Files
lammps/doc/html/compute_reduce.html
2025-01-13 14:55:48 +00:00

559 lines
51 KiB
HTML

<!DOCTYPE html>
<html class="writer-html5" lang="en" >
<head>
<meta charset="utf-8" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>compute reduce command &mdash; LAMMPS documentation</title>
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="_static/sphinx-design.min.css" type="text/css" />
<link rel="stylesheet" href="_static/css/lammps.css" type="text/css" />
<link rel="shortcut icon" href="_static/lammps.ico"/>
<link rel="canonical" href="https://docs.lammps.org/compute_reduce.html" />
<!--[if lt IE 9]>
<script src="_static/js/html5shiv.min.js"></script>
<![endif]-->
<script src="_static/jquery.js?v=5d32c60e"></script>
<script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
<script src="_static/documentation_options.js?v=5929fcd5"></script>
<script src="_static/doctools.js?v=9bcbadda"></script>
<script src="_static/sphinx_highlight.js?v=dc90522c"></script>
<script src="_static/design-tabs.js?v=f930bc37"></script>
<script async="async" src="_static/mathjax/es5/tex-mml-chtml.js?v=cadf963e"></script>
<script src="_static/js/theme.js"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="compute reduce/chunk command" href="compute_reduce_chunk.html" />
<link rel="prev" title="compute reaxff/atom command" href="compute_reaxff_atom.html" />
</head>
<body class="wy-body-for-nav">
<div class="wy-grid-for-nav">
<nav data-toggle="wy-nav-shift" class="wy-nav-side">
<div class="wy-side-scroll">
<div class="wy-side-nav-search" >
<a href="Manual.html">
<img src="_static/lammps-logo.png" class="logo" alt="Logo"/>
</a>
<div class="lammps_version">Version: <b>19 Nov 2024</b></div>
<div class="lammps_release">git info: </div>
<div role="search">
<form id="rtd-search-form" class="wy-form" action="search.html" method="get">
<input type="text" name="q" placeholder="Search docs" aria-label="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="Navigation menu">
<p class="caption" role="heading"><span class="caption-text">User Guide</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Intro.html">1. Introduction</a></li>
<li class="toctree-l1"><a class="reference internal" href="Install.html">2. Install LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Build.html">3. Build LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Run_head.html">4. Run LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Commands.html">5. Commands</a></li>
<li class="toctree-l1"><a class="reference internal" href="Packages.html">6. Optional packages</a></li>
<li class="toctree-l1"><a class="reference internal" href="Speed.html">7. Accelerate performance</a></li>
<li class="toctree-l1"><a class="reference internal" href="Howto.html">8. Howto discussions</a></li>
<li class="toctree-l1"><a class="reference internal" href="Examples.html">9. Example scripts</a></li>
<li class="toctree-l1"><a class="reference internal" href="Tools.html">10. Auxiliary tools</a></li>
<li class="toctree-l1"><a class="reference internal" href="Errors.html">11. Errors</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">Programmer Guide</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Library.html">1. LAMMPS Library Interfaces</a></li>
<li class="toctree-l1"><a class="reference internal" href="Python_head.html">2. Use Python with LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Modify.html">3. Modifying &amp; extending LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Developer.html">4. Information for Developers</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">Command Reference</span></p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="commands_list.html">Commands</a></li>
<li class="toctree-l1"><a class="reference internal" href="fixes.html">Fix Styles</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="computes.html">Compute Styles</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_adf.html">compute adf 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_ave_sphere_atom.html">compute ave/sphere/atom 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_born_matrix.html">compute born/matrix 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_chunk_spread_atom.html">compute chunk/spread/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_cluster_atom.html#compute-fragment-atom-command">compute fragment/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_cluster_atom.html#compute-aggregate-atom-command">compute aggregate/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_cnp_atom.html">compute cnp/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_composition_atom.html">compute composition/atom 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_count_type.html">compute count/type 