Page MenuHomec4science

compute_improper_local.html
No OneTemporary

File Metadata

Created
Mon, May 27, 10:23

compute_improper_local.html

<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>compute improper/local command &mdash; LAMMPS documentation</title>
<link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="_static/sphinxcontrib-images/LightBox2/lightbox2/css/lightbox.css" type="text/css" />
<link rel="top" title="LAMMPS documentation" href="index.html"/>
<link rel="up" title="Computes" href="computes.html"/>
<link rel="next" title="compute inertia/chunk command" href="compute_inertia_chunk.html"/>
<link rel="prev" title="compute improper command" href="compute_improper.html"/>
<script src="_static/js/modernizr.min.js"></script>
</head>
<body class="wy-body-for-nav" role="document">
<div class="wy-grid-for-nav">
<nav data-toggle="wy-nav-shift" class="wy-nav-side">
<div class="wy-side-nav-search">
<a href="Manual.html" class="icon icon-home"> LAMMPS
</a>
<div role="search">
<form id="rtd-search-form" class="wy-form" action="search.html" method="get">
<input type="text" name="q" placeholder="Search docs" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
<p class="caption"><span class="caption-text">User Documentation</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_start.html">2. Getting Started</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_commands.html">3. Commands</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_packages.html">4. Packages</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_accelerate.html">5. Accelerating LAMMPS performance</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_howto.html">6. How-to discussions</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_example.html">7. Example problems</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_perf.html">8. Performance &amp; scalability</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_tools.html">9. Additional tools</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_modify.html">10. Modifying &amp; extending LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_python.html">11. Python interface to LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_errors.html">12. Errors</a></li>
<li class="toctree-l1"><a class="reference internal" href="Section_history.html">13. Future and history</a></li>
</ul>
<p class="caption"><span class="caption-text">Index</span></p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="tutorials.html">Tutorials</a></li>
<li class="toctree-l1"><a class="reference internal" href="commands.html">Commands</a></li>
<li class="toctree-l1"><a class="reference internal" href="fixes.html">Fixes</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="computes.html">Computes</a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="compute_ackland_atom.html">compute ackland/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_angle.html">compute angle command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_angle_local.html">compute angle/local command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_angmom_chunk.html">compute angmom/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_basal_atom.html">compute basal/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_body_local.html">compute body/local command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_bond.html">compute bond command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_bond_local.html">compute bond/local command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_centro_atom.html">compute centro/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_chunk_atom.html">compute chunk/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_cluster_atom.html">compute cluster/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_cna_atom.html">compute cna/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_com.html">compute com command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_com_chunk.html">compute com/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_contact_atom.html">compute contact/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_coord_atom.html">compute coord/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_damage_atom.html">compute damage/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_dihedral.html">compute dihedral command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_dihedral_local.html">compute dihedral/local command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_dilatation_atom.html">compute dilatation/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_dipole_chunk.html">compute dipole/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_displace_atom.html">compute displace/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_dpd.html">compute dpd command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_dpd_atom.html">compute dpd/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_erotate_asphere.html">compute erotate/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_erotate_rigid.html">compute erotate/rigid command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_erotate_sphere.html">compute erotate/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_erotate_sphere_atom.html">compute erotate/sphere/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_event_displace.html">compute event/displace command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_fep.html">compute fep command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_group_group.html">compute group/group command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_gyration.html">compute gyration command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_gyration_chunk.html">compute gyration/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_heat_flux.html">compute heat/flux command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_hexorder_atom.html">compute hexorder/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_improper.html">compute improper command</a></li>
<li class="toctree-l2 current"><a class="current reference internal" href="#">compute improper/local command</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#syntax">Syntax</a></li>
<li class="toctree-l3"><a class="reference internal" href="#examples">Examples</a></li>
<li class="toctree-l3"><a class="reference internal" href="#description">Description</a></li>
<li class="toctree-l3"><a class="reference internal" href="#restrictions">Restrictions</a></li>
