**Syntax:**

variable name style args ...

- name = name of variable to define
- style =
*delete*or*index*or*loop*or*world*or*universe*or*uloop*or*string*or*format*or*getenv*or*file*or*internal*or*equal*or*particle*or*grid**delete*= no args*index*args = one or more strings*loop*args = N N = integer size of loop, loop from 1 to N inclusive*loop*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*loop*args = N1 N2 N1,N2 = loop from N1 to N2 inclusive*loop*args = N1 N2 pad N1,N2 = loop from N1 to N2 inclusive pad = all values will be same length, e.g. 050, 051, ..., 100*world*args = one string for each partition of processors*universe*args = one or more strings*uloop*args = N N = integer size of loop*uloop*args = N pad N = integer size of loop pad = all values will be same length, e.g. 001, 002, ..., 100*string*arg = one string*format*args = vname fstr vname = name of equal-style variable to evaluate fstr = C-style format string*getenv*arg = one string*file*arg = filename*internal*arg = numeric value*equal*or*particle*or*grid*args = one formula containing numbers, stats keywords, math operations, particle vectors, grid vectors, compute/fix/variable references numbers = 0.0, 100, -5.4, 2.8e-4, etc constants = PI stats keywords = step, np, vol, etc from stats_style math operators = (), -x, x+y, x-y, x*y, x/y, x^y, x%y, x==y, x!=y, xy, x>=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), erf(x), random(x,y), normal(x,y), ceil(x), floor(x), round(x) ramp(x,y), stagger(x,y), logfreq(x,y,z), stride(x,y,z), vdisplace(x,y), swiggle(x,y,z), cwiggle(x,y,z) special functions = sum(x), min(x), max(x), ave(x), trap(x), slope(x), next(x) particle vectors = mass, type, mu, x, y, z, vx, vy, vz grid vectors = xc, yc, zc compute references = c_ID, c_ID[i], c_ID[i][j] fix references = f_ID, f_ID[i], f_ID[i][j] surface collision model references = s_ID[i] surface reaction model references = r_ID[i] variable references = v_name

**Examples:**

variable x index run1 run2 run3 run4 run5 run6 run7 run8 variable LoopVar loop $n variable beta equal temp/3.0 variable beta equal "temp / 3.0" variable b equal c_myTemp variable b particle x*y/vol variable foo string myfile variable foo internal 3.5 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

**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 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 next command can be used to increment which
string is assigned to the variable. Variables of style *equal* store
a formula which when evaluated produces a single numeric value which
can be output either directly (see the print, fix
print, and run every commands) or as part
of statistical output (see the stats_style
command), or used as input to an averaging fix (see the fix
ave/time command). Variables of style *particle*
store a formula which when evaluated produces one numeric value per
particle which can be output to a dump file (see the dump
particle command). Variables of style *internal* are used
by a few commands which set their value directly.

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 an input script line is encountered that defines
a variable of style *equal* or *particle* or *grid* that contains a
formula, the formula is NOT immediately evaluated and the result
stored. See the discussion below about "Immediate Evaluation of
Variables" if you want to do this. This is also true of the *format*
style variable since it evaluates another variable when it is invoked.

Variables of style *equal* and *particle* and *grid* can be used as
inputs to various other commands which evaluate their formulas as
needed, e.g. at different timesteps during a run.

Variables of style *internal* can be used in place of an equal-style
variable, except by commands that set the value stored by the
internal-style variable. Thus any command that states it can use an
equal-style variable as an argument, can also use an internal-style
variable. This means that when the command evaluates the variable, it
will use the value set (internally) by another command.

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 or include commands. It also means that using the command-line switch -var will override a corresponding index variable setting in the input script.

There are two exceptions to this rule. First, variables of style
*string*, *getenv*, *internal*, *equal*, and *particle* 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 *equal* or *particle*
style variable can change if it contains a substitution for another
variable, e.g. $x or v_x.

