First Step to Computer Programming With FORTRAN 90

Kurdistan Iraqi Region

Ministry of Higher Education

University of Sulaimani

College of Science

Physics Department

Dr. Dlear R. Saber

Dr. Omed Gh. Abdullah

Mr. Ary A. Abdulrahman

Mr. Shaho Osman

2009 - 2010

First step to

Computer Programming

With FORTRAN 90

First stage

2

Problem (1): Write a Fortran program to calculate the value of function 𝒇𝒇(𝒙𝒙); where x= [-5, 0, 5]:

𝐟𝐟(𝐱𝐱) = � 𝐭𝐭𝐭𝐭𝐭𝐭−𝟏𝟏_{(𝐱𝐱) + 𝐞𝐞}𝐱𝐱 _{(𝐱𝐱 > 0)} 𝟎𝟎 (𝐱𝐱 = 𝟎𝟎) �𝐱𝐱𝟐𝟐_{+ 𝟐𝟐 (𝐱𝐱 < 2)} Solution: read*, x if(x>0) then y=Atan(x) +exp(x) print*, x, y elseif(x<0) then y=sqrt(x**2+2) print*, x, y else y=0 print*, x, y endif end #################################################################################

Problem (2): Write a program in Fortran 90 using coditional control statement to find the value of

(𝒁𝒁, 𝑾𝑾) according to value of 𝒙𝒙, 𝒚𝒚 from the equations below, if(𝒙𝒙 = 𝟑𝟑) and (𝒚𝒚 = 𝟐𝟐): 𝐳𝐳 = |𝐱𝐱| + (𝐱𝐱 + 𝐲𝐲) 𝐰𝐰 =_{|𝐱𝐱 − 𝐲𝐲|} 𝐳𝐳 � 𝐱𝐱 ≥ 𝟎𝟎 𝐳𝐳 = (𝐱𝐱 + 𝐲𝐲)_𝐱𝐱 𝟑𝟑(𝐱𝐱 + 𝐳𝐳) 𝐰𝐰 = 𝐱𝐱𝟐𝟐_{+ 𝟐𝟐𝐳𝐳} � 𝐱𝐱 < 0 Solution: do read*,x,y if(x==0.or.x>0) goto 50 z=(x+y)**3/(x+z) w=x**2+2*z goto 70 50 z=abs (x)+(x+y) w=z/abs(x+z) 70 print*, z,w read*, choice if (choice==0) exit enddo end #################################################################################

3

Problem (3): Write a Fortran program to calculate exponential of (1) from library function (𝑬𝑬𝑬𝑬𝑬𝑬)

and from the following series up to (15):

𝐞𝐞𝐱𝐱 _{= 𝟏𝟏 + 𝐱𝐱 +}𝐱𝐱𝟐𝟐 𝟐𝟐! + 𝐱𝐱𝟑𝟑 𝟑𝟑! + 𝐱𝐱𝟒𝟒 𝟒𝟒! + ⋯ Solution: x=1 s=1 do i=1,15 f=1 do j=1,i f=f*j enddo s=s+x**i/f enddo print*,s,exp(x) end #################################################################################

Problem (4): Write a Fortran program to calculate exponential of (1) from library function (𝑬𝑬𝑬𝑬𝑬𝑬)

and from the following series up to (15), [without using do-loops]:

𝐞𝐞𝐱𝐱 _{= 𝟏𝟏 + 𝐱𝐱 +}𝐱𝐱𝟐𝟐 𝟐𝟐! + 𝐱𝐱𝟑𝟑 𝟑𝟑! + 𝐱𝐱𝟒𝟒 𝟒𝟒! + ⋯ Solution: x=1 b=1 n=0 s=1 10 n=n+1 if (n<=15) then b=b*x/n s=s+b goto 10 endif z=exp(x) print*,s,z end #################################################################################

Problem (5): Write a fortran program to calculate 𝒄𝒄𝒄𝒄𝒄𝒄(𝒙𝒙) from library function (𝑪𝑪𝑪𝑪𝑪𝑪) and from following series up to power (20):

𝐜𝐜𝐜𝐜𝐜𝐜( 𝒙𝒙) = 𝟏𝟏 −

+

−

+ ⋯

Solution:

read*, x s=1

4 sign=-1 do i=2,20,2 f=1 do j=1,i f=f*j enddo s=s+(sign*x**i)/f sign=-1*sign enddo print*,s,cos(x) end #################################################################################

Problem (6): Write a Fortran program to calculate sin(x) from library function (𝑪𝑪𝑺𝑺𝑺𝑺) and the

following series up to power (15), [input the value of 𝒙𝒙 by degree]:

