| /* |
| * 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.ode.sampling; |
| |
| import java.io.IOException; |
| import java.io.ObjectInput; |
| import java.io.ObjectOutput; |
| import java.util.Arrays; |
| |
| import org.apache.commons.math4.legacy.exception.MaxCountExceededException; |
| import org.apache.commons.math4.legacy.linear.Array2DRowRealMatrix; |
| import org.apache.commons.math4.legacy.ode.EquationsMapper; |
| import org.apache.commons.math4.core.jdkmath.JdkMath; |
| |
| /** |
| * This class implements an interpolator for integrators using Nordsieck representation. |
| * |
| * <p>This interpolator computes dense output around the current point. |
| * The interpolation equation is based on Taylor series formulas. |
| * |
| * @see org.apache.commons.math4.legacy.ode.nonstiff.AdamsBashforthIntegrator |
| * @see org.apache.commons.math4.legacy.ode.nonstiff.AdamsMoultonIntegrator |
| * @since 2.0 |
| */ |
| |
| public class NordsieckStepInterpolator extends AbstractStepInterpolator { |
| |
| /** Serializable version identifier. */ |
| private static final long serialVersionUID = -7179861704951334960L; |
| |
| /** State variation. */ |
| protected double[] stateVariation; |
| |
| /** Step size used in the first scaled derivative and Nordsieck vector. */ |
| private double scalingH; |
| |
| /** Reference time for all arrays. |
| * <p>Sometimes, the reference time is the same as previousTime, |
| * sometimes it is the same as currentTime, so we use a separate |
| * field to avoid any confusion. |
| * </p> |
| */ |
| private double referenceTime; |
| |
| /** First scaled derivative. */ |
| private double[] scaled; |
| |
| /** Nordsieck vector. */ |
| private Array2DRowRealMatrix nordsieck; |
| |
| /** Simple constructor. |
| * This constructor builds an instance that is not usable yet, the |
| * {@link AbstractStepInterpolator#reinitialize} method should be called |
| * before using the instance in order to initialize the internal arrays. This |
| * constructor is used only in order to delay the initialization in |
| * some cases. |
| */ |
| public NordsieckStepInterpolator() { |
| } |
| |
| /** Copy constructor. |
| * @param interpolator interpolator to copy from. The copy is a deep |
| * copy: its arrays are separated from the original arrays of the |
| * instance |
| */ |
| public NordsieckStepInterpolator(final NordsieckStepInterpolator interpolator) { |
| super(interpolator); |
| scalingH = interpolator.scalingH; |
| referenceTime = interpolator.referenceTime; |
| if (interpolator.scaled != null) { |
| scaled = interpolator.scaled.clone(); |
| } |
| if (interpolator.nordsieck != null) { |
| nordsieck = new Array2DRowRealMatrix(interpolator.nordsieck.getDataRef(), true); |
| } |
| if (interpolator.stateVariation != null) { |
| stateVariation = interpolator.stateVariation.clone(); |
| } |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected StepInterpolator doCopy() { |
| return new NordsieckStepInterpolator(this); |
| } |
| |
| /** Reinitialize the instance. |
| * <p>Beware that all arrays <em>must</em> be references to integrator |
| * arrays, in order to ensure proper update without copy.</p> |
| * @param y reference to the integrator array holding the state at |
| * the end of the step |
| * @param forward integration direction indicator |
| * @param primaryMapper equations mapper for the primary equations set |
| * @param secondaryMappers equations mappers for the secondary equations sets |
| */ |
| @Override |
| public void reinitialize(final double[] y, final boolean forward, |
| final EquationsMapper primaryMapper, |
| final EquationsMapper[] secondaryMappers) { |
| super.reinitialize(y, forward, primaryMapper, secondaryMappers); |
| stateVariation = new double[y.length]; |
| } |
| |
| /** Reinitialize the instance. |
| * <p>Beware that all arrays <em>must</em> be references to integrator |
| * arrays, in order to ensure proper update without copy.</p> |
| * @param time time at which all arrays are defined |
| * @param stepSize step size used in the scaled and Nordsieck arrays |
| * @param scaledDerivative reference to the integrator array holding the first |
| * scaled derivative |
| * @param nordsieckVector reference to the integrator matrix holding the |
| * Nordsieck vector |
| */ |
| public void reinitialize(final double time, final double stepSize, |
| final double[] scaledDerivative, |
| final Array2DRowRealMatrix nordsieckVector) { |
| this.referenceTime = time; |
| this.scalingH = stepSize; |
| this.scaled = scaledDerivative; |
| this.nordsieck = nordsieckVector; |
| |
| // make sure the state and derivatives will depend on the new arrays |
