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### fix ave/spatial command

Syntax:

    fix ID group-ID ave/spatial Nevery Nrepeat Nfreq dim origin delta ... value1 value2 ... keyword args ...

- ID, group-ID are documented in fix command
- ave/spatial = 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
- dim, origin, delta can be repeated 1, 2, or 3 times for 1d, 2d, or 3d bins

        dim = x or y or z
        origin = lower or center or upper or coordinate value (distance units)
        delta = thickness of spatial bins in dim (distance units)

- one or more input values can be listed
- value = vx, vy, vz, fx, fy, fz, density/mass, density/number, c_ID, c_ID[I], f_ID, f_ID[I], v_name

        vx,vy,vz,fx,fy,fz = atom attribute (velocity, force component)
        density/number, density/mass = number or mass density
        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
        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
        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 units or file or ave or overwrite or title1 or title2 or title3 or std

        units arg = box or lattice or reduced
        norm arg = all or sample
        region arg = region-ID
          region-ID = ID of region atoms must be in to contribute to spatial averaging
        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
        file arg = filename
          filename = file to write results to
        overwrite arg = none = overwrite output file with only latest output
        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
        std arg = N1 N2 filename
      	N1 = lower limit of particle number per bin for sampling
      	N2 = upper limit of particle number per bin for sampling
      	filename = file to write results into

Examples:

    fix 1 all ave/spatial 10000 1 10000 z lower 0.02 c_myCentro units reduced &
                          title1 "My output values"
    fix 1 flow ave/spatial 100 10 1000 y 0.0 1.0 vx vz norm sample file vel.profile
    fix 1 flow ave/spatial 100 5 1000 z lower 1.0 y 0.0 2.5 density/mass ave running
    fix 1 all ave/spatial 1000 1 1000 x 0 1e-3 y 0 1e-3 z 0 1e-3 f_tracer[0] file bin_data.dat std 124 126 samples_data.dat

Description:

Use one or more per-atom vectors as inputs every few timesteps, bin their values spatially into 1d, 2d, or 3d bins based on current atom coordinates, and average the bin values over longer timescales. The resulting bin averages can be used by other output commands such as thermo_style custom, and can also be written to a file.

The group specified with the command means only atoms within the group contribute to bin averages. If the region keyword is used, the atom must be in both the group and the specified geometric region in order to contribute to bin averages.

Each listed value can be an atom attribute (position, velocity, force component), a mass or number density, or the result of a compute or fix or the evaluation of an atom-style variable. In the latter cases, the compute, fix, or variable must produce a per-atom quantity, not a global quantity. If you wish to time-average global quantities from a compute, fix, or variable, then see the fix ave/time command.

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

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

The size and dimensionality of the bins (1d = layers or slabs, 2d = pencils, 3d = boxes) are determined by the dim, origin, and delta settings and how many times they are specified (1, 2, or 3). See details below.

IMPORTANT NOTE: This fix works by creating an array of size Nbins by Nvalues on each processor. Nbins is the total number of bins; Nvalues is the number of input values specified. Each processor loops over its atoms, tallying its values to the appropriate bin. Then the entire array is summed across all processors. This means that using a large number of bins (easy to do for 2d or 3d bins) will incur an overhead in memory and computational cost (summing across processors), so be careful to use reasonable numbers of bins.

The Nevery, Nrepeat, and Nfreq arguments specify on what timesteps the input values will be used to bin them and contribute to the average. The final averaged quantities are generated on timesteps that are a multiples of Nfreq. The average is over Nrepeat quantities, computed in the preceding portion of the simulation every Nevery timesteps. Nfreq must be a multiple of Nevery and Nevery must be non-zero even if Nrepeat is 1. Also, the timesteps contributing to the average value cannot overlap, i.e. Nfreq > (Nrepeat-1)*Nevery is required.

For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on timesteps 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 Nrepeat=1 and Nfreq = 100, then no time averaging is done; values are simply generated on timesteps 100,200,etc.

