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 * 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
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 * 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
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package org.apache.commons.math3.ode.nonstiff;

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 5(4) Dormand-Prince integrator.
See Also:
DormandPrince54Integrator
Since:
1.2/**
 * This class represents an interpolator over the last step during an
 * ODE integration for the 5(4) Dormand-Prince integrator.
 *
 * @see DormandPrince54Integrator
 *
 * @since 1.2
 */

class DormandPrince54StepInterpolator
  extends RungeKuttaStepInterpolator {

    
Last row of the Butcher-array internal weights, element 0. /** Last row of the Butcher-array internal weights, element 0. */
    private static final double A70 =    35.0 /  384.0;

    // element 1 is zero, so it is neither stored nor used

    
Last row of the Butcher-array internal weights, element 2. /** Last row of the Butcher-array internal weights, element 2. */
    private static final double A72 =   500.0 / 1113.0;

    
Last row of the Butcher-array internal weights, element 3. /** Last row of the Butcher-array internal weights, element 3. */
    private static final double A73 =   125.0 /  192.0;

    
Last row of the Butcher-array internal weights, element 4. /** Last row of the Butcher-array internal weights, element 4. */
    private static final double A74 = -2187.0 / 6784.0;

    
Last row of the Butcher-array internal weights, element 5. /** Last row of the Butcher-array internal weights, element 5. */
    private static final double A75 =    11.0 /   84.0;

    
Shampine (1986) Dense output, element 0. /** Shampine (1986) Dense output, element 0. */
    private static final double D0 =  -12715105075.0 /  11282082432.0;

    // element 1 is zero, so it is neither stored nor used

    
Shampine (1986) Dense output, element 2. /** Shampine (1986) Dense output, element 2. */
    private static final double D2 =   87487479700.0 /  32700410799.0;

    
Shampine (1986) Dense output, element 3. /** Shampine (1986) Dense output, element 3. */
    private static final double D3 =  -10690763975.0 /   1880347072.0;

    
Shampine (1986) Dense output, element 4. /** Shampine (1986) Dense output, element 4. */
    private static final double D4 =  701980252875.0 / 199316789632.0;

    
Shampine (1986) Dense output, element 5. /** Shampine (1986) Dense output, element 5. */
    private static final double D5 =   -1453857185.0 /    822651844.0;

    
Shampine (1986) Dense output, element 6. /** Shampine (1986) Dense output, element 6. */
    private static final double D6 =      69997945.0 /     29380423.0;

    
Serializable version identifier. /** Serializable version identifier. */
    private static final long serialVersionUID = 20111120L;

    
First vector for interpolation. /** First vector for interpolation. */
    private double[] v1;

    
Second vector for interpolation. /** Second vector for interpolation. */
    private double[] v2;

    
Third vector for interpolation. /** Third vector for interpolation. */
    private double[] v3;

    
Fourth vector for interpolation. /** Fourth vector for interpolation. */
    private double[] v4;

    
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 DormandPrince54StepInterpolator() {
    super();
    v1 = null;
    v2 = null;
    v3 = null;
    v4 = 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
   */
  DormandPrince54StepInterpolator(final DormandPrince54StepInterpolator interpolator) {

    super(interpolator);

    if (interpolator.v1 == null) {

      v1 = null;
      v2 = null;
      v3 = null;
      v4 = null;
      vectorsInitialized = false;

    } else {

      v1 = interpolator.v1.clone();
      v2 = interpolator.v2.clone();
      v3 = interpolator.v3.clone();
      v4 = interpolator.v4.clone();
      vectorsInitialized = interpolator.vectorsInitialized;

    }

  }

  
{@inheritDoc} /** {@inheritDoc} */
  @Override
  protected StepInterpolator doCopy() {
    return new DormandPrince54StepInterpolator(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);
    v1 = null;
    v2 = null;
    v3 = null;
    v4 = null;
    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) {

    if (! vectorsInitialized) {

      if (v1 == null) {
        v1 = new double[interpolatedState.length];
        v2 = new double[interpolatedState.length];
        v3 = new double[interpolatedState.length];
        v4 = new double[interpolatedState.length];
      }

      // no step finalization is needed for this interpolator

      // we need to compute the interpolation vectors for this time step
      for (int i = 0; i < interpolatedState.length; ++i) {
          final double yDot0 = yDotK[0][i];
          final double yDot2 = yDotK[2][i];
          final double yDot3 = yDotK[3][i];
          final double yDot4 = yDotK[4][i];
          final double yDot5 = yDotK[5][i];
          final double yDot6 = yDotK[6][i];
          v1[i] = A70 * yDot0 + A72 * yDot2 + A73 * yDot3 + A74 * yDot4 + A75 * yDot5;
          v2[i] = yDot0 - v1[i];
          v3[i] = v1[i] - v2[i] - yDot6;
          v4[i] = D0 * yDot0 + D2 * yDot2 + D3 * yDot3 + D4 * yDot4 + D5 * yDot5 + D6 * yDot6;
      }

      vectorsInitialized = true;

    }

    // interpolate
    final double eta = 1 - theta;
    final double twoTheta = 2 * theta;
    final double dot2 = 1 - twoTheta;
    final double dot3 = theta * (2 - 3 * theta);
    final double dot4 = twoTheta * (1 + theta * (twoTheta - 3));
    if ((previousState != null) && (theta <= 0.5)) {
        for (int i = 0; i < interpolatedState.length; ++i) {
            interpolatedState[i] =
                    previousState[i] + theta * h * (v1[i] + eta * (v2[i] + theta * (v3[i] + eta * v4[i])));
            interpolatedDerivatives[i] = v1[i] + dot2 * v2[i] + dot3 * v3[i] + dot4 * v4[i];
        }
    } else {
        for (int i = 0; i < interpolatedState.length; ++i) {
            interpolatedState[i] =
                    currentState[i] - oneMinusThetaH * (v1[i] - theta * (v2[i] + theta * (v3[i] + eta * v4[i])));
            interpolatedDerivatives[i] = v1[i] + dot2 * v2[i] + dot3 * v3[i] + dot4 * v4[i];
        }
    }

  }

}