Kursus Matlab di Jakarta Selatan KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060: KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060

disp('Welcome to the Projectile Flight program');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Obtain inputs

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

muzzleVelocity = input('Please enter the muzzle velocity in metres/second...');

barrelAngle = input('Please enter the angle of the barrel in degrees...');

shots = input('How many entries would you like in the flight table? ');

shots = round(shots); % Incase they entered a non integer

barrelAngle = barrelAngle*pi/180.0;

% Convert to radians

Projectile Code (Cont)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Calculations

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

flightTime = 2*muzzleVelocity*sin(barrelAngle)/gravity;

% Time before shell impacts

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Construct a vector of times, being shots+1 in

% length with values linearly spaced between 0

% and the flight time of the shell

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

times = linspace(0,flightTime,shots+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Calculate all the x & y co-ordinates. Note

% that these are vector/matrix operations

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

horizontal = muzzleVelocity*cos(barrelAngle)*times;

vertical = muzzleVelocity*sin(barrelAngle)*times - ...

Kami ada di Jakarta Selatan. KAMI MEMBERIKAN KURSUS MATLAB ONLINE - HUBUNGI MASTER ENGINEERING EXPERT (MEE) 081219449060. Kami membuka kursus Matlab untuk pemula dan mahasiswa atau insinyur yang ingin memperdalam Matlab dan menerapkan dalam bidang teknikal, engineering, rekayasa, dsb. Format bimbingannya tugas-tugas yang bisa membantu Skripsi, Tesis, DISERTASI
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Dijamin Bisa, atau bisa mengulang kembali. Kami juga dapat membantumembuatkan aplikasi atau program matlab/lainnya. Anda akan dilatih oleh Tim Profesional - HUBUNGI MASTER ENGINEERING EXPERT (MEE) 081219449060. Email: kursusmatlab@gmail.com

0.5*gravity*times.*times;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Output results

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

fprintf('\n The total shell flight time is %5.2f seconds\n',flightTime);

fprintf('\n Time\t Horizontal\t Vertical\n');

combined = [times ; horizontal ; vertical];

fprintf('%5.2f\t%6.1f\t\t%6.1f\n',combined);

plot(horizontal,vertical,'+-');

xlabel('Horizontal Distance');

ylabel('Vertical Distance');

title(strcat('Projectile Motion with muzzle velocity',...

num2str(muzzleVelocity),' m/s and angle ', ...

num2str(barrelAngle/pi*180)));

17.16 Projectile Run

>> projectile

Welcome to the Projectile Flight program

Please enter the muzzle velocity in metres/second...70

Please enter the angle of the barrel in degrees...35

How many entries would you like in the flight table? 20

The total shell flight time is 8.19 seconds

Time Horizontal Vertical

0.00 0.0 0.0

0.41 23.5 15.6

0.82 46.9 29.6

1.23 70.4 41.9

1.64 93.9 52.6

2.05 117.3 61.6

2.46 140.8 69.0

2.86 164.3 74.8

3.27 187.7 78.9

3.68 211.2 81.3

4.09 234.7 82.2

4.50 258.2 81.3

4.91 281.6 78.9

5.32 305.1 74.8

5.73 328.6 69.0

6.14 352.0 61.6

6.55 375.5 52.6

6.96 399.0 41.9

7.37 422.4 29.6

7.78 445.9 15.6

8.19 469.4 0.0

17.17 Projectile Plot

17.18 Review

• Importance of I/O in a program

• disp

• format

• input

- input of strings

• file concept

• fprintf

• fscanf

18 ARRAYS IN MATLAB 1 – VECTORS

• Often desirable to collect a sequence of values together as a single object

- e.g., temperature readings for a day

- array is the general data structure for this supported by most languages

• Matlab is constructed around the concept of an array/Matrix

- MATrix LABoratory

- virtually all built-in operations work on arrays transparently

• Today’s lecture

- introduces vectors (1 dimensional arrays)

