1

Summary

BIL 106E

Introduction to Scientific & Engineering

Computing

2

Course Contentents Introduction to computing Basic F Selective execuation Repetitive execuation Input/output Programming with functions Arrays, Data types, Files Pointers and linked structures

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The F language

F & Fortran 90

FFortran 77

Fortran 90

Easy to learn to implement to understand

Powerful enough for use in large programs

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2.1 Data types

There are five basic data types in fortran 1) INTEGER 2) REAL 3) COMPLEX 4) CHARACTER 5) LOGICAL

Numerical-data types

Strings of characters

Logical data values

Non-numericaldata types

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Arithmetic operators in F

Operator Meaning+ Addition- Substraction* Multiplication/ Division** Exponentiation (or ‘rising the power of’)

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Arithmetic operator priorities

Operator Priority** High* and / Medium+ and - Low

Examples: W=c/d*b

Total=2**3+5*2=18 W=x+z-y

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Names & Declarations

A data object is a constant that never changes or a variable that can change during program execution.

Data object may have names. For example, Average, X, Y, Einstein, or Potential_Energy.

Names in a program must conform to 3 rules:1) A name may contain up to 31 letters, digits, and underscore

characters2) The first character of a name must be a letter3) Imbedded blank characters are not permitted in a name

IMPORTANT: keywords such as program, write, and end are not actually names

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Type Declarations

implicit noneinteger :: Counts, Loop_Indexreal :: Current, Resistance, Voltage

Names defined as part of the F language, including keywords and intrinsic function names (such as sin, tan, abs, etc.), must be written in lower case. Names that you invent can use any combination of upper and lower case, but each name must be written consistently.

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Type properties: Kind & Length

Kind : A variable of any numerical type has a kind type parameter, which designates a subtype or variant of the type.

Each type has a default computer representation For each numerical data type, F defines a set of integers to be used

as kind type parameter values (i.e., the number 4 for real representation, number 8 for the higher-precision variant)

Length : A variable of character data type has a string length property.

A character type declaration must specify string length

A type declaration appears in parentheses after the type name. If no

kind parameter is specified, F selects the default computer representa-

tion Type name (Type properties) :: List of names

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Constants The name of a constant looks like the name of a

variable and it must be listed in the type declaration The keyword parameter designates a named constant Houdini Principle: Don’t use magic numbers

use a named constant rather than a explicit constant give always explanations ( use !)

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Declaration for a Named Constant

Declaration of a named constant is as follows: Type name, parameter :: List of initializationswhere each list item has the form Name = Value definitionThe value definition is an explicit constant.Examples: integer, parameter :: LENGTH=12 real, parameter :: PLANK=6.6260755e-34, PI=3.141593 real, parameter :: GRAVITY=9.807,

AVAGADRO=6.0221367e23, & twoPI=2.0*PI integer, parameter :: A=20, HIGH=30, NEON=67 character (Len=2), parameter :: units=”Cm”

ATTENTION: Continuation line with ampersand symbol.

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Simple Input & Output

Read (unit = *, fmt = *) Input List Write (unit = *, fmt = *) Output List

An asterisk as the unit in a read or write control list designates the default input device (the keyboard) or the default output device (The terminal screen)

An asterisk as the format designates list-directed formatting. Input data values for on-line list-directed input are entered at the computer keyboard in free form. Consecutive values must be separated by blanks.

For example: read (unit = *, fmt = *) Radii, I, Current, Top can be entered as 9.75 10 15.32 765.3

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Mixed-mode assignment

Assume that, b is a real variable whose value is 100.0, while c and d are

integers having the values 9 and 10, respectively. a = b*c/d result is 90.0 a = c/d*b a gets 0 value.

This phenomenon is known as integer division

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Program style and design

A program must be correct, readable, and understandable. The basic principles for developing a good program are as follows:

1) Programs cannot be considered correct until they have been validated using test data.

