Manual Reference Pages - reduce (3fortran)
REDUCE(3) - [ARRAY:TRANSFORMATIONAL] General reduction of an array
SYNOPSIS
There are two forms to this function:
result = reduce(array, operation [,mask] [,identity] [,ordered] )or
result = reduce (array, operation, dim & & [,mask] [,identity] [,ordered] )type(TYPE(kind=KIND)) function reduce & & (array, operation, dim, mask, identity, ordered )
type(TYPE(kind=KIND)),intent(in) :: array pure function :: operation integer,intent(in),optional :: dim logical,optional :: mask type(TYPE),intent(in),optional :: identity logical,intent(in),optional :: ordered
CHARACTERISTICS
o ARRAY is an array of any type o OPERATION is a pure function with exactly two arguments
o each argument is scalar, non-allocatable, a nonpointer, nonpolymorphic and nonoptional with the same type and kind as array. o if one argument has the asynchronous, target, or value attribute so shall the other. o DIM is an integer scalar o MASK is a logical conformable with ARRAY o IDENTITY is a scalar with the same type and type parameters as ARRAY o ORDERED is a logical scalar o the result is of the same type and type parameters as ARRAY.
DESCRIPTION
REDUCE(3) reduces a list of conditionally selected values from an array to a single value by iteratively applying a binary function.
Common in functional programming, a REDUCE function applies a binary operator (a pure function with two arguments) to all elements cumulatively.
REDUCE is a "higher-order" function; ie. it is a function that receives other functions as arguments.
The REDUCE function receives a binary operator (a function with two arguments, just like the basic arithmetic operators). It is first applied to two unused values in the list to generate an accumulator value which is subsequently used as the first argument to the function as the function is recursively applied to all the remaining selected values in the input array.
OPTIONS
o ARRAY : An array of any type and allowed rank to select values from. o OPERATION : shall be a pure function with exactly two arguments; each argument shall be a scalar, nonallocatable, nonpointer, nonpolymorphic, nonoptional dummy data object with the same type and type parameters as ARRAY. If one argument has the ASYNCHRONOUS, TARGET, or VALUE attribute, the other shall have that attribute. Its result shall be a nonpolymorphic scalar and have the same type and type parameters as ARRAY. OPERATION should implement a mathematically associative operation. It need not be commutative.
NOTE
If OPERATION is not computationally associative, REDUCE without ORDERED=.TRUE. with the same argument values might not always produce the same result, as the processor can apply the associative law to the evaluation.
Many operations that mathematically are associative are not when applied to floating-point numbers. The order you sum values in may affect the result, for example.
| o |
DIM : An integer scalar with a value in the range 1<= DIM <= n,
where n is the rank of ARRAY.
| ||||||
RESULT
The result is of the same type and type parameters as ARRAY. It is scalar if DIM does not appear.
If DIM is present, it indicates the one dimension along which to perform the reduction, and the resultant array has a rank reduced by one relative to the input array.
EXAMPLES
The following examples all use the function MY_MULT, which returns the product of its two real arguments.
program demo_reduce implicit none character(len=*),parameter :: f=’("[",*(g0,",",1x),"]")’ integer,allocatable :: arr(:), b(:,:)Results:! Basic usage: ! the product of the elements of an array arr=[1, 2, 3, 4 ] write(*,*) arr write(*,*) ’product=’, reduce(arr, my_mult) write(*,*) ’sum=’, reduce(arr, my_sum)
! Examples of masking: ! the product of only the positive elements of an array arr=[1, -1, 2, -2, 3, -3 ] write(*,*)’positive value product=’,reduce(arr, my_mult, mask=arr>0) ! sum values ignoring negative values write(*,*)’sum positive values=’,reduce(arr, my_sum, mask=arr>0)
! a single-valued array returns the single value as the ! calls to the operator stop when only one element remains arr=[ 1234 ] write(*,*)’single value sum’,reduce(arr, my_sum ) write(*,*)’single value product’,reduce(arr, my_mult )
! Example of operations along a dimension: ! If B is the array 1 3 5 ! 2 4 6 b=reshape([1,2,3,4,5,6],[2,3]) write(*,f) REDUCE(B, MY_MULT),’should be [720]’ write(*,f) REDUCE(B, MY_MULT, DIM=1),’should be [2,12,30]’ write(*,f) REDUCE(B, MY_MULT, DIM=2),’should be [15, 48]’
contains
pure function my_mult(a,b) result(c) integer,intent(in) :: a, b integer :: c c=a*b end function my_mult
pure function my_sum(a,b) result(c) integer,intent(in) :: a, b integer :: c c=a+b end function my_sum
end program demo_reduce
> 1 2 3 4 > product= 24 > sum= 10 > positive value sum= 6 > sum positive values= 6 > single value sum 1234 > single value product 1234 > [720, should be [720], > [2, 12, 30, should be [2,12,30], > [15, 48, should be [15, 48],
STANDARD
Fortran 2018
SEE ALSO
o co_reduce(3)
RESOURCES
Fortran intrinsic descriptions (license: MIT) @urbanjost
o associative:wikipedia
| Nemo Release 3.1 | reduce (3fortran) | November 02, 2024 |
