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    <div class="moz-cite-prefix">Hi,<br>
      <br>
      I don't see why your current code doesn't work with 1D DD.<br>
      <br>
      You do call this code after the coordinate communication has been
      done?<br>
      <br>
      Cheers,<br>
      <br>
      Berk<br>
      <br>
      On 08/28/2015 05:45 PM, Xingcheng Lin wrote:<br>
    </div>
    <blockquote
cite="mid:CAPugp-ERa9LAy9ijh18rGfLH4+8K8uG_3i5wg-=J9fc9iAbbnA@mail.gmail.com"
      type="cite">
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        <div>
          <div>Hi Berk,<br>
            <br>
          </div>
          The 1D dd where I used 2 MPI processes with -dd 1 1 2 can only
          work if I do not turn on the -dlb yes. It seems the problem
          will always exist if I have atom pairs separated in two
          domains.<br>
          <br>
        </div>
        You mentioned I could get all pairs by only looking at home
        atoms for the i-atoms. Does it mean I can even make the code
        like this, by changing ga2la_get for aj to ga2la_get_home?<br>
        <br>
        // NP is number of tested pairs recorded in an array;<br>
        // If atom ai is one of the home atoms in a node, we start
        testing if aj is<br>
        available by the same node;<br>
        // rlist = 1.0nm, Coulombtype  =  Cut-off, cutoff-scheme =
        Verlet, ns_type<br>
        = grid, pbc = xyz;<br>
        <br>
        int Npairs = 0;<br>
        for (i=0; i&lt;NP; ++i)<br>
        {<br>
             int ai = datai[i] ;<br>
             int localai;<br>
             // Examine if ai it is within the home atoms index;<br>
             if (ga2la_get_home(cr-&gt;dd-&gt;ga2la, ai, &amp;localai))<br>
             {<br>
                aj = dataj[i] ;<br>
                // Examine if aj is available by local node;;<br>
                if (ga2la_get_home(cr-&gt;dd-&gt;ga2la, aj,
        &amp;localaj))<br>
                {<br>
                   FILE *fp;<br>
                   fp = fopen("pairs.dat","a");<br>
        <br>
                   fprintf(fp, "%d\t%d\n", ai, aj);<br>
                   fclose(fp);<br>
        <br>
                   r_N = 0.6 ;<br>
                   pbc_dx(&amp;pbc, x[localai], x[localaj], dx) ;<br>
                   dr2 = iprod( dx, dx ) ;<br>
                   dr  = sqrt( dr2 ) ;<br>
                   if (dr &lt; r_N)<br>
                   {<br>
                       Npairs += 1;<br>
                   }<br>
                }<br>
             }<br>
         }<br>
        <div>
          <div><br>
            <div>
              <div class="gmail_extra"><br>
                <div class="gmail_quote">On Fri, Aug 28, 2015 at 2:22
                  AM, <span dir="ltr">&lt;<a moz-do-not-send="true"
                      href="mailto:gromacs.org_gmx-developers-request@maillist.sys.kth.se"
                      target="_blank">gromacs.org_gmx-developers-request@maillist.sys.kth.se</a>&gt;</span>
                  wrote:<br>
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                    <br>
                    Today's Topics:<br>
                    <br>
                       1. Increase the scope of dd domains (Xingcheng
                    Lin)<br>
                       2. Re: energy group computation (Berk Hess)<br>
                       3. Re: dhdl expanded ensemble (Berk Hess)<br>
                       4. Re: Increase the scope of dd domains (Berk
                    Hess)<br>
                    <br>
                    <br>
----------------------------------------------------------------------<br>
                    <br>
                    Message: 1<br>
                    Date: Thu, 27 Aug 2015 23:35:30 -0500<br>
                    From: Xingcheng Lin &lt;<a moz-do-not-send="true"
                      href="mailto:linxingcheng50311@gmail.com">linxingcheng50311@gmail.com</a>&gt;<br>
                    To: <a moz-do-not-send="true"
                      href="mailto:gromacs.org_gmx-developers@maillist.sys.kth.se">gromacs.org_gmx-developers@maillist.sys.kth.se</a><br>
                    Subject: [gmx-developers] Increase the scope of dd
                    domains<br>
                    Message-ID:<br>
                            &lt;CAPugp-HQjXb8hYKJO9i-1fMSfpzQxe=<a
                      moz-do-not-send="true"
                      href="mailto:qZCOo8tPwPQrFraKEmw@mail.gmail.com"><a class="moz-txt-link-abbreviated" href="mailto:qZCOo8tPwPQrFraKEmw@mail.gmail.com">qZCOo8tPwPQrFraKEmw@mail.gmail.com</a></a>&gt;<br>
                    Content-Type: text/plain; charset="utf-8"<br>
                    <br>
                    Hi,<br>
                    <br>
                    I am trying to encode a "on the fly" calculation for
