| <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> |
| <!-- NewPage --> |
| <html lang="en"> |
| <head> |
| <meta http-equiv="Content-Type" content="text/html" charset="UTF-8"> |
| <title>HarmonicCurveFitter.ParameterGuesser (Apache Commons Math 3.3 API)</title> |
| <link rel="stylesheet" type="text/css" href="../../../../../stylesheet.css" title="Style"> |
| </head> |
| <body> |
| <script type="text/javascript"><!-- |
| if (location.href.indexOf('is-external=true') == -1) { |
| parent.document.title="HarmonicCurveFitter.ParameterGuesser (Apache Commons Math 3.3 API)"; |
| } |
| //--> |
| </script> |
| <noscript> |
| <div>JavaScript is disabled on your browser.</div> |
| </noscript> |
| <!-- ========= START OF TOP NAVBAR ======= --> |
| <div class="topNav"><a name="navbar_top"> |
| <!-- --> |
| </a><a href="#skip-navbar_top" title="Skip navigation links"></a><a name="navbar_top_firstrow"> |
| <!-- --> |
| </a> |
| <ul class="navList" title="Navigation"> |
| <li><a href="../../../../../overview-summary.html">Overview</a></li> |
| <li><a href="package-summary.html">Package</a></li> |
| <li class="navBarCell1Rev">Class</li> |
| <li><a href="class-use/HarmonicCurveFitter.ParameterGuesser.html">Use</a></li> |
| <li><a href="package-tree.html">Tree</a></li> |
| <li><a href="../../../../../deprecated-list.html">Deprecated</a></li> |
| <li><a href="../../../../../index-all.html">Index</a></li> |
| <li><a href="../../../../../help-doc.html">Help</a></li> |
| </ul> |
| <div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div> |
| </div> |
| <div class="subNav"> |
| <ul class="navList"> |
| <li><a href="../../../../../org/apache/commons/math3/fitting/HarmonicCurveFitter.html" title="class in org.apache.commons.math3.fitting"><span class="strong">Prev Class</span></a></li> |
| <li><a href="../../../../../org/apache/commons/math3/fitting/HarmonicFitter.html" title="class in org.apache.commons.math3.fitting"><span class="strong">Next Class</span></a></li> |
| </ul> |
| <ul class="navList"> |
| <li><a href="../../../../../index.html?org/apache/commons/math3/fitting/HarmonicCurveFitter.ParameterGuesser.html" target="_top">Frames</a></li> |
| <li><a href="HarmonicCurveFitter.ParameterGuesser.html" target="_top">No Frames</a></li> |
| </ul> |
| <ul class="navList" id="allclasses_navbar_top"> |
| <li><a href="../../../../../allclasses-noframe.html">All Classes</a></li> |
| </ul> |
| <div> |
| <script type="text/javascript"><!-- |
| allClassesLink = document.getElementById("allclasses_navbar_top"); |
| if(window==top) { |
| allClassesLink.style.display = "block"; |
| } |
| else { |
| allClassesLink.style.display = "none"; |
| } |
| //--> |
| </script> |
| </div> |
| <div> |
| <ul class="subNavList"> |
| <li>Summary: </li> |
| <li>Nested | </li> |
| <li>Field | </li> |
| <li><a href="#constructor_summary">Constr</a> | </li> |
| <li><a href="#method_summary">Method</a></li> |
| </ul> |
| <ul class="subNavList"> |
| <li>Detail: </li> |
| <li>Field | </li> |
| <li><a href="#constructor_detail">Constr</a> | </li> |
| <li><a href="#method_detail">Method</a></li> |
| </ul> |
| </div> |
| <a name="skip-navbar_top"> |
| <!-- --> |
| </a></div> |
| <!-- ========= END OF TOP NAVBAR ========= --> |
| <!-- ======== START OF CLASS DATA ======== --> |
| <div class="header"> |
| <div class="subTitle">org.apache.commons.math3.fitting</div> |
| <h2 title="Class HarmonicCurveFitter.ParameterGuesser" class="title">Class HarmonicCurveFitter.ParameterGuesser</h2> |
| </div> |
| <div class="contentContainer"> |
| <ul class="inheritance"> |
| <li><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li> |
