c_ID = global scalar calculated by a compute with ID
c_ID[I] = Ith component of global vector calculated by a compute with ID, I can include wildcard (see below)
f_ID = global scalar calculated by a fix with ID
f_ID[I] = Ith component of global vector calculated by a fix with ID, I can include wildcard (see below)
v_name = global value calculated by an equal-style variable with name
v_name[I] = Ith component of a vector-style variable with name
</pre>
</li>
<li><p class="first">zero or more keyword/arg pairs may be appended</p>
</li>
<li><p class="first">keyword = <em>type</em> or <em>ave</em> or <em>start</em> or <em>prefactor</em> or <em>file</em> or <em>overwrite</em> or <em>title1</em> or <em>title2</em> or <em>title3</em></p>
<pre class="literal-block">
<em>type</em> arg = <em>auto</em> or <em>upper</em> or <em>lower</em> or <em>auto/upper</em> or <em>auto/lower</em> or <em>full</em>
auto = correlate each value with itself
upper = correlate each value with each succeeding value
lower = correlate each value with each preceding value
auto/upper = auto + upper
auto/lower = auto + lower
full = correlate each value with every other value, including itself = auto + upper + lower
<em>ave</em> args = <em>one</em> or <em>running</em>
one = zero the correlation accumulation every Nfreq steps
running = accumulate correlations continuously
<em>start</em> args = Nstart
Nstart = start accumulating correlations on this timestep
<em>prefactor</em> args = value
value = prefactor to scale all the correlation data by
<em>file</em> arg = filename
filename = name of file to output correlation data to
<em>overwrite</em> arg = none = overwrite output file with only latest output
<em>title1</em> arg = string
string = text to print as 1st line of output file
<em>title2</em> arg = string
string = text to print as 2nd line of output file
<em>title3</em> arg = string
string = text to print as 3rd line of output file
</pre>
</li>
</ul>
</div>
<div class="section" id="examples">
<h2>Examples</h2>
<pre class="literal-block">
fix 1 all ave/correlate 5 100 1000 c_myTemp file temp.correlate
fix 1 all ave/correlate 1 50 10000 &
c_thermo_press[1] c_thermo_press[2] c_thermo_press[3] &
type upper ave running title1 "My correlation data"
</pre>
<p>fix 1 all ave/correlate 1 50 10000 c_thermo_press[*]</p>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>Use one or more global scalar values as inputs every few timesteps,
calculate time correlations bewteen them at varying time intervals,
and average the correlation data over longer timescales. The
resulting correlation values can be time integrated by
<a class="reference internal" href="variable.html"><span class="doc">variables</span></a> or used by other <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">output commands</span></a> such as <a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style custom</span></a>, and can also be written to a file. See the
<a class="reference internal" href="fix_ave_correlate_long.html"><span class="doc">fix ave/correlate/long</span></a> command for an
alternate method for computing correlation functions efficiently over
very long time windows.</p>
<p>The group specified with this command is ignored. However, note that
specified values may represent calculations performed by computes and
fixes which store their own “group” definitions.</p>
<p>Each listed value can be the result of a <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> or
<a class="reference internal" href="fix.html"><span class="doc">fix</span></a> or the evaluation of an equal-style or vector-style
<a class="reference internal" href="variable.html"><span class="doc">variable</span></a>. In each case, the compute, fix, or variable
must produce a global quantity, not a per-atom or local quantity. If
you wish to spatial- or time-average or histogram per-atom quantities
from a compute, fix, or variable, then see the <a class="reference internal" href="fix_ave_chunk.html"><span class="doc">fix ave/chunk</span></a>, <a class="reference internal" href="fix_ave_atom.html"><span class="doc">fix ave/atom</span></a>, or
<a class="reference internal" href="fix_ave_histo.html"><span class="doc">fix ave/histo</span></a> commands. If you wish to convert a
per-atom quantity into a single global value, see the <a class="reference internal" href="compute_reduce.html"><span class="doc">compute reduce</span></a> command.</p>
<p>The input values must either be all scalars. What kinds of
correlations between input values are calculated is determined by the
<em>type</em> keyword as discussed below.</p>
<p><a class="reference internal" href="compute.html"><span class="doc">Computes</span></a> that produce global quantities are those which
do not have the word <em>atom</em> in their style name. Only a few
<a class="reference internal" href="fix.html"><span class="doc">fixes</span></a> produce global quantities. See the doc pages for
individual fixes for info on which ones produce such values.
<a class="reference internal" href="variable.html"><span class="doc">Variables</span></a> of style <em>equal</em> and <em>vector</em> are the only
ones that can be used with this fix. Variables of style <em>atom</em> cannot
be used, since they produce per-atom values.</p>
<p>Note that for values from a compute or fix, 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 size of the vector (for <em>mode</em> = scalar) or the
number of columns in the array (for <em>mode</em> = 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).</p>
<p>Using a wildcard is the same as if the individual elements of the
vector had been listed one by one. E.g. these 2 fix ave/correlate
commands are equivalent, since the <a class="reference internal" href="compute_pressure.html"><span class="doc">compute pressure</span></a> command creates a global vector with 6
values.</p>
<pre class="literal-block">
compute myPress all pressure NULL
fix 1 all ave/correlate 1 50 10000 c_myPress[*]
fix 1 all ave/correlate 1 50 10000 &
c_myPress[1] c_myPress[2] c_myPress[3] &
c_myPress[4] c_myPress[5] c_myPress[6]
</pre>
<hr class="docutils" />
<p>The <em>Nevery</em>, <em>Nrepeat</em>, and <em>Nfreq</em> arguments specify on what
timesteps the input values will be used to calculate correlation data.
