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mo_combinatorics.f90
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mo_combinatorics.f90
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!> \file mo_combinatorics.f90
!> \brief Package for combinatorial calculations.
!> \details This package provides routines and functions for combinatorial calculations.
!> \authors Matthias Cuntz, Giovanni Dalmasso, Juliane Mai, Stephan Thober, Sebastian Mueller
!> \date Feb 2013
MODULE mo_combinatorics
! Written Matthias Cuntz, Giovanni Dalmasso, Juliane Mai, Stephan Thober Feb 2013
! Modified Matthias Cuntz, May 2014 - removed numerical recipes, use mo_functions
! License
! -------
! This file is part of the JAMS Fortran package, distributed under the MIT License.
!
! Copyright (c) 2011-2014 Matthias Cuntz, Giovanni Dalmasso, Juliane Mai, Stephan Thober, Sebastian Mueller
! mc (at) macu (dot) de
!
! Permission is hereby granted, free of charge, to any person obtaining a copy
! of this software and associated documentation files (the "Software"), to deal
! in the Software without restriction, including without limitation the rights
! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
! copies of the Software, and to permit persons to whom the Software is
! furnished to do so, subject to the following conditions:
!
! The above copyright notice and this permission notice shall be included in all
! copies or substantial portions of the Software.
!
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
! SOFTWARE.
USE mo_kind, ONLY: i4, i8, sp, dp
USE mo_functions, only: factln, factorial
IMPLICIT NONE
PUBLIC :: binomcoeffi ! Binomial coefficient (n choose k)
PUBLIC :: random_kofn ! Random selection of k of n
PUBLIC :: next_kofn ! Next selection of k of n to a given one
PUBLIC :: all_kofn ! All selections of k of n
PUBLIC :: random_permut ! Random permutation of a vector
PUBLIC :: random_index_permut ! Random permutation of (1..n)
PUBLIC :: next_index_permut ! Next permutation of (1..n) to a given one
PUBLIC :: all_index_permut ! All permutations of (1..n)
PUBLIC :: nextpart ! Next partition of n to a given one
PUBLIC :: prevpart ! Previous partition of n to a given one
PUBLIC :: isgoodpart ! checks if a given array is a partition of n
! ------------------------------------------------------------------
! NAME
! binomcoeffi
! PURPOSE
!
!> \brief The binomial coefficient.
!
!> \details Calculates the binomial coefficient (n choose k):
!> \f[ C(n,k) = \frac{n!}{k! (n-k)!} \f],
!> i.e. the number of possibilities to select from n numbers k
!> for real input it also calculates the generalized binomial coefficient which is used for the binomial series
!> \f[ C(x,k) = \prod_{i=1}^k \frac{x+1-i}{i} \f],
! INTENT(IN)
!> \param[in] "integer(i4/i8)/real(sp,dp) :: n/n(:)/x/x(:)" from n numbers ...
!> \param[in] "integer(i4/i8) :: k/k(:)" ... k will be selected
!
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
! None
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
!> \return integer(i4/i8)/real(sp,dp) :: binomcoeffi/binomcoeffi(:) — Binomial coefficient (n choose k)
!
! RESTRICTIONS
! None
!
! EXAMPLE
! bico = binomcoeffi(5,2)
! bico --> 10
! bico = binomcoeffi(1.5,2)
! bico --> 0.375
! -> see also example in test directory
! LITERATURE
!
! HISTORY
!> \author Matthias Cuntz, Juliane Mai
!> \date Feb 2013
! Modified, Sebastian Mueller June 2014
INTERFACE binomcoeffi
MODULE PROCEDURE binomcoeffi_i4_d0, binomcoeffi_i8_d0, binomcoeffi_i4_d1, binomcoeffi_i8_d1,&
binomcoeffi_sp_d0, binomcoeffi_dp_d0, binomcoeffi_sp_d1, binomcoeffi_dp_d1,&
binomcoeffi_dpi4_d0, binomcoeffi_dpi4_d1
END INTERFACE binomcoeffi
! ------------------------------------------------------------------
! NAME
! all_kofn
! PURPOSE
!
