ppm_combinatorics Module Reference

gathers some base routines for combinatorial problems More...

Data Types
interface	combination
	produce random selection and its complement More...
interface	is_permutation
	establish whether an array is a permutation of another array or a range More...
interface	permute
	randomly permute a given array More...
interface	prime_factorization
	compute list of prime factors (sorted, but duplicates included) More...
interface	selection
	produce random selection More...

Functions/Subroutines
subroutine	permute_randomly_i4 (a)
	randomly permute a given array
subroutine	permute_randomly_i8 (a)
	randomly permute a given array
pure logical function	is_permutation_of_range_i4 (a, r)
	establish whether one array of integers is a permutation of a range
pure logical function	is_permutation_of_array_i4 (a, b)
	establish whether one array of integers is a permutation of another
subroutine	random_selection_i4 (selected, range)
	produce random selection from range
subroutine	random_combination_i4 (selected, not_selected, range)
	produce random selection and its complement from range
pure subroutine	prime_factorization_i4 (n, factors)
	compute list of prime factors (sorted, but duplicates included)

Variables
character(len= *), parameter	filename = 'ppm_combinatorics.f90'

Detailed Description

gathers some base routines for combinatorial problems

Function/Subroutine Documentation

is_permutation_of_array_i4()

pure logical function ppm_combinatorics::is_permutation_of_array_i4 ( integer(i4), dimension(:), intent(in) a, integer(i4), dimension(:), intent(in) b )

private

establish whether one array of integers is a permutation of another

Parameters

a	first array
b	second array

Returns

.TRUE. if a is permutation of b

is_permutation_of_range_i4()

pure logical function ppm_combinatorics::is_permutation_of_range_i4 ( integer(i4), dimension(:), intent(in) a, type(iinterval), intent(in) r )

private

establish whether one array of integers is a permutation of a range

Parameters

a	array
r	range

Returns

.TRUE. if a is permutation of r, .FALSE. if not

permute_randomly_i4()

subroutine ppm_combinatorics::permute_randomly_i4 ( integer(i4), dimension(:), intent(inout) a )

private

randomly permute a given array

Parameters

a	array to permute

permute_randomly_i8()

subroutine ppm_combinatorics::permute_randomly_i8 ( integer(i8), dimension(:), intent(inout) a )

private

randomly permute a given array

Parameters

a	array to permute

prime_factorization_i4()

pure subroutine ppm_combinatorics::prime_factorization_i4 ( integer(i4), intent(in) n, integer(i4), dimension(:), intent(out), allocatable factors )

private

compute list of prime factors (sorted, but duplicates included)

Parameters

n	integer to factor
factors	integers, where factor(i) is prime and PRODUCT(factors)==n, factors is allocated to the necessary size

random_combination_i4()

subroutine ppm_combinatorics::random_combination_i4 ( integer(i4), dimension(:), intent(out) selected, integer(i4), dimension(:), intent(out) not_selected, type(iinterval), intent(in) range )

private

produce random selection and its complement from range

Parameters

	range	range to select from
[out]	selected	array where a random selection of integers from range are written to
[out]	not_selected	integers from range not written to selected are stored here

random_selection_i4()

subroutine ppm_combinatorics::random_selection_i4 ( integer(i4), dimension(:), intent(out) selected, type(iinterval), intent(in) range )

private

produce random selection from range

normally this procedure is only efficient when SIZE(selected) is significantly smaller than extent_size(range), when SIZE(selected) approaches extent_size(range) it's cheaper to produce a permutation and use the first SIZE(selected) elements

Parameters

[out]	selected	array to fill with random selection from range, where SIZE(selected) <= extent_size(range)
	range	set of integers to selected from