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Diffstat (limited to 'src/main/java/org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.java')
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diff --git a/src/main/java/org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.java b/src/main/java/org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.java new file mode 100644 index 0000000..ed5a4f9 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/analysis/polynomials/PolynomialSplineFunction.java @@ -0,0 +1,246 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * 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, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +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; + } + } +} |