Numerics

Elemental Functions

Apply Per Element

An elemental function works on a scalar but can be applied element-wise to a whole array.

Program

Play the program to double every element of an array.

elemental.f90
Replay: real traced execution (multi-file project)
program elemental_demo
    implicit none
    integer :: nums(4), doubled(4)
    nums = [1, 2, 3, 4]
    doubled = times_two(nums)
    print '(I0)', sum(doubled)
contains
    elemental function times_two(x) result(y)
        integer, intent(in) :: x
        integer :: y
        y = x * 2
    end function times_two
end program elemental_demo

  1. nums ← [1, 2, 3, 4]

    3integer :: nums(4), doubled(4)4nums = [1, 2, 3, 4]5doubled = times_two(nums)
    values this step[1, 2, 3, 4]nums

  2. doubled ← [2, 4, 6, 8]

    4nums = [1, 2, 3, 4]5doubled = times_two(nums)6print '(I0)', sum(doubled)
    values this step[2, 4, 6, 8]doubled[1, 2, 3, 4]nums

  3. print '(I0)', sum(doubled)

    5    doubled = times_two(nums)6    print '(I0)', sum(doubled)7contains
    output20
    values this step[2, 4, 6, 8]doubled

Follow the Elements

  1. nums starts as [1, 2, 3, 4].
  2. times_two(nums) applies the scalar function to each element.
  3. doubled becomes [2, 4, 6, 8].
  4. sum(doubled) adds those four values.
  5. The output is 20. | input element | doubled element | | --- | --- | | 1 | 2 | | 2 | 4 | | 3 | 6 | | 4 | 8 | | sum | 20 |
elemental `elemental function` applies to each element of an array argument.
scalar definition The body is written for a scalar, but works on arrays too.
intent(in) Elemental arguments are read-only.

Exercise: elemental.f90

Reproduce the output 20, then trace how [1, 2, 3, 4] becomes [2, 4, 6, 8] before summing.