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Java example source code file (AdamsFieldStepInterpolator.java)

This example Java source code file (AdamsFieldStepInterpolator.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.

Learn more about this Java project at its project page.

Java - Java tags/keywords

abstractfieldstepinterpolator, adamsfieldstepinterpolator, array2drowfieldmatrix, fieldequationsmapper, fieldodestateandderivative, override, realfieldelement, util

The AdamsFieldStepInterpolator.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 java.util.Arrays;

import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.linear.Array2DRowFieldMatrix;
import org.apache.commons.math3.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.ode.sampling.AbstractFieldStepInterpolator;
import org.apache.commons.math3.util.MathArrays;

/**
 * This class implements an interpolator for Adams integrators using Nordsieck representation.
 *
 * <p>This interpolator computes dense output around the current point.
 * The interpolation equation is based on Taylor series formulas.
 *
 * @see AdamsBashforthFieldIntegrator
 * @see AdamsMoultonFieldIntegrator
 * @param <T> the type of the field elements
 * @since 3.6
 */

class AdamsFieldStepInterpolator<T extends RealFieldElement extends AbstractFieldStepInterpolator {

    /** Step size used in the first scaled derivative and Nordsieck vector. */
    private T scalingH;

    /** Reference state.
     * <p>Sometimes, the reference state is the same as globalPreviousState,
     * sometimes it is the same as globalCurrentState, so we use a separate
     * field to avoid any confusion.
     * </p>
     */
    private final FieldODEStateAndDerivative<T> reference;

    /** First scaled derivative. */
    private final T[] scaled;

    /** Nordsieck vector. */
    private final Array2DRowFieldMatrix<T> nordsieck;

    /** Simple constructor.
     * @param stepSize step size used in the scaled and Nordsieck arrays
     * @param reference reference state from which Taylor expansion are estimated
     * @param scaled first scaled derivative
     * @param nordsieck Nordsieck vector
     * @param isForward integration direction indicator
     * @param globalPreviousState start of the global step
     * @param globalCurrentState end of the global step
     * @param equationsMapper mapper for ODE equations primary and secondary components
     */
    AdamsFieldStepInterpolator(final T stepSize, final FieldODEStateAndDerivative<T> reference,
                               final T[] scaled, final Array2DRowFieldMatrix<T> nordsieck,
                               final boolean isForward,
                               final FieldODEStateAndDerivative<T> globalPreviousState,
                               final FieldODEStateAndDerivative<T> globalCurrentState,
                               final FieldEquationsMapper<T> equationsMapper) {
        this(stepSize, reference, scaled, nordsieck,
             isForward, globalPreviousState, globalCurrentState,
             globalPreviousState, globalCurrentState, equationsMapper);
    }

    /** Simple constructor.
     * @param stepSize step size used in the scaled and Nordsieck arrays
     * @param reference reference state from which Taylor expansion are estimated
     * @param scaled first scaled derivative
     * @param nordsieck Nordsieck vector
     * @param isForward integration direction indicator
     * @param globalPreviousState start of the global step
     * @param globalCurrentState end of the global step
     * @param softPreviousState start of the restricted step
     * @param softCurrentState end of the restricted step
     * @param equationsMapper mapper for ODE equations primary and secondary components
     */
    private AdamsFieldStepInterpolator(final T stepSize, final FieldODEStateAndDerivative<T> reference,
                                       final T[] scaled, final Array2DRowFieldMatrix<T> nordsieck,
                                       final boolean isForward,
                                       final FieldODEStateAndDerivative<T> globalPreviousState,
                                       final FieldODEStateAndDerivative<T> globalCurrentState,
                                       final FieldODEStateAndDerivative<T> softPreviousState,
                                       final FieldODEStateAndDerivative<T> softCurrentState,
                                       final FieldEquationsMapper<T> equationsMapper) {
        super(isForward, globalPreviousState, globalCurrentState,
              softPreviousState, softCurrentState, equationsMapper);
        this.scalingH  = stepSize;
        this.reference = reference;
        this.scaled    = scaled.clone();
        this.nordsieck = new Array2DRowFieldMatrix<T>(nordsieck.getData(), false);
    }

    /** Create a new instance.
     * @param newForward integration direction indicator
     * @param newGlobalPreviousState start of the global step
     * @param newGlobalCurrentState end of the global step
     * @param newSoftPreviousState start of the restricted step
     * @param newSoftCurrentState end of the restricted step
     * @param newMapper equations mapper for the all equations
     * @return a new instance
     */
    @Override
    protected AdamsFieldStepInterpolator<T> create(boolean newForward,
                                                   FieldODEStateAndDerivative<T> newGlobalPreviousState,
                                                   FieldODEStateAndDerivative<T> newGlobalCurrentState,
                                                   FieldODEStateAndDerivative<T> newSoftPreviousState,
                                                   FieldODEStateAndDerivative<T> newSoftCurrentState,
                                                   FieldEquationsMapper<T> newMapper) {
        return new AdamsFieldStepInterpolator<T>(scalingH, reference, scaled, nordsieck,
                                                 newForward,
                                                 newGlobalPreviousState, newGlobalCurrentState,
                                                 newSoftPreviousState, newSoftCurrentState,
                                                 newMapper);

    }

    /** {@inheritDoc} */
    @Override
    protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper equationsMapper,
                                                                                   final T time, final T theta,
                                                                                   final T thetaH, final T oneMinusThetaH) {
        return taylor(reference, time, scalingH, scaled, nordsieck);
    }

    /** Estimate state by applying Taylor formula.
     * @param reference reference state
     * @param time time at which state must be estimated
     * @param stepSize step size used in the scaled and Nordsieck arrays
     * @param scaled first scaled derivative
     * @param nordsieck Nordsieck vector
     * @return estimated state
     * @param <S> the type of the field elements
     */
    public static <S extends RealFieldElement FieldODEStateAndDerivative taylor(final FieldODEStateAndDerivative reference,
                                                                                       final S time, final S stepSize,
                                                                                       final S[] scaled,
                                                                                       final Array2DRowFieldMatrix<S> nordsieck) {

        final S x = time.subtract(reference.getTime());
        final S normalizedAbscissa = x.divide(stepSize);

        S[] stateVariation = MathArrays.buildArray(time.getField(), scaled.length);
        Arrays.fill(stateVariation, time.getField().getZero());
        S[] estimatedDerivatives = MathArrays.buildArray(time.getField(), scaled.length);
        Arrays.fill(estimatedDerivatives, time.getField().getZero());

        // apply Taylor formula from high order to low order,
        // for the sake of numerical accuracy
        final S[][] nData = nordsieck.getDataRef();
        for (int i = nData.length - 1; i >= 0; --i) {
            final int order = i + 2;
            final S[] nDataI = nData[i];
            final S power = normalizedAbscissa.pow(order);
            for (int j = 0; j < nDataI.length; ++j) {
                final S d = nDataI[j].multiply(power);
                stateVariation[j]          = stateVariation[j].add(d);
                estimatedDerivatives[j] = estimatedDerivatives[j].add(d.multiply(order));
            }
        }

        S[] estimatedState = reference.getState();
        for (int j = 0; j < stateVariation.length; ++j) {
            stateVariation[j]    = stateVariation[j].add(scaled[j].multiply(normalizedAbscissa));
            estimatedState[j] = estimatedState[j].add(stateVariation[j]);
            estimatedDerivatives[j] =
                estimatedDerivatives[j].add(scaled[j].multiply(normalizedAbscissa)).divide(x);
        }

        return new FieldODEStateAndDerivative<S>(time, estimatedState, estimatedDerivatives);

    }

}

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