The Sobol sequence is a low-discrepancy sequence that can be used for more efficient (Quasi-)Monte-Carlo integration.

This repository contains a module, mod_sobseq.f90, which can be used to generate points in Sobol series, in a continuous or strided (2**n) manner.

To generate sobol sequences in many dimensions, direction numbers are needed. A good set of these was made by Joe and Kuo. The direction numbers for the first eight are reproduced here, and more can be found at the link above.

integer, parameter, dimension(1:12)   :: s = (/1,2,3,3,4,4,5,5,5,5,5,5/)
integer, parameter, dimension(1:12)   :: a = (/0,1,1,2,1,4,2,4,7,11,13,14/)
integer, parameter, dimension(5,1:12) :: m = reshape((/1,0,0,0,0, &
					1,3,0,0,0, &
					1,3,1,0,0, &
					1,1,1,0,0, &
					1,1,3,3,0, &
					1,3,5,13,0,&
					1,1,5,5,17,&
					1,1,5,5,5,&
					1,1,7,11,19,&
					1,1,5,1,1,&
					1,1,1,3,11,&
					1,3,5,5,31/), (/5,12/))

The following code snippet contains a small example.

integer, parameter :: n_dim=9
integer, parameter :: n_samples=200
type(sobol_state), dimension(n_dim) :: rng
integer :: i, j
real :: u(n_dim)

! Initialization
do i=1,n_dim
  call rng%initialize(s(i), a(i), m(:,i))
end do

! Generation
do j=1,n_samples
  do i=1,n_dim
    u(i) = rng(i)%next()
  end do

  ! do something with u
end do

The module also contains functions for generating numbers in a strided manner, which is useful for parallel operation. To use this, set n_streams to the 2-logarithm of the number of streams you want (if n_streams is not a power of 2 you might get distribution problems) and use the rng%next_strided() generator.

• Daan van Vugt [email protected]
• Koen Beljaars [email protected]

This work is released under the MIT license. A copy can be found in the file LICENSE in the repository.