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| <div class="subTitle">org.apache.commons.math3.analysis.polynomials</div> |
| <h2 title="Class PolynomialFunctionNewtonForm" class="title">Class PolynomialFunctionNewtonForm</h2> |
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| <li>org.apache.commons.math3.analysis.polynomials.PolynomialFunctionNewtonForm</li> |
| </ul> |
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| <dt>All Implemented Interfaces:</dt> |
| <dd><a href="../../../../../../org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.html" title="interface in org.apache.commons.math3.analysis.differentiation">UnivariateDifferentiableFunction</a>, <a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></dd> |
| </dl> |
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| <br> |
| <pre>public class <span class="strong">PolynomialFunctionNewtonForm</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> |
| implements <a href="../../../../../../org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.html" title="interface in org.apache.commons.math3.analysis.differentiation">UnivariateDifferentiableFunction</a></pre> |
| <div class="block">Implements the representation of a real polynomial function in |
| Newton Form. For reference, see <b>Elementary Numerical Analysis</b>, |
| ISBN 0070124477, chapter 2. |
| <p> |
| The formula of polynomial in Newton form is |
| p(x) = a[0] + a[1](x-c[0]) + a[2](x-c[0])(x-c[1]) + ... + |
| a[n](x-c[0])(x-c[1])...(x-c[n-1]) |
| Note that the length of a[] is one more than the length of c[]</p></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>1.2</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: PolynomialFunctionNewtonForm.java 1455194 2013-03-11 15:45:54Z luc $</dd></dl> |
| </li> |
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| <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/analysis/polynomials/PolynomialFunctionNewtonForm.html#PolynomialFunctionNewtonForm(double[], double[])">PolynomialFunctionNewtonForm</a></strong>(double[] a, |
| double[] c)</code> |
| <div class="block">Construct a Newton polynomial with the given a[] and c[].</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
| </ul> |
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| <caption><span>Methods</span><span class="tabEnd"> </span></caption> |
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| <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>protected void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#computeCoefficients()">computeCoefficients</a></strong>()</code> |
| <div class="block">Calculate the normal polynomial coefficients given the Newton form.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>int</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#degree()">degree</a></strong>()</code> |
| <div class="block">Returns the degree of the polynomial.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#evaluate(double[], double[], double)">evaluate</a></strong>(double[] a, |
| double[] c, |
| double z)</code> |
| <div class="block">Evaluate the Newton polynomial using nested multiplication.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#getCenters()">getCenters</a></strong>()</code> |
| <div class="block">Returns a copy of the centers array.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#getCoefficients()">getCoefficients</a></strong>()</code> |
| <div class="block">Returns a copy of the coefficients array.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double[]</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#getNewtonCoefficients()">getNewtonCoefficients</a></strong>()</code> |
| <div class="block">Returns a copy of coefficients in Newton form formula.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/analysis/differentiation/DerivativeStructure.html" title="class in org.apache.commons.math3.analysis.differentiation">DerivativeStructure</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#value(org.apache.commons.math3.analysis.differentiation.DerivativeStructure)">value</a></strong>(<a href="../../../../../../org/apache/commons/math3/analysis/differentiation/DerivativeStructure.html" title="class in org.apache.commons.math3.analysis.differentiation">DerivativeStructure</a> t)</code> |
| <div class="block">Simple mathematical function.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#value(double)">value</a></strong>(double z)</code> |
| <div class="block">Calculate the function value at the given point.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>protected static void</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#verifyInputArray(double[], double[])">verifyInputArray</a></strong>(double[] a, |
| double[] c)</code> |
| <div class="block">Verifies that the input arrays are valid.</div> |
| </td> |
| </tr> |
| </table> |
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| <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="PolynomialFunctionNewtonForm(double[], double[])"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>PolynomialFunctionNewtonForm</h4> |
| <pre>public PolynomialFunctionNewtonForm(double[] a, |
| double[] c) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre> |
| <div class="block">Construct a Newton polynomial with the given a[] and c[]. The order of |
| centers are important in that if c[] shuffle, then values of a[] would |
| completely change, not just a permutation of old a[]. |
| <p> |
| The constructor makes copy of the input arrays and assigns them.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - Coefficients in Newton form formula.</dd><dd><code>c</code> - Centers.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if any argument is <code>null</code>.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if any array has zero length.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the size difference between |
| <code>a</code> and <code>c</code> is not equal to 1.</dd></dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| <!-- ============ METHOD DETAIL ========== --> |
| <ul class="blockList"> |
| <li class="blockList"><a name="method_detail"> |
| <!-- --> |
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| <h3>Method Detail</h3> |
| <a name="value(double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>value</h4> |
