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mo_xor4096_apps.f90
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mo_xor4096_apps.f90
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!> \file mo_xor4096_apps.f90
!> \brief This module provides useful applications of the random number generator xor4096.
!> \details This module provides useful applications of the random number generator xor4096, e.g.
!> (1) generating several random numbers from one stream at once,
!> (2) generating multivariate normal distributed random numbers, and
!> (3) generation of random numbers within a given range.
!> \authors Juliane Mai, Stephan Thober
!> \date Feb 2013
MODULE mo_xor4096_apps
! This module is a template for the JAMS Fortran library.
! Written Juliane Mai, Feb 2013
! Modified Stephan Thober, Feb 2013 - add multivariate normal
! License
! -------
! This file is part of the JAMS Fortran package, distributed under the MIT License.
!
! Copyright (c) 2013 Juliane Mai, Stephan Thober
!
! 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_xor4096, ONLY: xor4096, xor4096g, n_save_state
IMPLICIT NONE
PUBLIC :: xor4096_array ! Generation of (subsequent) UNIFORM random numbers of stream(s)
PUBLIC :: xor4096g_array ! Generation of (subsequent) GAUSSIAN random numbers of stream(s)
PUBLIC :: xor4096g_mvn ! Generation of multivariate NORMAL distributed random numbers
PUBLIC :: xor4096_range ! Generation of UNIFORM random numbers within a given range [a,b]
! ------------------------------------------------------------------
! NAME
! xor4096_array
! PURPOSE
!> \brief Generation of (subsequent) UNIFORM random numbers of stream(s).
!
!> \details Generation of (subsequent) UNIFORM random numbers of stream(s).\n
!> It is calling the xor4096 several times and returns a vector of random numbers.\n
!> It can be called with an optional argument to save the state of the current stream
!> to allow for a later return to exactly this stream.\n
!> The save_state variable has to be (I4) when random numbers are (I4) or (SP) and
!> save_state variable has to be (I8) when random numbers are (I8) or (DP).
!> The first dimension of save_state can be allocated using n_save_state of the xor4096 module.
!> If there are N>1 streams used, the second dimension of save_state is N.
!
! CALLING SEQUENCE
! call xor4096_array( rn, save_state=save_state )
!
! INTENT(IN)
! None
!
! INTENT(INOUT)
! None
! INTENT(OUT)
!> \param[out] "integer(i4/i8)/real(sp/dp) :: RN(:)/RN(:,:)"
!> uniform distributed random numbers with
!> interval:\n
!> i4: (-2^31,2^31-1)\n
!> i8: (-2^63,2^63-1)\n
!> sp: (0.0_sp, 1.0_sp)\n
!> dp: (0.0_dp, 1.0_dp)\n
!> rn(i,j) is the i^{th} number in the j^{th} stream
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
!> \param[in, out] "integer(i4/i8) :: save_state(size(rn,2),n_save_state)"
!> array carrying state of random number stream\n
!> this should be used if several streams are used, i.e.
!> each stream has its own save_state
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
! None
!
! RESTRICTIONS
!> \note The random number generator has to be initialized before and therefore is called without a seed.
!
! EXAMPLE
! real(dp), dimension(100) :: rn
! integer(i8) :: seed
! integer(i8), dimension(n_save_state) :: save_state
!
! ! initialize random number stream
! seed = 13546_i8
! call xor4096(seed, rn, save_state=save_state)
!
! ! generating random numbers
! call xor4096_array(rn, save_state=save_state)
! rn --> 100 subsequent (dp) uniform random numbers from stream with seed 13546
!
! -> see also example in test directory
! LITERATURE
! None
! HISTORY
!> \author Juliane Mai
!> \date Feb 2013
! Modified, -
!
INTERFACE xor4096_array
MODULE PROCEDURE &
xor4096_array_i4_1d, xor4096_array_i4_2d, xor4096_array_i8_1d, xor4096_array_i8_2d, &
xor4096_array_sp_1d, xor4096_array_sp_2d, xor4096_array_dp_1d, xor4096_array_dp_2d
END INTERFACE xor4096_array
! ------------------------------------------------------------------
! NAME
! xor4096g_array
! PURPOSE
!> \brief Generation of (subsequent) GAUSSIAN random numbers of stream(s).
!