!> \brief All possible selections of k numbers from n.
!
!> \details Returns all possible selections of a k-subset from n numbers.
!
! INTENT(IN)
!> \param[in] "integer(i4/i8) :: n" select from n numbers ...
!> \param[in] "integer(i4/i8) :: k" ... k numbers
!
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
! None
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
!> \return integer(i4/i8), allocatable, dimension(:,:) :: alle — All selections. Dim_2=k.
!
! RESTRICTIONS
! None
!
! EXAMPLE
! alle = all_kofn(3, 2)
! alle --> (/ (/ 1,2 /), (/ 1,3 /), (/ 2,3 /) /)
! -> see also example in test directory
! LITERATURE
! Nijenhuis, A., & Wilf, H. S. (1978).
! Combinatorial algorithms for computers and calculators (2nd ed.).
! Academic Pr.
! HISTORY
!> \author Juliane Mai
!> \date Feb 2013
! Modified,
INTERFACE all_kofn
MODULE PROCEDURE all_kofn_i4, all_kofn_i8
END INTERFACE all_kofn
! ------------------------------------------------------------------
! NAME
! next_kofn
! PURPOSE
!
!> \brief The next selection of k numbers from n to a given one.
!
!> \details Determines the next selection of k numbers from k to a given one.\n
!> If one has n=5 numbers and want to pick k=3, the first possible selection is (1,2,3).
!> The next selection will be (1,2,4). The subsequent selection to (1,3,4) will be (1,3,5).\n
!> The given subset (previous) has to be sorted.
!
! INTENT(IN)
!> \param[in] "integer(i4/i8) :: n" select from n numbers ...
!> \param[in] "integer(i4/i8) :: k" ... k numbers
!> \param[in] "integer(i4/i8) :: previous(:)" previous selection (dim_1 = k)
!
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
! None
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
!> \return integer(i4/i8) :: next(size(previous)) — Next selection of k from n numbers
!
! RESTRICTIONS
!> \note The given subset (previous) has to be sorted.
!
! EXAMPLE
! next = next_kofn(5, 3, (/1,3,4/))
! next --> (/ 1,3,5 /)
! -> see also example in test directory
! LITERATURE
! Nijenhuis, A., & Wilf, H. S. (1978).
! Combinatorial algorithms for computers and calculators (2nd ed.).
! Academic Pr.
! HISTORY
!> \author Giovanni Dalmasso, Juliane Mai
!> \date Feb 2013
! Modified,
INTERFACE next_kofn
MODULE PROCEDURE next_kofn_i4, next_kofn_i8
END INTERFACE next_kofn
! ------------------------------------------------------------------
! NAME
! random_kofn
! PURPOSE
!
!> \brief A random selection of a k-subset of n numbers (1..n).
!
!> \details Returns a random k-subset of n numbers (1..n).\n
!> The returned subset will be sorted.\n
!> The code is adapted from Nijenhuis (1978) - routine RANKSB.
!
! INTENT(IN)
!> \param[in] "integer(i4/i8) :: n" select from n numbers ...
!> \param[in] "integer(i4/i8) :: k" ... k numbers
!
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
!> \param[in,out] "integer(i4/i8), optional :: save_state(n_save_state)" an array for saving the state
!> of an uniform random number stream
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
!> \return integer(i4/i8) :: set(k) — Random selection of k from n numbers
!
! RESTRICTIONS
!> \note A random number stream for generating uniform random numbers has to be initialized before running this function.
!
! EXAMPLE
! set = random_kofn(5, 3)
! set --> (/ 2,3,5 /)
! -> see also example in test directory
! LITERATURE
! Nijenhuis, A., & Wilf, H. S. (1978).
! Combinatorial algorithms for computers and calculators (2nd ed.).
