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			<div class="section" id="variable-command">
			<span id="index-0"></span><h1>variable command<a class="headerlink" href="#variable-command" title="Permalink to this headline">¶</a></h1>
			<div class="section" id="syntax">
			<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
			<div class="highlight-python"><div class="highlight"><pre>variable name style args ...
			</pre></div>
			</div>
			<ul class="simple">
			<li>name = name of variable to define</li>
			<li>style = <em>delete</em> or <em>index</em> or <em>loop</em> or <em>world</em> or <em>universe</em> or <em>uloop</em> or <em>string</em> or <em>format</em> or <em>getenv</em> or <em>file</em> or <em>atomfile</em> or <em>python</em> or <em>equal</em> or <em>vector</em> or <em>atom</em></li>
			</ul>
			<pre class="literal-block">
			<em>delete</em> = no args
			<em>index</em> args = one or more strings
			<em>loop</em> args = N
			N = integer size of loop, loop from 1 to N inclusive
			<em>loop</em> args = N pad
			N = integer size of loop, loop from 1 to N inclusive
			pad = all values will be same length, e.g. 001, 002, ..., 100
			<em>loop</em> args = N1 N2
			N1,N2 = loop from N1 to N2 inclusive
			<em>loop</em> args = N1 N2 pad
			N1,N2 = loop from N1 to N2 inclusive
			pad = all values will be same length, e.g. 050, 051, ..., 100
			<em>world</em> args = one string for each partition of processors
			<em>universe</em> args = one or more strings
			<em>uloop</em> args = N
			N = integer size of loop
			<em>uloop</em> args = N pad
			N = integer size of loop
			pad = all values will be same length, e.g. 001, 002, ..., 100
			<em>string</em> arg = one string
			<em>format</em> args = vname fstr
			vname = name of equal-style variable to evaluate
			fstr = C-style format string
			<em>getenv</em> arg = one string
			<em>file</em> arg = filename
			<em>atomfile</em> arg = filename
			<em>python</em> arg = function
			<em>equal</em> or <em>vector</em> or <em>atom</em> args = one formula containing numbers, thermo keywords, math operations, group functions, atom values and vectors, compute/fix/variable references
			numbers = 0.0, 100, -5.4, 2.8e-4, etc
			constants = PI, version, on, off, true, false, yes, no
			thermo keywords = vol, ke, press, etc from <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a>
			math operators = (), -x, x+y, x-y, x*y, x/y, x^y, x%y,
			x == y, x != y, x &lt y, x &lt= y, x &gt y, x &gt= y, x && y, x \|\| y, !x
			math functions = sqrt(x), exp(x), ln(x), log(x), abs(x),
			sin(x), cos(x), tan(x), asin(x), acos(x), atan(x), atan2(y,x),
			random(x,y,z), normal(x,y,z), ceil(x), floor(x), round(x)
			ramp(x,y), stagger(x,y), logfreq(x,y,z), logfreq2(x,y,z),
			stride(x,y,z), stride2(x,y,z,a,b,c),
			vdisplace(x,y), swiggle(x,y,z), cwiggle(x,y,z)
			group functions = count(group), mass(group), charge(group),
			xcm(group,dim), vcm(group,dim), fcm(group,dim),
			bound(group,dir), gyration(group), ke(group),
			angmom(group,dim), torque(group,dim),
			inertia(group,dimdim), omega(group,dim)
			region functions = count(group,region), mass(group,region), charge(group,region),
			xcm(group,dim,region), vcm(group,dim,region), fcm(group,dim,region),
			bound(group,dir,region), gyration(group,region), ke(group,reigon),
			angmom(group,dim,region), torque(group,dim,region),
			inertia(group,dimdim,region), omega(group,dim,region)
			special functions = sum(x), min(x), max(x), ave(x), trap(x), slope(x), gmask(x), rmask(x), grmask(x,y), next(x)
			feature functions = is_active(category,feature,exact), is_defined(category,id,exact)
			atom value = id[i], mass[i], type[i], mol[i], x[i], y[i], z[i], vx[i], vy[i], vz[i], fx[i], fy[i], fz[i], q[i]
			atom vector = id, mass, type, mol, x, y, z, vx, vy, vz, fx, fy, fz, q
			compute references = c_ID, c_ID[i], c_ID[i][j], C_ID, C_ID[i]
			fix references = f_ID, f_ID[i], f_ID[i][j], F_ID, F_ID[i]
			variable references = v_name, v_name[i]
			</pre>
			</div>
			<div class="section" id="examples">
			<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
			<div class="highlight-python"><div class="highlight"><pre>variable x index run1 run2 run3 run4 run5 run6 run7 run8
			variable LoopVar loop $n
			variable beta equal temp/3.0
			variable b1 equal x[234]+0.5*vol
			variable b1 equal "x[234] + 0.5*vol"
			variable b equal xcm(mol1,x)/2.0
			variable b equal c_myTemp
			variable b atom x*y/vol
			variable foo string myfile
			variable myPy python increase
			variable f file values.txt
			variable temp world 300.0 310.0 320.0 ${Tfinal}
			variable x universe 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
			variable x uloop 15 pad
			variable str format x %.6g
			variable x delete
			</pre></div>
			</div>
			</div>
			<div class="section" id="description">
			<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
			<p>This command assigns one or more strings to a variable name for
			evaluation later in the input script or during a simulation.</p>
			<p>Variables can thus be useful in several contexts. A variable can be
			defined and then referenced elsewhere in an input script to become
			part of a new input command. For variable styles that store multiple
			strings, the <a class="reference internal" href="next.html"><em>next</em></a> command can be used to increment which
			string is assigned to the variable. Variables of style <em>equal</em> store
			a formula which when evaluated produces a single numeric value which
			can be output either directly (see the <a class="reference internal" href="print.html"><em>print</em></a>, <a class="reference internal" href="fix_print.html"><em>fix print</em></a>, and <a class="reference internal" href="run.html"><em>run every</em></a> commands) or as part
			of thermodynamic output (see the <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a>
			command), or used as input to an averaging fix (see the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command). Variables of style <em>vector</em>
			store a formula which produces a vector of such values which can be
			used as input to various averaging fixes, or elements of which can be
			part of thermodynamic output. Variables of style <em>atom</em> store a
			formula which when evaluated produces one numeric value per atom which
			can be output to a dump file (see the <a class="reference internal" href="dump.html"><em>dump custom</em></a> command)
			or used as input to an averaging fix (see the <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> and <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>
			commands). Variables of style <em>atomfile</em> can be used anywhere in an
			input script that atom-style variables are used; they get their
			per-atom values from a file rather than from a formula. Variables of
			style <em>python</em> can be hooked to Python functions using code you
			provide, so that the variable gets its value from the evaluation of
			the Python code.</p>
			<div class="admonition note">
			<p class="first admonition-title">Note</p>
			<p class="last">As discussed in <a class="reference internal" href="Section_commands.html#cmd-2"><span>Section 3.2</span></a> of the
			manual, an input script can use “immediate” variables, specified as
			$(formula) with parenthesis, where the formula has the same syntax as
			equal-style variables described on this page. This is a convenient
			way to evaluate a formula immediately without using the variable
			command to define a named variable and then evaluate that
			variable. See below for a more detailed discussion of this feature.</p>
			</div>
			<p>In the discussion that follows, the “name” of the variable is the
			arbitrary string that is the 1st argument in the variable command.
			This name can only contain alphanumeric characters and underscores.
			The “string” is one or more of the subsequent arguments. The “string”
			can be simple text as in the 1st example above, it can contain other
			variables as in the 2nd example, or it can be a formula as in the 3rd
			example. The “value” is the numeric quantity resulting from
			evaluation of the string. Note that the same string can generate
			different values when it is evaluated at different times during a
			simulation.</p>
			<div class="admonition note">
			<p class="first admonition-title">Note</p>
			<p class="last">When the input script line is encountered that defines a
			variable of style <em>equal</em> or <em>vector</em> or <em>atom</em> or <em>python</em> that
			contains a formula or Python code, the formula is NOT immediately
			evaluated. It will be evaluated every time when the variable is
			<strong>used</strong> instead. If you simply want to evaluate a formula in place you
			can use as so-called. See the section below about “Immediate
			Evaluation of Variables” for more details on the topic. This is also
			true of a <em>format</em> style variable since it evaluates another variable
			when it is invoked.</p>
			</div>
			<div class="admonition note">
			<p class="first admonition-title">Note</p>
			<p class="last">Variables of style <em>equal</em> and <em>vector</em> and <em>atom</em> can be used
			as inputs to various other LAMMPS commands which evaluate their
			formulas as needed, e.g. at different timesteps during a
			<a class="reference internal" href="run.html"><em>run</em></a>. Variables of style <em>python</em> can be used in place of
			an equal-style variable so long as the associated Python function, as
			defined by the <a class="reference internal" href="python.html"><em>python</em></a> command, returns a numeric value.
			Thus any command that states it can use an equal-style variable as an
			argument, can also use such a python-style variable. This means that
			when the LAMMPS command evaluates the variable, the Python function
			will be executed.</p>
			</div>
			<div class="admonition note">
			<p class="first admonition-title">Note</p>
			<p class="last">When a variable command is encountered in the input script and
			the variable name has already been specified, the command is ignored.
