383 lines
18 KiB
HTML
383 lines
18 KiB
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<header id="title-block-header" class="quarto-title-block default">
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<div class="quarto-title">
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<h1 class="title">Sharktooth Functions in 1-dimension</h1>
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</header>
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<div class="cell" data-execution_count="32">
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<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> numpy <span class="im">as</span> np </span>
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<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> matplotlib.pyplot <span class="im">as</span> plt</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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</div>
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<div class="cell" data-execution_count="33">
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<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> max_conv_operator(samples, f_samples, <span class="bu">input</span>, L):</span>
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<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> np.<span class="bu">max</span>(f_samples <span class="op">-</span> L <span class="op">*</span> np.<span class="bu">abs</span>(<span class="bu">input</span> <span class="op">-</span> samples))</span>
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<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> sharktooth_function(function, x_start, x_stop, number_of_sharkteeth, L, plot_arg):</span>
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<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a> samples <span class="op">=</span> np.random.uniform(x_start,x_stop, number_of_sharkteeth)</span>
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<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a> f_samples <span class="op">=</span> function(samples)</span>
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<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a> x <span class="op">=</span> np.linspace(x_start, x_stop, <span class="dv">10000</span>)</span>
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<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a> approximate_y <span class="op">=</span> []</span>
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<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> i <span class="kw">in</span> <span class="bu">range</span>(<span class="bu">len</span>(x)):</span>
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<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a> approximate_y.append(max_conv_operator(samples, f_samples, x[i], L))</span>
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<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a> error <span class="op">=</span> np.<span class="bu">max</span>(np.<span class="bu">abs</span>(f(x) <span class="op">-</span> approximate_y))</span>
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<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> plot_arg <span class="op">==</span> <span class="dv">1</span>:</span>
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<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a> plt.plot(x,approximate_y)</span>
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<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a> <span class="cf">else</span>:</span>
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<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> error</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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</div>
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<div class="cell" data-execution_count="34">
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<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> f(x):</span>
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<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> x<span class="op">/</span>(x<span class="op">+</span><span class="dv">2</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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</div>
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<div class="cell" data-execution_count="35">
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<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>L <span class="op">=</span> [<span class="dv">1</span>,<span class="dv">4</span>,<span class="dv">8</span>,<span class="dv">16</span>]</span>
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<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>plt.figure(figsize<span class="op">=</span>(<span class="dv">17</span>,<span class="dv">5</span>))</span>
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<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> L <span class="kw">in</span> L:</span>
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<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a> errors <span class="op">=</span> []</span>
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<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> i <span class="kw">in</span> <span class="bu">range</span>(<span class="dv">1</span>,<span class="dv">50</span>):</span>
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<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a> errors.append(sharktooth_function(f,<span class="dv">0</span>,<span class="dv">1</span>,i,L,<span class="dv">0</span>))</span>
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<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a> <span class="im">import</span> matplotlib.pyplot <span class="im">as</span> plt</span>
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<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a> plt.plot(errors, label <span class="op">=</span>L)</span>
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<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a>plt.xlabel(<span class="st">"Number of teeth"</span>)</span>
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<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a>plt.ylabel(<span class="vs">r"$\sup_{x\in x_i} | f(x)- \mathfrak</span><span class="sc">{R}</span><span class="vs">_{\mathfrak</span><span class="sc">{r}</span><span class="vs">} ( \mathsf</span><span class="sc">{P}</span><span class="vs">)|$"</span>)</span>
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<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a>plt.legend()</span>
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<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a>plt.title(<span class="st">"Sup of deviance from f(x) as the number of teeth increase and as we get closer to L"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="cell-output cell-output-display" data-execution_count="35">
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<pre><code>Text(0.5, 1.0, 'Sup of deviance from f(x) as the number of teeth increase and as we get closer to L')</code></pre>
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</div>
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<div class="cell-output cell-output-display">
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<p><img src="sharktooth_functions_files/figure-html/cell-5-output-2.png" class="img-fluid"></p>
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</div>
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</div>
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</main>
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const targetAnnotation = annoteEl.getAttribute("data-target-annotation");
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||
|
|
const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation));
|
||
|
|
const lines = annoteSpan.getAttribute("data-code-lines").split(",");
|
||
|
|
const lineIds = lines.map((line) => {
|
||
|
|
return targetCell + "-" + line;
|
||
|
|
})
|
||
|
|
let top = null;
|
||
|
|
let height = null;
|
||
|
|
let parent = null;
|
||
|
|
if (lineIds.length > 0) {
|
||
|
|
//compute the position of the single el (top and bottom and make a div)
|
||
|
|
const el = window.document.getElementById(lineIds[0]);
|
||
|
|
top = el.offsetTop;
|
||
|
|
height = el.offsetHeight;
|
||
|
|
parent = el.parentElement.parentElement;
|
||
|
|
if (lineIds.length > 1) {
|
||
|
|
const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]);
|
||
|
|
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";
|
||
|
|
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;
|
||
|
|
};
|
||
|
|
// 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>
|