Random vector on a sphere

From SklogWiki
Revision as of 12:34, 21 October 2010 by Carl McBride (talk | contribs) (Slight tidy)
Jump to navigation Jump to search

The ability to generate a randomly orientated vector is very useful in Monte Carlo simulations of anisotropic models or molecular systems.

Marsaglia algorithm

This is the algorithm proposed by George Marsaglia [1]

  • Independently generate V1 and V2, taken from a uniform distribution on (-1,1) such that
  • The random vector is then (Eq. 4 in [1] ):

Fortran 90 implementation

This Fortran 90 implementation is adapted from Refs. [2] and [3]. The function ran() calls a randon number generator:

!    The following is taken from Allen & Tildesley, p. 349
!    Generate a random vector towards a point in the unit sphere
!    Daniel Duque 2004

subroutine random_vector(vctr)

  implicit none

  real, dimension(3) :: vctr

  real:: ran1,ran2,ransq,ranh
  real:: ran

  do
     ran1=1.0-2.0*ran()
     ran2=1.0-2.0*ran()
     ransq=ran1**2+ran2**2
     if(ransq.le.1.0) exit
  enddo

  ranh=2.0*sqrt(1.0-ransq)

  vctr(1)=ran1*ranh
  vctr(2)=ran2*ranh
  vctr(3)=(1.0-2.0*ransq)

end subroutine random_vector

References

This page contains computer source code. If you intend to compile and use this code you must check for yourself the validity of the code. Please read the SklogWiki disclaimer.