baskom 5 new

BASKOM-5 (YAKNI IDRIS) 1

In real programs we often need to handle a large amount of data in

the same way, e.g. to find the mean of a set of numbers, or to sort a

list of numbers or names, or to analyse a set of students' test

results, or to solve a system of linear equations.

Introduction to ARRAYS

To avoid an enormously clumsy program, where perhaps hundreds

of variable names are needed, we can use subscripted variables, or

arrays.

These may be regarded as variables with components, rather like

vectors or matrices.

They are written in the normal way, except that the subscripts are

enclosed in parentheses after the variable name, e.g. X(3), Y(I + 2 *

N)


XN

X ii

N

1

1

To illustrate the basic principles, let's compute the sample mean and

standard deviation of a set of N observations. The mean is defined as

where Xi is the ith observation. The standard deviation (s) is defined as

sN

X Xii

N2

2

1

1

1

Mean and Standard Deviation


IMPLICIT NONE

INTEGER :: I, N

REAL :: Std = 0

REAL, DIMENSION(100) :: X

REAL :: XBar = 0

OPEN (1, FILE = 'DATA')

READ (1, *) N

DO I = 1, N

READ (1, *) X(I)

XBar = Xbar + X(I)

END DO

XBar = XBar / N

DO I = 1, N

Std = Std + (X(I) - XBar) ** 2

END DO

Std = SQRT( Std / (N - 1) )

PRINT*, 'Mean: ', XBar

PRINT*, 'Std deviation: ', Std

END

Try this with some sample data (each

number on a separate line):

10 5.1 6.2 5.7 3.5 9.9 1.2 7.6 5.3 8.7 4.4

You should get a mean of 5.76 and a

standard deviation of 2.53 (to two decimal

places).


The DIMENSION(100) attribute in the type declaration statement for the array X sets

aside 100 memory locations, with names X(1), X(2), ..., X(100). However, the sample data

above consists of only 10 numbers, so only the first 10 locations are used. Note that the

value of N must be read first (and must be correct), before the N values may be read.

After the READ is complete, the memory area where the array is stored looks like this:

X(1) X(2) X(3) ... X(10)

5.1 6.2 5.7 ... 4.4

Now that the data are safely stored in the array, they may be used again, simply by

referencing the array name X with an element number, e.g. X(3). So the sum of the first

two elements may be computed as

SUM = X(1) + X(2)

This facility is necessary for computing s according to the formula above—the data must

all be read to compute the mean, and the mean must be computed before all the data is

re-used to compute s.


Having each data value on a separate line in the file is rather

cumbersome—this is required by the separate execution of each

READ (1, *) X(I) in the DO loop. Fortran allows the use of an implied

DO to read or print all or part of an array. Simply replace the entire

DO construct in the program with

READ (1, *) ( X(I), I = 1, N )

Note that the syntax requires parentheses around the implied DO.


Basic Rules and Notation

The array is our first example in Fortran 90 of a compound object, i.e. an object which

can have more than one value. Arrays can be fairly complicated creatures. Only the

basics are mentioned here; more advanced features will be introduced later.

The statement

REAL, DIMENSION(10) :: X

declares X to be an array (or list) with 10 real elements, denoted by X(1), X(2), ..., X(10).

The number of elements in an array is called its size (10 in this case). Each element of

an array is a scalar (single-valued).

Array elements are referenced by means of a subscript, indicated in parentheses after

the array name. The subscript must be an integer expression—its value must fall within

the range defined in the array declaration.

So X(I+1) is a valid reference for an element of X as declared above, as long as (I+1) is

in the range 1–10. A compiler error occurs if the subscript is out of range.


Basic Rules and Notation

By default arrays have a lower bound of 1 (the lowest value a subscript can take).

However, you can have any lower bound you like:

REAL, DIMENSION(0:100) :: A

declares A to have 101 elements, from A(0) to A(100). The upper bound must be

specified; if the lower bound is missing it defaults to 1.

An array may have more than one dimension. The bounds of each dimension must be

specified:

REAL, DIMENSION(2,3) :: A

A is a two-dimensional array. The number of elements along a dimension is called the

extent in that dimension. A has an extent of 2 in the first dimension, and an extent of 3 in

the second dimension (and a size of 6). Fortran allows up to seven dimensions. The

number of dimensions of an array is its rank, and the sequence of extents is its shape.

The shape of A is (2, 3), or (2x3) in matrix notation. A scalar is regarded as having a rank

of zero. We will concentrate mainly on one-dimensional arrays in this chapter—it is more

appropriate to discuss two-dimensional arrays in the context of matrices


Reading an unknown amount of data

The implied DO together with the IOSTAT specifier in READ provides a neat way of

reading an unknown amount of data into an array, where only the maximum size of the

array is given:

INTEGER, PARAMETER :: MAX = 100

REAL, DIMENSION(MAX) :: X

OPEN (1, FILE = 'DATA')

READ( 1, *, IOSTAT = IO ) ( X(I), I = 1, MAX )

IF (IO < 0) THEN

N = I - 1

ELSE

N = MAX

END IF

PRINT*, ( X(I), I = 1, N )

END

The data may be arranged in any format in the input file. Note that I is one greater than

the number of values read: it is incremented in the implied DO before the end-of-fileend-

of-filecondition is detected. Note also that on normal exit from the implied DO its value

would be MAX+1.


