Controlling the flow of Your Program

This chapter introduces the concept of comparison between two numbers or two character strings, and explains how such comparisons can be used to determine which of two, or more, alternatives sections of the code obeyed.

Introduction to Scientific & Engineering Computing

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In everyday life we frequently encounter a situation which involves several possible alternative courses of action, requiring us to choose one of them based on some decision-making criteria.

 The ability of a program to specify how these decisions are to be made is one of the most important aspects of programming.

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Choice and decision-making

if (criterion_1) then

action_1

else if (criterion_2) then

action_2

else if (criterion_3) then

action_3

else

action_4

endif

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Logical variables and expressions Logical variables + logical constants + logical operators

Decision criterion in F language depends upon whether assertion is “true” or “false”, which are called logical variables and are declared as follows :

  logical : : var_1, var_2, var_3

In F language we can simply write these logical values enclosed between dots :

  .true.

.false.

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Logical (relational) operators

An assertion or expression which can take one of the local variables “true” and “false”, is called a logical expression. The simplest forms of logical (relational) expressions are those expressing the relationship between 2 numeric values as,

a < b less thana <= b less than or equal toa > b greater thana >= b greater than or equala == b equala /= b not equal

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Logical (relational) operators

Similar to the relational operators, arithmetic expressions seen below can also be performed in F language so that all arithmetic operators have a higher priority than any relational operators :

expression_1 relational operator expression_2

where expression_i can be numeric, character and logical expressions.

Examples for these mixed typed logical examples which contain both arithmetic operators and relational operators can be seen below :

b ** 2 > = 4 * a *c b ** 2 - 4 * a * c > = 0

4 * a * c < = b ** 2 4 * a * c - b ** 2 < = 0 6

Compound logical expressionsIn F language composite or compound expressions are formed by combining logical expressions by using the logical operators given below regarding the priority rules also given at the end of this section :

EXAMPLES :

( a < b ) .or. ( c < d )

( x < = y ) .and. ( y < = z )

a < b .or. c < d , x < = y .and. y < = z

(no need for parenthesis)7

Logical operators

L1 L2 L1 .or. L2 L1 .and. L2

true true true true

true false true false

false true true false

false false false false

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Logical operators

L1 L2 L1 .eqv. L2 L1 .neqv. L2

true true true false

true false false true

false true false true

false false true false

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Examples

(a<b) .or. (c>d) (x<=y) .and. (y<=z) .not. (a<b) .eqv. (x<y) a<b .neqv. x<y

INVALID EXPRESSIONS

  I == 1.or.2(A.and.B) /= 0.0      

x > 0.0 .and. > 1.0        

0.0 < x < 1.010

Logical operator priorities

Operator Priority

.not. highest

.and.

.or.

.eqv. and .neqv. lowest

The operations are performed in the following order (priority rules): 

1.- arithmetic operations and functions

2.- relational operations

3.- logical operarions in the order mentioned before.

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The if constructIn the simplest selection structure, a sequence of statements (called a block of statements) is executed or bypassed depending on whether a given logical expression is true or false.

 If the logical expression is “true”, then the specified sequence of statements is executed ; otherwise it is bypassed.

 In either case, execution continues with the statement in the program following the “end if” statement. 

if ( logical_expression ) then

statement sequence

end if

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Program squarerootReal::xPrint*,”Enter a number ”Read*,xİf (x>0) then print*,”Root of the number= “,sqrt(x)EndifEndprogram squareroot

The if constructEXAMPLE :

 if ( x >= 0.0 ) then

y = x * x

z = sqrt (x)

end if

On the other hand, a general form of an if – construct has the following form:

if ( logical_expression ) then

statement_sequence_1

else

statement_sequence_2

end if 13

Program square_rootReal::xPrint*,”Enter a number”Read*,xİf (x>0) then print*,”root of the number=“,sqrt(x) else print*,”There is no root the number you entered" EndifEndprogram ......

The if construct

if (logical expression) thenblock of F statements

else if (logical expression) thenblock of F statements

else if (logical expression) thenblock of F statements

elseblock of F statements

endif

A typical structure for an general if – construct can be seen below :

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Simple if construct

if (logical expression) then

block of F statements

endif

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ExampleA) PROBLEM : A farmer has a triangular field which he wishes to sow with wheat. Write a program that reads the lenghts of the 3 sides of the field (in meters) and the sowing density (in grams per square meters)

Print the number of 10 kilo bags of wheat he must purchase in order to sow the whole field.

