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Efficient Fortran Programming: Mean Calculation and Vector Processing

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This comprehensive guide presents various Fortran programming techniques, including how to calculate the mean of a list, perform vector operations, and efficiently sort and search arrays. It explains passing arrays as arguments, using selection sort, linear search, and binary search algorithms. Detailed explanations and examples of multi-dimensional arrays are also provided, including initialization and reading data through nested loops. Ideal for students and professionals looking to enhance their knowledge of array operations in Fortran.

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Efficient Fortran Programming: Mean Calculation and Vector Processing

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  1. Arrays

  2. Arrays asArguments • Example: • Calculating the mean of a list. • (Fortran allows both the array and its size to be passed to the subprogram).

  3. PROGRAM Mean_of_a_List_2 IMPLICIT NONE INTEGER, PARAMETER :: NumItems = 10 REAL, DIMENSION(NumItems) :: Item PRINT *, "Enter the", NumItems, " real numbers:" READ *, Item PRINT '(1X, "Mean of the ", I3, " Numbers is ", F6.2)', & NumItems, Mean(Item, NumItems) CONTAINS

  4. FUNCTION Mean(X, NumElements) INTEGER, INTENT(IN) :: NumElements REAL, DIMENSION(NumElements), INTENT(IN) :: X REAL :: Mean Mean = SUM(X) / REAL(NumElements) END FUNCTION Mean END PROGRAM Mean_of_a_List_2

  5. Vector Processing • Two dimensional vectors can be represented algebraically as ordered pairs • (a1, a2) of real numbers • a1, a2 are called components • In general, n-dimensional vectors can be represented algebraically by ordered n-tuples (a1, a2, … an).

  6. The Norm of a Vector • The norm of an n-dimensional vector • a=(a1, a2, … an) is given by|a| = a21+ a22,+…+ a2n

  7. Function to Calculate the Norm • FUNCTION Norm(A, N) REAL :: Norm REAL, INTENT(IN), DIMENSION(N) :: A INTEGER, INTENT (IN) :: NNorm = SQRT(SUM(A*A))END FUNCTION Norm

  8. Sum & Difference of Vectors • Example: • a=(10, 20) • b=(30, 40) • The SumA + B = (40, 60) • The differenceA - B = (-20, -20)

  9. Sorting • Sorting: Arranging the items in a list so that they are in either ascending or descending order. 25, 33, 1, 14, 27, 451, 14, 25, 27, 33, 45

  10. program sort implicit none integer:: item(10), i, j, min, pos, temp item = (/10, 2, 15, 9, 1, 0, 33, 29, 50, 17/) do i = 1, 9 min = item(i) pos = i do j = i, 10 if (item(j)< min)then min = item(j) pos = j end if end do temp = item(i) item(i)= min item(pos) = temp end do write(*, "(1x, i2)") item end program sort

  11. SUBROUTINE SelectionSort(Item) INTEGER, DIMENSION(:), INTENT(INOUT) :: Item INTEGER :: NumItems, SmallestItem, I INTEGER, DIMENSION(1) :: MINLOC_array NumItems = SIZE(Item) DO I = 1, NumItems - 1 SmallestItem = MINVAL(Item(I:NumItems)) MINLOC_array = MINLOC(Item(I:NumItems)) LocationSmallest = (I - 1) + MINLOC_array(1) Item(LocationSmallest) = Item(I) Item(I) = SmallestItem END DO END SUBROUTINE SelectionSort

  12. Search • Linear Search • Example:

  13. PROGRAM LinearSearch INTEGER, DIMENSION(10) :: A = (/5,10,15,20,25,30,35,40,45,50/) INTEGER :: N, I, POS LOGICAL :: FOUND = .FALSE. WRITE(*,'(1X, A)',ADVANCE="NO") "Search for :" READ *, N DO I=1,10 IF (A(I) == N) THEN POS = I FOUND = .TRUE. EXIT END IF END DO IF (FOUND) PRINT *, "N = ",N," is in position = ",POS END PROGRAM LinearSearch

