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mo_ode_generator.f90
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mo_ode_generator.f90
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!> \file mo_ode_generator.f90
!> \brief Generating and solving systems of ODE.
!> \details Given N reactants generates & solves all the corresponding ODE system.
!> \authors Giovanni Dalmasso
!> \date Jul 2013
module mo_ode_generator
! This module generates & solves all the corresponding ODE system of N given reactants.
! Written Giovanni Dalmasso, Jul 2013
! License
! -------
! This file is part of the JAMS Fortran package, distributed under the MIT License.
!
! Copyright (c) 2013 Giovanni Dalmasso
!
! 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 : dp
implicit none
public :: ode_generator ! Generating and solving systems of linear ODEs.
! ------------------------------------------------------------------
! NAME
! ode_generator
! PURPOSE
!> \brief Generating and solving systems of ODEs.
!
!> \details Given N reactants generates & solves all the corresponding ODE system.
!
! INTENT(IN)
!> \param[in] "integer(i4) :: n_reac" number of reactants involved in the network
!> \param[in] "real(dp), :: dt" initial size time step
!> \param[in] "real(dp), :: t_start" initial time
!> \param[in] "real(dp), :: t_end" final time
!> \param[in] "real(dp), :: x_initial(:)" initial condition for each reactant
!> \param[in] "real(dp), :: para(:,:)" array of parameters: \n
!> par(j,k) is the reaction rate to convert
!> reactant j into reactant k (not all may be used)\n
!> par(j,j) = feedback loop\n
!> if reaction is not existing par(j,k) = 0.0\n
!> reaction rate has to be positive
!
! INTENT(INOUT)
! None
!
! INTENT(OUT)
!> \param[out] "real(dp), :: ode_results(:,:,:)" ode_results(i,j,k) concentration of reactant (k-1)
!> at the jth time point in network permutation i\n
!> jth time point is ode_results(i,j,1)\n
!> dim_1 = number of permutations\n
!> dim_2 = number of time points\n
!> dim_3 = number of reactants + 1 \n
!> (dim_3=1 : time points)\n
!> (dim_3=i : reactant i-1)\n
!
! INTENT(IN), OPTIONAL
!> \param[in] "integer(i8), optional :: jPerm" choosing one single permutation\n
!> ode_results(1,:,:) is returned\n
!> DEFAULT: all
!> \param[in] "logical, optional :: printflag" flag for printing results on screen\n
!> DEFAULT: false
!
! INTENT(INOUT), OPTIONAL
! None
!
! INTENT(OUT), OPTIONAL
! None
!
! RESTRICTIONS
!> \note No sink/ source terms. This means a reactant can not be produced or degraded.\n
!> No prior information can be passed. This means no reaction can be fixed or discarded
!> in each of the generated networks from the beginning.
!> Meaning that each generated network has to contain a specific reation or not.\n
!> Number of reactants less or equal then 7. This is due to the fact that the number of
!> permutations will be too large to be stored in integer i8.
!
! EXAMPLE
! -> see example in test directory
!
! LITERATURE
!