! Academic Pr.
! HISTORY
!> \author Juliane Mai
!> \date Feb 2013
! Modified,
INTERFACE random_kofn
MODULE PROCEDURE random_kofn_i4 , random_kofn_i8
END INTERFACE random_kofn
! ------------------------------------------------------------------
! NAME
! all_index_permut
! PURPOSE
!
!> \brief All possible permutations of n integers 1..n.
!
!> \details Determines all possible permutations of n integers 1..n. \n
!> The number of possibilities is the factorial of n (n!).
!> The code is adapted from Nijenhuis (1978) - routine NEXPER.
!
! INTENT(IN)
!> \param[in] "integer(i4/i8) :: n" permutation of n integers 1..n
!
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
! None
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
!> \return integer(i4/i8), allocatable :: permut(:,:) — All permutations of n integers \n
!> size(permut,1) = n! \n
!> size(permut,2) = n
!
! RESTRICTIONS
! None
!
! EXAMPLE
! permut = all_index_permut(3)
! permut --> (/ (/ 1,2,3 /), (/2,1,3/), (/3,1,2/), (/ 1,3,2 /), (/2,3,1/), (/3,2,1/) /)
! -> see also example in test directory
! LITERATURE
! Nijenhuis, A., & Wilf, H. S. (1978).
! Combinatorial algorithms for computers and calculators (2nd ed.).
! Academic Pr.
! HISTORY
!> \author Juliane Mai
!> \date Feb 2013
! Modified,
INTERFACE all_index_permut
MODULE PROCEDURE all_index_permut_i4, all_index_permut_i8
END INTERFACE all_index_permut
! ------------------------------------------------------------------
! NAME
! next_index_permut
! PURPOSE
!
!> \brief The next permutation of n integers 1..n to a given one.
!
!> \details Determines the next permutation of n integers 1..n to a given one.\n
!> If one has n=5 numbers, the first possible permutation is (1,2,3,4,5).
!> The next selection will be (2,1,3,4,5). \n
!> The code is adapted from Nijenhuis (1978) - routine NEXPER.
!
! INTENT(IN)
!> \param[in] "integer(i4/i8) :: n" permutation of n integers 1..n
!> \param[in] "integer(i4/i8) :: previous(:)" previous permutation (dim_1 = n)
!
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
! None
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
!> \return integer(i4/i8) :: next(n) — Next permutation of n integers
!
! RESTRICTIONS
! None
!
! EXAMPLE
! next = next_index_permut(5, (/1,2,3,4,5/))
! next --> (/ 2,1,3,4,5 /)
! -> see also example in test directory
! LITERATURE
! Nijenhuis, A., & Wilf, H. S. (1978).
! Combinatorial algorithms for computers and calculators (2nd ed.).
! Academic Pr.
! HISTORY
!> \author Juliane Mai
!> \date Feb 2013
! Modified,
INTERFACE next_index_permut
MODULE PROCEDURE next_index_permut_i4, next_index_permut_i8
END INTERFACE next_index_permut
! ------------------------------------------------------------------
! NAME
! random_index_permut
! PURPOSE
!
!> \brief A random permutation of the integers 1..n.
!
!> \details Returns a random permutation of n numbers (1..n)\n
!> The code adapted from the Fortran library of A. Miller.
!
! INTENT(IN)
!> \param[in] "integer(i4/i8) :: n" permutation of integers 1..n
!
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
!> \param[in,out] "integer(i4/i8), optional :: save_state(n_save_state)" an array for saving the state
!> of an uniform random number stream
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
!> \return integer(i4/i8) :: set(n) — Random permutation of n integers 1..n
!
! RESTRICTIONS
!> \note A random number stream for generating uniform random numbers has to be
!> initialized before running this function.
!
! EXAMPLE
! set = random_index_permut(5, 3)
! set --> (/ 2,1,3,5,4 /)
! -> see also example in test directory
! LITERATURE
! A. Miller, CSIRO Mathematical & Information Sciences,
! Clayton 3169, Victoria, Australia, Version 1.13, 2 October 2000.
