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<div class="section" id="fix-ave-correlate-command">
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<span id="index-0"></span><h1>fix ave/correlate command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">ave</span><span class="o">/</span><span class="n">correlate</span> <span class="n">Nevery</span> <span class="n">Nrepeat</span> <span class="n">Nfreq</span> <span class="n">value1</span> <span class="n">value2</span> <span class="o">...</span> <span class="n">keyword</span> <span class="n">args</span> <span class="o">...</span>
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</pre></div>
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</div>
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<ul class="simple">
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<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><span class="doc">fix</span></a> command</li>
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<li>ave/correlate = style name of this fix command</li>
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<li>Nevery = use input values every this many timesteps</li>
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<li>Nrepeat = # of correlation time windows to accumulate</li>
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<li>Nfreq = calculate time window averages every this many timesteps</li>
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<li>one or more input values can be listed</li>
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<li>value = c_ID, c_ID[N], f_ID, f_ID[N], v_name</li>
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</ul>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">c_ID</span> <span class="o">=</span> <span class="k">global</span> <span class="n">scalar</span> <span class="n">calculated</span> <span class="n">by</span> <span class="n">a</span> <span class="n">compute</span> <span class="k">with</span> <span class="n">ID</span>
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<span class="n">c_ID</span><span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="o">=</span> <span class="n">Ith</span> <span class="n">component</span> <span class="n">of</span> <span class="k">global</span> <span class="n">vector</span> <span class="n">calculated</span> <span class="n">by</span> <span class="n">a</span> <span class="n">compute</span> <span class="k">with</span> <span class="n">ID</span>
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<span class="n">f_ID</span> <span class="o">=</span> <span class="k">global</span> <span class="n">scalar</span> <span class="n">calculated</span> <span class="n">by</span> <span class="n">a</span> <span class="n">fix</span> <span class="k">with</span> <span class="n">ID</span>
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<span class="n">f_ID</span><span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="o">=</span> <span class="n">Ith</span> <span class="n">component</span> <span class="n">of</span> <span class="k">global</span> <span class="n">vector</span> <span class="n">calculated</span> <span class="n">by</span> <span class="n">a</span> <span class="n">fix</span> <span class="k">with</span> <span class="n">ID</span>
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<span class="n">v_name</span> <span class="o">=</span> <span class="k">global</span> <span class="n">value</span> <span class="n">calculated</span> <span class="n">by</span> <span class="n">an</span> <span class="n">equal</span><span class="o">-</span><span class="n">style</span> <span class="n">variable</span> <span class="k">with</span> <span class="n">name</span>
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<span class="n">v_name</span><span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="o">=</span> <span class="n">Ith</span> <span class="n">component</span> <span class="n">of</span> <span class="n">a</span> <span class="n">vector</span><span class="o">-</span><span class="n">style</span> <span class="n">variable</span> <span class="k">with</span> <span class="n">name</span>
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</pre></div>
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</div>
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<ul class="simple">
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<li>zero or more keyword/arg pairs may be appended</li>
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<li>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></li>
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</ul>
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<pre class="literal-block">
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<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>
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auto = correlate each value with itself
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upper = correlate each value with each succeeding value
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lower = correlate each value with each preceding value
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auto/upper = auto + upper
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auto/lower = auto + lower
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full = correlate each value with every other value, including itself = auto + upper + lower
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<em>ave</em> args = <em>one</em> or <em>running</em>
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one = zero the correlation accumulation every Nfreq steps
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running = accumulate correlations continuously
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<em>start</em> args = Nstart
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Nstart = start accumulating correlations on this timestep
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<em>prefactor</em> args = value
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value = prefactor to scale all the correlation data by
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<em>file</em> arg = filename
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filename = name of file to output correlation data to
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<em>overwrite</em> arg = none = overwrite output file with only latest output
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<em>title1</em> arg = string
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string = text to print as 1st line of output file
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<em>title2</em> arg = string
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string = text to print as 2nd line of output file
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<em>title3</em> arg = string
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string = text to print as 3rd line of output file
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</pre>
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</div>
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<div class="section" id="examples">
