Random vector on a sphere

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

Marsaglia algorithm[edit]

This is the algorithm proposed by George Marsaglia [1]

  • Independently generate V1 and V2, taken from a uniform distribution on (-1,1) such that
S=(V_1^2+V_2^2) < 1
  • The random vector is then (Eq. 4 in [1] ):
\left(2V_1 \sqrt{1-S},~ 2V_2 \sqrt{1-S},~ 1-2S\right)

Fortran 90 implementation[edit]

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[edit]

External links[edit]

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