Second, as described below, if a variable is iterated on to the end of
its list of strings via the next command, it is removed
from the list of active variables, and is thus available to be
re-defined in a subsequent variable command. The *delete* style does
the same thing.

Section 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 command. When there are no more strings to
assign, the variable is exhausted and a flag is set that causes the
next jump 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.

As explained above, an exhausted variable can be re-used in an input
script. The *delete* 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 if and jump
commands before the variable would become exhausted. For example,

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

This section describes how various variable styles are defined and what they store. 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.

For the *index* style, one or more strings are specified. Initially,
the 1st string is assigned to the variable. Each time a
next 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 Section
2.6 of the manual for details.

The *loop* style is identical to the *index* 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
next 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 *loop* 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.

For the *world* style, one or more strings are specified. There must
be one string for each processor partition or "world". See Section
2.6 of the manual for information on
running SPARTA 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.

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 for information
on running SPARTA with multiple partitions via the "-partition"
command-line switch. This variable command initially assigns one
string to each world. When a next 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.sparta.variable" and "tmp.sparta.variable.lock"
which you will see in your directory during such a SPARTA 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.

For the *string* style, a single string is assigned to the variable.
The only difference between this and using the *index* style with a
single string is that a variable with *string* style can be redefined.
E.g. by another command later in the input script, or if the script is
read again in a loop.

For the *format* 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 print command, if the
default format "%.15g" has too much precision.

For the *getenv* 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 SPARTA input scripts via
environment variable settings, or to retrieve information that has
been previously stored with the shell putenv command.
Note that because environment variable settings are stored by the
operating systems, they persist beyond a clear command.

For the *file* 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.

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 next command or the next() function in an equal- or particle- or grid-style variable, as discussed below.

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.

For the *internal* style a numeric value is provided. This value will
be assigned to the variable until a SPARTA command sets it to a new
value. There is currently only one command that requirew *internal*
variables as inputs, because it resets them:
create_particles. As mentioned above, an
internal-style variable can be used in place of an equal-style
variable anywhere else in an input script, e.g. as an argument to
another command that allows for equal-style variables.

For the *equal* and *particle* and *grid* 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 *particle* style variables the formula computes one
quantity for each particle whenever it is evaluated. For *grid* style
variables the formula computes one quantity for each grid cell
whenever it is evaluated. A *grid* style variable computes quantites
for all flavors of child grid cells in the simulation, which includes
unsplit, cut, split, and sub cells. See Section
4.8 of the manual gives details of how
SPARTA defines child, unsplit, split, and sub cells.

Note that *equal* and *particle* and *grid* 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 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".

The next command cannot be used with *equal* or *particle* or *grid*
style variables, since there is only one string.

The formula for an *equal* or *particle* or *grid* 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 "np + c_MyTemp / vol^(1/3)"

Specifically, a formula can contain numbers, stats keywords, math operators, math functions, particle vectors, grid vectors, compute references, fix references, and references to other variables.

Number | 0.2, 100, 1.0e20, -15.4, etc |

Constant | PI |

Stats keywords | step, np, vol, etc |

Math operators | (), -x, x+y, x-y, x*y, x/y, x^y, x%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), erf(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), stride(x,y,z), vdisplace(x,y), swiggle(x,y,z), cwiggle(x,y,z) |

Special functions | sum(x), min(x), max(x), ave(x), trap(x), slope(x), next(x) |

Particle vectors | mass, type, mu, x, y, z, vx, vy, vz |

Grid vectors | xc, yc, zc |

Compute references | c_ID, c_ID[i], c_ID[i][j] |

Fix references | f_ID, f_ID[i], f_ID[i][j] |

Surface collision model references | s_ID[i] |

Surface reaction model references | r_ID[i] |

Other variables | v_name |

Most of the formula elements produce a scalar value. A few produce a per-particle vector or per-grid vector of values. These are the particle vectors or grid vectors, compute references that represent a per-particle or per-grid vector, fix references that represent a per-particle or per-grid vector, and variables that are particle-style or grid-style variables. Math functions that operate on scalar values produce a scalar value; math function that operate on per-particle vectors do so element-by-element and produce a per-particle vector.

