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<h2 title="Class PolynomialSplineFunction" class="title">Class PolynomialSplineFunction</h2>
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<li>org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction</li>
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<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/analysis/DifferentiableUnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">DifferentiableUnivariateFunction</a>, <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>
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<pre>public class <span class="strong">PolynomialSplineFunction</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>
implements <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/DifferentiableUnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">DifferentiableUnivariateFunction</a></pre>
<div class="block">Represents a polynomial spline function.
<p>
A <strong>polynomial spline function</strong> consists of a set of
<i>interpolating polynomials</i> and an ascending array of domain
<i>knot points</i>, determining the intervals over which the spline function
is defined by the constituent polynomials. The polynomials are assumed to
have been computed to match the values of another function at the knot
points. The value consistency constraints are not currently enforced by
<code>PolynomialSplineFunction</code> itself, but are assumed to hold among
the polynomials and knot points passed to the constructor.</p>
<p>
N.B.: The polynomials in the <code>polynomials</code> property must be
centered on the knot points to compute the spline function values.
See below.</p>
<p>
The domain of the polynomial spline function is
<code>[smallest knot, largest knot]</code>. Attempts to evaluate the
function at values outside of this range generate IllegalArgumentExceptions.
</p>
<p>
The value of the polynomial spline function for an argument <code>x</code>
is computed as follows:
<ol>
<li>The knot array is searched to find the segment to which <code>x</code>
belongs. If <code>x</code> is less than the smallest knot point or greater
than the largest one, an <code>IllegalArgumentException</code>
is thrown.</li>
<li> Let <code>j</code> be the index of the largest knot point that is less
than or equal to <code>x</code>. The value returned is
<code>polynomials[j](x - knot[j])</code></li></ol></div>
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<th class="colOne" scope="col">Constructor and Description</th>
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<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.html#PolynomialSplineFunction(double[],%20org.apache.commons.math3.analysis.polynomials.PolynomialFunction[])">PolynomialSplineFunction</a></strong>(double[] knots,
<a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a>[] polynomials)</code>
<div class="block">Construct a polynomial spline function with the given segment delimiters
and interpolating polynomials.</div>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.html#derivative()">derivative</a></strong>()</code>
<div class="block">Get the derivative of the polynomial spline 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/PolynomialSplineFunction.html#getKnots()">getKnots</a></strong>()</code>
<div class="block">Get an array copy of the knot points.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.html#getN()">getN</a></strong>()</code>
<div class="block">Get the number of spline segments.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><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/PolynomialSplineFunction.html#getPolynomials()">getPolynomials</a></strong>()</code>
<div class="block">Get a copy of the interpolating polynomials array.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.html#isValidPoint(double)">isValidPoint</a></strong>(double x)</code>
<div class="block">Indicates whether a point is within the interpolation range.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialSplineFunction</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.html#polynomialSplineDerivative()">polynomialSplineDerivative</a></strong>()</code>
<div class="block">Get the derivative of the polynomial spline function.</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/PolynomialSplineFunction.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/PolynomialSplineFunction.html#value(double)">value</a></strong>(double v)</code>
<div class="block">Compute the value for the function.</div>
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<h3>Constructor Detail</h3>
<a name="PolynomialSplineFunction(double[], org.apache.commons.math3.analysis.polynomials.PolynomialFunction[])">
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<h4>PolynomialSplineFunction</h4>
<pre>public PolynomialSplineFunction(double[] knots,
<a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a>[] polynomials)
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/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</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/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></pre>
<div class="block">Construct a polynomial spline function with the given segment delimiters
and interpolating polynomials.
The constructor copies both arrays and assigns the copies to the knots
and polynomials properties, respectively.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>knots</code> - Spline segment interval delimiters.</dd><dd><code>polynomials</code> - Polynomial functions that make up the spline.</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 either of the input arrays is <code>null</code>.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if knots has length less than 2.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>polynomials.length != knots.length - 1</code>.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></code> - if the <code>knots</code> array is not strictly increasing.</dd></dl>
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<h3>Method Detail</h3>
<a name="value(double)">
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<h4>value</h4>
<pre>public double value(double v)</pre>
<div class="block">Compute the value for the function.
See <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.html" title="class in org.apache.commons.math3.analysis.polynomials"><code>PolynomialSplineFunction</code></a> for details on the algorithm for
computing the value of the function.</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>v</code> - Point for which the function value should be computed.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the value.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if <code>v</code> is outside of the domain of the
spline function (smaller than the smallest knot point or larger than the
largest knot point).</dd></dl>
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<a name="derivative()">
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<h4>derivative</h4>
<pre>public <a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a> derivative()</pre>
<div class="block">Get the derivative of the polynomial spline function.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/analysis/DifferentiableUnivariateFunction.html#derivative()">derivative</a></code> in interface <code><a href="../../../../../../org/apache/commons/math3/analysis/DifferentiableUnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">DifferentiableUnivariateFunction</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>the derivative function.</dd></dl>
</li>
</ul>
<a name="polynomialSplineDerivative()">
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<h4>polynomialSplineDerivative</h4>
<pre>public <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialSplineFunction</a> polynomialSplineDerivative()</pre>
<div class="block">Get the derivative of the polynomial spline function.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the derivative function.</dd></dl>
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<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>
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<a name="getN()">
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<h4>getN</h4>
<pre>public int getN()</pre>
<div class="block">Get the number of spline segments.
It is also the number of polynomials and the number of knot points - 1.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the number of spline segments.</dd></dl>
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<h4>getPolynomials</h4>
<pre>public <a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html" title="class in org.apache.commons.math3.analysis.polynomials">PolynomialFunction</a>[] getPolynomials()</pre>
<div class="block">Get a copy of the interpolating polynomials array.
It returns a fresh copy of the array. Changes made to the copy will
not affect the polynomials property.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the interpolating polynomials.</dd></dl>
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<h4>getKnots</h4>
<pre>public double[] getKnots()</pre>
<div class="block">Get an array copy of the knot points.
It returns a fresh copy of the array. Changes made to the copy
will not affect the knots property.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the knot points.</dd></dl>
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<h4>isValidPoint</h4>
<pre>public boolean isValidPoint(double x)</pre>
<div class="block">Indicates whether a point is within the interpolation range.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Point.</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>true</code> if <code>x</code> is a valid point.</dd></dl>
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