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<section id="pyocn" class="level1">
<h1>PyOCN</h1>
<p>This is a package to generate optimal channel networks (OCNs), based on the algorithm described in Carraro et al. (2020). <em>Generation and application of river network analogues for use in ecology and evolution. Ecology and Evolution.</em> doi:10.1002/ece3.6479 and mirrors some of the functionality of the OCNet R package (https://lucarraro.github.io/OCNet/).</p>
<p>This is a work in progress. I plan to release this as a package on PyPI in the near future. For now, you can clone the repository and build the package from source.</p>
<p>To compile libocn with <code>gcc</code> on MacOS or Linux, move the root directory into your project’s working directory andrun the following commands from the root directory:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode bash code-with-copy"><code class="sourceCode bash"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="bu">cd</span> PyOCN/c_src</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">bash</span> build.sh</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>or alternatively:</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode bash code-with-copy"><code class="sourceCode bash"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="bu">cd</span> PyOCN/c_src</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="fu">gcc</span> <span class="at">-fPIC</span> <span class="at">-O3</span> <span class="at">-flto</span> <span class="at">-c</span> ocn.c flowgrid.c status.c rng.c</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="fu">gcc</span> <span class="at">-shared</span> <span class="at">-O3</span> <span class="at">-flto</span> <span class="at">-o</span> libocn.so ocn.o flowgrid.o status.o rng.o</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="fu">mv</span> libocn.so ../libocn.so</span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a><span class="fu">rm</span> <span class="at">-f</span> ocn.o flowgrid.o status.o rng.o</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>If you have any questions or comments, please open an issue or contact me directly at https://www.afox.land</p>
</section>
<section id="ocn-algorithm" class="level1">
<h1>OCN Algorithm</h1>
<p>An initial stream network is generated as a directed acyclic graph (DAG) that is a spanning tree over a 2d grid of cells. Each cell in the grid (except the root) has a single outgoing edge that connects to one of its 8 neighboring cells. The OCN algorithm then iteratively modifies the DAG by randomly selecting a cell and changing its outflow to point to a different neighbor, ensuring that the spanning tree structure is maintained (<em>i.e. no cycles are introduced and each cell has a single outflow, except for the root cell</em>). The total energy at cell <span class="math inline">\(k\)</span> after iteration <span class="math inline">\(n\)</span> is given by:</p>
<p><span class="math display">\[
E_k[n] = \sum_{i} A_i^\gamma[n]
\]</span></p>
<p>Where <span class="math inline">\(A_i\)</span> is the cumulative drained area at cell <span class="math inline">\(i\)</span>, and <span class="math inline">\(i\in\mathrm{drained}(k)\)</span> is a cell drained by <span class="math inline">\(k\)</span>, including itself, and <span class="math inline">\(\gamma\)</span> controls how the energy scales with area. This change is accepted or rejected based on an annealing method, which is related to the Metropolis-Hastings algorithm. The probability of accepting a proposed change to the network is given by:</p>
<p><span class="math display">\[
P(\mathrm{accept}) = \min\left(1, \exp\left(-\frac{E_\mathrm{root}[n] - E_\mathrm{root}[n-1]}{T[n]}\right)\right)
\]</span></p>
<p>Where <span class="math inline">\(T[n]\)</span> is the “temperature” of the network at iteration <span class="math inline">\(n\)</span>. Initially, the temperature is set to a high value (<span class="math inline">\(\sim E[0]\)</span>) to encourage exploration of the solution space. The temperature is then set to exponentially decay over time, “annealing” the network as it settles into a low-energy configuration. Note that a proposed change is always accepted if it results in a lower energy state (<span class="math inline">\(E[n] < E[n-1]\)</span>).</p>
<p>Lower values of gamma allow very dendritic networks with lots fo branching. The following animation shows the process of optimizing an OCN with <span class="math inline">\(\gamma=0.7\)</span> on a 256x256 grid for 4M iterations, which took about 2 minutes to run on a Macbook pro.</p>
<div data-align="center">
<p><img src="generation.gif" alt="Optimizing an OCN"></p>
</div>
</section>
<section id="libocn" class="level1">
<h1>libocn</h1>
