1. By Deniz Savas, CiCS, Shef. Univ., 2015
Introduction to
Fortran95 Programming
Part II
By Deniz Savas, CiCS, Shef. Univ., 2015

2. Summary of topics covered
Data Declarations and Specifications
ARRAYS and Array Handling
Where & Forall statements

3. Data Specifications & Declarations
Type declarations ( built in and user-defined)
IMPLICIT statement
PARAMETER statement
DIMENSION statement
DATA statements
SAVE statement
USE statement

4. Type Declarations type [,attribute] :: list TYPE can be one of ;
INTEGER ( KIND= n) REAL ( KIND=n)
COMPLEX( KIND= n ) LOGICAL(KIND=n)
CHARACTER ( LEN=m,KIND=n)
where (KIND=n) is OPTIONAL
TYPE ( type-name)
ATTRIBUTE can be a combination of;
PARAMETER - PUBLIC PRIVATE
POINTER - TARGET - ALLOCATABLE
DIMENSION - INTENT(inout) - OPTIONAL
SAVE - EXTERNAL - INTRINSIC

5. Example Type Declarations
Old style , i.e. pre Fortran90
INTEGER N , M
PARAMETER ( N = 20 , M=30)
REAL X , Y , Z, PI
DIMENSION X(N) , Y(N) , Z(N)
DATA PI / /
New (Fortran90) style
INTEGER, PARAMETER :: N =20 , M = 30
REAL, DIMENSION(N) :: X , Y , Z
REAL :: PI = 3.146
Note: The above two segments of code are identical in effect.

6. Example use of KIND values in variable declarations
INTEGER , PARAMETER :: SMLINT=SELECTED_INT_KIND(2) INTEGER , PARAMETER :: BIGINT=SELECTED_INT_KIND(7) INTEGER,PARAMETER :: BIG=SELECTED_REAL_KIND(7,40) INTEGER(KIND=SMLINT) :: I , J , K INTEGER(KIND=BIGINT) :: ISUM , JSUM REAL ( KIND=BIG) :: A , B ,C The Intrinsic function KIND( ) returns the kind value of its argument. EXAMPLE: IKIND = KIND(1.0E60)

7. User Defined Types
Also referred to as Derived_Data_Types or Structures
EXAMPLE:
! First define the type structure
TYPE VERTEX
REAL X , Y, Z
END TYPE VERTEX
! Next declare variables of this type.
TYPE ( VERTEX ) :: CORNER1 , CORNER2
! Now we can initialise and use them
CORNER2%Y = 2.5 ; CORNER1=( 1.0,1.0,0.2)

8. Derived Types ( Examples)
TYPE VERTEX REAL :: X , Y, Z END TYPE VERTEX TYPE PATCH TYPE ( VERTEX ) :: CORNER(4) END TYPE PATCH TYPE (VERTEX) :: P1 , P2, P3 , P4 TYPE (PATCH) :: MYPATCH , YOURPATCH P1 = ( 0.0 , 0.0 , 0.0 ) ; P3 = ( 1.0 , 1.0 , 0.0 ) P2 = ( 1.0 , 0.0 , 0.0 ) ; P4 = ( 0.0 , 1.0 , 0.0 ) MYPATCH = ( P1 , P2, P3,P4 ) YOURPATCH = MYPATCH YOURPATCH%CORNER(1) = MYPATCH%CORNER(4) - & (1.0,1.0,1.0)

9. Derived Types ( More Examples)
TYPE USERNAME CHARACTER*2 :: DEPARTMENT INTEGER :: STATUS CHARACTER*4 :: INITIALS TYPE ( USERNAME ) , POINTER :: NEIGHBOUR END TYPE USERNAME TYPE ( USERNAME ) , DIMENSION(1000) :: USERS USERS(1) = ( ‘CS’ , 1 , ‘DS’ ) USERS(12) = (‘CS’ , 1 , ‘PF’ ) USERS(1)%NEIGHBOUR => USERS(12) NULLIFY( USERS(12)%NEIGHBOUR )

10. ARRAYS: Declarations SIMPLE INTEGER, PARAMETER :: N = 36
REAL :: A( 20) , B(-1:5) , C(4,N,N) , D(0:N,0:4)
INTEGER , DIMENSION(10,10) :: MX ,NX,OX
Note that up to 7 dimensional arrays are allowed.
ALLOCATABLE ( Dynamic global memory allocation)
REAL, ALLOCATABLE :: A(:) , B(:,:,:)
AUTOMATIC ( Dynamic local memory allocation)
REAL, DIMENSION SIZE(A) :: work
ASSUMED SHAPE ( Used for declaring arrays passed to procedures )
REAL A(* ) ! Fortran77 syntax
REAL :: A(:) !” or A(:,:) so on “ ! Fortran90 syntax

11. Allocatable Array Examples
Used for declaring arrays whose size will be determined during run-time.
REAL, ALLOCATABLE :: X(:) , Y(:,:) , Z(:) :
READ(*,*) N
ALLOCATE( X(N) )
ALLOCATE ( Y(-N:N,0:N ) , STAT=status)
ALLOCATE ( Z(SIZE(X) )
DEALLOCATE ( X,Y,Z)
END
Note: status is an integer variable that will contain 0 if allocation has been successful or a non-zero value to indicate error.

