rand.F90

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! Copyright (C) 2007-2012 Matthew West
! Licensed under the GNU General Public License version 2 or (at your
! option) any later version. See the file COPYING for details.
 
!> \file
!> The pmc_rand module.
 
!> Random number generators.
module pmc_rand
 
  use pmc_util
  use pmc_constants
  use pmc_mpi
#ifdef PMC_USE_GSL
  use iso_c_binding
#endif
 
  !> Length of a UUID string.
  integer, parameter :: pmc_uuid_len = 36
 
  !> Result code indicating successful completion.
  integer, parameter :: pmc_rand_gsl_success      = 0
  !> Result code indicating initialization failure.
  integer, parameter :: pmc_rand_gsl_init_fail    = 1
  !> Result code indicating the generator was not initialized when it
  !> should have been.
  integer, parameter :: pmc_rand_gsl_not_init     = 2
  !> Result code indicating the generator was already initialized when
  !> an initialization was attempted.
  integer, parameter :: pmc_rand_gsl_already_init = 3
 
contains
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
#ifdef PMC_USE_GSL
  !> Check the return value of a call to one of the GSL RNG functions.
  subroutine rand_check_gsl(code, value)
 
    !> Error code.
    integer :: code
    !> Return value.
    integer(kind=c_int) :: value
 
    if (value == pmc_rand_gsl_success) then
       return
    elseif (value == pmc_rand_gsl_init_fail) then
       call die_msg(code, "GSL RNG initialization failed")
    elseif (value == pmc_rand_gsl_not_init) then
       call die_msg(code, "GSL RNG has not been successfully initialized")
    elseif (value == pmc_rand_gsl_already_init) then
       call die_msg(code, "GSL RNG was already initialized")
    else
       call die_msg(code, "Unknown GSL RNG interface return value: " &
            // trim(integer_to_string(value)))
    end if
 
  end subroutine rand_check_gsl
#endif
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Initializes the random number generator to the state defined by
  !> the given seed plus offset. If the seed is 0 then a seed is
  !> auto-generated from the current time plus offset.
  subroutine pmc_srand(seed, offset)
 
    !> Random number generator seed.
    integer, intent(in) :: seed
    !> Random number generator offset.
    integer, intent(in) :: offset
 
    integer :: i, n, clock
    integer, allocatable :: seed_vec(:)
#ifdef PMC_USE_GSL
    integer(kind=c_int) :: c_clock
#endif
 
#ifdef PMC_USE_GSL
#ifndef DOXYGEN_SKIP_DOC
    interface
       integer(kind=c_int) function pmc_srand_gsl(seed) bind(c)
         use iso_c_binding
         integer(kind=c_int), value :: seed
       end function pmc_srand_gsl
    end interface
#endif
#endif
 
    if (seed == 0) then
       if (pmc_mpi_rank() == 0) then
          call system_clock(count = clock)
       end if
       ! ensure all nodes use exactly the same seed base, to avoid
       ! accidental correlations
       call pmc_mpi_bcast_integer(clock)
    else
       clock = seed
    end if
    clock = clock + 67 * offset
#ifdef PMC_USE_GSL
    c_clock = int(clock, kind=c_int)
    call rand_check_gsl(100489590, pmc_srand_gsl(c_clock))
#else
    call random_seed(size = n)
    allocate(seed_vec(n))
    i = 0 ! HACK to shut up gfortran warning
    seed_vec = clock + 37 * (/ (i - 1, i = 1, n) /)
    call random_seed(put = seed_vec)
    deallocate(seed_vec)
#endif
 
  end subroutine pmc_srand
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Cleanup the random number generator.
  subroutine pmc_rand_finalize()
 
#ifdef PMC_USE_GSL
 
#ifndef DOXYGEN_SKIP_DOC
    interface
       integer(kind=c_int) function pmc_rand_finalize_gsl() bind(c)
         use iso_c_binding
       end function pmc_rand_finalize_gsl
    end interface
#endif
 
    call rand_check_gsl(489538382, pmc_rand_finalize_gsl())
#endif
 
  end subroutine pmc_rand_finalize
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Returns a random number between 0 and 1.
  real(kind=dp) function pmc_random()
 
