|
|
<!DOCTYPE html>
<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><meta name="description" content="Function describing exponential decline from a defined starting value, with
a concentration dependent rate constant."><title>Indeterminate order rate equation kinetics — IORE.solution • mkin</title><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.2.2/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.2.2/bootstrap.bundle.min.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- bootstrap-toc --><script src="https://cdn.jsdelivr.net/gh/afeld/bootstrap-toc@v1.0.1/dist/bootstrap-toc.min.js" integrity="sha256-4veVQbu7//Lk5TSmc7YV48MxtMy98e26cf5MrgZYnwo=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- search --><script src="https://cdnjs.cloudflare.com/ajax/libs/fuse.js/6.4.6/fuse.js" integrity="sha512-zv6Ywkjyktsohkbp9bb45V6tEMoWhzFzXis+LrMehmJZZSys19Yxf1dopHx7WzIKxr5tK2dVcYmaCk2uqdjF4A==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/autocomplete.js/0.38.0/autocomplete.jquery.min.js" integrity="sha512-GU9ayf+66Xx2TmpxqJpliWbT5PiGYxpaG8rfnBEk1LL8l1KGkRShhngwdXK1UgqhAzWpZHSiYPc09/NwDQIGyg==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mark.js/8.11.1/mark.min.js" integrity="sha512-5CYOlHXGh6QpOFA/TeTylKLWfB3ftPsde7AnmhuitiTX4K5SqCLBeKro6sPS8ilsz1Q4NRx3v8Ko2IBiszzdww==" crossorigin="anonymous"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Indeterminate order rate equation kinetics — IORE.solution"><meta property="og:description" content="Function describing exponential decline from a defined starting value, with
a concentration dependent rate constant."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]--></head><body>
<a href="#main" class="visually-hidden-focusable">Skip to contents</a>
<nav class="navbar fixed-top navbar-default navbar-expand-lg bg-light"><div class="container">
<a class="navbar-brand me-2" href="../index.html">mkin</a>
<small class="nav-text text-default me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="Released version">1.2.6</small>
<button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
<span class="navbar-toggler-icon"></span>
</button>
<div id="navbar" class="collapse navbar-collapse ms-3">
<ul class="navbar-nav me-auto"><li class="active nav-item">
<a class="nav-link" href="../reference/index.html">Reference</a>
</li>
<li class="nav-item dropdown">
<a href="#" class="nav-link dropdown-toggle" data-bs-toggle="dropdown" role="button" aria-expanded="false" aria-haspopup="true" id="dropdown-articles">Articles</a>
<div class="dropdown-menu" aria-labelledby="dropdown-articles">
<a class="dropdown-item" href="../articles/mkin.html">Introduction to mkin</a>
<div class="dropdown-divider"></div>
<h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6>
<a class="dropdown-item" href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a>
<a class="dropdown-item" href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
<a class="dropdown-item" href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
<div class="dropdown-divider"></div>
<h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6>
<a class="dropdown-item" href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
<a class="dropdown-item" href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a>
<a class="dropdown-item" href="../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a>
<a class="dropdown-item" href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a>
<a class="dropdown-item" href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a>
<a class="dropdown-item" href="../articles/web_only/multistart.html">Short demo of the multistart method</a>
<div class="dropdown-divider"></div>
<h6 class="dropdown-header" data-toc-skip>Performance</h6>
<a class="dropdown-item" href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
<a class="dropdown-item" href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a>
<a class="dropdown-item" href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a>
<div class="dropdown-divider"></div>
<h6 class="dropdown-header" data-toc-skip>Miscellaneous</h6>
<a class="dropdown-item" href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
<a class="dropdown-item" href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
</div>
</li>
<li class="nav-item">
<a class="nav-link" href="../news/index.html">News</a>
</li>
</ul><form class="form-inline my-2 my-lg-0" role="search">
<input type="search" class="form-control me-sm-2" aria-label="Toggle navigation" name="search-input" data-search-index="../search.json" id="search-input" placeholder="Search for" autocomplete="off"></form>
<ul class="navbar-nav"><li class="nav-item">
<a class="external-link nav-link" href="https://github.com/jranke/mkin/" aria-label="github">
<span class="fab fa fab fa-github fa-lg"></span>
</a>
</li>
</ul></div>
</div>
</nav><div class="container template-reference-topic">
<div class="row">
<main id="main" class="col-md-9"><div class="page-header">
<img src="" class="logo" alt=""><h1>Indeterminate order rate equation kinetics</h1>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/parent_solutions.R" class="external-link"><code>R/parent_solutions.R</code></a></small>
<div class="d-none name"><code>IORE.solution.Rd</code></div>
</div>
<div class="ref-description section level2">
<p>Function describing exponential decline from a defined starting value, with
a concentration dependent rate constant.</p>
</div>
<div class="section level2">
<h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">IORE.solution</span><span class="op">(</span><span class="va">t</span>, <span class="va">parent_0</span>, <span class="va">k__iore</span>, <span class="va">N</span><span class="op">)</span></span></code></pre></div>