! http://jblevins.org/mirror/amiller/
! HISTORY
!> \author Matthias Cuntz
!> \date Feb 2013
! Modified,
INTERFACE random_index_permut
MODULE PROCEDURE random_index_permut_i4, random_index_permut_i8
END INTERFACE random_index_permut
! ------------------------------------------------------------------
! NAME
! random_permut
! PURPOSE
! Calculates a random permutation of n numbers
!
!> \brief Random permutation.
!
!> \details Randomly permutes the elements of a given vector.
!
! INTENT(IN)
! None
!
! INTENT(INOUT)
!> \param[inout] "integer(i4/i8)/real(sp/dp) :: vec(:)" 1D-array to be shuffled
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
!> \param[in,out] "integer(i4/i8), optional :: save_state(n_save_state)" an array for saving the state
!> of a uniform random number stream
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
! None
!
! RESTRICTIONS
!> \note A random number stream for generating uniform random numbers has to be
!> initialized before running this function.
!
! EXAMPLE
! a = (/5,3,2/)
! call random_permut(a)
! a --> (/ 2,5,3 /)
! -> see also example in test directory
! LITERATURE
! Nijenhuis, A., & Wilf, H. S. (1978).\n
! Combinatorial algorithms for computers and calculators (2nd ed.). Academic Pr., p. 63
! Algorithm RANPER
! HISTORY
!> \author Stephan Thober, Juliane Mai, Matthias Cuntz
!> \date Feb 2013
INTERFACE random_permut
MODULE PROCEDURE random_permut_i4, random_permut_i8, random_permut_sp, random_permut_dp
END INTERFACE random_permut
! ------------------------------------------------------------------
! NAME
! nextpart
! PURPOSE
! Calculates the next partition of n to a given one
!
!> \brief next partition of n to a given one
!
!> \details next greater partition of n to a given one where the partitions are sorted by inverse lexicographical ordering
!> for example: (2,0) > (0,1)
!
! INTENT(IN)
!> \param[in] "integer(i4/i8), dimension(:), intent(in) :: part" a given partition not equal to (n,0,..,0) [not last]
!
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
! None
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
!> \return "integer(i4/i8), dimension(:) :: nextpart" next partition of n
!
! RESTRICTIONS
!> \note the given partiton should not be the greatest one i.e. not (n,0,..,0)
!
! EXAMPLE
! nextpart((0,2,0,0)) = (2,1,0,0)
! LITERATURE
! none
! HISTORY
!> \author Sebastian Mueller
!> \date June 2014
INTERFACE nextpart
MODULE PROCEDURE nextpart_i4, nextpart_i8
END INTERFACE nextpart
! ------------------------------------------------------------------
! NAME
! prevpart
! PURPOSE
! Calculates the previous partition of n to a given one
!
!> \brief previous partition of n to a given one
!
!> \details next smaller partition of n to a given one where the partitions are sorted by inverse lexicographical ordering
!> for example: (2,0) > (0,1)
!
! INTENT(IN)
!> \param[in] "integer(i4/i8), dimension(:), intent(in) :: part" a given partition not equal to (0,..,0,1) [not first]
!
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
! None
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
!> \return "integer(i4/i8), dimension(:) :: prevpart" previous partition of n
!
! RESTRICTIONS
!> \note the given partiton should not be the smallest one i.e. not (0,..,0,1)
!
! EXAMPLE
! prevpart((2,1,0,0)) = (0,2,0,0)
! LITERATURE
! none
! HISTORY
!> \author Sebastian Mueller
!> \date July 2014
INTERFACE prevpart
MODULE PROCEDURE prevpart_i4, prevpart_i8
END INTERFACE prevpart
! ------------------------------------------------------------------
! NAME
! isgoodpart
! PURPOSE
! Checks if a given array is a partition of n
!
