Fall, 2006Selection1 Choices, Choices, Choices! Selection in FORTRAN Nathan Friedman Fall, 2006

Fall, 2006 Selection 1

Choices, Choices, Choices! Selection in FORTRAN

Nathan FriedmanFall, 2006

FORTRAN Selection

Last lecture we introduced the IF…THEN..ELSE…END IF

statement

IF (logical-expression) THEN

first statement block, s1

second statement block, s2

END IF

! ------------------------------------------------------------! Solve Ax^2 + Bx + C = 0 ! ------------------------------------------------------------PROGRAM QuadraticEquation IMPLICIT NONE! **** Same old declarations and set up ****

d = b*b - 4.0*a*c IF (d >= 0.0) THEN ! is it solvable? d = SQRT(d) root1 = (-b + d)/(2.0*a) root2 = (-b - d)/(2.0*a) WRITE(*,*) "Roots are ", root1, " and ", root2 ELSE ! complex roots WRITE(*,*) "There is no real root!" WRITE(*,*) "Discriminant = ", d END IFEND PROGRAM QuadraticEquation

Semantics of IF…THEN…ELSE…END IF

Evaluate the logical expression. It can have value .TRUE. or value .FALSE.

If the value is .TRUE., evaluate s1, the first block of statements

If the value is .FALSE., evaluate s2, the second block of statements

After finishing whichever of s1 or s2 that was chosen, execute the next statement following the END IF

What’s Going On?

What is a “logical expression” ?

What’s Going On?

What is a “logical expression” ? Where do the values .TRUE.

and .FALSE. come from?

What’s Going On?

What is a “logical expression” ? Where do the values .TRUE.

and .FALSE. come from? What are those periods around the

words true and false?

Logical Data Type FORTRAN has a LOGICAL data type, just

like it has INTEGER and REAL types Each type has its associated values

like it has INTEGER and REAL types Each type has its associated values There are only two values in the type

LOGICAL, true and false

like it has INTEGER and REAL types Each type has its associated values There are only two values in the type

LOGICAL, true and false To enable the compiler to distinguish

these values from variables, we represent them with periods around the words

Logical Data Type

We can declare variables of type LOGICAL

LOGICAL :: positive_x, condition

Logical Data Type

We can assign values to themcondition = .TRUE.positive_x = x > 0

Logical Data Type

We can assign values to themcondition = .TRUE.positive_x = x > 0

These variables can only take on one of the two values of type logical

Logical Expressions

Logical expressions, such as those that appear in IF statements, return a logical value

That is, they are expressions which evaluate to .TRUE. or .FALSE.

We have operators that return logical values.

Relational Operators

Relational operators compare two values and return the result .TRUE. or .FALSE.

<, <=, >, >=, ==, /=

Relational operators are of lower precedence than all arithmetic operators

2 + 7 >= 3 * 3 .TRUE.

<, <=, >, >=, ==, /=

Relational operators are of lower precedence than all arithmetic operators

2 + 7 >= 3 * 3 .TRUE.

There is no associativitya < b < c illegal

Danger Lurks

== or = ?

Note that == is the FORTRAN (and the C) syntax for a relational operator meaning “is equal to”

The expression x == y has the value .TRUE. if x and y are equal and .FALSE. if x and y are not equal

A single equal sign (=) is the FORTRAN (and C) syntax for assignment

The statement x = y means assign the value of y to the variable x

== or = ?

In FORTRAN you will get an error message if you use either operator incorrectly

Later on, when we study C, we will C that the program could work and give totally incorrect results if you confuse these operators

Is A Number Even or Odd?

IF (MOD(number, 2) == 0) THEN

WRITE(*,*) number, " is even"

WRITE(*,*) number, " is odd"

END IF

Is A Number Even or Odd?(alternate)

IF (number/2*number == number) THEN

WRITE(*,*) number, " is even"

WRITE(*,*) number, " is odd"

END IF

Find Absolute Value

REAL :: x, absolute_x x = ..... IF (x >= 0.0) THEN absolute_x = x ELSE absolute_x = -x END IF WRITE(*,*) “The absolute value of “,& x, “ is “, absolute_x Note the use of & to indicate “continue on next line”

Which value is smaller?