  14. SUBROUTINE LinearSearch(Item, ItemSought, Found, Location) CHARACTER(*), DIMENSION(:), INTENT(IN) :: Item CHARACTER(*), INTENT(IN) :: ItemSought LOGICAL, INTENT(OUT) :: Found INTEGER, INTENT(OUT) :: Location INTEGER :: NumItems NumItems = SIZE(Item) Location = 1 Found = .FALSE. DO IF ((Location > NumItems) .OR. Found) RETURN IF (ItemSought == Item(Location)) THEN Found = .TRUE. ELSE Location = Location + 1 END IF END DO END SUBROUTINE LinearSearch

  15. Passing Arrays as Arguments SUBROUTINE task(Item) INTEGER, DIMENSION(:), INTENT(IN) :: Item or SUBROUTINE task (Item, NumElements)INTEGER, INTENT(IN) :: NumElements INTEGER, INTENT(IN), DIMENSION(NumElements) :: Item

  16. Binary Search • Binary search can be used to search for an item more efficiently than linear search. • Example:

  17. SUBROUTINE BinarySearch(Item, ItemSought, Found, Location) CHARACTER(*), DIMENSION(:), INTENT(IN) :: Item CHARACTER(*), INTENT(IN) :: ItemSought LOGICAL, INTENT(OUT) :: Found INTEGER, INTENT(OUT) :: Location INTEGER :: First, Last, Middle First = 1 Last = SIZE(Item) Found = .FALSE. DO IF ((First > Last) .OR. Found) RETURN Middle = (First + Last) / 2 IF (ItemSought < Item(Middle)) THEN Last = Middle - 1 ELSE IF (ItemSought > Item(Middle)) THEN First = Middle + 1 ELSE Found = .TRUE. Location = Middle END IF END DO END SUBROUTINE BinarySearch

  18. Multidimensional Arrays • A multidimensional array has more than one subscript. • There is no limit to the number of dimensions Fortran can have, but there is a limit on the total array size.

  19. Declaring Multidimensional Arrays • General Form: • type, DIMENSION(l1:u1, l2:u2, l3:u3,…ln:un) :: &list-of-array-namesexamples:REAL, DIMENSION(24, 365) :: TemperatureREAL, DIMENSION(1:24, 1:365) :: Temperature

  20. Multidimensional Arrays • INTEGER, DIMENSION (3, 5) :: Data Columns Data 1 2 3 4 5 5 10 15 20 25 1 Rows 30 35 40 45 50 2 55 60 65 70 75 3

  21. Multidimensional Arrays • INTEGER, DIMENSION (3, 5) :: DataData(2, 3) 3 5 10 15 20 25 30 35 40 45 50 2 55 60 65 70 75

  22. Reading MD Arrays • Using Nested DO statements • INTEGER :: data (10, 5)DO I = 1, 10 DO J = 1, 5READ *, data (I, J) END DOEND DO

  23. Reading MD Arrays • Using Implied DO StatementsINTEGER :: data (10, 5)READ *, ((data (I, J), J= 1, 5), I=1, 10)

  24. PROGRAM Table_of_Temperatures REAL, DIMENSION(:, :), ALLOCATABLE :: Temperature INTEGER :: NumTimes, NumLocs, Time, Location READ *, NumTimes, NumLocs ALLOCATE (Temperature(NumTimes, NumLocs)) PRINT *, "Enter the temperatures at the first location," PRINT *, "then those at the second location, and so on:" READ *, ((Temperature(Time, Location), & Location = 1, NumLocs), Time = 1, NumTimes) PRINT * PRINT '(1X, T13, "Location" / 1X, "Time", 10I6)', & (Location, Location = 1, NumLocs) DO Time = 1, NumTimes PRINT '(/1X, I3, 2X, 10F6.1/)', & Time, (Temperature(Time, Location), Location=1,NumLocs) END DO DEALLOCATE (Temperature) END PROGRAM Table_of_Temperatures

  25. Matrix Multiplication • Class Exercise

  26. program maxarrays integer, dimension (5)::a, b, c read *, a read *, b c = arrayMax(a, b) print *, c contains function arrayMax (a, b) integer, intent (in), dimension (:) :: a, b integer, dimension(size(a)) :: arrayMax arrayMax = MAX(a, b) end function arrayMax end program maxarrays Exercise 8.3, Prob. 18.

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