[gmx-users] shake for water

[Berk Hess]

Hi,

I don't agree.
It uses the small 1+a approximation for the square.
Also mdrun prints the rmsd determined with independent code,
which is consistent with the (correct) tolerance.

Berk

> Date: Thu, 5 Feb 2009 22:41:47 +0100
> From: spoel at xray.bmc.uu.se
> To: gmx-users at gromacs.org
> Subject: Re: [gmx-users] shake for water
> 
> Berk Hess wrote:
> > 
> > 
> >  > Date: Thu, 5 Feb 2009 19:35:09 +0100
> >  > From: spoel at xray.bmc.uu.se
> >  > To: gmx-users at gromacs.org
> >  > Subject: Re: [gmx-users] shake for water
> >  >
> >  > David Mobley wrote:
> >  > > All,
> >  > >
> >  > > A quick question on constraints... I'm using TIP4P-Ew in gromacs 3.3.2
> >  > > and am concerned with reproducing energies from another code very
> >  > > precisely for several specific snapshots. I am doing a zero-step mdrun
> >  > > of a setup with one small molecule and two tip4p-ew water molecules.
> >  > >
> >  > > Anyway, I have set the shake tolerance to 1e-12 in the mdp file, but
> >  > > to my surprise the internal water distances are good only to 1e-06 and
> >  > > 1e-07. Is this expected behavior? Note that I am running in double
> >  > > precision. I assumed that, er, the distances should converge to the
> >  > > shake tolerance.
> >  > Well, the documentation might be lacking, but the code tells the truth.
> >  > It seems that the tolerance is used on the distance squared, which is
> >  > consistent with your observation of a precision of 1e-6. So try 1e-24.
> > 
> > No, it is not the square.
> > The code does a small 'a' approximation: (1+a)^2=1+2a+a^2 is approx 1+2a.
> > I have also tested/benchmark shake in gromacs for my first lincs paper
> > and the plincs paper and it always behaved the way I thought it would.
> 
> 
> First we compute the inverse square of the shake distance dA in tt[ll] 
> for each shake pair:
> 
>      if (bFEP)
>        toler = sqr(L1*ip[type].shake.dA + lambda*ip[type].shake.dB);
>      else
>        toler = sqr(ip[type].shake.dA);
>      dist2[ll] = toler;
>      tt[ll] = 1.0/(toler*tol2);
>    }
> 
> Then in the shake iteration we compute the difference between the 
> squared distances (variable diff below):
> 
>        tx      = xp[ix]-xp[jx];
>        ty      = xp[iy]-xp[jy];
>        tz      = xp[iz]-xp[jz];
>        rpij2   = tx*tx+ty*ty+tz*tz;
>        toler   = dist2[ll];
>        diff    = toler-rpij2;
> 
> Now we multiply the diff with tt[ll], in other words we get
> iconv = (1-rpij2/dist2)/(2 tol)
> 
>        /* iconv is zero when the error is smaller than a bound */
>        iconv   = fabs(diff)*tt[ll];
> 
> In other words, the tolerance operates on the squared distance.
> 
> 
> 
> 
> > 
> > The problem is not that you need more iterations than 1000?
> > 
> > And why not use settle that does it right at full precision at once?
> > 
> > Berk
> > 
> > 
> >  >
> >  > >
> >  > > Thanks,
> >  > > David
> >  > > _______________________________________________
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> >  >
> >  > --
> >  > David van der Spoel, Ph.D., Professor of Biology
> >  > Molec. Biophys. group, Dept. of Cell & Molec. Biol., Uppsala University.
> >  > Box 596, 75124 Uppsala, Sweden. Phone: +46184714205. Fax: +4618511755.
> >  > spoel at xray.bmc.uu.se spoel at gromacs.org http://folding.bmc.uu.se
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> 
> -- 
> David van der Spoel, Ph.D., Professor of Biology
> Molec. Biophys. group, Dept. of Cell & Molec. Biol., Uppsala University.
> Box 596, 75124 Uppsala, Sweden. Phone:	+46184714205. Fax: +4618511755.
> spoel at xray.bmc.uu.se	spoel at gromacs.org   http://folding.bmc.uu.se
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