                    the number of atom<br>
                    pairs within some distance (for example here, 6
                    angstroms).<br>
                    <br>
                    The problem happens when doing parallel domain
                    decomposition. Specifically,<br>
                    when two particles reside in different domains,
                    gromacs is not able to<br>
                    recognize this pair. I am trying to use
                    ga2la_get_home and ga2la_get for<br>
                    calculation, here is the code:<br>
                    <br>
                    // NP is number of tested pairs recorded in an
                    array;<br>
                    // If atom ai is one of the home atoms in a node, we
                    start testing if aj is<br>
                    available by the same node;<br>
                    // rlist = 1.0nm, Coulombtype  =  Cut-off,
                    cutoff-scheme = Verlet, ns_type<br>
                    = grid, pbc = xyz;<br>
                    <br>
                    int Npairs = 0;<br>
                    for (i=0; i&lt;NP; ++i)<br>
                    {<br>
                         int ai = datai[i] ;<br>
                         int localai;<br>
                         // Examine if ai it is within the home atoms
                    index;<br>
                         if (ga2la_get_home(cr-&gt;dd-&gt;ga2la, ai,
                    &amp;localai))<br>
                         {<br>
                            aj = dataj[i] ;<br>
                            // Examine if aj is available by local
                    node;;<br>
                            if (ga2la_get(cr-&gt;dd-&gt;ga2la, aj,
                    &amp;localaj, &amp;localcell))<br>
                            {<br>
                               FILE *fp;<br>
                               fp = fopen("pairs.dat","a");<br>
                    <br>
                               fprintf(fp, "%d\t%d\n", ai, aj);<br>
                               fclose(fp);<br>
                    <br>
                               r_N = 0.6 ;<br>
                               pbc_dx(&amp;pbc, x[localai], x[localaj],
                    dx) ;<br>
                               dr2 = iprod( dx, dx ) ;<br>
                               dr  = sqrt( dr2 ) ;<br>
                               if (dr &lt; r_N)<br>
                               {<br>
                                   Npairs += 1;<br>
                               }<br>
                            }<br>
                         }<br>
                     }<br>
                    <br>
                    The results show some atom pairs, while atoms less
                    than 6 angstroms apart,<br>
                    are missing here. I increase rlist, but it doesn't
                    help. Is there any way<br>
                    to increase the scope of atoms available in each
                    domain so that the missing<br>
                    atoms can be detected?<br>
                    <br>
                    Or are there any mistakes out of my notice in this
                    code?<br>
                    <br>
                    Thank you,<br>
                    Xingcheng<br>
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                    <br>
                    ------------------------------<br>
                    <br>
                    Message: 2<br>
                    Date: Fri, 28 Aug 2015 09:04:56 +0200<br>
                    From: Berk Hess &lt;<a moz-do-not-send="true"
                      href="mailto:hess@kth.se">hess@kth.se</a>&gt;<br>
                    To: <a moz-do-not-send="true"
                      href="mailto:gmx-developers@gromacs.org">gmx-developers@gromacs.org</a><br>
                    Subject: Re: [gmx-developers] energy group
                    computation<br>
                    Message-ID: &lt;<a moz-do-not-send="true"
                      href="mailto:55E00818.1060601@kth.se">55E00818.1060601@kth.se</a>&gt;<br>
                    Content-Type: text/plain; charset="windows-1252";
                    Format="flowed"<br>
                    <br>
                    Hi,<br>
                    <br>
                    This is a use, not a development question. Please
                    post such questions to<br>
                    gmx-users.<br>
                    <br>
                    But the quick answer is that although it's
                    technically possible to<br>
                    calculate this number, this number is useless (and
                    indeed high).<br>
                    <br>
                    Cheers,<br>
                    <br>
                    Berk<br>
                    <br>
                    On 2015-08-27 19:00, ANTHONY C MANSON wrote:<br>
