Editing Random vector on a sphere
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or molecular systems. | or molecular systems. | ||
==Marsaglia algorithm== | ==Marsaglia algorithm== | ||
This is the algorithm proposed by George Marsaglia | This is the algorithm proposed by George Marsaglia (Ref. 1): | ||
*Independently generate V<sub>1</sub> and V<sub>2</sub>, taken from a uniform distribution on (-1,1) such that | *Independently generate V<sub>1</sub> and V<sub>2</sub>, taken from a uniform distribution on (-1,1) such that | ||
:<math>S=(V_1^2+V_2^2) < 1</math> | :<math>S=(V_1^2+V_2^2) < 1</math> | ||
*The random vector is then (Eq. 4 | *The random vector is then (Ref. 1 Eq. 4): | ||
:<math>\left(2V_1 \sqrt{1-S},~ 2V_2 \sqrt{1-S},~ 1-2S\right)</math> | :<math>\left(2V_1 \sqrt{1-S},~ 2V_2 \sqrt{1-S},~ 1-2S\right)</math> | ||
==Fortran 90 implementation== | ==Fortran 90 implementation== | ||
This Fortran 90 implementation is adapted from | This Fortran 90 implementation is adapted from Ref. 2. The function '''ran()''' calls a [[Random_numbers | randon number generator]]: | ||
<small><pre> | <small><pre> | ||
! The following is taken from Allen & Tildesley, p. 349 | ! The following is taken from Allen & Tildesley, p. 349 | ||
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==References== | ==References== | ||
#[http://links.jstor.org/sici?sici=0003-4851%28197204%2943%3A2%3C645%3ACAPFTS%3E2.0.CO%3B2-%23 George Marsaglia "Choosing a Point from the Surface of a Sphere", The Annals of Mathematical Statistics '''43''' pp. 645-646 (1972)] | |||
#Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications" p. 410 Academic Press (1996) | |||
# M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", p. 349 Clarendon Press (1989) | |||
[[category: random numbers]] | [[category: random numbers]] | ||
[[category: computer simulation techniques]] | [[category: computer simulation techniques]] | ||