			This means variables can NOT be re-defined in an input script (with
			two exceptions, read further). This is to allow an input script to be
			processed multiple times without resetting the variables; see the
			<a class="reference internal" href="jump.html"><em>jump</em></a> or <a class="reference internal" href="include.html"><em>include</em></a> commands. It also means
			that using the <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a> -var
			will override a corresponding index variable setting in the input
			script.</p>
			</div>
			<p>There are two exceptions to this rule. First, variables of style
			<em>string</em>, <em>getenv</em>, <em>equal</em>, <em>vector</em>, <em>atom</em>, and <em>python</em> ARE
			redefined each time the command is encountered. This allows these
			style of variables to be redefined multiple times in an input script.
			In a loop, this means the formula associated with an <em>equal</em> or <em>atom</em>
			style variable can change if it contains a substitution for another
			variable, e.g. $x or v_x.</p>
			<p>Second, as described below, if a variable is iterated on to the end of
			its list of strings via the <a class="reference internal" href="next.html"><em>next</em></a> command, it is removed
			from the list of active variables, and is thus available to be
			re-defined in a subsequent variable command. The <em>delete</em> style does
			the same thing.</p>
			<hr class="docutils" />
			<p><a class="reference internal" href="Section_commands.html#cmd-2"><span>This section</span></a> of the manual explains how
			occurrences of a variable name in an input script line are replaced by
			the variable’s string. The variable name can be referenced as $x if
			the name “x” is a single character, or as ${LoopVar} if the name
			“LoopVar” is one or more characters.</p>
			<p>As described below, for variable styles <em>index</em>, <em>loop</em>, <em>file</em>,
			<em>universe</em>, and <em>uloop</em>, which string is assigned to a variable can be
			incremented via the <a class="reference internal" href="next.html"><em>next</em></a> command. When there are no more
			strings to assign, the variable is exhausted and a flag is set that
			causes the next <a class="reference internal" href="jump.html"><em>jump</em></a> command encountered in the input
			script to be skipped. This enables the construction of simple loops
			in the input script that are iterated over and then exited from.</p>
			<p>As explained above, an exhausted variable can be re-used in an input
			script. The <em>delete</em> style also removes the variable, the same as if
			it were exhausted, allowing it to be redefined later in the input
			script or when the input script is looped over. This can be useful
			when breaking out of a loop via the <a class="reference internal" href="if.html"><em>if</em></a> and <a class="reference internal" href="jump.html"><em>jump</em></a>
			commands before the variable would become exhausted. For example,</p>
			<div class="highlight-python"><div class="highlight"><pre>label loop
			variable a loop 5
			print "A = $a"
			if "$a > 2" then "jump in.script break"
			next a
			jump in.script loop
			label break
			variable a delete
			</pre></div>
			</div>
			<hr class="docutils" />
			<p>This section describes how all the various variable styles are defined
			and what they store. Except for the <em>equal</em> and <em>vector</em> and <em>atom</em>
			styles, which are explained in the next section.</p>
			<p>Many of the styles store one or more strings. Note that a single
			string can contain spaces (multiple words), if it is enclosed in
			quotes in the variable command. When the variable is substituted for
			in another input script command, its returned string will then be
			interpreted as multiple arguments in the expanded command.</p>
			<p>For the <em>index</em> style, one or more strings are specified. Initially,
			the 1st string is assigned to the variable. Each time a
			<a class="reference internal" href="next.html"><em>next</em></a> command is used with the variable name, the next
			string is assigned. All processors assign the same string to the
			variable.</p>
			<p><em>Index</em> style variables with a single string value can also be set by
			using the command-line switch -var; see <a class="reference internal" href="Section_start.html#start-7"><span>this section</span></a> for details.</p>
			<p>The <em>loop</em> style is identical to the <em>index</em> style except that the
			strings are the integers from 1 to N inclusive, if only one argument N
			is specified. This allows generation of a long list of runs
			(e.g. 1000) without having to list N strings in the input script.
			Initially, the string “1” is assigned to the variable. Each time a
			<a class="reference internal" href="next.html"><em>next</em></a> command is used with the variable name, the next
			string (“2”, “3”, etc) is assigned. All processors assign the same
			string to the variable. The <em>loop</em> style can also be specified with
			two arguments N1 and N2. In this case the loop runs from N1 to N2
			inclusive, and the string N1 is initially assigned to the variable.
			N1 <= N2 and N2 >= 0 is required.</p>
			<p>For the <em>world</em> style, one or more strings are specified. There must
			be one string for each processor partition or “world”. See <a class="reference internal" href="Section_start.html#start-7"><span>this section</span></a> of the manual for information on
			running LAMMPS with multiple partitions via the “-partition”
			command-line switch. This variable command assigns one string to each
			world. All processors in the world are assigned the same string. The
			next command cannot be used with <em>equal</em> style variables, since there
			is only one value per world. This style of variable is useful when
			you wish to run different simulations on different partitions, or when
			performing a parallel tempering simulation (see the
			<a class="reference internal" href="temper.html"><em>temper</em></a> command), to assign different temperatures to
			different partitions.</p>
			<p>For the <em>universe</em> style, one or more strings are specified. There
			must be at least as many strings as there are processor partitions or
			“worlds”. See <a class="reference internal" href="Section_start.html#start-7"><span>this page</span></a> for information
			on running LAMMPS with multiple partitions via the “-partition”
			command-line switch. This variable command initially assigns one
			string to each world. When a <a class="reference internal" href="next.html"><em>next</em></a> command is encountered
			using this variable, the first processor partition to encounter it, is
			assigned the next available string. This continues until all the
			variable strings are consumed. Thus, this command can be used to run
			50 simulations on 8 processor partitions. The simulations will be run
			one after the other on whatever partition becomes available, until
			they are all finished. <em>Universe</em> style variables are incremented
			using the files “tmp.lammps.variable” and “tmp.lammps.variable.lock”
			which you will see in your directory during such a LAMMPS run.</p>
			<p>The <em>uloop</em> style is identical to the <em>universe</em> style except that the
			strings are the integers from 1 to N. This allows generation of long
			list of runs (e.g. 1000) without having to list N strings in the input
			script.</p>
			<p>For the <em>string</em> style, a single string is assigned to the variable.
			The only difference between this and using the <em>index</em> style with a
			single string is that a variable with <em>string</em> style can be redefined.
			E.g. by another command later in the input script, or if the script is
			read again in a loop.</p>
			<p>For the <em>format</em> style, an equal-style variable is specified along
			with a C-style format string, e.g. “%f” or “%.10g”, which must be
			appropriate for formatting a double-precision floating-point value.
			This allows an equal-style variable to be formatted specifically for
			output as a string, e.g. by the <a class="reference internal" href="print.html"><em>print</em></a> command, if the
			default format “%.15g” has too much precision.</p>
			<p>For the <em>getenv</em> style, a single string is assigned to the variable
			which should be the name of an environment variable. When the
			variable is evaluated, it returns the value of the environment
			variable, or an empty string if it not defined. This style of
			variable can be used to adapt the behavior of LAMMPS input scripts via
			environment variable settings, or to retrieve information that has
			been previously stored with the <a class="reference internal" href="shell.html"><em>shell putenv</em></a> command.
			Note that because environment variable settings are stored by the
			operating systems, they persist beyond a <a class="reference internal" href="clear.html"><em>clear</em></a> command.</p>
			<p>For the <em>file</em> style, a filename is provided which contains a list of
			strings to assign to the variable, one per line. The strings can be
			numeric values if desired. See the discussion of the next() function
			below for equal-style variables, which will convert the string of a
			file-style variable into a numeric value in a formula.</p>
			<p>When a file-style variable is defined, the file is opened and the
			string on the first line is read and stored with the variable. This
			means the variable can then be evaluated as many times as desired and
			will return that string. There are two ways to cause the next string
			from the file to be read: use the <a class="reference internal" href="next.html"><em>next</em></a> command or the
			next() function in an equal- or atom-style variable, as discussed
			below.</p>
			<p>The rules for formatting the file are as follows. A comment character
			“#” can be used anywhere on a line; text starting with the comment
			character is stripped. Blank lines are skipped. The first “word” of
			a non-blank line, delimited by white space, is the “string” assigned
			to the variable.</p>
			<p>For the <em>atomfile</em> style, a filename is provided which contains one or
			more sets of values, to assign on a per-atom basis to the variable.
			The format of the file is described below.</p>
			<p>When an atomfile-style variable is defined, the file is opened and the
			first set of per-atom values are read and stored with the variable.
			This means the variable can then be evaluated as many times as desired
			and will return those values. There are two ways to cause the next
			set of per-atom values from the file to be read: use the
			<a class="reference internal" href="next.html"><em>next</em></a> command or the next() function in an atom-style
			variable, as discussed below.</p>
			<p>The rules for formatting the file are as follows. Each time a set of
			per-atom values is read, a non-blank line is searched for in the file.
