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* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
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* See the License for the specific language governing permissions and
* limitations under the License.
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package org.apache.commons.math3.analysis.polynomials;
import java.util.Arrays;
import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.MathArrays;
/**
* 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])}</li></ol>
*
*/
public class PolynomialSplineFunction implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
/**
* Spline segment interval delimiters (knots).
* Size is n + 1 for n segments.
*/
private final double knots[];
/**
* The polynomial functions that make up the spline. The first element
* determines the value of the spline over the first subinterval, the
* second over the second, etc. Spline function values are determined by
* evaluating these functions at {@code (x - knot[i])} where i is the
* knot segment to which x belongs.
*/
private final PolynomialFunction polynomials[];
/**
* Number of spline segments. It is equal to the number of polynomials and
* to the number of partition points - 1.
*/
private final int n;
/**
* 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.
*
* @param knots Spline segment interval delimiters.
* @param polynomials Polynomial functions that make up the spline.
* @throws NullArgumentException if either of the input arrays is {@code null}.
* @throws NumberIsTooSmallException if knots has length less than 2.
* @throws DimensionMismatchException if {@code polynomials.length != knots.length - 1}.
* @throws NonMonotonicSequenceException if the {@code knots} array is not strictly increasing.
*
*/
public PolynomialSplineFunction(double knots[], PolynomialFunction polynomials[])
throws NullArgumentException, NumberIsTooSmallException,
DimensionMismatchException, NonMonotonicSequenceException{
if (knots == null ||
polynomials == null) {
throw new NullArgumentException();
}
if (knots.length < 2) {
throw new NumberIsTooSmallException(LocalizedFormats.NOT_ENOUGH_POINTS_IN_SPLINE_PARTITION,
2, knots.length, false);
}
if (knots.length - 1 != polynomials.length) {
throw new DimensionMismatchException(polynomials.length, knots.length);
}
MathArrays.checkOrder(knots);
this.n = knots.length -1;
this.knots = new double[n + 1];
System.arraycopy(knots, 0, this.knots, 0, n + 1);
this.polynomials = new PolynomialFunction[n];
System.arraycopy(polynomials, 0, this.polynomials, 0, n);
}
/**
* Compute the value for the function.
* See {@link PolynomialSplineFunction} for details on the algorithm for
* computing the value of the function.
*
* @param v Point for which the function value should be computed.
* @return the value.
* @throws OutOfRangeException if {@code v} is outside of the domain of the
* spline function (smaller than the smallest knot point or larger than the
* largest knot point).
*/
public double value(double v) {
if (v < knots[0] || v > knots[n]) {
throw new OutOfRangeException(v, knots[0], knots[n]);
}
int i = Arrays.binarySearch(knots, v);
if (i < 0) {
i = -i - 2;
}
// This will handle the case where v is the last knot value
// There are only n-1 polynomials, so if v is the last knot
// then we will use the last polynomial to calculate the value.
if ( i >= polynomials.length ) {
i--;
}
return polynomials[i].value(v - knots[i]);
}
/**
* Get the derivative of the polynomial spline function.
*
* @return the derivative function.
*/
public UnivariateFunction derivative() {
return polynomialSplineDerivative();
}
/**
* Get the derivative of the polynomial spline function.
*
* @return the derivative function.
*/
public PolynomialSplineFunction polynomialSplineDerivative() {
PolynomialFunction derivativePolynomials[] = new PolynomialFunction[n];
for (int i = 0; i < n; i++) {
derivativePolynomials[i] = polynomials[i].polynomialDerivative();
}
return new PolynomialSplineFunction(knots, derivativePolynomials);
}
/** {@inheritDoc}
* @since 3.1
*/
public DerivativeStructure value(final DerivativeStructure t) {
final double t0 = t.getValue();
if (t0 < knots[0] || t0 > knots[n]) {
throw new OutOfRangeException(t0, knots[0], knots[n]);
}
int i = Arrays.binarySearch(knots, t0);
if (i < 0) {
i = -i - 2;
}
// This will handle the case where t is the last knot value
// There are only n-1 polynomials, so if t is the last knot
// then we will use the last polynomial to calculate the value.
if ( i >= polynomials.length ) {
i--;
}
return polynomials[i].value(t.subtract(knots[i]));
}
/**
* Get the number of spline segments.
* It is also the number of polynomials and the number of knot points - 1.
*
* @return the number of spline segments.
*/
public int getN() {
return n;
}
/**
* 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.
*
* @return the interpolating polynomials.
*/
public PolynomialFunction[] getPolynomials() {
PolynomialFunction p[] = new PolynomialFunction[n];
System.arraycopy(polynomials, 0, p, 0, n);
return p;
}
/**
* 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.
*
* @return the knot points.
*/
public double[] getKnots() {
double out[] = new double[n + 1];
System.arraycopy(knots, 0, out, 0, n + 1);
return out;
}
/**
* Indicates whether a point is within the interpolation range.
*
* @param x Point.
* @return {@code true} if {@code x} is a valid point.
*/
public boolean isValidPoint(double x) {
if (x < knots[0] ||
x > knots[n]) {
return false;
} else {
return true;
}
}
}