Write a program to find the student with the highest

mark in a class assumes that there is only one top

student. If there could be more than one name at the

top, you can use an array to make a list of the top

names.


IMPLICIT NONE

INTEGER :: I ! student counter

INTEGER :: IO ! value of IOSTAT

INTEGER, PARAMETER :: MAX = 100 ! maximum class size

INTEGER :: NumTop = 1 ! must be at least 1

REAL :: Mark ! general mark

REAL :: TopMark = 0 ! can't be less than 0

CHARACTER*15 :: Name ! general name

CHARACTER*15, DIMENSION(MAX) :: TopName ! top student

OPEN( 1, FILE = 'MARKS' )

DO

READ( 1, * , IOSTAT = IO) Name, Mark

IF (IO < 0) EXIT

IF (Mark > TopMark) THEN ! new top mark here

TopMark = Mark ! reset the top mark

NumTop = 1 ! only one at the top now

TopName(1) = Name ! here she is

ELSE IF (Mark == TopMark) THEN ! tie for top mark here

NumTop = NumTop + 1 ! advance top counter

TopName(NumTop) = Name ! add his name to the list

END IF

END DO

DO I = 1, NumTop

PRINT*, TopName(I), TopMark

END DO

END


To understand what the program does run through it by hand (make

a list of the variables, and enter their values) with the following data:

Botha 58

Essop 72

Jones 72

Murray 72

Rogers 90

Tutu 90

Then run it on the computer as a check. Note that at the end the

name Murray will still be in the array, in TopName(3), but his name

will not be printed because NumTop has been reset to 2.

You could try to rewrite this program with TopName as an

allocatable array to save memory space.


Variabel berlarik (berindeks)

Pernyataan DIMENSION

Bentuk umum:

DIMENSION array1(dim1), array2(dim2)

Kegunaan: untuk mendefinisikan sautu nama yang

merupakan suatu larik serta sekaligus menentukan

jumlah dari elemen-elemennya.

array1, array2 adalah nama larik yang didefinisikan .

dim1, dim2 adalah dimensi yang menunjukkan jumlah

elemen larik

Pernyataan DIMENSION hanya dapat diletakkan

dibagian awal dari program.


Tulislah sebuah program untuk membaca

sejumlah N data bilangan. Kemudian

program menghitung jumlah total bilangan

dan nilai rata-ratanya. Setelah itu, data

bilangan yang dibaca ditampilkan kembali

dan ditampilkan juga hasil perhitungan .


PROGRAM DIMENSI1

DIMENSION X(10)

WRITE(*,*) ' JUMLAH DATA = '

READ(*,*) N

TOTAL = 0.0

DO I=1,N

WRITE(*,'(A,I2)') ' DATA ',I

READ(*,*) X(I)

TOTAL = TOTAL + X(I)

END DO

RATA2 = TOTAL/N

WRITE(*,*) ' MENAMPILKAN KEMBALI DATA '

DO I=1,N

WRITE(*,'(A,I2,A,F12.4)') ' DATA',I, ' = ',X(I)

END DO

WRITE(*,*) ' HASIL PERHITUNGAN '

WRITE(*,'(A20,F12.4)') ' JUMLAH = ',TOTAL

WRITE(*,'(A20,F12.4)') ' NILAI RATA-RATA = ',RATA2

END


Tulislah program untuk membaca jumlah titik

serta koordinat x dan y masing-masing.

Kemudian program menghitung jarak antara

dua titik yang berurutan dengan rumus

Phytagoras. Setelah itu program menghitung

jarak total dari titik awal sampai titik ujung.


PROGRAM DIMENSI2

PARAMETER (M=100)

REAL X(M),Y(M), JARAK(M-1)

WRITE(*,*) ' JUMLAH TITIK = '

READ(*,*) N

DO I=1,N

WRITE(*,'(A,I2,A,\)') ' X',I,' = '

READ(*,*) X(I)

WRITE(*,'(A,I2,A,\)') ' Y',I,' = '

READ(*,*) Y(I)

END DO

WRITE(*,*) ' MENAMPILKAN KEMBALI DATA '

DO I=1,N

WRITE(*,100) ' X',I, ' ; Y',I,' =',X(I),' ;',Y(I)

END DO

100 FORMAT(A,I2,A,I2,A,F7.2,A,F7.2)

WRITE(*,*) ' HASIL PERHITUNGAN '

TOTAL = 0.0

DO I=1,N-1

DX = X(I+1) - X(I)

DY = Y(I+1) - Y(I)

JARAK(I)= (DX**2 + DY**2)**0.5

TOTAL = TOTAL + JARAK(I)