			A comment character “#” can be used anywhere on a line; text starting
			with the comment character is stripped. Blank lines are skipped. The
			first “word” of a non-blank line, delimited by white space, is read as
			the count N of per-atom lines to immediately follow. N can be be the
			total number of atoms in the system, or only a subset. The next N
			lines have the following format</p>
			<div class="highlight-python"><div class="highlight"><pre>ID value
			</pre></div>
			</div>
			<p>where ID is an atom ID and value is the per-atom numeric value that
			will be assigned to that atom. IDs can be listed in any order.</p>
			<div class="admonition note">
			<p class="first admonition-title">Note</p>
			<p class="last">Every time a set of per-atom lines is read, the value for all
			atoms is first set to 0.0. Thus values for atoms whose ID does not
			appear in the set, will remain 0.0.</p>
			</div>
			<p>For the <em>python</em> style a Python function name is provided. This needs
			to match a function name specified in a <a class="reference internal" href="python.html"><em>python</em></a> command
			which returns a value to this variable as defined by its <em>return</em>
			keyword. For exampe these two commands would be self-consistent:</p>
			<div class="highlight-python"><div class="highlight"><pre>variable foo python myMultiply
			python myMultiply return v_foo format f file funcs.py
			</pre></div>
			</div>
			<p>The two commands can appear in either order so long as both are
			specified before the Python function is invoked for the first time.</p>
			<p>Each time the variable is evaluated, the associated Python function is
			invoked, and the value it returns is also returned by the variable.
			Since the Python function can use other LAMMPS variables as input, or
			query interal LAMMPS quantities to perform its computation, this means
			the variable can return a different value each time it is evaluated.</p>
			<p>The type of value stored in the variable is determined by the <em>format</em>
			keyword of the <a class="reference internal" href="python.html"><em>python</em></a> command. It can be an integer
			(i), floating point (f), or string (s) value. As mentioned above, if
			it is a numeric value (integer or floating point), then the
			python-style variable can be used in place of an equal-style variable
			anywhere in an input script, e.g. as an argument to another command
			that allows for equal-style variables.</p>
			<hr class="docutils" />
			<p>For the <em>equal</em> and <em>vector</em> and <em>atom</em> styles, a single string is
			specified which represents a formula that will be evaluated afresh
			each time the variable is used. If you want spaces in the string,
			enclose it in double quotes so the parser will treat it as a single
			argument. For <em>equal</em>-style variables the formula computes a scalar
			quantity, which becomes the value of the variable whenever it is
			evaluated. For <em>vector</em>-style variables the formula computes a vector
			of quantities, which becomes the value of the variable whenever it is
			evaluated. For <em>atom</em>-style variables the formula computes one
			quantity for each atom whenever it is evaluated.</p>
			<p>Note that <em>equal</em>, <em>vector</em>, and <em>atom</em> variables can produce
			different values at different stages of the input script or at
			different times during a run. For example, if an <em>equal</em> variable is
			used in a <a class="reference internal" href="fix_print.html"><em>fix print</em></a> command, different values could
			be printed each timestep it was invoked. If you want a variable to be
			evaluated immediately, so that the result is stored by the variable
			instead of the string, see the section below on “Immediate Evaluation
			of Variables”.</p>
			<p>The next command cannot be used with <em>equal</em> or <em>vector</em> or <em>atom</em>
			style variables, since there is only one string.</p>
			<p>The formula for an <em>equal</em>, <em>vector</em>, or <em>atom</em> variable can contain a
			variety of quantities. The syntax for each kind of quantity is
			simple, but multiple quantities can be nested and combined in various
			ways to build up formulas of arbitrary complexity. For example, this
			is a valid (though strange) variable formula:</p>
			<div class="highlight-python"><div class="highlight"><pre>variable x equal "pe + c_MyTemp / vol^(1/3)"
			</pre></div>
			</div>
			<p>Specifically, a formula can contain numbers, constants, thermo
			keywords, math operators, math functions, group functions, region
			functions, atom values, atom vectors, compute references, fix
			references, and references to other variables.</p>
			<table border="1" class="docutils">
			<colgroup>
			<col width="6%" />
			<col width="94%" />
			</colgroup>
			<tbody valign="top">
			<tr class="row-odd"><td>Number</td>
			<td>0.2, 100, 1.0e20, -15.4, etc</td>
			</tr>
			<tr class="row-even"><td>Constant</td>
			<td>PI, version, on, off, true, false, yes, no</td>
			</tr>
			<tr class="row-odd"><td>Thermo keywords</td>
			<td>vol, pe, ebond, etc</td>
			</tr>
			<tr class="row-even"><td>Math operators</td>
			<td>(), -x, x+y, x-y, x*y, x/y, x^y, x%y,</td>
			</tr>
			<tr class="row-odd"><td>Math operators</td>
			<td>(), -x, x+y, x-y, x*y, x/y, x^y, x%y, x == y, x != y, x &lt y, x &lt= y, x &gt y, x &gt= y, x && y, x \|\| y, !x</td>
			</tr>
			<tr class="row-even"><td>Math functions</td>
			<td>sqrt(x), exp(x), ln(x), log(x), abs(x), sin(x), cos(x), tan(x), asin(x), acos(x), atan(x), atan2(y,x), random(x,y,z), normal(x,y,z), ceil(x), floor(x), round(x), ramp(x,y), stagger(x,y), logfreq(x,y,z), logfreq2(x,y,z), stride(x,y,z), stride2(x,y,z,a,b,c), vdisplace(x,y), swiggle(x,y,z), cwiggle(x,y,z)</td>
			</tr>
			<tr class="row-odd"><td>Group functions</td>
			<td>count(ID), mass(ID), charge(ID), xcm(ID,dim), vcm(ID,dim), fcm(ID,dim), bound(ID,dir), gyration(ID), ke(ID), angmom(ID,dim), torque(ID,dim), inertia(ID,dimdim), omega(ID,dim)</td>
			</tr>
			<tr class="row-even"><td>Region functions</td>
			<td>count(ID,IDR), mass(ID,IDR), charge(ID,IDR), xcm(ID,dim,IDR), vcm(ID,dim,IDR), fcm(ID,dim,IDR), bound(ID,dir,IDR), gyration(ID,IDR), ke(ID,IDR), angmom(ID,dim,IDR), torque(ID,dim,IDR), inertia(ID,dimdim,IDR), omega(ID,dim,IDR)</td>
			</tr>
			<tr class="row-odd"><td>Special functions</td>
			<td>sum(x), min(x), max(x), ave(x), trap(x), slope(x), gmask(x), rmask(x), grmask(x,y), next(x)</td>
			</tr>
			<tr class="row-even"><td>Atom values</td>
			<td>id[i], mass[i], type[i], mol[i], x[i], y[i], z[i], vx[i], vy[i], vz[i], fx[i], fy[i], fz[i], q[i]</td>
			</tr>
			<tr class="row-odd"><td>Atom vectors</td>
			<td>id, mass, type, mol, x, y, z, vx, vy, vz, fx, fy, fz, q</td>
			</tr>
			<tr class="row-even"><td>Compute references</td>
			<td>c_ID, c_ID[i], c_ID[i][j], C_ID, C_ID[i]</td>
			</tr>
			<tr class="row-odd"><td>Fix references</td>
			<td>f_ID, f_ID[i], f_ID[i][j], F_ID, F_ID[i]</td>
			</tr>
			<tr class="row-even"><td>Other variables</td>
			<td>v_name, v_name[i]</td>
			</tr>
			</tbody>
			</table>
			<p>Most of the formula elements produce a scalar value. Some produce a
			global or per-atom vector of values. Global vectors can be produced
			by computes or fixes or by other vector-style variables. Per-atom
			vectors are produced by atom vectors, compute references that
			represent a per-atom vector, fix references that represent a per-atom
			vector, and variables that are atom-style variables. Math functions
			that operate on scalar values produce a scalar value; math function
			that operate on global or per-atom vectors do so element-by-element
			and produce a global or per-atom vector.</p>
			<p>A formula for equal-style variables cannot use any formula element
			that produces a global or per-atom vector. A formula for a
			vector-style variable can use formula elements that produce either a
			scalar value or a global vector value, but cannot use a formula
			element that produces a per-atom vector. A formula for an atom-style
			variable can use formula elements that produce either a scalar value
			or a per-atom vector, but not one that produces a global vector.