INTEGER :: a, b, min READ(*,*) a, b IF (a <= b) THEN min = a ELSE min = b END IF WRITE(*,*) “The smaller of “, a, & “ and “, b, “ is “, min

The Missing ELSE

The IF-THEN-ELSE-END IF form allows us to choose between two alternatives

There is another simpler selection mechanism that allows us to choose whether or not to perform a single block of actions

We either perform the actions and go on, or skip them and go on

IF-THEN-END IF

Syntax:IF (logical expression) THEN

block of statements, s1

END IF

IF-THEN-END IF

Syntax:IF (logical expression) THEN

block of statements, s1

END IF

Semantics: Evaluate the logical expression If it evaluates to .TRUE. execute s1 and then continue

with the statement following the END IF If the result is .FALSE. skip s1 and continue with the

statement following the END IF

Examples of IF-THEN-END IF

absolute_x = x

IF (x < 0.0) THEN absolute_x = -x END IF WRITE(*,*) "The absolute value of ", x, & " is ", absolute_x

Examples of IF-THEN-END IF

INTEGER :: a, b, min READ(*,*) a, b min = a

IF (a > b) THEN min = b END IF

WRITE(*,*) "The smaller of ", & a, " and ", b, " is ", min

Logical IF

An even simpler form is sometimes useful. Syntax:IF (logical expression) single-statement

Semantics: This statement is equivalent toIF (logical expression) THEN single-statementEND IF

The single-statement cannot be an IF or we might end up with an ambiguous statement

Examples of Logical IF

absolute_x = x

IF (x < 0.0) absolute_x = -x

WRITE(*,*) "The absolute value of ", x, & " is" ,"absolute_x

Examples of Logical IF

INTEGER :: a, b, min

READ(*,*) a, b

min = a

IF (a > b) min = b

WRITE(*,*) "The smaller of ",& a, " and ", b, " is ", min

Quadratic Roots Revisited

The problem of finding the roots of a quadratic is a bit more complicated than we have been assuming

If the discriminant is zero there is only a single root

! ---------------------------------------------------! Solve Ax^2 + Bx + C = 0 ! Detect complex roots and repeated roots.! ---------------------------------------------------PROGRAM QuadraticEquation IMPLICIT NONE! **** same old declarations and setup statements omitted **** d = b*b - 4.0*a*c

IF (d > 0.0) THEN ! distinct roots? d = SQRT(d) root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root WRITE(*,*) 'Roots are ', root1, ' and ', root2 ELSE IF (d == 0.0) THEN ! repeated roots? WRITE(*,*) 'The repeated root is ', -b/(2.0*a) ELSE ! complex roots WRITE(*,*) 'There is no real roots!‘ WRITE(*,*) 'Discriminant = ', d END IF END IFEND PROGRAM QuadraticEquation

IF-THEN-ELSE IF-END IF

The nested IF statements in the last example are a bit complicated

When we use IF to select between several (not just two) alternatives, we end up with more than a single END IF, one for each of the branches

This can be simplified

Syntax ofIF-THEN-ELSE IF-END IF

IF (logical-exp, e1) THEN

statement block, s1

ELSE IF (logical-exp, e2) THEN

statement block, s2

ELSE IF (logical-exp, e3) THEN

statement block, s3

. . . . . . . . .ELSE

statement block, se

END IF

Semantics of IF-THEN-ELSE IF-END IF

Evaluate e1

If the result is .TRUE., execute s1 and go on to the statement that follows the END IF

If the result is .FALSE., evaluate e2. If it is .TRUE., execute s2 and go on to the statement that follows the END IF

If the result of e2 is false, repeat this process.

If none of the expressions, ei evaluate to .TRUE., execute se and then go on to the statement that follows the END IF

! ---------------------------------------------------! Solve Ax^2 + Bx + C = 0 ! Detect complex roots and repeated roots.! ---------------------------------------------------PROGRAM QuadraticEquation IMPLICIT NONE! **** same old declarations and setup statements omitted ****

d = b*b - 4.0*a*c

IF (d > 0.0) THEN ! distinct roots? d = SQRT(d) root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root WRITE(*,*) 'Roots are ', root1, ' and ', root2 ELSE IF (d == 0.0) THEN ! repeated roots? WRITE(*,*) 'The repeated root is ', -b/(2.0*a) ELSE ! complex roots WRITE(*,*) 'There is no real roots!‘ WRITE(*,*) 'Discriminant = ', d END IFEND PROGRAM QuadraticEquation

Quadratic Roots Final Version

The problem of finding the roots of a quadratic has some more complications

What if a is zero. Dividing by 2a would cause an error.

If a is zero, the equation is linear, not quadratic

If a and b are zero but c isn’t there is no solution

! ---------------------------------------------------! Solve Ax^2 + Bx + C = 0 ! Now, we are able to detect the following:! (1) unsolvable equation! (2) linear equation! (3) quadratic equation! (a) distinct real roots! (b) repeated root! (c) no real roots! --------------------------------------------------- PROGRAM QuadraticEquation IMPLICIT NONE

REAL :: a, b, c REAL :: d REAL :: root1, root2 ! read in the coefficients a, b and c

READ(*,*) a, b, c

IF (a == 0.0) THEN ! could be a linear equation IF (b == 0.0) THEN ! the input becomes c = 0 IF (c == 0.0) THEN ! all numbers are roots WRITE(*,*) 'All numbers are roots‘ ELSE ! Unsolvable WRITE(*,*) 'Unsolvable equation‘ END IF ELSE ! linear equation WRITE(*,*) 'This is linear equation, root = ', -c/b END IFELSE ! ok, we have a quadratic equation d = b*b - 4.0*a*c IF (d > 0.0) THEN ! distinct root d = SQRT(d) root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root WRITE(*,*) 'Roots are ', root1, ' and ', root2 ELSE IF (d == 0.0) THEN ! repeated roots? WRITE(*,*) 'The repeated root is ', -b/(2.0*a) ELSE ! complex roots WRITE(*,*) 'There is no real roots!‘ WRITE(*,*) 'Discriminant = ', d END IFEND IFEND PROGRAM QuadraticEquation

What Day is Tomorrow? Here is a new problem to solve.