| <li> |
| <ul class="inheritance"> |
| <li>org.apache.commons.math3.fitting.HarmonicCurveFitter.ParameterGuesser</li> |
| </ul> |
| </li> |
| </ul> |
| <div class="description"> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <dl> |
| <dt>Enclosing class:</dt> |
| <dd><a href="../../../../../org/apache/commons/math3/fitting/HarmonicCurveFitter.html" title="class in org.apache.commons.math3.fitting">HarmonicCurveFitter</a></dd> |
| </dl> |
| <hr> |
| <br> |
| <pre>public static class <span class="strong">HarmonicCurveFitter.ParameterGuesser</span> |
| extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre> |
| <div class="block">This class guesses harmonic coefficients from a sample. |
| <p>The algorithm used to guess the coefficients is as follows:</p> |
| |
| <p>We know \( f(t) \) at some sampling points \( t_i \) and want |
| to find \( a \), \( \omega \) and \( \phi \) such that |
| \( f(t) = a \cos (\omega t + \phi) \). |
| </p> |
| |
| <p>From the analytical expression, we can compute two primitives : |
| \[ |
| If2(t) = \int f^2 dt = a^2 (t + S(t)) / 2 |
| \] |
| \[ |
| If'2(t) = \int f'^2 dt = a^2 \omega^2 (t - S(t)) / 2 |
| \] |
| where \(S(t) = \frac{\sin(2 (\omega t + \phi))}{2\omega}\) |
| </p> |
| |
| <p>We can remove \(S\) between these expressions : |
| \[ |
| If'2(t) = a^2 \omega^2 t - \omega^2 If2(t) |
| \] |
| </p> |
| |
| <p>The preceding expression shows that \(If'2 (t)\) is a linear |
| combination of both \(t\) and \(If2(t)\): |
| \[ |
| If'2(t) = A t + B If2(t) |
| \] |
| </p> |
| |
| <p>From the primitive, we can deduce the same form for definite |
| integrals between \(t_1\) and \(t_i\) for each \(t_i\) : |
| \[ |
| If2(t_i) - If2(t_1) = A (t_i - t_1) + B (If2 (t_i) - If2(t_1)) |
| \] |
| </p> |
| |
| <p>We can find the coefficients \(A\) and \(B\) that best fit the sample |
| to this linear expression by computing the definite integrals for |
| each sample points. |
| </p> |
| |
| <p>For a bilinear expression \(z(x_i, y_i) = A x_i + B y_i\), the |
| coefficients \(A\) and \(B\) that minimize a least-squares criterion |
| \(\sum (z_i - z(x_i, y_i))^2\) are given by these expressions:</p> |
| \[ |
| A = \frac{\sum y_i y_i \sum x_i z_i - \sum x_i y_i \sum y_i z_i} |
| {\sum x_i x_i \sum y_i y_i - \sum x_i y_i \sum x_i y_i} |
| \] |
| \[ |
| B = \frac{\sum x_i x_i \sum y_i z_i - \sum x_i y_i \sum x_i z_i} |
| {\sum x_i x_i \sum y_i y_i - \sum x_i y_i \sum x_i y_i} |
| |
| \] |
| |
| <p>In fact, we can assume that both \(a\) and \(\omega\) are positive and |
| compute them directly, knowing that \(A = a^2 \omega^2\) and that |
| \(B = -\omega^2\). The complete algorithm is therefore:</p> |
| |
| For each \(t_i\) from \(t_1\) to \(t_{n-1}\), compute: |
| \[ f(t_i) \] |
| \[ f'(t_i) = \frac{f (t_{i+1}) - f(t_{i-1})}{t_{i+1} - t_{i-1}} \] |
| \[ x_i = t_i - t_1 \] |
| \[ y_i = \int_{t_1}^{t_i} f^2(t) dt \] |
| \[ z_i = \int_{t_1}^{t_i} f'^2(t) dt \] |
| and update the sums: |
| \[ \sum x_i x_i, \sum y_i y_i, \sum x_i y_i, \sum x_i z_i, \sum y_i z_i \] |
| |
| Then: |
| \[ |
| a = \sqrt{\frac{\sum y_i y_i \sum x_i z_i - \sum x_i y_i \sum y_i z_i } |
| {\sum x_i y_i \sum x_i z_i - \sum x_i x_i \sum y_i z_i }} |
| \] |
| \[ |
| \omega = \sqrt{\frac{\sum x_i y_i \sum x_i z_i - \sum x_i x_i \sum y_i z_i} |
| {\sum x_i x_i \sum y_i y_i - \sum x_i y_i \sum x_i y_i}} |
| \] |
| |
| <p>Once we know \(\omega\) we can compute: |
| \[ |
| fc = \omega f(t) \cos(\omega t) - f'(t) \sin(\omega t) |
| \] |
| \[ |
| fs = \omega f(t) \sin(\omega t) + f'(t) \cos(\omega t) |
| \] |
| </p> |
| |
| <p>It appears that \(fc = a \omega \cos(\phi)\) and |