| <pre>public double value(double z)</pre> |
| <div class="block">Calculate the function value at the given point.</div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html#value(double)">value</a></code> in interface <code><a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>z</code> - Point at which the function value is to be computed.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the function value.</dd></dl> |
| </li> |
| </ul> |
| <a name="value(org.apache.commons.math3.analysis.differentiation.DerivativeStructure)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>value</h4> |
| <pre>public <a href="../../../../../../org/apache/commons/math3/analysis/differentiation/DerivativeStructure.html" title="class in org.apache.commons.math3.analysis.differentiation">DerivativeStructure</a> value(<a href="../../../../../../org/apache/commons/math3/analysis/differentiation/DerivativeStructure.html" title="class in org.apache.commons.math3.analysis.differentiation">DerivativeStructure</a> t)</pre> |
| <div class="block">Simple mathematical function. |
| <p><a href="../../../../../../org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.html" title="interface in org.apache.commons.math3.analysis.differentiation"><code>UnivariateDifferentiableFunction</code></a> classes compute both the |
| value and the first derivative of the function.</p></div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.html#value(org.apache.commons.math3.analysis.differentiation.DerivativeStructure)">value</a></code> in interface <code><a href="../../../../../../org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.html" title="interface in org.apache.commons.math3.analysis.differentiation">UnivariateDifferentiableFunction</a></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>t</code> - function input value</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>function result</dd><dt><span class="strong">Since:</span></dt> |
| <dd>3.1</dd></dl> |
| </li> |
| </ul> |
| <a name="degree()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>degree</h4> |
| <pre>public int degree()</pre> |
| <div class="block">Returns the degree of the polynomial.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the degree of the polynomial</dd></dl> |
| </li> |
| </ul> |
| <a name="getNewtonCoefficients()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getNewtonCoefficients</h4> |
| <pre>public double[] getNewtonCoefficients()</pre> |
| <div class="block">Returns a copy of coefficients in Newton form formula. |
| <p> |
| Changes made to the returned copy will not affect the polynomial.</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>a fresh copy of coefficients in Newton form formula</dd></dl> |
| </li> |
| </ul> |
| <a name="getCenters()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getCenters</h4> |
| <pre>public double[] getCenters()</pre> |
| <div class="block">Returns a copy of the centers array. |
| <p> |
| Changes made to the returned copy will not affect the polynomial.</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>a fresh copy of the centers array.</dd></dl> |
| </li> |
| </ul> |
| <a name="getCoefficients()"> |
| <!-- --> |
| </a> |
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| <h4>getCoefficients</h4> |
| <pre>public double[] getCoefficients()</pre> |
| <div class="block">Returns a copy of the coefficients array. |
| <p> |
| Changes made to the returned copy will not affect the polynomial.</p></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>a fresh copy of the coefficients array.</dd></dl> |
| </li> |
| </ul> |
| <a name="evaluate(double[], double[], double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>evaluate</h4> |
| <pre>public static double evaluate(double[] a, |
| double[] c, |
| double z) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></pre> |
| <div class="block">Evaluate the Newton polynomial using nested multiplication. It is |
| also called <a href="http://mathworld.wolfram.com/HornersRule.html"> |
| Horner's Rule</a> and takes O(N) time.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - Coefficients in Newton form formula.</dd><dd><code>c</code> - Centers.</dd><dd><code>z</code> - Point at which the function value is to be computed.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the function value.</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if any argument is <code>null</code>.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if any array has zero length.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the size difference between |
| <code>a</code> and <code>c</code> is not equal to 1.</dd></dl> |
| </li> |
| </ul> |
| <a name="computeCoefficients()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>computeCoefficients</h4> |
| <pre>protected void computeCoefficients()</pre> |
| <div class="block">Calculate the normal polynomial coefficients given the Newton form. |
| It also uses nested multiplication but takes O(N^2) time.</div> |
| </li> |
| </ul> |
| <a name="verifyInputArray(double[], double[])"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>verifyInputArray</h4> |
| <pre>protected static void verifyInputArray(double[] a, |
| double[] c) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>, |
| <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre> |
| <div class="block">Verifies that the input arrays are valid. |
| <p> |
| The centers must be distinct for interpolation purposes, but not |
| for general use. Thus it is not verified here.</p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - the coefficients in Newton form formula</dd><dd><code>c</code> - the centers</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if any argument is <code>null</code>.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if any array has zero length.</dd> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the size difference between |
| <code>a</code> and <code>c</code> is not equal to 1.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/DividedDifferenceInterpolator.html#computeDividedDifference(double[], double[])"><code>DividedDifferenceInterpolator.computeDividedDifference(double[], |
| double[])</code></a></dd></dl> |
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