!> \brief Checks if a given array is a partition of n
!
!> \details Checks if a given array is a partition of n, where p=(p_1,..,p_n) is a partition of n iff
!> \f[ \sum_{i=1}^n p_i*i = p_1 + 2*p_2 + 3*p_3 + .. =n \f]
!
! INTENT(IN)
!> \param[in] "integer(i4/i8), dimension(:), intent(in) :: part" a given partition not equal to (n,0,..,0)
!
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
! None
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
!> \return "logical :: isgoodpart"
!
! RESTRICTIONS
!> \note the given array should be of dimension greater than one
!
! EXAMPLE
! isgoodpart((2,1,0)) = true
! isgoodpart((0,2)) = false
! LITERATURE
! none
! HISTORY
!> \author Sebastian Mueller
!> \date June 2014
INTERFACE isgoodpart
MODULE PROCEDURE isgoodpart_i4, isgoodpart_i8
END INTERFACE isgoodpart
! ------------------------------------------------------------------
PRIVATE
! ------------------------------------------------------------------
CONTAINS
FUNCTION binomcoeffi_i4_d0(n,k)
! Returns the binomial coefficient as an integer number.
IMPLICIT NONE
INTEGER(i4), INTENT(IN) :: n, k
INTEGER(i4) :: binomcoeffi_i4_d0
binomcoeffi_i4_d0 = nint(exp(factln(n)-factln(k)-factln(n-k)))
END FUNCTION binomcoeffi_i4_d0
FUNCTION binomcoeffi_i8_d0(n,k)
! Returns the binomial coefficient as an integer number.
IMPLICIT NONE
INTEGER(i8), INTENT(IN) :: n, k
INTEGER(i8) :: binomcoeffi_i8_d0
binomcoeffi_i8_d0 = nint(exp(factln(n)-factln(k)-factln(n-k)))
END FUNCTION binomcoeffi_i8_d0
FUNCTION binomcoeffi_i4_d1(n,k)
IMPLICIT NONE
INTEGER(i4), DIMENSION(:), INTENT(IN) :: n, k
INTEGER(i4), DIMENSION(size(n)) :: binomcoeffi_i4_d1
if (size(n) /= size(k)) stop 'Error binomcoeffi: size(n) /= size(k)'
binomcoeffi_i4_d1 = nint(exp(factln(n)-factln(k)-factln(n-k)))
END FUNCTION binomcoeffi_i4_d1
FUNCTION binomcoeffi_i8_d1(n,k)
IMPLICIT NONE
INTEGER(i8), DIMENSION(:), INTENT(IN) :: n, k
INTEGER(i8), DIMENSION(size(n)) :: binomcoeffi_i8_d1
if (size(n) /= size(k)) stop 'Error binomcoeffi: size(n) /= size(k)'
binomcoeffi_i8_d1 = nint(exp(factln(n)-factln(k)-factln(n-k)))
END FUNCTION binomcoeffi_i8_d1
!generalized binomial coefficient
FUNCTION binomcoeffi_sp_d0(x,k)
! Returns the generalized binomial coefficient as a real number.
IMPLICIT NONE
real(sp), INTENT(IN) :: x
INTEGER(i4), INTENT(IN) :: k
real(sp) :: binomcoeffi_sp_d0
integer(i4) :: i
if (k>0_i4) then
binomcoeffi_sp_d0 = 1.0_sp
do i=1_i4,k
binomcoeffi_sp_d0 = binomcoeffi_sp_d0*(x+1.0_sp-real(i,sp))/real(i,sp)
end do
else if (k<0_i4) then
binomcoeffi_sp_d0 = 0.0_sp
else
binomcoeffi_sp_d0 = 1.0_sp
endif
END FUNCTION binomcoeffi_sp_d0
FUNCTION binomcoeffi_dp_d0(x,k)
! Returns the generalized binomial coefficient as a real number.