#ifdef PMC_USE_GSL
    real(kind=c_double), target :: rnd
    type(c_ptr) :: rnd_ptr
#else
    real(kind=dp) :: rnd
#endif
 
#ifdef PMC_USE_GSL
#ifndef DOXYGEN_SKIP_DOC
    interface
       integer(kind=c_int) function pmc_rand_gsl(harvest) bind(c)
         use iso_c_binding
         type(c_ptr), value :: harvest
       end function pmc_rand_gsl
    end interface
#endif
#endif
 
#ifdef PMC_USE_GSL
    rnd_ptr = c_loc(rnd)
    call rand_check_gsl(843777138, pmc_rand_gsl(rnd_ptr))
    pmc_random = real(rnd, kind=dp)
#else
    call random_number(rnd)
    pmc_random = rnd
#endif
 
  end function pmc_random
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Returns a random integer between 1 and n.
  integer function pmc_rand_int(n)
 
    !> Maximum random number to generate.
    integer, intent(in) :: n
 
#ifdef PMC_USE_GSL
    integer(kind=c_int) :: n_c
    integer(kind=c_int), target :: harvest
    type(c_ptr) :: harvest_ptr
#endif
 
#ifdef PMC_USE_GSL
#ifndef DOXYGEN_SKIP_DOC
    interface
       integer(kind=c_int) function pmc_rand_int_gsl(n, harvest) bind(c)
         use iso_c_binding
         integer(kind=c_int), value :: n
         type(c_ptr), value :: harvest
       end function pmc_rand_int_gsl
    end interface
#endif
#endif
 
    call assert(669532625, n >= 1)
#ifdef PMC_USE_GSL
    n_c = int(n, kind=c_int)
    harvest_ptr = c_loc(harvest)
    call rand_check_gsl(388234845, pmc_rand_int_gsl(n_c, harvest_ptr))
    pmc_rand_int = int(harvest)
#else
    pmc_rand_int = mod(int(pmc_random() * real(n, kind=dp)), n) + 1
#endif
    call assert(515838689, pmc_rand_int >= 1)
    call assert(802560153, pmc_rand_int <= n)
 
  end function pmc_rand_int
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Round val to \c floor(val) or \c ceiling(val) with probability
  !> proportional to the relative distance from \c val. That is,
  !> Prob(prob_round(val) == floor(val)) = ceil(val) - val.
  integer function prob_round(val)
 
    !> Value to round.
    real(kind=dp), intent(in) :: val
 
    ! FIXME: can replace this with:
    ! prob_round = floor(val + pmc_random())
    if (pmc_random() < real(ceiling(val), kind=dp) - val) then
       prob_round = floor(val)
    else
       prob_round = ceiling(val)
    endif
 
  end function prob_round
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Generate a Poisson-distributed random number with the given
  !> mean.
  !!
  !! See http://en.wikipedia.org/wiki/Poisson_distribution for
  !! information on the method. The method used at present is rather
  !! inefficient and inaccurate (brute force for mean below 10 and
  !! normal approximation above that point).
  !!
  !! The best known method appears to be due to Ahrens and Dieter (ACM
  !! Trans. Math. Software, 8(2), 163-179, 1982) and is available (in
  !! various forms) from:
  !!     - http://www.netlib.org/toms/599
  !!     - http://www.netlib.org/random/ranlib.f.tar.gz
  !!     - http://users.bigpond.net.au/amiller/random/random.f90
  !!     - http://www.netlib.org/random/random.f90
  !!
  !! Unfortunately the above code is under the non-free license:
  !!     - http://www.acm.org/pubs/copyright_policy/softwareCRnotice.html
  !!
  !! For other reasonable methods see L. Devroye, "Non-Uniform Random
  !! Variate Generation", Springer-Verlag, 1986.
  integer function rand_poisson(mean)
 
