| /* |
| * 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.math.ode.nonstiff; |
| |
| import java.io.IOException; |
| import java.io.ObjectInput; |
| import java.io.ObjectOutput; |
| |
| import org.apache.commons.math.ode.AbstractIntegrator; |
| import org.apache.commons.math.ode.DerivativeException; |
| import org.apache.commons.math.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 |
| * |
| * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ |
| * @since 1.2 |
| */ |
| |
| class DormandPrince853StepInterpolator |
| extends RungeKuttaStepInterpolator { |
| |
| /** Serializable version identifier */ |
| private static final long serialVersionUID = 7152276390558450974L; |
| |
| /** 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) { |
| |
| super.reinitialize(integrator, y, yDotK, forward); |
| |
| 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 DerivativeException { |
| |
| 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))); |
| |
| 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 DerivativeException { |
| |
| 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 (DerivativeException e) { |
| IOException ioe = new IOException(e.getLocalizedMessage()); |
| ioe.initCause(e); |
| 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 { |
| |
| // 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); |
| |
| } |
| |
| } |
