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<div class="subTitle">edu.rit.numeric</div>
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<h2 title="Class MDMinimizationDownhillSimplex" class="title">Class MDMinimizationDownhillSimplex</h2>
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<div class="contentContainer">
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<ul class="inheritance">
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<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li>
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<li>edu.rit.numeric.MDMinimizationDownhillSimplex</li>
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<pre>public class <span class="strong">MDMinimizationDownhillSimplex</span>
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extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
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<div class="block">Class MDMinimizationDownhillSimplex finds a minimum of a multidimensional
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function using the downhill simplex method of Nelder and Mead. The function
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has <I>N</I> inputs and is represented by an object that implements interface
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<a href="../../../edu/rit/numeric/MDFunction.html" title="interface in edu.rit.numeric">MDFunction</a>. The <TT>minimize()</TT> method finds a (local)
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minimum in the function. The input to the <TT>minimize()</TT> method is an
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<I>N</I>-dimensional <I>simplex,</I> namely a group of <I>N</I>+1 points in
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<I>N</I> dimensions, each point different from all the others. Typically, one
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point of the simplex is an initial guess for the solution, and the other
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points of the simplex are perturbations of the initial guess. The
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<TT>minimize()</TT> method evaluates the function at each point of the
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simplex and moves the simplex through <I>N</I>-dimensional space to minimize
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the smallest function value of any point in the simplex, stopping when the
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relative difference between the smallest and largest function values of any
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points in the simplex falls below a tolerance. The output from the
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<TT>minimize()</TT> method is the final simplex, with the
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smallest-function-value point at position 0. The inputs to and outputs from
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the <TT>minimize()</TT> method are stored in the fields of an instance of
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class MDMinimizationDownhillSimplex.</div>
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<caption><span>Fields</span><span class="tabEnd"> </span></caption>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<th class="colLast" scope="col">Field and Description</th>
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<td class="colFirst"><code>boolean</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#debug">debug</a></strong></code>
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<div class="block">Debug flag.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>double[]</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#f">f</a></strong></code>
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<div class="block">Function values of the simplex points.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code><a href="../../../edu/rit/numeric/MDFunction.html" title="interface in edu.rit.numeric">MDFunction</a></code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#fcn">fcn</a></strong></code>
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<div class="block">The multidimensional function to be minimized.</div>
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</td>
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</tr>
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<td class="colFirst"><code>int</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#N">N</a></strong></code>
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<div class="block">The number of function arguments.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>double</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#tol">tol</a></strong></code>
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<div class="block">Tolerance.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>double[][]</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#x">x</a></strong></code>
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<div class="block">The simplex.</div>
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</td>
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<th class="colOne" scope="col">Constructor and Description</th>
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<td class="colOne"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#MDMinimizationDownhillSimplex(edu.rit.numeric.MDFunction)">MDMinimizationDownhillSimplex</a></strong>(<a href="../../../edu/rit/numeric/MDFunction.html" title="interface in edu.rit.numeric">MDFunction</a> theFunction)</code>
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<div class="block">Construct a new multidimensional minimization object for the given
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function.</div>
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</td>
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</tr>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<td class="colFirst"><code>void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#minimize()">minimize</a></strong>()</code>
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<div class="block">Minimize the multidimensional function.</div>
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</td>
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<td class="colFirst"><code>void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#setSimplex(double[], double)">setSimplex</a></strong>(double[] x,
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double delta)</code>
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<div class="block">Set the simplex to the given point plus the same perturbation along each
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dimension.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#setSimplex(double[], double[])">setSimplex</a></strong>(double[] x,
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double[] delta)</code>
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<div class="block">Set the simplex to the given point plus a different perturbation along
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each dimension.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>protected void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/MDMinimizationDownhillSimplex.html#subclassDebug(int, int)">subclassDebug</a></strong>(int iter,
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int eval)</code>
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<div class="block">Do debugging.</div>
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</td>
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<h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
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<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<h3>Field Detail</h3>
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<a name="fcn">
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<h4>fcn</h4>
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<pre>public final <a href="../../../edu/rit/numeric/MDFunction.html" title="interface in edu.rit.numeric">MDFunction</a> fcn</pre>
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<div class="block">The multidimensional function to be minimized.</div>
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</li>
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<a name="N">
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<h4>N</h4>
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<pre>public final int N</pre>
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<div class="block">The number of function arguments.</div>
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<h4>x</h4>
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<pre>public final double[][] x</pre>
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<div class="block">The simplex. This is an <I>N</I>+1-element array of <I>N</I>-element
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points. On input to the <TT>minimize()</TT> method, <TT>x</TT> contains a
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simplex with an initial estimate of the solution. On output from the
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<TT>minimize()</TT> method, <TT>x</TT> contains the final simplex, and
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<TT>x[0]</TT> contains the solution, namely the simplex point with the
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smallest function value.</div>
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<h4>f</h4>
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<pre>public final double[] f</pre>
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<div class="block">Function values of the simplex points. An <I>N</I>+1-element array. On
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output from the <TT>minimize()</TT> method, <TT>f[i]</TT> contains the
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function value for simplex point <TT>x[i]</TT>, 0 ≤ <TT>i</TT> ≤
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<I>N</I>−1. In particular, <TT>f[0]</TT> contains the minimized
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function value for the solution.</div>
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</li>
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<a name="tol">
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<h4>tol</h4>
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<pre>public double tol</pre>
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<div class="block">Tolerance. An input to the <TT>minimize()</TT> method. Must be > 0.