2) Programs should be well structured3) Each program unit should be documented4) A program should be formatted in a style that enhances

its readability5) Programs should be readable and understandable6) Programs should be general and flexible

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Fundamental types of numbers

Integers Whole numbers

(positive/negative/zero) Examples:

195234567878901230-2334567

Typical range on a 32-bit computer-2 x 109 to +2 x 109

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Fundamental types of numbers

Reals+/- xxx.yyyyy

xxx integer partyyyyy fractional part

A better representation: Sign: +/- Mantissa: a fraction between 0.1 and 1.0 Exponent: x 10e

- 0.923456 x 10-6 or -0.923456e-6

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real and integer variables

Variable declaration:type :: name

type :: name1, name2, … integer :: a, b, c real :: x, y, z

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List-directed input and output

read *, var_1, var_2, … only variables!

print *, item_1, item_2, … variables, constants, expressions, …

Value separators: Comma (,) Slash (/) End-of-line Space

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Named constants type, parameter :: name1=constant_expression1, …

real, parameter :: pi=3.1415926, pi_by_2 = pi/2.0

integer, parameter :: max_lines = 200

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program list_directed_input_example!integersinteger::int_1, int_2, int_3real::real_1, real_2, real_3!initial valuesint_1=-1int_2=-2int_3=-3real_1=-1.0real_2=-2.0real_3=-3.0!read dataread*, int_1, real_1, int_2, real_2,int_3, real_3!print new valuesprint*, int_1, real_1, int_2, real_2,int_3, real_3end program list_directed_input_example

Example

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Seven Golden Rules

Always plan ahead

Develop in stages

Modularize

Keep it simple

Test throughly

Document all programs

Enjoy your programming

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Programs and modules

Main program unit

program name

use statements...Specification statements (for variables)...Executable statements (for calculations)...

end program name

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Modules

Programs for solving complex problems should be designed in a modular fashion.

The problem should be divided into simpler subproblems, so that the subprograms can be written to solve each of them.

Every program must include exactly one main program and may also include one or more modules.

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Modules

•Modules are a second type of program unit.

•The basic structure of a module is similar to the main program unit.

•The initial module statement of each module specifies the name of

that module based on the F language rules.

•A module unit ends with an end program statement incuding its

name.

•A module does not contain any executable statements.

•A module may contain any number of subprograms which are

seperated from the other statements by a contain statement.

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Module program unit

module name

use statements...Specification statements.

contains(Procedure definitions)

subprogram_1subprogram_2..subprogram_n

end module name

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Procedures

Procedures - origin “Write your own” (homemade) Intrinsic (built-in, comes with F )

sin(x), cos(x), abs(x), … Written by someone else (libraries)

Procedures (subprograms) – form Functions Subroutines

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Procedures

name (argument_1, argument_2, ...)

Examples:

a + b * log (c)

-b + sqrt ( b * b – 4.0 * a * c)

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Functions

function name (d1, d2, …) result(result_name)

Specifications part..

Execution part end function name Variables

Internal (local) variables Result variable (keyword result) Dummy argument (keyword intent(in))

attribute

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Functions

function cube_root result(root)! A function to calculate the cube root of ! a positive real number! Dummy argument declaration

real, intent(in) :: x! Result variable declaration

real :: root! Local variable declaration

real :: log_x! Calculate cube root by using logs

log_x = log(x)root = exp(log_x/3.0)

end function cube_root

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Subroutinessubroutine roots (x, square_root, cube_root, fourth_root, & fifth_root)! Subroutine to calculate various roots of positive real! Number supplied as the first argument, and return them in! the second to fifth arguments

! Dummy argument declarations real, intent(in) :: x real, intent(out) :: square_root, cube_root, & fourth_root, fifth_root ! Local variable declaration real :: log_x ! Calculate square root using intrinsic sqrt square_root = sqrt(x) ! Calculate other roots by using logs log_x = log(x) cube_root = exp(log_x/3.0) fourth_root = exp(log_x/4.0) fifth_root = exp(log_x/5.0)end subroutine roots