The input values are sampled every <em>Nevery</em> timesteps. The
correlation data for the preceding samples is computed on timesteps
that are a multiple of <em>Nfreq</em>. Consider a set of samples from some
initial time up to an output timestep. The initial time could be the
beginning of the simulation or the last output time; see the <em>ave</em>
keyword for options. For the set of samples, the correlation value
Cij is calculated as:</p>
<pre class="literal-block">
Cij(delta) = ave(Vi(t)*Vj(t+delta))
</pre>
<p>which is the correlation value between input values Vi and Vj,
separated by time delta. Note that the second value Vj in the pair is
always the one sampled at the later time. The ave() represents an
average over every pair of samples in the set that are separated by
time delta. The maximum delta used is of size (<em>Nrepeat</em>-1)*<em>Nevery</em>.
Thus the correlation between a pair of input values yields <em>Nrepeat</em>
<p><em>Nfreq</em> must be a multiple of <em>Nevery</em>; <em>Nevery</em> and <em>Nrepeat</em> must be
non-zero. Also, if the <em>ave</em> keyword is set to <em>one</em> which is the
default, then <em>Nfreq</em> >= (<em>Nrepeat</em>-1)*<em>Nevery</em> is required.</p>
<hr class="docutils" />
<p>If a value begins with “c_”, a compute ID must follow which has been
previously defined in the input script. If no bracketed term is
appended, the global scalar calculated by the compute is used. If a
bracketed term is appended, the Ith element of the global vector
calculated by the compute is used. See the discussion above for how I
can be specified with a wildcard asterisk to effectively specify
multiple values.</p>
<p>Note that there is a <a class="reference internal" href="compute_reduce.html"><span class="doc">compute reduce</span></a> command
which can sum per-atom quantities into a global scalar or vector which
can thus be accessed by fix ave/correlate. Or it can be a compute
defined not in your input script, but by <a class="reference internal" href="thermo_style.html"><span class="doc">thermodynamic output</span></a> or other fixes such as <a class="reference internal" href="fix_nh.html"><span class="doc">fix nvt</span></a>
or <a class="reference internal" href="fix_temp_rescale.html"><span class="doc">fix temp/rescale</span></a>. See the doc pages for
these commands which give the IDs of these computes. Users can also
write code for their own compute styles and <a class="reference internal" href="Section_modify.html"><span class="doc">add them to LAMMPS</span></a>.</p>
<p>If a value begins with “f_”, a fix ID must follow which has been
previously defined in the input script. If no bracketed term is
appended, the global scalar calculated by the fix is used. If a
bracketed term is appended, the Ith element of the global vector
calculated by the fix is used. See the discussion above for how I can
be specified with a wildcard asterisk to effectively specify multiple
values.</p>
<p>Note that some fixes only produce their values on certain timesteps,
which must be compatible with <em>Nevery</em>, else an error will result.
Users can also write code for their own fix styles and <a class="reference internal" href="Section_modify.html"><span class="doc">add them to LAMMPS</span></a>.</p>
<p>If a value begins with “v_”, a variable name must follow which has
been previously defined in the input script. Only equal-style or
vector-style variables can be referenced; the latter requires a
bracketed term to specify the Ith element of the vector calculated by
the variable. See the <a class="reference internal" href="variable.html"><span class="doc">variable</span></a> command for details.
