GraggBulirschStoerStateInterpolator.java
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* this work for additional information regarding copyright ownership.
* The Hipparchus project licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
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*
* https://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
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package org.hipparchus.ode.nonstiff;
import org.hipparchus.ode.EquationsMapper;
import org.hipparchus.ode.ODEStateAndDerivative;
import org.hipparchus.ode.sampling.AbstractODEStateInterpolator;
import org.hipparchus.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>
*
* <blockquote>
* <p>Copyright (c) 2004, Ernst Hairer</p>
*
* <p>Redistribution and use in source and binary forms, with or
* without modification, are permitted provided that the following
* conditions are met:</p>
* <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>
*
* <p><strong>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></p>
* </blockquote>
*
* @see GraggBulirschStoerIntegrator
*/
class GraggBulirschStoerStateInterpolator
extends AbstractODEStateInterpolator {
/** Serializable version identifier. */
private static final long serialVersionUID = 20160329L;
/** Scaled derivatives at the middle of the step $\tau$.
* (element k is $h^{k} d^{k}y(\tau)/dt^{k}$ where h is step size...)
*/
private final double[][] yMidDots;
/** Interpolation polynomials. */
private final double[][] polynomials;
/** Error coefficients for the interpolation. */
private final double[] errfac;
/** Degree of the interpolation polynomials. */
private final int currentDegree;
/** Simple constructor.
* @param forward 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 mapper equations mapper for the all equations
* @param yMidDots scaled derivatives at the middle of the step $\tau$
* (element k is $h^{k} d^{k}y(\tau)/dt^{k}$ where h is step size...)
* @param mu degree of the interpolation polynomial
*/
GraggBulirschStoerStateInterpolator(final boolean forward,
final ODEStateAndDerivative globalPreviousState,
final ODEStateAndDerivative globalCurrentState,
final ODEStateAndDerivative softPreviousState,
final ODEStateAndDerivative softCurrentState,
final EquationsMapper mapper,
final double[][] yMidDots,
final int mu) {
super(forward,
globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
mapper);
this.yMidDots = yMidDots.clone();
this.currentDegree = mu + 4;
this.polynomials = new double[currentDegree + 1][getCurrentState().getCompleteStateDimension()];
// initialize the error factors array for interpolation
if (currentDegree <= 4) {
errfac = null;
} else {
errfac = new double[currentDegree - 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);
}
}
}
// compute the interpolation coefficients
computeCoefficients(mu);
}
/** {@inheritDoc} */
@Override
protected GraggBulirschStoerStateInterpolator create(final boolean newForward,
final ODEStateAndDerivative newGlobalPreviousState,
final ODEStateAndDerivative newGlobalCurrentState,
final ODEStateAndDerivative newSoftPreviousState,
final ODEStateAndDerivative newSoftCurrentState,
final EquationsMapper newMapper) {
return new GraggBulirschStoerStateInterpolator(newForward,
newGlobalPreviousState, newGlobalCurrentState,
newSoftPreviousState, newSoftCurrentState,
newMapper, yMidDots, currentDegree - 4);
}
/** Compute the interpolation coefficients for dense output.
* @param mu degree of the interpolation polynomial
*/
private void computeCoefficients(final int mu) {
final double[] y0Dot = getGlobalPreviousState().getCompleteDerivative();
final double[] y1Dot = getGlobalCurrentState().getCompleteDerivative();
final double[] y1 = getGlobalCurrentState().getCompleteState();
final double[] previousState = getGlobalPreviousState().getCompleteState();
final double h = getGlobalCurrentState().getTime() - getGlobalPreviousState().getTime();
for (int i = 0; i < previousState.length; ++i) {
final double yp0 = h * y0Dot[i];
final double yp1 = h * y1Dot[i];
final double ydiff = y1[i] - previousState[i];
final double aspl = ydiff - yp1;
final double bspl = yp0 - ydiff;
polynomials[0][i] = previousState[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 * (previousState[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 ODEStateAndDerivative computeInterpolatedStateAndDerivatives(final EquationsMapper mapper,
final double time, final double theta,
final double thetaH, final double oneMinusThetaH) {
final int dimension = mapper.getTotalDimension();
final double h = thetaH / theta;
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;
final double[] interpolatedState = new double[dimension];
final double[] interpolatedDerivatives = new double[dimension];
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);
}
return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
}
}