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) + 𝐞𝐞𝐱𝐱 (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 = 𝐳𝐳

|𝐱𝐱 − 𝐲𝐲| � 𝐱𝐱 ≥ 𝟎𝟎

�𝐳𝐳 = (𝐱𝐱 + 𝐲𝐲)𝟑𝟑𝐱𝐱 (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

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

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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 − 𝒙𝒙𝟐𝟐

𝟐𝟐!+ 𝒙𝒙𝟒𝟒

𝟒𝟒!− 𝒙𝒙𝟔𝟔

𝟔𝟔!+ ⋯

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 =𝐱𝐱𝟏𝟏!−𝐱𝐱𝟑𝟑

𝟑𝟑!+𝐱𝐱𝟓𝟓

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 ± √𝒃𝒃𝟐𝟐 − 𝟒𝟒𝟒𝟒𝒄𝒄

𝟐𝟐𝟒𝟒

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 =𝟏𝟏𝟐𝟐�𝒙𝒙 +

𝒃𝒃𝒙𝒙�

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 ∗ 𝐣𝐣𝟓𝟓

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� =𝟏𝟏𝐭𝐭�𝐱𝐱𝐬𝐬𝐭𝐭

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 = �𝐀𝐀𝐬𝐬𝟏𝟏𝟎𝟎

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 −𝟏𝟏𝟐𝟐𝟐𝟐

+𝟏𝟏𝟐𝟐𝟒𝟒

−𝟏𝟏𝟐𝟐𝟔𝟔

+𝟏𝟏𝟐𝟐𝟖𝟖

−𝟏𝟏𝟐𝟐𝟏𝟏𝟎𝟎

+𝟏𝟏𝟐𝟐𝟏𝟏𝟐𝟐

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)𝟐𝟐𝟏𝟏𝟐𝟐

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

=

=

906030805020704010

),(,963852741

),( JIBJIA

13

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

𝑺𝑺 = �𝟏𝟏 𝟒𝟒 𝟕𝟕 𝟏𝟏𝟎𝟎𝟐𝟐 𝟓𝟓 𝟖𝟖 𝟏𝟏𝟏𝟏𝟑𝟑 𝟔𝟔 𝟗𝟗 𝟏𝟏𝟐𝟐

�

Solution: program transpose_array integer,dimension(3,4):: N integer,dimension(4,3):: M do i=1,3 read(*,*)(N(i,j),j=1,4) enddo do i=1,3 do j=1,4 m(j,i) = N(i,j) enddo enddo do i=1,4 write(*,*)(M(i,j),j=1,3) enddo 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

×=

3654

KB

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 𝟑𝟑𝟏𝟏 𝟒𝟒

�

𝑩𝑩(𝟐𝟐,𝟑𝟑) = �−𝟏𝟏 𝟑𝟑 𝟒𝟒𝟐𝟐 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 #################################################################################