.. index:: fix ave/spatial fix ave/spatial command ======================= Syntax """""" .. parsed-literal:: fix ID group-ID ave/spatial Nevery Nrepeat Nfreq dim origin delta ... value1 value2 ... keyword args ... * ID, group-ID are documented in :doc:`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 .. parsed-literal:: 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 .. parsed-literal:: 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 *write_ts* or *std* .. parsed-literal:: *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 *write_ts* arg = yes or no yes or no = do nor do not write time-step info and number of samples to 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 """""""" .. parsed-literal:: 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 :ref:`output commands ` such as :doc:`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 :doc:`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 :doc:`compute ` or :doc:`fix ` or the evaluation of an atom-style :doc:`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 :doc:`fix ave/time ` command. :doc:`Computes ` that produce per-atom quantities are those which have the word *atom* in their style name. See the doc pages for individual :doc:`fixes ` to determine which ones produce per-atom quantities. :doc:`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. .. warning:: 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 :ref:`this section ` of the manual for a discussion of the geometry of triclinic boxes in LIGGGHTS(R)-PUBLIC. 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 :doc:`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 :doc:`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 :doc:`add them to LIGGGHTS(R)-PUBLIC `. 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 :doc:`add them to LIGGGHTS(R)-PUBLIC `. 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 :doc:`units ` command, e.g. Angstroms for units = real or metal. A *lattice* value means the distance units are in lattice spacings. The :doc:`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 :doc:`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. Output of this line can be supressed with the *write_ts* keyword. 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. LIGGGHTS(R)-PUBLIC uses default values for each of these, so they do not need to be specified. If either of them is specified as "", then the line is omitted By default, these header lines are as follows: .. parsed-literal:: # 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 :doc:`binary restart files `. None of the :doc:`fix_modify ` options are relevant to this fix. This fix computes a global array of values which can be accessed by various :ref:`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 :doc:`run ` command. This fix is not invoked during :doc:`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 """""""""""""""" :doc:`compute `, :doc:`fix ave/atom `, :doc:`fix ave/histo `, :doc:`fix ave/time `, :doc:`variable `, :doc:`fix ave/correlate `, Default """"""" The option defaults are units = box, norm = all, no file output, and ave = one, title 1,2,3 = strings as described above. .. _liws: http://www.cfdem.com .. _ld: Manual.html .. _lc: Section_commands.html#comm