AdamsIntegrator.java

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 * 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.
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package org.apache.commons.math3.ode.nonstiff;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.apache.commons.math3.ode.ExpandableStatefulODE;
import org.apache.commons.math3.ode.MultistepIntegrator;


/** Base class for {@link AdamsBashforthIntegrator Adams-Bashforth} and
 * {@link AdamsMoultonIntegrator Adams-Moulton} integrators.
 * @since 2.0
 */
public abstract class AdamsIntegrator extends MultistepIntegrator {

    /** Transformer. */
    private final AdamsNordsieckTransformer transformer;

    /**
     * Build an Adams integrator with the given order and step control parameters.
     * @param name name of the method
     * @param nSteps number of steps of the method excluding the one being computed
     * @param order order of the method
     * @param minStep minimal step (sign is irrelevant, regardless of
     * integration direction, forward or backward), the last step can
     * be smaller than this
     * @param maxStep maximal step (sign is irrelevant, regardless of
     * integration direction, forward or backward), the last step can
     * be smaller than this
     * @param scalAbsoluteTolerance allowed absolute error
     * @param scalRelativeTolerance allowed relative error
     * @exception NumberIsTooSmallException if order is 1 or less
     */
    public AdamsIntegrator(final String name, final int nSteps, final int order,
                           final double minStep, final double maxStep,
                           final double scalAbsoluteTolerance,
                           final double scalRelativeTolerance)
        throws NumberIsTooSmallException {
        super(name, nSteps, order, minStep, maxStep,
              scalAbsoluteTolerance, scalRelativeTolerance);
        transformer = AdamsNordsieckTransformer.getInstance(nSteps);
    }

    /**
     * Build an Adams integrator with the given order and step control parameters.
     * @param name name of the method
     * @param nSteps number of steps of the method excluding the one being computed
     * @param order order of the method
     * @param minStep minimal step (sign is irrelevant, regardless of
     * integration direction, forward or backward), the last step can
     * be smaller than this
     * @param maxStep maximal step (sign is irrelevant, regardless of
     * integration direction, forward or backward), the last step can
     * be smaller than this
     * @param vecAbsoluteTolerance allowed absolute error
     * @param vecRelativeTolerance allowed relative error
     * @exception IllegalArgumentException if order is 1 or less
     */
    public AdamsIntegrator(final String name, final int nSteps, final int order,
                           final double minStep, final double maxStep,
                           final double[] vecAbsoluteTolerance,
                           final double[] vecRelativeTolerance)
        throws IllegalArgumentException {
        super(name, nSteps, order, minStep, maxStep,
              vecAbsoluteTolerance, vecRelativeTolerance);
        transformer = AdamsNordsieckTransformer.getInstance(nSteps);
    }

    /** {@inheritDoc} */
    @Override
    public abstract void integrate(final ExpandableStatefulODE equations, final double t)
        throws NumberIsTooSmallException, DimensionMismatchException,
               MaxCountExceededException, NoBracketingException;

    /** {@inheritDoc} */
    @Override
    protected Array2DRowRealMatrix initializeHighOrderDerivatives(final double h, final double[] t,
                                                                  final double[][] y,
                                                                  final double[][] yDot) {
        return transformer.initializeHighOrderDerivatives(h, t, y, yDot);
    }

    /** Update the high order scaled derivatives for Adams integrators (phase 1).
     * <p>The complete update of high order derivatives has a form similar to:
     * <pre>
     * r<sub>n+1</sub> = (s<sub>1</sub>(n) - s<sub>1</sub>(n+1)) P<sup>-1</sup> u + P<sup>-1</sup> A P r<sub>n</sub>
     * </pre>
     * this method computes the P<sup>-1</sup> A P r<sub>n</sub> part.</p>
     * @param highOrder high order scaled derivatives
     * (h<sup>2</sup>/2 y'', ... h<sup>k</sup>/k! y(k))
     * @return updated high order derivatives
     * @see #updateHighOrderDerivativesPhase2(double[], double[], Array2DRowRealMatrix)
     */
    public Array2DRowRealMatrix updateHighOrderDerivativesPhase1(final Array2DRowRealMatrix highOrder) {
        return transformer.updateHighOrderDerivativesPhase1(highOrder);
    }

    /** Update the high order scaled derivatives Adams integrators (phase 2).
     * <p>The complete update of high order derivatives has a form similar to:
     * <pre>
     * r<sub>n+1</sub> = (s<sub>1</sub>(n) - s<sub>1</sub>(n+1)) P<sup>-1</sup> u + P<sup>-1</sup> A P r<sub>n</sub>
     * </pre>
     * this method computes the (s<sub>1</sub>(n) - s<sub>1</sub>(n+1)) P<sup>-1</sup> u part.</p>
     * <p>Phase 1 of the update must already have been performed.</p>
     * @param start first order scaled derivatives at step start
     * @param end first order scaled derivatives at step end
     * @param highOrder high order scaled derivatives, will be modified
     * (h<sup>2</sup>/2 y'', ... h<sup>k</sup>/k! y(k))
     * @see #updateHighOrderDerivativesPhase1(Array2DRowRealMatrix)
     */
    public void updateHighOrderDerivativesPhase2(final double[] start,
                                                 final double[] end,
                                                 final Array2DRowRealMatrix highOrder) {
        transformer.updateHighOrderDerivativesPhase2(start, end, highOrder);
    }

}