1. Summary
BIL 106
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

3. F The F language F & Fortran 90 Easy to learn to implement
to understand
Powerful enough for use in large programs F
Fortran 77
Fortran 90

4. 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
Non-numerical
data types
Logical data values

5. Arithmetic operators in F
Operator Meaning
+ Addition
- Substraction
* Multiplication
/ Division
** Exponentiation (or ‘rising the power of’)

6. 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

7. 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 characters
2) The first character of a name must be a letter
3) Imbedded blank characters are not permitted in a name
IMPORTANT: keywords such as program, write, and end are not actually names

8. Type Declarations implicit none integer :: Counts, Loop_Index
real :: 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.

9. 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

10. 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 !)

11. Declaration for a Named Constant
Declaration of a named constant is as follows:
Type name, parameter :: List of initializations
where each list item has the form
Name = Value definition
The value definition is an explicit constant.
Examples:
integer, parameter :: LENGTH=12
real, parameter :: PLANK= e-34, PI=
real, parameter :: GRAVITY=9.807, AVAGADRO= e23, &
twoPI=2.0*PI
integer, parameter :: A=20, HIGH=30, NEON=67
character (Len=2), parameter :: units=”Cm”
ATTENTION: Continuation line with ampersand symbol.

12. 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

13. 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

14. 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 structured
3) Each program unit should be documented
4) A program should be formatted in a style that enhances its readability
5) Programs should be readable and understandable
6) Programs should be general and flexible

15. Fundamental types of numbers
Integers
Whole numbers (positive/negative/zero)
Examples:
1952
Typical range on a 32-bit computer
-2 x 109 to +2 x 109

16. Fundamental types of numbers
Reals
+/- xxx.yyyyy
xxx integer part
yyyyy fractional part
A better representation:
Sign: +/-
Mantissa: a fraction between 0.1 and 1.0
Exponent: x 10e
x 10-6 or e-6

17. real and integer variables
Variable declaration:
type :: name
type :: name1, name2, …
integer :: a, b, c
real :: x, y, z

18. List-directed input and output
read *, var_1, var_2, …
only variables!
print *, item_1, item_2, …
variables, constants, expressions, …
Value separators:
Comma (,)
Space
Slash (/)
End-of-line

19. Named constants type, parameter :: name1=constant_expression1, …
real, parameter :: pi= , pi_by_2 = pi/2.0
integer, parameter :: max_lines = 200

20. Example
program list_directed_input_example !integers integer::int_1, int_2, int_3 real::real_1, real_2, real_3 !initial values int_1=-1 int_2=-2 int_3=-3 real_1=-1.0 real_2=-2.0 real_3=-3.0 !read data read*, int_1, real_1, int_2, real_2,int_3, real_3 !print new values print*, int_1, real_1, int_2, real_2,int_3, real_3 end program list_directed_input_example

21. Seven Golden Rules Always plan ahead Develop in stages Modularize
Keep it simple
Test throughly
Document all programs
Enjoy your programming

22. Programs and modules Main program unit program name use statements .
Specification statements (for variables)
Executable statements (for calculations)
end program name

23. 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.

24. 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.

25. Module program unit module name use statements .
Specification statements
contains
(Procedure definitions)
subprogram_1
subprogram_2
subprogram_n
end module name

26. Procedures Procedures - origin Procedures (subprograms) – form
“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

27. Procedures name (argument_1, argument_2, ...) Examples:
a + b * log (c)
-b + sqrt ( b * b – 4.0 * a * c)

28. 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

29. 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

30. Subroutines
subroutine 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

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

32. 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

33. 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, use
real, save :: list of real variables
real, save::a, b=1.23, c
İnteger, save::count=0

34. Example MAIN PROGRAM FUNCTION SUBPROGRAM program ……..
real : : Alpha, Beta, Gamma .
Alpha = Fkt ( Beta, Gamma )
end program ……….
FUNCTION SUBPROGRAM
function Fkt ( x, y )
real : : Fkt
real : : x, y
Fkt = x ** * y * y ** 2
x = 0.0
end function Fkt

35. 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

36. 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

37. 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.

38. Choice and decision-making
EXAMPLE : 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

39. Choice and decision-making
F provides a very similar construction for this decision-making problem as can be seen below :
If criterion 1 then
action 1
but if criterion 2 then
action 2
but if criterion 3 then
action 3
otherwise
action 4

40. 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

41. 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.