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<h2>Examples</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">ave</span><span class="o">/</span><span class="n">correlate</span> <span class="mi">5</span> <span class="mi">100</span> <span class="mi">1000</span> <span class="n">c_myTemp</span> <span class="n">file</span> <span class="n">temp</span><span class="o">.</span><span class="n">correlate</span>
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<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">ave</span><span class="o">/</span><span class="n">correlate</span> <span class="mi">1</span> <span class="mi">50</span> <span class="mi">10000</span> <span class="o">&</span>
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<span class="n">c_thermo_press</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="n">c_thermo_press</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="n">c_thermo_press</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">&</span>
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<span class="nb">type</span> <span class="n">upper</span> <span class="n">ave</span> <span class="n">running</span> <span class="n">title1</span> <span class="s2">"My correlation data"</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description</h2>
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<p>Use one or more global scalar values as inputs every few timesteps,
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calculate time correlations bewteen them at varying time intervals,
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and average the correlation data over longer timescales. The
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resulting correlation values can be time integrated by
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<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
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<a class="reference internal" href="fix_ave_correlate_long.html"><span class="doc">fix ave/correlate/long</span></a> command for an
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alternate method for computing correlation functions efficiently over
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very long time windows.</p>
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<p>The group specified with this command is ignored. However, note that
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specified values may represent calculations performed by computes and
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fixes which store their own “group” definitions.</p>
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<p>Each listed value can be the result of a <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> or
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<a class="reference internal" href="fix.html"><span class="doc">fix</span></a> or the evaluation of an equal-style or vector-style
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<a class="reference internal" href="variable.html"><span class="doc">variable</span></a>. In each case, the compute, fix, or variable
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must produce a global quantity, not a per-atom or local quantity. If
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you wish to spatial- or time-average or histogram per-atom quantities
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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
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<a class="reference internal" href="fix_ave_histo.html"><span class="doc">fix ave/histo</span></a> commands. If you wish to convert a
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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>
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<p><a class="reference internal" href="compute.html"><span class="doc">Computes</span></a> that produce global quantities are those which
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do not have the word <em>atom</em> in their style name. Only a few
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<a class="reference internal" href="fix.html"><span class="doc">fixes</span></a> produce global quantities. See the doc pages for
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individual fixes for info on which ones produce such values.
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<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
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ones that can be used with this fix. Variables of style <em>atom</em> cannot
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be used, since they produce per-atom values.</p>
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<p>The input values must either be all scalars. What kinds of
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correlations between input values are calculated is determined by the
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<em>type</em> keyword as discussed below.</p>
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<hr class="docutils" />
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<p>The <em>Nevery</em>, <em>Nrepeat</em>, and <em>Nfreq</em> arguments specify on what
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timesteps the input values will be used to calculate correlation data.
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The input values are sampled every <em>Nevery</em> timesteps. The
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correlation data for the preceding samples is computed on timesteps
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that are a multiple of <em>Nfreq</em>. Consider a set of samples from some
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initial time up to an output timestep. The initial time could be the
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beginning of the simulation or the last output time; see the <em>ave</em>
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keyword for options. For the set of samples, the correlation value
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Cij is calculated as:</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">Cij</span><span class="p">(</span><span class="n">delta</span><span class="p">)</span> <span class="o">=</span> <span class="n">ave</span><span class="p">(</span><span class="n">Vi</span><span class="p">(</span><span class="n">t</span><span class="p">)</span><span class="o">*</span><span class="n">Vj</span><span class="p">(</span><span class="n">t</span><span class="o">+</span><span class="n">delta</span><span class="p">))</span>
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</pre></div>
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</div>
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<p>which is the correlation value between input values Vi and Vj,
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separated by time delta. Note that the second value Vj in the pair is
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always the one sampled at the later time. The ave() represents an
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average over every pair of samples in the set that are separated by
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time delta. The maximum delta used is of size (<em>Nrepeat</em>-1)*<em>Nevery</em>.
