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<h3>Methods</h3>
<ul class="link-list" role="directory">
<li ><a href="#method-i-ludecomp">#ludecomp</a>
<li ><a href="#method-i-lusolve">#lusolve</a>
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<h1 id="module-LUSolve" class="module">
module LUSolve
</h1>
<section class="description">
<p>Solves a*x = b for x, using LU decomposition.</p>
</section>
<section id="5Buntitled-5D" class="documentation-section">
<section id="public-instance-5Buntitled-5D-method-details" class="method-section">
<header>
<h3>Public Instance Methods</h3>
</header>
<div id="method-i-ludecomp" class="method-detail ">
<div class="method-heading">
<span class="method-name">ludecomp</span><span
class="method-args">(a,n,zero=0,one=1)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Performs LU decomposition of the n by n matrix a.</p>
<div class="method-source-code" id="ludecomp-source">
<pre><span class="ruby-comment"># File ext/bigdecimal/lib/bigdecimal/ludcmp.rb, line 11</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier ruby-title">ludecomp</span>(<span class="ruby-identifier">a</span>,<span class="ruby-identifier">n</span>,<span class="ruby-identifier">zero</span>=<span class="ruby-value">0</span>,<span class="ruby-identifier">one</span>=<span class="ruby-value">1</span>)
<span class="ruby-identifier">prec</span> = <span class="ruby-constant">BigDecimal</span>.<span class="ruby-identifier">limit</span>(<span class="ruby-keyword">nil</span>)
<span class="ruby-identifier">ps</span> = []
<span class="ruby-identifier">scales</span> = []
<span class="ruby-keyword">for</span> <span class="ruby-identifier">i</span> <span class="ruby-keyword">in</span> <span class="ruby-value">0</span><span class="ruby-operator">...</span><span class="ruby-identifier">n</span> <span class="ruby-keyword">do</span> <span class="ruby-comment"># pick up largest(abs. val.) element in each row.</span>
<span class="ruby-identifier">ps</span> <span class="ruby-operator"><<=</span> <span class="ruby-identifier">i</span>
<span class="ruby-identifier">nrmrow</span> = <span class="ruby-identifier">zero</span>
<span class="ruby-identifier">ixn</span> = <span class="ruby-identifier">i</span><span class="ruby-operator">*</span><span class="ruby-identifier">n</span>
<span class="ruby-keyword">for</span> <span class="ruby-identifier">j</span> <span class="ruby-keyword">in</span> <span class="ruby-value">0</span><span class="ruby-operator">...</span><span class="ruby-identifier">n</span> <span class="ruby-keyword">do</span>
<span class="ruby-identifier">biggst</span> = <span class="ruby-identifier">a</span>[<span class="ruby-identifier">ixn</span><span class="ruby-operator">+</span><span class="ruby-identifier">j</span>].<span class="ruby-identifier">abs</span>
<span class="ruby-identifier">nrmrow</span> = <span class="ruby-identifier">biggst</span> <span class="ruby-keyword">if</span> <span class="ruby-identifier">biggst</span><span class="ruby-operator">></span><span class="ruby-identifier">nrmrow</span>
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">if</span> <span class="ruby-identifier">nrmrow</span><span class="ruby-operator">></span><span class="ruby-identifier">zero</span> <span class="ruby-keyword">then</span>
<span class="ruby-identifier">scales</span> <span class="ruby-operator"><<=</span> <span class="ruby-identifier">one</span>.<span class="ruby-identifier">div</span>(<span class="ruby-identifier">nrmrow</span>,<span class="ruby-identifier">prec</span>)
<span class="ruby-keyword">else</span>
<span class="ruby-identifier">raise</span> <span class="ruby-string">"Singular matrix"</span>
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">end</span>
<span class="ruby-identifier">n1</span> = <span class="ruby-identifier">n</span> <span class="ruby-operator">-</span> <span class="ruby-value">1</span>
<span class="ruby-keyword">for</span> <span class="ruby-identifier">k</span> <span class="ruby-keyword">in</span> <span class="ruby-value">0</span><span class="ruby-operator">...</span><span class="ruby-identifier">n1</span> <span class="ruby-keyword">do</span> <span class="ruby-comment"># Gaussian elimination with partial pivoting.</span>
<span class="ruby-identifier">biggst</span> = <span class="ruby-identifier">zero</span>;
<span class="ruby-keyword">for</span> <span class="ruby-identifier">i</span> <span class="ruby-keyword">in</span> <span class="ruby-identifier">k</span><span class="ruby-operator">...</span><span class="ruby-identifier">n</span> <span class="ruby-keyword">do</span>
