diff options
Diffstat (limited to 'src/main/java/org/apache/commons/math3/ode/sampling/NordsieckStepInterpolator.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/ode/sampling/NordsieckStepInterpolator.java | 293 |
1 files changed, 293 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/ode/sampling/NordsieckStepInterpolator.java b/src/main/java/org/apache/commons/math3/ode/sampling/NordsieckStepInterpolator.java new file mode 100644 index 0000000..39b05ab --- /dev/null +++ b/src/main/java/org/apache/commons/math3/ode/sampling/NordsieckStepInterpolator.java @@ -0,0 +1,293 @@ +/* + * 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.sampling; + +import java.io.IOException; +import java.io.ObjectInput; +import java.io.ObjectOutput; +import java.util.Arrays; + +import org.apache.commons.math3.exception.MaxCountExceededException; +import org.apache.commons.math3.linear.Array2DRowRealMatrix; +import org.apache.commons.math3.ode.EquationsMapper; +import org.apache.commons.math3.util.FastMath; + +/** + * 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.math3.ode.nonstiff.AdamsBashforthIntegrator + * @see org.apache.commons.math3.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 = FastMath.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; + } + + } + +} |