! HISTORY
!> \author Giovanni Dalmasso
!> \date Jul 2013
! Modified Giovanni Dalmasso, Apr 2014 - added printflag
! - added variable to store results
! - renamed variables
! Matthias Cuntz, Jan 2015 - removed nodata_value
! ------------------------------------------------------------------
interface ode_generator
module procedure ode_generator_dp
end interface ode_generator
! Private method
interface get_odes
module procedure get_odes_dp
end interface get_odes
interface set_alpha
module procedure set_alpha_dp
end interface set_alpha
interface set_beta
module procedure set_beta_dp
end interface set_beta
interface get_binary
module procedure get_binary_i4, get_binary_i8
end interface get_binary
interface get_binaryPer
module procedure get_binaryPer_dp
end interface get_binaryPer
private
!! module variables
real(dp), dimension(:,:), allocatable :: alpha ! on/off variables matrix
real(dp), dimension(:,:), allocatable :: beta ! parameters matrix
contains
subroutine ode_generator_dp( n_reac, dt, t_start, t_end, x_initial, para, & ! IN
ode_results, & ! OUT
jPerm, printflag & ! optional IN
)
use mo_kind, only : i4, i8, dp
use mo_ode_solver, only : RK4as
implicit none
!! Intent IN
integer(i4), intent(in) :: n_reac ! number of reactants involved in the network
real(dp), intent(in) :: dt ! initial size time step
real(dp), intent(in) :: t_start ! initial time
real(dp), intent(in) :: t_end ! final time
real(dp), dimension(:), intent(in) :: x_initial ! initial conditions
real(dp), dimension(:,:), intent(in) :: para ! array of paramenters
!! Intent IN optional
integer(i8), optional, intent(in) :: jPerm ! choosing one single permutation
logical, optional, intent(in) :: printflag ! flag for printing results on screen
!! Intent OUT
real(dp), dimension(:,:,:), allocatable, intent(out) :: ode_results
! ! ode_results(i,j,k) concentration of reactant (k-1)
! ! at the jth time point in network permutation i\n
! ! jth time point is ode_results(i,j,1)\n
! ! dim_1 = number of permutations\n
! ! dim_2 = number of time points\n
! ! dim_3 = number of reactants + 1 \n
! ! (dim_3=1 : time points)\n
! ! (dim_3=i : reactant i-1)
!! Internal variables
integer(i4) :: ii, jj ! counters
integer(i4) :: dim_new, dim_old ! dimensions needed for re-allocation
integer(i8) :: iPer ! current permutation
integer(i8) :: nPer ! number of permutations
real(dp) :: dt_min ! step size
real(dp), dimension(:), allocatable :: xout ! time
real(dp), dimension(:,:), allocatable :: yout ! concentration per reactant
real(dp), dimension(:,:,:), allocatable :: results_temp ! temp variable
logical :: printflagIn
!! Parameters
real(dp), parameter :: eps = 1e-9_dp ! epsilon for the ODE solver
dt_min = dt*1e-11_dp ! minimum allowed stepsize
nPer = 2_i8**(int(n_reac*n_reac,i4)) ! number of permutations
! check reaction rates
if ( any(para .lt. 0.0_dp) ) then
write(*,*) 'mo_ode_generator: Reaction rates need to be non-negative!'
stop
end if
printflagIn = .false.
if ( present(printflag) ) printflagIn = printflag
!! set up Betas in the ode generator
call set_beta( para )
if ( present(jPerm) ) then
!! ONLY ONE PERMUTATION (jPerm)
if( jPerm .gt. nPer ) stop 'mo_ode_generator: ode_generator_dp: maximum number of permutation exceeded!!!'
if( jPerm .lt. 1_i8 ) stop 'mo_ode_generator: ode_generator_dp: jPerm should be greater than 0!!!'