<span class="ruby-identifier">size</span> = <span class="ruby-identifier">a</span>[<span class="ruby-identifier">ps</span>[<span class="ruby-identifier">i</span>]<span class="ruby-operator">*</span><span class="ruby-identifier">n</span><span class="ruby-operator">+</span><span class="ruby-identifier">k</span>].<span class="ruby-identifier">abs</span><span class="ruby-operator">*</span><span class="ruby-identifier">scales</span>[<span class="ruby-identifier">ps</span>[<span class="ruby-identifier">i</span>]]
<span class="ruby-keyword">if</span> <span class="ruby-identifier">size</span><span class="ruby-operator">></span><span class="ruby-identifier">biggst</span> <span class="ruby-keyword">then</span>
<span class="ruby-identifier">biggst</span> = <span class="ruby-identifier">size</span>
<span class="ruby-identifier">pividx</span> = <span class="ruby-identifier">i</span>
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">end</span>
<span class="ruby-identifier">raise</span> <span class="ruby-string">"Singular matrix"</span> <span class="ruby-keyword">if</span> <span class="ruby-identifier">biggst</span><span class="ruby-operator"><=</span><span class="ruby-identifier">zero</span>
<span class="ruby-keyword">if</span> <span class="ruby-identifier">pividx</span><span class="ruby-operator">!=</span><span class="ruby-identifier">k</span> <span class="ruby-keyword">then</span>
<span class="ruby-identifier">j</span> = <span class="ruby-identifier">ps</span>[<span class="ruby-identifier">k</span>]
<span class="ruby-identifier">ps</span>[<span class="ruby-identifier">k</span>] = <span class="ruby-identifier">ps</span>[<span class="ruby-identifier">pividx</span>]
<span class="ruby-identifier">ps</span>[<span class="ruby-identifier">pividx</span>] = <span class="ruby-identifier">j</span>
<span class="ruby-keyword">end</span>
<span class="ruby-identifier">pivot</span> = <span class="ruby-identifier">a</span>[<span class="ruby-identifier">ps</span>[<span class="ruby-identifier">k</span>]<span class="ruby-operator">*</span><span class="ruby-identifier">n</span><span class="ruby-operator">+</span><span class="ruby-identifier">k</span>]
<span class="ruby-keyword">for</span> <span class="ruby-identifier">i</span> <span class="ruby-keyword">in</span> (<span class="ruby-identifier">k</span><span class="ruby-value">+1</span>)<span class="ruby-operator">...</span><span class="ruby-identifier">n</span> <span class="ruby-keyword">do</span>
<span class="ruby-identifier">psin</span> = <span class="ruby-identifier">ps</span>[<span class="ruby-identifier">i</span>]<span class="ruby-operator">*</span><span class="ruby-identifier">n</span>
<span class="ruby-identifier">a</span>[<span class="ruby-identifier">psin</span><span class="ruby-operator">+</span><span class="ruby-identifier">k</span>] = <span class="ruby-identifier">mult</span> = <span class="ruby-identifier">a</span>[<span class="ruby-identifier">psin</span><span class="ruby-operator">+</span><span class="ruby-identifier">k</span>].<span class="ruby-identifier">div</span>(<span class="ruby-identifier">pivot</span>,<span class="ruby-identifier">prec</span>)
<span class="ruby-keyword">if</span> <span class="ruby-identifier">mult</span><span class="ruby-operator">!=</span><span class="ruby-identifier">zero</span> <span class="ruby-keyword">then</span>
<span class="ruby-identifier">pskn</span> = <span class="ruby-identifier">ps</span>[<span class="ruby-identifier">k</span>]<span class="ruby-operator">*</span><span class="ruby-identifier">n</span>
<span class="ruby-keyword">for</span> <span class="ruby-identifier">j</span> <span class="ruby-keyword">in</span> (<span class="ruby-identifier">k</span><span class="ruby-value">+1</span>)<span class="ruby-operator">...</span><span class="ruby-identifier">n</span> <span class="ruby-keyword">do</span>
<span class="ruby-identifier">a</span>[<span class="ruby-identifier">psin</span><span class="ruby-operator">+</span><span class="ruby-identifier">j</span>] <span class="ruby-operator">-=</span> <span class="ruby-identifier">mult</span>.<span class="ruby-identifier">mult</span>(<span class="ruby-identifier">a</span>[<span class="ruby-identifier">pskn</span><span class="ruby-operator">+</span><span class="ruby-identifier">j</span>],<span class="ruby-identifier">prec</span>)
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">end</span>
<span class="ruby-identifier">raise</span> <span class="ruby-string">"Singular matrix"</span> <span class="ruby-keyword">if</span> <span class="ruby-identifier">a</span>[<span class="ruby-identifier">ps</span>[<span class="ruby-identifier">n1</span>]<span class="ruby-operator">*</span><span class="ruby-identifier">n</span><span class="ruby-operator">+</span><span class="ruby-identifier">n1</span>] <span class="ruby-operator">==</span> <span class="ruby-identifier">zero</span>
<span class="ruby-identifier">ps</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-lusolve" class="method-detail ">