| \(fs = -a \omega \sin(\phi)\), so we can use these |
| expressions to compute \(\phi\). The best estimate over the sample is |
| given by averaging these expressions. |
| </p> |
| |
| <p>Since integrals and means are involved in the preceding |
| estimations, these operations run in \(O(n)\) time, where \(n\) is the |
| number of measurements.</p></div> |
| </li> |
| </ul> |
| </div> |
| <div class="summary"> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <!-- ======== CONSTRUCTOR SUMMARY ======== --> |
| <ul class="blockList"> |
| <li class="blockList"><a name="constructor_summary"> |
| <!-- --> |
| </a> |
| <h3>Constructor Summary</h3> |
| <table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Constructor Summary table, listing constructors, and an explanation"> |
| <caption><span>Constructors</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colOne" scope="col">Constructor and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/fitting/HarmonicCurveFitter.ParameterGuesser.html#HarmonicCurveFitter.ParameterGuesser(java.util.Collection)">HarmonicCurveFitter.ParameterGuesser</a></strong>(<a href="http://docs.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</a><<a href="../../../../../org/apache/commons/math3/fitting/WeightedObservedPoint.html" title="class in org.apache.commons.math3.fitting">WeightedObservedPoint</a>> observations)</code> |
| <div class="block">Simple constructor.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
| </ul> |
| <!-- ========== METHOD SUMMARY =========== --> |
| <ul class="blockList"> |
| <li class="blockList"><a name="method_summary"> |
| <!-- --> |
| </a> |
| <h3>Method Summary</h3> |
| <table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation"> |
| <caption><span>Methods</span><span class="tabEnd"> </span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier and Type</th> |
| <th class="colLast" scope="col">Method and Description</th> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/fitting/HarmonicCurveFitter.ParameterGuesser.html#guess()">guess</a></strong>()</code> |
| <div class="block">Gets an estimation of the parameters.</div> |
| </td> |
| </tr> |
| </table> |
| <ul class="blockList"> |
| <li class="blockList"><a name="methods_inherited_from_class_java.lang.Object"> |
| <!-- --> |
| </a> |
| <h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3> |
| <code><a href="http://docs.oracle.com/javase/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/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/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </div> |
| <div class="details"> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <!-- ========= CONSTRUCTOR DETAIL ======== --> |
| <ul class="blockList"> |
| <li class="blockList"><a name="constructor_detail"> |
| <!-- --> |
| </a> |
| <h3>Constructor Detail</h3> |
| <a name="HarmonicCurveFitter.ParameterGuesser(java.util.Collection)"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>HarmonicCurveFitter.ParameterGuesser</h4> |
| <pre>public HarmonicCurveFitter.ParameterGuesser(<a href="http://docs.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</a><<a href="../../../../../org/apache/commons/math3/fitting/WeightedObservedPoint.html" title="class in org.apache.commons.math3.fitting">WeightedObservedPoint</a>> observations)</pre> |
| <div class="block">Simple constructor.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>observations</code> - Sampled observations.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if the sample is too short.</dd> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></code> - if the abscissa range is zero.</dd> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</a></code> - when the guessing procedure cannot |