			Atom-style variables are evaluated by other commands that define a
			<a class="reference internal" href="group.html"><em>group</em></a> on which they operate, e.g. a <a class="reference internal" href="dump.html"><em>dump</em></a> or
			<a class="reference internal" href="compute.html"><em>compute</em></a> or <a class="reference internal" href="fix.html"><em>fix</em></a> command. When they invoke
			the atom-style variable, only atoms in the group are included in the
			formula evaluation. The variable evaluates to 0.0 for atoms not in
			the group.</p>
			<hr class="docutils" />
			<div class="section" id="numers-constants-and-thermo-keywords">
			<h3>Numers, constants, and thermo keywords<a class="headerlink" href="#numers-constants-and-thermo-keywords" title="Permalink to this headline">¶</a></h3>
			<p>Numbers can contain digits, scientific notation
			(3.0e20,3.0e-20,3.0E20,3.0E-20), and leading minus signs.</p>
			<p>Constants are set at compile time and cannot be changed. <em>PI</em> will
			return the number 3.14159265358979323846; <em>on</em>, <em>true</em> or <em>yes</em> will
			return 1.0; <em>off</em>, <em>false</em> or <em>no</em> will return 0.0; <em>version</em> will
			return a numeric version code of the current LAMMPS version (e.g.
			version 2 Sep 2015 will return the number 20150902). The corresponding
			value for newer versions of LAMMPS will be larger, for older versions
			of LAMMPS will be smaller. This can be used to have input scripts
			adapt automatically to LAMMPS versions, when non-backwards compatible
			syntax changes are introduced. Here is an illustrative example (which
			will not work, since the <em>version</em> has been introduced more recently):</p>
			<div class="highlight-python"><div class="highlight"><pre>if $(version<20140513) then "communicate vel yes" else "comm_modify vel yes"
			</pre></div>
			</div>
			<p>The thermo keywords allowed in a formula are those defined by the
			<a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> command. Thermo keywords that
			require a <a class="reference internal" href="compute.html"><em>compute</em></a> to calculate their values such as
			“temp” or “press”, use computes stored and invoked by the
			<a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command. This means that you can
			only use those keywords in a variable if the style you are using with
			the thermo_style command (and the thermo keywords associated with that
			style) also define and use the needed compute. Note that some thermo
			keywords use a compute indirectly to calculate their value (e.g. the
			enthalpy keyword uses temp, pe, and pressure). If a variable is
			evaluated directly in an input script (not during a run), then the
			values accessed by the thermo keyword must be current. See the
			discussion below about “Variable Accuracy”.</p>
			</div>
			<hr class="docutils" />
			<div class="section" id="math-operators">
			<h3>Math Operators<a class="headerlink" href="#math-operators" title="Permalink to this headline">¶</a></h3>
			<p>Math operators are written in the usual way, where the “x” and “y” in
			the examples can themselves be arbitrarily complex formulas, as in the
			examples above. In this syntax, “x” and “y” can be scalar values or
			per-atom vectors. For example, “ke/natoms” is the division of two
			scalars, where “vy+vz” is the element-by-element sum of two per-atom
			vectors of y and z velocities.</p>
			<p>Operators are evaluated left to right and have the usual C-style
			precedence: unary minus and unary logical NOT operator ”!” have the
			highest precedence, exponentiation “^” is next; multiplication and
			division and the modulo operator “%” are next; addition and
			subtraction are next; the 4 relational operators “<”, “<=”, “>”, and
			“>=” are next; the two remaining relational operators “==” and ”!=”
			are next; then the logical AND operator “&&”; and finally the logical
			OR operator “\|\|” has the lowest precedence. Parenthesis can be used
			to group one or more portions of a formula and/or enforce a different
			order of evaluation than what would occur with the default precedence.</p>
			<div class="admonition note">
			<p class="first admonition-title">Note</p>
			<p class="last">Because a unary minus is higher precedence than exponentiation,
			the formula “-2^2” will evaluate to 4, not -4. This convention is
			compatible with some programming languages, but not others. As
			mentioned, this behavior can be easily overridden with parenthesis;
			the formula “-(2^2)” will evaluate to -4.</p>
			</div>
			<p>The 6 relational operators return either a 1.0 or 0.0 depending on
			whether the relationship between x and y is TRUE or FALSE. For
			example the expression x<10.0 in an atom-style variable formula will
			return 1.0 for all atoms whose x-coordinate is less than 10.0, and 0.0
			for the others. The logical AND operator will return 1.0 if both its
			arguments are non-zero, else it returns 0.0. The logical OR operator
			will return 1.0 if either of its arguments is non-zero, else it
			returns 0.0. The logical NOT operator returns 1.0 if its argument is
			0.0, else it returns 0.0.</p>
			<p>These relational and logical operators can be used as a masking or
			selection operation in a formula. For example, the number of atoms
			whose properties satifsy one or more criteria could be calculated by
			taking the returned per-atom vector of ones and zeroes and passing it
			to the <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> command.</p>
			</div>
			<hr class="docutils" />
			<div class="section" id="math-functions">
			<h3>Math Functions<a class="headerlink" href="#math-functions" title="Permalink to this headline">¶</a></h3>
			<p>Math functions are specified as keywords followed by one or more
			parenthesized arguments “x”, “y”, “z”, each of which can themselves be
			arbitrarily complex formulas. In this syntax, the arguments can
			represent scalar values or global vectors or per-atom vectors. In the
			latter case, the math operation is performed on each element of the
			vector. For example, “sqrt(natoms)” is the sqrt() of a scalar, where
			“sqrt(y*z)” yields a per-atom vector with each element being the
			sqrt() of the product of one atom’s y and z coordinates.</p>
			<p>Most of the math functions perform obvious operations. The ln() is
			the natural log; log() is the base 10 log.</p>
			<p>The random(x,y,z) function takes 3 arguments: x = lo, y = hi, and z =
			seed. It generates a uniform random number between lo and hi. The
			normal(x,y,z) function also takes 3 arguments: x = mu, y = sigma, and
			z = seed. It generates a Gaussian variate centered on mu with
			variance sigma^2. In both cases the seed is used the first time the
			internal random number generator is invoked, to initialize it. For
			equal-style and vector-style variables, every processor uses the same
			seed so that they each generate the same sequence of random numbers.
			For atom-style variables, a unique seed is created for each processor,
			based on the specified seed. This effectively generates a different
			random number for each atom being looped over in the atom-style
			variable.</p>
			<div class="admonition note">
			<p class="first admonition-title">Note</p>
			<p class="last">Internally, there is just one random number generator for all
			equal-style and vector-style variables and another one for all
			atom-style variables. If you define multiple variables (of each
			style) which use the random() or normal() math functions, then the
			internal random number generators will only be initialized once, which
			means only one of the specified seeds will determine the sequence of
			generated random numbers.</p>
			</div>
			<p>The ceil(), floor(), and round() functions are those in the C math
			library. Ceil() is the smallest integer not less than its argument.
			Floor() if the largest integer not greater than its argument. Round()
			is the nearest integer to its argument.</p>
			<p>The ramp(x,y) function uses the current timestep to generate a value
			linearly intepolated between the specified x,y values over the course
			of a run, according to this formula:</p>
			<div class="highlight-python"><div class="highlight"><pre><span class="n">value</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="p">(</span><span class="n">y</span><span class="o">-</span><span class="n">x</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">timestep</span><span class="o">-</span><span class="n">startstep</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">stopstep</span><span class="o">-</span><span class="n">startstep</span><span class="p">)</span>
			</pre></div>
			</div>
			<p>The run begins on startstep and ends on stopstep. Startstep and
			stopstep can span multiple runs, using the <em>start</em> and <em>stop</em> keywords
			of the <a class="reference internal" href="run.html"><em>run</em></a> command. See the <a class="reference internal" href="run.html"><em>run</em></a> command for
			details of how to do this.</p>
			<p>The stagger(x,y) function uses the current timestep to generate a new
			timestep. X,y > 0 and x > y are required. The generated timesteps
			increase in a staggered fashion, as the sequence
			x,x+y,2x,2x+y,3x,3x+y,etc. For any current timestep, the next
			timestep in the sequence is returned. Thus if stagger(1000,100) is
			used in a variable by the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a>
			command, it will generate the sequence of output timesteps:</p>
			<div class="highlight-python"><div class="highlight"><pre><span class="mi">100</span><span class="p">,</span><span class="mi">1000</span><span class="p">,</span><span class="mi">1100</span><span class="p">,</span><span class="mi">2000</span><span class="p">,</span><span class="mi">2100</span><span class="p">,</span><span class="mi">3000</span><span class="p">,</span><span class="n">etc</span>
			</pre></div>
			</div>
			<p>The logfreq(x,y,z) function uses the current timestep to generate a
			new timestep. X,y,z > 0 and y < z are required. The generated
			timesteps are on a base-z logarithmic scale, starting with x, and the
			y value is how many of the z-1 possible timesteps within one
			logarithmic interval are generated. I.e. the timesteps follow the
			sequence x,2x,3x,...yx,xz,2xz,3xz,...yxz,xz^2,2xz^2,etc. For
			any current timestep, the next timestep in the sequence is returned.