!> \details Generation of (subsequent) GAUSSIAN random numbers of stream(s).\n
!> It is calling the xor4096g several times and returns a vector of random numbers.\n
!> It can be called with an optional argument to save the state of the current stream
!> to allow for a later return to exactly this stream.\n
!> The save_state variable has to be (I4) when random numbers are (SP) and
!> save_state variable has to be (I8) when random numbers are (DP).
!> The first dimension of save_state can be allocated using n_save_state of the xor4096 module.
!> If there are N>1 streams used, the second dimension of save_state is N.
!
! CALLING SEQUENCE
! call xor4096g_array( rn, save_state=save_state )
!
! INTENT(IN)
! None
!
! INTENT(INOUT)
! None
! INTENT(OUT)
!> \param[out] "real(sp/dp) :: RN(:)/RN(:,:)"
!> gaussian distributed random numbers with
!> interval: mean 0.0 and variance 1.0
!> rn(i,j) is the i^{th} number in the j^{th} stream
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
!> \param[in, out] "integer(i4/i8) :: save_state(size(rn,2),n_save_state)"
!> array carrying state of random number stream\n
!> this should be used if several streams are used, i.e.
!> each stream has its own save_state
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
! None
!
! RESTRICTIONS
!> \note The random number generator has to be initialized before and therefore is called without a seed.
!
! EXAMPLE
! real(dp), dimension(100) :: rn
! integer(i8) :: seed
! integer(i8), dimension(n_save_state) :: save_state
!
! ! initialize random number stream
! seed = 13546_i8
! call xor4096g(seed, rn, save_state=save_state)
!
! ! generating random numbers
! call xor4096g_array(rn, save_state=save_state)
! rn --> 100 subsequent (dp) gaussian random numbers from stream with seed 13546
!
! -> see also example in test directory
! LITERATURE
! None
! HISTORY
!> \author Juliane Mai
!> \date Feb 2013
! Modified, -
!
INTERFACE xor4096g_array
MODULE PROCEDURE &
xor4096g_array_sp_1d, xor4096g_array_sp_2d, xor4096g_array_dp_1d, xor4096g_array_dp_2d
END INTERFACE xor4096g_array
! ------------------------------------------------------------------
! NAME
! xor4096g_mvn
! PURPOSE
!> \brief Generation of multivariate NORMAL distributed random numbers.
!
!> \details Generation of multivariate NORMAL distributed random numbers using a
!> specified covariance matrix (cov).\n
!> This function is a wrapper around the random number generator
!> xor4096g!\n
!> It can be called with an optional argument to save the state of the current stream
!> to allow for a later return to exactly this stream.\n
!> The save_state variable has to be (I4) when random numbers are (SP) and
!> save_state variable has to be (I8) when random numbers are (DP).
!> The first dimension of save_state can be allocated using n_save_state of the xor4096 module.
!> The second dimension of save_state is according to the dimension of the covariance matrix.
! CALLING SEQUENCE
! call xor4096g_mvn( lcho, rn, save_state=save_state )
! INTENT(IN)
!> \param[in] "real(sp/dp), dimension(:,:) :: lcho" lower cholesky factor of
!> covariance matrix cov
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
! INTENT(IN), OPTIONAL
! None
! INTENT(INOUT), OPTIONAL
!> \param[in, out] "integer(i4/i8) :: save_state( size(lcho,1),n_save_state)"
!> array carrying state of random number stream\n
!> this should be used if several streams are used, i.e.
!> each stream has its own save_state
! INTENT(OUT), OPTIONAL
!> \param[out] "real(sp/dp), dimension(size(lcho,1))/dimension(:,size(lcho,1)) :: xor4096_mvn"
!> array of multivariate gaussian variates
! RETURN
!> \return
! RESTRICTIONS
!> \note The random number generator has to be initialized before and therefore is called without a seed.
! EXAMPLE
! one can use LAPACK for calculating the lower
! Cholesky Factor of the covariance matrix, which is
! required by MVN
!
! external DPOTRF ! Lapack routine for calculating the cholesky factor
!
! integer(i4) :: info
! real(sp), dimension(2,2) :: cov ! covariance matrix
! real(sp), dimension(2,2) :: lcho ! lower cholesky factor
!
! cov = (/ 1., 0.25; 0.25, 1./)
! lcho = cov
! call DPOTRF('L', size(lcho,1), lcho, size(lcho,1), info) ! changes lower triangular (incl. main diagonal) of Lcho
! if ( info .gt. 0_i4 ) then
! write(*,*)'GetCholeskyFactor_dp: The algorithm failed!'
