.. index:: fix ave/grid

fix ave/grid command
=====================

Syntax
""""""

.. code-block:: LAMMPS

   fix ID group-ID ave/grid Nevery Nrepeat Nfreq Nx Ny Nz value1 value2 ... keyword args ...

* ID, group-ID are documented in :doc:`fix <fix>` command
* ave/grid = 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
* Nx, Ny, Nz = grid size in each dimension
* one or more per-atom or per-grid input values can be listed
* per-atom 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

* per-grid value = c_ID:gname:dname, c_ID:gname:dname[I], f_ID:gname:dname, f_ID:gname:dname[I]

  .. parsed-literal::

       gname = name of grid defined by compute or fix
       dname = name of data field defined by compute or fix
       c_ID = per-grid vector calculated by a compute with ID
       c_ID[I] = Ith column of per-grid array calculated by a compute with ID, I can include wildcard (see below)
       f_ID = per-grid vector calculated by a fix with ID
       f_ID[I] = Ith column of per-grid array calculated by a fix with ID, I can include wildcard (see below)

* zero or more keyword/arg pairs may be appended
* keyword = *discard* or *norm* or *ave* or *bias* or *adof* or *cdof*

  .. parsed-literal::

       *discard* arg = *yes* or *no*
         yes = discard an atom outside grid in a non-periodic dimension
         no = remap an atom outside grid in a non-periodic dimension to first or last grid cell
       *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_grid_cell
         dof_per_grid_cell = add this many degrees-of-freedom per grid_cell for temperature calculation

Examples
""""""""

.. code-block:: LAMMPS

   fix 1 all ave/grid 10000 1 10000 10 10 10 fx fy fz c_myMSD[*]
   fix 1 flow ave/grid 100 10 1000 20 20 30 f_TTM:grid:data

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

Overlay the 2d or 3d simulation box with a uniformly spaced 2d or 3d
grid and use it to either (a) time-average per-atom quantities for the
atoms in each grid cell, or to (b) time-average per-grid quantities
produced by other computes or fixes.  This fix operates in either
"per-atom mode" (all input values are per-atom) or in "per-grid mode"
(all input values are per-grid).  You cannot use both per-atom and
per-grid inputs in the same command.

The grid created by this command is distributed; each processor owns
the grid points that are within its subdomain.  This is similar to
the :doc:`fix ave/chunk <fix_ave_chunk>` command when it uses chunks
from the :doc:`compute chunk/atom <compute_chunk_atom>` command which
are 2d or 3d regular bins.  However, the per-bin outputs in that case
are global; each processor stores a copy of the entire set of bin
data.  Thus it more efficient to use the fix ave/grid command when the
grid is large and a simulation is run on many processors.

For per-atom mode, only atoms in the specified group contribute to the
summing and averaging calculations.  For per-grid mode, the specified
group is ignored.

----------

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 timestep 100.  Similarly for timesteps 190,192,194,196,198,200 on
timestep 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 timesteps
100,200,etc.

In per-atom mode, each input value can also be averaged over the atoms
in each grid cell.  The way the averaging is done across the :math:`N_\text{repeat}`
timesteps to produce output on the :math:`N_\text{freq}` timesteps, and across
multiple :math:`N_\text{freq}` outputs, is determined by the *norm* and *ave*
keyword settings, as discussed below.

----------

The *Nx*, *Ny*, and *Nz* arguments specify the size of the grid that
overlays the simulation box.  For 2d simulations, *Nz* must be 1.  The
*Nx*, *Ny*, *Nz* values can be any positive integer.  The grid can be
very coarse compared to the particle count, or very fine.  If one or
more of the values = 1, then bins are 2d planes or 1d slices of the
simulation domain.  Note that if the total number of grid cells is
small, it may be more efficient to use the :doc:`fix ave/chunk
<fix_ave_chunk>` command which can treat a grid defined by the
:doc:`compute chunk/atom <compute_chunk_atom>` command as a global
grid where each processor owns a copy of all the grid cells.  If *Nx*
= *Ny* = *Nz* = 1 is used, the same calculation would be more
efficiently performed by the :doc:`fix ave/atom <fix_ave_atom>`
command.

If the simulation box size or shape changes during a simulation, the
grid always conforms to the size/shape of the current simulation box.
If one more dimensions have non-periodic shrink-wrapped boundary
conditions, as defined by the :doc:`boundary <boundary>` command, then
the grid will extend over the (dynamic) shrink-wrapped extent in each
dimension.  If the box shape is triclinic, as explained in :doc:`Howto
triclinic <Howto_triclinic>`, then the grid is also triclinic; each
grid cell is a small triclinic cell with the same shape as the
simulation box.