B.) ANALYSIS : STRUCTURE PLAN of the PROBLEM

Read lenghts of the sides of the field ( a, b, c ), calculate the area of the field

area = ( s (s-a)(s-b)(s-c) ) ½ ===> 2s = a + b + c

         read the sowing density

        calculate the quantity of wheat seed required

        calculate the number of 10 kilo bags this represents

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a b

c

program wheat_sowing! This program calculates the quantity of wheat ! required to sow a triangular field! Variable declarationsreal::a,b,c,s,area,density,quantityinteger::num_bags! read the lengths of the sides of the fieldprint*,"type the lengths of the 3 sides of the field in metres : "read*,a,b,c! calculate the area of the fields=0.5*(a+b+c)area=sqrt(s*(s-a)*(s- b)*(s-c) ) ! read sowing densityprint*," What is the sowing density (gms/sq.m) ?"read*,density! calculate quantity of wheat in grams ! and the number of

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! full 10 kg bagsquantity=density*area! any part-full bag is excludednum_bags=0.0001*quantity! check to see if another bag is requiredif(quantity>10000*num_bags) thennum_bags = num_bags + 1end if! print resultsprint*,"the area of the field is “, & area , “sq. metres"print*,"and",num_bags,"10 kilo bags will be required"end program wheat_sowing

Comparing numbers

Accuracy/round-off– Number of significant digits for real numbers

Do not test whether two numbers are equal Test whether their difference is acceptably small

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Comparing character stringscollecting sequence of letters, digits and other characters based on ASCII standard.

26 upper-case letters can be collected in the following order : ABCDEFGHIJKLMNOPRSTUVWXYZ26 lower-case letters can be collected in the following order : abcdefghijklmnoprstuvwxyz  the 10 digits can be collected in the following order : 0 1 2 3 4 5 6 7 8 9 a space (or blank) is collected before both letters and digits digits are all collected before the letter A.upper-case letters are collacted before any lower-case letters.

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When 2 character operands are being compared there are 3 distinct stages in the process : 

1.- If two operands are not the same length, the shorter one is treated as though it were extended on the right with blanks until it is the same length as the longer one. 

2.- The two operands are compared character by character, starting with the left-most character, until either a difference is found or the end of the operand is reached. 

3.- If a difference is found, then the relationship between these two different characters defines the relationship between the two operands, with the character which comes earlier in collating sequence being deemed to be the lesser of the two. If no difference is found, then the strings are considered to be equal.

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EXAMPLES :

“A” < “F” is a “true” logical expression

“m” > “b” is a “true“ logical expression

Comparisons of 2 strings is done character by character, considering the numeric codes. If the first characters of the strings are the same, the second characters are compared, if these are the same, then the third characters are compared, etc.

 

 “cat” < “dog” ! is a “true” logical expression.

 “cat” < “cow” ! is a “true” logical expression.

 “June” > “July” ! is a “true” logical expression.

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EXAMPLES :Two strings with different lengths are compared so that blanks are appended to the shorter string. “cat” < “cattle” ! is a “true” logical expression, because blank characters (b) preceds all letters : (“catbbb” < “cattle”) “Adam” > “Eve”! is false, because A comes before E, thus, less than E “Adam” < “Adamant” ! “Adambbb” < “Adamant”! is true, because “Adam” has been extended using 3 blanks; a blank always comes before a letter  “120” < “1201” ! “120b” < “1201”! is true because a blank comes before a digit  “ADAM” < “Adam”! is true because the second digit “D” < “d” (i.e. upper-case letters come before lower-case letters.

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The case constructIn some situations it is necessary to have an ordering built into the decision as to which choice to take, because there is an overlap between some of the possible decision criteria.

EXAMPLE 1 : Consider that you are a basketball addict, but especially a Efes-Pilsen fun, then the decision as to what to do on Saturday afternoon might look like this,

if it is the basketball season and the Efess are at home then go to Abdi Ipekci

else if it is the basketball season and the EPs game is on TV thenget a six-pack and watch the game on TV

else if it is the basketball season then go to any nearby basketball game

else rent a basketball video and watch it at home.

