Introduction to Fortran95 Programming Part II By Deniz Savas, CiCS, 2007

Part II: Contents Data Declarations and Specifications ARRAYS and Array Handling Where & Forall statements

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

Type Declarations Syntax: 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

Example Type Declarations Old Style (FTN77) INTEGER N, M PARAMETER ( N = 20, M=30) REAL X, Y, Z, PI DIMENSION X(N), Y(N), Z(N) DATA PI / / New Style (FTN90 onwards) INTEGER, PARAMETER :: N =20, M = 30 REAL, DIMENSION(N) :: X, Y, Z REAL :: PI = Note: The above two code segments are identical in effect.

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)

User Defined Types Also referred as Derived-Data-Types or Structures EXAMPLE: TYPE VERTEX REAL X, Y, Z END TYPE VERTEX TYPE ( VERTEX ) :: CORNER1, CORNER2 CORNER2%Y = 2.5 ; CORNER1=( 1.0,1.0,0.2)

Derived Types ( Examples) TYPE VERTEX REAL :: X, Y, Z END TYPE VERTEX TYPE PATCH TYPE ( VERTEX ) :: CORNER(4) END 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)

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 )

Array Declarations STATIC 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

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 ), STATUS=status) ALLOCATE ( Z(SIZE(X) ) : DEALLOCATE ( X,Y,Z) END

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 END

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

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 2 - 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.

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(0:9,0:2,0:4) : C = A + B ; C = A*B ; B= C/A ; C =sqrt(A) All the above array expressions are valid.

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 array_assignments END WHERE Note: ELSE WHERE clause is optional.

Examples of where 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 END WHERE

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

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

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

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 )

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

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

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 )

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

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