/*
* 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.exception.MaxCountExceededException;
import org.apache.commons.math3.ode.AbstractIntegrator;
import org.apache.commons.math3.ode.EquationsMapper;
import org.apache.commons.math3.ode.sampling.StepInterpolator;
/**
* This class represents an interpolator over the last step during an
* ODE integration for the 8(5,3) Dormand-Prince integrator.
*
* @see DormandPrince853Integrator
*
* @since 1.2
*/
class DormandPrince853StepInterpolator
extends RungeKuttaStepInterpolator {
/** Serializable version identifier. */
private static final long serialVersionUID = 20111120L;
/** Propagation weights, element 1. */
private static final double B_01 = 104257.0 / 1920240.0;
// elements 2 to 5 are zero, so they are neither stored nor used
/** Propagation weights, element 6. */
private static final double B_06 = 3399327.0 / 763840.0;
/** Propagation weights, element 7. */
private static final double B_07 = 66578432.0 / 35198415.0;
/** Propagation weights, element 8. */
private static final double B_08 = -1674902723.0 / 288716400.0;
/** Propagation weights, element 9. */
private static final double B_09 = 54980371265625.0 / 176692375811392.0;
/** Propagation weights, element 10. */
private static final double B_10 = -734375.0 / 4826304.0;
/** Propagation weights, element 11. */
private static final double B_11 = 171414593.0 / 851261400.0;
/** Propagation weights, element 12. */
private static final double B_12 = 137909.0 / 3084480.0;
/** Time step for stage 14 (interpolation only). */
private static final double C14 = 1.0 / 10.0;
/** Internal weights for stage 14, element 1. */
private static final double K14_01 = 13481885573.0 / 240030000000.0 - B_01;
// elements 2 to 5 are zero, so they are neither stored nor used
/** Internal weights for stage 14, element 6. */
private static final double K14_06 = 0.0 - B_06;
/** Internal weights for stage 14, element 7. */
private static final double K14_07 = 139418837528.0 / 549975234375.0 - B_07;
/** Internal weights for stage 14, element 8. */
private static final double K14_08 = -11108320068443.0 / 45111937500000.0 - B_08;
/** Internal weights for stage 14, element 9. */
private static final double K14_09 = -1769651421925959.0 / 14249385146080000.0 - B_09;
/** Internal weights for stage 14, element 10. */
private static final double K14_10 = 57799439.0 / 377055000.0 - B_10;
/** Internal weights for stage 14, element 11. */
private static final double K14_11 = 793322643029.0 / 96734250000000.0 - B_11;
/** Internal weights for stage 14, element 12. */
private static final double K14_12 = 1458939311.0 / 192780000000.0 - B_12;
/** Internal weights for stage 14, element 13. */
private static final double K14_13 = -4149.0 / 500000.0;
/** Time step for stage 15 (interpolation only). */
private static final double C15 = 1.0 / 5.0;
/** Internal weights for stage 15, element 1. */
private static final double K15_01 = 1595561272731.0 / 50120273500000.0 - B_01;
// elements 2 to 5 are zero, so they are neither stored nor used
/** Internal weights for stage 15, element 6. */
private static final double K15_06 = 975183916491.0 / 34457688031250.0 - B_06;
/** Internal weights for stage 15, element 7. */
private static final double K15_07 = 38492013932672.0 / 718912673015625.0 - B_07;
/** Internal weights for stage 15, element 8. */
private static final double K15_08 = -1114881286517557.0 / 20298710767500000.0 - B_08;
/** Internal weights for stage 15, element 9. */
private static final double K15_09 = 0.0 - B_09;
/** Internal weights for stage 15, element 10. */
private static final double K15_10 = 0.0 - B_10;
/** Internal weights for stage 15, element 11. */
private static final double K15_11 = -2538710946863.0 / 23431227861250000.0 - B_11;
/** Internal weights for stage 15, element 12. */
private static final double K15_12 = 8824659001.0 / 23066716781250.0 - B_12;
