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<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.roots.root_finding_examples.lambda"></a><a class="link" href="lambda.html" title="Using C++11 Lambda's">Using
C++11 Lambda's</a>
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<p>
Since all the root finding functions accept a function-object, they can
be made to work (often in a lot less code) with C++11 lambda's. Here's
the much reduced code for our "toy" cube root function:
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
<span class="identifier">T</span> <span class="identifier">cbrt_2deriv_lambda</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">)</span>
<span class="special">{</span>
<span class="comment">// return cube root of x using 1st and 2nd derivatives and Halley.</span>
<span class="comment">//using namespace std; // Help ADL of std functions.</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">exponent</span><span class="special">;</span>
<span class="identifier">frexp</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="special">&</span><span class="identifier">exponent</span><span class="special">);</span> <span class="comment">// Get exponent of z (ignore mantissa).</span>
<span class="identifier">T</span> <span class="identifier">guess</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">exponent</span> <span class="special">/</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// Rough guess is to divide the exponent by three.</span>
<span class="identifier">T</span> <span class="identifier">min</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">0.5</span><span class="special">,</span> <span class="identifier">exponent</span> <span class="special">/</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// Minimum possible value is half our guess.</span>
<span class="identifier">T</span> <span class="identifier">max</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">2.</span><span class="special">,</span> <span class="identifier">exponent</span> <span class="special">/</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// Maximum possible value is twice our guess.</span>
<span class="keyword">const</span> <span class="keyword">int</span> <span class="identifier">digits</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">digits</span><span class="special">;</span> <span class="comment">// Maximum possible binary digits accuracy for type T.</span>
<span class="comment">// digits used to control how accurate to try to make the result.</span>
<span class="keyword">int</span> <span class="identifier">get_digits</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="keyword">int</span><span class="special">>(</span><span class="identifier">digits</span> <span class="special">*</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Accuracy triples with each step, so stop when just</span>
<span class="comment">// over one third of the digits are correct.</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span> <span class="identifier">maxit</span> <span class="special">=</span> <span class="number">20</span><span class="special">;</span>
<span class="identifier">T</span> <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">halley_iterate</span><span class="special">(</span>
<span class="comment">// lambda function:</span>
<span class="special">[</span><span class="identifier">x</span><span class="special">](</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">g</span><span class="special">){</span> <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">make_tuple</span><span class="special">(</span><span class="identifier">g</span> <span class="special">*</span> <span class="identifier">g</span> <span class="special">*</span> <span class="identifier">g</span> <span class="special">-</span> <span class="identifier">x</span><span class="special">,</span> <span class="number">3</span> <span class="special">*</span> <span class="identifier">g</span> <span class="special">*</span> <span class="identifier">g</span><span class="special">,</span> <span class="number">6</span> <span class="special">*</span> <span class="identifier">g</span><span class="special">);</span> <span class="special">},</span>
<span class="identifier">guess</span><span class="special">,</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">max</span><span class="special">,</span> <span class="identifier">get_digits</span><span class="special">,</span> <span class="identifier">maxit</span><span class="special">);</span>
<span class="keyword">return</span> <span class="identifier">result</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
Full code of this example is at <a href="../../../../../example/root_finding_example.cpp" target="_top">root_finding_example.cpp</a>,
</p>
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Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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