<p>The backend of PyOCN is the libocn C library. libocn implements the core algorithms for generating and manipulating OCNs. Unlike the OCNet R package which uses an adjacency matrix implementation representation of the flow grid (based on the SPArse Matrix library), the libocn C library directly represents the network as a DAG. Each grid cell in the network has an associated outflow direction (given as an integer, 0-7, representing the 8 possible directions to neighboring cells) and a list of the directions of its neighbors (given as an 8-bit integer, where each bit indicates whether there is an edge connecting the cell to one of its 8 neighbors). libocn also implements functions to traverse and manipulate the network structure according to the simulated annealing algorithm described in the orginal paper.</p>
</section>
<section id="pyocn-1" class="level1">
<h1>PyOCN</h1>
<p>The PyOCN frontend is a Python package that provides a high-level interface to the libocn C library. PyOCN uses the NetworkX library to expose the network graph and provides additional functions to manipulate and analyze the graph, as well as export the graph to various formats, including GeoTIFF. The main class in PyOCN is the <code>OCN</code> class, which includes methods for constructing an initial configuration and running the optimization algorithm.</p>
</section>
<section id="citing-pyocn" class="level1">
<h1>Citing PyOCN</h1>
<p>If you use PyOCN in your research, please cite this package and the original paper by Carraro et al.</p>
</section>
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const bottom = lastEl.offsetTop + lastEl.offsetHeight;
height = bottom - top;
}
if (top !== null && height !== null && parent !== null) {
// cook up a div (if necessary) and position it
let div = window.document.getElementById("code-annotation-line-highlight");
if (div === null) {
div = window.document.createElement("div");
div.setAttribute("id", "code-annotation-line-highlight");
div.style.position = 'absolute';
parent.appendChild(div);
}
div.style.top = top - 2 + "px";
div.style.height = height + 4 + "px";
div.style.left = 0;
let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter");
if (gutterDiv === null) {
gutterDiv = window.document.createElement("div");
gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter");
gutterDiv.style.position = 'absolute';
const codeCell = window.document.getElementById(targetCell);
const gutter = codeCell.querySelector('.code-annotation-gutter');
gutter.appendChild(gutterDiv);
}
gutterDiv.style.top = top - 2 + "px";
gutterDiv.style.height = height + 4 + "px";
}
selectedAnnoteEl = annoteEl;
}
};
const unselectCodeLines = () => {
const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"];
elementsIds.forEach((elId) => {
const div = window.document.getElementById(elId);
if (div) {
div.remove();
}
});
selectedAnnoteEl = undefined;
};
// Handle positioning of the toggle
window.addEventListener(
"resize",
throttle(() => {
elRect = undefined;
if (selectedAnnoteEl) {
selectCodeLines(selectedAnnoteEl);
}
}, 10)
);
function throttle(fn, ms) {
let throttle = false;
let timer;
return (...args) => {
if(!throttle) { // first call gets through
fn.apply(this, args);
throttle = true;
} else { // all the others get throttled
if(timer) clearTimeout(timer); // cancel #2
timer = setTimeout(() => {
fn.apply(this, args);
timer = throttle = false;
}, ms);
}
};
}
// Attach click handler to the DT
const annoteDls = window.document.querySelectorAll('dt[data-target-cell]');
for (const annoteDlNode of annoteDls) {
annoteDlNode.addEventListener('click', (event) => {
const clickedEl = event.target;
if (clickedEl !== selectedAnnoteEl) {
unselectCodeLines();
const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active');
if (activeEl) {
activeEl.classList.remove('code-annotation-active');
}
selectCodeLines(clickedEl);
clickedEl.classList.add('code-annotation-active');
} else {
// Unselect the line
unselectCodeLines();
clickedEl.classList.remove('code-annotation-active');
}
});
}
const findCites = (el) => {
const parentEl = el.parentElement;
if (parentEl) {
const cites = parentEl.dataset.cites;
if (cites) {
return {
el,
cites: cites.split(' ')
};
} else {
return findCites(el.parentElement)
}
} else {
return undefined;
}
};
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
for (var i=0; i<bibliorefs.length; i++) {
const ref = bibliorefs[i];
const citeInfo = findCites(ref);
if (citeInfo) {
tippyHover(citeInfo.el, function() {
var popup = window.document.createElement('div');
citeInfo.cites.forEach(function(cite) {
var citeDiv = window.document.createElement('div');
citeDiv.classList.add('hanging-indent');
citeDiv.classList.add('csl-entry');
var biblioDiv = window.document.getElementById('ref-' + cite);
if (biblioDiv) {
citeDiv.innerHTML = biblioDiv.innerHTML;
}
popup.appendChild(citeDiv);
});
return popup.innerHTML;
});
}
}
});
</script>
</div> <!-- /content -->
</body></html>