Re: [ESPResSo] bug in random.tcl in mbtools

[duenweg]

Hello,

indeed, to underline once again what Markus
already wrote: "My" procedure is not for
Gaussian RNs, but for RNs uniform on the
sphere. Markus' version (or Torsten's)
is an alternative, and if Torsten says
this is faster, I believe him.

For Gaussian RNs, one may use the so-called
Box-Muller algorithm, described, for example,
in Numerical Recipes. This has NOTHING to
do with uniformity on a sphere!

Regards
Burkhard.


> Hi all,
>
> to generate Random Walk Polymers (polymer-command), ESPResSo (internally)
> uses the following algorithm to generate homogeneously distributed points
> on the surface of a sphere with radius=bond_length:
>
>          zz     = (2.0*d_random()-1.0)*bond_length;
>          rr     = sqrt(SQR(bond_length)-SQR(zz));
>          phi    = 2.0*PI*d_random();
>          x      = rr*cos(phi);
>          y      = rr*sin(phi);
>          z      = zz;
>
> The advantage of this algorithm is, that it needs only two random
> numbers and you never have to throw away any numbers.
> Experience has shown, that on modern CPUs this algorithm runs faster
> than the one Burkhard proposed.
> It is based on the (not very intuitive) fact, that the projection of
> homogeneously distributed points on a sphere-surface onto any axis gives a
> normal distribution of points on that axis (a prove of that can be found
> in math books).
>
> Greetings,
> Torsten
>
>
> Tristan Bereau wrote:
>> Hello,
>>
>> I'm not sure whether a gaussian random number generator has already
>> been implemented in the TCL shell of ESPResSo, but if not, there is a
>> couple of methods described at the end of the "Old Testament" of
>> molecular simulations (i.e. Allen and Tildesley), and Burkhard's is
>> one of them.
>>
>> Best,
>>
>> Tristan
>>
>>
>> On Mar 19, 2009, at 4:52 AM, Jacob Kirkensgaard wrote:
>>
>>> Hi again
>>>
>>> Thanks to Tristan and Burkhard - you are of course right. For my
>>> purposes my suggestion is sufficient but I will see if I have time
>>> to implement a small routine to do it properly as outlined by
>>> Burkhard. Is there a routine for generating Gaussian random numbers?
>>> As Tristan mentioned this would be a quick way to solve the issue.
>>>
>>> Best,
>>> Jacob
>>>
>>>
>>>
>>> On Mar 19, 2009, at 9:40 AM, address@hidden wrote:
>>>
>>>> Hello,
>>>>
>>>> from Tristan's remarks I understand that there
>>>> is a question of how to get random numbers
>>>> uniformly in or on a sphere? If so, let me tell
>>>> you one possible answer:
>>>>
>>>> 1. You first draw 3 RNs u_1, u_2, u_3 from [0:1]
>>>> 2. Then you transform u_1 = 2 * u_1 - 1 etc.,
>>>>  resulting in RNs in [-1,1]
>>>> 3. Calculate r2 = u_1**2 + u_2**2 + u_3**2
>>>> 4. If r2 > 1 --> throw everything away,
>>>>  go to step 1, try again
>>>> 5. If r2 < 1: Either you are done (supposing
>>>>  that you want RN IN the sphere), or you set
>>>>  norm = 1 / sqrt(r2)
>>>>  u_1 = u_1 * norm etc.
>>>>  By this you project the output onto the
>>>>  surface of the unit sphere, so you get
>>>>  something ON the sphere.
>>>>
>>>> If that was trivial: Please accept my apologies
>>>> for bothering you.
>>>>
>>>> Regards
>>>> Burkhard.
>>>>
>>>>
>>>>
>>>>
>>>
>>
>>
>> _______________________________________________
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>> address@hidden
>> https://fias.uni-frankfurt.de/mailman/listinfo/espresso
>>
>
>
> --
> Dr. Torsten Stühn
> MPI für Polymerforschung
> Ackermannweg 10
> 55128 Mainz / Germany
>
> Tel.  +49-(0)6131-379268
> Fax   +49-(0)6131-379100
> EMail address@hidden
>
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