Each per-atom property is also averaged over atoms in each bin. Bins can be 1d layers or slabs, 2d pencils, or 3d boxes. This depends on how many times (1, 2, or 3) the dim, origin, and delta settings are specified in the fix ave/spatial command. For 2d or 3d bins, there is no restriction on specifying dim = x before dim = y, or dim = y before dim = z. Bins in a particular dim have a bin size in that dimension given by delta. Every Nfreq steps, when averaging is being performed and the per-atom property is calculated for the first time, the number of bins and the bin sizes and boundaries are computed. Thus if the simulation box changes size during a simulation, the number of bins and their boundaries may also change. In each dimension, bins are defined relative to a specified origin, which may be the lower/upper edge of the simulation box (in dim) or its center point, or a specified coordinate value. Starting at the origin, sufficient bins are created in both directions to completely cover the box. On subsequent timesteps every atom is mapped to one of the bins. Atoms beyond the lowermost/uppermost bin in a dimension are counted in the first/last bin in that dimension.

For orthogonal simulation boxes, the bins are also layers, pencils, or boxes aligned with the xyz coordinate axes. For triclinic (non-orthogonal) simulation boxes, the bins are so that they are parallel to the tilted faces of the simulation box. See this section of the manual for a discussion of the geometry of triclinic boxes in LAMMPS. As described there, a tilted simulation box has edge vectors a,b,c. In that nomenclature, bins in the x dimension have faces with normals in the "b" cross "c" direction. Bins in y have faces normal to the "a" cross "c" direction. And bins in z have faces normal to the "a" cross "b" direction. Note that in order to define the size and position of these bins in an unambiguous fashion, the units option must be set to reduced when using a triclinic simulation box, as noted below.

The atom attribute values (vx,vy,vz,fx,fy,fz) are self-explanatory. Note that other atom attributes (including atom postitions x,y,z) can be used as inputs to this fix by using the compute property/atom command and then specifying an input value from that compute.

The density/number value means the number density is computed in each bin, i.e. a weighting of 1 for each atom. The density/mass value means the mass density is computed in each bind, i.e. each atom is weighted by its mass. The resulting density is normalized by the volume of the bin so that units of number/volume or density are output. See the units command doc page for the definition of density for each choice of units, e.g. gram/cm^3.

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 add them to LAMMPS.

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 Nevery, else an error results. Users can also write code for their own fix styles and add them to LAMMPS.

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 spatially average.

Additional optional keywords also affect the operation of this fix.

The units keyword determines the meaning of the distance units used for the bin size delta and for origin if it is a coordinate value. For orthogonal simulation boxes, any of the 3 options may be used. For non-orthogonal (triclinic) simulation boxes, only the reduced option may be used.

A box value selects standard distance units as defined by the units command, e.g. Angstroms for units = real or metal. A lattice value means the distance units are in lattice spacings. The lattice command must have been previously used to define the lattice spacing. A reduced value means normalized unitless values between 0 and 1, which represent the lower and upper faces of the simulation box respectively. Thus an origin value of 0.5 means the center of the box in any dimension. A delta value of 0.1 means 10 bins span the box in that dimension.

Consider a non-orthogonal box, with bins that are 1d layers or slabs in the x dimension. No matter how the box is tilted, an origin of 0.0 means start layers at the lower "b" cross "c" plane of the simulation box and an origin of 1.0 means to start layers at the upper "b" cross "c" face of the box. A delta value of 0.1 means there will be 10 layers from 0.0 to 1.0, regardless of the current size or shape of the simulation box.

The norm keyword affects how averaging is done for the output produced every Nfreq timesteps. For an all setting, a bin quantity is summed over all atoms in all Nrepeat samples, as is the count of atoms in the bin. The printed value for the bin is Total-quantity / Total-count. In other words it is an average over the entire Nfreq timescale.

For a sample setting, the bin quantity is summed over atoms for only a single sample, as is the count, and a "average sample value" is computed, i.e. Sample-quantity / Sample-count. The printed value for the bin is the average of the Nrepeat "average sample values", In other words it is an average of an average.

