Metode Numerik (minggu 3)

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EXERCISE 2

By : Dr. Indra Komara

Civil Engineering Department - ITATS

72

Fourth Meeting

Practice 01

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Please calculate a simple program to count the area of rectangular shape.

The given dimension is informed as follows,

Length = 10 cm Width = 10 cm

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Practice 02

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of the angle of inclination as informed bellow:

X = [0:10:180]

Problem:

1. Calculate the sine date of Y1 =

sin

��.π 180

2. Analyses the sine of theta ^{Y1 =}^cos^��.π

180

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Practice 03

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Concerned to previous practice 01.

Please calculate a simple program to count the area of rectangular shape.

It is made as a simple function program.

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Practice 04

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Calculate the iteration if the simple matrix data of laboratory of

concrete. The data is considered to evaluate the behavior of modulus of elasticity.

Z = ��²+ (5 × ��)

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Practice 05

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Calculate the a volume of pool and compare to the volume of bucket. In fact, it is needed to be known how

many buckets requires to fill the whole pool if there is still a water inside.

While volume of pool > 0

the number of buckets will increase one of each iteration takes place and

the contents of the pool will

decrease as much as the contents of the bucket of each iteration are

being considered.

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Practice 06

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by the classification of point as illustrated bellows

UTS 1 = 20%

UTS 2 = 30%

UAS = 50%

If the presentation of in this term A = > 80

B = 70 – 80 C = 60 – 70 D = 50 – 60 E = < 60

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Quiz 1

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Evaluate the given matrix A = 1 5 3 which times with sin(0), -cos(150) and log(2000) × 100, respectively.

Plot the value into graph

x = value 1 : value 2 : value 3;

y = cos (x × pi / 180);

Plot (x,y)

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Grid on

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Practice 07

Evaluate several simple calculation

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as follows:

1. Square area 2. Square volume 3. Cylinder area 4. Cylinder volume

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Practice 08

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and matrix manipulation.

i = 1 : 100000 a = a + 1

x (i) = a

With the modification

y (i) = �� (��)²+ 15 & y (i) = ��

(��)²− 25

And count by using matrix manipulation;

y1 = (��1)²+15 & y2 = �� (��2)²

− 25

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Practice 09

In this practice you have to make a recall memory to be applicated in the practice 10. First data is indicated to be a data base as follows:

- First data 0 - Step data 5 - End data 180

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Practice 10

Recall data from practice 09. Illustrate the sin and cos data due to time

consideration.

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Practice 11

Evaluate the step of the calculation - First data 0

- Step data 2 - End data 90

X = [ first : step : end]

Y1 = ��²× sin ��

Y2 = ��²× sin ��²× cos ��

First, the output data should be saved and loaded for the next step.

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EVALUATION

Evaluate the step of the calculation First data 0

Step data 1 End data 10

X = [ first : step : end]

Y1 = ��²× sin ��

Y2 = ��²× sin

��²× cos ��

First data 20 Step

data 50 End data 120 First data 50 Step

data 100 End data 180

First, the output data should be saved and loaded for the next step.

Further, Plot the problem above and illustrate into the graph. As the information, the

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graph should be drawn in one figure with several information of X.

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Practice 12

Practice 11 follow the practice 12 to illustrate the graph

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Practice 13

1. After finishing you open another new file >> edit

2. Write new matrix in the file.m, namely dataku1.txt

3. nama_file_baca='C:\Users\indra\On eDrive\Documents\MATLAB\dataku 1.txt

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Practice 14

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Practice 14

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Practice 15

Write the content of format file with the

function of fprint, here the syntax command : fprint (fid, format, var) ;

fname1=input('Nama File Output = ');

foutput=fopen(fname1,'w');

fprintf(foutput,'%30s %8.2f\n','Total Volume Kolam = ',vkolam);

fprintf(foutput,'%30s %8.2f\n','Volume Ember Yang digunakan = ',vember);

fprintf(foutput,'---\n’);

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15

% Matlab Programming

% By: Indra Komara ST, MT

% --- clear all;

clc;

disp('---'); disp('Practice Program 15');

disp('---'); disp('Menghitung kebutuhan ember');

vkolam=input(' Volume kolam (ltr) = '); vember=input(' Volume ember (ltr) = ');

while vkolam > 0 nember=nember+1;

fprintf(foutput,'%6.0f %8.2f

%8.2f\n',nember,vkolam,vkolam-vember);

vkolam=vkolam-vember;

end;

fprintf(foutput,'---\n');

fprintf(foutput,'%30s %8.2f\n','Jumlah Ember Yang digunakan =',nember);

fclose(foutput);

disp(['Data Output disimpan dalam file -->' fname1]);

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Please write the command below to write the function by defining another function system.