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.html">compute dipole command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_dipole.html#compute-dipole-tip4p-command">compute dipole/tip4p 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_dipole_chunk.html#compute-dipole-tip4p-chunk-command">compute dipole/tip4p/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_edpd_temp_atom.html">compute edpd/temp/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_efield_atom.html">compute efield/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_efield_wolf_atom.html">compute efield/wolf/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_entropy_atom.html">compute entropy/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_fabric.html">compute fabric 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_fep_ta.html">compute fep/ta command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_global_atom.html">compute global/atom 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_gyration_shape.html">compute gyration/shape command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_gyration_shape_chunk.html">compute gyration/shape/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_hma.html">compute hma command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_improper.html">compute improper command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_improper_local.html">compute improper/local command</a></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_mliap.html">compute mliap command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_momentum.html">compute momentum 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_nbond_atom.html">compute nbond/atom 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_pace.html">compute pace 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_pod_atom.html">compute pod/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_pod_atom.html#compute-podd-atom-command">compute podd/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_pod_atom.html#compute-pod-local-command">compute pod/local command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_pod_atom.html#compute-pod-global-command">compute pod/global 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_pressure_alchemy.html">compute pressure/alchemy command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_pressure_uef.html">compute pressure/uef 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_grid.html">compute property/grid 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_ptm_atom.html">compute ptm/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_rattlers_atom.html">compute rattlers/atom 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_reaxff_atom.html">compute reaxff/atom command</a></li>
<li class="toctree-l2 current"><a class="current reference internal" href="#">compute reduce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="#compute-reduce-region-command">compute reduce/region 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="#output-info">Output info</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>
<li class="toctree-l3"><a class="reference internal" href="#default">Default</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="compute_reduce_chunk.html">compute reduce/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_rheo_property_atom.html">compute rheo/property/atom 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_slcsa_atom.html">compute slcsa/atom 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_vertices.html">compute smd/triangle/vertices command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_smd_ulsph_effm.html">compute smd/ulsph/effm command</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_sna_atom.html#compute-snap-command">compute snap command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_sna_atom.html#compute-sna-grid-command">compute sna/grid command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_sna_atom.html#compute-sna-grid-local-command">compute sna/grid/local command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_sph_e_atom.html">compute sph/e/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_sph_rho_atom.html">compute sph/rho/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_sph_t_atom.html">compute sph/t/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_spin.html">compute spin 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_stress_atom.html#compute-centroid-stress-atom-command">compute centroid/stress/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_stress_cartesian.html">compute stress/cartesian command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_stress_curvilinear.html">compute stress/cylinder command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_stress_curvilinear.html#compute-stress-spherical-command">compute stress/spherical command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_stress_mop.html">compute stress/mop command</a></li>