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Subroutines

call name (arg1, arg2, …) intent(in), intent(out), intent(inout)

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Attributes

intent (in): the dummy argument only provides information to the procedure and is not allowed to change its value any way

intent (out): the dummy argument only returns information from the procedure to the calling program

intent (inout): the dummy argument provides

information in both directions

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Saving the values of local objects

Local entities within a procedure are not accessible from outside that procedure

Once an exit has been made, they cease to exist

If you want their values to ‘survive’ between calls, usereal, save :: list of real variables

real, save::a, b=1.23, c

İnteger, save::count=0

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Example

MAIN PROGRAM

program ……..

real : : Alpha, Beta, Gamma

.

.

Alpha = Fkt ( Beta, Gamma )

.

.

end program ……….

 

 

FUNCTION SUBPROGRAM

function Fkt ( x, y )

real : : Fkt

real : : x, y

Fkt = x ** 2 - 2.5 * y + 3.7 * y ** 2

x = 0.0

end function Fkt

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Example: Write a subprogram which calculates the cube root of a positive real number

MAIN PROGRAM

program test_cube_root

use maths

real : : x

print *, “Type a positive real number”

read *, x

Print *, “ The cube root of “,x,” is “, cube_root(x)

.

a = b * cube_root(x) + d

.

end program test_cube_root

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module maths

Public::cube_root

contains

function cube_root (x) result (root)

! a function to calculate the cube root of a positive real number

! Dummy arguments

real , intent (in) : : x

! Result variable declaration

real : : root

! Local variable declaration

real : : log_x

! Calculate cube root by using logs

log_x = log (x)

root = exp (log_x / 3.0)

function cube_root

end module maths

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Controlling the flow of your program

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-makingEXAMPLE : Q : How do I get to Budapest from Vienna ?

  A : It depends how you want to travel :

* if you are in hurry then

you should fly from Schwechat airport in Vienna to Ferihegy airport in Budapest

* but if you are a romantic or like trains then

you should take the Orient Express from Südbahnhof

to Budapest’s Keleti palyudvar

* but if you have plenty of time then

you can travel on one of the boats which ply along the Danube

* otherwise

you can always go by road

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Choice and decision-making

If criterion 1 thenaction 1

but if criterion 2 thenaction 2

but if criterion 3 thenaction 3

otherwiseaction 4

F provides a very similar construction for this decision-making problem as can be seen below :

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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 variables logical :: var_1, var_2, … Logical valued functions

function name(arg1, …) result logical_variable

logical :: logical_variable

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Logical (relational) operatorsAn 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 operators

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

true true true true

true false true false

falsetrue true false

falsefalse false 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 < 1.0

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The if construct

In 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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The if construct

EXAMPLE : 

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

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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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PROBLEM : A function subprogram which returns the cube root , is needed to write down.

 function cube_root (x) result (root)

! This function program calculates the cube root of any real number

! Dummy argument and result declarations

real, intent (in) : : x

real : : root

! eliminate the zero case

if ( x == 0.0 ) then

root = 0.0

! calculate the cube root by using logs negative argument

else if ( x < 0.0 ) then

root = - exp ( log (-x) / 3.0 )

! positive argument

else

root = exp ( log (x) / 3.0

end if

end function cube_root

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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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Depending on the abovegiven 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 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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EXAMPLE : 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

! variable declarations

character (len= 10) : : date

character (len= 2) : : month

! read date

print *, “please type a date in the form yyyy-mm-dd”

read *, date

! extract month number

month = date ( 6 : 7 )

! print season

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select case (month)

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 default

print *, date, “is in not valid date”

end select

end program seasons

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Program repetition

In many cases, we have to repeat certain sections of a program

Many numerical methods involve repetition/iteration

We have to have construct to repeat a group of statements, to end the repetition, or to restart it when certain condition is fulfilled.