----------

In both per-atom and per-grid mode, input values from a compute or fix
that produces an array of values (multiple values per atom or per grid
point), 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 N = the number of
columns in the array (for *mode* = vector), then an asterisk with no
numeric values means all indices from 1 to N.  A leading asterisk
means all indices from 1 to n (inclusive).  A trailing asterisk means
all indices from n to 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.  E.g. if there were a compute fft/grid
command which produced 3 values for each grid point, these two fix
ave/grid commands would be equivalent:

.. code-block:: LAMMPS

   compute myFFT all fft/grid 10 10 10 ...
   fix 1 all ave/grid 100 1 100 10 10 10 c_myFFT:grid:data[*]
   fix 2 all ave/grid 100 1 100 10 10 10 c_myFFT:grid:data[*][1] c_myFFT:grid:data[*][2] c_myFFT:grid:data[3]

----------

*Per-atom mode*:

Each specified per-atom value can be an atom attribute (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.

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.

----------

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 grid cell, i.e. number/volume.  The *density/mass* value means
the mass density is computed for each grid/cell,
i.e. total-mass/volume.  The output values are in units of 1/volume or
density (mass/volume).  See the :doc:`units <units>` command page for
the definition of density for each choice of units, e.g. gram/cm\^3.

The *temp* value computes the temperature for each grid cell, by the
formula

.. math::

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

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

The DOF is calculated as N\*adof + cdof, where N = number of atoms in
the grid cell, adof = degrees of freedom per atom, and cdof = degrees
of freedom per grid cell.  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>`, or
: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 inside and outside a specific grid
cell, 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-grid-cell temperature calculated by this fix and the
:doc:`compute temp/chunk <compute_temp_chunk>` command (using bins)
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 grid cell on different timesteps
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 timesteps, 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 grid cells.

----------

*Per-grid mode*:

The attributes that begin with *c_ID* and *f_ID* both take
colon-separated fields *gname* and *dname*.  These refer to a grid
name and data field name which is defined by the compute or fix.  Note
that a compute or fix can define one or more grids (of different
sizes) and one or more data fields for each of those grids.  The sizes
of all grids used as values for one instance of this fix must be the
same.

The *c_ID:gname:dname* and *c_ID:gname:dname[I]* attributes allow
per-grid vectors or arrays calculated by a :doc:`compute <compute>` to
be accessed.  The ID in the attribute should be replaced by the actual
ID of the compute that has been defined previously in the input
script.

If *c_ID:gname:dname* is used as a attribute, then the per-grid vector
calculated by the compute is accessed.  If *c_ID:gname:dname[I]* is
used, then I must be in the range from 1-M, which will access the Ith
column of the per-grid array with M columns calculated by the compute.
See the discussion above for how I can be specified with a wildcard
asterisk to effectively specify multiple values.

The *f_ID:gname:dname* and *f_ID:gname:dname[I]* attributes allow
per-grid vectors or arrays calculated by a :doc:`fix <fix>` to be
output.  The ID in the attribute should be replaced by the actual ID
of the fix that has been defined previously in the input script.

If *f_ID:gname:dname* is used as a attribute, then the per-grid vector
calculated by the fix is printed.  If *f_ID:gname:dname[I]* is used,
then I must be in the range from 1-M, which will print the Ith column
of the per-grid with M columns calculated by the fix.  See the
discussion above for how I can be specified with a wildcard asterisk
to effectively specify multiple values.

----------

Additional optional keywords also affect the operation of this fix and
its outputs.  Some are only applicable to per-atom mode.  Some are
applicable to both per-atom and per-grid mode.

The *discard* keyword is only applicable to per-atom mode.  If a
dimension of the system is non-periodic, then grid cells will only
span the box dimension (fixed or shrink-wrap boundaries as set by the
:doc:`boundary` command).  An atom may thus be slightly outside the
range of grid cells on a particular timestep.  If *discard* is set to
*yes* (the default), then the atom will be assigned to the closest
grid cell (lowest or highest) in that dimension.  If *discard* is set
to *no* the atom will be ignored.

----------

The *norm* keyword is only applicable to per-atom mode.  In per-grid
mode, the *norm* keyword setting is ignored.  The output grid value on
an :math:`N_\text{freq}` timestep is the sum of the grid values in each of the
:math:`N_\text{repeat}` samples, divided by :math:`N_\text{repeat}`.

In per-atom mode, the *norm* keyword affects how averaging is done for
the per-grid values that are output on an :math:`N_\text{freq}` timestep. :math:`N_\text{repeat}`
samples contribute to the output.  The *norm* keyword has 3 possible
settings: *all* or *sample* or *none*.  *All* is the default.