    !> Mean of the distribution.
    real(kind=dp), intent(in) :: mean
 
#ifdef PMC_USE_GSL
    real(kind=c_double) :: mean_c
    integer(kind=c_int), target :: harvest
    type(c_ptr) :: harvest_ptr
#else
    real(kind=dp) :: l, p
    integer :: k
#endif
 
#ifdef PMC_USE_GSL
#ifndef DOXYGEN_SKIP_DOC
    interface
       integer(kind=c_int) function pmc_rand_poisson_gsl(mean, harvest) &
            bind(c)
         use iso_c_binding
         real(kind=c_double), value :: mean
         type(c_ptr), value :: harvest
       end function pmc_rand_poisson_gsl
    end interface
#endif
#endif
 
    call assert(368397056, mean >= 0d0)
#ifdef PMC_USE_GSL
    mean_c = real(mean, kind=c_double)
    harvest_ptr = c_loc(harvest)
    call rand_check_gsl(353483140, &
         pmc_rand_poisson_gsl(mean_c, harvest_ptr))
    rand_poisson = int(harvest)
#else
    if (mean <= 10d0) then
       ! exact method due to Knuth
       l = exp(-mean)
       k = 0
       p = 1d0
       do
          k = k + 1
          p = p * pmc_random()
          if (p < l) exit
       end do
       rand_poisson = k - 1
    else
       ! normal approximation with a continuity correction
       k = nint(rand_normal(mean, sqrt(mean)))
       rand_poisson = max(k, 0)
    end if
#endif
 
  end function rand_poisson
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Generate a Binomial-distributed random number with the given
  !> parameters.
  !!
  !! See http://en.wikipedia.org/wiki/Binomial_distribution for
  !! information on the method. The method used at present is rather
  !! inefficient and inaccurate (brute force for \f$np \le 10\f$ and
  !! \f$n(1-p) \le 10\f$, otherwise normal approximation).
  !!
  !! For better methods, see L. Devroye, "Non-Uniform Random Variate
  !! Generation", Springer-Verlag, 1986.
  integer function rand_binomial(n, p)
 
    !> Sample size.
    integer, intent(in) :: n
    !> Sample probability.
    real(kind=dp), intent(in) :: p
 
#ifdef PMC_USE_GSL
    integer(kind=c_int) :: n_c
    real(kind=c_double) :: p_c
    integer(kind=c_int), target :: harvest
    type(c_ptr) :: harvest_ptr
#else
    real(kind=dp) :: np, nomp, q, g_real
    integer :: k, g, sum
#endif
 
#ifdef PMC_USE_GSL
#ifndef DOXYGEN_SKIP_DOC
    interface
       integer(kind=c_int) function pmc_rand_binomial_gsl(n, p, harvest) &
            bind(c)
         use iso_c_binding
         integer(kind=c_int), value :: n
         real(kind=c_double), value :: p
         type(c_ptr), value :: harvest
       end function pmc_rand_binomial_gsl
    end interface
#endif
#endif
 
    call assert(130699849, n >= 0)
    call assert(754379796, p >= 0d0)
    call assert(678506029, p <= 1d0)
#ifdef PMC_USE_GSL
    n_c = int(n, kind=c_int)
    p_c = real(p, kind=c_double)
    harvest_ptr = c_loc(harvest)
    call rand_check_gsl(208869397, &
         pmc_rand_binomial_gsl(n_c, p_c, harvest_ptr))
    rand_binomial = int(harvest)
#else
    np = real(n, kind=dp) * p
    nomp = real(n, kind=dp) * (1d0 - p)
    if ((np >= 10d0) .and. (nomp >= 10d0)) then
       ! normal approximation with continuity correction
       k = nint(rand_normal(np, sqrt(np * (1d0 - p))))
       rand_binomial = min(max(k, 0), n)
    elseif (np < 1d-200) then
       rand_binomial = 0
    elseif (nomp < 1d-200) then
       rand_binomial = n
    else
       ! First waiting time method of Devroye (p. 525).
       ! We want p small, so if p > 1/2 then we compute with 1 - p and
       ! take n - k at the end.
       if (p <= 0.5d0) then
          q = p
       else
          q = 1d0 - p
       end if
       k = 0
       sum = 0
       do
          ! G is geometric(q)
          g_real = log(pmc_random()) / log(1d0 - q)
          ! early bailout for cases to avoid integer overflow
          if (g_real > real(n - sum, kind=dp)) exit
          g = ceiling(g_real)
          sum = sum + g
          if (sum > n) exit
          k = k + 1
       end do
       if (p <= 0.5d0) then
          rand_binomial = k
       else
          rand_binomial = n - k
       end if
       call assert(359087410, rand_binomial <= n)
    end if
#endif
 
