.. index:: fix ave/chunk

fix ave/chunk command
=====================

Syntax
""""""

.. code-block:: LAMMPS

   fix ID group-ID ave/chunk Nevery Nrepeat Nfreq chunkID value1 value2 ... keyword args ...

* ID, group-ID are documented in :doc:`fix <fix>` command
* ave/chunk = style name of this fix command
* Nevery = use input values every this many timesteps
* Nrepeat = # of times to use input values for calculating averages
* Nfreq = calculate averages every this many timesteps
* chunkID = ID of :doc:`compute chunk/atom <compute_chunk_atom>` command
* one or more input values can be listed
* value = *vx*, *vy*, *vz*, *fx*, *fy*, *fz*, *density/mass*, *density/number*, *mass*, *temp*, c_ID, c_ID[I], f_ID, f_ID[I], v_name

  .. parsed-literal::

       vx,vy,vz,fx,fy,fz,mass = atom attribute (velocity, force component, mass)
       density/number, density/mass = number or mass density (per volume)
       temp = temperature
       c_ID = per-atom vector calculated by a compute with ID
       c_ID[I] = Ith column of per-atom array calculated by a compute with ID, I can include wildcard (see below)
       f_ID = per-atom vector calculated by a fix with ID
       f_ID[I] = Ith column of per-atom array calculated by a fix with ID, I can include wildcard (see below)
       v_name = per-atom vector calculated by an atom-style variable with name

* zero or more keyword/arg pairs may be appended
* keyword = *norm* or *ave* or *bias* or *adof* or *cdof* or *file* or *append* or *overwrite* or *format* or *title1* or *title2* or *title3*

  .. parsed-literal::

       *norm* arg = *all* or *sample* or *none* = how output on *Nfreq* steps is normalized
         all = output is sum of atoms across all *Nrepeat* samples, divided by atom count
         sample = output is sum of *Nrepeat* sample averages, divided by *Nrepeat*
         none = output is sum of *Nrepeat* sample sums, divided by *Nrepeat*
       *ave* args = *one* or *running* or *window M*
         one = output new average value every Nfreq steps
         running = output cumulative average of all previous Nfreq steps
         window M = output average of M most recent Nfreq steps
       *bias* arg = bias-ID
         bias-ID = ID of a temperature compute that removes a velocity bias for temperature calculation
       *adof* value = dof_per_atom
         dof_per_atom = define this many degrees-of-freedom per atom for temperature calculation
       *cdof* value = dof_per_chunk
         dof_per_chunk = define this many degrees-of-freedom per chunk for temperature calculation
       *file* arg = filename
         filename = file to write results to
       *append* arg = filename
         filename = file to append results to
       *overwrite* arg = none = overwrite output file with only latest output
       *format* arg = string
         string = C-style format string
       *title1* arg = string
         string = text to print as 1st line of output file
       *title2* arg = string
         string = text to print as 2nd line of output file
       *title3* arg = string
         string = text to print as 3rd line of output file

Examples
""""""""

.. code-block:: LAMMPS

   fix 1 all ave/chunk 10000 1 10000 binchunk c_myCentro title1 "My output values"
   fix 1 flow ave/chunk 100 10 1000 molchunk vx vz norm sample file vel.profile
   fix 1 flow ave/chunk 100 5 1000 binchunk density/mass ave running
   fix 1 flow ave/chunk 100 5 1000 binchunk density/mass ave running


.. note::

   .. versionchanged:: 31May2016

   If you are trying to replace a deprecated fix ave/spatial command
   with the newer, more flexible fix ave/chunk and :doc:`compute
   chunk/atom <compute_chunk_atom>` commands, you simply need to split
   the fix ave/spatial arguments across the two new commands.  For
   example, this command:

   .. code-block:: LAMMPS

      fix 1 flow ave/spatial 100 10 1000 y 0.0 1.0 vx vz norm sample file vel.profile

   could be replaced by:

   .. code-block:: LAMMPS

      compute cc1 flow chunk/atom bin/1d y 0.0 1.0
      fix 1 flow ave/chunk 100 10 1000 cc1 vx vz norm sample file vel.profile

Description
"""""""""""

Use one or more per-atom vectors as inputs every few timesteps, sum
the values over the atoms in each chunk at each timestep, then average
the per-chunk values over longer timescales.  The resulting chunk
averages can be used by other :doc:`output commands <Howto_output>` such
as :doc:`thermo_style custom <thermo_style>`, and can also be written to
a file.

