<div dir="ltr">Hi,<div><br></div><div>Please don't reply to digests if you want to engage in discussion :-)</div><div><br></div><div class="gmail_quote"><div dir="ltr">On Tue, Apr 5, 2016 at 2:12 PM Carl Christian Kjelgaard Mikkelsen <<a href="mailto:spock@cs.umu.se">spock@cs.umu.se</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div text="#000000" bgcolor="#FFFFFF">
<blockquote type="cite"><pre></pre>
</blockquote>
<font face="Courier New, Courier, monospace">Hello,<br>
<br>
Thank you very much for confirming that I have identified the
exact constraint functions used by cshake().<br>
<br>
Would you please consider the second part of my conjecture and
confirm if I have the correct vector equation as well? Again, even
the smallest detail, such as the exact scaling of the Lagrange
multiplier is critical. As I stated in my first email, I believe
that cshake() is solving the non linear vector equation<br>
<br>
g(rprime - inv(M)*Dg(r)*lambda) = 0<br>
<br>
where<br>
<br>
rprime is the unconstrained atomic coordinates for the next time
step<br>
r is the constrained atomic coordinates at at current time
step<br>
M is the diagonal mass matrix<br>
lambda is a Lagrange multiplier<br>
<br>
cshake return both the new constrained atomic coordinates rnew
given by<br>
<br>
rnew:=</font><font face="Courier New, Courier, monospace"><font face="Courier New, Courier, monospace">rprime -
inv(M)*Dg(r)*lambda<br>
<br>
and the vector lambda itself.<br>
<br>
</font>I am afraid that the comment in cshake() which you refer to
has been a source of confusion for me. In particular, there is no
Greek letter eta used on page 336 of the original SHAKE paper.</font></div></blockquote><div><br></div><div>Sorry, literacy problem here. I meant gamma when I wrote those docs.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div text="#000000" bgcolor="#FFFFFF"><font face="Courier New, Courier, monospace">
Moreover, I have not been able to find any evidence of any
division with the constraint distance.</font></div></blockquote><div><br></div><div>You shouldn't expect to see a transliteration of the algebra, because this is floating-point computation and division should be routinely avoided. But you should expect to see something equivalent in the code that refers to constraint_distance_squared</div><div><br></div><div>Mark</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div text="#000000" bgcolor="#FFFFFF"><br>
<font face="Courier New, Courier, monospace">Kind regards<br>
<br>
Carl Christian<br>
</font><font face="Courier New, Courier, monospace">
</font>
</div>
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