                    &gt; Hello:<br>
                    &gt;<br>
                    &gt; I am trying to estimate the polar solvation
                    energy of a 76 residue<br>
                    &gt; protein at standard conditions.  I am using the
                    gromacs 4.5.3 dp release.<br>
                    &gt; I have set up a simulation with the solvated 
                    (using spce water) protein.<br>
                    &gt; I have defined two energygrps: Protein SOL in
                    the *.mdp file.<br>
                    &gt; I have run the simulation and have then run
                    g_energy on the *.edr file.<br>
                    &gt; I get the following choices from g_energy:<br>
                    &gt;<br>
                    &gt;   1  Bond       2  Angle            3 
                    Proper-Dih.      4  Improper-Dih.<br>
                    &gt;   5  LJ-14      6  Coulomb-14       7  LJ-(SR) 
                            8  Disper.-corr.<br>
                    &gt; 9  Coulomb-(SR)    10  Coul.-recip.    11 
                    Potential       12<br>
                    &gt;  Kinetic-En.<br>
                    &gt;  13  Total-Energy    14  Temperature     15 
                    Pres.-DC        16  Pressure<br>
                    &gt;  17  Vir-XX        18  Vir-XY          19 
                    Vir-XZ          20  Vir-YX<br>
                    &gt;  21  Vir-YY  22  Vir-YZ          23  Vir-ZX   
                        24  Vir-ZY<br>
                    &gt;  25  Vir-ZZ          26  Pres-XX         27 
                    Pres-XY   28  Pres-XZ<br>
                    &gt;  29  Pres-YX         30  Pres-YY   31  Pres-YZ 
                           32  Pres-ZX<br>
                    &gt;  33  Pres-ZY   34  Pres-ZZ         35 
                    #Surf*SurfTen   36  Mu-X<br>
                    &gt;  37  Mu-Y              38  Mu-Z<br>
                    &gt;  39  Coul-SR:Protein-Protein         40 
                    LJ-SR:Protein-Protein<br>
                    &gt;  41  Coul-14:Protein-Protein             42 
                    LJ-14:Protein-Protein<br>
                    &gt;  43  Coul-SR:Protein-SOL   44 
                    LJ-SR:Protein-SOL<br>
                    &gt;  45  Coul-14:Protein-SOL             46 
                    LJ-14:Protein-SOL<br>
                    &gt;  47  Coul-SR:SOL-SOL     48  LJ-SR:SOL-SOL<br>
                    &gt;  49  Coul-14:SOL-SOL                     50 
                    LJ-14:SOL-SOL<br>
                    &gt;  51  T-System<br>
                    &gt;<br>
                    &gt; I pick Coul-SR:Protein-SOL as a component of
                    the polar solvation energy.<br>
                    &gt; I note that the energy magnitude seems
                    extremely high:<br>
                    &gt;<br>
                    &gt; Energy              Average   Err.Est.   
                     RMSD  Tot-Drift<br>
                    &gt;
-------------------------------------------------------------------------------<br>
                    &gt; Coul-SR:Protein-SOL        -8343.86         46 
                      193.457  -192.93<br>
                    &gt;  (kJ/mol)<br>
                    &gt;<br>
                    &gt; This seems unreasonable to me.  I wanted to
                    understand how mdrun<br>
                    &gt; was calculating this value.  Perhaps it is
                    accumulating energies over<br>
                    &gt; many frames.  What part of the code (force.c
                    ...) handles this<br>
                    &gt; calculation so I can verify its action.<br>
                    &gt;<br>
                    &gt; Also, I tried running g_enemat on this with the
                    following groups.dat file.<br>
                    &gt;<br>
                    &gt; 2<br>
                    &gt; Protein<br>
                    &gt; SOL<br>
                    &gt;<br>
                    &gt; I use the command:<br>
                    &gt;<br>
                    &gt; g_enemat  -f ub_short.edr -e 100<br>
                    &gt;<br>
                    &gt; and get:<br>
                    &gt;<br>
                    &gt; Opened ub_short.edr as double precision energy
                    file<br>
                    &gt; Will read groupnames from in! putfile<br>
                    &gt; Read 2 groups<br>
                    &gt; group 0WARNING! could not find group
                    (null):Protein-Protein (0,0)in<br>
                    &gt; energy file<br>
                    &gt; WARNING! could not find group
                    (null):Protein-SOL (0,1)in energy file<br>
                    &gt; group 1WARNING! could not find group