In LAMMPS, chunks are collections of atoms defined by a :doc:`compute
chunk/atom <compute_chunk_atom>` command, which assigns each atom to a
single chunk (or no chunk).  The ID for this command is specified as
chunkID.  For example, a single chunk could be the atoms in a molecule
or atoms in a spatial bin.  See the :doc:`compute chunk/atom
<compute_chunk_atom>` page and the :doc:`Howto chunk <Howto_chunk>`
page for details of how chunks can be defined and examples of how they
can be used to measure properties of a system.

Note that if the :doc:`compute chunk/atom <compute_chunk_atom>`
command defines spatial bins, the fix ave/chunk command performs a
similar computation as the :doc:`fix ave/grid <fix_ave_grid>` command.
However, the per-bin outputs from the fix ave/chunk command are
global; each processor stores a copy of the entire set of bin data.
By contrast, the :doc:`fix ave/grid <fix_ave_grid>` command uses a
distributed grid where each processor owns a subset of the bins.  Thus
it is more efficient to use the :doc:`fix ave/grid <fix_ave_grid>`
command when the grid is large and a simulation is run on many
processors.

Note that only atoms in the specified group contribute to the summing
and averaging calculations.  The :doc:`compute chunk/atom
<compute_chunk_atom>` command defines its own group as well as an
optional region.  Atoms will have a chunk ID = 0, meaning they belong
to no chunk, if they are not in that group or region.  Thus you can
specify the "all" group for this command if you simply want to use the
chunk definitions provided by chunkID.

Each specified per-atom value can be an atom attribute (position,
velocity, force component), a number or mass density, a mass or
temperature, or the result of a :doc:`compute <compute>` or :doc:`fix
<fix>` or the evaluation of an atom-style :doc:`variable <variable>`.
In the latter cases, the compute, fix, or variable must produce a
per-atom quantity, not a global quantity.  Note that the :doc:`compute
property/atom <compute_property_atom>` command provides access to any
attribute defined and stored by atoms.  If you wish to time-average
global quantities from a compute, fix, or variable, then see the
:doc:`fix ave/time <fix_ave_time>` command.

The per-atom values of each input vector are summed and averaged
independently of the per-atom values in other input vectors.

:doc:`Computes <compute>` that produce per-atom quantities are those
which have the word *atom* in their style name.  See the doc pages for
individual :doc:`fixes <fix>` to determine which ones produce per-atom
quantities.  :doc:`Variables <variable>` of style *atom* are the only
ones that can be used with this fix since all other styles of variable
produce global quantities.

Note that for values from a compute or fix that produces a per-atom
array (multiple values per atom), the bracketed index I can be
specified using a wildcard asterisk with the index to effectively
specify multiple values.  This takes the form "\*" or "\*n" or "n\*"
or "m\*n".  If :math:`N` = the size of the vector (for *mode* = scalar) or the
number of columns in the array (for *mode* = vector), then an asterisk
with no numeric values means all indices from 1 to :math:`N`.  A leading
asterisk means all indices from 1 to n (inclusive).  A trailing
asterisk means all indices from m to :math:`N` (inclusive).  A middle asterisk
means all indices from m to n (inclusive).

Using a wildcard is the same as if the individual columns of the array
had been listed one by one.  For example, these two fix ave/chunk commands are
equivalent, since the :doc:`compute property/atom
<compute_property_atom>` command creates, in this case, a per-atom
array with three columns:

.. code-block:: LAMMPS

   compute myAng all property/atom angmomx angmomy angmomz
   fix 1 all ave/chunk 100 1 100 cc1 c_myAng[*] file tmp.angmom
   fix 2 all ave/chunk 100 1 100 cc1 c_myAng[1] c_myAng[2] c_myAng[3] file tmp.angmom

.. note::

   This fix works by creating an array of size
   :math:`N_\text{chunk} \times N_\text{values}` on each processor.
   :math:`N_\text{chunk}` is the number of chunks, which is defined by the
   :doc:`compute chunk/atom <compute_chunk_atom>` command.
   :math:`N_\text{values}` is the number of input values specified.
   Each processor loops over its atoms, tallying its values to the appropriate
   chunk.  Then the entire array is summed across all processors.  This means
   that using a large number of chunks will incur an overhead in memory and
   computational cost (summing across processors), so be careful to
   define a reasonable number of chunks.

