lammps/doc/variable.txt

"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

variable command :h3

[Syntax:]

variable name style args ... :pre

name = name of variable to define :ulb,l
style = {index} or {loop} or {world} or {universe} or {uloop} or {equal} or {atom} :l
  {index} args = one or more strings
  {loop} args = N = integer size of loop
  {world} args = one string for each partition of processors
  {universe} args = one or more strings
  {uloop} args = N = integer size of loop
  {equal} or {atom} 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
    thermo keywords = vol, ke, press, etc from "thermo_style"_thermo_style.html
    math operations = (), -x, x+y, x-y, x*y, x/y, x^y, sqrt(x), exp(x), ln(x)
    group functions = count(group), mass(group), charge(group),
		      xcm(group,dim), vcm(group,dim), fcm(group,dim),
		      bound(group,xmin), gyration(group)
    atom value = mass\[N\], x\[N\], y\[N\], z\[N\],
                 vx\[N\], vy\[N\], vz\[N\], fx\[N\], fy\[N\], fz\[N\]
    atom vector = mass\[\], x\[\], y\[\], z\[\],
                  vx\[\], vy\[\], vz\[\], fx\[\], fy\[\], fz\[\]
    compute references = c_ID, c_ID\[2\], c_ID\[N\], c_ID\[N\]\[2\], c_ID\[\], c_ID\[\]\[2\]
    fix references = f_ID, f_ID\[2\], f_ID\[N\], f_ID\[N\]\[2\], f_ID\[\], f_ID\[\]\[2\]
    other variables = v_abc, v_abc\[N\], v_abc\[\] :pre
:ule

[Examples:]

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 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 :pre

[Description:]

This command assigns one or more strings to a variable name for
evaluation later in the input script or during a simulation.

Variables can be used in several ways in LAMMPS.  A variable can be
referenced elsewhere in an input script to become part of a new input
command.  For variable styles that store multiple strings, the
"next"_next.html command can be used to increment which string is
assigned to the variable.  Variables of style {equal} can be evaluated
to produce a single numeric value which can be output either directly
(see the "print"_print.html, "fix print"_fix_print.html, and "run
every"_run.html commands) or as part of thermodynamic output (see the
"thermo_style"_thermo_style.html command), or used as input to an
averaging fix (see the "fix ave/time"_fix_ave/time command).
Variables of style {atom} can be evaluated to produce one numeric
value per atom which can be output to a dump file (see the "dump
custom"_dump.html command) or used as input to an averaging fix (see
the "fix ave/spatial"_fix_ave_spatial.html and "fix
ave/atom"_fix_ave_atom.html commands).

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.

IMPORTANT NOTE: 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 2 exceptions, read further).  This is to allow an input
script to be processed multiple times without resetting the variables;
see the "jump"_jump.html or "include"_include.html commands.  It also
means that using the "command-line switch"_Section_start.html#2_6 -var
will override a corresponding variable setting in the input script.

There are two exceptions to this rule.  First, variables of style
{equal} and {atom} ARE redefined each time the command is encountered.
This allows them to be reset, when their formulas contain a
substitution for another variable, e.g. $x.  This can be useful in a
loop.  This also means an {equal}-style variable will re-define a
command-line switch -var setting, so an {index}-style variable should
be used for such settings instead, as in bench/in.lj.

Second, as described below, if a variable is iterated on to the end of
its list of strings via the "next"_next.html command, it is removed
from the list of active varaibles, and is thus available to be
re-defined in a subsequent variable command.

:line

"This section"_Section_commands.html#3_2 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.

As described below, for variable styles {index}, {loop}, {universe},
and {uloop}, which string is assigned to a variable can be incremented
via the "next"_next.html command.  When there are no more strings to
assign, the variable is exhausted and a flag is set that causes the
next "jump"_jump.html 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.

:line

For the {index} style, one or more strings are specified.  Initially,
the 1st string is assigned to the variable.  Each time a
"next"_next.html command is used with the variable name, the next
string is assigned.  All processors assign the same string to the
variable.

{Index} style variables with a single string value can also be set by
using the command-line switch -var; see "this
section"_Section_start.html#2_6 for details.