! stop
! end if
!
! ! DONT forget to set upper triangular matrix to zero
! lcho(1,2) = 0._sp
!
! call xor4096g_mvn( lcho , mvn )
! CAUTION: one has to sample a time series to stabilize the covariances
! between the entries of mvn
! LITERATURE
! see affine transformation at
! http://en.wikipedia.org/wiki/Multivariate_normal_distribution
! HISTORY
!> \author Stephan Thober
!> \date Oct 2012
interface xor4096g_mvn
module procedure mvn_sp_1d, mvn_dp_1d, mvn_sp_2d, mvn_dp_2d
end interface xor4096g_mvn
! ------------------------------------------------------------------
! NAME
! xor4096_range
! PURPOSE
!> \brief Generation of UNIFORM random numbers within a given range [a,b].
!
!> \details Generation of UNIFORM random numbers within a given range [a,b].\n
!> It is calling the xor4096 and scales the random numbers to the given range.\n
!> It can be called with an optional argument to save the state of the current stream
!> to allow for a later return to exactly this stream.\n
!> The save_state variable has to be (I4) when random numbers are (I4) or (SP) and
!> save_state variable has to be (I8) when random numbers are (I8) or (DP).
!> The first dimension of save_state can be allocated using n_save_state of the xor4096 module.
!> If there are N>1 streams used, the second dimension of save_state is N.
!
! CALLING SEQUENCE
! call xor4096_range( range, rn, save_state=save_state )
!
! INTENT(IN)
!> \param[in] "integer(i4/i8)/real(sp/dp) :: rn_range(2)" lower and upper bound of the random number
!
! INTENT(INOUT)
! None
! INTENT(OUT)
!> \param[out] "integer(i4/i8)/real(sp/dp) :: RN/RN(:)/RN(:,:)"
!> uniform distributed random numbers with
!> interval:\n
!> i4: [a,b]\n
!> i8: [a,b]\n
!> sp: [a,b]\n
!> dp: [a,b]\n
!> rn(i,j) is the i^{th} number in the j^{th} stream
!
! INTENT(IN), OPTIONAL
! None
!
! INTENT(INOUT), OPTIONAL
!> \param[in, out] "integer(i4/i8) :: save_state(size(rn,2),n_save_state)"
!> array carrying state of random number stream\n
!> this should be used if several streams are used, i.e.
!> each stream has its own save_state
!
! INTENT(OUT), OPTIONAL
! None
!
! RETURN
! None
!
! RESTRICTIONS
!> \note The random number generator has to be initialized before and therefore is called without a seed.
!
! EXAMPLE
! real(dp), dimension(100) :: rn
! integer(i8) :: seed
! integer(i8), dimension(n_save_state) :: save_state
!
! ! initialize random number stream
! seed = 13546_i8
! call xor4096(seed, rn, save_state=save_state)
!
! ! generating random numbers
! call xor4096_range((/2.0_dp,4.0_dp/), rn, save_state=save_state)
! rn --> 100 subsequent (dp) uniform random numbers in interval [2.0,4.0] from stream with seed 13546
!
! -> see also example in test directory
! LITERATURE
! None
! HISTORY
!> \author Juliane Mai
!> \date Feb 2013
! Modified, -
!