                    (null):SOL-SOL (1,1)in energy file<br>
                    &gt;<br>
                    &gt; Will select half-matrix of energies with 6
                    elements<br>
                    &gt; Read frame: 1000, Time: 100.000e  100.000<br>
                    &gt; Will build energy half-matrix of 2 groups, 6
                    elements, over 1001 frames<br>
                    &gt; Segmentation fault<br>
                    &gt;<br>
                    &gt;<br>
                    &gt; Cheers<br>
                    &gt; Anthony Manson Ph.D.<br>
                    &gt;<br>
                    &gt;<br>
                    <br>
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                    <br>
                    ------------------------------<br>
                    <br>
                    Message: 3<br>
                    Date: Fri, 28 Aug 2015 09:09:49 +0200<br>
                    From: Berk Hess &lt;<a moz-do-not-send="true"
                      href="mailto:hess@kth.se">hess@kth.se</a>&gt;<br>
                    To: <a moz-do-not-send="true"
                      href="mailto:gmx-developers@gromacs.org">gmx-developers@gromacs.org</a>,
                    "<a moz-do-not-send="true"
                      href="mailto:michael.shirts@virginia.edu">michael.shirts@virginia.edu</a>"<br>
                            &lt;<a moz-do-not-send="true"
                      href="mailto:michael.shirts@virginia.edu">michael.shirts@virginia.edu</a>&gt;<br>
                    Subject: Re: [gmx-developers] dhdl expanded ensemble<br>
                    Message-ID: &lt;<a moz-do-not-send="true"
                      href="mailto:55E0093D.2000804@kth.se">55E0093D.2000804@kth.se</a>&gt;<br>
                    Content-Type: text/plain; charset=windows-1252;
                    format=flowed<br>
                    <br>
                    No. To be more precise dhdl is only (fully)
                    calculated at each step<br>
                    where free energies are calculated, i.e. every
                    nstdhdl steps.<br>
                    To find where the final values are stored, it's
                    often easiest to look in<br>
                    mdebin.c, in this case at line 1244.<br>
                    <br>
                    Cheers,<br>
                    <br>
                    Berk<br>
                    <br>
                    On 2015-08-28 03:52, Shirts, Michael R. (mrs5pt)
                    wrote:<br>
                    &gt; Dhdl is automatically calculated at every step
                    if free energies are<br>
                    &gt; calculated. Look in sum_dhdl -- difference
                    components are stored in<br>
                    &gt; enerd-&gt;term.<br>
                    &gt;<br>
                    &gt; Unless it's a new development you would rather
                    keep private for now, you<br>
                    &gt; should consider posting the proposed
                    enhancement on redmine.  You would<br>
                    &gt; likely get some tips about how to do it in a
                    way that could be more easily<br>
                    &gt; included in later gromcs versions.<br>
                    &gt;<br>
                    &gt; Best,<br>
                    &gt; ~~~~~~~~~~~~<br>
                    &gt; Michael Shirts<br>
                    &gt; Associate Professor<br>
                    &gt; Department of Chemical Engineering<br>
                    &gt; University of Virginia<br>
                    &gt; <a moz-do-not-send="true"
                      href="mailto:michael.shirts@virginia.edu">michael.shirts@virginia.edu</a><br>
                    &gt; <a moz-do-not-send="true"
                      href="tel:%28434%29%20243-1821"
                      value="+14342431821">(434) 243-1821</a><br>
                    &gt;<br>
                    &gt;<br>
                    &gt; From:  &lt;Mirabzadeh&gt;, "Christopher   (<a
                      moz-do-not-send="true"
                      href="mailto:mira2978@vandals.uidaho.edu"><a class="moz-txt-link-abbreviated" href="mailto:mira2978@vandals.uidaho.edu">mira2978@vandals.uidaho.edu</a></a>)"<br>
                    &gt; &lt;<a moz-do-not-send="true"
                      href="mailto:mira2978@vandals.uidaho.edu">mira2978@vandals.uidaho.edu</a>&gt;<br>
                    &gt; Reply-To:  "<a moz-do-not-send="true"
                      href="mailto:gmx-developers@gromacs.org">gmx-developers@gromacs.org</a>"
                    &lt;<a moz-do-not-send="true"
                      href="mailto:gmx-developers@gromacs.org">gmx-developers@gromacs.org</a>&gt;<br>
                    &gt; Date:  Thursday, August 27, 2015 at 12:20 PM<br>
                    &gt; To:  "<a moz-do-not-send="true"