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EXAMPLE 2 : Consider that you are a Fenerbahce soccer fan, and are only interested in watching football matches in which they are playing (whether at home or away), then your Saturday evening decision plan might be rather different :

 

 if (it is the football season and Fenerbahce is playing at home) then

go to Sukru Saracoglu and support the Canaries

else if (it is the football season and Fenerbahce is playing away ) then

go to whenever they are playing and support the Canaries

else

get a six-pack and watch some of your old Fenerbahce videos at home.

endif

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Depending on the above given example the following alternatives can be selected as appropriate case - structure :

Case 1 : It is it is the football season and Fenerbahce is playing at home

decision: go to Sukru Saracoglu and and support the Canaries

Case 2 : it is the football season and Fenerbahce is playing away

decision: go to wherever they are playing and support the Canaries

Case 3 : any other situation

decision: get a six-pack and whatch some of your old Fenerbahce videos at home

As is clearly seen from the above- given example, case – construct is not as general as “else if” – construct ; but it is useful for implementing some selection structures and provides better program comprehensibility and reliability.

 

The case construct

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The case construct

select case (case_expression)

case (case_selector)

block_of_statements

...

case default

block_of_statements

end select

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The case constructselector : (i.e. case_expression) is an integer, character or logical expressions

label_list i : (i.e. case_selector_i) each of this list is a list of one and more possible values of the selector, enclosed in parentheses. The case_selector_i can take one of the four forms :

( case_value )

( low_value : )

( : high_value )

( low_value : high_value )

case : case - values that determine which block is to be executed must be specified by initialization expressions, which are simple expressions that may contain constants but no variables (see selector).

case - values must not overlap ; thus, no block can be eligible for selection in more than one case.

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The case construct Case expression:

– either integer or character expression Case selector:

– case_value• case_expression = = case_value

– low_value:• low_value <= case_expression

– :high_value• case_expression <= high_value

– low_value:high_value• low_value <= case_expression .and.

case_expression <= high_value

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Exacution of the case - constructExecution of the case – construct begins with evaluation of the selector expression in the “select case” – statement.

 

The case – statements are then executed in the order of their appearance ; that is, in each case – statement, the value of selector expression is compared with the label-list item (in order) :

 

1.- if the value of selector expression is in the range of the label-list item, a match occurs.

2.- if no match occurs during examination of the label_list in all case statements and case default statement is present, case default is then selected for execution.

3.- if a case block is selected, its execution proceeds normally, beginning with the first statement in the block.

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! Example:Rank two numbers.

program D04

implicit none

real :: X, Y

character (len = 7) :: X_Rank, Y_Rank

! start program D04

write (unit = *, fmt = *) " Please enter a pair of real numbers to be ranked. "

read (unit = *, fmt = *) X, Y

write (unit = *, fmt = *) " You have entered: ", X, Y

if (X > Y) then

X_Rank = "larger "

Y_Rank = "smaller"

else

X_Rank = "smaller"

Y_Rank = "larger "

end if

write (unit = *, fmt = *) X, " is ", X_Rank, " and ", Y, " is ", Y_Rank

end program D0430

! Example: Trade the values 1 and 2.

program D05

implicit none

integer :: I

! start program D05

write (unit = *, fmt = *) " Please enter 1 or 2. "

read (unit = *, fmt = *) I

write (unit = *, fmt = *) " Thank you. You have entered: ", I

if (I == 1) then ! if construct

I = 2 ! if construct

else ! if construct

I = 1 ! if construct

end if ! if construct

write (unit = *, fmt = *) " Your value was changed to: ", I

stop

end program D0531

! Example: Compute Y by one of three formulas, depending on X.