• construction

• addressing

• usage

References: For Engineers (Ch. 1, 2)

Mastering (Ch. 6)

User’s Guide (Ch. 6)

18.1 Motivation

• Often it is desirable to collect a number of data values together “in one place”

For instance:

Table of under-water depths and pressures

Class results for an exam

Heating results for an aero-foil at different speeds

• Advantages:

- a single “handle” on the data

- individual elements (datum) may still be accessed

- operations on entire data can often be carried out simply

- size of data may vary each time and indeed (depending on programming language) may be varied dynamically (grown & shrunk)

18.2 Visualising a 1D Array (Vector)

• One common view of arrays is:

- a series of numbered boxes

- each box may hold a single data value

- each particular box is addressed by using its number

- the collection of boxes together has the name of the array

• For example a table of temperatures:

- the array (vector) is called celcius

- it has 5 elements (numbered 1 to 5)

- element number 2 contains the value 20

18.3 Matlab & Arrays

• Matlab was designed to strongly support arrays

- most operations treat scalars and arrays in exactly the same way

e.g.,

X = Y + Z

X may be a scalar, vector or multi-dimensional array depending on what Y and Z are.

• in most programming languages different code would be required for each of the above cases

- arrays can be dynamically created and altered in size

e.g.,

arr1 = 1:10;

arr1(11) = 11;

• in most programming languages the size of an array is fixed at compile time and may not be altered in the program

• This in-built support for arrays in Matlab means:

- it is often relatively easy and straight-forward to solve problems (many problems in engineering & science are naturally expressed with matrices)

- it is easy for novice programmers (even experienced) to make errors

18.4 Vector Creation

• Matlab provides a number of mechanisms for the explicit creation of arrays:

square brackets [] When the individual elements are listed

colon operator : When a starting value, final value and step-size are known (sequence)

linspace & logspace To create linear and exponential sequences of a set size

• For example:

>> theta=[0 pi/4 pi/2 3*pi/4 pi]

theta =

0 0.7854 1.5708 2.3562 3.1416

>> theta = [theta pi+theta(2:end)]

theta =

Columns 1 through 7

0 0.7854 1.5708 2.3562 3.1416 3.9270 4.7124

Columns 8 through 9

5.4978 6.2832

>> sinValues=sin(theta)

sinValues =

Columns 1 through 7

0 0.7071 1.0000 0.7071 0.0000 -0.7071 -1.0000

Columns 8 through 9

18.5 Vector Creation Example

-0.7071 -0.0000

>> gamma = 0:0.25:2

gamma =

Columns 1 through 7

0 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000

Columns 8 through 9

1.7500 2.0000

>> gamma = gamma*pi

gamma =

Columns 1 through 7

0 0.7854 1.5708 2.3562 3.1416 3.9270 4.7124

Columns 8 through 9

5.4978 6.2832

>> cosValues = cos(gamma)

cosValues =

Columns 1 through 7

1.0000 0.7071 0.0000 -0.7071 -1.0000 -0.7071 -0.0000

Columns 8 through 9

0.7071 1.0000

Vector Creation (Cont)

>> cosPlusSin = cosValues + sinValues

cosPlusSin =

Columns 1 through 7

1.0000 1.4142 1.0000 0.0000 -1.0000 -1.4142 -1.0000

Columns 8 through 9

-0.0000 1.0000

>> sigma = linspace(0,2*pi,9)

sigma =

Columns 1 through 7

0 0.7854 1.5708 2.3562 3.1416 3.9270 4.7124

Columns 8 through 9

5.4978 6.2832

>> tanValues = tan(sigma)

tanValues =

1.0e+16 *

Columns 1 through 7

0 0.0000 1.6331 -0.0000 -0.0000 0.0000 0.5444

Columns 8 through 9

-0.0000 -0.0000

18.6 Addressing the Elements of a Vector

• Elements of a vector are accessing by specifying their number

- indexing uses integer values, and starts with 1 for the first element

• Circle brackets () used to enclose indexes

• Indexes can be scalars, or arrays themselves!