𝐜𝐜𝐬𝐬𝐭𝐭 𝐱𝐱 =_{𝟏𝟏! −}𝐱𝐱 𝐱𝐱_{𝟑𝟑! +}𝟑𝟑 𝐱𝐱_{𝟓𝟓! − ⋯}𝟓𝟓 Solution: read*, x c=(22./7)/180 x=x*c sign=1 s=0 do i=1,15,2 f=1 do j=1,i f=f*j enddo s=s+sign*x**i/f sign=-1*sign enddo print*,s,sin(x) end #################################################################################

Problem (7): Write a Fortran program to calculate the sum of series from one to (n) integer [without using do-loops]:

Solution: integer i,n read*,n sum=0 do 10 i=1,n sum=sum+i print*,i,sum

5

10 continue print*,sum end

#################################################################################

Problem (8): Write afortran program to print the following series, [without using do-loops]:

( 𝟏𝟏 , 𝟐𝟐 , 𝟒𝟒 , 𝟖𝟖 , 𝟏𝟏𝟔𝟔 , 𝟑𝟑𝟐𝟐 , 𝟔𝟔𝟒𝟒 , 𝟏𝟏𝟐𝟐𝟖𝟖 ) Solution: integer n n=1 10 print*,n If (n<=100) then n=2*n goto 10 endif end #################################################################################

Problem (9): Write a Fortran program to find the real solution of the function:

𝒇𝒇(𝒙𝒙) = 𝒙𝒙𝟐𝟐_{+ 𝟐𝟐𝒙𝒙 − 𝟏𝟏}

Using the equation:

𝒙𝒙 =−𝒃𝒃 ± √𝒃𝒃_{𝟐𝟐𝟒𝟒}𝟐𝟐− 𝟒𝟒𝟒𝟒𝒄𝒄 Solution: read*, a,b,c s=b**2-4*a*c if (s<0) then print*,'ther is no solution' else x1=(-b+sqrt(S))/(2*a) x2=(-b-sqrt(s))/(2*a) print*,x1,x2 endif end #################################################################################

Problem (10): Write a Fortran program to read a two number (𝟒𝟒, 𝒃𝒃), and check if (𝟒𝟒) is posetive or negative or zero , and compare (𝟒𝟒) with (𝒃𝒃):

Solution:

read*,a,b if (a>0) then if (a>b) then

6

print*,'(a) is posetive and greater than (b)' elseif (a<b) then

print*,'(a) is posetive and smaller than (b)' else

print*,'(a) is posetive and equal to (b)' endif

elseif (a<0) then if (a>b) then

print*,'(a) is negative and greater than (b)' elseif (a<b) then

print*,'(a) is negative and smaller than (b)' else

print*,'(a) is negative and equal to (b)' endif

else

if (a>b) then

print*,'(a) is zero and greater than (b)' elseif (a<b) then

print*,'(a) is zero and smaller than (b)' else

print*,'(a) is zero and (b) is zero ' endif

endif end

#################################################################################

Problem (11): Write a loop to read (𝒏𝒏) real numbers and print their sum after all aditions:

Solution: s=0.0 read*, n summation: do i=1,n read*,i sum=sum+i print*,sum end do summation end #################################################################################

Problem (12): Write a Fortran program to find the maximum and minimum values among ten numbers; [read the the numbers from text data file]:

Solution:

open(5,file='data.txt') read(5,*)x

7 max=x min=x do i=1,9 read(5,*)x if (x>max) max=x if (x<min) min=x enddo

write(*,*) 'maximum no.=',max write(*,*) 'minimum no.=',min end

#################################################################################

Problem (13): Write a Fortran program to find the number of odd and even integers among (15) numbers; [read the the numbers from text data file]:

Solution: open(5,file='data.txt') odd=0 even=0 do i=1,15 read(5,*)x if (x==(int(x/2)*2)) then even=even+1 else odd=odd+1 endif enddo write(*,*)'number of odd=',odd write(*,*)'number of even=',even end #################################################################################

Problem (14): Write a Fortran program to sort (15) numbers, from minimum to maximum; [read the the numbers from text data file]:

Solution: dimension a(15) open (5,file='data.txt') do i=1,15 read(5,*) a(i) enddo do i=1,14 do j=i+1,15 if (a(i)>a( j))then x=a(i)

8 a(i)=a(j) a(j)=x endif enddo enddo do i=1,15 write(*,*) a(i) enddo end #################################################################################

Problem (15): Write a Fortran program to computes the square rootes of 1, 1.5, 2, 2.5, 3, ..., 10 by Newton’s method: 𝑺𝑺𝑵𝑵𝑵𝑵 𝒙𝒙 =𝟏𝟏_𝟐𝟐�𝒙𝒙 +𝒃𝒃_𝒙𝒙� Solution: do b=1,10,0.5 x=b do xn=0.5*(x+b/x) if (abs (x-xn)<0.00001) exit x=xn enddo print*,'sqrt(',b,')=',x enddo end #################################################################################