The {loop} style is identical to the {index} style except that the
strings are the integers from 1 to N.  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 "next"_next.html command is used with the variable name,
the next string ("2", "3", etc) is assigned.  All processors assign
the same string to the variable.

For the {world} style, one or more strings are specified.  There must
be one string for each processor partition or "world".  See "this
section"_Section_start.html#2_6 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 {equal} 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
"temper"_temper.html command), to assign different temperatures to
different partitions.

For the {universe} style, one or more strings are specified.  There
must be at least as many strings as there are processor partitions or
"worlds".  See "this page"_Section_start.html#2_6 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 "next"_next.html 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.  {Universe} 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.

The {uloop} style is identical to the {universe} 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.

:line

For the {equal} and {atom} 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
{equal} style variables the formula computes a scalar quantity, which
becomes the value of the variable whenever it is evaluated.  For
{atom} style variables the formula computes one quantity for each
atom whenever it is evaluated.

Note that {equal} and {atom} variables can produce different values at
different stages of the input script or at different times during a
run.  For example, if an {equal} variable is used in a "fix
print"_fix_print.html command, different values could be printed each
timestep it was invoked.

The next command cannot be used with {equal} or {atom} style
variables, since there is only one string.

The formula for an {equal} or {atom} 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:

variable x equal "pe + c_MyTemp / vol^(1/3)" :pre

Specifically, an formula can contain numbers, thermo keywords, math
operations, group functions, atom values, atom vectors, compute
references, fix references, and references to other variables.

Number: 0.2, 100, 1.0e20, -15.4, etc
Thermo keywords: vol, pe, ebond, etc
Math operations: (), -x, x+y, x-y, x*y, x/y, x^y, sqrt(x), exp(x), ln(x)
Group functions: count(ID), mass(ID), charge(ID), xcm(ID,dim), \
                 vcm(ID,dim), fcm(ID,dim), bound(ID,dir), gyration(ID)
Atom values: mass\[N\], x\[N\], y\[N\], z\[N\], \
             vx\[N\], vy\[N\], vz\[N\], fx\[N\], fy\[N\], fz\[N\]
Atom vectors: mass\[\], x\[\], y\[\], z\[\], \
              vx\[\], vy\[\], vz\[\], fx\[\], fy\[\], fz\[\]
Compute references: c_ID, c_ID\[2\], c_ID\[N\], c_ID\[N\]\[2\], c_ID\[\], c_ID\[\]\[2\]
Fix references: f_ID, f_ID\[2\], f_ID\[N\], f_ID\[N\]\[2\], f_ID\[\], f_ID\[\]\[2\]
Other variables: v_abc, v_abc\[N\], v_abc\[\] :tb(s=:)

Note that formula elements that contain empty brackets, such as an
atom vector, produce per-atom values.  All other formula elements
produce a global value.

A formula for equal-style variables cannot use any formula element
that produces per-atom values.  A formula for an atom-style variable
can use formula elements that produce either global values or per-atom
values.

The thermo keywords allowed in a formula are those defined by the
"thermo_style custom" command.  Since many thermodyanmic quantities
are only computable after the a simulation has begun, these keywords
cannot be used if a variable is evaluated before the first simulation
begins.

Math operations are written in the usual way, where the "x" and "y" in
the examples above can be another section of the formula.  Operators
are evaluated left to right and have the usual precedence: unary minus
before exponentiation, exponentiation before multiplication and
division, and multiplication and division before addition and
subtraction.  Parenthesis can be used to group one or more portions of
a formula and enforce a desired order of operations.  Additional math
operations can be specified as keywords followed by a parenthesized
argument, e.g. sqrt(v_ke).

Group functions take one or two arguments in a specific format.  The
first argument is the group-ID.  The {dim} argument, if it exists, is
{x} or {y} or {z}.  The {dir} argument, if it exists, is {xmin},
{xmax}, {ymin}, {ymax}, {zmin}, or {zmax}.  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 "fix
gyration"_fix_gyration.html command for a definition of the formula.

Atom values take a single integer argument from 1-N, which is the
desired atom-ID, e.g. x\[243\]., which means use the x coordinate of
the atom with ID=243.