Note that variables of style <em>equal</em> or <em>vector</em> define a formula
which can reference individual atom properties or thermodynamic
keywords, or they can invoke other computes, fixes, or variables when
they are evaluated, so this is a very general means of specifying
quantities to time correlate.</p>
<hr class="docutils" />
<p>Additional optional keywords also affect the operation of this fix.</p>
<p>The <em>type</em> keyword determines which pairs of input values are
correlated with each other. For N input values Vi, for i = 1 to N,
let the number of pairs = Npair. Note that the second value in the
pair Vi(t)*Vj(t+delta) is always the one sampled at the later time.</p>
<ul class="simple">
<li>If <em>type</em> is set to <em>auto</em> then each input value is correlated with
itself. I.e. Cii = Vi*Vi, for i = 1 to N, so Npair = N.</li>
<li>If <em>type</em> is set
to <em>upper</em> then each input value is correlated with every succeeding
value. I.e. Cij = Vi*Vj, for i < j, so Npair = N*(N-1)/2.</li>
<li>If <em>type</em> is set
to <em>lower</em> then each input value is correlated with every preceeding
value. I.e. Cij = Vi*Vj, for i > j, so Npair = N*(N-1)/2.</li>
<li>If <em>type</em> is set to <em>auto/upper</em> then each input value is correlated
with itself and every succeeding value. I.e. Cij = Vi*Vj, for i >= j,
so Npair = N*(N+1)/2.</li>
<li>If <em>type</em> is set to <em>auto/lower</em> then each input value is correlated
with itself and every preceding value. I.e. Cij = Vi*Vj, for i <= j,
so Npair = N*(N+1)/2.</li>
<li>If <em>type</em> is set to <em>full</em> then each input value is correlated with
itself and every other value. I.e. Cij = Vi*Vj, for i,j = 1,N so
Npair = N^2.</li>
</ul>
<p>The <em>ave</em> keyword determines what happens to the accumulation of
correlation samples every <em>Nfreq</em> timesteps. If the <em>ave</em> setting is
<em>one</em>, then the accumulation is restarted or zeroed every <em>Nfreq</em>
timesteps. Thus the outputs on successive <em>Nfreq</em> timesteps are
essentially independent of each other. The exception is that the
Cij(0) = Vi(T)*Vj(T) value at a timestep T, where T is a multiple of
<em>Nfreq</em>, contributes to the correlation output both at time T and at
time T+Nfreq.</p>
<p>If the <em>ave</em> setting is <em>running</em>, then the accumulation is never
zeroed. Thus the output of correlation data at any timestep is the
average over samples accumulated every <em>Nevery</em> steps since the fix
was defined. it can only be restarted by deleting the fix via the
<a class="reference internal" href="unfix.html"><span class="doc">unfix</span></a> command, or by re-defining the fix by re-specifying
it.</p>
<p>The <em>start</em> keyword specifies what timestep the accumulation of
correlation samples will begin on. The default is step 0. Setting it
to a larger value can avoid adding non-equilibrated data to the
correlation averages.</p>
<p>The <em>prefactor</em> keyword specifies a constant which will be used as a
multiplier on the correlation data after it is averaged. It is
effectively a scale factor on Vi*Vj, which can be used to account for
the size of the time window or other unit conversions.</p>
<p>The <em>file</em> keyword allows a filename to be specified. Every <em>Nfreq</em>
steps, an array of correlation data is written to the file. The
number of rows is <em>Nrepeat</em>, as described above. The number of
columns is the Npair+2, also as described above. Thus the file ends
up to be a series of these array sections.</p>
<p>The <em>overwrite</em> 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 <em>ave running</em> setting.</p>
<p>The <em>title1</em> and <em>title2</em> and <em>title3</em> keywords allow specification of
the strings that will be printed as the first 3 lines of the output
file, assuming the <em>file</em> keyword was used. LAMMPS uses default
values for each of these, so they do not need to be specified.</p>
<p>By default, these header lines are as follows:</p>
<pre class="literal-block">
# Time-correlated data for fix ID
# TimeStep Number-of-time-windows
# Index TimeDelta Ncount valueI*valueJ valueI*valueJ ...
</pre>
<p>In the first line, ID is replaced with the fix-ID. The second line
describes the two values that are printed at the first of each section
of output. In the third line the value pairs are replaced with the
appropriate fields from the fix ave/correlate command.</p>
<hr class="docutils" />
<p>Let Sij = a set of time correlation data for input values I and J,
<p>As explained below, these datums are output as one column of a global
array, which is effectively the correlation matrix.</p>
<p>The <em>trap</em> function defined for <a class="reference internal" href="variable.html"><span class="doc">equal-style variables</span></a>
can be used to perform a time integration of this vector of datums,
using a trapezoidal rule. This is useful for calculating various
quantities which can be derived from time correlation data. If a
normalization factor is needed for the time integration, it can be
included in the variable formula or via the <em>prefactor</em> keyword.</p>
<hr class="docutils" />
<p><strong>Restart, fix_modify, output, run start/stop, minimize info:</strong></p>
<p>No information about this fix is written to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>. None of the <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> options
are relevant to this fix.</p>
<p>This fix computes a global array of values which can be accessed by
various <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">output commands</span></a>. The values can
only be accessed on timesteps that are multiples of <em>Nfreq</em> since that
is when averaging is performed. The global array has # of rows =
<em>Nrepeat</em> and # of columns = Npair+2. The first column has the time
delta (in timesteps) between the pairs of input values used to
calculate the correlation, as described above. The 2nd column has the
number of samples contributing to the correlation average, as
described above. The remaining Npair columns are for I,J pairs of the
N input values, as determined by the <em>type</em> keyword, as described
above.</p>
<ul class="simple">
<li>For <em>type</em> = <em>auto</em>, the Npair = N columns are ordered: C11, C22, ...,
CNN.</li>
<li>For <em>type</em> = <em>upper</em>, the Npair = N*(N-1)/2 columns are ordered: C12,
<p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
the <a class="reference internal" href="run.html"><span class="doc">run</span></a> command. This fix is not invoked during <a class="reference internal" href="minimize.html"><span class="doc">energy minimization</span></a>.</p>
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