<li class="toctree-l2"><a class="reference internal" href="compute_stress_mop.html#compute-stress-mop-profile-command">compute stress/mop/profile 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-heat-flux-virial-tally-command">compute heat/flux/virial/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_tdpd_cc_atom.html">compute tdpd/cc/atom 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_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_temp_uef.html">compute temp/uef 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_viscosity_cos.html">compute viscosity/cos 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">Bond Styles</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>
<li class="toctree-l1"><a class="reference internal" href="dumps.html">Dump Styles</a></li>
<li class="toctree-l1"><a class="reference internal" href="fix_modify_atc_commands.html">fix_modify AtC commands</a></li>
<li class="toctree-l1"><a class="reference internal" href="Bibliography.html">Bibliography</a></li>
</ul>
</div>
</div>
</nav>
<section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" >
<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 style-external-links">
<div role="navigation" aria-label="Page navigation">
<ul class="wy-breadcrumbs">
<li><a href="Manual.html" class="icon icon-home" aria-label="Home"></a></li>
<li class="breadcrumb-item"><a href="computes.html">Compute Styles</a></li>
<li class="breadcrumb-item active">compute reduce command</li>
<li class="wy-breadcrumbs-aside">
<a href="https://www.lammps.org"><img src="_static/lammps-logo.png" width="64" height="16" alt="LAMMPS Homepage"></a> | <a href="Commands_all.html">Commands</a>
</li>
</ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation">
<a href="compute_reaxff_atom.html" class="btn btn-neutral float-left" title="compute reaxff/atom command" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
<a href="compute_reduce_chunk.html" class="btn btn-neutral float-right" title="compute reduce/chunk command" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
</div>
<hr/>
</div>
<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
<div itemprop="articleBody">
<p><span class="math notranslate nohighlight">\(\renewcommand{\AA}{\text{Å}}\)</span></p>
<section id="compute-reduce-command">
<span id="index-1"></span><span id="index-0"></span><h1>compute reduce command<a class="headerlink" href="#compute-reduce-command" title="Link to this heading"></a></h1>
</section>
<section id="compute-reduce-region-command">
<h1>compute reduce/region command<a class="headerlink" href="#compute-reduce-region-command" title="Link to this heading"></a></h1>
<section id="syntax">
<h2>Syntax<a class="headerlink" href="#syntax" title="Link to this heading"></a></h2>
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">compute </span><span class="nv nv-Identifier">ID</span><span class="w"> </span><span class="nv nv-Identifier">group-ID</span><span class="w"> </span><span class="n">style</span><span class="w"> </span><span class="n">arg</span><span class="w"> </span><span class="n">mode</span><span class="w"> </span><span class="n">input1</span><span class="w"> </span><span class="n">input2</span><span class="w"> </span><span class="n">...</span><span class="w"> </span><span class="n">keyword</span><span class="w"> </span><span class="n">args</span><span class="w"> </span><span class="n">...</span>
</pre></div>
</div>
<ul>
<li><p>ID, group-ID are documented in <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> command</p></li>
<li><p>style = <em>reduce</em> or <em>reduce/region</em></p>
<pre class="literal-block"><em>reduce</em> arg = none
<em>reduce/region</em> arg = region-ID
region-ID = ID of region to use for choosing atoms</pre>
</li>
<li><p>mode = <em>sum</em> or <em>min</em> or <em>minabs</em> or <em>max</em> or <em>maxabs</em> or <em>ave</em> or <em>sumsq</em> or <em>avesq</em> or <em>sumabs</em> or <em>aveabs</em></p></li>
<li><p>one or more inputs can be listed</p></li>
<li><p>input = <em>x</em> or <em>y</em> or <em>z</em> or <em>vx</em> or <em>vy</em> or <em>vz</em> or <em>fx</em> or <em>fy</em> or <em>fz</em> or c_ID or c_ID[N] or f_ID or f_ID[N] or v_name</p>
<pre class="literal-block"><em>x</em>,<em>y</em>,<em>z</em>,<em>vx</em>,<em>vy</em>,<em>vz</em>,<em>fx</em>,<em>fy</em>,<em>fz</em> = atom attribute (position, velocity, force component)
c_ID = per-atom or local vector calculated by a compute with ID
c_ID[I] = Ith column of per-atom or local array calculated by a compute with ID, I can include wildcard (see below)
