| <!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>PolynomialsUtils (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="PolynomialsUtils (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/PolynomialsUtils.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/analysis/polynomials/PolynomialSplineFunction.html" title="class in org.apache.commons.math3.analysis.polynomials"><span class="strong">Prev Class</span></a></li> |
| <li>Next Class</li> |
| </ul> |
| <ul class="navList"> |
| <li><a href="../../../../../../index.html?org/apache/commons/math3/analysis/polynomials/PolynomialsUtils.html" target="_top">Frames</a></li> |
| <li><a href="PolynomialsUtils.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>Constr | </li> |
| <li><a href="#method_summary">Method</a></li> |
| </ul> |
| <ul class="subNavList"> |
| <li>Detail: </li> |
| <li>Field | </li> |
| <li>Constr | </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.analysis.polynomials</div> |
| <h2 title="Class PolynomialsUtils" class="title">Class PolynomialsUtils</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.analysis.polynomials.PolynomialsUtils</li> |
| </ul> |
| </li> |
| </ul> |
| <div class="description"> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <hr> |
| <br> |
| <pre>public class <span class="strong">PolynomialsUtils</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">A collection of static methods that operate on or return polynomials.</div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>2.0</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: PolynomialsUtils.java 1517203 2013-08-24 21:55:35Z psteitz $</dd></dl> |
| </li> |
| </ul> |
| </div> |
| <div class="summary"> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <!-- ========== 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>static <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialsUtils.html#createChebyshevPolynomial(int)">createChebyshevPolynomial</a></strong>(int degree)</code> |
| <div class="block">Create a Chebyshev polynomial of the first kind.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialsUtils.html#createHermitePolynomial(int)">createHermitePolynomial</a></strong>(int degree)</code> |
| <div class="block">Create a Hermite polynomial.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialsUtils.html#createJacobiPolynomial(int, int, int)">createJacobiPolynomial</a></strong>(int degree, |
| int v, |
| int w)</code> |
| <div class="block">Create a Jacobi polynomial.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialsUtils.html#createLaguerrePolynomial(int)">createLaguerrePolynomial</a></strong>(int degree)</code> |
| <div class="block">Create a Laguerre polynomial.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialsUtils.html#createLegendrePolynomial(int)">createLegendrePolynomial</a></strong>(int degree)</code> |
| <div class="block">Create a Legendre polynomial.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>static double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialsUtils.html#shift(double[], double)">shift</a></strong>(double[] coefficients, |
| double shift)</code> |
| <div class="block">Compute the coefficients of the polynomial <code>P<sub>s</sub>(x)</code> |
| whose values at point <code>x</code> will be the same as the those from the |
| original polynomial <code>P(x)</code> when computed at <code>x + shift</code>.</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"> |
| <!-- ============ METHOD DETAIL ========== --> |
| <ul class="blockList"> |
| <li class="blockList"><a name="method_detail"> |
| <!-- --> |
| </a> |
| <h3>Method Detail</h3> |
| <a name="createChebyshevPolynomial(int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>createChebyshevPolynomial</h4> |
| <pre>public static <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a> createChebyshevPolynomial(int degree)</pre> |
| <div class="block">Create a Chebyshev polynomial of the first kind. |
| <p><a href="http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html">Chebyshev |
| polynomials of the first kind</a> are orthogonal polynomials. |
| They can be defined by the following recurrence relations: |
| <pre> |
| T<sub>0</sub>(X) = 1 |
| T<sub>1</sub>(X) = X |
| T<sub>k+1</sub>(X) = 2X T<sub>k</sub>(X) - T<sub>k-1</sub>(X) |
| </pre></p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>degree</code> - degree of the polynomial</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>Chebyshev polynomial of specified degree</dd></dl> |
| </li> |
| </ul> |
| <a name="createHermitePolynomial(int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>createHermitePolynomial</h4> |
| <pre>public static <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a> createHermitePolynomial(int degree)</pre> |
| <div class="block">Create a Hermite polynomial. |
| <p><a href="http://mathworld.wolfram.com/HermitePolynomial.html">Hermite |
| polynomials</a> are orthogonal polynomials. |
| They can be defined by the following recurrence relations: |
| <pre> |
| H<sub>0</sub>(X) = 1 |
| H<sub>1</sub>(X) = 2X |
