Array Reduction Intrinsics

 

Reduction functions are aptly named because an array is operated upon and a result obtained which has a smaller rank than the original source array. For a rank n array, if DIM is absent or n = 1 then the result is scalar, otherwise the result is of rank n-1.

• SUM(SOURCE[,DIM][,MASK])
  • SUM returns the sum of array elements, along an optionally specified dimension under an optionally specified mask.
  • if DIM is absent the whole array is considered and the result is a scalar.

     
    Figure 17: SUM of a 1D Array
    

    If DIM is not specified for the SUM of a 2D array then the result is obtained by adding all the elements together

     
    Figure 18: SUM of a 2D Array
    

  • if DIM is specified the result is an array of rank n-1 of sums, for example, summing down the columns

     
    Figure 19: Summing along Dimension 1 of a 2D Array
    

    or along the rows,

     
    Figure 20: Summing along Dimension 2 of a 2D Array
    

  • if MASK is present then the sum only involves elements of SOURCE which correspond to .TRUE. elements of MASK, for example, only the highlighted elements are considered,

     
    Figure 21: SUM Under the Control of a Mask
    

  • if the array is zero sized then the sum is 0

• PRODUCT(SOURCE[,DIM][,MASK])
  • PRODUCT returns the product of all array elements, along an optionally specified dimension under an optionally specified mask,
  • if DIM is absent the whole array is considered and the result is a scalar.
  • if DIM is specified the result is an array of rank n-1 of products, for example, if

    

       PRINT*, PRODUCT(A,DIM=1)
       PRINT*, PRODUCT(A,DIM=2)

    gives

       2 12 30
      15 48

  • if MASK is present then the product only involves elements of SOURCE which correspond to .TRUE. elements of MASK, for example,

       PRINT*, PRODUCT(A,MASK=A.LT.4)

    gives

       6

  • if the array is zero sized then the product is 1.

• ALL(MASK[,DIM])
  • ALL returns .TRUE. if all values of the mask are .TRUE. (along an optionally specified) dimension DIM. If DIM is specified then the result is an array of rank n-1, otherwise a scalar is returned.

    For example, consider a 2D array, if DIM=2 then the function returns a 1D vector with the result being as if the ALL function has been applied to each column in turn. If DIM=1 the result is as if the ALL function had been applied to each row in turn.

    If A is as before, and

    

    then the following

       PRINT*, ALL(A.NE.B,DIM=1)

    gives

        T F F

    recall that dimension 1 runs up and down the page.

    Similarly

       PRINT*, ALL(A.NE.B,DIM=2)

    gives,

        F F

    where dimension 2 run across the page.

  • if DIM is absent then the whole array is considered, for example,

       PRINT*, ALL(A.NE.B)

    gives the scalar value,

        F

  • if the array is zero sized then ALL returns .TRUE.,

• ANY(MASK[,DIM])
  • ANY returns .TRUE. if any values of the mask are .TRUE. (along an optionally specified dimension DIM). If DIM is given then the result is an array of rank n-1, for example,

       PRINT*, ANY(A.NE.B,DIM=1)
       PRINT*, ANY(A.NE.B,DIM=2)

    gives

      T F T
      T T

  • if DIM is absent then the whole array is considered, for example,

       PRINT*, ANY(A.NE.B)

    gives the scalar value,

        T

  • if the array is zero sized then ANY returns .FALSE..
• COUNT(MASK[,DIM])
  • COUNT returns the number of .TRUE. elements in a specified LOGICAL array along dimension DIM. The result is an array of rank n-1, for example,

       PRINT*, COUNT(A.NE.B,DIM=1)
       PRINT*, COUNT(A.NE.B,DIM=2)

    gives

        2 0 1
        1 2

  • if DIM is absent then the whole array is considered, for example,

       PRINT*, COUNT(A.NE.B)

    gives the scalar,

        3

  • if the array is zero sized then COUNT returns zero.
• MAXVAL(SOURCE[,DIM][,MASK])
  • MAXVAL returns the maximum values in an array along an optionally specified dimension under an optionally specified mask,
  • if DIM is specified the result is an array of rank n-1 of maximum values in other dimensions, for example,

     
       PRINT*, MAXVAL(A,DIM=1)
       PRINT*, MAXVAL(A,DIM=2)

    gives

        2 4 6
        5 6

  • if DIM is absent the whole array is considered and the result is a scalar.
  • if MASK is present then the survey is only performed on elements of SOURCE which correspond to .TRUE. elements of MASK, for example,

       PRINT*, MAXVAL(A,MASK=A.LT.4)

    only considers elements of A that are less than 4 and gives

       3

  • the largest negative number of the appropriate kind is returned if the array is zero sized.

• MINVAL(SOURCE[,DIM][,MASK])
  • MINVAL returns the minimum value in an array along an optionally specified dimension under an optionally specified mask,
  • if DIM is specified the result is an array of rank n-1 of minimum values in other dimensions, for example,

       PRINT*, MINVAL(A,DIM=1)
       PRINT*, MINVAL(A,DIM=2)

    gives

        1 3 5
        1 2

  • if DIM is absent the whole array is considered and the result is a scalar.
  • if MASK is present then the survey is only performed on elements of SOURCE which correspond to .TRUE. elements of MASK, for example,

       PRINT*, MINVAL(A,MASK=A.GT.4)

    gives

       5

  • the smallest positive number of the appropriate kind is returned if the array is zero sized.

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