			Thus if logfreq(100,4,10) is used in a variable by the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command, it will generate this sequence of
			output timesteps:</p>
			<div class="highlight-python"><div class="highlight"><pre><span class="mi">100</span><span class="p">,</span><span class="mi">200</span><span class="p">,</span><span class="mi">300</span><span class="p">,</span><span class="mi">400</span><span class="p">,</span><span class="mi">1000</span><span class="p">,</span><span class="mi">2000</span><span class="p">,</span><span class="mi">3000</span><span class="p">,</span><span class="mi">4000</span><span class="p">,</span><span class="mi">10000</span><span class="p">,</span><span class="mi">20000</span><span class="p">,</span><span class="n">etc</span>
			</pre></div>
			</div>
			<p>The logfreq2(x,y,z) function is similar to logfreq, except a single
			logarithmic interval is divided into y equally-spaced timesteps and
			all of them are output. Y < z is not required. Thus, if
			logfreq2(100,18,10) is used in a variable by the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command, then the interval between 100 and
			1000 is divided as 900/18 = 50 steps, and it will generate the
			sequence of output timesteps:</p>
			<div class="highlight-python"><div class="highlight"><pre><span class="mi">100</span><span class="p">,</span><span class="mi">150</span><span class="p">,</span><span class="mi">200</span><span class="p">,</span><span class="o">...</span><span class="mi">950</span><span class="p">,</span><span class="mi">1000</span><span class="p">,</span><span class="mi">1500</span><span class="p">,</span><span class="mi">2000</span><span class="p">,</span><span class="o">...</span><span class="mi">9500</span><span class="p">,</span><span class="mi">10000</span><span class="p">,</span><span class="mi">15000</span><span class="p">,</span><span class="n">etc</span>
			</pre></div>
			</div>
			<p>The stride(x,y,z) function uses the current timestep to generate a new
			timestep. X,y >= 0 and z > 0 and x <= y are required. The generated
			timesteps increase in increments of z, from x to y, i.e. it generates
			the sequece x,x+z,x+2z,...,y. If y-x is not a multiple of z, then
			similar to the way a for loop operates, the last value will be one
			that does not exceed y. For any current timestep, the next timestep
			in the sequence is returned. Thus if stride(1000,2000,100) is used
			in a variable by the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command, it
			will generate the sequence of output timesteps:</p>
			<div class="highlight-python"><div class="highlight"><pre><span class="mi">1000</span><span class="p">,</span><span class="mi">1100</span><span class="p">,</span><span class="mi">1200</span><span class="p">,</span> <span class="o">...</span> <span class="p">,</span><span class="mi">1900</span><span class="p">,</span><span class="mi">2000</span>
			</pre></div>
			</div>
			<p>The stride2(x,y,z,a,b,c) function is similar to the stride() function
			except it generates two sets of strided timesteps, one at a coarser
			level and one at a finer level. Thus it is useful for debugging,
			e.g. to produce output every timestep at the point in simulation when
			a problem occurs. X,y >= 0 and z > 0 and x <= y are required, as are
			a,b >= 0 and c > 0 and a < b. Also, a >= x and b <= y are required so
			that the second stride is inside the first. The generated timesteps
			increase in increments of z, starting at x, until a is reached. At
			that point the timestep increases in increments of c, from a to b,
			then after b, increments by z are resumed until y is reached. For any
			current timestep, the next timestep in the sequence is returned. Thus
			if stride(1000,2000,100,1350,1360,1) is used in a variable by the
			<a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command, it will generate the
			sequence of output timesteps:</p>
			<div class="highlight-python"><div class="highlight"><pre>1000,1100,1200,1300,1350,1351,1352, ... 1359,1360,1400,1500, ... ,2000
			</pre></div>
			</div>
			<p>The vdisplace(x,y) function takes 2 arguments: x = value0 and y =
			velocity, and uses the elapsed time to change the value by a linear
			displacement due to the applied velocity over the course of a run,
			according to this formula:</p>
			<div class="highlight-python"><div class="highlight"><pre><span class="n">value</span> <span class="o">=</span> <span class="n">value0</span> <span class="o">+</span> <span class="n">velocity</span><span class="o"></span><span class="p">(</span><span class="n">timestep</span><span class="o">-</span><span class="n">startstep</span><span class="p">)</span><span class="o"></span><span class="n">dt</span>
			</pre></div>
			</div>
			<p>where dt = the timestep size.</p>
			<p>The run begins on startstep. Startstep can span multiple runs, using
			the <em>start</em> keyword of the <a class="reference internal" href="run.html"><em>run</em></a> command. See the
			<a class="reference internal" href="run.html"><em>run</em></a> command for details of how to do this. Note that the
			<a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> keyword elaplong =
			timestep-startstep.</p>
			<p>The swiggle(x,y,z) and cwiggle(x,y,z) functions each take 3 arguments:
			x = value0, y = amplitude, z = period. They use the elapsed time to
			oscillate the value by a sin() or cos() function over the course of a
			run, according to one of these formulas, where omega = 2 PI / period:</p>
			<div class="highlight-python"><div class="highlight"><pre><span class="n">value</span> <span class="o">=</span> <span class="n">value0</span> <span class="o">+</span> <span class="n">Amplitude</span> <span class="o"></span> <span class="n">sin</span><span class="p">(</span><span class="n">omega</span><span class="o"></span><span class="p">(</span><span class="n">timestep</span><span class="o">-</span><span class="n">startstep</span><span class="p">)</span><span class="o">*</span><span class="n">dt</span><span class="p">)</span>
			<span class="n">value</span> <span class="o">=</span> <span class="n">value0</span> <span class="o">+</span> <span class="n">Amplitude</span> <span class="o"></span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">cos</span><span class="p">(</span><span class="n">omega</span><span class="o"></span><span class="p">(</span><span class="n">timestep</span><span class="o">-</span><span class="n">startstep</span><span class="p">)</span><span class="o">*</span><span class="n">dt</span><span class="p">))</span>
			</pre></div>
			</div>
			<p>where dt = the timestep size.</p>
			<p>The run begins on startstep. Startstep can span multiple runs, using
			the <em>start</em> keyword of the <a class="reference internal" href="run.html"><em>run</em></a> command. See the
			<a class="reference internal" href="run.html"><em>run</em></a> command for details of how to do this. Note that the
			<a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> keyword elaplong =
			timestep-startstep.</p>
			</div>
			<hr class="docutils" />
			<div class="section" id="group-and-region-functions">
			<h3>Group and Region Functions<a class="headerlink" href="#group-and-region-functions" title="Permalink to this headline">¶</a></h3>
			<p>Group functions are specified as keywords followed by one or two
			parenthesized arguments. The first argument <em>ID</em> is the group-ID.
			The <em>dim</em> argument, if it exists, is <em>x</em> or <em>y</em> or <em>z</em>. The <em>dir</em>
			argument, if it exists, is <em>xmin</em>, <em>xmax</em>, <em>ymin</em>, <em>ymax</em>, <em>zmin</em>, or
			<em>zmax</em>. The <em>dimdim</em> argument, if it exists, is <em>xx</em> or <em>yy</em> or <em>zz</em>
			or <em>xy</em> or <em>yz</em> or <em>xz</em>.</p>
			<p>The group function count() is the number of atoms in the group. The
			group functions mass() and charge() are the total mass and charge of
			the group. Xcm() and vcm() return components of the position and
			velocity of the center of mass of the group. Fcm() returns a
			component of the total force on the group of atoms. Bound() returns
			the min/max of a particular coordinate for all atoms in the group.
			Gyration() computes the radius-of-gyration of the group of atoms. See
			the <a class="reference internal" href="compute_gyration.html"><em>compute gyration</em></a> command for a definition
			of the formula. Angmom() returns components of the angular momentum
			of the group of atoms around its center of mass. Torque() returns
			components of the torque on the group of atoms around its center of
			mass, based on current forces on the atoms. Inertia() returns one of
			6 components of the symmetric inertia tensor of the group of atoms
			around its center of mass, ordered as Ixx,Iyy,Izz,Ixy,Iyz,Ixz.
			Omega() returns components of the angular velocity of the group of
			atoms around its center of mass.</p>
			<p>Region functions are specified exactly the same way as group functions
			except they take an extra final argument <em>IDR</em> which is the region ID.