IMPLICIT NONE
real(dp), INTENT(IN) :: x
INTEGER(i8), INTENT(IN) :: k
real(dp) :: binomcoeffi_dp_d0
integer(i8) :: i
if (k>0_i8) then
binomcoeffi_dp_d0 = 1.0_sp
do i=1_i8,k
binomcoeffi_dp_d0 = binomcoeffi_dp_d0*(x+1.0_dp-real(i,dp))/real(i,dp)
end do
else if (k<0_i8) then
binomcoeffi_dp_d0 = 0.0_dp
else
binomcoeffi_dp_d0 = 1.0_dp
endif
END FUNCTION binomcoeffi_dp_d0
FUNCTION binomcoeffi_sp_d1(x,k)
IMPLICIT NONE
real(sp), DIMENSION(:), INTENT(IN) :: x
INTEGER(i4), DIMENSION(:), INTENT(IN) :: k
real(sp), DIMENSION(size(x)) :: binomcoeffi_sp_d1
integer(i4) :: i
if (size(x) /= size(k)) stop 'Error binomcoeffi: size(n) /= size(k)'
do i=1_i4, size(x)
binomcoeffi_sp_d1(i) = binomcoeffi_sp_d0(x(i),k(i))
end do
END FUNCTION binomcoeffi_sp_d1
FUNCTION binomcoeffi_dp_d1(x,k)
IMPLICIT NONE
real(dp), DIMENSION(:), INTENT(IN) :: x
INTEGER(i8), DIMENSION(:), INTENT(IN) :: k
real(dp), DIMENSION(size(x)) :: binomcoeffi_dp_d1
integer(i8) :: i
if (size(x) /= size(k)) stop 'Error binomcoeffi: size(n) /= size(k)'
do i=1_i8, size(x)
binomcoeffi_dp_d1(i) = binomcoeffi_dp_d0(x(i),k(i))
end do
END FUNCTION binomcoeffi_dp_d1
FUNCTION binomcoeffi_dpi4_d0(x,k)
! Returns the generalized binomial coefficient as a real number.
IMPLICIT NONE
real(dp), INTENT(IN) :: x
INTEGER(i4), INTENT(IN) :: k
real(dp) :: binomcoeffi_dpi4_d0
integer(i4) :: i
if (k>0_i4) then
binomcoeffi_dpi4_d0 = 1.0_sp
do i=1_i4,k
binomcoeffi_dpi4_d0 = binomcoeffi_dpi4_d0*(x+1.0_dp-real(i,dp))/real(i,dp)
end do
else if (k<0_i4) then
binomcoeffi_dpi4_d0 = 0.0_dp
else
binomcoeffi_dpi4_d0 = 1.0_dp
endif
END FUNCTION binomcoeffi_dpi4_d0
FUNCTION binomcoeffi_dpi4_d1(x,k)
IMPLICIT NONE
real(dp), DIMENSION(:), INTENT(IN) :: x
INTEGER(i4), DIMENSION(:), INTENT(IN) :: k
real(dp), DIMENSION(size(x)) :: binomcoeffi_dpi4_d1
integer(i4) :: i
if (size(x) /= size(k)) stop 'Error binomcoeffi: size(n) /= size(k)'
do i=1_i4, size(x)
binomcoeffi_dpi4_d1(i) = binomcoeffi_dpi4_d0(x(i),k(i))
end do
END FUNCTION binomcoeffi_dpi4_d1
! ------------------------------------------------------------------
FUNCTION all_kofn_i4(n, k) result(alle)
IMPLICIT NONE
INTEGER(I4), INTENT(IN) :: n ! from n numbers will be selected
INTEGER(I4), INTENT(IN) :: k ! k numbers will be selected
INTEGER(I4), DIMENSION(:,:), allocatable :: alle ! all subsets
! local variables
integer(i4) :: bico
integer(i4) :: i
bico = binomcoeffi(n,k)
allocate(alle(bico,k))
forall(i=1:k) alle(1,i) = i
do i=2,bico
alle(i,:) = next_kofn(n, k, alle(i-1,:))
end do
END FUNCTION all_kofn_i4
FUNCTION all_kofn_i8(n, k) result(alle)
IMPLICIT NONE
INTEGER(I8), INTENT(IN) :: k ! k numbers will be selected
INTEGER(I8), INTENT(IN) :: n ! from n numbers will be selected
INTEGER(I8), DIMENSION(:,:), allocatable :: alle ! all subsets