Problem (16): Write a Foretran program to show how to write a counting loop with real numbers.

variable 𝐱𝐱 receves values −𝟏𝟏. 𝟎𝟎 , −𝟎𝟎. 𝟕𝟕𝟓𝟓 , −𝟎𝟎. 𝟓𝟓 , −𝟎𝟎. 𝟐𝟐𝟓𝟓 , 𝟎𝟎. , 𝟎𝟎. 𝟐𝟐𝟓𝟓 , 𝟎𝟎. 𝟓𝟓 , 𝟎𝟎. 𝟕𝟕𝟓𝟓 𝟒𝟒𝒏𝒏𝒂𝒂 𝟏𝟏. 𝟎𝟎; [without using do-loops]

Solution:

real , parameter :: lower = -1.0 real , parameter :: upper = 1.0 real , parameter :: step = 0.25 real :: x=lower do if (x>upper) exit print*, x x=x+ step enddo end #################################################################################

9

Problem (17): Write a Fortran program to multiple i and j , where i=1:9 , j=1:9

Solution: integer i, j do i=1,9 do j=1,9 k= i*j print*,k enddo enddo end #################################################################################

Problem (18): Write a program in Fortran 90 to calculate the value of 𝑪𝑪 from the equation below: 𝐜𝐜 = � � 𝐬𝐬 ∗ 𝐣𝐣 𝟓𝟓 𝐣𝐣=𝟏𝟏 𝟑𝟑 𝐬𝐬=𝟏𝟏 Solution: program summation s=0.0 do i=1,3 do j=1,5 s=s+i*j enddo enddo

write(*,*)'The result value of S=', s end program summation

#################################################################################

Problem (19): Write a Fortran program to sort the following numbers from biger to smaller [use

Data comand to read the numbers]:

𝐱𝐱 = [𝟓𝟓 , 𝟖𝟖 , −𝟐𝟐 , 𝟐𝟐 , 𝟔𝟔 , 𝟑𝟑 , 𝟎𝟎 , 𝟒𝟒 , 𝟗𝟗 , 𝟏𝟏] Solution: dimension x (10) Parameter (n=10) data (x(i),i=1,n) /5,8,0,2,6,3,-2,4,9,1/ k=1 10 do i=k,n if (x(k)<x(i)) then s=x(k) x(k)=x(i) x(i)=s endif enddo k=k+1

10

If (k<=n) goto 10 print*,(x(i),i=1,n) end

#################################################################################

Problem (20): Write a Fortran program to computes these two quantites from (10) numbers; [read the the numbers from text data file]:

𝐱𝐱� =_{𝐭𝐭 � 𝐱𝐱𝐬𝐬}𝟏𝟏 𝐭𝐭 𝐬𝐬=𝟏𝟏 𝐜𝐜𝟐𝟐₌ 𝟏𝟏 𝐭𝐭 − 𝟏𝟏 �(𝐱𝐱𝐬𝐬 − 𝐱𝐱�) 𝐭𝐭 𝐬𝐬=𝟏𝟏 Solution: dimension x(10) real::xbar=0 std=0 n=10 open(1,file='data.text') do i=1,n read(1,*) x(i) xbar=xbar+x(i) enddo xbar=xbar/n do i=1,n std=std+(x(i)-xbar)**2 enddo std=sqrt(std/(n-1)) write(*,*)'mean=',xbar write(*,*)'std=',std end #################################################################################

Problem (21): Write a Fortran program to calculate the ages average of (10) students in the first stage; [read the the numbers from text data file], where:

𝐭𝐭𝐚𝐚𝐞𝐞 𝐭𝐭𝐚𝐚𝐞𝐞𝐚𝐚𝐭𝐭𝐚𝐚𝐞𝐞 = � 𝐀𝐀𝐬𝐬 𝟏𝟏𝟎𝟎 𝐈𝐈=𝟏𝟏 Solution: real,dimension(10)::a open(4,file='data.txt') sum=0.0 do i=1,10 read(4,*) a(i) sum=sum+a(i) enddo

11

average = sum/10

print*,'the age average of student is =',average end

#################################################################################

Problem (22): Write a Fortran program to find the average marks of class (10 students) for computer examination using dimension statement; [read the data from screan]:

Solution:

real,dimension(10)::x real::s

s=0.0 do i=1,10

print*,'supply mark of student no.',i read*, x(i) s=s+x(i) end do print*,'average s core is ', s/10 end #################################################################################

Problem (23): Write a program in Fortran 90 to find the value of ( S ) from sireas bellow:

