

%% Program 1.b Basic operations on Matrices

% Arithmetic operations on two matrices

clc;

clear all;

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

b=[2 3 4;5 6 8;9 1 7] %try b with another size

addition_val=a+b

sbtraction_val=a-bnormalmulti_val=a*b

arraymulti_val=a.*b % element wise multiplication and also try a(1,:).*b(1,:)

division_val=a/b %a*inv(b)

arraydivision_val=a./b %element wise division or array division

power_val=a^3arraypower_val=a.^3 %v=power(a,3)

PROGRAM 1.c: Concatenation of matrices


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%% Program 1.c Concatenation of matrices

clc;

clear all;

x=[1 2 3]

y=[1 1 1]

z=[x,y] %concatenating the matrices

z1=z(4) %choosing 4thelement

z(4)=[] %assigning the 4thelement with null valuez(6)=3 %adding an element to the concatenated matrix

p=[1 2 3;7 8 9]

q=[4 5 6;10 11 12]

r=[p(1,:),q(1,:)] %concatenating 1st rows of two matrices

PROGRAM 1.d: Scalar functions


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%% Program 1.d Scalar functions

clc;

clear all;

sine_fun=sin(pi/2)

cosine_fun=cos(pi/2) %answer is almost 0tangent_fun=tan(pi/4)

inverse_sine_fun=asin(pi/2)

inverse_cosine_fun=acos(pi/2)

inverse_tangent_fun=atan(pi/4)

exp_fun=exp(5)

natlog_fun=log(5)comonlog_fun=log10(5)

absolute_fun=abs(-5)

sign_fun=sign(-5) %answer is -1 for 0;answer is 0 for

=0

squareroot_fun=sqrt(25)

remainder_fun=rem(12,4)rounding_fun=round(1.4) %answer is 1 i.e; rounds to nearest integer

% rounding_fun=round(1.5) and answer is 2

floor_fun=floor(1.4) %answer is 1 i.e; rounds towards -ve infinity

ceil_fun=ceil(1.4) %answer is 2 i.e; rounds towards +ve infinity

PROGRAM 1.e: Vector functions


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%% Program 1.e Vector functions

clc;

clear all;z=[1 2 6 4 5]

maximum_fun=max(z)

minimum_fun=min(z)

length_fun=length(z)

sort_fun=sort(z)

sum_fun=sum(z)product_fun=prod(z)

meadian_fun=median(z) %answer is 4 i.e; middle value

mean_fun=mean(z)

standard_deviation_fun=std(z) %square root of mean

PROGRAM 1.f: Relational and Logical operations


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%% program 1.f Relational and Logical operations

%for relational operations, the result is 1 if the relation is true else 0

clc;clear all;

x=5

y=3

greaterthan_val=x>y %result is 1

lessthan_val=x=y1 %result is 1

lessthanequal_val=x1


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%% program 1.g Complex Numbers

clc;

clear all;

x=complex(2,3) %directly we can give x=2+3iabsolute_val=abs(x)

angle_val=angle(x)

real_val=real(x)

imaginary_val=imag(x)


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THANK YOU

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