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Termination occurs when the relative difference between the smallest and
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largest function values of points in the simplex is less than the
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tolerance. The default tolerance is 1×10<SUP>−6</SUP>.</div>
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<h4>debug</h4>
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<pre>public boolean debug</pre>
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<div class="block">Debug flag. An input to the <TT>minimize()</TT> method. If true, the
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<TT>subclassDebug()</TT> method is called at the beginning of every
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iteration. The default setting is false.</div>
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</li>
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</ul>
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</li>
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</ul>
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<h3>Constructor Detail</h3>
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<a name="MDMinimizationDownhillSimplex(edu.rit.numeric.MDFunction)">
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<h4>MDMinimizationDownhillSimplex</h4>
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<pre>public MDMinimizationDownhillSimplex(<a href="../../../edu/rit/numeric/MDFunction.html" title="interface in edu.rit.numeric">MDFunction</a> theFunction)</pre>
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<div class="block">Construct a new multidimensional minimization object for the given
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function. Field <TT>fcn</TT> is set to <TT>theFunction</TT>. Field
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<TT>N</TT> is set by calling the function's <TT>argumentLength()</TT>
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method. Field <TT>x</TT>, the simplex, is allocated with the proper size;
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all simplex points are initially 0. Field <TT>f</TT>, the function
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values, is allocated with the proper size.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>theFunction</code> - Multidimensional function to be minimized.</dd>
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<dt><span class="strong">Throws:</span></dt>
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<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - (unchecked exception) Thrown if <TT>theFunction</TT> is null.</dd></dl>
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<h3>Method Detail</h3>
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<a name="setSimplex(double[], double)">
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<h4>setSimplex</h4>
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<pre>public void setSimplex(double[] x,
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double delta)</pre>
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<div class="block">Set the simplex to the given point plus the same perturbation along each
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dimension. The field <TT>x[0]</TT> is set to <TT>x</TT>; the field
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<TT>x[1]</TT> is set to <TT>x</TT> with <TT>delta</TT> added to element
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0; the field <TT>x[2]</TT> is set to <TT>x</TT> with <TT>delta</TT> added
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to element 1; and so on.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Simplex point. Must be an <I>N</I>-element array.</dd><dd><code>delta</code> - Perturbation along every dimension. Must be nonzero.</dd></dl>
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<a name="setSimplex(double[], double[])">
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<h4>setSimplex</h4>
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<pre>public void setSimplex(double[] x,
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double[] delta)</pre>
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<div class="block">Set the simplex to the given point plus a different perturbation along
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each dimension. The field <TT>x[0]</TT> is set to <TT>x</TT>; the field
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<TT>x[1]</TT> is set to <TT>x</TT> with <TT>delta[0]</TT> added to
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element 0; the field <TT>x[2]</TT> is set to <TT>x</TT> with
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<TT>delta[1]</TT> added to element 1; and so on.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Simplex point. Must be an <I>N</I>-element array.</dd><dd><code>delta</code> - Perturbations along each dimension. All must be nonzero.</dd></dl>
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<a name="minimize()">
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<h4>minimize</h4>
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<pre>public void minimize()</pre>
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<div class="block">Minimize the multidimensional function. On input, the field <TT>x</TT>
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must be filled in with an initial simplex, and the field <TT>tol</TT>
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must be set to the desired tolerance. On output, the field <TT>x</TT>
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contains the solution. For further information, see the documentation for
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each field.</div>
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<dl><dt><span class="strong">Throws:</span></dt>
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<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - (unchecked exception) Thrown if <TT>tol</TT> ≤ 0.</dd>
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<dd><code><a href="../../../edu/rit/numeric/TooManyIterationsException.html" title="class in edu.rit.numeric">TooManyIterationsException</a></code> - (unchecked exception) Thrown if too many function evaluations (5,000)
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occurred without finding a minimum.</dd></dl>
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<h4>subclassDebug</h4>
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<pre>protected void subclassDebug(int iter,
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int eval)</pre>
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<div class="block">Do debugging. If the <TT>debug</TT> field is true, the
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<TT>subclassDebug()</TT> method is called at the beginning of every
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iteration. The fields of this object contain the current state of the
|
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algorithm. The fields of this object must not be altered.
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<P>
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The default implementation of the <TT>subclassDebug()</TT> method does
|
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nothing. A subclass can override the <TT>subclassDebug()</TT> method to
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do something, such as print debugging information.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>iter</code> - Iteration number.</dd><dd><code>eval</code> - Number of function evaluations.</dd></dl>
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<p class="legalCopy"><small><FONT SIZE="-2">Copyright © 2013–2016 by Alan Kaminsky. All rights reserved. Send comments to ark</FONT><FONT SIZE="1" COLOR="#FFFFFF">­</FONT><FONT SIZE="-2">@</FONT><FONT SIZE="1" COLOR="#FFFFFF">­</FONT><FONT SIZE="-2">cs.rit.edu.</FONT></small></p>
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