basic comphy ch3

8/8/2019 Basic Comphy Ch3

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Ch. 3 Fortran 90: Selective & Repetitiveexecutions

References:

1. T.M.R. Ellis et al., Fortran 90 programming, Chs. 5, 6

2. L. Nyhoff & S. Leestma, Introduction to FORTRAN 90, Ch. 3, 4


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Outline

3.1 Selective execution

3.2 Repetitive execution


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3.1 Selective execution

Decision-making

How would I spend this Sunday?

Ifmy wife and son don't complaint, thenI will go back to office alone :-)

but ifthey complaint, thenI will stay home :-( [....what next is usually not my decision!]

but ifonly my son complaints, thenI will ask whether he wants to go with me:

Ifyes, thenI will go back to office with my son :-|

Ifno, thenI will stay home :-( [...what next is usually not my decision!]

but ifonly my wife complaints, then I will ask whether she wants to go with me: Ifyes, thenI will go back to office with my wife and son :-|

Ifno, thenI will go back to office alone anyway ;-)


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Logical expressions

* We see in the previous example that each decision depends upon whethersome criterion is true or false.

* An expression which can take one of these two values (true or false) is called a logicalexpression.

Logical values

Example: x < 3 is a logical expression

ifx = 2, the logical expression x < 3 is true.

ifx = 4, the logical expression x < 3 is false.

relational operator

* In Fortran, the logical values are given by:

.TRUE..FALSE.


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* Fortran provides the following 6 relational operators:

Symbol Meaning

< or .LT. Is less than

> or .GT. Is greater than

== or .EQ. Is equal to

= or .GE. Is greater than or equal to

/= or .NE. Is not equal to

expression1 relational-operator expression

2Usage:

* expression1

& expression2

must be both arithmetic or both be strings

* All arithmetic operators have a higher priority than any relational operator

All relational operatorshave equal priority


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Example: For the expression b**2 >= 4*a*c ,

b**2 and 4*a*c are evaluated before >= is evaluated

Example: The following expressions give the same results

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

4*a*c = 4*a*c ) is .FALSE.

Remark: The 6 relational operators can also be used to compare character strings.But we shall not discuss this issue.(see, e.g., Sec. 5.5 of Ellis et al.)


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Question: How to represent the comparisonsx


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* Let p and q be logical expressions, the logical operators are defined by :

p .NOT. p

.TRUE. .FALSE.

.FALSE. .TRUE.

p q p .AND. q p .OR. q p .EQV. q p .NEQV. q

.TRUE. .TRUE. .TRUE. .TRUE. .TRUE. .FALSE.

.TRUE. .FALSE. .FALSE. .TRUE. .FALSE. .TRUE.

.FALSE. .TRUE. .FALSE. .TRUE. .FALSE. .TRUE.

.FALSE. .FALSE. .FALSE. .FALSE. .TRUE. .FALSE.

Priority order:

1. Arithmetic operations (and functions)2. Relational operations3. Logical operations in the order .NOT., .AND., .OR., .EQV. (or .NEQV.)

Usage: expression1 logical-operator expression

2

* expression1

& expression2

are logical expressions


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Example: ifN = 4, what is the logical value of the following logical expression?

(N**2 + 1 > 10) .AND. .NOT. (N < 3)

.TRUE.

.FALSE.

.TRUE.

=> The logical value of the entire expression is .TRUE.

Example: The following 2 expressions are equivalent in their effect

.NOT. (a < b .AND. b < c)

a >= b .OR. b >= c


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Classwork 1


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The block IF construct

block IF constructIF (logical-expression) THEN

statement-sequence

END IF

Example:

IF ( b**2 > 4*a*c ) THEN

PRINT *, ' There are two real roots '

END IF

IF ( b**2 == 4*a*c ) THEN

PRINT *, ' There is one (repeated) root '

END IF

IF ( b**2 < 4*a*c ) THEN

PRINT *, ' There is no real root '

END IF


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IF-ELSE IF construct

IF (logical-expression1) THEN

statement-sequence1

ELSE IF (logical-expression2) THEN

statement-sequence2

ELSE IF (logical-expression3) THEN

.

.

.

