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Commons Math example source code file (DormandPrince853StepInterpolator.java)
The Commons Math DormandPrince853StepInterpolator.java 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.math.ode.nonstiff; import java.io.IOException; import java.io.ObjectInput; import java.io.ObjectOutput; import org.apache.commons.math.MathRuntimeException; 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: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $ * @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]; // 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(previousTime + 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(previousTime + 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(previousTime + C16 * h, yTmp, yDotKLast[2]); } /** {@inheritDoc} */ @Override public void writeExternal(final ObjectOutput out) throws IOException { try { // save the local attributes finalizeStep(); } catch (DerivativeException e) { throw MathRuntimeException.createIOException(e); } 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); } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math DormandPrince853StepInterpolator.java source code file: |
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