----------

The :math:`N_\text{every}`, :math:`N_\text{repeat}`, and :math:`N_\text{freq}`
arguments specify on what time steps the input values will be accessed and
contribute to the average.  The final averaged quantities are generated on time
steps that are a multiples of :math:`N_\text{freq}`\ .  The average is over
:math:`N_\text{repeat}` quantities, computed in the preceding portion of the
simulation every :math:`N_\text{every}` time steps.  :math:`N_\text{freq}`
must be a multiple of :math:`N_\text{every}` and :math:`N_\text{every}` must be
non-zero even if :math:`N_\text{repeat} = 1`\ .  Also, the time steps
contributing to the average value cannot overlap (i.e.,
:math:`N_\text{repeat} \times N_\text{every}` cannot exceed :math:`N_\text{freq}`).

For example, if :math:`N_\text{every}=2`, :math:`N_\text{repeat}=6`, and
:math:`N_\text{freq}=100`, then values on
time steps 90, 92, 94, 96, 98, 100 will be used to compute the final average
on time step 100.  Similarly for time steps 190, 192, 194, 196, 198, 200 on
time step 200, etc.  If :math:`N_\text{repeat}=1` and
:math:`N_\text{freq} = 100`, then no time averaging is done; values are simply
generated on time steps 100, 200, etc.

Each input value can also be averaged over the atoms in each chunk.
The way the averaging is done across the :math:`N_\text{repeat}` time steps to
produce output on the :math:`N_\text{freq}` time steps, and across multiple
:math:`N_\text{freq}` outputs, is determined by the *norm* and *ave* keyword
settings, as discussed below.

.. note::

   To perform per-chunk averaging within a :math:`N_\text{freq}` time window,
   the number of chunks :math:`N_\text{chunk}` defined by the
   :doc:`compute chunk/atom <compute_chunk_atom>` command must remain
   constant.  If the *ave* keyword is set to *running* or *window* then
   :math:`N_\text{chunk}` must remain constant for the duration of the
   simulation.  This fix forces the chunk/atom compute specified by chunkID to
   hold :math:`N_\text{chunk}` constant for the appropriate time windows,
   by not allowing it to re-calculate :math:`N_\text{chunk}`, which can also
   affect how it assigns chunk IDs to atoms.  This is particularly important to
   understand if the chunks defined by the :doc:`compute chunk/atom
   <compute_chunk_atom>` command are spatial bins.  If its *units*
   keyword is set to *box* or *lattice*, then the number of bins
   :math:`N_\text{chunk}` and size of each bin will be fixed over the
   :math:`N_\text{freq}` time window, which can affect which atoms are
   discarded if the simulation box size changes.  If its *units* keyword is set
   to *reduced*, then the number of bins :math:`N_\text{chunk}` will still be
   fixed, but the size of each bin can vary at each time step if the
   simulation box size changes (e.g., for an NPT simulation).

----------

The atom attribute values (*vx*, *vy*, *vz*, *fx*, *fy*, *fz*, *mass*) are
self-explanatory.  As noted above, any other atom attributes can be
used as input values to this fix by using the :doc:`compute
property/atom <compute_property_atom>` command and then specifying an
input value from that compute.

The *density/number* value means the number density is computed for
each chunk (i.e., number/volume).  The *density/mass* value means the
mass density is computed for each chunk (i.e., total-mass/volume).  The
output values are in units of 1/volume or mass density (mass/volume).  See
the :doc:`units <units>` command page for the definition of density
for each choice of units (e.g., g/cm\ :math:`^3`).  If the chunks defined by
the :doc:`compute chunk/atom <compute_chunk_atom>` command are spatial
bins, the volume is the bin volume.  Otherwise, it is the volume of the
entire simulation box.

The *temp* value means the temperature is computed for each chunk,
by the formula

.. math::

   \text{KE} = \frac{\text{DOF}}{2} k_B T,

where KE is the total kinetic energy of the chunk of atoms (sum of
:math:`\frac{1}{2} m v^2`), DOF is the the total number of degrees of freedom
for all atoms in the chunk, :math:`k_B` is the Boltzmann constant, and
:math:`T` is the absolute temperature.

The DOF is calculated as :math:`N`\ \*adof + cdof, where :math:`N` is the
number of atoms in the chunk, adof is the number of degrees of freedom per
atom, and cdof is the number of degrees of freedom per chunk.  By default,
adof = 2 or 3 = dimensionality of system,
as set via the :doc:`dimension <dimension>` command, and cdof = 0.0.
This gives the usual formula for temperature.

