Hi Amey.
On Wed, 7 Jun 2017 01:15:01 +0530, Amey Jadiye wrote:
> Hi,
>
> Gamma class is written keeping in mind that it should handle fair
> situation
> (if n < 20) it computes with normal gamma function else it uses
> LanczosApproximation
> for higher numbers, for now I think we should keep it behaviour as
it
> is
> and do just code segrigation, by segregation of there
functionalities
> we
> are making it switchable so Gamma class by optional providing
> constructor
> args of Lanzoz, Stinling or Spouge's algo, same thing we have to
do
> in
> Math's Gamma distribution.
>
> Ex.
> Gamma g = Gamma(Algo.LANCZOS));
Just from the look of it, it is difficult to figure out whether
alternative algorithms are useful when numbers are represented
as 64-bits "double".
If you are willing to go that route, you should provide code that
shows the advantages (speed and/or precision).
Now, if we want to support an arbirary precision number type[1],
then the alternate algorithms that can provide accuracy below
~1e-16 would certainly be worth considering.[2]
> I'd like other people from group chime in discussion.
Regards,
Gilles
[1] See the "Dfp" class in CM's "o.a.c.math4.dfp" package.
[2] But IMO this should be postponed to after 1.0 since there
is perhaps a need of a general discussion about designing
high-precision algorithms (and whether there are volunteers
to develop and support them in the long term).
I may be wrong, but somehow I have the intuition that people
requiring those functionalities might not be using Java...
>
> Regards,
> Amey
>
> On Tue, Jun 6, 2017 at 3:31 AM, Gilles
<gil...@harfang.homelinux.org>
> wrote:
>
>> On Tue, 6 Jun 2017 01:14:38 +0530, Amey Jadiye wrote:
>>
>>> Hi All,
>>>
>>> Coming from discussion happened here
>>> https://issues.apache.org/jira/browse/NUMBERS-38
>>>
>>> As Gamma is nothing but advanced factorial function
gamma(n)=(n-1)!
>>> with
>>> advantages like we can have factorial of whole numbers as well
as
>>> factional. Now as [Gamma functions (
>>> https://en.wikipedia.org/wiki/Gamma_function ) which is having
>>> general
>>> formula {{Gamma( x ) = integral( t^(x-1) e^(-t), t = 0 ..
>>> infinity)}} is a
>>> plane old base function however Lanczos approximation /
Stirling's
>>> approximation /Spouge's Approximation *is a* gamma function so
>>> they
>>> should
>>> be extend Gamma.
>>>
>>> Exact algorithm and formulas here :
>>> - Lanczo's Approximation -
>>> https://en.wikipedia.org/wiki/Lanczos_approximation
>>> - Stirling's Approximation -
>>> https://en.wikipedia.org/wiki/Stirling%27s_approximation
>>> - Spouge's Approximation -
>>> https://en.wikipedia.org/wiki/Spouge%27s_approximation
>>>
>>> Why to refactor code is because basic gamma function computes
not
>>> so
>>> accurate/precision values so someone who need quick computation
>>> without
>>> precision can choose it, while someone who need precision overs
>>> cost of
>>> performance (Lanczos approximation is accurate so its slow takes
>>> more cpu
>>> cycle) can choose which algorithm they want.
>>>
>>> for some scientific application all values should be computed
with
>>> great
>>> precision, with out Gamma class no choice is given for choosing
>>> which
>>> algorithm user want.
>>>
>>> I'm proposing to create something like:
>>>
>>> Gamma gammaFun = new Gamma(); gammaFun.value( x );
>>> Gamma gammaFun = new LanczosGamma(); gammaFun.value( x );
>>> Gamma gammaFun = new StirlingsGamma(); gammaFun.value( x );
>>> Gamma gammaFun = new SpougesGamma(); gammaFun.value( x );
>>>
>>> Also as the class name suggestion {{LanczosApproximation}} it
>>> should
>>> execute/implement full *Lanczos Algoritham* but we are just
>>> computing
>>> coefficients in that class which is incorrect, so just
refactoring
>>> is
>>> needed which wont break any dependency of this class anywhere.
>>> (will
>>> modify
>>> code such way).
>>>
>>> let me know your thoughts?
>>>
>>>
>> I've added a comment (about the multiple implementations) on the
>> JIRA page.
>>
>> I agree that if the class currently named "LanczosApproximation"
is
>> not what the references define as "Lanczos' approximation", it
>> should
>> be renamed.
>> My preference would be to "hide" it inside the "Gamma" class, if
we
>> can sort out how to modify the "GammaDistribution" class (in
Commons
>> Math) accordingly.
>>
>> Regards,
>> Gilles
>>
>>