A formula for equal-style variables cannot use any formula element that produces a per-particle or per-grid vector. A formula for a particle-style variable can use formula elements that produce either a scalar value or a per-particle vector, but not a per-grid vector. Likewise a grid-style variable can use formula elements that produce either a scalar value or a per-grid vector, but not a per-particle vector.

The stats keywords allowed in a formula are those defined by the stats_style custom command. If a variable is evaluated directly in an input script (not during a run), then the values accessed by the stats keyword must be current. See the discussion below about "Variable Accuracy".

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-particle or per-grid vectors. For example, "vol/np" is the division of two scalars, where "vy+vz" is the element-by-element sum of two per-particle vectors of y and z velocities.

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.

IMPORTANT NOTE: 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.

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 a particle-style variable formula will return 1.0 for all particles 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.

These relational and logical operators can be used as a masking or selection operation in a formula. For example, the number of particles whose properties satifsy one or more criteria could be calculated by taking the returned per-particle vector of ones and zeroes and passing it to the compute reduce command.

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 per-particle or per-grid vectors. In the latter cases, the math operation is performed on each element of the vector. For example, "sqrt(np)" is the sqrt() of a scalar, where "sqrt(y*z)" yields a per-particle vector with each element being the sqrt() of the product of one particle's y and z coordinates.

Most of the math functions perform obvious operations. The ln() is the natural log; log() is the base 10 log.

The random(x,y) function takes 2 arguments: x = lo and y = hi. It generates a uniform random number between lo and hi. The normal(x,y) function also takes 2 arguments: x = mu and y = sigma. It generates a Gaussian variate centered on mu with variance sigma^2. For equal-style variables, every processor uses the same random number seed so that they each generate the same sequence of random numbers. For particle-style or grid-style variables, a unique seed is created for each processor. This effectively generates a different random number for each particle or grid cell being looped over in the particle-style or grid-style variable.

IMPORTANT NOTE: Internally, there is just one random number generator for all equal-style variables and one for all particle-style and grid-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.

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.

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:

value = x + (y-x) * (timestep-startstep) / (stopstep-startstep)

The run begins on startstep and ends on stopstep. Startstep and
stopstep can span multiple runs, using the *start* and *stop* keywords
of the run command. See the run command for
details of how to do this.

IMPORTANT NOTE: Currently, the run command does not currently support the start/stop keywords. In the formula above startstep = 0 and stopstep = the number of timesteps being performed by the run.

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 dump_modify every command, it will generate the sequence of output timesteps:

100,1000,1100,2000,2100,3000,etc

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 increase in a logarithmic fashion, as the sequence x,2x,3x,...y*x,z*x,2*z*x,3*z*x,...y*z*x,z*z*x,2*z*x*x,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 dump_modify every command, it will generate the sequence of output timesteps:

100,200,300,400,1000,2000,3000,4000,10000,20000,etc

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 stagger(1000,2000,100) is used in a variable by the dump_modify every command, it will generate the sequence of output timesteps:

1000,1100,1200, ... ,1900,2000

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:

value = value0 + velocity*(timestep-startstep)*dt

where dt = the timestep size.

The run begins on startstep. Startstep can span multiple runs, using
the *start* keyword of the run command. See the
run command for details of how to do this. Note that the
stats_style keyword *elaplong* =
timestep-startstep.

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:

value = value0 + Amplitude * sin(omega*(timestep-startstep)*dt) value = value0 + Amplitude * (1 - cos(omega*(timestep-startstep)*dt))

where dt = the timestep size.

The run begins on startstep. Startstep can span multiple runs, using
the *start* keyword of the run command. See the
run command for details of how to do this. Note that the
stats_style keyword *elaplong* =
timestep-startstep.

Special functions take specific kinds of arguments, meaning their arguments cannot be formulas themselves.

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]". 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.