/** Internal weights for stage 15, element 13. */
private static final double K15_13 = -11518334563.0 / 33831184612500.0;
/** Internal weights for stage 15, element 14. */
private static final double K15_14 = 1912306948.0 / 13532473845.0;
/** Time step for stage 16 (interpolation only). */
private static final double C16 = 7.0 / 9.0;
/** Internal weights for stage 16, element 1. */
private static final double K16_01 = -13613986967.0 / 31741908048.0 - B_01;
// elements 2 to 5 are zero, so they are neither stored nor used
/** Internal weights for stage 16, element 6. */
private static final double K16_06 = -4755612631.0 / 1012344804.0 - B_06;
/** Internal weights for stage 16, element 7. */
private static final double K16_07 = 42939257944576.0 / 5588559685701.0 - B_07;
/** Internal weights for stage 16, element 8. */
private static final double K16_08 = 77881972900277.0 / 19140370552944.0 - B_08;
/** Internal weights for stage 16, element 9. */
private static final double K16_09 = 22719829234375.0 / 63689648654052.0 - B_09;
/** Internal weights for stage 16, element 10. */
private static final double K16_10 = 0.0 - B_10;
/** Internal weights for stage 16, element 11. */
private static final double K16_11 = 0.0 - B_11;
/** Internal weights for stage 16, element 12. */
private static final double K16_12 = 0.0 - B_12;
/** Internal weights for stage 16, element 13. */
private static final double K16_13 = -1199007803.0 / 857031517296.0;
/** Internal weights for stage 16, element 14. */
private static final double K16_14 = 157882067000.0 / 53564469831.0;
/** Internal weights for stage 16, element 15. */
private static final double K16_15 = -290468882375.0 / 31741908048.0;
/** Interpolation weights.
* (beware that only the non-null values are in the table)
*/
private static final double[][] D = {
{ -17751989329.0 / 2106076560.0, 4272954039.0 / 7539864640.0,
-118476319744.0 / 38604839385.0, 755123450731.0 / 316657731600.0,
3692384461234828125.0 / 1744130441634250432.0, -4612609375.0 / 5293382976.0,
2091772278379.0 / 933644586600.0, 2136624137.0 / 3382989120.0,
-126493.0 / 1421424.0, 98350000.0 / 5419179.0,
-18878125.0 / 2053168.0, -1944542619.0 / 438351368.0},
{ 32941697297.0 / 3159114840.0, 456696183123.0 / 1884966160.0,
19132610714624.0 / 115814518155.0, -177904688592943.0 / 474986597400.0,
-4821139941836765625.0 / 218016305204281304.0, 30702015625.0 / 3970037232.0,
-85916079474274.0 / 2800933759800.0, -5919468007.0 / 634310460.0,
2479159.0 / 157936.0, -18750000.0 / 602131.0,
-19203125.0 / 2053168.0, 15700361463.0 / 438351368.0},
{ 12627015655.0 / 631822968.0, -72955222965.0 / 188496616.0,
-13145744952320.0 / 69488710893.0, 30084216194513.0 / 56998391688.0,
-296858761006640625.0 / 25648977082856624.0, 569140625.0 / 82709109.0,
-18684190637.0 / 18672891732.0, 69644045.0 / 89549712.0,
-11847025.0 / 4264272.0, -978650000.0 / 16257537.0,
519371875.0 / 6159504.0, 5256837225.0 / 438351368.0},
{ -450944925.0 / 17550638.0, -14532122925.0 / 94248308.0,
-595876966400.0 / 2573655959.0, 188748653015.0 / 527762886.0,
2545485458115234375.0 / 27252038150535163.0, -1376953125.0 / 36759604.0,
53995596795.0 / 518691437.0, 210311225.0 / 7047894.0,
-1718875.0 / 39484.0, 58000000.0 / 602131.0,
-1546875.0 / 39484.0, -1262172375.0 / 8429834.0}
};
/** Last evaluations. */
private double[][] yDotKLast;
/** Vectors for interpolation. */
private double[][] v;
/** Initialization indicator for the interpolation vectors. */
private boolean vectorsInitialized;
/** Simple constructor.
* This constructor builds an instance that is not usable yet, the
* {@link #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. The {@link EmbeddedRungeKuttaIntegrator} uses the
* prototyping design pattern to create the step interpolators by
* cloning an uninitialized model and latter initializing the copy.