| produce sensible results.</dd></dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| <!-- ============ METHOD DETAIL ========== --> |
| <ul class="blockList"> |
| <li class="blockList"><a name="method_detail"> |
| <!-- --> |
| </a> |
| <h3>Method Detail</h3> |
| <a name="guess()"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>guess</h4> |
| <pre>public double[] guess()</pre> |
| <div class="block">Gets an estimation of the parameters.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the guessed parameters, in the following order: |
| <ul> |
| <li>Amplitude</li> |
| <li>Angular frequency</li> |
| <li>Phase</li> |
| </ul></dd></dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </div> |
| </div> |
| <!-- ========= END OF CLASS DATA ========= --> |
| <!-- ======= START OF BOTTOM NAVBAR ====== --> |
| <div class="bottomNav"><a name="navbar_bottom"> |
| <!-- --> |
| </a><a href="#skip-navbar_bottom" title="Skip navigation links"></a><a name="navbar_bottom_firstrow"> |
| <!-- --> |
| </a> |
| <ul class="navList" title="Navigation"> |
| <li><a href="../../../../../overview-summary.html">Overview</a></li> |
| <li><a href="package-summary.html">Package</a></li> |
| <li class="navBarCell1Rev">Class</li> |
| <li><a href="class-use/HarmonicCurveFitter.ParameterGuesser.html">Use</a></li> |
| <li><a href="package-tree.html">Tree</a></li> |
| <li><a href="../../../../../deprecated-list.html">Deprecated</a></li> |
| <li><a href="../../../../../index-all.html">Index</a></li> |
| <li><a href="../../../../../help-doc.html">Help</a></li> |
| </ul> |
| <div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div> |
| </div> |
| <div class="subNav"> |
| <ul class="navList"> |
| <li><a href="../../../../../org/apache/commons/math3/fitting/HarmonicCurveFitter.html" title="class in org.apache.commons.math3.fitting"><span class="strong">Prev Class</span></a></li> |
| <li><a href="../../../../../org/apache/commons/math3/fitting/HarmonicFitter.html" title="class in org.apache.commons.math3.fitting"><span class="strong">Next Class</span></a></li> |
| </ul> |
| <ul class="navList"> |
| <li><a href="../../../../../index.html?org/apache/commons/math3/fitting/HarmonicCurveFitter.ParameterGuesser.html" target="_top">Frames</a></li> |
| <li><a href="HarmonicCurveFitter.ParameterGuesser.html" target="_top">No Frames</a></li> |
| </ul> |
| <ul class="navList" id="allclasses_navbar_bottom"> |
| <li><a href="../../../../../allclasses-noframe.html">All Classes</a></li> |
| </ul> |
| <div> |
| <script type="text/javascript"><!-- |
| allClassesLink = document.getElementById("allclasses_navbar_bottom"); |
| if(window==top) { |
| allClassesLink.style.display = "block"; |
| } |
| else { |
| allClassesLink.style.display = "none"; |
| } |
| //--> |
| </script> |
| </div> |
| <div> |
| <ul class="subNavList"> |
| <li>Summary: </li> |
| <li>Nested | </li> |
| <li>Field | </li> |
| <li><a href="#constructor_summary">Constr</a> | </li> |
| <li><a href="#method_summary">Method</a></li> |
| </ul> |
| <ul class="subNavList"> |
| <li>Detail: </li> |
| <li>Field | </li> |
| <li><a href="#constructor_detail">Constr</a> | </li> |
| <li><a href="#method_detail">Method</a></li> |
| </ul> |
| </div> |
| <a name="skip-navbar_bottom"> |
| <!-- --> |
| </a></div> |
| <!-- ======== END OF BOTTOM NAVBAR ======= --> |
| <p class="legalCopy"><small>Copyright © 2003–2014 <a href="http://www.apache.org/">The Apache Software Foundation</a>. All rights reserved.</small></p> |
| </body> |
| </html> |