ELSE

END IF

Example: IF ( b**2 > 4*a*c ) THEN

PRINT *, ' There are two real roots '

ELSE IF ( b**2 == 4*a*c ) THEN

PRINT *, ' There is one (repeated) root '

ELSE

PRINT *, ' There is no real root '

ENDIF


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Example: (Quadratic equation)

PROGRAM Quadratic

IMPLICIT NONE

REAL :: a, b, c, Delta, root_1, root_2

PRINT *, 'Enter the coefficients a, b, c'

READ(*,*) a, b, c

Delta = b**2 - 4*a*c

IF ( Delta > 0.0 ) THEN

Delta = SQRT(Delta)

root_1 = ( -b + Delta ) / (2.0*a)

root_2 = ( -b - Delta ) / (2.0*a)

PRINT *, ' Two real roots = ', root_1, root_2

ELSE IF ( Delta == 0.0 ) THEN

root_1 = - b / (2.0*a)

PRINT *, ' One repeated root = ', root_1

ELSE

PRINT *, ' No real root '

END IF

END PROGRAM Quadratic

This line can also be written asELSE IF(Delta < 0.0 ) THEN


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What happens if a = 0.0?

Enter the coefficients a, b, c

0.0, 2.0, 1.0

Two real roots = NaN -Infinity

My input

(Not aNumber)

* We can modify the code by

....

....

....


READ(*,*) a, b, c

IF ( a == 0.0 ) THEN

PRINT *, ' the coefficient a should not be zero! '

STOPEND IF

...

...

...

This terminates the execution of the program immediately


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Remark: Consider the following part of the code

ELSE IF (Delta == 0.0 ) THEN

root_1 = - b / (2.0*a)

PRINT *, ' One repeated root = ', root_1

Remember that real arithmetic is only an approximation.=> two numbers which are mathematically equal will often

differ very slightly in numerical calculations

Hence, we should not compare two real numbers for equality.

* A better way to write the above part of the code is:

ELSE IF ( ABS(Delta) < epsilon ) THEN

....

....

where the parameter epsilon is a very small number (eg, 1.E-8) defined by the user:

REAL, PARAMETER :: epsilon = 1.E-8


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Logical IF statement

IF (logical-expression) Fortran-statement

* This is equivalent to the following simplest block IF construct:

Only one statement

IF (logical-expression) THEN

Fortran-statement

END IF

Example:PROGRAM Absolute

IMPLICIT NONE

REAL :: x, abs_x

PRINT *, ' Input a number x'

READ(*,*) x

abs_x = x

IF (x < 0.0) abs_x = x

PRINT *, '|x| = ', abs_x

END PROGRAM Absolute

IF (x < 0.0) THEN

abs_x = x

END IF

A 'shorthand' version of


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LOGICAL variables

* We have two logical values: .TRUE. & .FALSE.

* We can declare LOGICAL variables to store these values:

LOGICAL :: var_1, var_2, var_3,....

Example: Let us illustrate how to use the various concepts together by writing a Fortran codeto decide what should I do on Sunday.

LOGICAL :: wife_complaint, son_complaint

LOGICAL :: wife_go, son_go

First, we need to define some logical variables:

wife_complaint = .TRUE. (if my wife complaints) = .FLASE. (if my wife doesn't complaint)

wife_go = .TRUE. (if my wife agrees to go to my office)

= .FALSE. (if my wife doesn't want to go to my office)

Similar meanings apply to son_complaint & son_go

Meaning:


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PROGRAM My_Sunday

IMPLICIT NONE

LOGICAL :: wife_complaint, son_complaint

LOGICAL :: wife_go, son_go

PRINT *, 'Input the logical values of wife_complaint, son_complaint'

READ(*,*) wife_complaint, son_complaint

IF (wife_complaint .AND. son_complaint ) THENPRINT *, ' Stay home :-( '

ELSE IF ( .NOT. wife_complaint ) THEN

IF (son_complaint) THEN

PRINT *, ' Input the logical value of son_go '

READ(*,*) son_go

IF (son_go) PRINT *, ' Take him to office :-| '

IF (.NOT. son_go) PRINT *, ' Stay home :-( ' ELSE

PRINT *, ' Go to office alone :-) '

ENDIF

ELSE IF ( .NOT. son_complaint ) THEN

IF (wife_complaint) THEN

PRINT *, ' Input the logical value of wife_go '

READ(*,*) wife_go

IF (wife_go) PRINT *, ' Take them to office :-| '

IF (.NOT. wife_go) PRINT *, 'Go to office alone ;-) '

ELSE

PRINT *, ' Go to office alone :-) '

ENDIF

ENDIF

END PROGRAM My_Sunday

Nested IF:

block IF constructs

inside another blockIF construct


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Sample runs of the program My_Sunday:

Input the logical values of wife_complaint, son_complaint

.TRUE., .TRUE.

Stay home :-(


.FALSE., .TRUE.

Input the logical value of son_go

.FALSE.

Stay home :-(


.TRUE., .FALSE.

Input the logical value of wife_go

.FALSE.

