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### Transcript of Pemrograman Komputer - 03 Matlab

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Matlab

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Matlab

1. the command window,

2. the command-history window,

3. the current directory window or (hidden in this

view) the workspace(variable window),

4. the file information window,

5. the icon toolbar with the choice menu for the

current directory,

6. the shortcut toolbar, and7. the start button.

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1. the command window,

2. the command-history window,

3. the current directory window or (hidden in this view) the

workspace(variable window), 4. the file information window,

5. the icon toolbar with the choice menu for the current

directory,

6. the shortcut toolbar, and

7. the start button.

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Arithmetic

Penambahan +

Pengurangan -

Perkalian * Pembagian /

Pangkat

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Operation Algebraic form Matlab Example

Addition a + b a + b 5 +3

Subtraction a b a - b 23-12

Multiplication a b a * b 3.14*0.85

Right division a b a / b 56/8

Left division b a a \ b 8\56

Exponentiation ab a b 5

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Arithmetic

>> 32 - (5 + 4)/2 + 6*3

ans =

22.5000

>> ans2 + sqrt(ans)

ans =

510.9934

>> u = cos(10)

u =

-0.8391

>> v = sin(10)

v =

-0.5440

>> u2 + v2

ans =

1

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Aljabar

Perhitungan dgn simbol gunakansyms untuk variabel

>> syms x y

>> (x - y)*(x - y)2

ans =

(x-y)^3

>> expand(ans)

ans =

x^3-3*x^2*y+3*x*y^2-y^3

>> factor(ans)

ans =

(x-y)^3

Penyederhanaan

>> simplify((x3 - y3)/(x - y))

ans =

x^2+x*y+y^2

The command expand

told MATLAB to multiply out theexpression, and

factor forced MATLAB

to restore it to factored form.

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Aljabar

>> cos(pi/2)

ans =

6.1232e-17

>> cos(sym(pi/2))ans =

0

>> sym(1/2) + sym(1/3)

ans =

5/6

variable-precisionarithmetic vpa.

50 digits 2

>> vpa(sqrt(2), 50)

ans =

1.41421356237309504

88016887242096980785696718753769

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Variables and Assignments

>> x = 7

x =

7

variable x akan bernilai 7 kapanpun MATLABmelihat huruf x

Misal y adalah symbolic:

>> x2 - 2*x*y + yans =

49-13*y

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To clear the value of the variable x, type clear x.

You can make very general assignments for symbolicvariables and then manipulate them. For example,

>> clear x; syms x y>> z = x2 - 2*x*y + y

z =

x^2-2*x*y+y

>> 5*y*zans =

5*y*(x^2-2*x*y+y)

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Penyelesaian Persamaan

Gunakan solve or fzero.

Contoh: x2 2x 4 = 0

>> solve(x2 - 2*x - 4 = 0)ans =

[ 5^(1/2)+1]

[ 1-5^(1/2)]

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>> [x, y] = solve(x2 - y = 2, y - 2*x = 5)

x =

[ 1+2*2^(1/2)]

[ 1-2*2^(1/2)]

y =

[ 7+4*2^(1/2)]

[ 7-4*2^(1/2)]

>> x(1)

ans =

1+2*2^(1/2)

>> y(1)

ans =

7+4*2^(1/2)

The second solution can be extracted with x(2) and y(2).

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Coba

>> x= 1.23

x=1.23

>> vector = [1 2 -3]

vector =

1 2 -3

>> thematrix = [3 1+2*i 2; 8 0 -5]

thematrix =3.0000 1.0000 + 2.0000i 2.0000

8.0000 0 -5.0000

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>> colvector = [2; 4; 3; -1; 1-4*j]

colvector =

2.00004.0000

3.0000

-1.00001.0000 - 4.0000i

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>> [2,3,4; 3,-1,0]

ans =

2 3 43 -1 0

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>> who

Your variables are:

ans colvector thematrix vector x

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>> whos

Name Size Bytes Class

ans 2x3 48 double array

colvector 5x1 80 double array (complex)

thematrix 2x3 96 double array (complex)

vector 1x3 24 double array

x 1x1 8 double array

Grand total is 21 elements using 256 bytes

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The workspace browser

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Representation of a matrix in the

array editor

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>> thematrix = [thematrix; 1 2 3]

thematrix =

3.0000 1.0000 + 2.0000i 2.00004.0000 0 -5.0000

1.0000 2.0000 3.0000

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>> thematrix = [thematrix, [1;2;3]]