call set_alpha( n_reac, jPerm - 1_i8 )
call RK4as( x_initial, t_start, t_end, dt, get_odes_dp, xout, yout, hmin=dt_min, eps=eps )
!! filling the results in ode_results
if( allocated(ode_results) ) deallocate(ode_results)
allocate( ode_results( 1_4, size(xout), n_reac+1_i4 ) )
ode_results(1,:,1) = xout
forall ( ii = 2:n_reac+1_i4 ) ode_results(1,:,ii) = yout(:,ii-1_i4)
!! writing the solutions of the current system of ODEs
if ( printflagIn ) then
write(*,*) ''
write(*,*) 'permutation num -->', jPerm
write(*,*) ' t y(t,j) ( j=1 ,...,', n_reac,')'
do jj=1, size(xout)
write(*,*) xout(jj), yout(jj,:)
end do
write(*,*) ''
end if
else
!! LOOPING OVER ALL THE POSSIBLE PERMUTATIONS
dim_old = 0_i4
!! looping over all the permutations
do iPer=0_i8, nPer-1_i8
call set_alpha( n_reac, iPer )
call RK4as( x_initial, t_start, t_end, dt, get_odes_dp, xout, yout, hmin=dt_min, eps=eps )
dim_new = size(xout)
if ( dim_old .lt. dim_new ) then
dim_old = dim_new
if ( .not.( allocated(ode_results) ) ) then
!! 1st time allocation
allocate( ode_results( nPer, dim_new, n_reac+1_i4 ) )
allocate( results_temp( nPer, dim_new, n_reac+1_i4 ) )
!! save results
ode_results(iPer+1_i8,:,1) = xout
forall ( jj = 2:n_reac+1_i4 ) ode_results(iPer+1_i8,:,jj) = yout(:,jj-1_i4)
else
if( allocated(results_temp) ) deallocate(results_temp)
allocate( results_temp( size(ode_results,1), size(ode_results,2), size(ode_results,3) ) )
!! save a copy of the old array
results_temp(:,:,:) = ode_results(:,:,:)
!! dealloc + realloc
if( allocated(ode_results) ) deallocate(ode_results) ! to be sure!
allocate( ode_results( nPer, dim_new, n_reac+1_i4 ) )
ode_results(:,:,:) = -9999.9_dp
!! copy old results back
ode_results(1:size(results_temp,1), 1:size(results_temp,2), 1:size(results_temp,3)) = results_temp(:,:,:)
!! save new results
ode_results(iPer+1_i8,:,1) = xout
forall ( jj = 2:n_reac+1_i4 ) ode_results(iPer+1_i8,:,jj) = yout(:,jj-1_i4)
end if
else
!! save results
ode_results(iPer+1_i8,1:dim_new,1) = xout
forall ( jj = 2:n_reac+1_i4 ) ode_results(iPer+1_i8,1:dim_new,jj) = yout(:,jj-1_i4)
end if
!! writing the solutions of the current system of ODEs
if ( printflagIn ) then
write(*,*) ''
write(*,*) 'num permutation -->', iPer+1_i4
write(*,*) ' t y(t,j) ( j=1 ,...,', n_reac,')'
do jj=1, size(xout)
write(*,*) xout(jj), yout(jj,:)
end do
write(*,*) ''
end if
end do
end if
end subroutine ode_generator_dp
! ============================================================================
! PRIVATE METHODS
! ============================================================================
!! GENERATE ODES
subroutine get_odes_dp( x, y, dydx )
use mo_kind, only : i4, dp
use mo_nrutil, only : assert_eq
implicit none
!! Intent IN
real(dp), intent(in) :: x ! space variable
real(dp), dimension(:), intent(in) :: y ! variables of the equations
!! Intent OUT
real(dp), dimension(:), intent(out) :: dydx ! derivative of y
!! Internal variables
integer(i4) :: j, k ! counters
integer(i4) :: nVar ! number of equations
!! dummy line
dydx(1) = x
dydx(:) = huge(1.0_dp)
!! number of equations & checkin dimension
nVar = assert_eq( size(y), size(alpha,1), size(beta,1), 'get_odes_dp')
!! generating odes...