! local variables
integer(i8) :: bico
integer(i8) :: i
bico = binomcoeffi(n,k)
allocate(alle(bico,k))
forall(i=1:k) alle(1,i) = i
do i=2,bico
alle(i,:) = next_kofn(n, k, alle(i-1,:))
end do
END FUNCTION all_kofn_i8
! ------------------------------------------------------------------
FUNCTION next_kofn_i4(n, k, previous) result(next)
IMPLICIT NONE
INTEGER(I4), INTENT(IN) :: k ! k numbers will be selected
INTEGER(I4), INTENT(IN) :: n ! from n numbers will be selected
INTEGER(I4), DIMENSION(k), INTENT(IN) :: previous ! previous subset
INTEGER(I4), DIMENSION(k) :: next ! next subset
! local variables
integer(i4) :: indx
logical :: found
integer(i4) :: i
! find index from the back to start changing the values
indx = k
found = .false.
do while ( (.not. found) .and. (indx .gt. 1) )
if ( previous(indx) .eq. n-k+indx ) then
indx = indx-1
else
found = .true.
end if
end do
if( (indx .gt. 1) .or. ( previous(1) .ne. (n-k+1)) ) then
! it is a subset in between
next = previous
next(indx) = previous(indx) + 1
forall(i=indx+1:k) next(i) = next(indx) + i-indx
else
! there do not exist a next subset and first one (/1, ..., k/) is returned
forall(i=1:k) next(i) = i
end if
END FUNCTION next_kofn_i4
FUNCTION next_kofn_i8(n, k, previous) result(next)
IMPLICIT NONE
INTEGER(I8), INTENT(IN) :: k ! k numbers will be selected
INTEGER(I8), INTENT(IN) :: n ! from n numbers will be selected
INTEGER(I8), DIMENSION(k), INTENT(IN) :: previous ! previous subset
INTEGER(I8), DIMENSION(k) :: next ! next subset
! local variables
integer(i8) :: indx
logical :: found
integer(i8) :: i
! find index from the back to start changing the values
indx = k
found = .false.
do while ( (.not. found) .and. (indx .gt. 1) )
if ( previous(indx) .eq. n-k+indx ) then
indx = indx-1
else
found = .true.
end if
end do
if( (indx .gt. 1) .or. ( previous(1) .ne. (n-k+1)) ) then
! it is a subset in between
next = previous
next(indx) = previous(indx) + 1
forall(i=indx+1:k) next(i) = next(indx) + i-indx
else
! there do not exist a next subset and first one (/1, ..., k/) is returned
forall(i=1:k) next(i) = i
end if
END FUNCTION next_kofn_i8
! ------------------------------------------------------------------
FUNCTION random_kofn_i4(n, k, save_state) result(set)
use mo_xor4096, only: xor4096, n_save_state
implicit none
INTEGER(I4), INTENT(IN) :: k ! k numbers will be selected
INTEGER(I4), INTENT(IN) :: n ! from n numbers will be selected
INTEGER(I4), DIMENSION(n_save_state), OPTIONAL, INTENT(INOUT) :: save_state ! for saving state of a uniform, sp
! ! random number stream
INTEGER(I4), DIMENSION(k) :: set ! random subset
! local variables
logical :: gout
integer(i4) :: x, r, ds, p, s, c, i, l, m,m0, iseed
real(sp) :: rn
iseed = 0_i4
! (A)