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EXAMPLE for a TYPICAL CYCLE :

Repeat the following 3 steps 21 times considering 5oC intervals from 0oC till to 100oC without the need for any data to be read at all :

  1.step : read the initial and last Celcius temperature

2.step : calculate the corresponding Fahrenheit temperature for 5oC intervals

3.step : print both tempratures

 A sequence of statements which are repeated is called a “loop.“

 The do – constructs provides the means for controlling the repetition of statements within a loop.

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do construct

do count = initial, final, incblock of statements

end doloop

count_variable : must be an integer

initial_value, final_value : are arbitrary expressions of integer type

selected step_size = inc : must be an integer

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Examplesdo statement iteration count do variable values 

do i = 1,10 10 1,2,3,4,5,6,7,8,9,10

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

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

do q = 4, 5, 6 1 4

do r = 6, 5, 4 0 (6)

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

do n = 25, 0, -5 6 25,20,15,10,5,0

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

 

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do number = 1, 10, 2

print *, number, number **2

end do 

 OUTPUT produced will display following results :

1         1

3 9

5            25

7 49

9 81

 

Example

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Count-controlled do loops

do count = initial, final, incdo count = initial, final (inc = 1)do

Iteration count:How many times we will go through the loop?

max((final-initial+inc)/inc, 0)

Integer variable

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NESTED DO - LOOPS

The body of a do loop may contain another do loop. In this case,the second do loop is said to be “nested” within the first do loop.

EXAMPLE :

 do m = 1, 4

do n = 1, 3

product = m * n

print *, m, n, product

end do

end do

 

OUTPUT  

1 1 1

1 2 2

1 3 3

2 1 2

2 2 4

2 3 6

3 1 3

3 2 6

3 3 9

4 1 4

4 2 8

4 3 12

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Some flexibility...do

.

.

.if (condition) then

exitend if

.

.

.end do.

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Some more flexibility...

do ...if (condition) then

cycleend if

.

.

.end do.

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Dealing with exceptional situations:

stop statement simply terminates execution

return statement causes execution of the procedure to

be terminated immediately and control transferred back to the program unit which called or referenced the procedure

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Vectors, matrices and cubesOne-dimensional and two-dimensional arrays may be interpreted

in special ways according to the rules of linear algebra. An array of rank 1 is a vector, an array of rank 2 is a matrix and an array of rank 3 may be viewed as a stack of cubes forming a large block (parallelepiped).

Examples:One-dimensional array; vector:

integer, dimension(3) :: A

Two-dimensional array; integer, dimension(3,3) :: B

A(1) A(2) A(3)

B(1,1) B(1,2) B(1,3)

B(2,1) B(2,2) B(2,3)

B(3,1) B(3,2) B(3,3)

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Vectors, matrices and cubesThree-dimensional array;Integer, dimension(3,3,3) :: C

C(1,1,1) C(1,1,2) C(1,1,3)

C(1,2,1) C(1,2,2) C(1,2,3)

C(1,3,1) C(1,3,2) C(1,3,3)

C(2,1,1) C(2,1,2) C(2,1,3)

C(2,2,1) C(2,2,2) C(2,2,3)

C(2,3,1) C(2,3,2) C(2,3,3)

C(3,1,1) C(3,1,2) C(3,1,3)

C(3,2,1) C(3,2,2) C(3,2,3)

C(3,3,1) C(3,3,2) C(3,3,3)

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The array concept A set with n (=6) object, named A In mathematical terms, we can call

A, a vector And we refer to its elements as

A1, A2, A3, …

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The array concept In F, we call such an ordered set of

related variables an array Individual items within an array

array elements A(1), A(2), A(3), …, A(n)

72

The array concept Subscripts can be:

x(10)

y(i+4)

z(3*i+max(i, j, k))

x(int(y(i)*z(j)+x(k)))

x(1)=x(2)+x(4)+1

print*,x(5)