  end function rand_binomial
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Generates a normally distributed random number with the given
  !> mean and standard deviation.
  real(kind=dp) function rand_normal(mean, stddev)
 
    !> Mean of distribution.
    real(kind=dp), intent(in) :: mean
    !> Standard deviation of distribution.
    real(kind=dp), intent(in) :: stddev
 
#ifdef PMC_USE_GSL
    real(kind=c_double) :: mean_c, stddev_c
    real(kind=c_double), target :: harvest
    type(c_ptr) :: harvest_ptr
#else
    real(kind=dp) :: u1, u2, r, theta, z0, z1
#endif
 
#ifdef PMC_USE_GSL
#ifndef DOXYGEN_SKIP_DOC
    interface
       integer(kind=c_int) function pmc_rand_normal_gsl(mean, stddev, &
            harvest) bind(c)
         use iso_c_binding
         real(kind=c_double), value :: mean
         real(kind=c_double), value :: stddev
         type(c_ptr), value :: harvest
       end function pmc_rand_normal_gsl
    end interface
#endif
#endif
 
    call assert(898978929, stddev >= 0d0)
#ifdef PMC_USE_GSL
    mean_c = real(mean, kind=c_double)
    stddev_c = real(stddev, kind=c_double)
    harvest_ptr = c_loc(harvest)
    call rand_check_gsl(102078576, &
         pmc_rand_normal_gsl(mean_c, stddev_c, harvest_ptr))
    rand_normal = real(harvest, kind=dp)
#else
    ! Uses the Box-Muller transform
    ! http://en.wikipedia.org/wiki/Box-Muller_transform
    u1 = pmc_random()
    u2 = pmc_random()
    r = sqrt(-2d0 * log(u1))
    theta = 2d0 * const%pi * u2
    z0 = r * cos(theta)
    z1 = r * sin(theta)
    ! z0 and z1 are now independent N(0,1) random variables
    ! We throw away z1, but we could use a SAVE variable to only do
    ! the computation on every second call of this function.
    rand_normal = stddev * z0 + mean
#endif
 
  end function rand_normal
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Generates a vector of normally distributed random numbers with
  !> the given means and standard deviations. This is a set of
  !> normally distributed scalars, not a normally distributed vector.
  subroutine rand_normal_array_1d(mean, stddev, val)
 
    !> Array of means.
    real(kind=dp), intent(in) :: mean(:)
    !> Array of standard deviations.
    real(kind=dp), intent(in) :: stddev(size(mean))
    !> Array of sampled normal random variables.
    real(kind=dp), intent(out) :: val(size(mean))
 
    integer :: i
 
    do i = 1,size(mean)
       val(i) = rand_normal(mean(i), stddev(i))
    end do
 
  end subroutine rand_normal_array_1d
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Sample the given continuous probability density function.
  !!
  !! That is, return a number k = 1,...,n such that prob(k) = pdf(k) /
  !! sum(pdf). Uses accept-reject.
  integer function sample_cts_pdf(pdf)
 
