Added compute for Polyhedral Template Matching

doc/src/Eqs/ptm_rmsd.tex

@@ -0,0 +1,21 @@
+\documentclass[12pt,article]{article}
+
+\usepackage{indentfirst}
+\usepackage{amsmath}
+
+\newcommand{\set}[1]{\ensuremath{\mathbf{#1}}}
+\newcommand{\mean}[1]{\ensuremath{\overline{#1}}}
+\newcommand{\norm}[1]{\ensuremath{\left|\left|{#1}\right|\right|}}
+
+\begin{document}
+
+\begin{equation*}
+\text{RMSD}(\set{u}, \set{v}) = \min_{s, \set{Q}} \sqrt{\frac{1}{N} \sum\limits_{i=1}^{N}
+\norm{
+s[\vec{u_i} - \mean{\set{u}}]
+-
+\set{Q} \vec{v_i}
+}^2}
+\end{equation*}
+
+\end{document}

doc/src/compute_ptm_atom.txt

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+"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
+
+:link(lws,http://lammps.sandia.gov)
+:link(ld,Manual.html)
+:link(lc,Section_commands.html#comm)
+
+:line
+
+compute ptm/atom command :h3
+
+[Syntax:]
+
+compute ID group-ID ptm/atom structures threshold :pre
+
+ID, group-ID are documented in "compute"_compute.html command
+ptm/atom = style name of this compute command
+structures = structure types to search for
+threshold = lattice distortion threshold (RMSD) :ul
+
+[Examples:]
+
+compute 1 all ptm/atom default 0.1
+compute 1 all ptm/atom fcc-hcp-dcub-dhex 0.15
+compute 1 all ptm/atom all 0 :pre
+
+[Description:]
+
+Define a computation that determines the local lattice structure
+around an atom using the PTM (Polyhedral Template Matching) method.
+The PTM method is described in "(Larsen)"_#Larsen.
+
+Currently, there are seven lattice structures PTM recognizes:
+
+fcc = 1
+hcp = 2
+bcc = 3
+ico (icosahedral) = 4
+sc (simple cubic) = 5
+dcub (diamond cubic) = 6
+dhex (diamond hexagonal) = 7
+other = 8 :ul
+
+The value of the PTM structure will be 0 for atoms not in the specified
+compute group.  The choice of structures to search for can be specified using the "structures"
+argument, which is a hyphen-separated list of structure keywords.
+Two convenient pre-set options are provided:
+
+default: fcc-hcp-bcc-ico
+all: fcc-hcp-bcc-ico-sc-dcub-dhex :ul
+
+The 'default' setting detects the same structures as the Common Neighbor Analysis method.
+The 'all' setting searches for all structure types.  A small performance penalty is
+incurred for the diamond structures, so it is not recommended to use this option if
+it is known that the simulation does not contain diamond structures.
+
+
+PTM identifies structures using two steps.  First, a graph isomorphism test is used
+to identify potential structure matches.  Next, the deviation is computed between the
+local structure (in the simulation) and a template of the ideal lattice structure.
+The deviation is calculated as:
+
+:c,image(Eqs/ptm_rmsd.jpg)
+
+Here, u and v contain the coordinates of the local and ideal structures respectively,
+s is a scale factor, and Q is a rotation.  The best match is identified by the
+lowest RMSD value, using the optimal scaling, rotation, and correspondence between the
+points.
+
+The 'threshold' keyword sets an upper limit on the maximum permitted deviation before
+a local structure is identified as disordered.  Typical values are in the range 0.1-0.15,
+but larger values may be desirable at higher temperatures.
+A value of 0 is equivalent to infinity and can be used if no threshold is desired.
+
+
+The neighbor list needed to compute this quantity is constructed each
+time the calculation is performed (e.g. each time a snapshot of atoms
+is dumped).  Thus it can be inefficient to compute/dump this quantity
+too frequently or to have multiple compute/dump commands, each with a
+{ptm/atom} style.
+
+[Output info:]
+
+This compute calculates a per-atom array, which can be accessed by
+any command that uses per-atom values from a compute as input.  See
+"Section 6.15"_Section_howto.html#howto_15 for an overview of
+LAMMPS output options.
+
+Results are stored in the per-atom array in the following order:
+
+type
+rmsd
+interatomic distance
+qw
+qx
+qy
+qw :ul
+
+The type is a number from 0 to 8.  The rmsd is a positive real number.
+The interatomic distance is computed from the scale factor in the RMSD equation.
+The (qw,qx,qy,qz) parameters represent the orientation of the local structure
+in quaternion form.  The reference coordinates for each template (from which the
+orientation is determined) can be found in the {ptm_constants.h} file in the PTM source directory.
+
+[Restrictions:] none
+
+[Related commands:]
+
+"compute centro/atom"_compute_centro_atom.html
+"compute cna/atom"_compute_cna_atom.html
+
+[Default:] none
+
+:line
+
+:link(Larsen)
+[(Larsen)] Larsen, Schmidt, Schiøtz, Modelling Simul Mater Sci Eng, 24, 055007 (2016).
+