Array:
The numerical values which are generally elements of an associated group is known as array.
There are several dimensional array
1. One dimensional array
2. Two dimensional array
3. Multidimensional array
One dimensional array:
One dimensional array can be written as
x1 x2 x3 x4 ………….xn
But in Fortran it can be written as
x(1) x(2) x(3) ………..x(n)
Two dimensional array:
The variable which has two subscripts is known as two dimensional array. It is written as
x1,1 x1,2
x2,1 x2,2
Here 1,1 1,2 2,1 2,2 are the subscripted variable.
But in Fortran it can be written as x(1,1) x(2,2) x(2,1) x(2,2)
Multidimensional array:
The variable which is more then two subscripts is known as multidimensional array.
Let’s start calculation with Dimension statement. To solve a problem we first have to declare the dimension through the dimension statement.
Example:
Find Mean Variance Standard deviation absolute deviation of following array.
x
|
12
|
23
|
16
|
14
|
18
|
24
|
25
|
30
|
35
|
20
|
Solution :
1234567890
Dimension x(10)
Write(*,*) 'Enter the value of N'
Read(*,*) N
Do i = 1,N
Write(*,*) 'Enter the value of the array x(',i,')'
Read(*,*) x(i)
End do
sum = 0.0
Do j = 1,N
sum = sum+ x(j)
End do
Ave = sum / N
Var = 0.0
Do k = 1,N
Var = Var + (x(k)-Ave)**2/N
End do
Absd=0.0
Do M = 1,N
Absd = Absd+ abs(x(M)-Ave)
End do
sd = sqrt(Var)
write(*,*) ' The variance of the array is = ', Var ,Ave
Write(*,*) 'The standard deviation of the array is =', sd
Write(*,*) ' The absolute deviation is = ' ,Absd
End
Here the output will be like this:
Enter the value of N
10
Enter the value of the array x( 1)
12
Enter the value of the array x( 2)
23
Enter the value of the array x( 3)
16
Enter the value of the array x( 4)
14
Enter the value of the array x( 5)
18
Enter the value of the array x( 6)
24
Enter the value of the array x( 7)
25
Enter the value of the array x( 8)
30
Enter the value of the array x( 9)
35
Enter the value of the array x( 10)
20
The variance of the array is = 46.6100006
The standard deviation of the array is = 6.82715178
The absolute deviation is = 57.
**Find the correlation coefficient and regression coefficient of Y on X of the following array.
x
|
7
|
3
|
5
|
3
|
8
|
9
|
2
|
6
|
12
|
6
|
y
|
5
|
3
|
8
|
9
|
4
|
2
|
4
|
3
|
7
|
10
|
x
|
13
|
3
|
5
|
9
|
6
|
4
|
7
|
3
|
5
|
12
|
y
|
15
|
7
|
8
|
6
|
5
|
16
|
13
|
2
|
7
|
1
|
x
|
16
|
12
|
17
|
19
|
14
|
3
|
7
|
9
|
7
|
3
|
y
|
12
|
3
|
16
|
19
|
10
|
12
|
5
|
9
|
10
|
7
|
Solution:
We know that
Correlation coefficient is
And regression coefficient of Y on X is
From the above formula we see that we need sum of x , sum of y , sum square of x , sum square of y and sum product of xy. So at first we have to calculate following terms
1234567890
dimension x(100) ,Y(100)
do i = 1,30
print*, 'enter value of array x'
read(*,*) x(i)
Write(*,*) 'Enter the value of array y'
Read(*,*) y(i)
end do
sumx=0
do i=1,30
sumx=sumx+x(i)
enddo
avex=sumx/10.0
avey=sumy/10.0
sum1=0
sum2=0
spxy=0
do i=1,30
sum1=sum1+(x(i)-avex)**2
sum2=sum2+(y(i)-avey)**2
spxy=spxy+(x(i)-avex)*(y(i)-avey)
end do
correlation= spxy/sqrt(sum1*sum2)
Byx=spxy/sum1
print*, 'the value of corr',correlation
print*, 'Byx is=',Byx
stop
End
Description:
Here we use do I = 1,30 because there are 30 observation in array x and 30 observation in array y. So to read and calculation we have to use do I = 1,30.
** Find the multiplication of following matrix
Solution:
1234567890
Dimension A(3,2),B(2,3),C(3,3)
write(*,*) 'Enter the value of matrix A'
Do 10 k = 1,3
Do 10 j = 1,2
Read(*,*) A(k,j)
10 Continue
Write(*,*) 'Enter the value of matrix B'
Do 20 i = 1,2
Do 20 l = 1,3
Read(*,*) B(i,l)
20 Continue
Do 30 i = 1,3
Do 30 j = 1,3
C(i,j) = 0.0
Do 30 k = 1,2
C(i,j) = C(i,j) + A(i,k)*B(k,j)
30 Continue
Write(*,*) C( 1,1) , C(1,2) ,C(1,3)
Write(*,*) C( 2,1) , C(2,2) ,C(2,3)
Write(*,*) C(3,1) , C(3,2) ,C(3,3)
End
Here the output will be like this.
Enter the value of matrix A
4
3
6
5
8
9
Enter the value of matrix B
4
6
4
7
7
5
37. 45. 31.
59. 71. 49.
95. 111. 77.
Here we have to put the values row wise.
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