<li class="toctree-l3"><a class="reference internal" href="#related-commands">Related commands</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="compute_inertia_chunk.html">compute inertia/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_ke.html">compute ke command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_ke_atom.html">compute ke/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_ke_atom_eff.html">compute ke/atom/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_ke_eff.html">compute ke/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_ke_rigid.html">compute ke/rigid command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_meso_e_atom.html">compute meso/e/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_meso_rho_atom.html">compute meso/rho/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_meso_t_atom.html">compute meso/t/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_msd.html">compute msd command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_msd_chunk.html">compute msd/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_msd_nongauss.html">compute msd/nongauss command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_omega_chunk.html">compute omega/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_orientorder_atom.html">compute orientorder/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_pair.html">compute pair command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_pair_local.html">compute pair/local command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_pe.html">compute pe command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_pe_atom.html">compute pe/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_plasticity_atom.html">compute plasticity/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_pressure.html">compute pressure command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_property_atom.html">compute property/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_property_chunk.html">compute property/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_property_local.html">compute property/local command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_rdf.html">compute rdf command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_reduce.html">compute reduce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_reduce.html#compute-reduce-region-command">compute reduce/region command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_rigid_local.html">compute rigid/local command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_saed.html">compute saed command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_slice.html">compute slice command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_contact_radius.html">compute smd/contact/radius command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_damage.html">compute smd/damage command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_hourglass_error.html">compute smd/hourglass/error command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_internal_energy.html">compute smd/internal/energy command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_plastic_strain.html">compute smd/plastic/strain command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_plastic_strain_rate.html">compute smd/plastic/strain/rate command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_rho.html">compute smd/rho command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_defgrad.html">compute smd/tlsph/defgrad command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_dt.html">compute smd/tlsph/dt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_num_neighs.html">compute smd/tlsph/num/neighs command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_shape.html">compute smd/tlsph/shape command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_strain.html">compute smd/tlsph/strain command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_strain_rate.html">compute smd/tlsph/strain/rate command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_stress.html">compute smd/tlsph/stress command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_triangle_mesh_vertices.html">compute smd/triangle/mesh/vertices</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_ulsph_num_neighs.html">compute smd/ulsph/num/neighs command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_ulsph_strain.html">compute smd/ulsph/strain command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_ulsph_strain_rate.html">compute smd/ulsph/strain/rate command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_ulsph_stress.html">compute smd/ulsph/stress command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_vol.html">compute smd/vol command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_sna_atom.html">compute sna/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_sna_atom.html#compute-snad-atom-command">compute snad/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_sna_atom.html#compute-snav-atom-command">compute snav/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_stress_atom.html">compute stress/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_tally.html">compute force/tally command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_tally.html#compute-heat-flux-tally-command">compute heat/flux/tally command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_tally.html#compute-pe-tally-command">compute pe/tally command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_tally.html#compute-pe-mol-tally-command">compute pe/mol/tally command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_tally.html#compute-stress-tally-command">compute stress/tally command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp.html">compute temp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp.html#compute-temp-kk-command">compute temp/kk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_asphere.html">compute temp/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_body.html">compute temp/body command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_chunk.html">compute temp/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_com.html">compute temp/com command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_cs.html">compute temp/cs command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_deform.html">compute temp/deform command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_deform_eff.html">compute temp/deform/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_drude.html">compute temp/drude command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_eff.html">compute temp/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_partial.html">compute temp/partial command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_profile.html">compute temp/profile command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_ramp.html">compute temp/ramp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_region.html">compute temp/region command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_region_eff.html">compute temp/region/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_rotate.html">compute temp/rotate command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_temp_sphere.html">compute temp/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_ti.html">compute ti command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_torque_chunk.html">compute torque/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_vacf.html">compute vacf command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_vcm_chunk.html">compute vcm/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_voronoi_atom.html">compute voronoi/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_xrd.html">compute xrd command</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="pairs.html">Pair Styles</a></li>
