Solution

9 marks in total for all three parts.

1. 5 marks
   • 3 for ALIGN and DISTRIBUTE\
   • 1 for DOT_PRODUCT or MATMUL,
   • 1 for correct program

   PROGRAM Main
    IMPLICIT NONE
    INTEGER :: n
    INTEGER :: i
    REAL, ALLOCATABLE, DIMENSION(:,:) :: A
    REAL, ALLOCATABLE, DIMENSION(:)   :: x, y
   
   !HPF$ PROCESSORS, DIMENSION(4)    :: P
   !HPF$ ALIGN (:) WITH A(*,:)       :: X
   !HPF$ ALIGN (:) WITH A(:,*)       :: Y
   !HPF$ DISTRIBUTE(CYCLIC,*) ONTO P :: A
   
     PRINT*, "Type in the size of matrix"
     READ*, n
     ALLOCATE (A(n,n))
     ALLOCATE (x(n))
     ALLOCATE (y(n))
     CALL RANDOM_NUMBER(A)
     CALL RANDOM_NUMBER(X)
     DO I = 1,n
      Y(i) = DOT_PRODUCT(A(i,:),X(:))
     END DO
     PRINT*,Y
     DEALLOCATE(A,x,y)
   END PROGRAM

2. 3 marks
   • 3 for ALIGN and DISTRIBUTE

   PROGRAM Main
    IMPLICIT NONE
   
    INTEGER :: n
    INTEGER :: i
    REAL, ALLOCATABLE, DIMENSION(:,:) :: A
    REAL, ALLOCATABLE, DIMENSION(:)   :: x, y
   
   !HPF$ PROCESSORS, DIMENSION(2,2)       :: P
   !HPF$ TEMPLATE, DIMENSION(n,n)         :: T
   !HPF$ ALIGN (:,:) WITH T(:,:)          :: A
   !HPF$ ALIGN (:)   WITH T(*,:)          :: X
   !HPF$ ALIGN (:) WITH A(:,*)            :: Y
   !HPF$ DISTRIBUTE(CYCLIC,CYCLIC) ONTO P :: T
   
     PRINT*, "Type in the size of matrix"
     READ*, n
     ALLOCATE (A(n,n))
     ALLOCATE (x(n))
     ALLOCATE (y(n))
     CALL RANDOM_NUMBER(A)
     CALL RANDOM_NUMBER(X)
     DO I = 1,n
      Y(i) = DOT_PRODUCT(A(i,:),X(:))
     END DO
     PRINT*,Y
     DEALLOCATE(A,x,y)
   END PROGRAM

1 mark for the last part:

The 2D grid version involves communications along the rows. The 1D version doesn't involve any communication, thusly 1D version is best.