Note that currently this temperature only includes translational
degrees of freedom for each atom.  No rotational degrees of freedom
are included for finite-size particles.  Also, no degrees of freedom
are subtracted for any velocity bias or constraints that are applied,
such as :doc:`compute temp/partial <compute_temp_partial>`,
:doc:`fix shake <fix_shake>`, or :doc:`fix rigid <fix_rigid>`.  This is
because those degrees of freedom (e.g., a constrained bond) could apply
to sets of atoms that are both included and excluded from a specific
chunk, and hence the concept is somewhat ill-defined.  In some cases,
you can use the *adof* and *cdof* keywords to adjust the calculated
degrees of freedom appropriately, as explained below.

Also note that a bias can be subtracted from atom velocities before
they are used in the above formula for KE, by using the *bias*
keyword.  This allows, for example, a thermal temperature to be
computed after removal of a flow velocity profile.

Note that the per-chunk temperature calculated by this fix and the
:doc:`compute temp/chunk <compute_temp_chunk>` command can be
different.  The compute calculates the temperature for each chunk for
a single snapshot.  This fix can do that but can also time average
those values over many snapshots, or it can compute a temperature as
if the atoms in the chunk on different time steps were collected
together as one set of atoms to calculate their temperature.  The
compute allows the center-of-mass velocity of each chunk to be
subtracted before calculating the temperature; this fix does not.

If a value begins with "c\_", a compute ID must follow which has been
previously defined in the input script.  If no bracketed integer is
appended, the per-atom vector calculated by the compute is used.  If a
bracketed integer is appended, the Ith column of the per-atom array
calculated by the compute is used.  Users can also write code for
their own compute styles and :doc:`add them to LAMMPS <Modify>`.
See the discussion above for how I can be specified with a wildcard
asterisk to effectively specify multiple values.

If a value begins with "f\_", a fix ID must follow which has been
previously defined in the input script.  If no bracketed integer is
appended, the per-atom vector calculated by the fix is used.  If a
bracketed integer is appended, the Ith column of the per-atom array
calculated by the fix is used.  Note that some fixes only produce
their values on certain time steps, which must be compatible with
:math:`N_\text{every}`, else an error results.  Users can also write code for
their own fix styles and :doc:`add them to LAMMPS <Modify>`.  See the
discussion above for how I can be specified with a wildcard asterisk
to effectively specify multiple values.

If a value begins with "v\_", a variable name must follow which has
been previously defined in the input script.  Variables of style
*atom* can reference thermodynamic keywords and various per-atom
attributes, or invoke other computes, fixes, or variables when they
are evaluated, so this is a very general means of generating per-atom
quantities to average within chunks.

----------

Additional optional keywords also affect the operation of this fix
and its outputs.

The *norm* keyword affects how averaging is done for the per-chunk
values that are output every :math:`N_\text{freq}` time steps.

It the *norm* setting is *all*, which is the default, a chunk value is summed
over all atoms in all :math:`N_\text{repeat}` samples, as is the count of
atoms in the chunk.  The averaged output value for the chunk on the
:math:`N_\text{freq}` time steps is Total-sum / Total-count.  In other words it
is an average over atoms across the entire :math:`N_\text{freq}` timescale.
For the *density/number* and *density/mass* values, the volume (bin volume or
system volume) used in the final normalization will be the volume at
the final :math:`N_\text{freq}` time step. For the *temp* values, degrees of
freedom and kinetic energy are summed separately across the entire
:math:`N_\text{freq}` timescale, and the output value is calculated by dividing
those two sums.

If the *norm* setting is *sample*, the chunk value is summed over
atoms for each sample, as is the count, and an "average sample value"
is computed for each sample (i.e., Sample-sum / Sample-count).  The
output value for the chunk on the :math:`N_\text{freq}` time steps is the
average of the :math:`N_\text{repeat}` "average sample values" (i.e., the sum
of :math:`N_\text{repeat}` "average sample values" divided by
:math:`N_\text{repeat}`\ ).  In other words, it is an average of an average.
For the *density/number* and *density/mass* values, the volume (bin volume or
system volume) used in the per-sample normalization will be the current volume
at each sampling step.