Atom vectors use empty brackets, i.e. they take no argument.  They
generate one value per atom, so that a reference like x\[\] means the
x-coord of each atom will be used when evaluating the variable.

Compute references access one or more quantities calculated by a
"compute"_compute.html.  The ID in the reference should be replaced by
the actual ID of the compute defined elsewhere in the input script.
See the doc pages for individual computes to see which ones calculate
global versus per-atom quantities.  If the compute reference contains
empty brackets, then per-atom values calculated by the compute are
accessed.  Otherwise a single value (global or per-atom) calculated by
the compute is accessed.

The different kinds of compute references are as follows.  M is a
positive integer <= the number of vector values calculated by the
compute.  N is a global atom ID (positive integer).

c_ID: scalar value of a global compute
c_ID\[2\]: vector component of a global compute
c_ID\[N\]: single atom's scalar value of a per-atom compute
c_ID\[N\]\[M\]: single atom's vector component of a per-atom compute
c_ID\[\]: per-atom scalar from a per-atom compute
c_ID\[\]\[M\]: per-atom vector component from a per-atom compute :tb(s=:)

Fix references access one or more quantities calculated by a
"fix"_fix.html.  The ID in the reference should be replaced by
the actual ID of the fix defined elsewhere in the input script.
See the doc pages for individual computes to see which ones calculate
global versus per-atom quantities.  If the compute reference contains
empty brackets, then per-atom values calculated by the compute are
accessed.  Otherwise a single value (global or per-atom) calculated by
the compute is accessed.

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 "fix ave/time"_fix_ave_time.html
command may only generate averaged quantities every 100 steps.  See
the doc pages for individual fix commands for details.

The different kinds of fix references are exactly the same as the
compute references listed in the above table, where "c_" is replaced
by "f_", and the word "compute" is replaced by "fix".

The current values of other variables can be accessed by prepending a
"v_" to the variable name.  This will cause that variable to be
evaulated.  Atom-style variables generate per-atom values; all other
styles of variables generate a single scalar value.

The different kinds of variable references are as follows.  N is a
global atom ID (positive integer).

v_ID: scalar value of a non atom-style variable
v_ID\[N\]: single atom's scalar value from an atom-style variable
v_ID\[\]: per-atom value from an atom-style variable :tb(s=:)

IMPORTANT NOTE: If you define variables in circular manner like this:

variable a equal v_b
variable b equal v_a
print $a :pre

then LAMMPS will run for a while when the print statement is invoked!

Another way to reference a variable in a formula is using the $x form
instead of v_x.  There is a subtle difference between the two
references that has to do with when the evaluation of the included
variable is done.

Using a $x, the value of the include variable is substituted for
immediately when the line is read from the input script, just as it
would be in other input script command.  This could be the desired
behavior if a static value is desired.  Or it could be the desired
behavior for an equal-style variable if the variable command appears
in a loop (see the "jump"_jump.html and "next"_next.html commmands),
since the substitution will be performed anew each time thru the loop
as the command is re-read.  Note that if the variable formula is
enclosed in double quotes, this prevents variable substitution and
thus an error will be generated when the variable formula is
evaluated.

Using a v_x, the value of the included variable will not be accessed
until the variable formula is evaluated.  Thus the value may change
each time the evaluation is performed.  This may also be desired
behavior.

As an example, if the current simulation box volume is 1000.0, then
these lines:

variable x equal vol
variable y equal 2*$x :pre

will associate the equation string "2*1000.0" with variable y.

By contrast, these lines:

variable x equal vol
variable y equal 2*v_x :pre

wlll associate the equation string "2*v_x" with variable y.

Thus if the variable y were evaluated periodically during a run where
the box volume changed, the resulting value would always be 2000.0 for
the first case, but would change dynamically for the second case.

:line

[Restrictions:]

Indexing any formula element by global atom ID, such as an atom value,
requires the atom style 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 "atom_modify
map"_atom_modify.html command can override the default.

All {universe}- and {uloop}-style variables defined in an input script
must have the same number of values.

[Related commands:]

"next"_next.html, "jump"_jump.html, "include"_include.html,
"temper"_temper.html, "fix print"_fix_print.html, "print"_print.html

[Default:] none