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The array concept

A

1

2

3

4

-1 0 1 2 3

A20

A31

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Array declarationstype, dimension(subscript bounds) ::

list_of_array_names

type, dimension(n:m) :: variable_name_list

real, dimension(0:4) :: gravity, pressure

integer, dimension(1:100) :: scores

logical, dimension(-1, 3) :: table

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Examples for Shape Arrays

real, dimension ( 0 : 49 ) : : z

! the array “z” has 50 elements

 

real, dimension ( 11 : 60 ) : : a, b, c

! a,b,c has 50 elements

 

real, dimension ( -20 : -1 ) : : x

! the array “x” has 20 elements

 

real, dimension ( -9 : 10 ) : : y

! the array “y” has 20 elements

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Array sections with increment (stride) designator

real, dimension (18) :: V

V(2:9)

V(1: 15: 2)

V(2: 17: 5)

77

Array declarations Up to 7 dimensions Number of permissible subscripts:

rank Number of elements in a particular

dimension: extent Total number of elements of an array:

size Shape of an array is determined by its

rank and the extent of each dimension

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Examplesinteger, dimension ( 10 ) : : arr

 

arr = (/ 3, 5, 7, 3, 27, 8, 12, 31, 4, 22 /)

 

 arr ( 1 ) = 3

 arr ( 5 ) = 27

! the value 27 is storen in the 5th location of the array “arr”

 arr ( 7 ) = 12

arr ( 10 ) = 22

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Array constructors

(/ value_1, value_2, … /) arr = (/ 123, 234, 567, 987 /) Regular patterns are common:

implied do(/ value_list, implied_do_control /)

arr = (/ (i, i = 1, 10) /) arr = (/ -1, (0, i = 1, 48), 1 /)

80

Initialization

You can declare and initialize an array at the same time:

integer, dimension(50) :: my_array = (/ (0, i = 1, 50) /)

81

Input and output Array elements treated as scalar

variables Array name may appear: whole

array Subarrays can be referred tooEXAMPLE :

integer, dimension ( 5 ) : : value

read *, value

read *, value(3)

82

real, dimension(5) :: p, qinteger, dimension(4) :: rprint *, p, q(3), rread *, p(3), r(1), qprint *, p, q (3), q (4), rprint *, q (2)

! displays the value in the 2nd location of the array “q”

print *, p! displays all the values storen in the array “p”

Examples

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Using arrays and array elements...

An array can be treated as a single object Two arrays are conformable if they

have the same shape A scalar, including a constant, is

conformable with any array All intrinsic operations are defined

between two conformable objects

84

Using arrays and array elements...

.real, dimension(20) :: a, b, c..a = b*c

do i = 1, 20 a(i) = b(i)*c(i)end do

Arrays having the same number of elements may be applied to arrays and simple expressions. In this case, operation applied toan array are carried out elementwise.

85

Exampleinteger, dimension ( 4 ) : : a, b

integer, dimension ( 0 : 3 ) : : c

integer, dimension ( 6 : 9 ) : : d

 

a = (/ 1, 2, 3, 4 /)

b = (/ 5, 6, 7, 8 /)

c = (/ -1, 3, -5, 7 /)

c(0) c(1) c(2) c(3)

a = a + b ! will result a = (/ 6, 8, 10, 12 /)

d = 2 * abs ( c ) + 1 ! will result d = (/ 3, 7, 11, 15 /)

d(6) d(7) d(8) d(9)

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do I = 1, 3 do J=1, 3 B(I,J) = I + J end do end do

RESULT: 2 3 4 3 4 5 4 5 6

87

do I =1, 3 do J = 1, 3 if ( I < J) then A(I,J) = -1 else if (I == J) then A(I,J)= 0 else A(I,J) = 1 end if end do end do

88

Intrinsic procedures with arrays Elemental intrinsic procedures with

arraysarray_1 = sin(array_2)

arr_max = max(100.0, a, b, c, d, e)

Some special intrinsic functions:maxval(arr)

maxloc(arr)

minval(arr)

minloc(arr)

size(arr)

sum(arr)

89

Sub-arrays Array sections can be extracted from a

parent array in a rectangular grid usinf subscript triplet notation or using vector subscript notation

Subscript triplet:subscript_1 : subscript_2 : stride

Similar to the do – loops, a subscript triplet defines an ordered set of subscripts

beginning with subscript_1,     ending with subscript_2 and

 considering a seperation of stride between the consecutive subscripts. The value of stride must not be “zero”.