12. Assumed Shape Array Examples
Used for declaring the dummy array arguments’ dimensions to procedures when these vary from call to call.
PROGRAM TEST
REAL :: AX1(20) , AX2(30) , AY(10,10) , BX1(80) , BX2(90),BY(20,30) :
Call spline( AX1, AX2, AY)
Call spline (BX1, BX2, BY)
END
SUBROUTINE SPLINE( X1 , X2 , Y )
REAL , DIMENSION(:) :: X1 , X2
REAL , DIMENSION(:,:) :: Y
RETURN

13. Automatic Array Examples
Use this method when you need short term storage for intermediate results. WORK arrays in NAG library are good examples ! SUBROUTINE INTERMIT( X1 , X2 , Y ,M) REAL , DIMENSION(:) :: X1 , X2 , Y INTEGER :: M REAL , DIMENSION(SIZE(Y) ) :: WORK COMPLEX , DIMENSION(M) :: CWORK : RETURN END

14. Above only A and B are conformable with each other.
Array Terminology
RANK , EXTENT, SHAPE and SIZE
Determines the conformance
CONFORMANCE
REAL A( 4,10) , B( 0:3,10) , C( 4,5,2) , D(0:2 , -1:4 , 6 )
A & B are: rank=2, extents=4 and 10 shape=4,10, size=40
C is rank=3, extents=4,5and shape=4,5,2 - size=40
D is rank=3 - extents=3 , 6 and 6 - shape=3,6,6 - size= 108
For two arrays to be conformable their rank, shape and size must match up.
Above only A and B are conformable with each other.

15. Whole Array Operations
Whole array operations can be performed on conformable arrays. This avoids using DO loops.
REAL :: A(10,3,4) , B( 0:9,3,2:5) , C(0:9,0:2,0:3) :
C = A + B ; C = A*B ; B= C/A ; C =sqrt(A)
All the above array expressions are valid.

16. WHERE Statement
This feature is a way of implementing vector operation masks. It can be seen as the vector equivalent of the IF statement
WHERE (logical_array_expr ) array_var=array_expr
WHERE (logical_array_expr )
array_assignments
ELSE WHERE
END WHERE
Note: ELSE WHERE clause is optional.

17. Examples
REAL :: A(300) , B(300) WHERE ( A > 1.0 ) A = 1.0/A WHERE ( A > B) A = B END WHERE WHERE ( A > 0.0 .AND. A>B ) A = LOG10( A ) ELSEWHERE A = 0.0

18. FORALL statement
This is a new Fortran95 feature. Extending the ability of Fortran Array Processing that was introduced by the WHERE statement. Syntax: FORALL (index=subscript_triplet, scalar_mask_expression) block of executable statements END FORALL

19. FORALL statement example
FORALL ( II=1:100,A(II)>0 )
X(II)=X(II)+Y(II)
Y(II)= Y(II) * X(II)
END FORALL
Mask is elements of A between 1 and 100 whose values are positive

20. Referencing Array Elements
REAL A (10) , X(10,20,30) , value INTEGER I , K(10) value = A( 8) OK VALUE = A(12) WRONG !!!! I = 2; value = A( I ) OK J = 3 ; I = 4 ; VALUE = X ( J, 10 , I ) OK Value = X (1.5 ) WRONG !!! X(:,1,1) = A(K) ! OK assuming K has values within the range 1 to 10

21. Referencing Array Sections
REAL :: A(10) , B(4,8) , C(4,5,6) I = 2 ; J=3 ; K=4 Referencing the array elements: A(2) B(3,4) C( 3,1,1) A(K) B(I,4) C(I,J,K) Referencing the array section: A(2:5) B(1,1:6) C( 1:1,3:4, 1:6 ) A(I:K) B( I:J,K) C(1:I,1:J,5 )

22. Referencing Array Sections (cont.)
It is also possible to use a stride index when referring to array sections. The rule is : array(start-index:stop-index:stride , ….) Stride can be a negative integer. If start-index is omitted it is assumed to be the lower_bound If stop-index is omitted it is assumed to be the upper_bound For example if array A is declared with DIMENSION(10,20) we can reference a subsections that contains only the even colums as; A(2:10:2,: ) The following are some other examples: A(1:9:3,1:20:2) this is the same as A(1:9:3,::2) A(10:1:-1,: ) this reverses the ordering of first dimension

23. Array Intrinsics
Many of the elemental numeric functions such as those listed below can be called with array arguments to return array results ( of same shape and size).
abs , sin, acos , exp , log , int , sqrt ...
There are also additional Vector/Matrix algebra functions designed to perform vector/matrix operations:
dot_product , matmul , transpose , minval , sum , size , lbound , ubound , merge , maxloc , pack

24. Array Assignments
REAL A(10,10) , B(10) , C(0:9) , D(0:30) A = 1.0 ; B=0.55 B = (/ 3. , 5. ,6. ,1., 22. ,8. ,16. , 4. ,9. , 12.0 /) I = 3 C = A( I,1:10) D(11:20) = A(I+1,1:10) D(1:10) = D(11:20) D(3:10) = D(5:12) A(2,:) = SIN( B )

25. Acknowledgement &References:
Thanks to Manchester and North High Performance Computing, Training & Education Centre for the Student Notes.
See APPENDIX A of the above notes for a list of useful reference books
Fortran 90 for Scientists and Engineers, Brian D Hahn, ISBN
Fortran 90 Explained by Metcalf & Reid is available from Blackwells ‘ St Georges Lib.’
Oxford Science Publications, ISBN