program D12

implicit none

real :: X, Y

write (unit = *, fmt = *) " Please enter the value of X. "

read (unit = *, fmt = *) X

if (X < 0.0) then

Y = 1.0

else if (X <= 1.0) then ! Else if (X>=0.0 .and. X<=1.0) then

Y = 4.0 * X + 1.0

else

Y = -10.0 * X + 15.0

end if

write (unit = *, fmt = *) " The values of X and Y are: ", X, Y

stop

end program D1232

! Example: Choose formula for Z according to (X, Y) quadrant. program D13 implicit none real :: X, Y, Zwrite (unit = *, fmt = *) " Please enter values of X and Y. " read (unit = *, fmt = *) X, Y if (Y > 0.0) then ! Northeast and northwest quadrants Z = sqrt( Y ) else if (X < 0.0) then ! Southwest quadrant Z = Y else ! Southeast quadrant Z = X * Y end if write (unit = *, fmt = *) " Values of X, Y, and Z are: ", X, Y, Zend program D13

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x

y

Z=sqrt(Y)

Z = Y Z = X * Y

!Write a program to analysis of ID NumberProgram readdata! This program is written for reading your IDİnteger::fak,yil,bol,siraprint*,”Please enter your ID number? (010030323)”Read(unit=*,fmt=“(i2,i3,2i2)”)fak,yil,bol,siraİf (fak==1) then print*,”You are student in Civil Engineering” else if(fak==2) then print*,”You are student in ....”................ else print*,”You are not student in ITU” endif endifEndprogram readdata

! Write a program to find Days of the month

program D17

integer :: Month, Year, NDays

write (unit = *, fmt = *) " Please enter the year (4 digits). "

read (unit = *, fmt = *) Year

write (unit = *, fmt = *) " Please enter the month number (1 to 12). "

read (unit = *, fmt = *) Month

select case (Month)

case (9, 4, 6, 11) ! Sep, Apr, Jun, Nov

NDays = 30

case (2) ! February

if (modulo( Year, 4 ) == 0) then

NDays = 29 !Leap year

else

NDays = 28

end if 35

case default ! Jan, Mar, May, Jul, Aug, Oct, Dec

NDays = 31

end select

write (unit = *, fmt = *) " The number of days in month: ", Month, " is: ", NDays

stop

end program D17

program ex_of_modreal::x,yprint*,"modunu almak istediginiz sayiyi ve kacinci modunu almak istiyorsaniz giriniz?"read*,x,yprint*,x,"in ",y," e gore modu=",modulo(x,y)endprogram ex_of_mod

!Write a program to find a month in the fall or spring semesters.

program D19

implicit none

integer :: M

write (unit = *, fmt = *) " Please enter a month number between 1 and 12. "

read (unit = *, fmt = *) M

select case (M)

case (9: 12, 1)

write (unit = *, fmt = *) " Month ", M, " is in the fall semester. "

case (2: 6)

write (unit = *, fmt = *) " Month ", M, " is in the spring semester. "

case default

write (unit = *, fmt = *) " School is not in session during month ", M

end select

stop

end program D1936

PROBLEM : Read a date in the International Standard form ( yyyy-mm-dd) and print a message to indicate whether on this date in Istanbul, Turkey, it will be winter, spring, summer or autumn.

program seasons ! a program to calculate in which season a specified date lies

character (len=10) ::date ! variable declarations

character (len=2) ::month ! variable declarations

print *, "please type a date in the form yyyy-mm-dd" ! read date

read *, date

month=date (6:7) ! extract month number

select case (month) ! print season

case ("09":"11")

print *, date, "is in the autumn"

case ("12" , "01" : "02")print *, date, "is in the winter"case ("03":"05")print *,date,"is in the spring"case ("06":"08")print*,date,"is in the summer"case defaultprint*,date,"is in not valid date"end selectend program seasons

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! Name :! Address :! Date :! Comments : This program written to find which student goto lab A or lab B depending on their ID even or oddprogram exercise_1_1 real :: x print *,"please type a number" read *,x if (x>0) then print *,"your number is positive" else if (x<0) then print *,"your number is negative" else print *,"your number is zero" end if end program exercise_1_1

program labsreal::xinteger::id,ycharacter(len=49)::namePrint*,”Please enter your name”read*,namePrint*,”Please enter your ID” read*,idx=id/2.0y=id/2if (x==y) thenprint*," You must goto lab A"elseprint*,"you must goto labs B"end ifendprogram labs

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if (modulo(id,2)==0.0) thenprint*," You must goto lab A"elseprint*,"you must goto labs B"end ifendprogram labs

