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https://issues.apache.org/jira/browse/RNG-160?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Alex Herbert updated RNG-160:
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Attachment: Gaussian.jpg
> Performance of modified Ziggurat samplers
> -----------------------------------------
>
> Key: RNG-160
> URL: https://issues.apache.org/jira/browse/RNG-160
> Project: Commons RNG
> Issue Type: Improvement
> Components: sampling
> Affects Versions: 1.4
> Reporter: Alex Herbert
> Priority: Minor
> Fix For: 1.4
>
> Attachments: Exp.jpg, Gaussian.jpg
>
>
> The modified ziggurat algorithm implemented in RNG-151 has a variation for
> sampling from the overhang regions at the ziggurat edges, region A below:
> {noformat}
> \
> ----------+\
> | \
> B |A \
> -------------+\
> | \
> {noformat}
> Note: Region B is the ziggurat layer which is entirely within the
> distribution PDF.
> These overhangs can be convex, concave or an inflection (change from convex
> to concave). Samples from the region A must be below the distribution density
> curve (PDF). When sampling from region A, the sampler will create a random
> point (x,y) uniformly within the rectangle. This is tested to determine if it
> is below the curve. Convex and concave curves can use a fast method that
> knows the largest possible triangle that fits above or below the curve. If a
> sampled point (x,y) is within these triangles then the actual curve position
> (pdf( x)) for the point x does not need to be computed. This can save time if
> the pdf is computationally expensive. In the case of exponential (exp(-x)) or
> Gaussian (exp(-0.5 * x * x)) this involves a call to Math.exp.
> The current sampler implements the fast look-up method. The alternative is to
> always compute pdf( x) and determine if y is below the curve. This is known
> as 'simple overhangs'.
> Investigate the use of simple overhangs on the performance of the sampler.
> Note: The Marsaglia version of the ziggurat sampler uses the 'simple
> overhangs' method.
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