90

Sub-arrays

Subscript triplet:subscript_1 : subscript_2 :

stride Simpler forms:

subscript_1 : subscript_2subscript_1 :subscript_1 : : stride: subscript_2: subscript_2 : stride: : stride:

91

Examplereal, dimension ( 10 ) : : arr

arr ( 1 : 10 )

! rank-one array containing all the elements of arr.

arr ( : )

! rank-one array containing all the elements of arr.

arr ( 3 : 5 )

! rank-one array containing the elements arr (3), arr(4), arr(5).

arr ( : 9 )

! rank-one array containing the elements arr (1), arr(2),…., arr(9).

arr ( : : 4 )

! rank-one array containing the elements arr (1), arr(5),arr(9).

92

Example

integer, dimension ( 10 ) : : a

integer, dimension ( 5 ) : : b, i

integer : : j

 

a = (/ 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 /)

i = (/ 6, 5, 3, 9, 1 /)

  b = a ( i ) ! will result b = ( 66, 55, 33, 99, 11 /)

a ( 2 : 10 : 2 ) ! will result a = ( 22, 44, 66, 88, 110 /)

  a ( 1 : 10 : 2 ) = (/ j ** 2, ( j = 1, 5 ) /)

! will result a = ( 1, 4, 9, 16, 25 /)

a(1) a(3) a(5) a(7) a(9)

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Type of printing sub-arrayswork = ( / 3, 7, 2 /)

print *, work (1), work (2), work (3)

! or

print *, work ( 1 : 3 )

! or

print *, work ( : : 1 )

! or

integer : : i

do i = 1, 3, 1

print *, work (i)

end do

! or another example

print *, sum ( work (1: 3) )

! or another example

print *, sum ( work (1: 3 : 2) )

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Type of INPUT of sub-arraysinteger, dimension ( 10 ) : : a

integer, dimension ( 3 ) : : b

.

b = a ( 4 : 6 ) ! b (1 ) = a (4)

! b (2 ) = a (5)

! b (3 ) = a (6)

  .

a ( 1 : 3 ) = 0 ! a(1) = a(2) = a(3) = 0

a ( 1 : : 2 ) = 1 ! a(1) = a(3) =…….= a(9) = 1

a ( 1 : : 2 ) = a ( 2 : : 2 ) + 1 ! a(1) = a(2) +1

! a(3) = a(4) +1

! a(5) = a(6) +1

! etc.

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Arrays and procedures Explicit-shape array: no

freedom! Assumed-shape array

If an array is a procedure dummy argument, it must be declared in the procedure as an assumed-shape array!

96

Arrays and procedures

97

Example

main program unit: real, dimension ( b : 40 ) : : a

subprogram: real, dimension ( d : ) : : x

x ( d ) ---------------------- a ( b )

x ( d + 1 ) ---------------------- a ( b + 1 )

x ( d + 2 ) ---------------------- a ( b + 2 )

x ( d + 3 ) ---------------------- a ( b + 3 )

.

.

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Exampleinteger , dimension ( 4 ) : : section = (/ 5, 1, 2, 3 /)

real , dimension ( 9 ) : : a

call array_example_3 ( a ( 4 : 8 : 2 ), a ( section ) )

dummy_array_1 = (/ a (4), a (6), a (8) /) 

dummy_array_2 = (/ a (5), a (1), a (2), a (3) /) 

dummy_argument_2 (4) dummy_argument_2 (3)

dummy_argument_2 (2)

dummy_argument_2 (1)

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ExamplePROBLEM : Write a subroutine that will sort a set of names into alphabetic order.

