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<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_start.html">2. Getting Started</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_commands.html">3. Commands</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_packages.html">4. Packages</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_accelerate.html">5. Accelerating LAMMPS performance</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_howto.html">6. How-to discussions</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_example.html">7. Example problems</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_perf.html">8. Performance & scalability</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_tools.html">9. Additional tools</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_modify.html">10. Modifying & extending LAMMPS</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_python.html">11. Python interface to LAMMPS</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_errors.html">12. Errors</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_history.html">13. Future and history</a></li>
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<a href="Section_commands.html#comm">Commands</a>
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<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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<div class="section" id="balance-command">
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<span id="index-0"></span><h1>balance command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">balance</span> <span class="n">thresh</span> <span class="n">style</span> <span class="n">args</span> <span class="o">...</span> <span class="n">keyword</span> <span class="n">value</span> <span class="o">...</span>
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</pre></div>
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</div>
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<ul class="simple">
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<li>thresh = imbalance threshhold that must be exceeded to perform a re-balance</li>
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<li>one style/arg pair can be used (or multiple for <em>x</em>,<em>y</em>,<em>z</em>)</li>
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<li>style = <em>x</em> or <em>y</em> or <em>z</em> or <em>shift</em> or <em>rcb</em></li>
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</ul>
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<pre class="literal-block">
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<em>x</em> args = <em>uniform</em> or Px-1 numbers between 0 and 1
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<em>uniform</em> = evenly spaced cuts between processors in x dimension
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numbers = Px-1 ascending values between 0 and 1, Px - # of processors in x dimension
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<em>x</em> can be specified together with <em>y</em> or <em>z</em>
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<em>y</em> args = <em>uniform</em> or Py-1 numbers between 0 and 1
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<em>uniform</em> = evenly spaced cuts between processors in y dimension
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numbers = Py-1 ascending values between 0 and 1, Py - # of processors in y dimension
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<em>y</em> can be specified together with <em>x</em> or <em>z</em>
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<em>z</em> args = <em>uniform</em> or Pz-1 numbers between 0 and 1
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<em>uniform</em> = evenly spaced cuts between processors in z dimension
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numbers = Pz-1 ascending values between 0 and 1, Pz - # of processors in z dimension
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<em>z</em> can be specified together with <em>x</em> or <em>y</em>
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<em>shift</em> args = dimstr Niter stopthresh
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dimstr = sequence of letters containing "x" or "y" or "z", each not more than once
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Niter = # of times to iterate within each dimension of dimstr sequence
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stopthresh = stop balancing when this imbalance threshhold is reached
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<em>rcb</em> args = none
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</pre>
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<ul class="simple">
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<li>zero or more keyword/value pairs may be appended</li>
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<li>keyword = <em>out</em></li>
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</ul>
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<pre class="literal-block">
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<em>out</em> value = filename
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filename = write each processor's sub-domain to a file
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</pre>
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</div>
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<div class="section" id="examples">
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<h2>Examples</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">balance</span> <span class="mf">0.9</span> <span class="n">x</span> <span class="n">uniform</span> <span class="n">y</span> <span class="mf">0.4</span> <span class="mf">0.5</span> <span class="mf">0.6</span>
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<span class="n">balance</span> <span class="mf">1.2</span> <span class="n">shift</span> <span class="n">xz</span> <span class="mi">5</span> <span class="mf">1.1</span>
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<span class="n">balance</span> <span class="mf">1.0</span> <span class="n">shift</span> <span class="n">xz</span> <span class="mi">5</span> <span class="mf">1.1</span>
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<span class="n">balance</span> <span class="mf">1.1</span> <span class="n">rcb</span>
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<span class="n">balance</span> <span class="mf">1.0</span> <span class="n">shift</span> <span class="n">x</span> <span class="mi">20</span> <span class="mf">1.0</span> <span class="n">out</span> <span class="n">tmp</span><span class="o">.</span><span class="n">balance</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description</h2>
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<p>This command adjusts the size and shape of processor sub-domains
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within the simulation box, to attempt to balance the number of
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particles and thus the computational cost (load) evenly across
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processors. The load balancing is “static” in the sense that this
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command performs the balancing once, before or between simulations.