These functions operate on the global vector of inputs and reduce it to a single scalar value. This is analagous to the operation of the compute reduce command, which invokes the same functions on per-particle or per-grid vectors.

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.

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 integratiion 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().

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.

The next(x) function takes 1 argument which is a variable ID (not "v_foo", just "foo"). It must be for a file-style variable. Each time the next() function is invoked (i.e. each time the equal-style or particle-style or grid-style variable is evaluated), the following steps occur.

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.

Since file-style variables read and store the first line of the file when they are defined in the input script, this is the value that will be returned the first time the next() function is invoked. If next() is invoked more times than there are lines in the file, the variable is deleted, similar to how the next command operates.

Particle vectors generate one value per particle, so that a reference like "vx" means the x-component of each particles's velocity will be used when evaluating the variable. Some values are per-species values, like mass and mu. A reference like "mass" means the mass for the particle's species.

The meaning of the different particle vectors is self-explanatory.

Particle vectors can only be used in *particle* style variables,
not in *equal* or *grid* style varaibles.

Particle vectors generate one value per grid cell, so that a reference like "xc" means the x-component of the center point of the grid cell.

The xc, yc, zc values are for the geometric center point of the grid cell.

Grid vectors can only be used in *grid* style variables, not in
*equal* or *particle* style varaibles.

Compute references access quantities calculated by a compute. 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 compute command, computes can produce global, per-particle, per-grid, or per-surf values. Only global and per-particle and per-grid values can be used in a variable. Computes 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 vector or array. Particle-style variables can use the same scalar values. They can also use per-particle vector values. A vector value can be a per-particle vector itself, or a column of an per-particle array. Grid-style variables can use the same scalar values. They can also use per-grid vector values. A vector value can be a per-grid vector itself, or a column of an per-grid array. See the doc pages for individual computes to see what kind of values they produce.

Examples of different kinds of compute references are as follows. There is no ambiguity as to what a reference means, since computes only produce global or per-particle or per-grid quantities, never more than one kind of quantity.

c_ID | global scalar, or per-particle or per-grid vector |

c_ID[I] | Ith element of global vector, or Ith column from per-particle or per-grid array |

c_ID[I][J] | I,J element of global array |

For I and J, integers can be specified or 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 expect particle-style. 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.

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".

Fix references access quantities calculated by a fix. 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 fix command, fixes can produce global, per-particle, per-grid, or per-surf values. Only global and per-particle and per-grid 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 vector or array. Particle-style variables can use the same scalar values. They can also use per-particle vector values. A vector value can be a per-particle vector itself, or a column of an per-particle array. Grid-style variables can use the same scalar values. They can also use per-grid vector values. A vector value can be a per-grid vector itself, or a column of an per-grid array. See the doc pages for individual fixes to see what kind of values they produce.

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_". Again, there is no ambiguity as to what a reference means, since fixes only produce global or per-particle or per-grid quantities, never more than one kind of quantity.

f_ID | global scalar, or per-particle or per-grid vector |

f_ID[I] | Ith element of global vector, or Ith column from per-particle or per-grid array |

f_ID[I][J] | I,J element of global array |

For I and J, 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 "Compute References" discussion above.

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".

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 command may only generate averaged quantities every 100 steps. See the doc pages for individual fix commands for details.

These references access quantities calculated by a surf_collide or surf_react command. The ID in the reference should be replaced by the ID of a surface collision or surface reaction model defined elsewhere in the input script. As discussed in the doc pages for the surf_collide and surf_react commands, these commmands produce global vectors, the elements of which can be accessed by equal-style or particle-style or grid-style variables, e.g.

s_ID[I] | Ith element of global vector for a surface collision model |

r_ID[I] | Ith element of global vector for a surface reaction model |

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.

As discussed on this doc page, equal-style variables generate a global scalar numeric value; particle-style variables generate a per-particle vector of numeric values; grid-style variables generate a per-grid vector of numeric values; all other variables store a string. The formula for an equal-style variable can use any style of variable except a particle- or grid-style. The formula for a particle-style variable can use any style of variable except a grid-style. The formula for a grid-style variable can use any style of variable except a particle-style. 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. The formula for a particle-style variable can use any style of variable, including other particle-style variables.