</div>
<div class="section level2">
<h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
<dl><dt>t</dt>
<dd><p>Time.</p></dd>
<dt>parent_0</dt>
<dd><p>Starting value for the response variable at time zero.</p></dd>
<dt>k__iore</dt>
<dd><p>Rate constant. Note that this depends on the concentration
units used.</p></dd>
<dt>N</dt>
<dd><p>Exponent describing the nonlinearity of the rate equation</p></dd>
</dl></div>
<div class="section level2">
<h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
<p>The value of the response variable at time <code>t</code>.</p>
</div>
<div class="section level2">
<h2 id="note">Note<a class="anchor" aria-label="anchor" href="#note"></a></h2>
<p>The solution of the IORE kinetic model reduces to the
<code><a href="SFO.solution.html">SFO.solution</a></code> if N = 1. The parameters of the IORE model can
be transformed to equivalent parameters of the FOMC mode - see the NAFTA
guidance for details.</p>
</div>
<div class="section level2">
<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2>
<p>NAFTA Technical Working Group on Pesticides (not dated) Guidance
for Evaluating and Calculating Degradation Kinetics in Environmental Media</p>
</div>
<div class="section level2">
<h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
<div class="dont-index"><p>Other parent solutions:
<code><a href="DFOP.solution.html">DFOP.solution</a>()</code>,
<code><a href="FOMC.solution.html">FOMC.solution</a>()</code>,
<code><a href="HS.solution.html">HS.solution</a>()</code>,
<code><a href="SFO.solution.html">SFO.solution</a>()</code>,
<code><a href="SFORB.solution.html">SFORB.solution</a>()</code>,
<code><a href="logistic.solution.html">logistic.solution</a>()</code></p></div>
</div>
<div class="section level2">
<h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span></span></span>
<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu">IORE.solution</span><span class="op">(</span><span class="va">x</span>, <span class="fl">100</span>, <span class="fl">0.2</span>, <span class="fl">1.3</span><span class="op">)</span>, <span class="fl">0</span>, <span class="fl">2</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">100</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-plt img"><img src="IORE.solution-1.png" alt="" width="700" height="433"></span>
<span class="r-in"><span> <span class="co"># \dontrun{</span></span></span>
<span class="r-in"><span> <span class="va">fit.fomc</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="va">FOCUS_2006_C</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
<span class="r-in"><span> <span class="va">fit.iore</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"IORE"</span>, <span class="va">FOCUS_2006_C</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
<span class="r-in"><span> <span class="va">fit.iore.deS</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"IORE"</span>, <span class="va">FOCUS_2006_C</span>, solution_type <span class="op">=</span> <span class="st">"deSolve"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Error in is.loaded(initfunc, PACKAGE = dllname, type = "") : </span>
<span class="r-out co"><span class="r-pr">#></span> invalid 'PACKAGE' argument</span>
<span class="r-in"><span></span></span>
<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span><span class="va">fit.fomc</span><span class="op">$</span><span class="va">par</span>, <span class="va">fit.iore</span><span class="op">$</span><span class="va">par</span>, <span class="va">fit.iore.deS</span><span class="op">$</span><span class="va">par</span>,</span></span>
<span class="r-in"><span> row.names <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"model par"</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> fit.fomc.par fit.iore.par fit.iore.deS.par</span>
<span class="r-out co"><span class="r-pr">#></span> model par 1 85.87489063 85.874890 85.874890</span>
<span class="r-out co"><span class="r-pr">#></span> model par 2 0.05192238 -4.826631 -4.826631</span>
<span class="r-out co"><span class="r-pr">#></span> model par 3 0.65096665 1.949403 1.949403</span>
<span class="r-out co"><span class="r-pr">#></span> model par 4 1.85744396 1.857444 1.857444</span>
<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span>fomc <span class="op">=</span> <span class="fu"><a href="endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fit.fomc</span><span class="op">)</span><span class="op">$</span><span class="va">distimes</span>, iore <span class="op">=</span> <span class="fu"><a href="endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fit.iore</span><span class="op">)</span><span class="op">$</span><span class="va">distimes</span>,</span></span>
<span class="r-in"><span> iore.deS <span class="op">=</span> <span class="fu"><a href="endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fit.iore</span><span class="op">)</span><span class="op">$</span><span class="va">distimes</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> DT50 DT90 DT50back</span>
<span class="r-out co"><span class="r-pr">#></span> fomc 1.785233 15.1479 4.559973</span>
<span class="r-out co"><span class="r-pr">#></span> iore 1.785233 15.1479 4.559973</span>
<span class="r-out co"><span class="r-pr">#></span> iore.deS 1.785233 15.1479 4.559973</span>
<span class="r-in"><span> <span class="co"># }</span></span></span>
<span class="r-in"><span></span></span>
</code></pre></div>
</div>
</main><aside class="col-md-3"><nav id="toc"><h2>On this page</h2>
</nav></aside></div>
<footer><div class="pkgdown-footer-left">
<p></p><p>Developed by Johannes Ranke.</p>
</div>
<div class="pkgdown-footer-right">
<p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
</div>
</footer></div>
</body></html>
|
