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diff --git a/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/optimization/fitting/HarmonicFitter.ParameterGuesser.html b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/optimization/fitting/HarmonicFitter.ParameterGuesser.html new file mode 100644 index 0000000..1a956c8 --- /dev/null +++ b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/optimization/fitting/HarmonicFitter.ParameterGuesser.html @@ -0,0 +1,377 @@ +<!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>HarmonicFitter.ParameterGuesser (Apache Commons Math 3.6.1 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="HarmonicFitter.ParameterGuesser (Apache Commons Math 3.6.1 API)"; 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+ 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.optimization.fitting</div> +<h2 title="Class HarmonicFitter.ParameterGuesser" class="title">Class HarmonicFitter.ParameterGuesser</h2> +</div> +<div class="contentContainer"> +<ul class="inheritance"> +<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> +<li> +<ul class="inheritance"> +<li>org.apache.commons.math3.optimization.fitting.HarmonicFitter.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/optimization/fitting/HarmonicFitter.html" title="class in org.apache.commons.math3.optimization.fitting">HarmonicFitter</a></dd> +</dl> +<hr> +<br> +<pre>public static class <span class="strong">HarmonicFitter.ParameterGuesser</span> +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> +<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<sub>i</sub> and want to find a, + ω and φ such that f (t) = a cos (ω t + φ). + </p> + + <p>From the analytical expression, we can compute two primitives : + <pre> + If2 (t) = ∫ f<sup>2</sup> = a<sup>2</sup> × [t + S (t)] / 2 + If'2 (t) = ∫ f'<sup>2</sup> = a<sup>2</sup> ω<sup>2</sup> × [t - S (t)] / 2 + where S (t) = sin (2 (ω t + φ)) / (2 ω) + </pre> + </p> + + <p>We can remove S between these expressions : + <pre> + If'2 (t) = a<sup>2</sup> ω<sup>2</sup> t - ω<sup>2</sup> If2 (t) + </pre> + </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<sub>1</sub> and t<sub>i</sub> for each t<sub>i</sub> : + <pre> + If2 (t<sub>i</sub>) - If2 (t<sub>1</sub>) = A × (t<sub>i</sub> - t<sub>1</sub>) + B × (If2 (t<sub>i</sub>) - If2 (t<sub>1</sub>)) + </pre> + </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<sub>i</sub>, y<sub>i</sub>) = A × x<sub>i</sub> + B × y<sub>i</sub>, the + coefficients A and B that minimize a least square criterion + ∑ (z<sub>i</sub> - z (x<sub>i</sub>, y<sub>i</sub>))<sup>2</sup> are given by these expressions:</p> + <pre> + + ∑y<sub>i</sub>y<sub>i</sub> ∑x<sub>i</sub>z<sub>i</sub> - ∑x<sub>i</sub>y<sub>i</sub> ∑y<sub>i</sub>z<sub>i</sub> + A = ------------------------ + ∑x<sub>i</sub>x<sub>i</sub> ∑y<sub>i</sub>y<sub>i</sub> - ∑x<sub>i</sub>y<sub>i</sub> ∑x<sub>i</sub>y<sub>i</sub> + + ∑x<sub>i</sub>x<sub>i</sub> ∑y<sub>i</sub>z<sub>i</sub> - ∑x<sub>i</sub>y<sub>i</sub> ∑x<sub>i</sub>z<sub>i</sub> + B = ------------------------ + ∑x<sub>i</sub>x<sub>i</sub> ∑y<sub>i</sub>y<sub>i</sub> - ∑x<sub>i</sub>y<sub>i</sub> ∑x<sub>i</sub>y<sub>i</sub> + </pre> + </p> + + + <p>In fact, we can assume both a and ω are positive and + compute them directly, knowing that A = a<sup>2</sup> ω<sup>2</sup> and that + B = - ω<sup>2</sup>. The complete algorithm is therefore:</p> + <pre> + + for each t<sub>i</sub> from t<sub>1</sub> to t<sub>n-1</sub>, compute: + f (t<sub>i</sub>) + f' (t<sub>i</sub>) = (f (t<sub>i+1</sub>) - f(t<sub>i-1</sub>)) / (t<sub>i+1</sub> - t<sub>i-1</sub>) + x<sub>i</sub> = t<sub>i</sub> - t<sub>1</sub> + y<sub>i</sub> = ∫ f<sup>2</sup> from t<sub>1</sub> to t<sub>i</sub> + z<sub>i</sub> = ∫ f'<sup>2</sup> from t<sub>1</sub> to t<sub>i</sub> + update the sums ∑x<sub>i</sub>x<sub>i</sub>, ∑y<sub>i</sub>y<sub>i</sub>, ∑x<sub>i</sub>y<sub>i</sub>, ∑x<sub>i</sub>z<sub>i</sub> and ∑y<sub>i</sub>z<sub>i</sub> + end for + + |-------------------------- + \ | ∑y<sub>i</sub>y<sub>i</sub> ∑x<sub>i</sub>z<sub>i</sub> - ∑x<sub>i</sub>y<sub>i</sub> ∑y<sub>i</sub>z<sub>i</sub> + a = \ | ------------------------ + \| ∑x<sub>i</sub>y<sub>i</sub> ∑x<sub>i</sub>z<sub>i</sub> - ∑x<sub>i</sub>x<sub>i</sub> ∑y<sub>i</sub>z<sub>i</sub> + + + |-------------------------- + \ | ∑x<sub>i</sub>y<sub>i</sub> ∑x<sub>i</sub>z<sub>i</sub> - ∑x<sub>i</sub>x<sub>i</sub> ∑y<sub>i</sub>z<sub>i</sub> + ω = \ | ------------------------ + \| ∑x<sub>i</sub>x<sub>i</sub> ∑y<sub>i</sub>y<sub>i</sub> - ∑x<sub>i</sub>y<sub>i</sub> ∑x<sub>i</sub>y<sub>i</sub> + + </pre> + </p> + + <p>Once we know ω, we can compute: + <pre> + fc = ω f (t) cos (ω t) - f' (t) sin (ω t) + fs = ω f (t) sin (ω t) + f' (t) cos (ω t) + </pre> + </p> + + <p>It appears that <code>fc = a ω cos (φ)</code> and + <code>fs = -a ω sin (φ)</code>, so we can use these + expressions to compute φ. 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/optimization/fitting/HarmonicFitter.ParameterGuesser.html#HarmonicFitter.ParameterGuesser(org.apache.commons.math3.optimization.fitting.WeightedObservedPoint[])">HarmonicFitter.ParameterGuesser</a></strong>(<a href="../../../../../../org/apache/commons/math3/optimization/fitting/WeightedObservedPoint.html" title="class in org.apache.commons.math3.optimization.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/optimization/fitting/HarmonicFitter.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/7/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/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,%20int)" 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="HarmonicFitter.ParameterGuesser(org.apache.commons.math3.optimization.fitting.WeightedObservedPoint[])"> +<!-- --> +</a> +<ul class="blockListLast"> +<li class="blockList"> +<h4>HarmonicFitter.ParameterGuesser</h4> +<pre>public HarmonicFitter.ParameterGuesser(<a href="../../../../../../org/apache/commons/math3/optimization/fitting/WeightedObservedPoint.html" title="class in org.apache.commons.math3.optimization.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" 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