f_ID = per-atom or local vector calculated by a fix with ID
f_ID[I] = Ith column of per-atom or local array calculated by a fix with ID, I can include wildcard (see below)
v_name = per-atom vector calculated by an atom-style variable with name</pre>
</li>
<li><p>zero or more keyword/args pairs may be appended</p></li>
<li><p>keyword = <em>replace</em> or <em>inputs</em></p>
<pre class="literal-block"><em>replace</em> args = vec1 vec2
vec1 = reduced value from this input vector will be replaced
vec2 = replace it with vec1[N] where N is index of max/min value from vec2
<em>inputs</em> arg = peratom or local
peratom = all inputs are per-atom quantities (default)
local = all input are local quantities</pre>
</li>
</ul>
</section>
<section id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Link to this heading"></a></h2>
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">compute </span><span class="nv nv-Identifier">1</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">reduce</span><span class="w"> </span><span class="n">sum</span><span class="w"> </span><span class="n">c_force</span>
<span class="k">compute </span><span class="nv nv-Identifier">1</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">reduce</span><span class="o">/</span><span class="k">region </span><span class="nv nv-Identifier">subbox</span><span class="w"> </span><span class="n">sum</span><span class="w"> </span><span class="n">c_force</span>
<span class="k">compute </span><span class="nv nv-Identifier">2</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">reduce</span><span class="w"> </span><span class="n">min</span><span class="w"> </span><span class="n">c_press[2]</span><span class="w"> </span><span class="n">f_ave</span><span class="w"> </span><span class="n">v_myKE</span>
<span class="k">compute </span><span class="nv nv-Identifier">2</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">reduce</span><span class="w"> </span><span class="n">min</span><span class="w"> </span><span class="n">c_press[</span><span class="o">*</span><span class="n">]</span><span class="w"> </span><span class="n">f_ave</span><span class="w"> </span><span class="n">v_myKE</span><span class="w"> </span><span class="n">inputs</span><span class="w"> </span><span class="n">peratom</span>
<span class="k">compute </span><span class="nv nv-Identifier">3</span><span class="w"> </span><span class="nv nv-Identifier">fluid</span><span class="w"> </span><span class="n">reduce</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="n">c_index[1]</span><span class="w"> </span><span class="n">c_index[2]</span><span class="w"> </span><span class="n">c_dist</span><span class="w"> </span><span class="n">replace</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">3</span><span class="w"> </span><span class="n">replace</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="m">3</span>
<span class="k">compute </span><span class="nv nv-Identifier">4</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">reduce</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="n">c_bond</span><span class="w"> </span><span class="n">inputs</span><span class="w"> </span><span class="n">local</span>
</pre></div>
</div>
</section>
<section id="description">
<h2>Description<a class="headerlink" href="#description" title="Link to this heading"></a></h2>
<p>Define a calculation that “reduces” one or more vector inputs into
scalar values, one per listed input. For the compute reduce command,
the inputs can be either per-atom or local quantities and must all be
of the same kind (per-atom or local); see discussion of the optional
<em>inputs</em> keyword below. The compute reduce/region command can only be
used with per-atom inputs.</p>
<p>Atom attributes are per-atom quantities, <a class="reference internal" href="compute.html"><span class="doc">computes</span></a> and
<a class="reference internal" href="fix.html"><span class="doc">fixes</span></a> can generate either per-atom or local quantities,
and <a class="reference internal" href="variable.html"><span class="doc">atom-style variables</span></a> generate per-atom
quantities. See the <a class="reference internal" href="variable.html"><span class="doc">variable</span></a> command and its
special functions which can perform the same reduction operations as
the compute reduce command on global vectors.</p>
<p>The reduction operation is specified by the <em>mode</em> setting. The <em>sum</em>
option adds the values in the vector into a global total. The <em>min</em>
or <em>max</em> options find the minimum or maximum value across all vector
values. The <em>minabs</em> or <em>maxabs</em> options find the minimum or maximum
value across all absolute vector values. The <em>ave</em> setting adds the
