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<h1 id="class-CAS::AutoDiff::DualNumber" class="class">
class CAS::AutoDiff::DualNumber
</h1>
<section class="description">
</section>
<section id="5Buntitled-5D" class="documentation-section">
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<h3>Attributes</h3>
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<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 32</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">initialize</span>(<span class="ruby-identifier">x</span>, <span class="ruby-identifier">y</span>)
<span class="ruby-ivar">@x</span>, <span class="ruby-ivar">@y</span> = <span class="ruby-identifier">x</span>, <span class="ruby-identifier">y</span>
<span class="ruby-keyword">end</span></pre>
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<h3>Public Instance Methods</h3>
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<span class="method-name">*</span><span
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<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 44</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">*</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">DualNumber</span>.<span class="ruby-identifier">new</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">*</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">x</span>, <span class="ruby-ivar">@y</span> <span class="ruby-operator">*</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">x</span> <span class="ruby-operator">+</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">*</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">y</span>
<span class="ruby-keyword">end</span></pre>
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<div class="method-heading">
<span class="method-name">**</span><span
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<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 56</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">**</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-identifier">t</span> = (<span class="ruby-identifier">v</span>.<span class="ruby-identifier">y</span> <span class="ruby-operator">==</span> <span class="ruby-value">0</span> <span class="ruby-operator">?</span> <span class="ruby-value">0</span> <span class="ruby-operator">:</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">*</span> <span class="ruby-identifier">log</span>(<span class="ruby-ivar">@x</span>) <span class="ruby-operator">*</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">y</span>)
<span class="ruby-constant">DualNumber</span>.<span class="ruby-identifier">new</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">**</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">x</span>, (<span class="ruby-ivar">@x</span> <span class="ruby-operator">**</span> (<span class="ruby-identifier">v</span>.<span class="ruby-identifier">x</span> <span class="ruby-operator">-</span> <span class="ruby-value">1</span>)) <span class="ruby-operator">*</span> (<span class="ruby-identifier">v</span>.<span class="ruby-identifier">x</span> <span class="ruby-operator">*</span> <span class="ruby-ivar">@y</span> <span class="ruby-operator">+</span> <span class="ruby-identifier">t</span>)
<span class="ruby-keyword">end</span></pre>
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<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 36</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">+</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">DualNumber</span>.<span class="ruby-identifier">new</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">+</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">x</span>, <span class="ruby-ivar">@y</span> <span class="ruby-operator">+</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">y</span>
<span class="ruby-keyword">end</span></pre>
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<div id="method-i-2D" class="method-detail ">
<div class="method-heading">
<span class="method-name">-</span><span
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<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 40</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">-</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">DualNumber</span>.<span class="ruby-identifier">new</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">-</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">x</span>, <span class="ruby-ivar">@y</span> <span class="ruby-operator">-</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">y</span>
<span class="ruby-keyword">end</span></pre>
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<span class="method-name">-@</span><span
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<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 52</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">-@</span>
<span class="ruby-constant">DualNumber</span>.<span class="ruby-identifier">new</span>(<span class="ruby-operator">-</span><span class="ruby-ivar">@x</span>, <span class="ruby-operator">-</span><span class="ruby-ivar">@y</span>)
<span class="ruby-keyword">end</span></pre>
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<div id="method-i-2F" class="method-detail ">
<div class="method-heading">
<span class="method-name">/</span><span
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<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 48</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">/</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">DualNumber</span>.<span class="ruby-identifier">new</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">/</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">x</span>, (<span class="ruby-ivar">@y</span> <span class="ruby-operator">*</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">x</span> <span class="ruby-operator">-</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">*</span> <span class="ruby-identifier">v</span>.<span class="ruby-identifier">y</span>) <span class="ruby-operator">/</span> (<span class="ruby-identifier">v</span>.<span class="ruby-identifier">x</span> <span class="ruby-operator">**</span> <span class="ruby-value">2</span>)
<span class="ruby-keyword">end</span></pre>
</div>
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<div id="method-i-abs" class="method-detail ">
<div class="method-heading">
<span class="method-name">abs</span><span
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<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 61</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">abs</span>
<span class="ruby-keyword">return</span> <span class="ruby-constant">DualNumber</span>.<span class="ruby-identifier">new</span>(<span class="ruby-value">0</span>, <span class="ruby-value">0</span>) <span class="ruby-keyword">if</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">==</span> <span class="ruby-value">0</span>
<span class="ruby-constant">DualNumber</span>.<span class="ruby-identifier">new</span> <span class="ruby-ivar">@x</span>.<span class="ruby-identifier">abs</span>, <span class="ruby-ivar">@y</span> <span class="ruby-operator">*</span> (<span class="ruby-ivar">@x</span> <span class="ruby-operator"><=></span> <span class="ruby-value">0</span>)
<span class="ruby-keyword">end</span></pre>
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<div id="method-i-diff" class="method-detail ">
<div class="method-heading">
<span class="method-name">diff</span><span
class="method-args">()</span>
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<div class="method-description">
<div class="method-source-code" id="diff-source">
<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 69</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">diff</span>; <span class="ruby-ivar">@y</span>; <span class="ruby-keyword">end</span></pre>
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<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 67</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">inspect</span>; <span class="ruby-node">"<#{@x},#{@y}>"</span>; <span class="ruby-keyword">end</span></pre>
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<div class="method-source-code" id="real-source">
<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 68</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">real</span>; <span class="ruby-ivar">@x</span>; <span class="ruby-keyword">end</span></pre>
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<div id="method-i-to_s" class="method-detail ">
<div class="method-heading">
<span class="method-name">to_s</span><span
class="method-args">()</span>
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<pre><span class="ruby-comment"># File lib/Mr.CAS/auto-diff.rb, line 66</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">to_s</span>; <span class="ruby-keyword">self</span>.<span class="ruby-identifier">inspect</span>; <span class="ruby-keyword">end</span></pre>
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