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The processor sub-domains will then remain static during the
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subsequent run. To perform “dynamic” balancing, see the <a class="reference internal" href="fix_balance.html"><span class="doc">fix balance</span></a> command, which can adjust processor
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sub-domain sizes and shapes on-the-fly during a <a class="reference internal" href="run.html"><span class="doc">run</span></a>.</p>
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<p>Load-balancing is typically only useful if the particles in the
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simulation box have a spatially-varying density distribution. E.g. a
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model of a vapor/liquid interface, or a solid with an irregular-shaped
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geometry containing void regions. In this case, the LAMMPS default of
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dividing the simulation box volume into a regular-spaced grid of 3d
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bricks, with one equal-volume sub-domain per procesor, may assign very
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different numbers of particles per processor. This can lead to poor
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performance when the simulation is run in parallel.</p>
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<p>Note that the <a class="reference internal" href="processors.html"><span class="doc">processors</span></a> command allows some control
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over how the box volume is split across processors. Specifically, for
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a Px by Py by Pz grid of processors, it allows choice of Px, Py, and
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Pz, subject to the constraint that Px * Py * Pz = P, the total number
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of processors. This is sufficient to achieve good load-balance for
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some problems on some processor counts. However, all the processor
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sub-domains will still have the same shape and same volume.</p>
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<p>The requested load-balancing operation is only performed if the
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current “imbalance factor” in particles owned by each processor
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exceeds the specified <em>thresh</em> parameter. The imbalance factor is
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defined as the maximum number of particles owned by any processor,
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divided by the average number of particles per processor. Thus an
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imbalance factor of 1.0 is perfect balance.</p>
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<p>As an example, for 10000 particles running on 10 processors, if the
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most heavily loaded processor has 1200 particles, then the factor is
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1.2, meaning there is a 20% imbalance. Note that a re-balance can be
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forced even if the current balance is perfect (1.0) be specifying a
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<em>thresh</em> < 1.0.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">Balancing is performed even if the imbalance factor does not
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exceed the <em>thresh</em> parameter if a “grid” style is specified when the
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current partitioning is “tiled”. The meaning of “grid” vs “tiled” is
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explained below. This is to allow forcing of the partitioning to
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“grid” so that the <a class="reference internal" href="comm_style.html"><span class="doc">comm_style brick</span></a> command can then
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be used to replace a current <a class="reference internal" href="comm_style.html"><span class="doc">comm_style tiled</span></a>
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setting.</p>
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</div>
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<p>When the balance command completes, it prints statistics about the
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result, including the change in the imbalance factor and the change in
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the maximum number of particles on any processor. For “grid” methods
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(defined below) that create a logical 3d grid of processors, the
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positions of all cutting planes in each of the 3 dimensions (as
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fractions of the box length) are also printed.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">This command attempts to minimize the imbalance factor, as
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defined above. But depending on the method a perfect balance (1.0)
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may not be achieved. For example, “grid” methods (defined below) that
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create a logical 3d grid cannot achieve perfect balance for many
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irregular distributions of particles. Likewise, if a portion of the
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system is a perfect lattice, e.g. the intiial system is generated by
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the <a class="reference internal" href="create_atoms.html"><span class="doc">create_atoms</span></a> command, then “grid” methods may
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be unable to achieve exact balance. This is because entire lattice
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planes will be owned or not owned by a single processor.</p>
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</div>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">The imbalance factor is also an estimate of the maximum speed-up
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you can hope to achieve by running a perfectly balanced simulation
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versus an imbalanced one. In the example above, the 10000 particle
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simulation could run up to 20% faster if it were perfectly balanced,
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versus when imbalanced. However, computational cost is not strictly
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proportional to particle count, and changing the relative size and
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shape of processor sub-domains may lead to additional computational
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and communication overheads, e.g. in the PPPM solver used via the
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<a class="reference internal" href="kspace_style.html"><span class="doc">kspace_style</span></a> command. Thus you should benchmark
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the run times of a simulation before and after balancing.</p>
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</div>
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<hr class="docutils" />
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<p>The method used to perform a load balance is specified by one of the
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listed styles (or more in the case of <em>x</em>,<em>y</em>,<em>z</em>), which are
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described in detail below. There are 2 kinds of styles.</p>
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<p>The <em>x</em>, <em>y</em>, <em>z</em>, and <em>shift</em> styles are “grid” methods which produce
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a logical 3d grid of processors. They operate by changing the cutting
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planes (or lines) between processors in 3d (or 2d), to adjust the
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volume (area in 2d) assigned to each processor, as in the following 2d
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diagram where processor sub-domains are shown and atoms are colored by
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the processor that owns them. The leftmost diagram is the default
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partitioning of the simulation box across processors (one sub-box for
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each of 16 processors); the middle diagram is after a “grid” method
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has been applied.</p>
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<a class=""
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data-lightbox="group-default"
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href="_images/balance_uniform.jpg"
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title=""
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data-title=""