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 a per-particle or per-grid vector, never more than one of these quantities.

v_name | scalar, or per-particle or per-grid vector |

**Immediate Evaluation of Variables:**

There is a difference between referencing a variable with a leading $ sign (e.g. $x or ${abc}) versus with a leading "v_" (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 Section commands 3.2 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.

Referencing a variable with a leading "v_" is an optional or required kind of argument for some commands (e.g. the fix ave/spatial or dump custom or stats_style 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.

As an example, suppose you use this command in your input script to define the variable "n" as

variable n equal np

before a run where the particle count changes. You might think this will assign the initial count to the variable "n". That is not the case. Rather it assigns a formula which evaluates the count (using the stats_style keyword "np") to the variable "n". If you use the variable "n" in some other command like fix ave/time then the current particle count will be evaluated continuously during the run.

If you want to store the initial particle count of the system, it can be done in this manner:

variable n equal np variable n0 equal $n

The second command will force "n" to be evaluated (yielding the initial count) and assign that value to the variable "n0". Thus the command

stats_style custom step v_n v_n0

would print out both the current and initial particle count periodically during the run.

Also note that it is a mistake to enclose a variable formula in quotes if it contains variables preceeded by $ signs. For example,

variable nratio equal "${nfinal}/${n0}"

This is because the quotes prevent variable substitution (see Section 2.2 of the manual on parsing input script commands), and thus an error will occur when the formula for "nratio" is evaluated later.

**Variable Accuracy:**

Obviously, SPARTA attempts to evaluate variables containing formulas
(*equal* and *particle* and *grid* style variables) accurately
whenever the evaluation is performed. Depending on what is included
in the formula, this may require invoking a compute, or
accessing a value previously calculated by a compute, or accessing a
value calculated and stored by a fix. If the compute is
one that calculates certain properties of the system such as the
pressure induced on a global boundary due to collisions, then these
quantities need to be tallied during the timesteps on which the
variable will need the values.

SPARTA keeps track of all of this during a run. An error will be generated if you attempt to evaluate a variable on timesteps when it cannot produce accurate values. For example, if a stats_style custom command prints a variable which accesses values stored by a fix ave/time command and the timesteps on which stats output is generated are not multiples of the averaging frequency used in the fix command, then an error will occur.

An input script can also request variables be evaluated before or after or in between runs, e.g. by including them in a print command. In this case, if a compute is needed to evaluate a variable (either directly or indirectly), SPARTA 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:

(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.

(2) SPARTA 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 compute that has not been invoked on the current timestep, SPARTA 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 stats output.

One way to get around this problem is to perform a 0-timestep run before using the variable. For example, these commands

compute myTemp grid all temp variable t equal c_myTemp1print "Initial temperature = $t" run 1000

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.

However, this sequence of commands would be fine:

compute myTemp grid all temp variable t equal c_myTemp1run 0 print "Initial temperature = $t" run 1000

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 stats or dump 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 stats output.

Unlike computes, fixes 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 fix indent 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.

(3) The variable may be evaluated incorrectly. And SPARTA may have no way to detect this has occurred. Consider the following sequence of commands:

compute myTemp grid all temp variable t equal c_myTemp1run 1000 create_particles all n 10000 print "Final temperature = $t"

The first run is performed using the current set of particles. The temperature is evaluated on the final timestep and stored by the compute grid compute (when invoked by the stats_style command). Then new particles are added by the create_particles command, altering the temperature of the system. When the temperature is printed via the "t" variable, SPARTA will use the temperature value stored by the compute grid 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.

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 temperature that reflected the new particles:

compute myTemp grid all temp variable t equal c_myTemp1run 1000 create_particles all n 10000 run 0 print "Final temperature = $t"

**Restrictions:**

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

**Related commands:**

next, jump, include, fix print, print

**Default:** none