INTERFACE xor4096_range
MODULE PROCEDURE &
xor4096_range_i4_0d, xor4096_range_i4_1d, xor4096_range_i4_2d, &
xor4096_range_i8_0d, xor4096_range_i8_1d, xor4096_range_i8_2d, &
xor4096_range_sp_0d, xor4096_range_sp_1d, xor4096_range_sp_2d, &
xor4096_range_dp_0d, xor4096_range_dp_1d, xor4096_range_dp_2d
END INTERFACE xor4096_range
! ------------------------------------------------------------------
PRIVATE
! ------------------------------------------------------------------
CONTAINS
! *********************************************************************
! TEST XOR4096_ARRAY
! *********************************************************************
SUBROUTINE xor4096_array_i4_1d(rn, save_state)
IMPLICIT NONE
INTEGER(I4), DIMENSION(:), INTENT(OUT) :: rn
INTEGER(I4), DIMENSION(n_save_state), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
if (present(save_state)) then
do i=1, size(rn,1)
call xor4096(0_i4, rn(i), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096(0_i4, rn(i))
end do
endif
END SUBROUTINE xor4096_array_i4_1d
SUBROUTINE xor4096_array_i4_2d(rn, save_state)
IMPLICIT NONE
INTEGER(I4), DIMENSION(:,:), INTENT(OUT) :: rn ! dim2=number of streams
INTEGER(I4), DIMENSION(:,:), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
INTEGER(I4), DIMENSION(size(rn,2)) :: seed_tmp
seed_tmp = 0_i4
if (present(save_state)) then
if (size(save_state,1) .ne. size(rn,2) .or. size(save_state,2) .ne. n_save_state) then
stop 'xor4096_array_i4_2d: dimensions of save_state matrix are not correct'
end if
do i=1, size(rn,1)
call xor4096(seed_tmp, rn(i,:), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096(seed_tmp, rn(i,:))
end do
endif
END SUBROUTINE xor4096_array_i4_2d
SUBROUTINE xor4096_array_i8_1d(rn, save_state)
IMPLICIT NONE
INTEGER(I8), DIMENSION(:), INTENT(OUT) :: rn
INTEGER(I8), DIMENSION(n_save_state), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
if (present(save_state)) then
do i=1, size(rn,1)
call xor4096(0_i8, rn(i), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096(0_i8, rn(i))
end do
endif
END SUBROUTINE xor4096_array_i8_1d
SUBROUTINE xor4096_array_i8_2d(rn, save_state)
IMPLICIT NONE
INTEGER(I8), DIMENSION(:,:), INTENT(OUT) :: rn ! dim2=number of streams
INTEGER(I8), DIMENSION(:,:), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
INTEGER(I8), DIMENSION(size(rn,2)) :: seed_tmp
seed_tmp = 0_i8
if (present(save_state)) then
if (size(save_state,1) .ne. size(rn,2) .or. size(save_state,2) .ne. n_save_state) then
stop 'xor4096_array_i8_2d: dimensions of save_state matrix are not correct'
end if
do i=1, size(rn,1)
call xor4096(seed_tmp, rn(i,:), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096(seed_tmp, rn(i,:))
end do
endif
END SUBROUTINE xor4096_array_i8_2d
SUBROUTINE xor4096_array_sp_1d(rn, save_state)
IMPLICIT NONE
REAL(SP), DIMENSION(:), INTENT(OUT) :: rn
INTEGER(I4), DIMENSION(n_save_state), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
if (present(save_state)) then
do i=1, size(rn,1)
call xor4096(0_i4, rn(i), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096(0_i4, rn(i))
end do
endif
END SUBROUTINE xor4096_array_sp_1d
SUBROUTINE xor4096_array_sp_2d(rn, save_state)
IMPLICIT NONE
REAL(SP), DIMENSION(:,:), INTENT(OUT) :: rn ! dim2=number of streams
INTEGER(I4), DIMENSION(:,:), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
INTEGER(I4), DIMENSION(size(rn,2)) :: seed_tmp
seed_tmp = 0_i4
if (present(save_state)) then
if (size(save_state,1) .ne. size(rn,2) .or. size(save_state,2) .ne. n_save_state) then
stop 'xor4096_array_sp_2d: dimensions of save_state matrix are not correct'
end if
do i=1, size(rn,1)
call xor4096(seed_tmp, rn(i,:), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096(seed_tmp, rn(i,:))
end do
endif
END SUBROUTINE xor4096_array_sp_2d
SUBROUTINE xor4096_array_dp_1d(rn, save_state)
IMPLICIT NONE
REAL(DP), DIMENSION(:), INTENT(OUT) :: rn
INTEGER(I8), DIMENSION(n_save_state), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
if (present(save_state)) then
do i=1, size(rn,1)
call xor4096(0_i8, rn(i), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096(0_i8, rn(i))
end do
endif
END SUBROUTINE xor4096_array_dp_1d
SUBROUTINE xor4096_array_dp_2d(rn, save_state)
IMPLICIT NONE
REAL(DP), DIMENSION(:,:), INTENT(OUT) :: rn ! dim2=number of streams