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><img src="_images/balance_uniform.jpg"
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class="align-center"
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width="25%"
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height="auto"
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alt=""/>
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</a><a class=""
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data-lightbox="group-default"
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href="_images/balance_nonuniform.jpg"
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title=""
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data-title=""
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><img src="_images/balance_nonuniform.jpg"
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class="align-center"
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width="25%"
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height="auto"
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alt=""/>
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</a><a class=""
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data-lightbox="group-default"
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href="_images/balance_rcb.jpg"
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title=""
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data-title=""
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><img src="_images/balance_rcb.jpg"
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class="align-center"
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width="25%"
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height="auto"
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alt=""/>
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</a><p>The <em>rcb</em> style is a “tiling” method which does not produce a logical
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3d grid of processors. Rather it tiles the simulation domain with
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rectangular sub-boxes of varying size and shape in an irregular
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fashion so as to have equal numbers of particles in each sub-box, as
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in the rightmost diagram above.</p>
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<p>The “grid” methods can be used with either of the
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<a class="reference internal" href="comm_style.html"><span class="doc">comm_style</span></a> command options, <em>brick</em> or <em>tiled</em>. The
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“tiling” methods can only be used with <a class="reference internal" href="comm_style.html"><span class="doc">comm_style tiled</span></a>. Note that it can be useful to use a “grid”
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method with <a class="reference internal" href="comm_style.html"><span class="doc">comm_style tiled</span></a> to return the domain
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partitioning to a logical 3d grid of processors so that “comm_style
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brick” can afterwords be specified for subsequent <a class="reference internal" href="run.html"><span class="doc">run</span></a>
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commands.</p>
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<p>When a “grid” method is specified, the current domain partitioning can
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be either a logical 3d grid or a tiled partitioning. In the former
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case, the current logical 3d grid is used as a starting point and
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changes are made to improve the imbalance factor. In the latter case,
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the tiled partitioning is discarded and a logical 3d grid is created
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with uniform spacing in all dimensions. This becomes the starting
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point for the balancing operation.</p>
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<p>When a “tiling” method is specified, the current domain partitioning
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(“grid” or “tiled”) is ignored, and a new partitioning is computed
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from scratch.</p>
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<hr class="docutils" />
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<p>The <em>x</em>, <em>y</em>, and <em>z</em> styles invoke a “grid” method for balancing, as
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described above. Note that any or all of these 3 styles can be
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specified together, one after the other, but they cannot be used with
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any other style. This style adjusts the position of cutting planes
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between processor sub-domains in specific dimensions. Only the
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specified dimensions are altered.</p>
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<p>The <em>uniform</em> argument spaces the planes evenly, as in the left
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diagrams above. The <em>numeric</em> argument requires listing Ps-1 numbers
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that specify the position of the cutting planes. This requires
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knowing Ps = Px or Py or Pz = the number of processors assigned by
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LAMMPS to the relevant dimension. This assignment is made (and the
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Px, Py, Pz values printed out) when the simulation box is created by
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the “create_box” or “read_data” or “read_restart” command and is
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influenced by the settings of the <a class="reference internal" href="processors.html"><span class="doc">processors</span></a>
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command.</p>
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<p>Each of the numeric values must be between 0 and 1, and they must be
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listed in ascending order. They represent the fractional position of
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the cutting place. The left (or lower) edge of the box is 0.0, and
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the right (or upper) edge is 1.0. Neither of these values is
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specified. Only the interior Ps-1 positions are specified. Thus is
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there are 2 procesors in the x dimension, you specify a single value
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such as 0.75, which would make the left processor’s sub-domain 3x
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larger than the right processor’s sub-domain.</p>
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<hr class="docutils" />
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<p>The <em>shift</em> style invokes a “grid” method for balancing, as
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described above. It changes the positions of cutting planes between
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processors in an iterative fashion, seeking to reduce the imbalance
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factor, similar to how the <a class="reference internal" href="fix_balance.html"><span class="doc">fix balance shift</span></a>
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command operates.</p>
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<p>The <em>dimstr</em> argument is a string of characters, each of which must be
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an “x” or “y” or “z”. Eacn character can appear zero or one time,
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since there is no advantage to balancing on a dimension more than
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once. You should normally only list dimensions where you expect there
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to be a density variation in the particles.</p>
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<p>Balancing proceeds by adjusting the cutting planes in each of the
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dimensions listed in <em>dimstr</em>, one dimension at a time. For a single
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dimension, the balancing operation (described below) is iterated on up
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to <em>Niter</em> times. After each dimension finishes, the imbalance factor
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is re-computed, and the balancing operation halts if the <em>stopthresh</em>
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criterion is met.</p>
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<p>A rebalance operation in a single dimension is performed using a
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recursive multisectioning algorithm, where the position of each
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cutting plane (line in 2d) in the dimension is adjusted independently.
