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<div class="moz-cite-prefix">Hi,<br>
<br>
I'll just chime in and say that if there are triple bonds four
atoms will, with a rather high possibility, be on a straight line
in atomic force fields as well.<br>
<br>
Cheers,<br>
<br>
Magnus<br>
<br>
On 2017-10-29 09:18, Erik Lindahl wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAEJJM8Gwcz6-n+W54DFH6tGp5GZDoHco-Up_3f3LL3icxS2egw@mail.gmail.com">
<div dir="ltr">Hi Pavel,
<div><br>
</div>
<div>Molecular Dynamics is a chaotic process, so no matter what
precision you use the results will diverge - it will just take
a bit longer in double precision.</div>
<div><br>
</div>
<div>The reason why the method works is that we rely on sampling
phase space (with realistic dynamics) rather than making an
infinite-precision prediction of how a particle/atom will move
- remember that we anyway won't know the initial conditions
(in particular atom velocities) perfectly. For this reason,
single precision is virtually always accurate enough, apart
from a few places where we do summation of forces. One good
way to test this is to check the extent to which the total
energy is conserved.</div>
<div><br>
</div>
<div>For the dihedral formula, IIRC the reason we changed it is
that we wanted to be able to use so-called "coarse-grained"
force fields. For normal atomic force fields the four atoms
can *never* be on a straight line (since the angle potentials
are too large and will prevent that), but for coarse-grained
force fields the dihedral angles won't correspond directly to
four bonded atoms, and then they can all be very close to
linear once in a blue moon.</div>
<div><br>
</div>
<div>In that case, the scalar product between the two vectors
will be *very* close to 1 or -1. Both the way you calculate
the scalar product (where you might add a very small term to a
large one) and the behavior of the acos() function (whose
derivative approaches infinity at -1 and +1) can lead to very
large numerical errors.</div>
<div><br>
</div>
<div>Cheers,</div>
<div><br>
</div>
<div>Erik</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
</div>
<div class="gmail_extra"><br>
<div class="gmail_quote">On Sun, Oct 29, 2017 at 12:00 AM, Pavel
Panchekha <span dir="ltr"><<a
href="mailto:me@pavpanchekha.com" target="_blank"
moz-do-not-send="true">me@pavpanchekha.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="ltr">
<div class="gmail_default" style="font-size:small">Berk,
thank you for the reply. The quality of the GROMACS
source code is clear from reading it.</div>
<div class="gmail_default" style="font-size:small"><br>
</div>
<div class="gmail_default" style="font-size:small">Thank
you for explaining that the sign is not used except in
computing the angle. Do you know how much error in the
angle is acceptable? I am trying some variations on the
dihedral angle computation and seeing answers that
differ by 1e-8. Could that small a difference possibly
matter?<br>
</div>
<div class="gmail_default" style="font-size:small"><br>
</div>
<div class="gmail_default" style="font-size:small">I've
noticed that earlier versions of GROMACS used a slightly
different formula to compute <u>dih_angle</u> (using <u>acos</u>
instead of <u>atan2</u>). Did the switch cause any
known changes in behavior?<br>
</div>
</div>
<div class="gmail_extra"><br clear="all">
<div>
<div class="m_-5706029853271738848gmail_signature"
data-smartmail="gmail_signature">
<div dir="ltr">—Pavel Panchekha</div>
</div>
</div>
<br>
<div class="gmail_quote">
<div>
<div class="h5">On Sat, Oct 28, 2017 at 1:06 AM, Berk
Hess <span dir="ltr"><<a
href="mailto:hess@kth.se" target="_blank"
moz-do-not-send="true">hess@kth.se</a>></span>
wrote:<br>
</div>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>
<div class="h5">
<div text="#000000" bgcolor="#FFFFFF">
<div
class="m_-5706029853271738848m_3495107603991124129moz-cite-prefix">Hi,<br>
<br>
In molecular dynamics it's rather likely that
you hit corner cases, so we pay a lot of
attention to numerical issues when writing and
reviewing code. Therefore it is unlikely that
there are cases that can be improved, but you
are welcome to look.<br>
<br>
It is good that you mention the sign in
dihedral angle. The return value is actually
never used. The sign is only used to set the
sign of the angle, which switches at angle=0,
so there is no stability issue.<br>
<br>
Cheers,<br>
<br>
Berk
<div>
<div class="m_-5706029853271738848h5"><br>
<br>
On 10/28/2017 07:16 AM, Pavel Panchekha
wrote:<br>
</div>
</div>
</div>
<div>
<div class="m_-5706029853271738848h5">
<blockquote type="cite">
<div dir="ltr">
<div class="gmail_default"
style="font-size:small">Hello,</div>
<div class="gmail_default"
style="font-size:small"><br>
</div>
<div class="gmail_default"
style="font-size:small">I'm a student
at the University of Washington
working on numerical accuracy, and
I've been looking into GROMACS as an
example of a beloved and important
large numerical program. Browsing
through the code base, I was struck by
the computation of the dihedral angle
in <u>bonded.c</u>, at line 1569 (in
GROMACS 5.1.4).</div>
<div class="gmail_default"
style="font-size:small"><br>
</div>
<div class="gmail_default"
style="font-size:small">I wonder if it
is possible for the <u>sign</u>
variable to get the wrong value, if
the input points are close to one
another or have some other reason to
experience cancellation when doing the
cross product. I think this is fixable
using an adaptive algorithm. Could
changing the sign of the angle
computed by <u>dih_angle</u> affect
GROMACS's results?<br>
</div>
<div class="gmail_default"
style="font-size:small"><br>
</div>
<div class="gmail_default"
style="font-size:small">More broadly,
has anyone ever had numerical accuracy
issues with GROMACS? Would there be
interest in reviewing a patch that
improved the accuracy (for edge case
inputs) for the dihedral angle
computation?<br>
</div>
<div class="gmail_default"
style="font-size:small"><br
clear="all">
</div>
<div>
<div
class="m_-5706029853271738848m_3495107603991124129m_3853295731210088818gmail_signature"
data-smartmail="gmail_signature">
<div dir="ltr">—Pavel Panchekha</div>
</div>
</div>
</div>
<br>
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<div dir="ltr">
<div>
<div dir="ltr">
<div>
<div dir="ltr">
<div>
<div dir="ltr">
<div>Erik Lindahl <<a
href="mailto:erik.lindahl@dbb.su.se"
target="_blank" moz-do-not-send="true">erik.lindahl@dbb.su.se</a>></div>
<div>Professor of Biophysics, Dept. Biochemistry
& Biophysics, Stockholm University</div>
<div>Science for Life Laboratory, Box 1031,
17121 Solna, Sweden</div>
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