<li class="toctree-l1"><a class="reference internal" href="bonds.html">Bonds</a></li>
<li class="toctree-l1"><a class="reference internal" href="angles.html">Angle Styles</a></li>
<li class="toctree-l1"><a class="reference internal" href="dihedrals.html">Dihedral Styles</a></li>
<li class="toctree-l1"><a class="reference internal" href="impropers.html">Improper Styles</a></li>
</ul>
</div>
&nbsp;
</nav>
<section data-toggle="wy-nav-shift" class="wy-nav-content-wrap">
<nav class="wy-nav-top" role="navigation" aria-label="top navigation">
<i data-toggle="wy-nav-top" class="fa fa-bars"></i>
<a href="Manual.html">LAMMPS</a>
</nav>
<div class="wy-nav-content">
<div class="rst-content">
<div role="navigation" aria-label="breadcrumbs navigation">
<ul class="wy-breadcrumbs">
<li><a href="Manual.html">Docs</a> &raquo;</li>
<li><a href="computes.html">Computes</a> &raquo;</li>
<li>compute improper/local command</li>
<li class="wy-breadcrumbs-aside">
<a href="http://lammps.sandia.gov">Website</a>
<a href="Section_commands.html#comm">Commands</a>
</li>
</ul>
<hr/>
<div class="rst-footer-buttons" style="margin-bottom: 1em" role="navigation" aria-label="footer navigation">
<a href="compute_inertia_chunk.html" class="btn btn-neutral float-right" title="compute inertia/chunk command" accesskey="n">Next <span class="fa fa-arrow-circle-right"></span></a>
<a href="compute_improper.html" class="btn btn-neutral" title="compute improper command" accesskey="p"><span class="fa fa-arrow-circle-left"></span> Previous</a>
</div>
</div>
<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
<div itemprop="articleBody">
<div class="section" id="compute-improper-local-command">
<span id="index-0"></span><h1>compute improper/local command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">compute</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">improper</span><span class="o">/</span><span class="n">local</span> <span class="n">value1</span> <span class="n">value2</span> <span class="o">...</span>
</pre></div>
</div>
<ul>
<li><p class="first">ID, group-ID are documented in <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> command</p>
</li>
<li><p class="first">improper/local = style name of this compute command</p>
</li>
<li><p class="first">one or more values may be appended</p>
</li>
<li><p class="first">value = <em>chi</em></p>
<pre class="literal-block">
<em>chi</em> = tabulate improper angles
</pre>
</li>
</ul>
</div>
<div class="section" id="examples">
<h2>Examples</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">compute</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">improper</span><span class="o">/</span><span class="n">local</span> <span class="n">chi</span>
</pre></div>
</div>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>Define a computation that calculates properties of individual improper
interactions. The number of datums generated, aggregated across all
processors, equals the number of impropers in the system, modified by
the group parameter as explained below.</p>
<p>The value <em>chi</em> is the improper angle, as defined in the doc pages for
the individual improper styles listed on
<a class="reference internal" href="improper_style.html"><span class="doc">improper_style</span></a> doc page.</p>
<p>The local data stored by this command is generated by looping over all
the atoms owned on a processor and their impropers. An improper will
only be included if all 4 atoms in the improper are in the specified
compute group.</p>
<p>Note that as atoms migrate from processor to processor, there will be
no consistent ordering of the entries within the local vector or array
from one timestep to the next. The only consistency that is
guaranteed is that the ordering on a particular timestep will be the
same for local vectors or arrays generated by other compute commands.
For example, improper output from the <a class="reference internal" href="compute_property_local.html"><span class="doc">compute property/local</span></a> command can be combined
with data from this command and output by the <a class="reference internal" href="dump.html"><span class="doc">dump local</span></a>
command in a consistent way.</p>
<p>Here is an example of how to do this:</p>
<pre class="literal-block">
compute 1 all property/local itype iatom1 iatom2 iatom3 iatom4
compute 2 all improper/local chi
dump 1 all local 1000 tmp.dump index c_1[1] c_1[2] c_1[3] c_1[4] c_1[5] c_2[1]
</pre>
<p><strong>Output info:</strong></p>
<p>This compute calculates a local vector or local array depending on the
number of keywords. The length of the vector or number of rows in the
array is the number of impropers. If a single keyword is specified, a
local vector is produced. If two or more keywords are specified, a
local array is produced where the number of columns = the number of
keywords. The vector or array can be accessed by any command that
uses local values from a compute as input. See <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">this section</span></a> for an overview of LAMMPS output
options.</p>
<p>The output for <em>chi</em> will be in degrees.</p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<blockquote>
<div>none</div></blockquote>
</div>
<div class="section" id="related-commands">
<h2>Related commands</h2>
<p><a class="reference internal" href="dump.html"><span class="doc">dump local</span></a>, <a class="reference internal" href="compute_property_local.html"><span class="doc">compute property/local</span></a></p>
<p><strong>Default:</strong> none</p>
</div>
</div>
</div>
</div>
<footer>
<div class="rst-footer-buttons" role="navigation" aria-label="footer navigation">
<a href="compute_inertia_chunk.html" class="btn btn-neutral float-right" title="compute inertia/chunk command" accesskey="n">Next <span class="fa fa-arrow-circle-right"></span></a>
<a href="compute_improper.html" class="btn btn-neutral" title="compute improper command" accesskey="p"><span class="fa fa-arrow-circle-left"></span> Previous</a>
</div>
<hr/>
<div role="contentinfo">
<p>
&copy; Copyright 2013 Sandia Corporation.
</p>
</div>
Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/snide/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>.
</footer>
</div>
</div>
</section>
</div>
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT:'./',
VERSION:'',
COLLAPSE_INDEX:false,
FILE_SUFFIX:'.html',
HAS_SOURCE: true
};
</script>
<script type="text/javascript" src="_static/jquery.js"></script>
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="_static/sphinxcontrib-images/LightBox2/lightbox2/js/jquery-1.11.0.min.js"></script>
<script type="text/javascript" src="_static/sphinxcontrib-images/LightBox2/lightbox2/js/lightbox.min.js"></script>
<script type="text/javascript" src="_static/sphinxcontrib-images/LightBox2/lightbox2-customize/jquery-noconflict.js"></script>
<script type="text/javascript" src="_static/js/theme.js"></script>
<script type="text/javascript">
jQuery(function () {
SphinxRtdTheme.StickyNav.enable();
});
</script>
</body>
</html>

Event Timeline