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Java example source code file (AdamsNordsieckTransformerTest.java)

This example Java source code file (AdamsNordsieckTransformerTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

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Java - Java tags/keywords

adamsnordsiecktransformer, adamsnordsiecktransformertest, array2drowrealmatrix, polynomialfunction, test, univariatefunction

The AdamsNordsieckTransformerTest.java Java example source code

/*
 * 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.ode.nonstiff;


import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.junit.Assert;
import org.junit.Test;

public class AdamsNordsieckTransformerTest {

    @Test
    public void testPolynomialExtraDerivative() {
        checkNordsieckStart(new PolynomialFunction(new double[] { 6, 5, 4, 3, 2, 1 }),
                            5, 0.0, 0.125, 3.2e-16);
    }

    @Test
    public void testPolynomialRegular() {
        checkNordsieckStart(new PolynomialFunction(new double[] { 6, 5, 4, 3, 2, 1 }),
                            4, 0.0, 0.125, 3.1e-16);
    }

    @Test
    public void testPolynomialMissingLastDerivative() {
        // this test intentionally uses not enough start points,
        // the Nordsieck vector is therefore not expected to match the exact scaled derivatives
        checkNordsieckStart(new PolynomialFunction(new double[] { 6, 5, 4, 3, 2, 1 }),
                            3, 0.0, 0.125, 1.6e-4);
    }

    @Test
    public void testTransformExact() {
        // a 5 steps transformer handles a degree 5 polynomial exactly
        // the Nordsieck vector holds the full information about the function
        // transforming the vector from t0 to t0+h or recomputing it from scratch
        // at t0+h yields the same result
        checkTransform(new PolynomialFunction(new double[] { 6, 5, 4, 3, 2, 1 }), 5, 2.567e-15);
    }

    @Test
    public void testTransformInexact() {
        // a 4 steps transformer cannot handle a degree 5 polynomial exactly
        // the Nordsieck vector lacks some high degree information about the function
        // transforming the vector from t0 to t0+h or recomputing it from scratch
        // at t0+h yields different results
        checkTransform(new PolynomialFunction(new double[] { 6, 5, 4, 3, 2, 1 }), 4, 5.658e-4);
    }

    private void checkNordsieckStart(final PolynomialFunction polynomial, final int nbSteps, final double t0,
                                     final double h, final double epsilon) {

        final AdamsNordsieckTransformer transformer = AdamsNordsieckTransformer.getInstance(nbSteps);
        PolynomialFunction derivative = polynomial.polynomialDerivative();
        final Array2DRowRealMatrix nordsieck = start(transformer, nbSteps, t0, h, polynomial, derivative);

        Assert.assertEquals(nbSteps - 1, nordsieck.getRowDimension());
        double coeff = h;
        for (int i = 0; i < nordsieck.getRowDimension(); ++i) {
            coeff *= h / (i + 2);
            derivative = derivative.polynomialDerivative();
            Assert.assertEquals(derivative.value(t0) * coeff, nordsieck.getEntry(i, 0), epsilon);
        }

    }

    private void checkTransform(final PolynomialFunction polynomial, final int nbSteps, final double expectedError) {

        final AdamsNordsieckTransformer transformer = AdamsNordsieckTransformer.getInstance(nbSteps);
        final PolynomialFunction derivative = polynomial.polynomialDerivative();

        final double t0 = 0.0;
        final double h  = 0.125;
        final Array2DRowRealMatrix n0 = start(transformer, nbSteps, t0, h, polynomial, derivative);
        final Array2DRowRealMatrix n1 = transformer.updateHighOrderDerivativesPhase1(n0);
        transformer.updateHighOrderDerivativesPhase2(new double[] { h * derivative.value(t0)     },
                                                     new double[] { h * derivative.value(t0 + h) },
                                                     n1);
        final Array2DRowRealMatrix n2 = start(transformer, nbSteps, t0 + h, h, polynomial, derivative);

        Assert.assertEquals(expectedError, n2.subtract(n1).getNorm(), expectedError * 0.001);

    }

    private Array2DRowRealMatrix start(final AdamsNordsieckTransformer transformer, final int nbSteps,
                                       final double t0, final double h,
                                       final UnivariateFunction f0, final UnivariateFunction f1) {

        final int        nbStartPoints = (nbSteps + 3) / 2;
        final double[]   t             = new double[nbStartPoints];
        final double[][] y             = new double[nbStartPoints][1];
        final double[][] yDot          = new double[nbStartPoints][1];
        for (int i = 0; i < nbStartPoints; ++i) {
            t[i]       = t0 + i * h;
            y[i][0]    = f0.value(t[i]);
            yDot[i][0] = f1.value(t[i]);
        }

        return transformer.initializeHighOrderDerivatives(h, t, y, yDot);

    }

}

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