/*
 * 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 Also:
DormandPrince853Integrator
Since:
1.2/**
 * 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. /** Serializable version identifier. */
    private static final long serialVersionUID = 20111120L;

    
Propagation weights, element 1. /** 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. /** Propagation weights, element 6. */
    private static final double B_06 =        3399327.0 / 763840.0;

    
Propagation weights, element 7. /** Propagation weights, element 7. */
    private static final double B_07 =       66578432.0 / 35198415.0;

    
Propagation weights, element 8. /** Propagation weights, element 8. */
    private static final double B_08 =    -1674902723.0 / 288716400.0;

    
Propagation weights, element 9. /** Propagation weights, element 9. */
    private static final double B_09 = 54980371265625.0 / 176692375811392.0;

    
Propagation weights, element 10. /** Propagation weights, element 10. */
    private static final double B_10 =        -734375.0 / 4826304.0;

    
Propagation weights, element 11. /** Propagation weights, element 11. */
    private static final double B_11 =      171414593.0 / 851261400.0;

    
Propagation weights, element 12. /** Propagation weights, element 12. */
    private static final double B_12 =         137909.0 / 3084480.0;

    
Time step for stage 14 (interpolation only). /** Time step for stage 14 (interpolation only). */
    private static final double C14    = 1.0 / 10.0;

    
Internal weights for stage 14, element 1. /** 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. /** Internal weights for stage 14, element 6. */
    private static final double K14_06 =                 0.0                       - B_06;

    
Internal weights for stage 14, element 7. /** 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. /** 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. /** 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. /** 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. /** 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. /** 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. /** Internal weights for stage 14, element 13. */
    private static final double K14_13 =             -4149.0 / 500000.0;

    
Time step for stage 15 (interpolation only). /** Time step for stage 15 (interpolation only). */
    private static final double C15    = 1.0 / 5.0;


    
Internal weights for stage 15, element 1. /** 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. /** 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. /** 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. /** 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. /** Internal weights for stage 15, element 9. */
    private static final double K15_09 =                 0.0                       - B_09;

    
Internal weights for stage 15, element 10. /** Internal weights for stage 15, element 10. */
    private static final double K15_10 =                 0.0                       - B_10;

    
Internal weights for stage 15, element 11. /** 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. /** 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. /** Internal weights for stage 15, element 13. */
    private static final double K15_13 =      -11518334563.0 / 33831184612500.0;

    
Internal weights for stage 15, element 14. /** Internal weights for stage 15, element 14. */
    private static final double K15_14 =        1912306948.0 / 13532473845.0;

    
Time step for stage 16 (interpolation only). /** Time step for stage 16 (interpolation only). */
    private static final double C16    = 7.0 / 9.0;


    
Internal weights for stage 16, element 1. /** 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. /** 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. /** 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. /** 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. /** 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. /** Internal weights for stage 16, element 10. */
    private static final double K16_10 =                 0.0                       - B_10;

    
Internal weights for stage 16, element 11. /** Internal weights for stage 16, element 11. */
    private static final double K16_11 =                 0.0                       - B_11;

    
Internal weights for stage 16, element 12. /** Internal weights for stage 16, element 12. */
    private static final double K16_12 =                 0.0                       - B_12;

    
Internal weights for stage 16, element 13. /** Internal weights for stage 16, element 13. */
    private static final double K16_13 =       -1199007803.0 / 857031517296.0;

    
Internal weights for stage 16, element 14. /** Internal weights for stage 16, element 14. */
    private static final double K16_14 =      157882067000.0 / 53564469831.0;

    
Internal weights for stage 16, element 15. /** 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)
/** 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. /** Last evaluations. */
    private double[][] yDotKLast;

    
Vectors for interpolation. /** Vectors for interpolation. */
    private double[][] v;

    
Initialization indicator for the interpolation vectors. /** Initialization indicator for the interpolation vectors. */
    private boolean vectorsInitialized;

  
Simple constructor. This constructor builds an instance that is not usable yet, the AbstractStepInterpolator.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 EmbeddedRungeKuttaIntegrator uses the prototyping design pattern to create the step interpolators by cloning an uninitialized model and latter initializing the copy. /** 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.
   */
  // CHECKSTYLE: stop RedundantModifier
  // the public modifier here is needed for serialization
  public DormandPrince853StepInterpolator() {
    super();
    yDotKLast = null;
    v         = null;
    vectorsInitialized = false;
  }
  // CHECKSTYLE: resume RedundantModifier

  
Copy constructor.
Params:
interpolator – interpolator to copy from. The copy is a deep
copy: its arrays are separated from the original arrays of the
instance/** 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
   */
  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} /** {@inheritDoc} */
  @Override
  protected StepInterpolator doCopy() {
    return new DormandPrince853StepInterpolator(this);
  }

  
{@inheritDoc} /** {@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} /** {@inheritDoc} */
  @Override
  public void storeTime(final double t) {
    super.storeTime(t);
    vectorsInitialized = false;
  }

  
{@inheritDoc} /** {@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} /** {@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} /** {@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} /** {@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);

  }

}