vector values into a global total, then divides by the number of
values in the vector. The <em>sumsq</em> option sums the square of the
values in the vector into a global total. The <em>avesq</em> setting does
the same as <em>sumsq</em>, then divides the sum of squares by the number of
values. The last two options can be useful for calculating the
variance of some quantity (e.g., variance = sumsq <span class="math notranslate nohighlight">\(-\)</span> ave<span class="math notranslate nohighlight">\(^2\)</span>). The <em>sumabs</em> option sums the absolute values in the
vector into a global total. The <em>aveabs</em> setting does the same as
<em>sumabs</em>, then divides the sum of absolute values by the number of
values.</p>
<p>Each listed input is operated on independently. For per-atom inputs,
the group specified with this command means only atoms within the
group contribute to the result. Likewise for per-atom inputs, if the
compute reduce/region command is used, the atoms must also currently
be within the region. Note that an input that produces per-atom
quantities may define its own group which affects the quantities it
returns. For example, if a compute is used as an input which
generates a per-atom vector, it will generate values of 0.0 for atoms
that are not in the group specified for that compute.</p>
<p>Each listed input can be an atom attribute (position, velocity, force
component) or can be the result of a <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> or
<a class="reference internal" href="fix.html"><span class="doc">fix</span></a> or the evaluation of an atom-style
<a class="reference internal" href="variable.html"><span class="doc">variable</span></a>.</p>
<p>Note that for values from a compute or fix, the bracketed index <span class="math notranslate nohighlight">\(I\)</span> can
be specified using a wildcard asterisk with the index to effectively
specify multiple values. This takes the form “*” or “*n” or “m*” or
“m*n”. If <span class="math notranslate nohighlight">\(N\)</span> is the size of the vector (for <em>mode</em> = scalar) or the
number of columns in the array (for <em>mode</em> = vector), then an asterisk
with no numeric values means all indices from 1 to <span class="math notranslate nohighlight">\(N\)</span>. A leading
asterisk means all indices from 1 to n (inclusive). A trailing
asterisk means all indices from m to <span class="math notranslate nohighlight">\(N\)</span> (inclusive). A middle asterisk
means all indices from m to n (inclusive).</p>
<p>Using a wildcard is the same as if the individual columns of the array
had been listed one by one. For example, the following two compute reduce
commands are equivalent, since the
<a class="reference internal" href="compute_stress_atom.html"><span class="doc">compute stress/atom</span></a> command creates a per-atom
array with six columns:</p>
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">compute </span><span class="nv nv-Identifier">myPress</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">stress</span><span class="o">/</span><span class="n">atom</span><span class="w"> </span><span class="n">NULL</span>
<span class="k">compute </span><span class="nv nv-Identifier">2</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">reduce</span><span class="w"> </span><span class="n">min</span><span class="w"> </span><span class="n">c_myPress[</span><span class="o">*</span><span class="n">]</span>
<span class="k">compute </span><span class="nv nv-Identifier">2</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">reduce</span><span class="w"> </span><span class="n">min</span><span class="w"> </span><span class="n">c_myPress[1]</span><span class="w"> </span><span class="n">c_myPress[2]</span><span class="w"> </span><span class="n">c_myPress[3]</span><span class="w"> </span><span class="o">&amp;</span>
<span class="w"> </span><span class="n">c_myPress[4]</span><span class="w"> </span><span class="n">c_myPress[5]</span><span class="w"> </span><span class="n">c_myPress[6]</span>
</pre></div>
</div>
<hr class="docutils" />
<p>The atom attribute values (<em>x</em>, <em>y</em>, <em>z</em>, <em>vx</em>, <em>vy</em>, <em>vz</em>, <em>fx</em>,
<em>fy</em>, and <em>fz</em>) are self-explanatory. Note that other atom attributes
can be used as inputs to this fix by using the <a class="reference internal" href="compute_property_atom.html"><span class="doc">compute
property/atom</span></a> command and then specifying an
input value from that compute.</p>
<p>If a value begins with “c_”, a compute ID must follow which has been
previously defined in the input script. Valid computes can generate
per-atom or local quantities. See the individual <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> page for details. If no bracketed integer is appended, the