The Output will be illustrated below >> y=Practice16(12) y =

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3310

Practice 16

function y=fungsiku(x)

% --- - % Practice program 15

% --- - %

% Fungsi y=x^3+12x^2- 15x+34 %

% Cara menggunakan :

% y=fungsiku(12.7)

% --- - y=x.^3+12*x.^2-15*x+34;

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Practice 17beam

This practice is made to support the Practice 18. Several m files are used to make the collaboration. First Practice17beam.m

function [area, content]=beam(p,l,t)

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% Practice program 17

% ---

%

% Calculate the area and the content of beam

% area = 2pl + 2pt + 2lt

% content = plt

%

% How to use :

% [ area, content]=beam(length, width, height)

% --- area=2*p.*l+2*p.*t+2*l.*t;

content=p.*l.*t;

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Practice 17cylinder

Second Practice17cylinder.m

function [area, content]=cylinder(radius,height)

% ---

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% ---

%

% Calculate the area and the content of cylinder

% area = (2(pi))x r x t) + 2(pi x r^2)

% content = pi x r^2 x t;

%

% How to use :

% [area, content]=cylinder(radius,height)

% --- area=(2*pi*radius*height)+2*(pi*radius^2);

content=pi*radius^2*height;

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Practice 18

Second Practice17cylinder.m

% --- % Practice program 18

% ---

clear all;

clc;

disp('---'); disp('Practice Program 18');

disp('---'); disp('Choice of

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disp('2.Cylinder');

disp(' ');

pilih=input('pilihan anda (1-2) ->'); switch pilih case 1

disp('Calculate the area and content of square');

disp('---');

pjg=input('square length=');

lbr=input('square width=');

tg=input('square height=');

[area,content]=Practice17beam(pjg,lbr,tg);

disp(['square volume=' num2str(content)]);

case 2

disp('Calculate of area and content of cylinder');

disp('---');

r=input('radius of cylinder=');

tg=input('height of cylinder=');

[area,content]=Practice17cylinder(r,tg);

disp(['area of cylinder=' num2str(area)]);

disp(['volume of cylinder=' num2str(content)]);

otherwise

disp('cinta anda ditolak!!!') end;

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Practice 19

Plot variations. You may plot all of the criteria

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% ---

% --- clear all;

clc;

disp('---');

disp('Practice Program 19');

disp('---');

sdt=[0:10:180];

y=sin(sdt*pi/180);

plot(sdt,y,'*r');

title('Grafik Sinus');

xlabel('Sudut dalam derajat');

ylabel('Nilai sinus');

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Practice 19a

% ---

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% --- clear all;

clc;

disp('---');

disp('Practice Program 19a');

disp('---');

sdt=[0:10:180];

y=sin(sdt*pi/180);

plot(sdt,y,'oy');

hold on;

plot(sdt,y,'-w');

grid on;

set(gca,'color',[0.5 0.5 0.4],'fontname','arial');

title('grafik sinus','color',[0 0 1],'fontweight','bold','fontsize',16);

xlabel('Sudut dalam derajat','color',[.5 .4

1],'fontweight','bold','fontsize',9); ylabel('Nilai sinus','color',[1 0 .5],'fontweight','bold','fontsize',9);

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Practice 19b

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% --- -

% Practice program 19b

% --- -

clear all;

clc;

disp('--- ');

disp('Practice Program 19b');

disp('--- ');

sdt=[0:10:180];

y1=sin(sdt*pi/180);

y2=sin(sdt*pi/180);

plot(sdt,y1,'*r',sdt,y2,'+b') title('Grafic sinus & cosinus') xlabel('sudut dalam derajat');

ylabel('Nilai Y');

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Practice 19c

% --- --

% Practice program 19c

% --- --

clear all;

clc;

disp('--- ');

disp('Practice Program 19c');

disp('--- ');

sdt=[0:10:180];

y1=sin(sdt*pi/180);

y2=cos(sdt*pi/180);

plot(sdt,y1,'*r');

hold on;

plot(sdt,y2,'+b');

title('Grafic sinus & cosinus') xlabel('sudut dalam derajat');

ylabel('Nilai Y');