INTEGER(I8), DIMENSION(:,:), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
INTEGER(I8), DIMENSION(size(rn,2)) :: seed_tmp
seed_tmp = 0_i8
if (present(save_state)) then
if (size(save_state,1) .ne. size(rn,2) .or. size(save_state,2) .ne. n_save_state) then
stop 'xor4096_array_dp_2d: dimensions of save_state matrix are not correct'
end if
do i=1, size(rn,1)
call xor4096(seed_tmp, rn(i,:), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096(seed_tmp, rn(i,:))
end do
endif
END SUBROUTINE xor4096_array_dp_2d
! *********************************************************************
! TEST XOR4096G_ARRAY
! *********************************************************************
SUBROUTINE xor4096g_array_sp_1d(rn, save_state)
IMPLICIT NONE
REAL(SP), DIMENSION(:), INTENT(OUT) :: rn
INTEGER(I4), DIMENSION(n_save_state), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
if (present(save_state)) then
do i=1, size(rn,1)
call xor4096g(0_i4, rn(i), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096g(0_i4, rn(i))
end do
endif
END SUBROUTINE xor4096g_array_sp_1d
SUBROUTINE xor4096g_array_sp_2d(rn, save_state)
IMPLICIT NONE
REAL(SP), DIMENSION(:,:), INTENT(OUT) :: rn ! dim2=number of streams
INTEGER(I4), DIMENSION(:,:), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
INTEGER(I4), DIMENSION(size(rn,2)) :: seed_tmp
seed_tmp = 0_i4
if (present(save_state)) then
if (size(save_state,1) .ne. size(rn,2) .or. size(save_state,2) .ne. n_save_state) then
stop 'xor4096g_array_sp_2d: dimensions of save_state matrix are not correct'
end if
do i=1, size(rn,1)
call xor4096g(seed_tmp, rn(i,:), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096g(seed_tmp, rn(i,:))
end do
endif
END SUBROUTINE xor4096g_array_sp_2d
SUBROUTINE xor4096g_array_dp_1d(rn, save_state)
IMPLICIT NONE
REAL(DP), DIMENSION(:), INTENT(OUT) :: rn
INTEGER(I8), DIMENSION(n_save_state), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
if (present(save_state)) then
do i=1, size(rn,1)
call xor4096g(0_i8, rn(i), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096g(0_i8, rn(i))
end do
endif
END SUBROUTINE xor4096g_array_dp_1d
SUBROUTINE xor4096g_array_dp_2d(rn, save_state)
IMPLICIT NONE
REAL(DP), DIMENSION(:,:), INTENT(OUT) :: rn ! dim2=number of streams
INTEGER(I8), DIMENSION(:,:), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
INTEGER(I8), DIMENSION(size(rn,2)) :: seed_tmp
seed_tmp = 0_i8
if (present(save_state)) then
if (size(save_state,1) .ne. size(rn,2) .or. size(save_state,2) .ne. n_save_state) then
stop 'xor4096g_array_dp_2d: dimensions of save_state matrix are not correct'
end if
do i=1, size(rn,1)
call xor4096g(seed_tmp, rn(i,:), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096g(seed_tmp, rn(i,:))
end do
endif
END SUBROUTINE xor4096g_array_dp_2d
! *********************************************************************
! XOR4096G_MVN
! *********************************************************************
subroutine mvn_SP_1d(lcho, mvn, save_state)
implicit none
real(sp), dimension(:,:), intent(in) :: lcho
real(sp), dimension(size(lcho,1)), intent(out) :: mvn
integer(i4), dimension(:,:), optional, intent(inout) :: save_state
! local variables
integer(i4), dimension(size(lcho,1)) :: seed_tmp
seed_tmp = 0_i4
! consistency check
if ( size(lcho,1) /= size(lcho,2) ) then
stop 'mvn_sp_1d: size mismatch in variable lcho.'
end if
! ! initialize if non-zero
! if ( all(seed .ne. 0_i4) ) then
! if ( present(save_state) ) then
! call xor4096g(seed, mvn, save_state=save_state)
! else
! call xor4096g(seed, mvn)
! end if
! seed = 0_i4
! end if
! generate random
if ( present(save_state) ) then
if (size(save_state,1) .ne. size(lcho,1) .or. size(save_state,2) .ne. n_save_state) then
stop 'mvn_sp_1d: dimensions of save_state matrix are not correct'
end if
call xor4096g(seed_tmp, mvn, save_state=save_state)
else
call xor4096g(seed_tmp, mvn)
end if
mvn = matmul(lcho,mvn)
end subroutine mvn_SP_1d
subroutine mvn_DP_1d(lcho, mvn, save_state)
implicit none
real(dp), dimension(:,:), intent(in) :: lcho
real(dp), dimension(size(lcho,1)), intent(out) :: mvn
integer(i8), dimension(:,:), optional, intent(inout) :: save_state
! local variables
integer(i8), dimension(size(lcho,1)) :: seed_tmp
seed_tmp = 0_i8
! consistency check
if ( size(lcho,1) /= size(lcho,2) ) then
stop 'mvn_dp_1d: size mismatch in variable lcho.'