• For example:

>> tanValues(1), tanValues(2)

ans =

1.0000

>> cosValues(1:2:9)

ans =

1.0000 0.0000 -1.0000 -0.0000 1.0000

>> sinValues([2 6 5])

ans =

0.7071 -0.7071 0.0000

>> sinValues(9:-1:1)

ans =

Columns 1 through 7

-0.0000 -0.7071 -1.0000 -0.7071 0.0000 0.7071 1.0000

Columns 8 through 9

0.7071 0

18.7 Column vs. Row Vectors

• By default vectors in Matlab are row vectors

- a single row with multiple columns

• Matlab also supports column vectors

• Means of creation are:

- square bracket [] constructor with semi-colons or single elements per line

- transposing a row vector

Note: An array with multiple columns & vectors is a matrix (2D array). That is next lecture’s topic.

18.8 Column vs Row Example

>> a = [1 2 3 4 5]

a =

1 2 3 4 5

>> b=a'

b =

>> a*b

ans =

>> c=[6; 7; 8; 9; 10]

c =

>> d=[11

15]

d =

18.9 Scalar-Array Mathematics

• Scalars & arrays may be combined in a single expression using the normal operators +*-/

- extremely useful & intuitive

• Basic rule

apply the scalar operation to each element of the array

• For example:

>> quarters=0:0.25:2

quarters =

Columns 1 through 7

0 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000

Columns 8 through 9

1.7500 2.0000

>> circle=quarters*pi

circle =

Columns 1 through 7

0 0.7854 1.5708 2.3562 3.1416 3.9270 4.7124

Columns 8 through 9

5.4978 6.2832

>> strictlyPositive = quarters*4 + 1

strictlyPositive =

1 2 3 4 5 6 7 8 9

18.10 Example cel2far.m

A program to produce a table of conversions from temperature in celcius to fahrenheit.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% cel2far.m

% Program to produce a table of conversion

% from temperature in celcius to fahrenheit

% using the formula

% F = C*1.8 + 32

% User enters lower and upper bounds, as

% well as the step interval for temperatures

% in celcius. Program produces a table of

% celcius versus fahrenheit entries.

% Author: Spike

% Date: 17/2/1999

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%

% Get inputs

%%%%%%%%%%%%%%%%%%%%%%%%

disp('Celcius to Fahrenheit conversion');

lower = input('Please enter the min. temp. in celcius...');

upper = input('Please enter the max. temp. in celcius...');

step = input('Please enter the step size in degrees for the table...');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Calculations

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

celcius = lower:step:upper;

fahrenheit = 1.8*celcius + 32;

combined = [celcius; fahrenheit];

fprintf('%8s\t%s\n','Celcius','Fahrenheit');

disp('

--');

fprintf('%5.1f\t\t%5.1f\n',combined);

18.11 cel2far Run

>> cel2far

Celcius to Fahrenheit conversion

Please enter the min. temp. in celcius...-10

Please enter the max. temp. in celcius...40

Please enter the step size in degrees for the table...5

Celcius Fahrenheit

10.0 14.0

-5.0 23.0

0.0 32.0

5.0 41.0

10.0 50.0

15.0 59.0

20.0 68.0

25.0 77.0

30.0 86.0

35.0 95.0

40.0 104.0

>> diary off

18.12 Array-Array Mathematics

• Matlab also supports mathematical operations between arrays

- arrays must be of same size & dimensionality

- standard operators interpreted as per mathematical definitions (matrix operations – see next lecture)

- additional “dot” operators provided to mimic scalar operations

• For example:

>> strictlyPositive

strictlyPositive =

1 2 3 4 5 6 7 8 9

>> squares = strictlyPositive.^2

squares =

1 4 9 16 25 36 49 64 81

>> strictlyPositive = quarters+quarters+quarters+quarters+1

strictlyPositive =

1 2 3 4 5 6 7 8 9

>> cubes = squares .* strictlyPositive

cubes =

1 8 27 64 125 216 343 512 729

>> oneOnX = squares ./ cubes

oneOnX =

Columns 1 through 7

1.0000 0.5000 0.3333 0.2500 0.2000 0.1667 0.1429

Columns 8 through 9

0.1250 0.1111

18.13 Example – bouncing.m

A program to calculate the height of an object as it bounces.