𝑪𝑪 = 𝟏𝟏 −_𝟐𝟐𝟏𝟏_𝟐𝟐+_𝟐𝟐𝟏𝟏_𝟒𝟒−_𝟐𝟐𝟏𝟏_𝟔𝟔+_𝟐𝟐𝟏𝟏_𝟖𝟖−_𝟐𝟐𝟏𝟏_{𝟏𝟏𝟎𝟎}+_𝟐𝟐𝟏𝟏_{𝟏𝟏𝟐𝟐} Solution: s=1 j=0 do i=2,20,2 j=j+1 s=s+(-1)**j/2.**i enddo print*,'the value of S =',s end #################################################################################

Problem (24): Write a Fortran program to calculate (𝑬𝑬) from following equation:

𝑬𝑬 = ��(𝒏𝒏 + 𝟓𝟓) 𝟏𝟏𝟎𝟎 𝒏𝒏=𝟏𝟏 � 𝟏𝟏/𝟐𝟐 Solution: p=0.0 do n=1,10 p=p+(n+5)

12 enddo p=sqrt(p) print*,p end #################################################################################

Problem (25): Write a Fortran program to calculat the value of (𝑨𝑨𝑨𝑨) from the following equation, when (𝒏𝒏 = 𝟓𝟓) and (𝒎𝒎 = 𝟕𝟕): 𝑨𝑨𝑨𝑨 = ��(𝒎𝒎 + 𝒏𝒏)𝟐𝟐 𝟏𝟏𝟐𝟐 𝒊𝒊=𝟏𝟏 � 𝟏𝟏/𝟐𝟐 Solution: Al=0.0 n=5 m=7 do i=1,12 Al=Al+(m+n)**2 enddo Al=sqrt(Al) print*, Al end #################################################################################

Problem (26): Write a program in Fortran 90 to calculate the resultant matrix 𝑪𝑪(𝑺𝑺, 𝑱𝑱) from [𝑪𝑪(𝑺𝑺, 𝑱𝑱) = 𝑨𝑨(𝑺𝑺, 𝑱𝑱) + 𝑩𝑩(𝑺𝑺, 𝑱𝑱)] when: Solution: integer,dimension(3,3):: a,b,c do j=1,3 do i=1,3 read(*,*)a(i,j),b(i,j) enddo enddo do j=1,3 do i=1,3 c(i,j)=a(i,j)+b(i,j) enddo enddo do i=1,3 write(*,*)(c(i,j),j=1,3) enddo

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=

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

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=

90

60

30

80

50

20

70

40

10

)

,

(

,

9

6

3

8

5

2

7

4

1

)

,

(

I

J

B

I

J

A

13

end

#################################################################################

Problem (27): Write a program in Fortran 90 to find the transpose of the following matrix:

𝑺𝑺 = �

𝟏𝟏 𝟒𝟒 𝟕𝟕 𝟏𝟏𝟎𝟎

𝟐𝟐 𝟓𝟓 𝟖𝟖 𝟏𝟏𝟏𝟏

𝟑𝟑 𝟔𝟔 𝟗𝟗 𝟏𝟏𝟐𝟐

�

end Program transpose_array

#################################################################################

Problem (28): Write a program in Fortran 90 to find the value of matrix 𝑩𝑩 when 𝑲𝑲 = 𝟓𝟓:

Solution: program B_array integer,dimension(2,2)::A,B read(*,*)K do J=1,2 do I=1,2 read(*,*)A(I,J) B(I,J)=K*A(I,J) enddo enddo

print*,'The result of matrix' do I=1,2

write(*,*)(B(I,J),J=1,2) enddo

end Program B_array



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

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×

=

3

6

5

4

K

B

14

#################################################################################

Problem (29): Write a Fortran program to find the result of multiplication of two matrix

𝑪𝑪(𝟑𝟑, 𝟑𝟑) = 𝑨𝑨(𝟑𝟑, 𝟐𝟐) ∗ 𝑩𝑩(𝟐𝟐, 𝟑𝟑), where: 𝑨𝑨(𝟑𝟑, 𝟐𝟐) = �𝟐𝟐 −𝟐𝟐𝟒𝟒 𝟑𝟑 𝟏𝟏 𝟒𝟒 � 𝑩𝑩(𝟐𝟐, 𝟑𝟑) = �−𝟏𝟏 𝟑𝟑 𝟒𝟒_{𝟐𝟐 𝟓𝟓 𝟎𝟎�} Solution: integer,dimension(3,2):: A integer,dimension(2,3):: B integer,dimension(3,3):: C

write(*,*)'Input the matrix A(3,2)' do i=1,3

read(*,*) (A(i,j),j=1,2) enddo

write(*,*)'Input the matrix B(2,3)' do i=1,2 read(*,*) (B(i,j),j=1,3) enddo do i=1,3 do j=1,3 C(i,j)=0 do k= 1,2 C(i,j)=C(i,j)+A(i,k)*B(k,j) enddo enddo enddo do I=1,3 print*, (c(i,j),j=1,3) enddo end #################################################################################