			The function is computed for all atoms that are in both the group and
			the region. If the group is “all”, then the only criteria for atom
			inclusion is that it be in the region.</p>
			</div>
			<hr class="docutils" />
			<div class="section" id="special-functions">
			<h3>Special Functions<a class="headerlink" href="#special-functions" title="Permalink to this headline">¶</a></h3>
			<p>Special functions take specific kinds of arguments, meaning their
			arguments cannot be formulas themselves.</p>
			<p>The sum(x), min(x), max(x), ave(x), trap(x), and slope(x) functions
			each take 1 argument which is of the form “c_ID” or “c_ID[N]” or
			“f_ID” or “f_ID[N]” or “v_name”. The first two are computes and the
			second two are fixes; the ID in the reference should be replaced by
			the ID of a compute or fix defined elsewhere in the input script. The
			compute or fix must produce either a global vector or array. If it
			produces a global vector, then the notation without “[N]” should be
			used. If it produces a global array, then the notation with “[N]”
			should be used, when N is an integer, to specify which column of the
			global array is being referenced. The last form of argument “v_name”
			is for a vector-style variable where “name” is replaced by the name of
			the variable.</p>
			<p>These functions operate on a global vector of inputs and reduce it to
			a single scalar value. This is analagous to the operation of the
			<a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> command, which performs similar
			operations on per-atom and local vectors.</p>
			<p>The sum() function calculates the sum of all the vector elements. The
			min() and max() functions find the minimum and maximum element
			respectively. The ave() function is the same as sum() except that it
			divides the result by the length of the vector.</p>
			<p>The trap() function is the same as sum() except the first and last
			elements are multiplied by a weighting factor of 1/2 when performing
			the sum. This effectively implements an integration via the
			trapezoidal rule on the global vector of data. I.e. consider a set of
			points, equally spaced by 1 in their x coordinate: (1,V1), (2,V2),
			..., (N,VN), where the Vi are the values in the global vector of
			length N. The integral from 1 to N of these points is trap(). When
			appropriately normalized by the timestep size, this function is useful
			for calculating integrals of time-series data, like that generated by
			the <a class="reference internal" href="fix_ave_correlate.html"><em>fix ave/correlate</em></a> command.</p>
			<p>The slope() function uses linear regression to fit a line to the set
			of points, equally spaced by 1 in their x coordinate: (1,V1), (2,V2),
			..., (N,VN), where the Vi are the values in the global vector of
			length N. The returned value is the slope of the line. If the line
			has a single point or is vertical, it returns 1.0e20.</p>
			<p>The gmask(x) function takes 1 argument which is a group ID. It
			can only be used in atom-style variables. It returns a 1 for
			atoms that are in the group, and a 0 for atoms that are not.</p>
			<p>The rmask(x) function takes 1 argument which is a region ID. It can
			only be used in atom-style variables. It returns a 1 for atoms that
			are in the geometric region, and a 0 for atoms that are not.</p>
			<p>The grmask(x,y) function takes 2 arguments. The first is a group ID,
			and the second is a region ID. It can only be used in atom-style
			variables. It returns a 1 for atoms that are in both the group and
			region, and a 0 for atoms that are not in both.</p>
			<p>The next(x) function takes 1 argument which is a variable ID (not
			“v_foo”, just “foo”). It must be for a file-style or atomfile-style
			variable. Each time the next() function is invoked (i.e. each time
			the equal-style or atom-style variable is evaluated), the following
			steps occur.</p>
			<p>For file-style variables, the current string value stored by the
			file-style variable is converted to a numeric value and returned by
			the function. And the next string value in the file is read and
			stored. Note that if the line previously read from the file was not a
			numeric string, then it will typically evaluate to 0.0, which is
			likely not what you want.</p>
			<p>For atomfile-style variables, the current per-atom values stored by
			the atomfile-style variable are returned by the function. And the
			next set of per-atom values in the file is read and stored.</p>
			<p>Since file-style and atomfile-style variables read and store the first
			line of the file or first set of per-atoms values when they are
			defined in the input script, these are the value(s) that will be
			returned the first time the next() function is invoked. If next() is
			invoked more times than there are lines or sets of lines in the file,
			the variable is deleted, similar to how the <a class="reference internal" href="next.html"><em>next</em></a> command
			operates.</p>
			</div>
			<hr class="docutils" />
			<div class="section" id="feature-functions">
			<h3>Feature Functions<a class="headerlink" href="#feature-functions" title="Permalink to this headline">¶</a></h3>
			<p>Feature functions allow to probe the running LAMMPS executable for
			whether specific features are either active, defined, or available.
			The functions take two arguments, a <em>category</em> and a corresponding
			<em>argument</em>. The arguments are strings thus cannot be formulas
			themselves (only $-style immediate variable expansion is possible).
			Return value is either 1.0 or 0.0 depending on whether the function
			evaluates to true or false, respectively.</p>
			<p>The <em>is_active()</em> function allows to query for active settings which
			are grouped by categories. Currently supported categories and
			arguments are:</p>
			<ul class="simple">
			<li><em>package</em> (argument = <em>cuda</em> or <em>gpu</em> or <em>intel</em> or <em>kokkos</em> or <em>omp</em>)</li>
			<li><em>newton</em> (argument = <em>pair</em> or <em>bond</em> or <em>any</em>)</li>
			<li><em>pair</em> (argument = <em>single</em> or <em>respa</em> or <em>manybody</em> or <em>tail</em> or <em>shift</em>)</li>
			<li><em>comm_style</em> (argument = <em>brick</em> or <em>tiled</em>)</li>
			<li><em>min_style</em> (argument = any of the compiled in minimizer styles)</li>
			<li><em>run_style</em> (argument = any of the compiled in run styles)</li>
			<li><em>atom_style</em> (argument = any of the compiled in atom styles)</li>
			<li><em>pair_style</em> (argument = any of the compiled in pair styles)</li>
			<li><em>bond_style</em> (argument = any of the compiled in bond styles)</li>
			<li><em>angle_style</em> (argument = any of the compiled in angle styles)</li>
			<li><em>dihedral_style</em> (argument = any of the compiled in dihedral styles)</li>
			<li><em>improper_style</em> (argument = any of the compiled in improper styles)</li>
			<li><em>kspace_style</em> (argument = any of the compiled in kspace styles)</li>
			</ul>
			<p>Most of the settings are self-explanatory, the <em>single</em> argument in the
			<em>pair</em> category allows to check whether a pair style supports a
			Pair::single() function as needed by compute group/group and others
			features or LAMMPS, <em>respa</em> allows to check whether the inner/middle/outer
			mode of r-RESPA is supported. In the various style categories,
			the checking is also done using suffix flags, if available and enabled.</p>
			<p>Example 1: disable use of suffix for pppm when using GPU package (i.e. run it on the CPU concurrently to running the pair style on the GPU), but do use the suffix otherwise (e.g. with USER-OMP).</p>
			<div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/coul/long 14.0
			if $(is_active(package,gpu)) then "suffix off"
			kspace_style pppm
			</pre></div>
			</div>
			<p>Example 2: use r-RESPA with inner/outer cutoff, if supported by pair style, otherwise fall back to using pair and reducing the outer time step</p>
			<div class="highlight-python"><div class="highlight"><pre>timestep $(2.0(1.0+is_active(pair,respa))
			if $(is_active(pair,respa)) then "run_style respa 4 3 2 2 improper 1 inner 2 5.5 7.0 outer 3 kspace 4" else "run_style respa 3 3 2 improper 1 pair 2 kspace 3"
			</pre></div>
			</div>
			<p>The <em>is_defined()</em> function allows to query categories like <em>compute</em>,
			<em>dump</em>, <em>fix</em>, <em>group</em>, <em>region</em>, and <em>variable</em> whether an entry
			with the provided name or id is defined.</p>
			<p>The <em>is_available()</em> function allows to query whether a specific
			optional feature is available, i.e. compiled in. This currently
			works for the following categories: <em>command</em>, <em>compute</em>, <em>fix</em>,
			and <em>pair_style</em>. For all categories except <em>command</em> also appending
			active suffixes is tried before reporting failure.</p>
			</div>
			<hr class="docutils" />
			<div class="section" id="atom-values-and-vectors">
			<h3>Atom Values and Vectors<a class="headerlink" href="#atom-values-and-vectors" title="Permalink to this headline">¶</a></h3>
			<p>Atom values take an integer argument I from 1 to N, where I is the
			atom-ID, e.g. x[243], which means use the x coordinate of the atom
			with ID = 243. Or they can take a variable name, specified as v_name,
			where name is the name of the variable, like x[v_myIndex]. The
			variable can be of any style except <em>vector</em> or <em>atom</em> or <em>atomfile</em>
			variables. The variable is evaluated and the result is expected to be
			numeric and is cast to an integer (i.e. 3.4 becomes 3), to use an an
			index, which must be a value from 1 to N. Note that a “formula”
			cannot be used as the argument between the brackets, e.g. x[243+10]
			or x[v_myIndex+1] are not allowed. To do this a single variable can
			be defined that contains the needed formula.</p>
			<p>Note that the 0 < atom-ID <= N, where N is the largest atom ID
			in the system. If an ID is specified for an atom that does not
			currently exist, then the generated value is 0.0.</p>
			<p>Atom vectors generate one value per atom, so that a reference like
			“vx” means the x-component of each atom’s velocity will be used when
			evaluating the variable.</p>
			<p>The meaning of the different atom values and vectors is mostly
			self-explanatory. <em>Mol</em> refers to the molecule ID of an atom, and is
			only defined if an <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> is being used that
			defines molecule IDs.</p>
			<p>Note that many other atom attributes can be used as inputs to a
			variable by using the <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command and then specifying
			a quantity from that compute.</p>
			</div>
			<hr class="docutils" />
			<div class="section" id="compute-references">
			<h3>Compute References<a class="headerlink" href="#compute-references" title="Permalink to this headline">¶</a></h3>
			<p>Compute references access quantities calculated by a
			<a class="reference internal" href="compute.html"><em>compute</em></a>. The ID in the reference should be replaced by
			the ID of a compute defined elsewhere in the input script. As
			discussed in the doc page for the <a class="reference internal" href="compute.html"><em>compute</em></a> command,
			computes can produce global, per-atom, or local values. Only global
			and per-atom values can be used in a variable. Computes can also
			produce a scalar, vector, or array.</p>
			<p>An equal-style variable can only use scalar values, which means a
			global scalar, or an element of a global or per-atom vector or array.