User supplies the initial height from which the object is dropped, the number of bounces to simulate, and the elasticity of the object.

The elasticity determines how high the object returns after a bounce via the following formula:

>> bouncing

Please input the initial height...100

Please input the object's elasticity [0-1]...0.7

Please input the number of bounces required...5

Bounce Table

bounce: 0 1 2 3 4 5

height: 100.0 49.0 24.0 11.8 5.8 2.8

18.14 bouncing.m Code

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% bouncing.m

% A script to simulate the bouncing of a ball or

% other similar object. The user enters three

% values: the initial height from which the

% object is dropped, the elasticity of the

% object (a value between 0 and 1, 1 meaning

% "perfect" elasticity) and the number of

% bounces to be simulated.

% The program employs the following equation to

% determine the height of a new bounce:

% Hnew = Hold*Elasticity^2

% i.e., New height is the old height times the

% square of the object's elasticity.

% Rewriting the equation so we may use vectors

% we see

% Hn = H0*Elasticity^(2*n)

% i.e., height on bounce n is the height of

% initial drop times the elasticity raised to

% the 2n.

% Author: Spike

% Date: 17/2/1999

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Obtain inputs

%%%%%%%%%%%%%%%%%%%%%%%%%%%%

initialHeight = input('Please input the initial height...');

elasticity = input('Please input the object''s elasticity [0-1]...');

bounces = input('Please input the number of bounces required...');

bouncing.m (Cont)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Create the two "building block" vectors that

% are needed. bounceVector is simply a vector

% counting the number of bounces. It is used in

% output and the calculations. elasticRep is

% simply a vector of size (bounces+1) with

% each element set to the elasticity of the

% object. It is used to obtain a vector of

% elasticities ^2n

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

bounceVector = 0:bounces;

elasticRep = linspace(elasticity,elasticity,bounces+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Heart of the program. The vector heights is

% built using the rewritten equation.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

heights = initialHeight*elasticRep.^(2*bounceVector);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Output the results

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

fprintf('\nBounce Table\n');

fprintf('%8s:','bounce');

fprintf('%5.0f ',bounceVector);

disp(' ');

fprintf('%8s:','height');

fprintf('%5.1f ',heights);

disp(' ');

18.15 Review

• vectors as models of the real-world

• arrays in Matlab

• Creating vectors

- square brackets

- colon operator

- linspace & logspace

• Addressing vector elements

• Row vs. column vectors

• scalar-array mathematics

• array-array mathematics

19 MATLAB ARRAYS 2 – MATRICES

• As already seen arrays are a useful data type

• Arrays need not be limited to 1-dimension:

- many real-world problems have higher dimensionality

• Today’s lecture:

- continues with arrays in Matlab

- concentrates on 2D (matrices) and higher dimensioned arrays

References: For Engineers (Ch. 1, 3, 6)

User’s Guide (Ch. 6, 7)

Mastering (Ch. 6, 7, 16)

19.1 2D(+) Arrays – Motivation

• Much real-world data has a higher dimensionality than one.

- Image on the monitor. Can be viewed as a 2D grid of pixels, where for each pixel an R-G-B intensity is kept.

- Terrain map. Can be viewed as a 2D grid of map heights.

- Class results. Can be viewed as a 2D grid with each row being a different student and each column being a different assignment or exam.

Kursus Matlab di Jakarta Selatan KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060

Selasa, 13 Januari 2015

KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060

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