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Practice 20

% ---

% --- clear all;

clc;

disp('--- '); disp('Practice Program 20');

disp('--- ');

sdt=[0:10:180];

y1=sin(sdt*pi/180);

y2=cos(sdt*pi/180);

y3=y1+y2;

subplot(3,1,1);

plot(sdt,y1,'*b');

title('Grafic sinus') ylabel('Nilai Y1');

subplot(3,1,2);

plot(sdt,y2,'+r');

title('Grafic cosinus') ylabel('Nilai Y2');

subplot(3,1,3);

plot(sdt,y3,'ok');

title('Grafic Y3') ylabel('Nilai Y1');

xlabel('sudut dalam

derajat'); ylabel('Nilai Y1+Y2');

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Visualization of 2D data

Visualisasi 2D (2 dimensi) artinya adalah menempatkan satu atau lebih titik data pada media bidang kartesian maupun polar. Memvisualisasikan data pada bidang pemodelan numerik, terkadang tidak cukup hanya dengan plotting garis atau titik saja. Dalam banyak kesempatan, misalnya presentasi ilmiah, penelitian dan sebagainya, plot garis atau titik dirasakan kurang memadai.

Sampai saat practice sebelumnya kita sudah terbiasa dengan penggunaan fungsi plot. Tapi sebenernya MATLAB menyediakan beberapa fungsi visualisasi yang umum digunakan, yaitu:

Fungsi bar : bar (x,y);

Fungsi stem : stem (x,y);

Fungsi stairs : stairs (x,y);

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Practice 20a

Bar Function

% ---

% Practice program 20a

% --- clear all;

clc;

disp('---');

disp('Practice Program 20a');

disp('---');

sdt=[0:5:160];

y=sin(sdt*pi/180);

bar(sdt,y)

title('grafik Sinus');

xlabel('Sudut dalam derajat');

ylabel('Nilai sudut');

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Practice 20b

Stem Function

% --- -

% Practice program 20b

% --- -

clear all;

clc;

disp('--- ');

disp('Practice Program 20b');

disp('---');

x=[-50:2.5:50];

y1=(x.^2).*sin(x);

stem(x,y1);

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Practice 20c

Stairs Function

% ---

% Practice program 20c

% --- clear all;

clc;

disp('---');

disp('Practice Program 20c');

disp('---');

x=[-50:5:150];

y1=(x.^2).*cos(x);

stairs(x,y1);

Illustrate another plot by using >> demo

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Visualization of 3D data

Visualisasi 3D (3 dimensi) artinya adalah menempatkan satu atau lebih titik data pada media ruang. Teknik visualisasi 3D ini sama berguna dalam bidang permodelan yang berhubungan dengan ruang (x, y, z), dimana z berarti nilai bobot pada titik (x,y) yang berupa data ketinggian, temperature, kecepatan dan lain-lain. Beberapa fungsi yang umum digunakan untuk visualisasi data 3D adalah:

Fungsi plot3 Fungsi mesh Fungsi Surfl Fungsi pcolor Fungsi imagesc Fungsi contour Fungsi contour

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Practice 21

Plot3 Function

% making data of x y and z

% x y z

t = [5 6 12;

2 3 4;

4 2 9;

4 7 9;

11 10 20;

9 7 7;

5 6 12];

plot3(t(:,1),t(:,2),t(:,3),'ob');

hold on;

plot3(t(:,1),t(:,2),t(:,3),'-r');

grid on;

set (gca,'fontsize',8);

title('Grafik 3D

plot3','fontweight','bold','fontsize',12);

xlabel('Sumbu-x','fontweight','bold');

ylabel('Sumbu-y','fontweight','bold');

zlabel('Sumbu-z','fontweight','bold');

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Practice 21a

Mesh function

% x y z

t = [5 6 12;

2 3 4;

4 2 9;

4 7 9;

11 10 20;

9 7 7;

5 6 12];

mesh(t);

hold on;

mesh(t);

grid on;

set (gca,'color',[.7 1 0.4],'fontsize',8);

title('Grafik 3D

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Practice 21a

Mesh function

% x y z

t = [5 6 12;

2 3 4;

4 2 9;

4 7 9;

11 10 20;

9 7 7;

5 6 12];

mesh(t);

hold on;

mesh(t);

grid on;

title('Grafik 3D

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Practice 21b

Surf function

% x y z

t = [5 6 12;

2 3 4;

4 2 9;

4 7 9;

11 10 20;

9 7 7;