In the formulas that follow, SumI is the sum of a per-atom property
over the CountI atoms in a grid cell for a single sample I, where I
varies from 1 to N, and N = Nrepeat.  These formulas are used for any
per-atom input value listed above, except *density/number*,
*density/mass*, and *temp*.  Those input values are discussed below.

In per-atom mode, for *norm all* the output grid value on the :math:`N_\text{freq}`
timestep is an average over atoms across the entire :math:`N_\text{freq}` timescale:

Output = (Sum1 + Sum2 + ... + SumN) / (Count1 + Count2 + ... + CountN)

In per-atom mode, for *norm sample* the output grid value on the
:math:`N_\text{freq}` timestep is an average of an average:

Output = (Sum1/Count1 + Sum2/Count2 + ... + SumN/CountN) / Nrepeat

In per-atom mode, for *norm none* the output grid value on the
:math:`N_\text{freq}` timestep is not normalized by the atom counts:

Output = (Sum1 + Sum2 + ... SumN) / Nrepeat

For *density/number* and *density/mass*, the output value is the same
as in the formulas above for *norm all* and *norm sample*, except that
the result is also divided by the grid cell volume.  For *norm all*,
this will be the volume at the final :math:`N_\text{freq}` timestep.  For *norm
sample*, the divide-by-volume is done for each sample, using the grid
cell volume at the sample timestep.  For *norm none*, the output is
the same as for *norm all*.

For *temp*, the output temperature uses the formula for kinetic energy
KE listed above, and is normalized similarly to the formulas above for
*norm all* and *norm sample*, except for the way the degrees of
freedom (DOF) are calculated.  For *norm none*, the output is the same
as for *norm all*.

For *norm all*, the DOF = :math:`N_\text{repeat} \times` *cdof* plus *Count* times
*adof*, where *Count* = (Count1 + Count2 + ... + CountN).  The *cdof*
and *adof* keywords are discussed below.  The output temperature is
computed with all atoms across all samples contributing.

For *norm sample*, the DOF for a single sample = *cdof* plus *Count*
times *adof*, where *Count* = CountI for a single sample.  The output
temperature is the average of *Nsample* temperatures calculated for
each sample.

Finally, for all 3 *norm* settings the output count of atoms per grid
cell is:

Output count = (Count1 + Count2 + ... CountN) / Nrepeat

This count is the same for all per-atom input values, including
*density/number*, *density/mass*, and *temp*.

----------

The *ave* keyword is applied to both per-atom and per-grid mode.  It
determines how the per-grid values produced once 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.

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

If the *ave* setting is *running*, then the grid values produced on
:math:`N_\text{freq}` timesteps are summed and averaged in a cumulative sense before
being output.  Each output grid value is thus the average of the grid
value produced on that timestep with all preceding values for the same
grid value.  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 grid values produced on
:math:`N_\text{freq}` timesteps are summed and averaged within a moving "window" of
time, so that the last M values for the same grid are used to produce
the output.  E.g. if M = 3 and Nfreq = 1000, then the grid value
output on step 10000 will be the average of the grid values on steps
8000,9000,10000.  Outputs on early steps will average over less than M
values if they are not available.

----------

The *bias*, *adof*, and *cdof* keywords are only applicable to
per-atom mode.

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 grid cell 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 grid cell.  They are only used when the *temp* value is
calculated.  They can be used to calculate a more appropriate
temperature in some cases.  Here are 3 examples:

If grid cells 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 6 degrees of freedom (DOF) (3
translational, 3 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 x component of velocity to contribute
to the temperature, then *adof* = 1.0 would be appropriate.

Using *cdof* = -2 or -3 (for 2d or 3d simulations) will subtract out 2
or 3 degrees of freedom for each grid cell, similar to how the
:doc:`compute temp <compute_temp>` command subtracts out 3 DOF for the
entire system.

----------

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 calculates a per-grid array which has one column for each of
the specified input values.  The units for each column with be in the
:doc:`units <units>` for the per-atom or per-grid quantity for the
corresponding input value.  If the fix is used in per-atom mode, it
also calculates a per-grid vector with the count of atoms in each grid
cell.  The number of rows in the per-grid array and number of values
in the per-grid vector (distributed across all processors) is Nx *
Ny * Nz.

For access by other commands, the name of the single grid produced by
this fix is "grid".  The names of its two per-grid datums are "data"
for the per-grid array and "count" for the per-grid vector (if using
per-atom values).  Both datums can be accessed by various :doc:`output
commands <Howto_output>`.

In per-atom mode, the per-grid array values calculated by this fix are
treated as "intensive", since they are typically already normalized by
the count of atoms in each grid cell.

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:`fix ave/atom <fix_ave_atom>`, :doc:`fix ave/chunk <fix_ave_chunk>`

Default
"""""""

The option defaults are discard = yes, norm = all, ave = one, and bias
= none.