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Thus the correlation between a pair of input values yields <em>Nrepeat</em>
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correlation datums:</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">Cij</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">Cij</span><span class="p">(</span><span class="n">Nevery</span><span class="p">),</span> <span class="n">Cij</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">Nevery</span><span class="p">),</span> <span class="o">...</span><span class="p">,</span> <span class="n">Cij</span><span class="p">((</span><span class="n">Nrepeat</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">Nevery</span><span class="p">)</span>
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</pre></div>
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</div>
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<p>For example, if Nevery=5, Nrepeat=6, and Nfreq=100, then values on
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timesteps 0,5,10,15,...,100 will be used to compute the final averages
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on timestep 100. Six averages will be computed: Cij(0), Cij(5),
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Cij(10), Cij(15), Cij(20), and Cij(25). Cij(10) on timestep 100 will
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be the average of 19 samples, namely Vi(0)*Vj(10), Vi(5)*Vj(15),
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Vi(10)*V j20), Vi(15)*Vj(25), ..., Vi(85)*Vj(95), Vi(90)*Vj(100).</p>
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<p><em>Nfreq</em> must be a multiple of <em>Nevery</em>; <em>Nevery</em> and <em>Nrepeat</em> must be
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non-zero. Also, if the <em>ave</em> keyword is set to <em>one</em> which is the
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default, then <em>Nfreq</em> >= (<em>Nrepeat</em>-1)*<em>Nevery</em> is required.</p>
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<hr class="docutils" />
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<p>If a value begins with “<a href="#id3"><span class="problematic" id="id4">c_</span></a>”, a compute ID must follow which has been
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previously defined in the input script. If no bracketed term is
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appended, the global scalar calculated by the compute is used. If a
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bracketed term is appended, the Ith element of the global vector
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calculated by the compute is used.</p>
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<p>Note that there is a <a class="reference internal" href="compute_reduce.html"><span class="doc">compute reduce</span></a> command
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which can sum per-atom quantities into a global scalar or vector which
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can thus be accessed by fix ave/correlate. Or it can be a compute
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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>
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or <a class="reference internal" href="fix_temp_rescale.html"><span class="doc">fix temp/rescale</span></a>. See the doc pages for
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these commands which give the IDs of these computes. Users can also
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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>
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<p>If a value begins with “<a href="#id5"><span class="problematic" id="id6">f_</span></a>”, a fix ID must follow which has been
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previously defined in the input script. If no bracketed term is
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appended, the global scalar calculated by the fix is used. If a
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bracketed term is appended, the Ith element of the global vector
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calculated by the fix is used.</p>
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<p>Note that some fixes only produce their values on certain timesteps,
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which must be compatible with <em>Nevery</em>, else an error will result.
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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>
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<p>If a value begins with “<a href="#id7"><span class="problematic" id="id8">v_</span></a>”, a variable name must follow which has
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been previously defined in the input script. Only equal-style or
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vector-style variables can be referenced; the latter requires a
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bracketed term to specify the Ith element of the vector calculated by
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the variable. See the <a class="reference internal" href="variable.html"><span class="doc">variable</span></a> command for details.
