FirstOrderConverter.java

/*
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 * 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
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 * 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.math4.legacy.ode;


/** This class converts second order differential equations to first
 * order ones.
 *
 * <p>This class is a wrapper around a {@link
 * SecondOrderDifferentialEquations} which allow to use a {@link
 * FirstOrderIntegrator} to integrate it.</p>
 *
 * <p>The transformation is done by changing the n dimension state
 * vector to a 2n dimension vector, where the first n components are
 * the initial state variables and the n last components are their
 * first time derivative. The first time derivative of this state
 * vector then really contains both the first and second time
 * derivative of the initial state vector, which can be handled by the
 * underlying second order equations set.</p>
 *
 * <p>One should be aware that the data is duplicated during the
 * transformation process and that for each call to {@link
 * #computeDerivatives computeDerivatives}, this wrapper does copy 4n
 * scalars : 2n before the call to {@link
 * SecondOrderDifferentialEquations#computeSecondDerivatives
 * computeSecondDerivatives} in order to dispatch the y state vector
 * into z and zDot, and 2n after the call to gather zDot and zDDot
 * into yDot. Since the underlying problem by itself perhaps also
 * needs to copy data and dispatch the arrays into domain objects,
 * this has an impact on both memory and CPU usage. The only way to
 * avoid this duplication is to perform the transformation at the
 * problem level, i.e. to implement the problem as a first order one
 * and then avoid using this class.</p>
 *
 * @see FirstOrderIntegrator
 * @see FirstOrderDifferentialEquations
 * @see SecondOrderDifferentialEquations
 * @since 1.2
 */

public class FirstOrderConverter implements FirstOrderDifferentialEquations {

    /** Underlying second order equations set. */
    private final SecondOrderDifferentialEquations equations;

    /** second order problem dimension. */
    private final int dimension;

    /** state vector. */
    private final double[] z;

    /** first time derivative of the state vector. */
    private final double[] zDot;

    /** second time derivative of the state vector. */
    private final double[] zDDot;

  /** Simple constructor.
   * Build a converter around a second order equations set.
   * @param equations second order equations set to convert
   */
  public FirstOrderConverter (final SecondOrderDifferentialEquations equations) {
      this.equations = equations;
      dimension      = equations.getDimension();
      z              = new double[dimension];
      zDot           = new double[dimension];
      zDDot          = new double[dimension];
  }

  /** Get the dimension of the problem.
   * <p>The dimension of the first order problem is twice the
   * dimension of the underlying second order problem.</p>
   * @return dimension of the problem
   */
  @Override
public int getDimension() {
    return 2 * dimension;
  }

  /** Get the current time derivative of the state vector.
   * @param t current value of the independent <I>time</I> variable
   * @param y array containing the current value of the state vector
   * @param yDot placeholder array where to put the time derivative of the state vector
   */
  @Override
public void computeDerivatives(final double t, final double[] y, final double[] yDot) {

    // split the state vector in two
    System.arraycopy(y, 0,         z,    0, dimension);
    System.arraycopy(y, dimension, zDot, 0, dimension);

    // apply the underlying equations set
    equations.computeSecondDerivatives(t, z, zDot, zDDot);

    // build the result state derivative
    System.arraycopy(zDot,  0, yDot, 0,         dimension);
    System.arraycopy(zDDot, 0, yDot, dimension, dimension);
  }
}