                      href="mailto:gromacs.org_gmx-developers@maillist.sys.kth.se">gromacs.org_gmx-developers@maillist.sys.kth.se</a>"<br>
                    &gt; &lt;<a moz-do-not-send="true"
                      href="mailto:gromacs.org_gmx-developers@maillist.sys.kth.se">gromacs.org_gmx-developers@maillist.sys.kth.se</a>&gt;<br>
                    &gt; Subject:  [gmx-developers]  dhdl expanded
                    ensemble<br>
                    &gt;<br>
                    &gt;<br>
                    &gt;<br>
                    &gt; Hello,<br>
                    &gt;<br>
                    &gt; What I'm trying to do;<br>
                    &gt;<br>
                    &gt; I'm attempting to add functionality to expanded
                    ensemble.<br>
                    &gt;<br>
                    &gt;<br>
                    &gt; What I've done so far;<br>
                    &gt;<br>
                    &gt; I've added functionality to accept my mdp
                    options and found pre-written<br>
                    &gt; functions to take advantage of.<br>
                    &gt;<br>
                    &gt; Where I'm stuck;<br>
                    &gt;<br>
                    &gt; I need the derivative of the Hamiltonian with
                    respect to lambda at every<br>
                    &gt; md step. I'm having a hard time narrowing down
                    this variable. I know it's<br>
                    &gt; calculated and I see in mdebin.c there is a
                    line that says "/* store_dh is<br>
                    &gt; dE */". Is the derivative
                    "store_dhdl[]=enerd-&gt;term[F_DVDL]"?<br>
                    &gt;    Or, is this already being called somewhere
                    in expanded.c that I can take<br>
                    &gt; advantage of, maybe dfhist?<br>
                    &gt;<br>
                    &gt; Is the dhdl automatically calculated? Where is
                    it stored? If dhdl isn?t<br>
                    &gt; being calculated automatically, is there an mdp
                    option or mdrun flag that<br>
                    &gt; I need?<br>
                    &gt;<br>
                    &gt; I appreciate any advice that can be offered.<br>
                    &gt;<br>
                    &gt;<br>
                    &gt; -ChrisM<br>
                    &gt;<br>
                    &gt; Mirabzadeh, Christopher<br>
                    &gt; Graduate Research Assistant/Physics Instructor<br>
                    &gt; Department of Physics<br>
                    &gt; University of Idaho<br>
                    &gt; Moscow, Id<br>
                    &gt; <a moz-do-not-send="true"
                      href="tel:%28509%29339-5647" value="+15093395647">(509)339-5647</a><br>
                    &gt;<br>
                    &gt;<br>
                    &gt;<br>
                    &gt;<br>
                    &gt;<br>
                    <br>
                    <br>
                    <br>
                    ------------------------------<br>
                    <br>
                    Message: 4<br>
                    Date: Fri, 28 Aug 2015 09:20:44 +0200<br>
                    From: Berk Hess &lt;<a moz-do-not-send="true"
                      href="mailto:hess@kth.se">hess@kth.se</a>&gt;<br>
                    To: <a moz-do-not-send="true"
                      href="mailto:gmx-developers@gromacs.org">gmx-developers@gromacs.org</a><br>
                    Subject: Re: [gmx-developers] Increase the scope of
                    dd domains<br>
                    Message-ID: &lt;<a moz-do-not-send="true"
                      href="mailto:55E00BCC.4040506@kth.se">55E00BCC.4040506@kth.se</a>&gt;<br>
                    Content-Type: text/plain; charset="windows-1252";
                    Format="flowed"<br>
                    <br>
                    Hi,<br>
                    <br>
                    Gromacs uses a neutral-territory eighth-shell domain
                    decomposition<br>
                    method. So you can get all pairs by only looking at
                    home-atoms for the<br>
                    i-atoms. You code should work though for 1D
                    decomposition, is that the case?<br>
                    <br>
                    To get this to work with 2D or 3D decomposition, you
                    need to replace<br>
                    ga2la_get_home by ga2la_get and then only consider
                    i-j pairs where the<br>
                    cell values are in the cell pair list given by
                    dd-&gt;comm-&gt;zones. cell_i<br>
                    should be &lt; zones-&gt;nizone and
                    zones-&gt;izone[cell_i].j0 &lt;= cell_j &lt;<br>