vector calculated by the compute is used. If a bracketed integer is
appended, the Ith column of the array calculated by the compute is
used. Users can also write code for their own compute styles and
<a class="reference internal" href="Modify.html"><span class="doc">add them to LAMMPS</span></a>. See the discussion above for how
<span class="math notranslate nohighlight">\(I\)</span> can be specified with a wildcard asterisk to effectively
specify multiple values.</p>
<p>If a value begins with “f_”, a fix ID must follow which has been
previously defined in the input script. Valid fixes can generate
per-atom or local quantities. See the individual <a class="reference internal" href="fix.html"><span class="doc">fix</span></a>
page for details. Note that some fixes only produce their values on
certain timesteps, which must be compatible with when compute reduce
references the values, else an error results. If no bracketed integer
is appended, the vector calculated by the fix is used. If a bracketed
integer is appended, the Ith column of the array calculated by the fix
is used. Users can also write code for their own fix style and
<a class="reference internal" href="Modify.html"><span class="doc">add them to LAMMPS</span></a>. See the discussion above for how
<span class="math notranslate nohighlight">\(I\)</span> can be specified with a wildcard asterisk to effectively
specify multiple values.</p>
<p>If a value begins with “v_”, a variable name must follow which has
been previously defined in the input script. It must be an
<a class="reference internal" href="variable.html"><span class="doc">atom-style variable</span></a>. Atom-style variables can
reference thermodynamic keywords and various per-atom attributes, or
invoke other computes, fixes, or variables when they are evaluated, so
this is a very general means of generating per-atom quantities to
reduce.</p>
<hr class="docutils" />
<p>If the <em>replace</em> keyword is used, two indices <em>vec1</em> and <em>vec2</em> are
specified, where each index ranges from 1 to the number of input
values. The replace keyword can only be used if the <em>mode</em> is <em>min</em>
or <em>max</em>. It works as follows. A min/max is computed as usual on
the <em>vec2</em> input vector. The index <span class="math notranslate nohighlight">\(N\)</span> of that value within
<em>vec2</em> is also stored. Then, instead of performing a min/max on the
<em>vec1</em> input vector, the stored index is used to select the <span class="math notranslate nohighlight">\(N\)</span>th element of the <em>vec1</em> vector.</p>
<p>Thus, for example, if you wish to use this compute to find the bond
with maximum stretch, you can do it as follows:</p>
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">compute </span><span class="nv nv-Identifier">1</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">property</span><span class="o">/</span><span class="n">local</span><span class="w"> </span><span class="n">batom1</span><span class="w"> </span><span class="n">batom2</span>
<span class="k">compute </span><span class="nv nv-Identifier">2</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">bond</span><span class="o">/</span><span class="n">local</span><span class="w"> </span><span class="n">dist</span>
<span class="k">compute </span><span class="nv nv-Identifier">3</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">reduce</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="n">c_1[1]</span><span class="w"> </span><span class="n">c_1[2]</span><span class="w"> </span><span class="n">c_2</span><span class="w"> </span><span class="n">replace</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">3</span><span class="w"> </span><span class="n">replace</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="m">3</span>
<span class="k">thermo_style</span><span class="w"> </span><span class="n">custom</span><span class="w"> </span><span class="n">step</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="n">c_3[1]</span><span class="w"> </span><span class="n">c_3[2]</span><span class="w"> </span><span class="n">c_3[3]</span>
</pre></div>
</div>
<p>The first two input values in the compute reduce command are vectors
with the IDs of the two atoms in each bond, using the
<a class="reference internal" href="compute_property_local.html"><span class="doc">compute property/local</span></a> command. The last input
value is bond distance, using the
<a class="reference internal" href="compute_bond_local.html"><span class="doc">compute bond/local</span></a> command. Instead of taking the
max of the two atom ID vectors, which does not yield useful
information in this context, the <em>replace</em> keywords will extract the