İnitial order 7 1 8 4 6 3 5 2

After 1st exc. 1 7 8 4 6 3 5 2

After 2nd exc. 1 2 8 4 6 3 5 7

After 3rd exc. 1 2 3 4 6 8 5 7

After 4th exc. 1 2 3 4 6 8 5 7

After 5th exc. 1 2 3 4 5 8 6 7

After 6th exc. 1 2 3 4 5 6 8 7

After 7th exc. 1 2 3 4 5 6 7 8

 

100

Array-valued functions A function can return an array Such a function is called an

array-valued function

function name(…..) result(arr)real, dimension(dim) :: arr...

end function name

Explicit-shape

101

ExampleWrite a function that takes 2 real arrays as its arguments, returns an array in which each element is the maximum of the 2 corresponding elements in the input array

function max_array ( array_1, array_2 ) result (maximum_array)

! this function returns the maximum of 2 arrays on an element-by-element basis dummy arguments

real, dimension ( : ) , intent (in) : : array_1, array_2

! result variable

real, dimension ( size (array_1) ) : : maximum_array

! use the intrinsic function “max” to compare elements

maximum_array = max ( array_1, array_2)

! or use a do-loop instead of the intrinsic function max to compare elements

do i = 1, size (array_2)

maximum_array ( i ) = max ( array_1 ( i ), array_2 ( i ) )

end do

end function max_array

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! Bu program açıklamalar, boşluklar ve gun 12 ay verisi şeklinde devam eden peşpeşe yıllar ve farklı istasyon verilerini okuyup istenilen yillarin verileri yazmak için yazılmıştır. program verisuz character(len=50)::istadi,s1,s2,s3 integer::i,j,istno,yil,ios open(unit=1,file="gunortsi.out",status="old",action="read") open(unit=2,file="gunortsi.dat",status="unknown",action="write") print*,"Lütfen Bekleyiniz"do read(unit=1,fmt="(a8,2i7,a,a)",iostat=ios)istadi,istno,yil,s1,s2 if (ios<0) then exit end if if (yil<1965 .or. yil>2006) then cycle else write(unit=2,fmt="(a8,2i7,a,a)")istadi,istno,yil,s1,s2 end if end doclose (unit=1)close (unit=2)end program verisuz

103

! Bu program istadı, no, gun 12 ay verisi şeklinde devam eden peşpeşe yıllar ve! farklı istasyon verilerini okuyup boşlara 9999.9 yazmak için yazılmıştır. program verisuz2 character(len=86)::istadi,s1 integer::i,j,istno,yil,gun,ios! real::a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12character(len=7)::a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12 open(unit=1,file="gunmaksi.dat",status="old",action="read") open(unit=2,file="gunmaksi.a",status="unknown",action="write") print*,"Lutfen Bekleyiniz"

do read(unit=1,fmt="(a8,3i7,12a7)",iostat=ios)istadi,istno,yil,gun,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12 if (ios<0) then exit end if if (gun==0) then print*,istadi,yil,gun cycle else if (a1=="") thena1="999.9" end if if (a2=="") then a2="999.9" end if if (a3=="") thena3="999.9" end if if (a4=="") thena4="999.9" end if if (a5=="") then a5="999.9" end if if (a6=="") thena6="999.9" end if if (a7=="") thena7="999.9" end if if (a8=="") thena8="999.9" end if if (a9=="") thena9="999.9" end if if (a10=="") thena10="999.9" end if if (a11=="") thena11="999.9" end if if (a12=="") thena12="999.9" end if write(unit=2,fmt="(a8,3i7,3x,12a7)",iostat=ios)istadi,istno,yil,gun,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12 end ifend do

close (unit=1)

close (unit=2)end program verisuz2