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<title>User Guide — DCProgs 0.9 documentation</title>
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<div class="header" role="banner"><h1 class="heading"><a href="index.html">
<span>DCProgs 0.9 documentation</span></a></h1>
<h2 class="heading"><span>User Guide</span></h2>
</div>
<div class="topnav" role="navigation" aria-label="top navigation">
<p>
«  <a href="index.html">Welcome to DCProgs’s documentation!</a>
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<a class="uplink" href="index.html">Contents</a>
  ::  
<a href="manual/qmatrix.html">The <span class="math">\(Q\)</span>-matrix</a>  »
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<div class="content">
<div class="section" id="user-guide">
<h1>User Guide<a class="headerlink" href="#user-guide" title="Permalink to this headline">¶</a></h1>
<p>The likelihood <span class="math">\(L\)</span> of a sequence of observed open and shut events <span class="math">\(\{t_{oi}, t_{si}\}\)</span>
can be computed as a series over the missed-events likelihoods for open events,
<span class="math">\({}^e\mathcal{G}_{AF}(t_{oi})\)</span> and the missed-events likelihoods for shut events,
<span class="math">\({}^e\mathcal{G}_{FA}(t_{oi})\)</span> <a class="reference internal" href="index.html#colquhoun-1996" id="id1">[CHS96]</a>:</p>
<div class="math" id="log10likelihood-equation">
\[L(Q, \{t_{oi}, t_{si}\})
= \phi_A
\left[\prod_i^{n-1}{}^e\mathcal{G}_{AF}(t_{oi}){}^e\mathcal{G}_{AF}(t_{si})\right]
{}^e\mathcal{G}_{AF}(t_{on}) \phi_e\]</div>
<p>where <span class="math">\(Q\)</span> is the transition rate matrix, and <span class="math">\(\phi_A\)</span> and <span class="math">\(\phi_e\)</span> are the initial
and final occupancies. All these objects – as well as their components – can be accessed both from
python and from c++. In the following, we try and show how they can be created and manipulated from
either language.</p>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="manual/qmatrix.html">The <span class="math">\(Q\)</span>-matrix</a></li>
<li class="toctree-l1"><a class="reference internal" href="manual/likelihood_of_Q.html">Likelihood <span class="math">\(L(Q)\)</span></a></li>
<li class="toctree-l1"><a class="reference internal" href="manual/missedeventsG.html">Missed-Events Likelihood <span class="math">\({}^eG(t)\)</span></a><ul>
<li class="toctree-l2"><a class="reference internal" href="manual/missedeventsG.html#initialization-from-a-matrix">Initialization from a <span class="math">\(Q\)</span>-matrix</a></li>
<li class="toctree-l2"><a class="reference internal" href="manual/missedeventsG.html#initialization-from-the-roots-and-determinant-equations">Initialization from the roots and determinant equations</a></li>
<li class="toctree-l2"><a class="reference internal" href="manual/missedeventsG.html#initialization-from-the-matrix-and-a-root-finding-function">Initialization from the <span class="math">\(Q\)</span>-matrix and a root finding function</a></li>
<li class="toctree-l2"><a class="reference internal" href="manual/missedeventsG.html#computing-and">Computing <span class="math">\({}^eG_{AF}(t)\)</span> and <span class="math">\({}^eG_{FA}(t)\)</span></a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="manual/idealG.html">Ideal Likelihood <span class="math">\(\mathcal{G}(t)\)</span></a></li>
<li class="toctree-l1"><a class="reference internal" href="manual/occupancies.html">Occupancies</a></li>
<li class="toctree-l1"><a class="reference internal" href="manual/exact_survivor.html">Exact Survivor Function <span class="math">\(R_A(t)\)</span></a></li>
<li class="toctree-l1"><a class="reference internal" href="manual/approx_survivor.html">Approximate Survivor Function <span class="math">\(R_A(t)\)</span></a></li>
<li class="toctree-l1"><a class="reference internal" href="manual/determinant_equation.html">Determinant Equation <span class="math">\(W(s) = sI - H(s)\)</span></a></li>
<li class="toctree-l1"><a class="reference internal" href="manual/roots.html">Searching for Roots</a></li>
</ul>
</div>
<div class="section" id="how-to-read-this-manual">
<h2>How to read this manual<a class="headerlink" href="#how-to-read-this-manual" title="Permalink to this headline">¶</a></h2>
<p>Each topic below is illustrated by an example in c++, and another in python. These examples can be
found in the source code of the package within the directory <code class="docutils literal"><span class="pre">documentation/code</span></code>. In any case,
one can copy paste.</p>
<p>The user guide should read using the left eye only, and keeping the right eye on the api, or
vice-versa. Most of the c++ functions and python bindings offer more functionality or parameters
than mentioned in the manual.</p>
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  ::  
<a href="manual/qmatrix.html">The <span class="math">\(Q\)</span>-matrix</a>  »
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