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Re: Re: normal distribution random number generation
*To*: mathgroup at smc.vnet.net
*Subject*: [mg51267] Re: [mg51217] Re: normal distribution random number generation
*From*: DrBob <drbob at bigfoot.com>
*Date*: Mon, 11 Oct 2004 01:25:26 -0400 (EDT)
*References*: <ck0ccp$o1u$1@smc.vnet.net> <200410090818.EAA09618@smc.vnet.net> <opsfm2itcmiz9bcq@monster.cox-internet.com> <95492AA4-1AD1-11D9-BEB1-000A95B4967A@mimuw.edu.pl>
*Reply-to*: drbob at bigfoot.com
*Sender*: owner-wri-mathgroup at wolfram.com
I really didn't contribute enough to earn a mention, Andrzej.
I'm still scratching my head trying to eliminate the named helper function.
Bobby
On Mon, 11 Oct 2004 00:32:23 +0900, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
> I have put on both my web sites a new version of the Random[] fix
> incorporating the ideas of Ray and Bob. The package is now called
> RadnomReplacement.m and is a proper Mathematica package, which defines
> its own context: RandomReplacement`. When loaded, it will replace the
> built in Random[] function with one based on the Wolfram CA algorithm.
>
> I have also put on the same page another "package' called
> MarsagliaNormal.m which changes the definition of the normal
> distribution generator in the Statistics`NormalDistribution` package to
> that of Marsaglia's. This is not a "true package", in that it does not
> define any new contexts, and has to be read in using Get and its full
> name including the extension *.m. It can be read in after or before the
> Statistics`NormalDistribution` package. In the latter case it will
> automatically load the package and seamlessly redifine the normal
> generator. Doing this seems to have two advantages. It seems to be
> marginally faster than the Box-Muller generator, though this may be
> hardware dependent. It also seems to "eliminate' the problem caused by
> "insufficient randomness' of Random[] so if one is dealing only with
> normally distributed quantities it may not be necessary to read in the
> RandomReplacement package.
>
> Andrzej
>
>
> On 10 Oct 2004, at 14:21, DrBob wrote:
>
>>
>> I'm trying to combine that idea with Andrzej Kozlowski's recent fix
>> for Random, and here's what I came up with:
>>
>> Unprotect[Random];
>> With[{m1 = 1/(2.^30 - 1.), m2 = 2^30 - 2},
>> randomSubstitutionFunction =
>> Compile[{}, ((Random[Integer, m2] + .5)*m1 + Random[Integer,
>> m2])*m1];
>> Random[] := randomSubstitutionFunction[]
>> ]
>> Random[Real, {a_Real, b_Real}] := a + Random[]*(b - a)
>> Random[Real, b_Real] := Random[Real, {0, b}]
>> Random[Real] := Random[Real, {0, 1}]
>> Random[Complex, {a_Complex | a_Real | a_Integer, b_Complex | b_Real | \
>> b_Integer}] := a + Random[]*Re[(b - a)] + Random[]*Im[(b - a)]*I
>> Random[Complex] := Random[Complex, {0, 1 + I}]
>> Protect[Random];
>>
>> I wanted NOT to use a Global (randomSubstitutionFunction) for the
>> Compiled function, but I haven't stumbled on a way to manage it.
>>
>> Bobby
>>
>> On Sat, 9 Oct 2004 04:18:30 -0400 (EDT), Ray Koopman <koopman at sfu.ca>
>> wrote:
>>
>>> Bill Rowe <readnewsciv at earthlink.net> wrote in message
>>> news:<ck0ccp$o1u$1 at smc.vnet.net>...
>>>> [...]
>>>> you will have modified Random to use the Wolfram rule 30 cellular
>>>> automaton and avoid the subtract with borrow algorithm. The main
>>>> consequence of this is Random will now be considerably slower.
>>>> [...]
>>>
>>> If time is an issue, you might want to consider generating integers
>>> on 0...2^n-2 instead of 0...2^n-1. It's always much faster. And if
>>> you're willing to spend a little of the time you've saved, you can
>>> add a half and avoid ever having to worry about getting a zero.
>>>
>>> In[1]:= ToString[TableForm[Table[With[{m1 = 2^n - 1, m2 = 2^n - 2},
>>> {n, First[Timing[Do[Random[Integer,m1],{1*^6}]]]/.Second->1.,
>>>
>>> First[Timing[Do[Random[Integer,m2],{1*^6}]]]/.Second->1.}],
>>> {n,2,30}],TableSpacing->{0,2}]]
>>>
>>> Out[1]= 2 1.96 1.42
>>> 3 2.12 1.5
>>> 4 2.38 1.61
>>> 5 2.66 1.73
>>> 6 2.91 1.86
>>> 7 3.16 2.
>>> 8 3.41 2.1
>>> 9 3.68 2.19
>>> 10 3.92 2.35
>>> 11 4.21 2.56
>>> 12 4.5 2.68
>>> 13 4.79 2.82
>>> 14 5.07 3.02
>>> 15 5.34 3.08
>>> 16 5.56 3.26
>>> 17 5.84 3.38
>>> 18 6.09 3.53
>>> 19 6.33 3.64
>>> 20 6.57 3.77
>>> 21 6.84 3.87
>>> 22 7.1 4.03
>>> 23 7.33 4.2
>>> 24 7.63 4.25
>>> 25 7.89 4.37
>>> 26 8.15 4.56
>>> 27 8.4 4.61
>>> 28 8.56 4.79
>>> 29 8.95 4.95
>>> 30 9.16 5.07
>>>
>>> In[2]:= ran1 = With[{m = 2.^-30, m1 = 2^30 - 1},
>>> Compile[{},(Random[Integer,m1]*m + Random[Integer,m1])*m]];
>>>
>>> In[3]:= ran2 = With[{m1 = 1/(2.^30 - 1.), m2 = 2^30 - 2},
>>> Compile[{},(Random[Integer,m2]*m1 + Random[Integer,m2])*m1]];
>>>
>>> In[4]:= ran2h = With[{m1 = 1/(2.^30 - 1.), m2 = 2^30 - 2},
>>>
>>> Compile[{},((Random[Integer,m2]+.5)*m1+Random[Integer,m2])*m1]];
>>>
>>> In[5]:= First/@{Timing@Do[ran1[],{1*^5}],Timing@Do[ran2[],{1*^5}],
>>> Timing@Do[ran2h[],{1*^5}]}
>>> Out[5]= {2.03 Second, 1.05 Second, 1.08 Second}
>>>
>>>
>>>
>>>
>>
>>
>>
>> --
>> DrBob at bigfoot.com
>> www.eclecticdreams.net
>>
>
>
>
>
--
DrBob at bigfoot.com
www.eclecticdreams.net
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