WRITE(*,'(A,I2,A,F12.4)')'JARAK',I,' = ',JARAK(I)

END DO

WRITE(*,'(A,F12.4)') ' JARAK TOTAL = ',TOTAL

END


Program untuk menghitung jumlah 2 buah matrik PROGRAM JUMLAH MATRIK

DIMENSION A(10,10),B(10,10),C(10,10)

CHARACTER*72 FIN,FOUT,JUDUL1,JUDUL2,JUDUL3

C menanyakan nama file masukan dan file keluaran

WRITE(*,90) 'NAMA FILE MASUKAN = '

READ(*,'(A)') FIN

WRITE(*,90) 'NAMA FILE KELUARAN = '

READ(*,'(A)') FOUT

OPEN(1,FILE=FIN,STATUS='UNKNOWN')

OPEN(2,FILE=FOUT,STATUS='UNKNOWN')

90 FORMAT(1X,A,\)

c membaca baris pertama dan kedua dari file masukan

READ(1,'(A)') JUDUL1

WRITE(*,*) JUDUL1

READ(1,*) JB,JK

WRITE(*,95) ' BARIS =',JB,' KOLOM =',JK

95 FORMAT(A,I2,A,I2)

c membaca baris ketiga dst dari file masukan

c data ini adalah data matrik pertama ([A])


WRITE(*,*) JUDUL2

DO I=1,JB

READ(1,*) (A(I,J),J=1,JK)

WRITE(*,100) (A(I,J),J=1,JK)

END DO

100 FORMAT(10(1X,F7.2))


c membaca baris berikutnya dari file masukan

c data ini adalah data matrik kedua ([B])


WRITE(*,*) JUDUL3

DO I=1,JB

READ(1,*) (B(I,J),J=1,JK)

WRITE(*,100) (A(I,J),J=1,JK)

END DO

c menjumlahkan matrik -> [C] = [A] + [B]

DO I=1,JB

DO J=1,JK

C(I,J) = A(I,J) + B(I,J)

END DO

END DO

c menampilkan matrik hasil penjumlahan ([C])

WRITE(*,*) ' Hasil penjumlahan matrik'

WRITE(2,*) ' Hasil penjumlahan matrik'

DO I=1,JB

WRITE(*,100) (C(I,J),J=1,JK)

WRITE(2,100) (C(I,J),J=1,JK)

END DO

END


kj

JK1

1kikij B*AC

Program untuk menghitung perkalian dua matrik dengan rumus

Dimana nilai: i=1 s/d JB1 JB1 =jumlah baris matrik 1

j=1 s/d JK2 JK1=jumlah kolom matrik 1

k=1 s/d JK1 JK2=jumlah kolom matrik 2


PROGRAM PERKALIAN MATRIK

DIMENSION A(10,10),B(10,10),C(10,10)

CHARACTER*72 FIN,FOUT,JUDUL1,JUDUL2,JUDUL3,JUDUL4

C menanyakan nama file masukan dan file keluaran

WRITE(*,90) 'NAMA FILE MASUKAN = '

READ(*,'(A)') FIN

WRITE(*,90) 'NAMA FILE KELUARAN = '

READ(*,'(A)') FOUT

OPEN(1,FILE=FIN,STATUS='UNKNOWN')

OPEN(2,FILE=FOUT,STATUS='UNKNOWN')

90 FORMAT(1X,A,\)

c membaca baris pertama dan kedua dari file masukan


WRITE(*,*) JUDUL1

READ(1,*) JB1,JK1

WRITE(*,95) ' BARIS =',JB1,' KOLOM =',JK1

95 FORMAT(A,I2,A,I2)

c membaca baris ketiga dst dari file masukan

c data ini adalah data matrik pertama ([A])


WRITE(*,*) JUDUL2

DO I=1,JB1

READ(1,*) (A(I,J),J=1,JK1)

WRITE(*,100) (A(I,J),J=1,JK1)

END DO

100 FORMAT(10(1X,F7.2))


c membaca baris berikutnya dari file masukan

c data ini adalah data matrik kedua ([B])


WRITE(*,*) JUDUL3

READ(1,*) JK2

WRITE(*,95) ' BARIS =',JK1,' KOLOM =',JK2


WRITE(*,*) JUDUL4

DO I=1,JK1

READ(1,*) (B(I,J),J=1,JK2)

WRITE(*,100) (B(I,J),J=1,JK2)

END DO

c mengalikankan matrik -> [C] = [A] * [B]

DO I=1,JB1

DO J=1,JK2

C(I,J) = 0.0

DO K=1,JK1

C(I,J)=C(I,J)+A(I,K)*B(K,J)

END DO

END DO

END DO

c menampilkan matrik hasil perkalian ([C])

WRITE(*,*) ' Hasil perkalian matrik'

WRITE(2,*) ' Hasil perkalian matrik'

DO I=1,JB1

WRITE(*,100) (C(I,J),J=1,JK2)

WRITE(2,100) (C(I,J),J=1,JK2)

END DO

END

baskom 5 new

Documents