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This is similar to a recursive bisectioning for a single value, except
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that the bounds used for each bisectioning take advantage of
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information from neighboring cuts if possible. At each iteration, the
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count of particles on either side of each plane is tallied. If the
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counts do not match the target value for the plane, the position of
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the cut is adjusted to be halfway between a low and high bound. The
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low and high bounds are adjusted on each iteration, using new count
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information, so that they become closer together over time. Thus as
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the recustion progresses, the count of particles on either side of the
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plane gets closer to the target value.</p>
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<p>Once the rebalancing is complete and final processor sub-domains
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assigned, particles are migrated to their new owning processor, and
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the balance procedure ends.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">At each rebalance operation, the bisectioning for each cutting
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plane (line in 2d) typcially starts with low and high bounds separated
|
|
by the extent of a processor’s sub-domain in one dimension. The size
|
|
of this bracketing region shrinks by 1/2 every iteration. Thus if
|
|
<em>Niter</em> is specified as 10, the cutting plane will typically be
|
|
positioned to 1 part in 1000 accuracy (relative to the perfect target
|
|
position). For <em>Niter</em> = 20, it will be accurate to 1 part in a
|
|
million. Thus there is no need ot set <em>Niter</em> to a large value.
|
|
LAMMPS will check if the threshold accuracy is reached (in a
|
|
dimension) is less iterations than <em>Niter</em> and exit early. However,
|
|
<em>Niter</em> should also not be set too small, since it will take roughly
|
|
the same number of iterations to converge even if the cutting plane is
|
|
initially close to the target value.</p>
|
|
</div>
|
|
<hr class="docutils" />
|
|
<p>The <em>rcb</em> style invokes a “tiled” method for balancing, as described
|
|
above. It performs a recursive coordinate bisectioning (RCB) of the
|
|
simulation domain. The basic idea is as follows.</p>
|
|
<p>The simulation domain is cut into 2 boxes by an axis-aligned cut in
|
|
the longest dimension, leaving one new box on either side of the cut.
|
|
All the processors are also partitioned into 2 groups, half assigned
|
|
to the box on the lower side of the cut, and half to the box on the
|
|
upper side. (If the processor count is odd, one side gets an extra
|
|
processor.) The cut is positioned so that the number of atoms in the
|
|
lower box is exactly the number that the processors assigned to that
|
|
box should own for load balance to be perfect. This also makes load
|
|
balance for the upper box perfect. The positioning is done
|
|
iteratively, by a bisectioning method. Note that counting atoms on
|
|
either side of the cut requires communication between all processors
|
|
at each iteration.</p>
|
|
<p>That is the procedure for the first cut. Subsequent cuts are made
|
|
recursively, in exactly the same manner. The subset of processors
|
|
assigned to each box make a new cut in the longest dimension of that
|
|
box, splitting the box, the subset of processsors, and the atoms in
|
|
the box in two. The recursion continues until every processor is
|
|
assigned a sub-box of the entire simulation domain, and owns the atoms
|
|
in that sub-box.</p>
|
|
<hr class="docutils" />
|
|
<p>The <em>out</em> keyword writes a text file to the specified <em>filename</em> with
|
|
the results of the balancing operation. The file contains the bounds
|
|
of the sub-domain for each processor after the balancing operation
|
|
completes. The format of the file is compatible with the
|
|
<a class="reference external" href="pizza">Pizza.py</a> <em>mdump</em> tool which has support for manipulating and
|
|
visualizing mesh files. An example is shown here for a balancing by 4
|
|
processors for a 2d problem:</p>
|
|
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">ITEM</span><span class="p">:</span> <span class="n">TIMESTEP</span>