end if
! ! initialize if non-zero
! if ( all(seed .ne. 0_i8) ) then
! if ( present(save_state) ) then
! call xor4096g(seed, mvn, save_state=save_state)
! else
! call xor4096g(seed, mvn)
! end if
! seed = 0_i8
! end if
! generate random
if ( present(save_state) ) then
if (size(save_state,1) .ne. size(lcho,1) .or. size(save_state,2) .ne. n_save_state) then
stop 'mvn_dp_1d: dimensions of save_state matrix are not correct'
end if
call xor4096g(seed_tmp, mvn, save_state=save_state)
else
call xor4096g(seed_tmp, mvn)
end if
mvn = matmul(lcho,mvn)
end subroutine mvn_DP_1d
subroutine mvn_SP_2d(lcho, mvn, save_state)
implicit none
real(sp), dimension(:,:), intent(in) :: lcho
real(sp), dimension(:,:), intent(out) :: mvn ! dim1=number of sets,
! ! dim2=size(lcho,1)
integer(i4), dimension(:,:), optional, intent(inout) :: save_state
! local variables
integer(i4) :: i
integer(i4), dimension(size(lcho,1)) :: seed_tmp
seed_tmp = 0_i4
! consistency check
if ( size(lcho,1) /= size(lcho,2) ) then
stop 'mvn_sp_2d: size mismatch in variable lcho.'
end if
! ! initialize if non-zero
! if ( all(seed .ne. 0_i4) ) then
! if ( present(save_state) ) then
! call xor4096g(seed, mvn(1,:), save_state=save_state)
! else
! call xor4096g(seed, mvn(1,:))
! end if
! seed = 0_i4
! end if
! generate random
if ( present(save_state) ) then
if (size(save_state,1) .ne. size(lcho,1) .or. size(save_state,2) .ne. n_save_state) then
stop 'mvn_sp_2d: dimensions of save_state matrix are not correct'
end if
do i=1, size(mvn,1)
call xor4096g(seed_tmp, mvn(i,:), save_state=save_state)
mvn(i,:) = matmul(lcho,mvn(i,:))
end do
else
do i=1, size(mvn,1)
call xor4096g(seed_tmp, mvn(i,:))
mvn(i,:) = matmul(lcho,mvn(i,:))
end do
end if
end subroutine mvn_SP_2d
subroutine mvn_DP_2d(lcho, mvn, save_state)
!
implicit none
!
real(dp), dimension(:,:), intent(in) :: lcho
real(dp), dimension(:,:), intent(out) :: mvn ! dim1=number of sets,
! ! dim2=size(lcho,1)
integer(i8), dimension(:,:), optional, intent(inout) :: save_state
! local variables
integer(i4) :: i
integer(i8), dimension(size(lcho,1)) :: seed_tmp
seed_tmp = 0_i8
! consistency check
if ( size(lcho,1) /= size(lcho,2) ) then
stop 'mvn_dp_2d: size mismatch in variable lcho.'