If the *norm* setting is *none*, a similar computation as for the
*sample* setting is done, except the individual "average sample
values" are "summed sample values".  A summed sample value is simply
the chunk value summed over atoms in the sample, without dividing by
the number of atoms in the sample.  The output value for the chunk on
the :math:`N_\text{freq}` timesteps is the average of the
:math:`N_\text{repeat}` "summed sample values" (i.e., the sum of
:math:`N_\text{repeat}` "summed sample values" divided by
:math:`N_\text{repeat}`\ ).
For the *density/number* and *density/mass* values, the
volume (bin volume or system volume) used in the per-sample sum
normalization will be the current volume at each sampling step.

----------

The *ave* keyword determines how the per-chunk values produced every
:math:`N_\text{freq}` steps are averaged with values produced on previous steps
that were multiples of :math:`N_\text{freq}`, before they are accessed by
another output command or written to a file.

If the *ave* setting is *one*, which is the default, then the chunk
values produced on timesteps that are multiples of :math:`N_\text{freq}` are
independent of each other; they are output as-is without further averaging.

If the *ave* setting is *running*, then the chunk values produced on
timesteps that are multiples of :math:`N_\text{freq}` are summed and averaged
in a cumulative sense before being output.  Each output chunk value is thus
the average of the chunk value produced on that timestep with all
preceding values for the same chunk.  This running average begins when
the fix is defined; it can only be restarted by deleting the fix via
the :doc:`unfix <unfix>` command, or re-defining the fix by re-specifying it.

If the *ave* setting is *window*, then the chunk values produced on
timesteps that are multiples of :math:`N_\text{freq}` are summed and averaged
within a moving "window" of time, so that the last :math:`M` values for the
same chunk are used to produce the output.  For example, if :math:`M = 3` and
:math:`N_\text{freq} = 1000`, then the output on step 10000 will be the average
of the individual chunk values on time steps 8000, 9000, and 10000.  Outputs on
early steps will average over less than :math:`M` values if they are not
available.

----------

The *bias* keyword specifies the ID of a temperature compute that
removes a "bias" velocity from each atom, specified as *bias-ID*\ .
It is only used when the *temp* value is calculated, to compute the
thermal temperature of each chunk after the translational kinetic
energy components have been altered in a prescribed way (e.g., to
remove a flow velocity profile).  See the doc pages for individual
computes that calculate a temperature to see which ones implement a bias.

The *adof* and *cdof* keywords define the values used in the degree of
freedom (DOF) formula described above for temperature calculation
for each chunk.  They are only used when the *temp* value is
calculated.  They can be used to calculate a more appropriate
temperature for some kinds of chunks.  Here are three examples:

If spatially binned chunks contain some number of water molecules and
:doc:`fix shake <fix_shake>` is used to make each molecule rigid, then
you could calculate a temperature with six degrees of freedom (DOF) (three
translational, three rotational) per molecule by setting *adof* to 2.0.

If :doc:`compute temp/partial <compute_temp_partial>` is used with the
*bias* keyword to only allow the :math:`x` component of velocity to contribute
to the temperature, then *adof* = 1.0 would be appropriate.

If each chunk consists of a large molecule, with some number of its
bonds constrained by :doc:`fix shake <fix_shake>` or the entire molecule
by :doc:`fix rigid/small <fix_rigid>`, *adof* = 0.0 and *cdof* could be
set to the remaining degrees of freedom for the entire molecule
(entire chunk in this case), that is, 6 for 3d or 3 for 2d for a rigid
molecule.

----------

.. versionadded:: 17Apr2024
   new keyword *append*

The *file* or *append* keywords allow a filename to be specified.  If
*file* is used, then the filename is overwritten if it already exists.
If *append* is used, then the filename is appended to if it already
exists, or created if it does not exist.  Every :math:`N_\text{freq}`
timesteps, a section of chunk info will be written to a text file in the
following format.  A line with the timestep and number of chunks is
written.  Then one line per chunk is written, containing the chunk ID
:math:`(1-N_\text{chunk}),` an optional original ID value, optional
coordinate values for chunks that represent spatial bins, the number of
atoms in the chunk, and one or more calculated values.  More explanation
of the optional values is given below.  The number of values in each
line corresponds to the number of values specified in the fix ave/chunk
command.  The number of atoms and the value(s) are summed or average
quantities, as explained above.

The *overwrite* keyword will continuously overwrite the output file
with the latest output, so that it only contains one timestep worth of
output.  This option can only be used with the *ave running* setting.

The *format* keyword sets the numeric format of each value when it is
printed to a file via the *file* keyword.  Note that all values are
floating point quantities.  The default format is %g.  You can specify
a higher precision if desired (e.g., %20.16g).

