logic.ApacheInterpolation.java Source code

Introduction

Here is the source code for logic.ApacheInterpolation.java

Source

/*
 * 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 logic;

import java.io.Serializable;
import java.math.BigInteger;
import java.util.ArrayList;

import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.interpolation.UnivariateInterpolator;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunctionNewtonForm;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;

import utility.Node;

/**
 * Implements the <a href="
 * http://mathworld.wolfram.com/NewtonsDividedDifferenceInterpolationFormula.html">
 * Divided Difference Algorithm</a> for interpolation of real univariate
 * functions. For reference, see <b>Introduction to Numerical Analysis</b>,
 * ISBN 038795452X, chapter 2.
 * <p>
 * The actual code of Neville's evaluation is in PolynomialFunctionLagrangeForm,
 * this class provides an easy-to-use interface to it.</p>
 *
 * @since 1.2
 * 
 * Note the original source code licensed to Apache, this is just a modification version for my system.
 */
public class ApacheInterpolation implements UnivariateInterpolator, Serializable {
    /** serializable version identifier */
    private static final long serialVersionUID = 107049519551235069L;

    /**
     * Compute an interpolating function for the dataset.
     *
     * @param x Interpolating points array.
     * @param y Interpolating values array.
     * @return a function which interpolates the dataset.
     * @throws DimensionMismatchException if the array lengths are different.
     * @throws NumberIsTooSmallException if the number of points is less than 2.
     * @throws NonMonotonicSequenceException if {@code x} is not sorted in
     * strictly increasing order.
     */
    public ApachePolyNewtonForm interpolate(ArrayList<Node> node_list)
            throws DimensionMismatchException, NumberIsTooSmallException, NonMonotonicSequenceException {
        /**
         * a[] and c[] are defined in the general formula of Newton form:
         * 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])
         */
        //         No need to check, the condition is fulfilled by default
        //        PolynomialFunctionLagrangeForm.verifyInterpolationArray(x, y, true);

        /**
         * When used for interpolation, the Newton form formula becomes
         * p(x) = f[x0] + f[x0,x1](x-x0) + f[x0,x1,x2](x-x0)(x-x1) + ... +
         *        f[x0,x1,...,x[n-1]](x-x0)(x-x1)...(x-x[n-2])
         * Therefore, a[k] = f[x0,x1,...,xk], c[k] = x[k].
         * <p>
         * Note x[], y[], a[] have the same length but c[]'s size is one less.</p>
         */
        double[] x = new double[node_list.size()];
        BigInteger[] y = new BigInteger[node_list.size()];
        for (int i = 0; i < node_list.size(); i++) {
            x[i] = node_list.get(i).getX();
            y[i] = node_list.get(i).getY();
        }
        final double[] c = new double[x.length - 1];
        System.arraycopy(x, 0, c, 0, c.length);

        final BigInteger[] a = computeDividedDifference(x, y);
        return new ApachePolyNewtonForm(a, c);
    }

    /**
     * Return a copy of the divided difference array.
     * <p>
     * The divided difference array is defined recursively by <pre>
     * f[x0] = f(x0)
     * f[x0,x1,...,xk] = (f[x1,...,xk] - f[x0,...,x[k-1]]) / (xk - x0)
     * </pre></p>
     * <p>
     * The computational complexity is O(N^2).</p>
     *
     * @param x Interpolating points array.
     * @param y Interpolating values array.
     * @return a fresh copy of the divided difference array.
     * @throws DimensionMismatchException if the array lengths are different.
     * @throws NumberIsTooSmallException if the number of points is less than 2.
     * @throws NonMonotonicSequenceException
     * if {@code x} is not sorted in strictly increasing order.
     */
    protected static BigInteger[] computeDividedDifference(final double x[], final BigInteger y[])
            throws DimensionMismatchException, NumberIsTooSmallException, NonMonotonicSequenceException {

        //        No need to check, the condition must be valid according to the paper
        //        PolynomialFunctionLagrangeForm.verifyInterpolationArray(x, y, true);

        final BigInteger[] divdiff = y.clone(); // initialization

        final int n = x.length;
        final BigInteger[] a = new BigInteger[n];
        a[0] = divdiff[0];
        for (int i = 1; i < n; i++) {
            for (int j = 0; j < n - i; j++) {
                final BigInteger denominator = BigInteger.valueOf((long) (x[j + i] - x[j]));
                divdiff[j] = (divdiff[j + 1].subtract(divdiff[j])).divide(denominator);
            }
            a[i] = divdiff[0];
        }

        return a;
    }

    @Override
    public UnivariateFunction interpolate(double[] arg0, double[] arg1)
            throws MathIllegalArgumentException, DimensionMismatchException {
        // TODO Auto-generated method stub
        return null;
    }
}