end if
! ! initialize if non-zero
! if ( all(seed .ne. 0_i8) ) then
! if ( present(save_state) ) then
! call xor4096g(seed, mvn(1,:), save_state=save_state)
! else
! call xor4096g(seed, mvn(1,:))
! end if
! seed = 0_i8
! end if
! generate random
if ( present(save_state) ) then
if (size(save_state,1) .ne. size(lcho,1) .or. size(save_state,2) .ne. n_save_state) then
stop 'mvn_dp_2d: dimensions of save_state matrix are not correct'
end if
do i=1, size(mvn,1)
call xor4096g(seed_tmp, mvn(i,:), save_state=save_state)
mvn(i,:) = matmul(lcho,mvn(i,:))
end do
else
do i=1, size(mvn,1)
call xor4096g(seed_tmp, mvn(i,:))
mvn(i,:) = matmul(lcho,mvn(i,:))
end do
end if
end subroutine mvn_DP_2d
! *********************************************************************
! XOR4096_RANGE
! *********************************************************************
SUBROUTINE xor4096_range_i4_0d(rn_range, rn, save_state)
IMPLICIT NONE
INTEGER(I4), DIMENSION(2), INTENT(IN) :: rn_range ! lower and upper bound
INTEGER(I4), INTENT(OUT) :: rn
INTEGER(I4), DIMENSION(n_save_state), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
REAL(SP) :: rn_tmp
if ( rn_range(1) .gt. rn_range(2) ) then
stop 'xor4096_range_i4_0d: lower bound larger than upper bound'
end if
if (present(save_state)) then
call xor4096(0_i4, rn, save_state=save_state)
else
call xor4096(0_i4, rn)
endif
! scale [-2^31, 2^31) to [0.0, 1.0)
rn_tmp = real(rn,sp) / 2.0_sp**32_i4 + 0.5_sp
! scale [0.0, 1.0) to [rn_range(1),rn_range(2)]
rn = int( rn_tmp * ( real(rn_range(2) - rn_range(1) + 1_i4,sp) ) + real(rn_range(1),sp) , i4)
END SUBROUTINE xor4096_range_i4_0d
SUBROUTINE xor4096_range_i4_1d(rn_range, rn, save_state)
IMPLICIT NONE
INTEGER(I4), DIMENSION(2), INTENT(IN) :: rn_range ! lower and upper bound
INTEGER(I4), DIMENSION(:), INTENT(OUT) :: rn
INTEGER(I4), DIMENSION(n_save_state), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
REAL(SP), DIMENSION(size(rn,1)) :: rn_tmp
if ( rn_range(1) .gt. rn_range(2) ) then
stop 'xor4096_range_i4_1d: lower bound larger than upper bound'
end if
if (present(save_state)) then
do i=1, size(rn,1)
call xor4096(0_i4, rn(i), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096(0_i4, rn(i))
end do
endif
! scale [-2^31, 2^31) to [0.0, 1.0)
rn_tmp = real(rn,sp) / 2.0_sp**32_i4 + 0.5_sp
! scale [0.0, 1.0) to [rn_range(1),rn_range(2)]
rn = int( rn_tmp * ( real(rn_range(2) - rn_range(1) + 1_i4,sp) ) + real(rn_range(1),sp) , i4)
END SUBROUTINE xor4096_range_i4_1d
SUBROUTINE xor4096_range_i4_2d(rn_range, rn, save_state)
IMPLICIT NONE
INTEGER(I4), DIMENSION(2), INTENT(IN) :: rn_range ! lower and upper bound
INTEGER(I4), DIMENSION(:,:), INTENT(OUT) :: rn ! dim2=number of streams
INTEGER(I4), DIMENSION(:,:), OPTIONAL, INTENT(INOUT) :: save_state
! local variables
INTEGER(I4) :: i
REAL(SP), DIMENSION(size(rn,1), size(rn,2)) :: rn_tmp
INTEGER(I4), DIMENSION(size(rn,2)) :: seed_tmp
seed_tmp = 0_i4
if ( rn_range(1) .gt. rn_range(2) ) then
stop 'xor4096_range_i4_2d: lower bound larger than upper bound'
end if
if (present(save_state)) then
if (size(save_state,1) .ne. size(rn,2) .or. size(save_state,2) .ne. n_save_state) then
stop 'xor4096_range_i4_2d: dimensions of save_state matrix are not correct'
end if
do i=1, size(rn,1)
call xor4096(seed_tmp, rn(i,:), save_state=save_state)
end do
else
do i=1, size(rn,1)
call xor4096(seed_tmp, rn(i,:))
end do
endif
! scale [-2^31, 2^31) to [0.0, 1.0)
rn_tmp = real(rn,sp) / 2.0_sp**32_i4 + 0.5_sp
! scale [0.0, 1.0) to [rn_range(1),rn_range(2)]
rn = int( rn_tmp * ( real(rn_range(2) - rn_range(1) + 1_i4,sp) ) + real(rn_range(1),sp) , i4)
END SUBROUTINE xor4096_range_i4_2d
SUBROUTINE xor4096_range_i8_0d(rn_range, rn, save_state)
IMPLICIT NONE
INTEGER(I8), DIMENSION(2), INTENT(IN) :: rn_range ! lower and upper bound
INTEGER(I8), INTENT(OUT) :: rn