| setInterpolatedTime(getInterpolatedTime()); |
| |
| } |
| |
| /** Rescale the instance. |
| * <p>Since the scaled and Nordsieck arrays are shared with the caller, |
| * this method has the side effect of rescaling this arrays in the caller too.</p> |
| * @param stepSize new step size to use in the scaled and Nordsieck arrays |
| */ |
| public void rescale(final double stepSize) { |
| |
| final double ratio = stepSize / scalingH; |
| for (int i = 0; i < scaled.length; ++i) { |
| scaled[i] *= ratio; |
| } |
| |
| final double[][] nData = nordsieck.getDataRef(); |
| double power = ratio; |
| for (int i = 0; i < nData.length; ++i) { |
| power *= ratio; |
| final double[] nDataI = nData[i]; |
| for (int j = 0; j < nDataI.length; ++j) { |
| nDataI[j] *= power; |
| } |
| } |
| |
| scalingH = stepSize; |
| |
| } |
| |
| /** |
| * Get the state vector variation from current to interpolated state. |
| * <p>This method is aimed at computing y(t<sub>interpolation</sub>) |
| * -y(t<sub>current</sub>) accurately by avoiding the cancellation errors |
| * that would occur if the subtraction were performed explicitly.</p> |
| * <p>The returned vector is a reference to a reused array, so |
| * it should not be modified and it should be copied if it needs |
| * to be preserved across several calls.</p> |
| * @return state vector at time {@link #getInterpolatedTime} |
| * @see #getInterpolatedDerivatives() |
| * @exception MaxCountExceededException if the number of functions evaluations is exceeded |
| */ |
| public double[] getInterpolatedStateVariation() throws MaxCountExceededException { |
| // compute and ignore interpolated state |
| // to make sure state variation is computed as a side effect |
| getInterpolatedState(); |
| return stateVariation; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected void computeInterpolatedStateAndDerivatives(final double theta, final double oneMinusThetaH) { |
| |
| final double x = interpolatedTime - referenceTime; |
| final double normalizedAbscissa = x / scalingH; |
| |
| Arrays.fill(stateVariation, 0.0); |
| Arrays.fill(interpolatedDerivatives, 0.0); |
| |
| // apply Taylor formula from high order to low order, |
| // for the sake of numerical accuracy |
| final double[][] nData = nordsieck.getDataRef(); |
| for (int i = nData.length - 1; i >= 0; --i) { |
| final int order = i + 2; |
| final double[] nDataI = nData[i]; |
| final double power = JdkMath.pow(normalizedAbscissa, order); |
| for (int j = 0; j < nDataI.length; ++j) { |
| final double d = nDataI[j] * power; |
| stateVariation[j] += d; |
| interpolatedDerivatives[j] += order * d; |
| } |
| } |
| |
| for (int j = 0; j < currentState.length; ++j) { |
| stateVariation[j] += scaled[j] * normalizedAbscissa; |
| interpolatedState[j] = currentState[j] + stateVariation[j]; |
| interpolatedDerivatives[j] = |
| (interpolatedDerivatives[j] + scaled[j] * normalizedAbscissa) / x; |
| } |
| |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public void writeExternal(final ObjectOutput out) |
| throws IOException { |
| |
| // save the state of the base class |
| writeBaseExternal(out); |
| |
| // save the local attributes |
| out.writeDouble(scalingH); |
| out.writeDouble(referenceTime); |
| |
| final int n = (currentState == null) ? -1 : currentState.length; |
| if (scaled == null) { |
| out.writeBoolean(false); |
| } else { |
| out.writeBoolean(true); |
| for (int j = 0; j < n; ++j) { |
| out.writeDouble(scaled[j]); |
| } |
| } |
| |
| if (nordsieck == null) { |
| out.writeBoolean(false); |
| } else { |
| out.writeBoolean(true); |
| out.writeObject(nordsieck); |
| } |
| |
| // we don't save state variation, it will be recomputed |
| |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public void readExternal(final ObjectInput in) |
| throws IOException, ClassNotFoundException { |
| |
| // read the base class |
| final double t = readBaseExternal(in); |
| |
| // read the local attributes |
| scalingH = in.readDouble(); |
| referenceTime = in.readDouble(); |
| |
| final int n = (currentState == null) ? -1 : currentState.length; |
| final boolean hasScaled = in.readBoolean(); |
| if (hasScaled) { |
| scaled = new double[n]; |
| for (int j = 0; j < n; ++j) { |
| scaled[j] = in.readDouble(); |
| } |
| } else { |
| scaled = null; |
| } |
| |
| final boolean hasNordsieck = in.readBoolean(); |
| if (hasNordsieck) { |
| nordsieck = (Array2DRowRealMatrix) in.readObject(); |
| } else { |
| nordsieck = null; |
| } |
| |
| if (hasScaled && hasNordsieck) { |
| // we can now set the interpolated time and state |
| stateVariation = new double[n]; |
| setInterpolatedTime(t); |
| } else { |
| stateVariation = null; |
| } |
| |
| } |
| |
| } |