*/
public DormandPrince853StepInterpolator() {
super();
yDotKLast = null;
v = null;
vectorsInitialized = false;
}
/** 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 DormandPrince853StepInterpolator(final DormandPrince853StepInterpolator interpolator) {
super(interpolator);
if (interpolator.currentState == null) {
yDotKLast = null;
v = null;
vectorsInitialized = false;
} else {
final int dimension = interpolator.currentState.length;
yDotKLast = new double[3][];
for (int k = 0; k < yDotKLast.length; ++k) {
yDotKLast[k] = new double[dimension];
System.arraycopy(interpolator.yDotKLast[k], 0, yDotKLast[k], 0,
dimension);
}
v = new double[7][];
for (int k = 0; k < v.length; ++k) {
v[k] = new double[dimension];
System.arraycopy(interpolator.v[k], 0, v[k], 0, dimension);
}
vectorsInitialized = interpolator.vectorsInitialized;
}
}
/** {@inheritDoc} */
@Override
protected StepInterpolator doCopy() {
return new DormandPrince853StepInterpolator(this);
}
/** {@inheritDoc} */
@Override
public void reinitialize(final AbstractIntegrator integrator,
final double[] y, final double[][] yDotK, final boolean forward,
final EquationsMapper primaryMapper,
final EquationsMapper[] secondaryMappers) {
super.reinitialize(integrator, y, yDotK, forward, primaryMapper, secondaryMappers);
final int dimension = currentState.length;
yDotKLast = new double[3][];
for (int k = 0; k < yDotKLast.length; ++k) {
yDotKLast[k] = new double[dimension];
}
v = new double[7][];
for (int k = 0; k < v.length; ++k) {
v[k] = new double[dimension];
}
vectorsInitialized = false;
}
/** {@inheritDoc} */
@Override
public void storeTime(final double t) {
super.storeTime(t);
vectorsInitialized = false;
}
/** {@inheritDoc} */
@Override
protected void computeInterpolatedStateAndDerivatives(final double theta,
final double oneMinusThetaH)
throws MaxCountExceededException {
if (! vectorsInitialized) {
if (v == null) {
v = new double[7][];
for (int k = 0; k < 7; ++k) {
v[k] = new double[interpolatedState.length];
}
}
// perform the last evaluations if they have not been done yet
finalizeStep();
// compute the interpolation vectors for this time step
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot1 = yDotK[0][i];
final double yDot6 = yDotK[5][i];
final double yDot7 = yDotK[6][i];
final double yDot8 = yDotK[7][i];
final double yDot9 = yDotK[8][i];
final double yDot10 = yDotK[9][i];
final double yDot11 = yDotK[10][i];
final double yDot12 = yDotK[11][i];
final double yDot13 = yDotK[12][i];
final double yDot14 = yDotKLast[0][i];
final double yDot15 = yDotKLast[1][i];
final double yDot16 = yDotKLast[2][i];
v[0][i] = B_01 * yDot1 + B_06 * yDot6 + B_07 * yDot7 +
B_08 * yDot8 + B_09 * yDot9 + B_10 * yDot10 +
B_11 * yDot11 + B_12 * yDot12;
v[1][i] = yDot1 - v[0][i];
v[2][i] = v[0][i] - v[1][i] - yDotK[12][i];
for (int k = 0; k < D.length; ++k) {
v[k+3][i] = D[k][0] * yDot1 + D[k][1] * yDot6 + D[k][2] * yDot7 +
D[k][3] * yDot8 + D[k][4] * yDot9 + D[k][5] * yDot10 +
D[k][6] * yDot11 + D[k][7] * yDot12 + D[k][8] * yDot13 +
D[k][9] * yDot14 + D[k][10] * yDot15 + D[k][11] * yDot16;
}
}
vectorsInitialized = true;
}
final double eta = 1 - theta;
final double twoTheta = 2 * theta;
final double theta2 = theta * theta;
final double dot1 = 1 - twoTheta;
final double dot2 = theta * (2 - 3 * theta);
final double dot3 = twoTheta * (1 + theta * (twoTheta -3));
final double dot4 = theta2 * (3 + theta * (5 * theta - 8));
final double dot5 = theta2 * (3 + theta * (-12 + theta * (15 - 6 * theta)));
final double dot6 = theta2 * theta * (4 + theta * (-15 + theta * (18 - 7 * theta)));