do j=1, nVar
do k=1, nVar
if ( k .eq. j ) cycle ! skipping when k = j
dydx(j) = alpha(k,j)*beta(k,j)*y(k) - alpha(j,k)*beta(j,k)*y(j) + alpha(j,j)*beta(j,j)*y(j)
end do
end do
end subroutine get_odes_dp
!! SET ALPHA on/off variables matrix
subroutine set_alpha_dp( nVar, line )
use mo_kind, only : i4, i8
implicit none
!! Intent IN
integer(i4), intent(in) :: nVar ! number of variables
integer(i8), intent(in) :: line ! line of set_alpha_dp
if (.not. allocated(alpha)) then
allocate(alpha(nVar,nVar))
else
deallocate(alpha)
allocate(alpha(nVar,nVar))
endif
alpha = get_binaryPer(nVar, line)
end subroutine set_alpha_dp
!! SET BETA paramenters matrix
subroutine set_beta_dp( para )
use mo_kind, only : dp
implicit none
!! Intent IN
real(dp), dimension(:,:), intent(in) :: para ! matrix of parameters
if( allocated(beta) ) deallocate(beta)
allocate( beta(size(para,1),size(para,1)) )
beta = para
end subroutine set_beta_dp
!! decimal into a binary
function get_binary_i4( decimal, nDigits )
use mo_kind, only : i4, dp
implicit none
!! Intent IN
integer(i4), intent(in) :: decimal ! decimal number to convert
integer(i4), intent(in) :: nDigits ! number of digits required
!! OUTPUT
integer(i4), dimension(:), allocatable :: get_binary_i4 ! binary number
!! Internal variables
integer(i4) :: j ! counters
integer(i4) :: decimalIn
!! checking the nuber of digits required for the binary
if ( decimal .ne. 0_i4 .and. &
nDigits .lt. 4_i4*( int(log(real(decimal,dp))/log(16.0_dp), i4) ) ) stop 'get_binary_i4 --> to less digits!!!'
allocate( get_binary_i4(nDigits) )
get_binary_i4 = 0_i4
!! converting decimal into binary
if ( decimal .eq. 0_i4 ) then
get_binary_i4 = 0_i4
else
decimalIn = decimal
do j=1, nDigits
get_binary_i4(j) = mod(decimalIn,2)
decimalIn = decimalIn/2_i4
end do
!! inverting array
get_binary_i4(nDigits:1:-1) = get_binary_i4(1:nDigits)
end if
end function get_binary_i4
!! decimal into a binary
function get_binary_i8( decimal, nDigits )
use mo_kind, only : i4, i8, dp
implicit none
!! Intent IN
integer(i8), intent(in) :: decimal ! decimal number to convert
integer(i4), intent(in) :: nDigits ! number of digits required
!! OUTPUT
integer(i8), dimension(:), allocatable :: get_binary_i8 ! binary number
!! Internal variables
integer(i8) :: j ! counters
integer(i8) :: decimalIn
!! checking the nuber of digits required for the binary
if ( decimal .ne. 0_i8 .and. &
nDigits .lt. 4_i4*( int(log(real(decimal,dp))/log(16.0_dp), i4) ) ) stop 'get_binary_i8 --> to less digits!!!'
allocate( get_binary_i8(nDigits) )
get_binary_i8 = 0_i8
!! converting decimal into binary
if ( decimal .eq. 0_i8 ) then
get_binary_i8 = 0_i8
else
decimalIn = decimal
do j=1_i8, nDigits
get_binary_i8(j) = mod(decimalIn,2_i8)
decimalIn = decimalIn/2_i8
end do
!! inverting array
get_binary_i8(nDigits:1:-1) = get_binary_i8(1:nDigits)
end if
end function get_binary_i8
!! binary permutations
function get_binaryPer_dp( nVar, line )
use mo_kind, only : i4, i8, dp
implicit none
!! Intent IN
integer(i4), intent(in) :: nVar ! number of digits I need
integer(i8), intent(in) :: line ! which permutation I want --> decimal number to convert
!! OUTPUT
real(dp), dimension(nVar, nVar) :: get_binaryPer_dp ! binary number
!! Internal variables
!real(dp), dimension(:), allocatable :: get_binTemp
real(dp), dimension(nVar*nVar) :: get_binTemp
get_binTemp = real( get_binary(line, nVar*nVar), dp )
get_binaryPer_dp(:,:) = reshape( get_binTemp(:), (/ nVar, nVar /) )
end function get_binaryPer_dp
end module mo_ode_generator