                    zones-&gt;izone[cell_j].j1 When the DD cells get
                    smaller than the cutoff,<br>
                    you need to use cell % zones-&gt;n.<br>
                    <br>
                    Note that since the ga2la_get calls are expensive,
                    such an approach is<br>
                    only efficient when you have only few atoms / atom
                    pairs.<br>
                    For improving performance, it can help to first
                    lookup locala and cell<br>
                    for all atoms and store them and then do the pair
                    double loop after<br>
                    that. And instead of using sqrt, check dr2 &lt;
                    r_N*r_N.<br>
                    <br>
                    Cheers,<br>
                    <br>
                    Berk<br>
                    <br>
                    On 2015-08-28 06:35, Xingcheng Lin wrote:<br>
                    &gt; Hi,<br>
                    &gt;<br>
                    &gt; I am trying to encode a "on the fly"
                    calculation for the number of<br>
                    &gt; atom pairs within some distance (for example
                    here, 6 angstroms).<br>
                    &gt;<br>
                    &gt; The problem happens when doing parallel domain
                    decomposition.<br>
                    &gt; Specifically, when two particles reside in
                    different domains, gromacs<br>
                    &gt; is not able to recognize this pair. I am trying
                    to use ga2la_get_home<br>
                    &gt; and ga2la_get for calculation, here is the
                    code:<br>
                    &gt;<br>
                    &gt; // NP is number of tested pairs recorded in an
                    array;<br>
                    &gt; // If atom ai is one of the home atoms in a
                    node, we start testing if<br>
                    &gt; aj is available by the same node;<br>
                    &gt; // rlist = 1.0nm, Coulombtype  =  Cut-off,
                    cutoff-scheme = Verlet,<br>
                    &gt; ns_type  = grid, pbc = xyz;<br>
                    &gt;<br>
                    &gt; int Npairs = 0;<br>
                    &gt; for (i=0; i&lt;NP; ++i)<br>
                    &gt; {<br>
                    &gt;      int ai = datai[i] ;<br>
                    &gt;      int localai;<br>
                    &gt;      // Examine if ai it is within the home
                    atoms index;<br>
                    &gt;      if (ga2la_get_home(cr-&gt;dd-&gt;ga2la,
                    ai, &amp;localai))<br>
                    &gt;      {<br>
                    &gt;         aj = dataj[i] ;<br>
                    &gt;         // Examine if aj is available by local
                    node;;<br>
                    &gt;         if (ga2la_get(cr-&gt;dd-&gt;ga2la, aj,
                    &amp;localaj, &amp;localcell))<br>
                    &gt;         {<br>
                    &gt;            FILE *fp;<br>
                    &gt;            fp = fopen("pairs.dat","a");<br>
                    &gt;<br>
                    &gt;            fprintf(fp, "%d\t%d\n", ai, aj);<br>
                    &gt;            fclose(fp);<br>
                    &gt;<br>
                    &gt;            r_N = 0.6 ;<br>
                    &gt;            pbc_dx(&amp;pbc, x[localai],
                    x[localaj], dx) ;<br>
                    &gt;            dr2 = iprod( dx, dx ) ;<br>
                    &gt;            dr  = sqrt( dr2 ) ;<br>
                    &gt;            if (dr &lt; r_N)<br>
                    &gt;            {<br>
                    &gt;                Npairs += 1;<br>
                    &gt;            }<br>
                    &gt;         }<br>
                    &gt;      }<br>
                    &gt;  }<br>
                    &gt;<br>
                    &gt; The results show some atom pairs, while atoms
                    less than 6 angstroms<br>
                    &gt; apart, are missing here. I increase rlist, but
                    it doesn't help. Is<br>
                    &gt; there any way to increase the scope of atoms
                    available in each domain<br>
                    &gt; so that the missing atoms can be detected?<br>
                    &gt;<br>
                    &gt; Or are there any mistakes out of my notice in
                    this code?<br>
                    &gt;<br>
                    &gt; Thank you,<br>
                    &gt; Xingcheng<br>
                    &gt;<br>
                    &gt;<br>
                    &gt;<br>
                    &gt;<br>
                    <br>
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