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* * <tr> * * <tr> * </table> * * @see GraggBulirschStoerIntegrator * @since 1.2 */ class GraggBulirschStoerStepInterpolator extends AbstractStepInterpolator { /** Serializable version identifier. */ private static final long serialVersionUID = 20110928L; /** Slope at the beginning of the step. */ private double[] y0Dot; /** State at the end of the step. */ private double[] y1; /** Slope at the end of the step. */ private double[] y1Dot; /** Derivatives at the middle of the step. * element 0 is state at midpoint, element 1 is first derivative ... */ private double[][] yMidDots; /** Interpolation polynomials. */ private double[][] polynomials; /** Error coefficients for the interpolation. */ private double[] errfac; /** Degree of the interpolation polynomials. */ private int currentDegree; /** Simple constructor. * This constructor should not be used directly, it is only intended * for the serialization process. */ // CHECKSTYLE: stop RedundantModifier // the public modifier here is needed for serialization public GraggBulirschStoerStepInterpolator() { y0Dot = null; y1 = null; y1Dot = null; yMidDots = null; resetTables(-1); } // CHECKSTYLE: resume RedundantModifier /** Simple constructor. * @param y reference to the integrator array holding the current state * @param y0Dot reference to the integrator array holding the slope * at the beginning of the step * @param y1 reference to the integrator array holding the state at * the end of the step * @param y1Dot reference to the integrator array holding the slope * at the end of the step * @param yMidDots reference to the integrator array holding the * derivatives at the middle point 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 */ GraggBulirschStoerStepInterpolator(final double[] y, final double[] y0Dot, final double[] y1, final double[] y1Dot, final double[][] yMidDots, final boolean forward, final EquationsMapper primaryMapper, final EquationsMapper[] secondaryMappers) { super(y, forward, primaryMapper, secondaryMappers); this.y0Dot = y0Dot; this.y1 = y1; this.y1Dot = y1Dot; this.yMidDots = yMidDots; resetTables(yMidDots.length + 4); } /** 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 */ GraggBulirschStoerStepInterpolator(final GraggBulirschStoerStepInterpolator interpolator) { super(interpolator); final int dimension = currentState.length; // the interpolator has been finalized, // the following arrays are not needed anymore y0Dot = null; y1 = null; y1Dot = null; yMidDots = null; // copy the interpolation polynomials (up to the current degree only) if (interpolator.polynomials == null) { polynomials = null; currentDegree = -1; } else { resetTables(interpolator.currentDegree); for (int i = 0; i < polynomials.length; ++i) { polynomials[i] = new double[dimension]; System.arraycopy(interpolator.polynomials[i], 0, polynomials[i], 0, dimension); } currentDegree = interpolator.currentDegree; } } /** Reallocate the internal tables. * Reallocate the internal tables in order to be able to handle * interpolation polynomials up to the given degree * @param maxDegree maximal degree to handle */ private void resetTables(final int maxDegree) { if (maxDegree < 0) { polynomials = null; errfac = null; currentDegree = -1; } else { final double[][] newPols = new double[maxDegree + 1][]; if (polynomials != null) { System.arraycopy(polynomials, 0, newPols, 0, polynomials.length); for (int i = polynomials.length; i < newPols.length; ++i) { newPols[i] = new double[currentState.length]; } } else { for (int i = 0; i < newPols.length; ++i) { newPols[i] = new double[currentState.length]; } } polynomials = newPols; // initialize the error factors array for interpolation if (maxDegree <= 4) { errfac = null; } else { errfac = new double[maxDegree - 4]; for (int i = 0; i < errfac.length; ++i) { final int ip5 = i + 5; errfac[i] = 1.0 / (ip5 * ip5); final double e = 0.5 * FastMath.sqrt (((double) (i + 1)) / ip5); for (int j = 0; j <= i; ++j) { errfac[i] *= e / (j + 1); } } } currentDegree = 0; } } /** {@inheritDoc} */ @Override protected StepInterpolator doCopy() { return new GraggBulirschStoerStepInterpolator(this); } /** Compute the interpolation coefficients for dense output. * @param mu degree of the interpolation polynomial * @param h current step */ public void computeCoefficients(final int mu, final double h) { if ((polynomials == null) || (polynomials.length <= (mu + 4))) { resetTables(mu + 4); } currentDegree = mu + 4; for (int i = 0; i < currentState.length; ++i) { final double yp0 = h * y0Dot[i]; final double yp1 = h * y1Dot[i]; final double ydiff = y1[i] - currentState[i]; final double aspl = ydiff - yp1; final double bspl = yp0 - ydiff; polynomials[0][i] = currentState[i]; polynomials[1][i] = ydiff; polynomials[2][i] = aspl; polynomials[3][i] = bspl; if (mu < 0) { return; } // compute the remaining coefficients final double ph0 = 0.5 * (currentState[i] + y1[i]) + 0.125 * (aspl + bspl); polynomials[4][i] = 16 * (yMidDots[0][i] - ph0); if (mu > 0) { final double ph1 = ydiff + 0.25 * (aspl - bspl); polynomials[5][i] = 16 * (yMidDots[1][i] - ph1); if (mu > 1) { final double ph2 = yp1 - yp0; polynomials[6][i] = 16 * (yMidDots[2][i] - ph2 + polynomials[4][i]); if (mu > 2) { final double ph3 = 6 * (bspl - aspl); polynomials[7][i] = 16 * (yMidDots[3][i] - ph3 + 3 * polynomials[5][i]); for (int j = 4; j <= mu; ++j) { final double fac1 = 0.5 * j * (j - 1); final double fac2 = 2 * fac1 * (j - 2) * (j - 3); polynomials[j+4][i] = 16 * (yMidDots[j][i] + fac1 * polynomials[j+2][i] - fac2 * polynomials[j][i]); } } } } } } /** Estimate interpolation error. * @param scale scaling array * @return estimate of the interpolation error */ public double estimateError(final double[] scale) { double error = 0; if (currentDegree >= 5) { for (int i = 0; i < scale.length; ++i) { final double e = polynomials[currentDegree][i] / scale[i]; error += e * e; } error = FastMath.sqrt(error / scale.length) * errfac[currentDegree - 5]; } return error; } /** {@inheritDoc} */ @Override protected void computeInterpolatedStateAndDerivatives(final double theta, final double oneMinusThetaH) { final int dimension = currentState.length; final double oneMinusTheta = 1.0 - theta; final double theta05 = theta - 0.5; final double tOmT = theta * oneMinusTheta; final double t4 = tOmT * tOmT; final double t4Dot = 2 * tOmT * (1 - 2 * theta); final double dot1 = 1.0 / h; final double dot2 = theta * (2 - 3 * theta) / h; final double dot3 = ((3 * theta - 4) * theta + 1) / h; for (int i = 0; i < dimension; ++i) { final double p0 = polynomials[0][i]; final double p1 = polynomials[1][i]; final double p2 = polynomials[2][i]; final double p3 = polynomials[3][i]; interpolatedState[i] = p0 + theta * (p1 + oneMinusTheta * (p2 * theta + p3 * oneMinusTheta)); interpolatedDerivatives[i] = dot1 * p1 + dot2 * p2 + dot3 * p3; if (currentDegree > 3) { double cDot = 0; double c = polynomials[currentDegree][i]; for (int j = currentDegree - 1; j > 3; --j) { final double d = 1.0 / (j - 3); cDot = d * (theta05 * cDot + c); c = polynomials[j][i] + c * d * theta05; } interpolatedState[i] += t4 * c; interpolatedDerivatives[i] += (t4 * cDot + t4Dot * c) / h; } } if (h == 0) { // in this degenerated case, the previous computation leads to NaN for derivatives // we fix this by using the derivatives at midpoint System.arraycopy(yMidDots[1], 0, interpolatedDerivatives, 0, dimension); } } /** {@inheritDoc} */ @Override public void writeExternal(final ObjectOutput out) throws IOException { final int dimension = (currentState == null) ? -1 : currentState.length; // save the state of the base class writeBaseExternal(out); // save the local attributes (but not the temporary vectors) out.writeInt(currentDegree); for (int k = 0; k <= currentDegree; ++k) { for (int l = 0; l < dimension; ++l) { out.writeDouble(polynomials[k][l]); } } } /** {@inheritDoc} */ @Override public void readExternal(final ObjectInput in) throws IOException, ClassNotFoundException { // read the base class final double t = readBaseExternal(in); final int dimension = (currentState == null) ? -1 : currentState.length; // read the local attributes final int degree = in.readInt(); resetTables(degree); currentDegree = degree; for (int k = 0; k <= currentDegree; ++k) { for (int l = 0; l < dimension; ++l) { polynomials[k][l] = in.readDouble(); } } // we can now set the interpolated time and state setInterpolatedTime(t); } }