			A vector-style variable can use scalar values or a global vector of
			values, or a column of a global array of values, Atom-style variables
			can use global scalar values. They can also use per-atom vector
			values. A vector value can be a per-atom vector itself, or a column
			of a per-atom array. See the doc pages for individual computes to see
			what kind of values they produce.</p>
			<p>Examples of different kinds of compute references are as follows.
			There is typically no ambiguity (see exception below) as to what a
			reference means, since computes only produce either global or per-atom
			quantities, never both.</p>
			<table border="1" class="docutils">
			<colgroup>
			<col width="10%" />
			<col width="90%" />
			</colgroup>
			<tbody valign="top">
			<tr class="row-odd"><td>c_ID</td>
			<td>global scalar, or per-atom vector</td>
			</tr>
			<tr class="row-even"><td>c_ID[I]</td>
			<td>Ith element of global vector, or atom I’s value in per-atom vector, or Ith column from per-atom array</td>
			</tr>
			<tr class="row-odd"><td>c_ID[I][J]</td>
			<td>I,J element of global array, or atom I’s Jth value in per-atom array</td>
			</tr>
			</tbody>
			</table>
			<p>For I and J indices, integers can be specified or a variable name,
			specified as v_name, where name is the name of the variable. The
			rules for this syntax are the same as for the “Atom Values and
			Vectors” discussion above.</p>
			<p>One source of ambiguity for compute references is when a vector-style
			variable refers to a compute that produces both a global scalar and a
			global vector. Consider a compute with ID “foo” that does this,
			referenced as follows by variable “a”, where “myVec” is another
			vector-style variable:</p>
			<div class="highlight-python"><div class="highlight"><pre>variable a vector c_foo*v_myVec
			</pre></div>
			</div>
			<p>The reference “c_foo” could refer to either the global scalar or
			global vector produced by compute “foo”. In this case, “c_foo” will
			always refer to the global scalar, and “C_foo” can be used to
			reference the global vector. Similarly if the compute produces both a
			global vector and global array, then “c_foo[I]” will always refer to
			an element of the global vector, and “C_foo[I]” can be used to
			reference the Ith column of the global array.</p>
			<p>Note that if a variable containing a compute is evaluated directly in
			an input script (not during a run), then the values accessed by the
			compute must be current. See the discussion below about “Variable
			Accuracy”.</p>
			</div>
			<hr class="docutils" />
			<div class="section" id="fix-references">
			<h3>Fix References<a class="headerlink" href="#fix-references" title="Permalink to this headline">¶</a></h3>
			<p>Fix references access quantities calculated by a <a class="reference internal" href="compute.html"><em>fix</em></a>.
			The ID in the reference should be replaced by the ID of a fix defined
			elsewhere in the input script. As discussed in the doc page for the
			<a class="reference internal" href="fix.html"><em>fix</em></a> command, fixes can produce global, per-atom, or local
			values. Only global and per-atom values can be used in a variable.
			Fixes can also produce a scalar, vector, or array. An equal-style
			variable can only use scalar values, which means a global scalar, or
			an element of a global or per-atom vector or array. Atom-style
			variables can use the same scalar values. They can also use per-atom
			vector values. A vector value can be a per-atom vector itself, or a
			column of an per-atom array. See the doc pages for individual fixes
			to see what kind of values they produce.</p>
			<p>The different kinds of fix references are exactly the same as the
			compute references listed in the above table, where “<a href="#id1"><span class="problematic" id="id2">c_</span></a>” is replaced
			by “<a href="#id3"><span class="problematic" id="id4">f_</span></a>”. Again, there is typically no ambiguity (see exception below)
			as to what a reference means, since fixes only produce either global
			or per-atom quantities, never both.</p>
			<table border="1" class="docutils">
			<colgroup>
			<col width="10%" />
			<col width="90%" />
			</colgroup>
			<tbody valign="top">
			<tr class="row-odd"><td>f_ID</td>
			<td>global scalar, or per-atom vector</td>
			</tr>
			<tr class="row-even"><td>f_ID[I]</td>
			<td>Ith element of global vector, or atom I’s value in per-atom vector, or Ith column from per-atom array</td>
			</tr>
			<tr class="row-odd"><td>f_ID[I][J]</td>
			<td>I,J element of global array, or atom I’s Jth value in per-atom array</td>
			</tr>
			</tbody>
			</table>
			<p>For I and J indices, integers can be specified or a variable name,
			specified as v_name, where name is the name of the variable. The
			rules for this syntax are the same as for the “Atom Values and
			Vectors” discussion above.</p>
			<p>One source of ambiguity for fix references is the same ambiguity
			discussed for compute references above. Namely when a vector-style
			variable refers to a fix that produces both a global scalar and a
			global vector. The solution is the same as for compute references.
			For a fix with ID “foo”, “f_foo” will always refer to the global
			scalar, and “F_foo” can be used to reference the global vector. And
			similarly for distinguishing between a fix’s global vector versus
			global array with “f_foo[I]” versus “F_foo[I]”.</p>
			<p>Note that if a variable containing a fix is evaluated directly in an
			input script (not during a run), then the values accessed by the fix
			should be current. See the discussion below about “Variable
			Accuracy”.</p>
			<p>Note that some fixes only generate quantities on certain timesteps.
			If a variable attempts to access the fix on non-allowed timesteps, an
			error is generated. For example, the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>
			command may only generate averaged quantities every 100 steps. See
			the doc pages for individual fix commands for details.</p>
			</div>
			<hr class="docutils" />
			<div class="section" id="variable-references">
			<h3>Variable References<a class="headerlink" href="#variable-references" title="Permalink to this headline">¶</a></h3>
			<p>Variable references access quantities stored or calculated by other
			variables, which will cause those variables to be evaluated. The name
			in the reference should be replaced by the name of a variable defined
			elsewhere in the input script.</p>
			<p>As discussed on this doc page, equal-style variables generate a single
			global numeric value, vector-style variables gerarate a vector of
			global numeric values, and atom-style and atomfile-style variables
			generate a per-atom vector of numeric values. All other variables
			store one or more strings. A vector-style variable can be referenced
			wtih a</p>
			<p>The formula for an equal-style variable can use any style of variable
			including a vector_style or atom-style or atomfile-style. In these
			latter cases, a subscript must be used to access a single value from
			the vector-, atom-, or atomfile-style variable. If a string-storing
			variable is used, the string is converted to a numeric value. Note
			that this will typically produce a 0.0 if the string is not a numeric
			string, which is likely not what you want.</p>
			<p>The formula for an atom-style variable can use any style of variable,
			including other atom-style or atomfile-style variables.</p>
			<p>The formula for an atom-style variable can use any style of variable,
			including other atom-style or atomfile-style variables.</p>
			<p>Examples of different kinds of variable references are as follows.