42. logical variables logical :: var_1, var_2, … Logical valued functions
function name(arg1, …) result logical_variable
logical :: logical_variable

43. 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 than
a <= b less than or equal to
a > b greater than
a >= b greater than or equal
a == b equal
a /= b not equal

44. 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

45. 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

46. 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

47. The if construct EXAMPLE : if ( x >= 0.0 ) then y = x * x
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

48. The if construct if (logical expression) then block of F statements
A typical structure for an general if – construct can be seen below :
if (logical expression) then
block of F statements
else if (logical expression) then
else
endif

49. Simple if construct if (logical expression) then block of F statements
endif

50. 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

51. 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.

52. 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.

53. The case construct
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.

54. The case construct select case (case_expression) case (case_selector)
block_of_statements
...
case default
end select

55. The case construct Case expression: Case selector:
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

56. 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

57. 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

58. 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.

59. 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.

60. do construct do count = initial, final, inc block of statements end do
loop
count_variable : must be an integer
initial_value, final_value : are arbitrary expressions of integer type
selected step_size = inc : must be an integer

61. Examples do statement iteration count do variable values
do i = 1, ,2,3,4,5,6,7,8,9,10
do j = 20, 50, ,25,30,35,40,45,50
do p = 7, 19, ,11,15,19
do q = 4, 5,
do r = 6, 5, (6)
do x = -20,20, ,-14,-8,-2,4,10,16
do n = 25, 0, ,20,15,10,5,0
do m = 20, -20, ,14,8,2,-4,-10,-16

62. Example 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

63. Count-controlled do loops
do count = initial, final, inc
do 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

64. 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

65. Some flexibility... do .
if (condition) then
exit
end if
end do

66. Some more flexibility... do .
if (condition) then
cycle
end if
end do

67. 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

68. The array concept 1 2 3 4 5 6 A

69. 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, …

70. 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)

71. 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)

72. The array concept
A20 A 1 2 3 4 -1
A31

73. Array declarations
type, 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

74. 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

75. 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

76. Examples integer, 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

77. Array constructors (/ value_1, value_2, … /)
Regular patterns are common: implied do (/ value_list, implied_do_control /)
arr = (/ (i, i = 1, 10) /)
arr = (/ -1, (0, i = 1, 48), 1 /)

78. Initialization
You can declare and initialize an array at the same time:
integer, dimension(50) :: my_array = (/ (0, i = 1, 50) /)

79. Input and output Array elements treated as scalar variables
Array name may appear: whole array
Subarrays can be referred too
EXAMPLE :
integer, dimension ( 5 ) : : value
read *, value
read *, value(3)

80. Examples
real, dimension(5) :: p, q integer, dimension(4) :: r print *, p, q(3), r read *, p(3), r(1), q
print *, p, q (3), q (4), r
print *, q (2)
! displays the value in the 2nd location of the array “q”
print *, p
! displays all the values storen in the array “p”

81. 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

82. Using arrays and array elements...
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. .
real, dimension(20) :: a, b, c
a = b*c
do i = 1, 20
a(i) = b(i)*c(i)
end do

83. Example integer, 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 ) ! will result d = (/ 3, 7, 11, 15 /)
d(6) d(7) d(8) d(9)

84. Intrinsic procedures with arrays
Elemental intrinsic procedures with arrays
array_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)

85. 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”.

86. Sub-arrays Subscript triplet: subscript_1 : subscript_2 : stride
Simpler forms:
subscript_1 : subscript_2
subscript_1 :
subscript_1 : : stride
: subscript_2
: subscript_2 : stride
: : stride :

87. Example real, dimension ( 10 ) : : arr arr ( 1 : 10 ) arr ( : )
! rank-one array containing all the elements of arr.
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).

88. 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)

89. Type of printing sub-arrays
work = ( / 3, 7, 2 /)
print *, work (1), work (2), work (3)
! or
print *, work ( 1 : 3 )
print *, work ( : : 1 )
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) )

90. Type of INPUT of sub-arrays
integer, 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 ) ! a(1) = a(2) +1
! a(3) = a(4) +1
! a(5) = a(6) +1
! etc.

91. 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!

92. Arrays and procedures Explicit-shape Assumed-shape Calling program

93. Arrays and procedures

94. 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 ) .

95. Example integer , 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)

96. Example
PROBLEM : Write a subroutine that will sort a set of names into alphabetic order.
İnitial order
After 1st exc
After 2nd exc
After 3rd exc
After 4th exc
After 5th exc
After 6th exc
After 7th exc

97. 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

98. Example
Write 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