The *title1* and *title2* and *title3* keywords allow specification of
the strings that will be printed as the first three lines of the output
file, assuming the *file* keyword was used.  LAMMPS uses default
values for each of these, so they do not need to be specified.

By default, these header lines are as follows:

.. parsed-literal::

   # Chunk-averaged data for fix ID and group name
   # Timestep Number-of-chunks
   # Chunk (OrigID) (Coord1) (Coord2) (Coord3) Ncount value1 value2 ...

In the first line, ID and name are replaced with the fix-ID and group
name.  The second line describes the two values that are printed at
the first of each section of output.  In the third line the values are
replaced with the appropriate value names (e.g., *fx* or c_myCompute[2]).

The words in parenthesis only appear with corresponding columns if the
chunk style specified for the :doc:`compute chunk/atom
<compute_chunk_atom>` command supports them.  The OrigID column is
only used if the *compress* keyword was set to *yes* for the
:doc:`compute chunk/atom <compute_chunk_atom>` command.  This means
that the original chunk IDs (e.g., molecule IDs) will have been
compressed to remove chunk IDs with no atoms assigned to them.  Thus a
compressed chunk ID of 3 may correspond to an original chunk ID or
molecule ID of 415.  The OrigID column will list 415 for the third chunk.

The CoordN columns only appear if a *binning* style was used in the
:doc:`compute chunk/atom <compute_chunk_atom>` command.  For *bin/1d*,
*bin/2d*, and *bin/3d* styles the column values are the center point
of the bin in the corresponding dimension.  Just Coord1 is used for
*bin/1d*, Coord2 is added for *bin/2d*, Coord3 is added for *bin/3d*\ .
For *bin/sphere*, just Coord1 is used, and it is the radial
coordinate.  For *bin/cylinder*, Coord1 and Coord2 are used.  Coord1
is the radial coordinate (away from the cylinder axis), and coord2 is
the coordinate along the cylinder axis.

Note that if the value of the *units* keyword used in the
:doc:`compute chunk/atom command <compute_chunk_atom>` is *box* or
*lattice*, the coordinate values will be in distance :doc:`units <units>`.
If the value of the *units* keyword is *reduced*, the
coordinate values will be in unitless reduced units (0--1).  This is
not true for the Coord1 value of style *bin/sphere* or *bin/cylinder*
which both represent radial dimensions.  Those values are always in
distance :doc:`units <units>`.

----------

Restart, fix_modify, output, run start/stop, minimize info
"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

No information about this fix is written to :doc:`binary restart files
<restart>`.  None of the :doc:`fix_modify <fix_modify>` options are
relevant to this fix.

This fix computes a global array of values which can be accessed by
various :doc:`output commands <Howto_output>`.  The values can only be
accessed on timesteps that are multiples of :math:`N_\text{freq}`, since
that is when averaging is performed.  The global array has # of rows =
the number of chunks :math:`N_\text{chunk}`, as calculated by the
specified :doc:`compute chunk/atom <compute_chunk_atom>` command.  The #
of columns is :math:`M+1+N_\text{values}`, where :math:`M \in
\{1,\dotsc,4\}`, depending on whether the optional columns for OrigID
and CoordN are used, as explained above.  Following the optional
columns, the next column contains the count of atoms in the chunk, and
the remaining columns are the Nvalue quantities.  When the array is
accessed with a row :math:`I` that exceeds the current number of chunks,
than a 0.0 is returned by the fix instead of an error, since the number
of chunks can vary as a simulation runs depending on how that value is
computed by the compute chunk/atom command.

The array values calculated by this fix are treated as "intensive",
since they are typically already normalized by the count of atoms in
each chunk.

No parameter of this fix can be used with the *start/stop* keywords of
the :doc:`run <run>` command.  This fix is not invoked during
:doc:`energy minimization <minimize>`.

Restrictions
""""""""""""
 none

Related commands
""""""""""""""""

:doc:`compute <compute>`, :doc:`fix ave/atom <fix_ave_atom>`,
:doc:`fix ave/histo <fix_ave_histo>`, :doc:`fix ave/time <fix_ave_time>`,
:doc:`variable <variable>`, :doc:`fix ave/correlate <fix_ave_correlate>`,
:doc:`fix ave/grid <fix_ave_grid>`


Default
"""""""

The option defaults are norm = all, ave = one, bias = none, no file
output, and title 1,2,3 = strings as described above.