The ave keyword determines how the bin values produced every Nfreq steps are averaged with bin values produced on previous steps that were multiples of Nfreq, before they are accessed by another output command or written to a file.

If the ave setting is one, then the bin values produced on timesteps that are multiples of Nfreq are independent of each other; they are output as-is without further averaging.

If the ave setting is running, then the bin values produced on timesteps that are multiples of Nfreq are summed and averaged in a cumulative sense before being output. Each output bin value is thus the average of the bin value produced on that timestep with all preceding values for the same bin. This running average begins when the fix is defined; it can only be restarted by deleting the fix via the unfix command, or re-defining the fix by re-specifying it.

If the ave setting is window, then the bin values produced on timesteps that are multiples of Nfreq are summed and averaged within a moving "window" of time, so that the last M values for the same bin are used to produce the output. E.g. if M = 3 and Nfreq = 1000, then the output on step 10000 will be the average of the individual bin values on steps 8000,9000,10000. Outputs on early steps will average over less than M values if they are not available.

The file keyword allows a filename to be specified. Every Nfreq timesteps, a section of bin info will be written to a text file in the following format. A line with the timestep and number of bin is written. Then one line per bin is written, containing the bin ID (1-N), the coordinate of the center of the bin, the number of atoms in the bin, and one or more calculated values. The number of values in each line corresponds to the number of values specified in the fix ave/spatial command. The number of atoms and the value(s) are average quantities. If the value of the units keyword is box or lattice, the "coord" is printed in box units. If the value of the units keyword is reduced, the "coord" is printed in reduced units (0-1).

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 title1 and title2 and title3 keywords allow specification of the strings that will be printed as the first 3 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:

    # Spatial-averaged data for fix ID and group name
    # Timestep Number-of-bins
    # Bin Coord1 Coord2 Coord3 Count 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 fields from the fix ave/spatial command. The Coord2 and Coord3 entries in the third line only appear for 2d and 3d bins respectively. For 1d bins, the word Coord1 is replaced by just Coord.

If the std keyword is set, mean and standard deviation of the specified values (value1, value2, etc.) over samples of a defined size are calculated. The sample size has to be defined by a lower limit (N1) and an upper limit (N2>N1). All bins containing a particle count between N1 and N2 (including N1 and N2) are used as samples. Every Nfreq timestep a line is written to a file specified after N1 and N2, including the following numbers: timestep, total number of atoms, total number of bins, maximum number of atoms per bin, number of empty bins, number of bins including less atoms than N1, number of bins including more atoms than N2, number of samples, average number of atoms per sample, followed by three quantities for each defined value: true average (over all atoms), average over the chosen samples, standard deviation over the chosen samples. For the calculation of the standard deviation the (known) true average is used instead of the samples average (the latter is only an estimate for the true average!).

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

No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix.

This fix computes a global array of values which can be accessed by various output commands. The values can only be accessed on timesteps that are multiples of Nfreq since that is when averaging is performed. The global array has # of rows = Nbins and # of columns = Ndim+1+Nvalues, where Ndim = 1,2,3 for 1d,2d,3d bins. The first 1 or 2 or 3 columns have the bin coordinates (center of the bin) in the appropriate dimensions, the next column has the count of atoms in that bin, and the remaining columns are the Nvalue quantities. When the array is accessed with an I that exceeds the current number of bins, than a 0.0 is returned by the fix instead of an error, since the number of bins can vary as a simulation runs, depending on the simulation box size. 2d or 3d bins are ordered so that the last dimension(s) vary fastest. The array values calculated by this fix are "intensive", since they are already normalized by the count of atoms in each bin.

No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.

Restrictions:

When the ave keyword is set to running or window then the number of bins must remain the same during the simulation, so that the appropriate averaging can be done. This will be the case if the simulation box size doesn't change or if the units keyword is set to reduced.

Related commands:

compute, fix ave/atom, fix ave/histo, fix ave/time, variable, fix ave/correlate,

Default:

The option defaults are units = lattice, norm = all, no file output, and ave = one, title 1,2,3 = strings as described above.