if ((previousState != null) && (theta <= 0.5)) {
for (int i = 0; i < interpolatedState.length; ++i) {
interpolatedState[i] = previousState[i] +
theta * h * (v[0][i] +
eta * (v[1][i] +
theta * (v[2][i] +
eta * (v[3][i] +
theta * (v[4][i] +
eta * (v[5][i] +
theta * (v[6][i])))))));
interpolatedDerivatives[i] = v[0][i] + dot1 * v[1][i] + dot2 * v[2][i] +
dot3 * v[3][i] + dot4 * v[4][i] +
dot5 * v[5][i] + dot6 * v[6][i];
}
} else {
for (int i = 0; i < interpolatedState.length; ++i) {
interpolatedState[i] = currentState[i] -
oneMinusThetaH * (v[0][i] -
theta * (v[1][i] +
theta * (v[2][i] +
eta * (v[3][i] +
theta * (v[4][i] +
eta * (v[5][i] +
theta * (v[6][i])))))));
interpolatedDerivatives[i] = v[0][i] + dot1 * v[1][i] + dot2 * v[2][i] +
dot3 * v[3][i] + dot4 * v[4][i] +
dot5 * v[5][i] + dot6 * v[6][i];
}
}
}
/** {@inheritDoc} */
@Override
protected void doFinalize() throws MaxCountExceededException {
if (currentState == null) {
// we are finalizing an uninitialized instance
return;
}
double s;
final double[] yTmp = new double[currentState.length];
final double pT = getGlobalPreviousTime();
// k14
for (int j = 0; j < currentState.length; ++j) {
s = K14_01 * yDotK[0][j] + K14_06 * yDotK[5][j] + K14_07 * yDotK[6][j] +
K14_08 * yDotK[7][j] + K14_09 * yDotK[8][j] + K14_10 * yDotK[9][j] +
K14_11 * yDotK[10][j] + K14_12 * yDotK[11][j] + K14_13 * yDotK[12][j];
yTmp[j] = currentState[j] + h * s;
}
integrator.computeDerivatives(pT + C14 * h, yTmp, yDotKLast[0]);
// k15
for (int j = 0; j < currentState.length; ++j) {
s = K15_01 * yDotK[0][j] + K15_06 * yDotK[5][j] + K15_07 * yDotK[6][j] +
K15_08 * yDotK[7][j] + K15_09 * yDotK[8][j] + K15_10 * yDotK[9][j] +
K15_11 * yDotK[10][j] + K15_12 * yDotK[11][j] + K15_13 * yDotK[12][j] +
K15_14 * yDotKLast[0][j];
yTmp[j] = currentState[j] + h * s;
}
integrator.computeDerivatives(pT + C15 * h, yTmp, yDotKLast[1]);
// k16
for (int j = 0; j < currentState.length; ++j) {
s = K16_01 * yDotK[0][j] + K16_06 * yDotK[5][j] + K16_07 * yDotK[6][j] +
K16_08 * yDotK[7][j] + K16_09 * yDotK[8][j] + K16_10 * yDotK[9][j] +
K16_11 * yDotK[10][j] + K16_12 * yDotK[11][j] + K16_13 * yDotK[12][j] +
K16_14 * yDotKLast[0][j] + K16_15 * yDotKLast[1][j];
yTmp[j] = currentState[j] + h * s;
}
integrator.computeDerivatives(pT + C16 * h, yTmp, yDotKLast[2]);
}
/** {@inheritDoc} */
@Override
public void writeExternal(final ObjectOutput out)
throws IOException {
try {
// save the local attributes
finalizeStep();
} catch (MaxCountExceededException mcee) {
final IOException ioe = new IOException(mcee.getLocalizedMessage());
ioe.initCause(mcee);
throw ioe;
}
final int dimension = (currentState == null) ? -1 : currentState.length;
out.writeInt(dimension);
for (int i = 0; i < dimension; ++i) {
out.writeDouble(yDotKLast[0][i]);
out.writeDouble(yDotKLast[1][i]);
out.writeDouble(yDotKLast[2][i]);
}
// save the state of the base class
super.writeExternal(out);
}
/** {@inheritDoc} */
@Override
public void readExternal(final ObjectInput in)
throws IOException, ClassNotFoundException {
// read the local attributes
yDotKLast = new double[3][];
final int dimension = in.readInt();
yDotKLast[0] = (dimension < 0) ? null : new double[dimension];
yDotKLast[1] = (dimension < 0) ? null : new double[dimension];
yDotKLast[2] = (dimension < 0) ? null : new double[dimension];
for (int i = 0; i < dimension; ++i) {
yDotKLast[0][i] = in.readDouble();
yDotKLast[1][i] = in.readDouble();
yDotKLast[2][i] = in.readDouble();
}
// read the base state
super.readExternal(in);
}
}