| H<sub>k+1</sub>(X) = 2X H<sub>k</sub>(X) - 2k H<sub>k-1</sub>(X) |
| </pre></p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>degree</code> - degree of the polynomial</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>Hermite polynomial of specified degree</dd></dl> |
| </li> |
| </ul> |
| <a name="createLaguerrePolynomial(int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>createLaguerrePolynomial</h4> |
| <pre>public static <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a> createLaguerrePolynomial(int degree)</pre> |
| <div class="block">Create a Laguerre polynomial. |
| <p><a href="http://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre |
| polynomials</a> are orthogonal polynomials. |
| They can be defined by the following recurrence relations: |
| <pre> |
| L<sub>0</sub>(X) = 1 |
| L<sub>1</sub>(X) = 1 - X |
| (k+1) L<sub>k+1</sub>(X) = (2k + 1 - X) L<sub>k</sub>(X) - k L<sub>k-1</sub>(X) |
| </pre></p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>degree</code> - degree of the polynomial</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>Laguerre polynomial of specified degree</dd></dl> |
| </li> |
| </ul> |
| <a name="createLegendrePolynomial(int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>createLegendrePolynomial</h4> |
| <pre>public static <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a> createLegendrePolynomial(int degree)</pre> |
| <div class="block">Create a Legendre polynomial. |
| <p><a href="http://mathworld.wolfram.com/LegendrePolynomial.html">Legendre |
| polynomials</a> are orthogonal polynomials. |
| They can be defined by the following recurrence relations: |
| <pre> |
| P<sub>0</sub>(X) = 1 |
| P<sub>1</sub>(X) = X |
| (k+1) P<sub>k+1</sub>(X) = (2k+1) X P<sub>k</sub>(X) - k P<sub>k-1</sub>(X) |
| </pre></p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>degree</code> - degree of the polynomial</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>Legendre polynomial of specified degree</dd></dl> |
| </li> |
| </ul> |
| <a name="createJacobiPolynomial(int, int, int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>createJacobiPolynomial</h4> |
| <pre>public static <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a> createJacobiPolynomial(int degree, |
| int v, |
| int w)</pre> |
| <div class="block">Create a Jacobi polynomial. |
| <p><a href="http://mathworld.wolfram.com/JacobiPolynomial.html">Jacobi |
| polynomials</a> are orthogonal polynomials. |
| They can be defined by the following recurrence relations: |
| <pre> |
| P<sub>0</sub><sup>vw</sup>(X) = 1 |
| P<sub>-1</sub><sup>vw</sup>(X) = 0 |
| 2k(k + v + w)(2k + v + w - 2) P<sub>k</sub><sup>vw</sup>(X) = |
| (2k + v + w - 1)[(2k + v + w)(2k + v + w - 2) X + v<sup>2</sup> - w<sup>2</sup>] P<sub>k-1</sub><sup>vw</sup>(X) |
| - 2(k + v - 1)(k + w - 1)(2k + v + w) P<sub>k-2</sub><sup>vw</sup>(X) |
| </pre></p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>degree</code> - degree of the polynomial</dd><dd><code>v</code> - first exponent</dd><dd><code>w</code> - second exponent</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>Jacobi polynomial of specified degree</dd></dl> |
| </li> |
| </ul> |
| <a name="shift(double[], double)"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>shift</h4> |
| <pre>public static double[] shift(double[] coefficients, |
| double shift)</pre> |
| <div class="block">Compute the coefficients of the polynomial <code>P<sub>s</sub>(x)</code> |
| whose values at point <code>x</code> will be the same as the those from the |
| original polynomial <code>P(x)</code> when computed at <code>x + shift</code>. |
| Thus, if <code>P(x) = Σ<sub>i</sub> a<sub>i</sub> x<sup>i</sup></code>, |
| then |
| <pre> |
| <table> |
| <tr> |
| <td><code>P<sub>s</sub>(x)</td> |
| <td>= Σ<sub>i</sub> b<sub>i</sub> x<sup>i</sup></code></td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>= Σ<sub>i</sub> a<sub>i</sub> (x + shift)<sup>i</sup></code></td> |
| </tr> |
| </table> |
| </pre></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>coefficients</code> - Coefficients of the original polynomial.</dd><dd><code>shift</code> - Shift value.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the coefficients <code>b<sub>i</sub></code> of the shifted |
| polynomial.</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/PolynomialsUtils.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/analysis/polynomials/PolynomialSplineFunction.html" title="class in org.apache.commons.math3.analysis.polynomials"><span class="strong">Prev Class</span></a></li> |
| <li>Next Class</li> |
| </ul> |
| <ul class="navList"> |
| <li><a href="../../../../../../index.html?org/apache/commons/math3/analysis/polynomials/PolynomialsUtils.html" target="_top">Frames</a></li> |
| <li><a href="PolynomialsUtils.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>Constr | </li> |
| <li><a href="#method_summary">Method</a></li> |
| </ul> |
| <ul class="subNavList"> |
| <li>Detail: </li> |
| <li>Field | </li> |
| <li>Constr | </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> |
