| /* |
| * 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.math4.legacy.analysis.polynomials; |
| |
| import java.util.Arrays; |
| |
| import org.apache.commons.math4.legacy.analysis.differentiation.DerivativeStructure; |
| import org.apache.commons.math4.legacy.analysis.differentiation.UnivariateDifferentiableFunction; |
| import org.apache.commons.math4.legacy.exception.DimensionMismatchException; |
| import org.apache.commons.math4.legacy.exception.NonMonotonicSequenceException; |
| import org.apache.commons.math4.legacy.exception.NullArgumentException; |
| import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException; |
| import org.apache.commons.math4.legacy.exception.OutOfRangeException; |
| import org.apache.commons.math4.legacy.exception.util.LocalizedFormats; |
| import org.apache.commons.math4.legacy.core.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 { |
| /** |
| * 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, |
| knots.length, 2, true); |
| } |
| 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). |
| */ |
| @Override |
| 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 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 |
| */ |
| @Override |
| 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) { |
| return !(x < knots[0] || |
| x > knots[n]); |
| } |
| } |