Given today’s date (day,month,year) Compute and output tomorrow’s date

What’s the problem?

What’s the problem? If the date is the last day of the month,

we have to update the day and month If it is the last day of the year, we also

have to update the year

First Validate the Dataprogram nextday

implicit noneinteger day, month, yearinteger lastdaywrite (*,*) "Please enter the date, day month and year:"read (*,*) day, month, year

! validate month

if (month < 1 .or. month > 12) then write (*,*) "Invalid month" stopend if

! Validation of year and day omitted to save space

Compute the last day of the month

if (month == 1 .or. month == 3 .or. month == 5 .or. month == 7 .or. month == 8 .or. month == 10 .or. month == 12) then

lastday =31else if (month == 4 .or. month == 6 .or. month == 9 .or.

month == 12) then lastday =30else if ((mod(year,4) == 0 .and. mod(year,100) /= 0) .or.

mod(year,400) == 0) then lastday = 29else lastday = 28end if

Compute Tomorrow’s Date! The usual caseday = day + 1

! Handling the end of the month or year

if (day > lastday) then day = 1 month = month + 1 if (month > 12) then month = 1 year = year + 1 end ifend if

write (*,*) day, month, year

end program nextday

Logical Operators

In addition to relational operators, more complex logical expressions can be formed using logical operators

The Logical Operators listed in order of decreasing precedence are:.NOT..AND. (or &&).OR. (or ||).EQV. (or ==), .NEQV. (or /=)

The precedence of all logical operators is lower than all relational operators

They all associate from left to right

Area of a Triangle

Heron’s formula gives the area of a triangle in terms of the lengths of its sides.

Where a, b, and c are the lengths of the sides and

))()(( csbsassarea

Area of a Triangle

To use it, we must make sure that the sides form a triangle.

There are two necessary and sufficient conditions:

1. All side lengths must be positive2. The sum of any two sides must be greater

than the third

Area of a Triangle(program preamble)

! ------------------------------------------------------! Compute the area of a triangle using Heron's formula! ------------------------------------------------------

PROGRAM HeronFormula IMPLICIT NONE

REAL :: a, b, c ! three sides REAL :: s ! half of perimeter REAL :: Area LOGICAL :: Cond_1, Cond_2 READ(*,*) a, b, c

Area of a Triangle(main body of program)

Cond_1 = (a > 0.) .AND. (b > 0.) .AND. (c > 0.0) Cond_2 = (a+b > c) .AND. (a+c > b) .AND. (b+c > a)] IF (Cond_1 .AND. Cond_2) THEN s = (a + b + c) / 2.0 Area = SQRT(s*(s-a)*(s-b)*(s-c)) WRITE(*,*) "Triangle area = ", Area ELSE WRITE(*,*) "ERROR: this is not a triangle!“ END IF

END PROGRAM HeronFormula

Data Type Character(A Brief Digression)

We have seen character string constants in examples.

“Hello World”

“Hello World”FORTRAN also allows us to declare variables that

can hold character string valuesCHARACTER(LEN=5) :: message_1CHARACTER(LEN=20) :: message_2

“Hello World”FORTRAN also allows us to declare variables that

can hold character string valuesCHARACTER(LEN=5) :: message_1CHARACTER(LEN=20) :: message_2

We can assign values to these variables.message_1 = “Hello World”message_2 = “Hello World”

What happens if we assign values that don't match the declared length

CHARACTER(LEN=5) :: message_1CHARACTER(LEN=20) :: message_2message_1 = “Hello World”message_2 = “Hello World”

If the length is too short, the string is truncatedmessage_1 contains “Hello”

If it is too long it is padded with extra blanksmessage_2 contains “Hello World_________”

Operations on Character Strings

Comparison using relational operators The ordering for comparison is called lexicographic (or

dictionary) ordering A string is less than another if it would come first in the

dictionary Concatenation (//)

We can join two strings together by concatenating themCHARACTER(len=21) :: instructor

CHARACTER(len=8) :: surname

surname = “Friedman”

instructor = “Prof. ” // “Nathan ” // surname

Fall, 2006Selection1 Choices, Choices, Choices! Selection in FORTRAN Nathan Friedman Fall, 2006

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