    !> Probability density function (not normalized).
    real(kind=dp), intent(in) :: pdf(:)
 
    real(kind=dp) :: pdf_max
    integer :: k
    logical :: found
 
    ! use accept-reject
    pdf_max = maxval(pdf)
    if (minval(pdf) < 0d0) then
       call die_msg(121838078, 'pdf contains negative values')
    end if
    if (pdf_max <= 0d0) then
       call die_msg(119208863, 'pdf is not positive')
    end if
    found = .false.
    do while (.not. found)
       k = pmc_rand_int(size(pdf))
       if (pmc_random() < pdf(k) / pdf_max) then
          found = .true.
       end if
    end do
    sample_cts_pdf = k
 
  end function sample_cts_pdf
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Sample the given discrete probability density function.
  !!
  !! That is, return a number k = 1,...,n such that prob(k) = pdf(k) /
  !! sum(pdf). Uses accept-reject.
  integer function sample_disc_pdf(pdf)
 
    !> Probability density function.
    integer, intent(in) :: pdf(:)
 
    integer :: pdf_max, k
    logical :: found
 
    ! use accept-reject
    pdf_max = maxval(pdf)
    if (minval(pdf) < 0) then
       call die_msg(598024763, 'pdf contains negative values')
    end if
    if (pdf_max <= 0) then
       call die_msg(109961454, 'pdf is not positive')
    end if
    found = .false.
    do while (.not. found)
       k = pmc_rand_int(size(pdf))
       if (pmc_random() < real(pdf(k), kind=dp) / real(pdf_max, kind=dp)) then
          found = .true.
       end if
    end do
    sample_disc_pdf = k
 
  end function sample_disc_pdf
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Convert a real-valued vector into an integer-valued vector by
  !> sampling.
  !!
  !! Use n_samp samples. Each discrete entry is sampled with a PDF
  !! given by vec_cts. This is very slow for large n_samp or large n.
  subroutine sample_vec_cts_to_disc(vec_cts, n_samp, vec_disc)
 
    !> Continuous vector.
    real(kind=dp), intent(in) :: vec_cts(:)
    !> Number of discrete samples to use.
    integer, intent(in) :: n_samp
    !> Discretized vector.
    integer, intent(out) :: vec_disc(size(vec_cts))
 
    integer :: i_samp, k
 
    call assert(617770167, n_samp >= 0)
    vec_disc = 0
    do i_samp = 1,n_samp
       k = sample_cts_pdf(vec_cts)
       vec_disc(k) = vec_disc(k) + 1
    end do
 
  end subroutine sample_vec_cts_to_disc
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Generate a random hexadecimal character.
  character function rand_hex_char()
 
    integer :: i
 
    i = pmc_rand_int(16)
    if (i <= 10) then
       rand_hex_char = achar(iachar('0') + i - 1)
    else
       rand_hex_char = achar(iachar('A') + i - 11)
    end if
 
  end function rand_hex_char
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  !> Generate a version 4 UUID as a string.
  !!
  !! See http://en.wikipedia.org/wiki/Universally_Unique_Identifier
  !! for format details.
  subroutine uuid4_str(uuid)
 
    !> The newly generated UUID string.
    character(len=PMC_UUID_LEN), intent(out) :: uuid
 
    integer :: i
 
    do i = 1,8
       uuid(i:i) = rand_hex_char()
    end do
    uuid(9:9) = '-'
    do i = 1,4
       uuid((i + 9):(i + 9)) = rand_hex_char()
    end do
    uuid(14:14) = '-'
    do i = 1,4
       uuid((i + 14):(i + 14)) = rand_hex_char()
    end do
    uuid(19:19) = '-'
    do i = 1,4
       uuid((i + 19):(i + 19)) = rand_hex_char()
    end do
    uuid(24:24) = '-'
    do i = 1,12
       uuid((i + 24):(i + 24)) = rand_hex_char()
    end do
 
    uuid(15:15) = '4'
 
    i = pmc_rand_int(4)
    if (i <= 2) then
       uuid(20:20) = achar(iachar('8') + i - 1)
    else
       uuid(20:20) = achar(iachar('A') + i - 3)
    end if
 
  end subroutine uuid4_str
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
end module pmc_rand