|
|
<span class="mi">0</span>
|
|
<span class="n">ITEM</span><span class="p">:</span> <span class="n">NUMBER</span> <span class="n">OF</span> <span class="n">NODES</span>
|
|
<span class="mi">16</span>
|
|
<span class="n">ITEM</span><span class="p">:</span> <span class="n">BOX</span> <span class="n">BOUNDS</span>
|
|
<span class="mi">0</span> <span class="mi">10</span>
|
|
<span class="mi">0</span> <span class="mi">10</span>
|
|
<span class="mi">0</span> <span class="mi">10</span>
|
|
<span class="n">ITEM</span><span class="p">:</span> <span class="n">NODES</span>
|
|
<span class="mi">1</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">0</span>
|
|
<span class="mi">2</span> <span class="mi">1</span> <span class="mi">5</span> <span class="mi">0</span> <span class="mi">0</span>
|
|
<span class="mi">3</span> <span class="mi">1</span> <span class="mi">5</span> <span class="mi">5</span> <span class="mi">0</span>
|
|
<span class="mi">4</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">5</span> <span class="mi">0</span>
|
|
<span class="mi">5</span> <span class="mi">1</span> <span class="mi">5</span> <span class="mi">0</span> <span class="mi">0</span>
|
|
<span class="mi">6</span> <span class="mi">1</span> <span class="mi">10</span> <span class="mi">0</span> <span class="mi">0</span>
|
|
<span class="mi">7</span> <span class="mi">1</span> <span class="mi">10</span> <span class="mi">5</span> <span class="mi">0</span>
|
|
<span class="mi">8</span> <span class="mi">1</span> <span class="mi">5</span> <span class="mi">5</span> <span class="mi">0</span>
|
|
<span class="mi">9</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">5</span> <span class="mi">0</span>
|
|
<span class="mi">10</span> <span class="mi">1</span> <span class="mi">5</span> <span class="mi">5</span> <span class="mi">0</span>
|
|
<span class="mi">11</span> <span class="mi">1</span> <span class="mi">5</span> <span class="mi">10</span> <span class="mi">0</span>
|
|
<span class="mi">12</span> <span class="mi">1</span> <span class="mi">10</span> <span class="mi">5</span> <span class="mi">0</span>
|
|
<span class="mi">13</span> <span class="mi">1</span> <span class="mi">5</span> <span class="mi">5</span> <span class="mi">0</span>
|
|
<span class="mi">14</span> <span class="mi">1</span> <span class="mi">10</span> <span class="mi">5</span> <span class="mi">0</span>
|
|
<span class="mi">15</span> <span class="mi">1</span> <span class="mi">10</span> <span class="mi">10</span> <span class="mi">0</span>
|
|
<span class="mi">16</span> <span class="mi">1</span> <span class="mi">5</span> <span class="mi">10</span> <span class="mi">0</span>
|
|
<span class="n">ITEM</span><span class="p">:</span> <span class="n">TIMESTEP</span>
|
|
<span class="mi">0</span>
|
|
<span class="n">ITEM</span><span class="p">:</span> <span class="n">NUMBER</span> <span class="n">OF</span> <span class="n">SQUARES</span>
|
|
<span class="mi">4</span>
|
|
<span class="n">ITEM</span><span class="p">:</span> <span class="n">SQUARES</span>
|
|
<span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span>
|
|
<span class="mi">2</span> <span class="mi">1</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span>
|
|
<span class="mi">3</span> <span class="mi">1</span> <span class="mi">9</span> <span class="mi">10</span> <span class="mi">11</span> <span class="mi">12</span>
|
|
<span class="mi">4</span> <span class="mi">1</span> <span class="mi">13</span> <span class="mi">14</span> <span class="mi">15</span> <span class="mi">16</span>
|
|
</pre></div>
|
|
</div>
|
|
<p>The coordinates of all the vertices are listed in the NODES section, 5
|
|
per processor. Note that the 4 sub-domains share vertices, so there
|
|
will be duplicate nodes in the list.</p>
|
|
<p>The “SQUARES” section lists the node IDs of the 4 vertices in a
|
|
rectangle for each processor (1 to 4).</p>
|
|
<p>For a 3d problem, the syntax is similar with 8 vertices listed for
|
|
each processor, instead of 4, and “SQUARES” replaced by “CUBES”.</p>
|
|
</div>
|
|
<hr class="docutils" />
|
|
<div class="section" id="restrictions">
|
|
<h2>Restrictions</h2>
|
|
<p>For 2d simulations, the <em>z</em> style cannot be used. Nor can a “z”
|
|
appear in <em>dimstr</em> for the <em>shift</em> style.</p>
|
|
</div>
|
|
<div class="section" id="related-commands">
|
|
<h2>Related commands</h2>
|
|
<p><a class="reference internal" href="processors.html"><span class="doc">processors</span></a>, <a class="reference internal" href="fix_balance.html"><span class="doc">fix balance</span></a></p>
|
|
<p><strong>Default:</strong> none</p>
|
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</div>
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