Go to office alone ;-)


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Classwork 2


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The CASE construct

* Besides the block IF construct, Fortran 90 provides another form of selective execution

statement:

SELECT CASE (case-expression)

CASE (case_selector1)

statement-sequence1


statement-sequence2


.

.

.

CASE DEFAULT

statement-defaultEND SELECT

CASE construct

may be integer expression,character expression orlogical expression(BUT not real expression)

This part is optional

* The case construct can deal with the alternative situation in which the variousalternatives are mutually exclusive (and the order is unimportant)


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* case_selector can take the following forms:

case_value

low_value:

:high_value

low_value:high_value

1. case_value the statement-sequence is executed iff

case_expression == case_value (when case_expression is an

integer expression)

case_expression .EQV. case_value (when case_expression is alogical expression)

2. low_value: the statement-sequence is executed iff

low_value


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Example: (This program determines in which season a specified date lies)

PROGRAM Seasons

IMPLICIT NONE

CHARACTER(LEN=10) :: date

CHARACTER(LEN=2) :: month

PRINT *, 'Type a date in the form yyyy-mm-dd'

READ(*,*) date

month = date(6:7)

SELECT CASE (month)

CASE ("03":"05")

PRINT *, date, ' is in the spring'

CASE ("06":"08")

PRINT *, date, ' is in the summer'

CASE("09":"11")

PRINT *, date, ' is in the autumn'

CASE("12","01","02")

PRINT *, date, ' is in the winter'

CASE DEFAULT

PRINT *, date, ' is not a valid date'

END SELECT

END PROGRAM Seasons

recall: substring (Ch. 2)

CASE (03,04,05)

can also be written as

E l (Q d i b )


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PROGRAM Quadratic_case

IMPLICIT NONE

REAL :: a, b, c, Delta

INTEGER :: selector

REAL, PARAMETER :: epsilon = 1.E-8


READ(*,*) a, b, c

Delta = b**2 - 4*a*c

selector = Delta / epsilon

SELECT CASE (selector)

CASE (1:)

PRINT *, ' Two real roots '

CASE (0)

PRINT *, 'One (repeated) root 'CASE (:-1)

PRINT *, 'No real root'

END SELECT

END PROGRAM Quadratic_case

Example: (Quadratic by CASE)

The result will be truncated to aninteger(Note: it is usually a bad idea to

divide by a very small number)

If|Delta| < epsilon, then

their ratio will be between -1 & +1=> selector = 0

(selector is an integer)

3 2 Repetitive execution


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3.2 Repetitive execution

Program repetition

* In numerical calculations, it is often required to carry out the same, or similar,actions repeatedly (Repetitive execution).

* Two basic types of repetition:

1. Repetition controlled by a counter

(ie, repeat sequences of statements a predetermined number of times)

2. Repetition controlled by a logical expression(ie, repeat sequences of statements until some condition is satisfied)

Examples:

1. Calculate 1 + 2 + 3 + ......+ 98 + 99 + 100.

2. Calculate 1 + 2 + 3 +...... until the sum is larger than 50.

The block DO construct


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The block DO construct

Count-controlledDO loop

DO count = initial, final, step

.

.

block-of-statements

.

.

END DO

INTEGER :: sum, i

sum = 0

DO i=1,100, 1

sum = sum + i

END DO

PRINT *, 'sum = ', sum

Example:

count = integer variable

initial = initial value (integer expression)final = final value (integer expression)

step = step size (integer expression & cannot be 0)

step is optional. The default

value is1

.This line can also be written asDO i=1,100

Note: It is not permitted to

change these variablesinside the DO loop


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Examples:

DO statement Iteration count DO variable values

DO j=20,50,5 7 20,25,30,35,40,45,50

DO p=7,19,4 4 7,11,15,19

DO p=7,19,5 3 7,12,17

DO q=4,5,6 1 4

DO x=-20,20,6 7 -20,-14,-8,-2,4,10,16

DO m=20,-20,-6 7 20,14,8,2,-4,-10,-16

step < 0 (ie, counting down)

Example: (Nested DO loop)


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Example: (Nested DO loop)

PROGRAM Multiplication_table

IMPLICIT NONEINTEGER :: i, j

OPEN(UNIT=15, FILE='multi_table.dat', STATUS='UNKNOWN')

DO i=1,10

WRITE(15,*), ' '

WRITE(15,*), i, ' times tables '

DO j=1,10

WRITE(15,*), i, ' times ', j, ' is ', i*j

END DO

END DO

CLOSE (15)

END PROGRAM Multiplication_table

* This program print a set of multiplication tables from 1 to 10

a Do loop inside another Do loop

Output file


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.

.