5 6 12];

surf(t);

hold on;

surf(t);

grid on;

title('Grafik 3D

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Practice 21c

Surfl function

% x y z

t = [5 6 12;

2 3 4;

4 2 9;

4 7 9;

11 10 20;

9 7 7;

5 6 12];

surfl(t);

hold on;

surfl(t);

grid on;

title('Grafik 3D

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Practice 21d

Pcolor function

% x y z

t = [5 6 12;

2 3 4;

4 2 9;

4 7 9;

11 10 20;

9 7 7;

5 6 12];

pcolor(t);

hold on;

pcolor(t);

grid on;

title('Grafik 3D

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Practice 21e

Imagesc function

% x y z

t = [5 6 12;

2 3 4;

4 2 9;

4 7 9;

11 10 20;

9 7 7;

5 6 12];

imagesc(t);

hold on;

imagesc(t);

grid on;

title('Grafik 3D

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Practice 21f

Contourf function

% x y z

t = [5 6 12;

2 3 4;

4 2 9;

4 7 9;

11 10 20;

9 7 7;

5 6 12];

contourf(t);

hold on;

contourf(t);

grid on;

title('Grafik 3D

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Practice 21g

Contour function

% x y z

t = [5 6 12;

2 3 4;

4 2 9;

4 7 9;

11 10 20;

9 7 7;

5 6 12];

contour(t);

hold on;

contour(t);

grid on;

title('Grafik 3D

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Practice 22

Contour function

% x y z

t = [5 6 12;

2 3 4;

4 2 9;

4 7 9;

11 10 20;

9 7 7;

5 6 12];

contour(t);

hold on;

contour(t);

grid on;

title('Grafik 3D

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115

Practice 22

% ---

% --- clear all;

clc;

disp('---'); disp('Practice Program 22'); disp('---');

% X Y Z

data= [ 1.0000 1.0000 10; 50.0000 50.0000 -15;

30.0000 25.0000 30;

40.0000 10.0000 -20;

1.0000 50.0000 -4;

50.0000 1.0000 5];

xmin=min(data(:,1));

xmax=min(data(:,1));

ymin=min(data(:,2));

ymax=min(data(:,2));

[XI,YI]=meshgrid(linspace(xmin,xmax,50),linspace(ym in,y max,50));

X=data(:,1);

Y=data(:,2);

Z=data(:,3);

ZI=griddata(X,Y,Z,XI,YI,'cubic');

disp('Pilihan Visualisasi 3D');

disp('---');

disp('1. mesh');

disp('2. surf');

disp('3. surfl');

disp('4. pcolor');

disp('5. imagesc');

disp('6. contour');

disp('7. contourf');

disp(' ')

pilih=input('pilihan anda (1-7) -> ');

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Practice 22 - Continued

switch pilih case 1

mesh(ZI);

set(gca,'color',[.7 1

0.4],'fontsize',8); title('Grafik 3D menggunakan

MESH','fontweight','bold','fontsize',12) xlabel('Sumbu-x','fontweight','bold');

case 2

surf(ZI);

SURF','fontweight','bold','fontsize',12) xlabel('Sumbu-x','fontweight','bold');

case 3

surfl(ZI);

SURFL','fontweight','bold','fontsize',12) xlabel('Sumbu-x','fontweight','bold');

case 4

pcolor(ZI);

PCOLOR','fontweight','bold','fontsize',12) xlabel('Sumbu-x','fontweight','bold');

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Practice 22 - Continued

case 5

case 7

imagesc(ZI);

set(gca,'color',[.7 1 0.4],'fontsize',8);

title('Grafik 3D menggunakan

IMAGESC','fontweight','bold','fontsize',12) xlabel('Sumbu-x','fontweight','bold');

zlabel('Sumbu-z','fontweight','bold'); case 6 cc=contour(ZI);

clabel(cc,'fontsize',10,'color','white');

set(gca,'color',[0 0 0],'fontsize',8);

CONTOUR','fontweight','bold','fontsize',12) xlabel('Sumbu-x','fontweight','bold');

cc=contourf(ZI);

clabel(cc,'fontsize',10,'color','white');

set(gca,'color',[0 0 0],'fontsize',8);

CONTOURF','fontweight','bold','fontsize',12) xlabel('Sumbu-x','fontweight','bold');

otherwise

disp ('pilihan anda ngawuur!!!') end;

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WINDOW PROGRAM PART 1 (GUI)

By : INDRA KOMARA ST., MT

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Civil Engineering Department - ITATS

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