Difference between revisions of "Numbers with a Gaussian distribution"

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(New page: {{Source}} Random number generators usually provide numbers with a uniform (flat) distribution. Sometimes it is desirable to generate numbers with some other distributions. The Gaussia...)
 
m (Slight tidy up.)
 
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{{Source}}
 
{{Source}}
[[Random number]] generators usually provide numbers with a uniform (flat)
+
[[Random_numbers |Random number generators]] usually provide numbers having a uniform (flat)
distribution. Sometimes it is desirable to generate numbers with some
+
distribution. However, sometimes it is desirable to generate numbers with some
other distributions. The Gaussian (normal) distribution is of paramount imporance.
+
other distributions. For example, the [[Gaussian distribution |Gaussian (normal) distribution]] is of paramount importance.
 
==Fortran 90 implementation==
 
==Fortran 90 implementation==
This Fortran 90 implementation is adapted from Ref. 1, based on an algorithm from the Numerical Recipes collection, Ref. 2. The function '''ran()''' calls a [[Random_numbers | randon number generator]]:
+
This Fortran 90 function is adapted from Ref. 1, based on an algorithm from the Numerical Recipes collection (Ref. 2). The function '''ran()''' calls a random number generator:
 
<small><pre>
 
<small><pre>
 
! Returns random numbers distributed following a Gaussian with
 
! Returns random numbers distributed following a Gaussian with
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==References==
 
==References==
 
# Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications" p. 411 Academic Press (1996)
 
# Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications" p. 411 Academic Press (1996)
# [http://www.nr.com Numerical Recipes]
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# [http://www.nr.com Numerical Recipes (Third Edition) website ]
  
 
[[category: random numbers]]
 
[[category: random numbers]]
 
[[category: computer simulation techniques]]
 
[[category: computer simulation techniques]]

Latest revision as of 13:31, 13 November 2007

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Random number generators usually provide numbers having a uniform (flat) distribution. However, sometimes it is desirable to generate numbers with some other distributions. For example, the Gaussian (normal) distribution is of paramount importance.

Fortran 90 implementation[edit]

This Fortran 90 function is adapted from Ref. 1, based on an algorithm from the Numerical Recipes collection (Ref. 2). The function ran() calls a random number generator:

! Returns random numbers distributed following a Gaussian with
! unit variance

function gauss()

  implicit none

  real gauss

  real v1,v2,r

  real ranmar

  do
     v1=2.0*ranmar()-1.0
     v2=2.0*ranmar()-1.0
     r=v1*v1+v2*v2
     if(r.lt.1.0) exit
  enddo

  gauss=v1*sqrt(-2.0*log(r)/r)

  return

end function gauss

References[edit]

  1. Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications" p. 411 Academic Press (1996)
  2. Numerical Recipes (Third Edition) website