!Write a program to find a given number is ! positive, zero or negativeprogram exercise_1_2 real ,parameter :: r=1e-6 real :: x integer :: z print *,"please type a number" read *,x z=x/r select case (z) case (1:) print *,"your number is positive" case (0) print *,"your number is zero" case (:-1) print *,"your number is negative" end select end program exercise_1_2

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40

program excercise_3real :: i,p,vprint *, ”Please type the power rating (watt) and supply voltage (volt)"

read *,p,vi=p/vif (i<5)thenprint *,"You should buy 5 amps cable"else if (5<=i.and.i<13) thenprint *,"You shuld buy 13 amps cable" else if (13<=i.and.i<30) thenprint *,"You should buy 30 amps cable" elseprint *,"We do not have the cable which you need"end if

end program excercise_3 41

program quadratic_equation_solution! A program to solve a quadratic equation using an if ! construct to distinguish between the three cases.!! Constant declaration

real, parameter :: small=1.e-6! Variable declarations

real :: a,b,c,d,x1,x2!! read coefficients

print *," Type the three coefficients a, b and c"read *, a,b,c

! Calculate b^2-4acd = b**2 - 4.0**a*c

! calculate an print rootsif (d > small) then

! two roots casex1 = (-b - sqrt(d)) / (2.0*a)x2 = (-b + sqrt(d)) / (2.0*a)print *," The equation has two roots:"print *," x1=",x1," x2=",x2else if (-small <= d .and. d <= small) then

! two coincident roots casex1 = -b / (2.0*a)print *," The equation has two coincident roots:"print *," x1=x2=",x1 else

! No root caseprint *," The equation has no real roots"end if

! end program quadratic_equation_solution 42

program seasons! A program to calculate in which season a specified date lies.! variable declarations

character(len=10) :: datecharacter(len=2) :: month

! read dateprint *, "Please type a date in the form dd-mm-yyy"read *, date

! extract month numbermonth = date(4:5)

! extract from 4th to 5th character of string date and assign them to character variable month! print season

select case(month)! case("03","04","05")

case("03":"05")print *, date , " is in the spring"case("06","07","08")print *, date , " is in the summer"case("09","10","11")print *, date , " is in the fall"case("12","01","02")print *, date , " is in the winter"case defaultprint *, date , " is invalid date"end select

end program seasons 43

program watch_discount integer :: number,gross_cost

real :: discount,net_costinteger ,parameter :: price=15print*,"Please type how many watch have you bought"read *,numberselect case(number)case (1)discount=0gross_cost=price*numbernet_cost=gross_cost*(1-discount)case (2:4)discount=0.05gross_cost=price*numbernet_cost=gross_cost*(1-discount)case (5:9)discount=0.1gross_cost=price*numbernet_cost=gross_cost*(1-discount)case (10:29)discount=0.15gross_cost=price*numbernet_cost=gross_cost*(1-discount)case (30:99)discount=0.2gross_cost=price*numbernet_cost=gross_cost*(1-discount)case (100:299)discount=0.25gross_cost=price*numbernet_cost=gross_cost*(1-discount)case defaultdiscount=0.3gross_cost=price*numbernet_cost=gross_cost*(1-discount)end selectprint *,"gross cost is equal to",gross_costprint *,"net cost is equal to",net_costend program watch_discount

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HOMEWORK

 Using a case – structure prepare a computer program which shows your program on

Thursday and on Friday, as can be seen below :

Thursday

09.00 : 10.50 “Physics”

11.00 : 12.50 “Chemistry”

--- etc.

Then, carry out 2 sample runs for different days and hours.

Print the input values as well as the messages obtained as results.

45

Write a program to read the coefficients of a quadratic equation and print its roots

46

A firm produces pencil and sells them for 5 YTL each. However, it gives a discount for multiple orders as follows:

Number ordered Discount

<10 0%

<50 5 %

<70 10 %

<90 15 %

>=90 20 %

47

program aritmetitortalama

integer::say,urunadet,i,tutar,uruntutar

say=0

tutar=0

do i=1,3

read*,urunadet,uruntutar

say=say+urunadet

tutar=tutar+uruntutar*urunadet

enddo

print*,"ortalama siparis adeti",say/3

print*,"ortalama siparis fiyati",tutar/say

end program aritmetitortalama48