thematrix =

3.0000 1.0000 + 2.0000i 2.0000 1.00004.0000 0 -5.0000 2.0000

1.0000 2.0000 3.0000 3.0000

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>> v = [1;2;3]

v =

1

2

3

>> thematrix = [thematrix, v]

thematrix =

3.0000 1.0000 + 2.0000i 2.0000 1.0000

4.0000 0 -5.0000 2.0000

1.0000 2.0000 3.0000 3.0000

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>> thematrix(:,2) = [] %menghapus kolom 2

thematrix =

3 2 1

4 -5 2

1 3 3

>> thematrix(1,:) =[] %menghapus baris 1

thematrix =

4 -5 2

1 3 3

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Vector Step 2

>> largevector = (0:2:5000)

largevector =

Columns 1 through 12

0 2 4 6 8 10 12 14 16 ...Columns 13 through 24

24 26 28 30 etc.

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Memilih baris tertentu

>> firstrow = thematrix(1,:)

firstrow =

4 -5 2

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The Colon Operator

The expression

1:10

is a row vector containing the integers from 1 to 10

1 2 3 4 5 6 7 8 9 10

To obtain non unit spacing, specify an increment. For example,

100:-7:50

is

100 93 86 79 72 65 58 51

and

0:pi/4:piis

0 0.7854 1.5708 2.3562 3.1416

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>> t=(0:1:5) % (0= start, 1 = sela, 5=end)

t =

0 1 2 3 4 5

>> s=sin(t)

s =

0 0.8415 0.9093 0.1411 -0.7568 -0.9589

The sine of the specified vector t is again a vector,specifically, the vector

s = ( sin (0), sin (1), sin (2), , sin (5)) .

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plot

>> t = (0:1:5);

>> s = sin(t);

>> plot(t,s)

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Creating a Plot

The plot function has different forms, depending on the input arguments.

If y is a vector, plot(y) produces a piecewise linear graph of the elements of y

versus the index of the elements of y.

If you specify two vectors as arguments, plot(x,y) produces a graph of y versusx.

For example, these statements use the colon operator to create a vector of x

values ranging from zero to , compute the sine of these values, and plot the

result.

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

y = sin(x);

plot(x,y)

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Creating a Plot

Now label the axes and add a title.

The characters \pi create the symbol .

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

ylabel('Sine of x')

title('Plot of the Sine Function','FontSize',12)

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Multiple Data Sets in One Graph

Multiple x-y pair arguments create multiple graphswith a single call to plot.

MATLAB automatically cycles through a predefined(but user settable) list of colors to allow discrimination

between each set of data. For example, these statements plot three related

functions of x, each curve in a separate distinguishingcolor.

y2 = sin(x-.25);

y3 = sin(x-.5);

plot(x,y,x,y2,x,y3)

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Multiple Data Sets in One Graph

Legend

legend('sin(x)','sin(x-.25)','sin(x-.5)')

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Specifying Line Styles and Colors

It is possible to specify color, line styles, and

markers (such as plus signs or circles) when

you plot your data using the plot command.

plot(x,y,'color_style_marker')

Color strings:

'c', 'm', 'y', 'r', 'g', 'b', 'w', and 'k'.

cyan, magenta, yellow, red, green, blue, white, and

black.

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Line & Marker

Linestyle strings:

'-' for solid,

'--' for dashed,

':' for dotted,'-.' for dash-dot,

'none' for no line.

The marker types:'+', 'o', '*', and 'x'

the filled marker types

's for square,

'd' for diamond,

'^' for up triangle,'v' for down triangle,

'> for right triangle,

'

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Plotting Lines and Markers

>>plot(x,y,'ks') plots black squares at each data point, but does not connect the

markers with a line.

>>plot(x,y,'r:+')

plots a red dotted line and places plus sign markers at each datapoint.

This example plots the data twice using a different number ofpoints for the dotted line and marker plots.

x1 = 0:pi/100:2*pi;x2 = 0:pi/10:2*pi;

plot(x1,sin(x1),'r:',x2,sin(x2),'r+')

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Axis Labels and Titles

The xlabel, ylabel, and zlabel commands add

x-, y-, and z-axis labels.t = -pi:pi/100:pi;

y = sin(t);plot(t,y)

axis([-pi pi -1 1])

xlabel('-\pi \leq {\itt} \leq \pi')

ylabel('sin(t)')title('Graph of the sine function')

text(1,-1/3,'{\itNote the odd symmetry.}')

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