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Java - Java tags/keywords

abstractstepinterpolator, classnotfoundexception, equationsmapper, graggbulirschstoerstepinterpolator, ioexception, objectinput, objectoutput, override

The GraggBulirschStoerStepInterpolator.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.io.IOException;
import java.io.ObjectInput;
import java.io.ObjectOutput;

import org.apache.commons.math3.ode.EquationsMapper;
import org.apache.commons.math3.ode.sampling.AbstractStepInterpolator;
import org.apache.commons.math3.ode.sampling.StepInterpolator;
import org.apache.commons.math3.util.FastMath;

/**
 * This class implements an interpolator for the Gragg-Bulirsch-Stoer
 * integrator.
 *
 * <p>This interpolator compute dense output inside the last step
 * produced by a Gragg-Bulirsch-Stoer integrator.</p>
 *
 * <p>
 * This implementation is basically a reimplementation in Java of the
 * <a
 * href="http://www.unige.ch/math/folks/hairer/prog/nonstiff/odex.f">odex</a>
 * fortran code by E. Hairer and G. Wanner. The redistribution policy
 * for this code is available <a
 * href="http://www.unige.ch/~hairer/prog/licence.txt">here</a>, for
 * convenience, it is reproduced below.</p>
 * </p>
 *
 * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
 * <tr>
Copyright (c) 2004, Ernst Hairer
Redistribution and use in source and binary forms, with or * without modification, are permitted provided that the following * conditions are met: * <ul> * <li>Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer.</li> * <li>Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution.</li> * </ul>
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND * CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, * BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</strong>


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