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package org.apache.commons.math3.ode;
This class converts second order differential equations to first
order ones.
This class is a wrapper around a SecondOrderDifferentialEquations which allow to use a FirstOrderIntegrator to integrate it.
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.
One should be aware that the data is duplicated during the transformation process and that for each call to computeDerivatives, this wrapper does copy 4n scalars : 2n before the call to
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.
See Also: Since: 1.2
/** 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. /** Underlying second order equations set. */
private final SecondOrderDifferentialEquations equations;
second order problem dimension. /** second order problem dimension. */
private final int dimension;
state vector. /** state vector. */
private final double[] z;
first time derivative of the state vector. /** first time derivative of the state vector. */
private final double[] zDot;
second time derivative of the state vector. /** second time derivative of the state vector. */
private final double[] zDDot;
Simple constructor.
Build a converter around a second order equations set.
Params: - equations – second order equations set to convert
/** 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.
The dimension of the first order problem is twice the
dimension of the underlying second order problem.
Returns: dimension of the problem
/** 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
*/
public int getDimension() {
return 2 * dimension;
}
Get the current time derivative of the state vector.
Params: - t – current value of the independent time variable
- y – array containing the current value of the state vector
- yDot – placeholder array where to put the time derivative of the state vector
/** 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
*/
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);
}
}