atom IDs for the two atoms in the bond of maximum stretch. These atom
IDs and the bond stretch will be printed with thermodynamic output.</p>
<div class="versionadded">
<p><span class="versionmodified added">Added in version 21Nov2023.</span></p>
</div>
<p>The <em>inputs</em> keyword allows selection of whether all the inputs are
per-atom or local quantities. As noted above, all the inputs must be
the same kind (per-atom or local). Per-atom is the default setting. If
a compute or fix is specified as an input, it must produce per-atom or
local data to match this setting. If it produces both, like for example
the <a class="reference internal" href="compute_voronoi_atom.html"><span class="doc">compute voronoi/atom</span></a> command, then
this keyword selects between them. If a compute <em>only</em> produces local
data, like for example the <a class="reference internal" href="compute_bond_local.html"><span class="doc">compute bond/local command</span></a>, the setting “inputs local” is <em>required</em>.</p>
<hr class="docutils" />
<p>If a single input is specified this compute produces a global scalar
value. If multiple inputs are specified, this compute produces a
global vector of values, the length of which is equal to the number of
inputs specified.</p>
<p>As discussed below, for the <em>sum</em>, <em>sumabs</em>, and <em>sumsq</em> modes, the
value(s) produced by this compute are all “extensive”, meaning their
value scales linearly with the number of atoms involved. If
normalized values are desired, this compute can be accessed by the
<a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style custom</span></a> command with
<a class="reference internal" href="thermo_modify.html"><span class="doc">thermo_modify norm yes</span></a> set as an option. Or it
can be accessed by a <a class="reference internal" href="variable.html"><span class="doc">variable</span></a> that divides by the
appropriate atom count.</p>
</section>
<hr class="docutils" />
<section id="output-info">
<h2>Output info<a class="headerlink" href="#output-info" title="Link to this heading"></a></h2>
<p>This compute calculates a global scalar if a single input value is
specified or a global vector of length <span class="math notranslate nohighlight">\(N\)</span>, where <span class="math notranslate nohighlight">\(N\)</span> is
the number of inputs, and which can be accessed by indices 1 to
<span class="math notranslate nohighlight">\(N\)</span>. These values can be used by any command that uses global
scalar or vector values from a compute as input. See the <a class="reference internal" href="Howto_output.html"><span class="doc">Howto
output</span></a> doc page for an overview of LAMMPS output
options.</p>
<p>All the scalar or vector values calculated by this compute are
“intensive”, except when the <em>sum</em>, <em>sumabs</em>, or <em>sumsq</em> modes are used on
per-atom or local vectors, in which case the calculated values are
“extensive”.</p>
<p>The scalar or vector values will be in whatever <a class="reference internal" href="units.html"><span class="doc">units</span></a>
the quantities being reduced are in.</p>
</section>
<section id="restrictions">
<h2>Restrictions<a class="headerlink" href="#restrictions" title="Link to this heading"></a></h2>
<p>As noted above, the compute reduce/region command can only be used
with per-atom inputs.</p>
</section>
<section id="related-commands">
<h2>Related commands<a class="headerlink" href="#related-commands" title="Link to this heading"></a></h2>
<p><a class="reference internal" href="compute.html"><span class="doc">compute</span></a>, <a class="reference internal" href="fix.html"><span class="doc">fix</span></a>, <a class="reference internal" href="variable.html"><span class="doc">variable</span></a></p>
</section>
<section id="default">
<h2>Default<a class="headerlink" href="#default" title="Link to this heading"></a></h2>
<p>The default value for the <em>inputs</em> keyword is peratom.</p>
</section>
</section>
</div>
</div>
<footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
<a href="compute_reaxff_atom.html" class="btn btn-neutral float-left" title="compute reaxff/atom command" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
<a href="compute_reduce_chunk.html" class="btn btn-neutral float-right" title="compute reduce/chunk command" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
</div>
<hr/>
<div role="contentinfo">
<p>&#169; Copyright 2003-2025 Sandia Corporation.</p>
</div>
Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
<a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
provided by <a href="https://readthedocs.org">Read the Docs</a>.
</footer>
</div>
</div>
</section>
</div>
<script>
jQuery(function () {
SphinxRtdTheme.Navigation.enable(false);
});
</script>
</body>
</html>