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Note that variables of style <em>equal</em> or <em>vector</em> define a formula
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which can reference individual atom properties or thermodynamic
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keywords, or they can invoke other computes, fixes, or variables when
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they are evaluated, so this is a very general means of specifying
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quantities to time correlate.</p>
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<hr class="docutils" />
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<p>Additional optional keywords also affect the operation of this fix.</p>
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<p>The <em>type</em> keyword determines which pairs of input values are
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correlated with each other. For N input values Vi, for i = 1 to N,
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let the number of pairs = Npair. Note that the second value in the
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pair Vi(t)*Vj(t+delta) is always the one sampled at the later time.</p>
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<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>
|
|
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Time-correlated data for fix ID</span>
|
|
<span class="c1"># TimeStep Number-of-time-windows</span>
|
|
<span class="c1"># Index TimeDelta Ncount valueI*valueJ valueI*valueJ ...</span>
|
|
</pre></div>
|
|
</div>
|
|
<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,
|
|
namely the <em>Nrepeat</em> values:</p>
|
|
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">Sij</span> <span class="o">=</span> <span class="n">Cij</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">Cij</span><span class="p">(</span><span class="n">Nevery</span><span class="p">),</span> <span class="n">Cij</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">Nevery</span><span class="p">),</span> <span class="o">...</span><span class="p">,</span> <span class="n">Cij</span><span class="p">(</span><span class="o">*</span><span class="n">Nrepeat</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">Nevery</span><span class="p">)</span>
|
|
</pre></div>
|
|
</div>
|
|
<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>
|
|
</div>
|
|
<hr class="docutils" />
|
|
<div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
|
|
<h2>Restart, fix_modify, output, run start/stop, minimize info</h2>
|
|
<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,
|
|
C13, ..., C1N, C23, ..., C2N, C34, ..., CN-1N.</li>
|
|
<li>For <em>type</em> = <em>lower</em>, the Npair = N*(N-1)/2 columns are ordered: C21,
|
|
C31, C32, C41, C42, C43, ..., CN1, CN2, ..., CNN-1.</li>
|
|
<li>For <em>type</em> = <em>auto/upper</em>, the Npair = N*(N+1)/2 columns are ordered:
|
|
C11, C12, C13, ..., C1N, C22, C23, ..., C2N, C33, C34, ..., CN-1N,
|
|
CNN.</li>
|
|
<li>For <em>type</em> = <em>auto/lower</em>, the Npair = N*(N+1)/2 columns are ordered:
|
|
C11, C21, C22, C31, C32, C33, C41, ..., C44, CN1, CN2, ..., CNN-1,
|
|
CNN.</li>
|
|
<li>For <em>type</em> = <em>full</em>, the Npair = N^2 columns are ordered: C11, C12,
|
|
..., C1N, C21, C22, ..., C2N, C31, ..., C3N, ..., CN1, ..., CNN-1,
|
|
CNN.</li>
|
|
</ul>
|
|
<p>The array values calculated by this fix are treated as intensive. If
|
|
you need to divide them by the number of atoms, you must do this in a
|
|
later processing step, e.g. when using them in a
|
|
<a class="reference internal" href="variable.html"><span class="doc">variable</span></a>.</p>
|
|
<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>
|
|
</div>
|
|
<div class="section" id="restrictions">
|
|
<h2>Restrictions</h2>
|
|
<blockquote>
|
|
<div>none</div></blockquote>
|
|
</div>
|
|
<div class="section" id="related-commands">
|
|
<h2>Related commands</h2>
|
|
<p><a class="reference internal" href="fix_ave_correlate_long.html"><span class="doc">fix ave/correlate/long</span></a>,
|
|
<a class="reference internal" href="compute.html"><span class="doc">compute</span></a>, <a class="reference internal" href="fix_ave_time.html"><span class="doc">fix ave/time</span></a>, <a class="reference internal" href="fix_ave_atom.html"><span class="doc">fix ave/atom</span></a>, <a class="reference internal" href="fix_ave_chunk.html"><span class="doc">fix ave/chunk</span></a>,
|
|
<a class="reference internal" href="fix_ave_histo.html"><span class="doc">fix ave/histo</span></a>, <a class="reference internal" href="variable.html"><span class="doc">variable</span></a></p>
|
|
<p><strong>Default:</strong> none</p>
|
|
<p>The option defaults are ave = one, type = auto, start = 0, no file
|
|
output, title 1,2,3 = strings as described above, and prefactor = 1.0.</p>
|
|
</div>
|
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</div>
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