<div class="method-heading">
<span class="method-name">lusolve</span><span
class="method-args">(a,b,ps,zero=0.0)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Solves a*x = b for x, using LU decomposition.</p>
<p>a is a matrix, b is a constant vector, x is the solution vector.</p>
<p>ps is the pivot, a vector which indicates the permutation of rows performed during LU decomposition.</p>
<div class="method-source-code" id="lusolve-source">
<pre><span class="ruby-comment"># File ext/bigdecimal/lib/bigdecimal/ludcmp.rb, line 67</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier ruby-title">lusolve</span>(<span class="ruby-identifier">a</span>,<span class="ruby-identifier">b</span>,<span class="ruby-identifier">ps</span>,<span class="ruby-identifier">zero</span>=<span class="ruby-value">0.0</span>)
<span class="ruby-identifier">prec</span> = <span class="ruby-constant">BigDecimal</span>.<span class="ruby-identifier">limit</span>(<span class="ruby-keyword">nil</span>)
<span class="ruby-identifier">n</span> = <span class="ruby-identifier">ps</span>.<span class="ruby-identifier">size</span>
<span class="ruby-identifier">x</span> = []
<span class="ruby-keyword">for</span> <span class="ruby-identifier">i</span> <span class="ruby-keyword">in</span> <span class="ruby-value">0</span><span class="ruby-operator">...</span><span class="ruby-identifier">n</span> <span class="ruby-keyword">do</span>
<span class="ruby-identifier">dot</span> = <span class="ruby-identifier">zero</span>
<span class="ruby-identifier">psin</span> = <span class="ruby-identifier">ps</span>[<span class="ruby-identifier">i</span>]<span class="ruby-operator">*</span><span class="ruby-identifier">n</span>
<span class="ruby-keyword">for</span> <span class="ruby-identifier">j</span> <span class="ruby-keyword">in</span> <span class="ruby-value">0</span><span class="ruby-operator">...</span><span class="ruby-identifier">i</span> <span class="ruby-keyword">do</span>
<span class="ruby-identifier">dot</span> = <span class="ruby-identifier">a</span>[<span class="ruby-identifier">psin</span><span class="ruby-operator">+</span><span class="ruby-identifier">j</span>].<span class="ruby-identifier">mult</span>(<span class="ruby-identifier">x</span>[<span class="ruby-identifier">j</span>],<span class="ruby-identifier">prec</span>) <span class="ruby-operator">+</span> <span class="ruby-identifier">dot</span>
<span class="ruby-keyword">end</span>
<span class="ruby-identifier">x</span> <span class="ruby-operator"><<=</span> <span class="ruby-identifier">b</span>[<span class="ruby-identifier">ps</span>[<span class="ruby-identifier">i</span>]] <span class="ruby-operator">-</span> <span class="ruby-identifier">dot</span>
<span class="ruby-keyword">end</span>
(<span class="ruby-identifier">n</span><span class="ruby-value">-1</span>).<span class="ruby-identifier">downto</span>(<span class="ruby-value">0</span>) <span class="ruby-keyword">do</span> <span class="ruby-operator">|</span><span class="ruby-identifier">i</span><span class="ruby-operator">|</span>
<span class="ruby-identifier">dot</span> = <span class="ruby-identifier">zero</span>
<span class="ruby-identifier">psin</span> = <span class="ruby-identifier">ps</span>[<span class="ruby-identifier">i</span>]<span class="ruby-operator">*</span><span class="ruby-identifier">n</span>
<span class="ruby-keyword">for</span> <span class="ruby-identifier">j</span> <span class="ruby-keyword">in</span> (<span class="ruby-identifier">i</span><span class="ruby-value">+1</span>)<span class="ruby-operator">...</span><span class="ruby-identifier">n</span> <span class="ruby-keyword">do</span>
<span class="ruby-identifier">dot</span> = <span class="ruby-identifier">a</span>[<span class="ruby-identifier">psin</span><span class="ruby-operator">+</span><span class="ruby-identifier">j</span>].<span class="ruby-identifier">mult</span>(<span class="ruby-identifier">x</span>[<span class="ruby-identifier">j</span>],<span class="ruby-identifier">prec</span>) <span class="ruby-operator">+</span> <span class="ruby-identifier">dot</span>
<span class="ruby-keyword">end</span>
<span class="ruby-identifier">x</span>[<span class="ruby-identifier">i</span>] = (<span class="ruby-identifier">x</span>[<span class="ruby-identifier">i</span>]<span class="ruby-operator">-</span><span class="ruby-identifier">dot</span>).<span class="ruby-identifier">div</span>(<span class="ruby-identifier">a</span>[<span class="ruby-identifier">psin</span><span class="ruby-operator">+</span><span class="ruby-identifier">i</span>],<span class="ruby-identifier">prec</span>)
<span class="ruby-keyword">end</span>
<span class="ruby-identifier">x</span>
<span class="ruby-keyword">end</span></pre>
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