			There is no ambiguity as to what a reference means, since variables
			produce only a global scalar or global vector or per-atom vector.</p>
			<table border="1" class="docutils">
			<colgroup>
			<col width="14%" />
			<col width="86%" />
			</colgroup>
			<tbody valign="top">
			<tr class="row-odd"><td>v_name</td>
			<td>global scalar from equal-style variable</td>
			</tr>
			<tr class="row-even"><td>v_name</td>
			<td>global vector from vector-style variable</td>
			</tr>
			<tr class="row-odd"><td>v_name</td>
			<td>per-atom vector from atom-style or atomfile-style variable</td>
			</tr>
			<tr class="row-even"><td>v_name[I]</td>
			<td>Ith element of a global vector from vector-style variable</td>
			</tr>
			<tr class="row-odd"><td>v_name[I]</td>
			<td>value of atom with ID = I from atom-style or atomfile-style variable</td>
			</tr>
			</tbody>
			</table>
			<p>For the I index, an integer can be specified or a variable name,
			specified as v_name, where name is the name of the variable. The
			rules for this syntax are the same as for the “Atom Values and
			Vectors” discussion above.</p>
			<hr class="docutils" />
			<p><strong>Immediate Evaluation of Variables:</strong></p>
			<p>If you want an equal-style variable to be evaluated immediately, it
			may be the case that you do not need to define a variable at all. See
			<a class="reference internal" href="Section_commands.html#cmd-2"><span>Section 3.2</span></a> of the manual, which
			describes the use of “immediate” variables in an input script,
			specified as $(formula) with parenthesis, where the formula has the
			same syntax as equal-style variables described on this page. This
			effectively evaluates a formula immediately without using the variable
			command to define a named variable.</p>
			<p>More generally, there is a difference between referencing a variable
			with a leading $ sign (e.g. $x or ${abc}) versus with a leading “<a href="#id5"><span class="problematic" id="id6">v_</span></a>”
			(e.g. v_x or v_abc). The former can be used in any input script
			command, including a variable command. The input script parser
			evaluates the reference variable immediately and substitutes its value
			into the command. As explained in <span class="xref std std-ref">Section commands 3.2</span> for “Parsing rules”, you can also use
			un-named “immediate” variables for this purpose. For example, a
			string like this $((xlo+xhi)/2+sqrt(v_area)) in an input script
			command evaluates the string between the parenthesis as an equal-style
			variable formula.</p>
			<p>Referencing a variable with a leading “<a href="#id7"><span class="problematic" id="id8">v_</span></a>” is an optional or required
			kind of argument for some commands (e.g. the <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a> or <a class="reference internal" href="dump.html"><em>dump custom</em></a> or
			<a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> commands) if you wish it to evaluate
			a variable periodically during a run. It can also be used in a
			variable formula if you wish to reference a second variable. The
			second variable will be evaluated whenever the first variable is
			evaluated.</p>
			<p>As an example, suppose you use this command in your input script to
			define the variable “v” as</p>
			<div class="highlight-python"><div class="highlight"><pre>variable v equal vol
			</pre></div>
			</div>
			<p>before a run where the simulation box size changes. You might think
			this will assign the initial volume to the variable “v”. That is not
			the case. Rather it assigns a formula which evaluates the volume
			(using the thermo_style keyword “vol”) to the variable “v”. If you
			use the variable “v” in some other command like <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> then the current volume of the box will be
			evaluated continuously during the run.</p>
			<p>If you want to store the initial volume of the system, you can do it
			this way:</p>
			<div class="highlight-python"><div class="highlight"><pre>variable v equal vol
			variable v0 equal $v
			</pre></div>
			</div>
			<p>The second command will force “v” to be evaluated (yielding the
			initial volume) and assign that value to the variable “v0”. Thus the
			command</p>
			<div class="highlight-python"><div class="highlight"><pre>thermo_style custom step v_v v_v0
			</pre></div>
			</div>
			<p>would print out both the current and initial volume periodically
			during the run.</p>
			<p>Note that it is a mistake to enclose a variable formula in double
			quotes if it contains variables preceeded by $ signs. For example,</p>
			<div class="highlight-python"><div class="highlight"><pre>variable vratio equal "${vfinal}/${v0}"
			</pre></div>
			</div>
			<p>This is because the quotes prevent variable substitution (see <a class="reference internal" href="Section_commands.html#cmd-2"><span>this section</span></a> on parsing input script
			commands), and thus an error will occur when the formula for “vratio”
			is evaluated later.</p>
			<hr class="docutils" />
			<p><strong>Variable Accuracy:</strong></p>
			<p>Obviously, LAMMPS attempts to evaluate variables containing formulas
			(<em>equal</em> and <em>atom</em> style variables) accurately whenever the
			evaluation is performed. Depending on what is included in the
			formula, this may require invoking a <a class="reference internal" href="compute.html"><em>compute</em></a>, either
			directly or indirectly via a thermo keyword, or accessing a value
			previously calculated by a compute, or accessing a value calculated
			and stored by a <a class="reference internal" href="fix.html"><em>fix</em></a>. If the compute is one that calculates
			the pressure or energy of the system, then these quantities need to be
			tallied during the evaluation of the interatomic potentials (pair,
			bond, etc) on timesteps that the variable will need the values.</p>
			<p>LAMMPS keeps track of all of this during a <a class="reference internal" href="run.html"><em>run</em></a> or <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>. An error will be generated if you
			attempt to evaluate a variable on timesteps when it cannot produce
			accurate values. For example, if a <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> command prints a variable which accesses
			values stored by a <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command and the
			timesteps on which thermo output is generated are not multiples of the
			averaging frequency used in the fix command, then an error will occur.</p>
			<p>An input script can also request variables be evaluated before or
			after or in between runs, e.g. by including them in a
			<a class="reference internal" href="print.html"><em>print</em></a> command. In this case, if a compute is needed to
			evaluate a variable (either directly or indirectly), LAMMPS will not
			invoke the compute, but it will use a value previously calculated by
			the compute, and can do this only if it was invoked on the current
			timestep. Fixes will always provide a quantity needed by a variable,
			but the quantity may or may not be current. This leads to one of
			three kinds of behavior:</p>
			<p>(1) The variable may be evaluated accurately. If it contains
			references to a compute or fix, and these values were calculated on
			the last timestep of a preceeding run, then they will be accessed and
			used by the variable and the result will be accurate.</p>
			<p>(2) LAMMPS may not be able to evaluate the variable and will generate
			an error message stating so. For example, if the variable requires a
			quantity from a <a class="reference internal" href="compute.html"><em>compute</em></a> that has not been invoked on
			the current timestep, LAMMPS will generate an error. This means, for
			example, that such a variable cannot be evaluated before the first run
			has occurred. Likewise, in between runs, a variable containing a
			compute cannot be evaluated unless the compute was invoked on the last
			timestep of the preceding run, e.g. by thermodynamic output.</p>
			<p>One way to get around this problem is to perform a 0-timestep run
			before using the variable. For example, these commands</p>
			<div class="highlight-python"><div class="highlight"><pre>variable t equal temp
			print "Initial temperature = $t"
			run 1000
			</pre></div>
			</div>
			<p>will generate an error if the run is the first run specified in the
			input script, because generating a value for the “t” variable requires
			a compute for calculating the temperature to be invoked.</p>
			<p>However, this sequence of commands would be fine:</p>
			<div class="highlight-python"><div class="highlight"><pre>run 0
			variable t equal temp
			print "Initial temperature = $t"
			run 1000
			</pre></div>
			</div>
			<p>The 0-timestep run initializes and invokes various computes, including
			the one for temperature, so that the value it stores is current and
			can be accessed by the variable “t” after the run has completed. Note
			that a 0-timestep run does not alter the state of the system, so it
			does not change the input state for the 1000-timestep run that
			follows. Also note that the 0-timestep run must actually use and
			invoke the compute in question (e.g. via <a class="reference internal" href="thermo_style.html"><em>thermo</em></a> or
			<a class="reference internal" href="dump.html"><em>dump</em></a> output) in order for it to enable the compute to be
			used in a variable after the run. Thus if you are trying to print a
			variable that uses a compute you have defined, you can insure it is
			invoked on the last timestep of the preceding run by including it in
			thermodynamic output.</p>
			<p>Unlike computes, <a class="reference internal" href="fix.html"><em>fixes</em></a> will never generate an error if
			their values are accessed by a variable in between runs. They always
			return some value to the variable. However, the value may not be what
			you expect if the fix has not yet calculated the quantity of interest
			or it is not current. For example, the <a class="reference internal" href="fix_indent.html"><em>fix indent</em></a>
			command stores the force on the indenter. But this is not computed
			until a run is performed. Thus if a variable attempts to print this
			value before the first run, zeroes will be output. Again, performing
			a 0-timestep run before printing the variable has the desired effect.</p>
			<p>(3) The variable may be evaluated incorrectly and LAMMPS may have no
			way to detect this has occurred. Consider the following sequence of
			commands:</p>
			<div class="highlight-python"><div class="highlight"><pre>pair_coeff 1 1 1.0 1.0
			run 1000
			pair_coeff 1 1 1.5 1.0
			variable e equal pe
			print "Final potential energy = $e"
			</pre></div>
			</div>
			<p>The first run is performed using one setting for the pairwise
			potential defined by the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> and
			<a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> commands. The potential energy is
			evaluated on the final timestep and stored by the <a class="reference internal" href="compute_pe.html"><em>compute pe</em></a> compute (this is done by the
			<a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command). Then a pair coefficient is
			changed, altering the potential energy of the system. When the
			potential energy is printed via the “e” variable, LAMMPS will use the
			potential energy value stored by the <a class="reference internal" href="compute_pe.html"><em>compute pe</em></a>
			compute, thinking it is current. There are many other commands which
			could alter the state of the system between runs, causing a variable
			to evaluate incorrectly.</p>
			<p>The solution to this issue is the same as for case (2) above, namely
			perform a 0-timestep run before the variable is evaluated to insure
			the system is up-to-date. For example, this sequence of commands
			would print a potential energy that reflected the changed pairwise
			coefficient:</p>
			<div class="highlight-python"><div class="highlight"><pre>pair_coeff 1 1 1.0 1.0
			run 1000
			pair_coeff 1 1 1.5 1.0
			run 0
			variable e equal pe
			print "Final potential energy = $e"
			</pre></div>
			</div>
			</div>
			</div>
			<hr class="docutils" />
			<div class="section" id="restrictions">
			<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
			<p>Indexing any formula element by global atom ID, such as an atom value,
			requires the <a class="reference internal" href="atom_style.html"><em>atom style</em></a> to use a global mapping in
			order to look up the vector indices. By default, only atom styles
			with molecular information create global maps. The <a class="reference internal" href="atom_modify.html"><em>atom_modify map</em></a> command can override the default, e.g. for
			atomic-style atom styles.</p>
			<p>All <em>universe</em>- and <em>uloop</em>-style variables defined in an input script
			must have the same number of values.</p>
			</div>
			<div class="section" id="related-commands">
			<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
			<p><a class="reference internal" href="next.html"><em>next</em></a>, <a class="reference internal" href="jump.html"><em>jump</em></a>, <a class="reference internal" href="include.html"><em>include</em></a>,
			<a class="reference internal" href="temper.html"><em>temper</em></a>, <a class="reference internal" href="fix_print.html"><em>fix print</em></a>, <a class="reference internal" href="print.html"><em>print</em></a></p>
			<p><strong>Default:</strong> none</p>
			</div>
			</div>


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