1 times 8 is 8

1 times 9 is 91 times 10 is 10

2 times tables

2 times 1 is 2

2 times 2 is 4

2 times 3 is 6

2 times 4 is 8

2 times 5 is 10

2 times 6 is 12

2 times 7 is 14

2 times 8 is 16

2 times 9 is 18

2 times 10 is 20

3 times tables

3 times 1 is 3

3 times 2 is 6

3 times 3 is 9

.

.

Part of the results produced by the program Multiplication_table :


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Classwork 3

Example: (Read data file)


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Example: (Read data file)

PROGRAM Read_data

IMPLICIT NONE

INTEGER :: i, N

REAL :: t, v

OPEN(UNIT=10, FILE='expt.dat', STATUS='OLD')

OPEN(UNIT=15, FILE='log_v.dat',STATUS='UNKNOWN')

N = 10

DO i = 1, N

READ(10,*) t, v

WRITE(15,*) t, LOG(v)

END DO

CLOSE (10)

CLOSE (15)

END PROGRAM Read_data

Number of data

Read dataOutput data

File: expt.dat (experimental data)


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0.0 10.25

1.0 8.37

2.0 6.88

3.0 5.64

4.0 4.615.0 3.76

6.0 3.08

7.0 2.54

8.0 2.07

9.0 1.68

10.0 1.39

File: expt.dat ( experimental data )

0.0000000E+00 2.327278

1.000000 2.124654

2.000000 1.928619

3.000000 1.729884

4.000000 1.528228

5.000000 1.324419

6.000000 1.124930

7.000000 0.9321641

8.000000 0.7275486

9.000000 0.5187938

10.00000 0.3293037

Output file: log_v.dat

Example: Calculate 1+2+3+.... until the sum is larger than (or equal to) 50


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INTEGER :: sum, i

sum = 0

DO i=1,2000

IF ( sum >= 50 ) EXIT

sum = sum + i

PRINT *, i, sum

END DO

PRINT *, 'Final sum = ', sum

a p e Ca cu ate 3 u t t e su s a ge t a (o equa to) 50

EXITstatement

Predefined maximum number ofiterations

If the condition is satisfied(ie, sum >= 50), EXITwill

transfer the control to thestatement immediatelyafter the DO loop.

1 1

2 3

3 6

4 10

5 15

6 21

7 28

8 36

9 45

10 55

Final sum = 55

Output:


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INTEGER :: sum, i

sum = 0

DO i=1,2000

IF ( sum >= 50 ) THEN

GO TO 100

ELSE

sum = sum + i

PRINT *, i, sum

ENDIF

END DO

100 PRINT *, 'Final sum = ', sum

GO TO statement

Line label

* The result is the same as the previous code using the EXIT statement


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DO

statement-sequence1

IF (logical-expression1) EXIT

statement-sequence2END DO

General DO-Loop with EXIT

INTEGER :: sum, n

sum = 0

n = 0

DO

n = n + 1

IF (sum >= 50) EXIT

sum = sum + nPRINT *, n, sum

END DO


Example:

No counter (hence, no need to put in a predefined maximumnumber of iterations)

Exit the DO loop only if the condition

(sum >= 50) is satisfied

Example:


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DO

n = n + 1

IF (sum < 50) THEN

sum = sum + nPRINT *, n, sum

ELSE

EXIT

END IF

END DO


Example:

* The format is different from the previous code, but the results are the same.

Remark: In cases if the condition for obeying the EXIT statement never occur then


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Remark: In cases if the condition for obeying the EXIT statement never occur, then

the non-counting form of the general DO statement will become an infinite loop.

Example:Continue executing until the program isterminated by some external means(eg, killed by the user)

* If the input N is negative, then the code will continue executing!

READ(*,*) N

DO i = 1, max_step

IF (N==0) EXIT

N = N 1

END DO

* It is usually better to use the counting form & introduce a predefined maximum number ofiterations:

READ(*,*) N

DO

IF (N==0) EXIT

N = N 1

END DO

An integer value (usually a very large number)

defined by the user

* The EXIT statement terminates the DO loop by transferring control to the statement


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DO-CYCLE construct

p y g

immediately following the END DO statement.

* But sometimes it is necessary to terminate only the current step and jump ahead to the nextone:

DO control-info

statement-sequence1

CYCLE

statement-sequence2

END DO

control-info is empty for

a non-counting form

Example:DO i = 1, 20

IF ( MOD(i,3) == 0 ) CYCLE

PRINT *, i

END DO

This code only prints the integers(between 1 and 20) which arenot divisible by 3(ie, 1, 2, 4, 5, 7,....20)

Recall: intrinsic functions (Ch. 2)

basic comphy ch3

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