FieldExpandableODE

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 *      https://www.apache.org/licenses/LICENSE-2.0
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package org.hipparchus.ode;

import java.util.ArrayList;
import java.util.List;

import org.hipparchus.CalculusFieldElement;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.MathIllegalStateException;
import org.hipparchus.util.MathArrays;


/**
 * This class represents a combined set of first order differential equations,
 * with at least a primary set of equations expandable by some sets of secondary
 * equations.
 * <p>
 * One typical use case is the computation of the Jacobian matrix for some ODE.
 * In this case, the primary set of equations corresponds to the raw ODE, and we
 * add to this set another bunch of secondary equations which represent the Jacobian
 * matrix of the primary set.
 * </p>
 * <p>
 * We want the integrator to use <em>only</em> the primary set to estimate the
 * errors and hence the step sizes. It should <em>not</em> use the secondary
 * equations in this computation. The {@link FieldODEIntegrator integrator} will
 * be able to know where the primary set ends and so where the secondary sets begin.
 * </p>
 *
 * @see FieldOrdinaryDifferentialEquation
 * @see FieldSecondaryODE
 *
 * @param <T> the type of the field elements
 */

public class FieldExpandableODE<T extends CalculusFieldElement<T>> {

    /** Primary differential equation. */
    private final FieldOrdinaryDifferentialEquation<T> primary;

    /** Components of the expandable ODE. */
    private List<FieldSecondaryODE<T>> components;

    /** Mapper for all equations. */
    private FieldEquationsMapper<T> mapper;

    /** Build an expandable set from its primary ODE set.
     * @param primary the primary set of differential equations to be integrated.
     */
    public FieldExpandableODE(final FieldOrdinaryDifferentialEquation<T> primary) {
        this.primary    = primary;
        this.components = new ArrayList<>();
        this.mapper     = new FieldEquationsMapper<>(null, primary.getDimension());
    }

    /** Get the primary set of differential equations to be integrated.
     * @return primary set of differential equations to be integrated
     * @since 2.2
     */
    public FieldOrdinaryDifferentialEquation<T> getPrimary() {
        return primary;
    }

    /** Get the mapper for the set of equations.
     * @return mapper for the set of equations
     */
    public FieldEquationsMapper<T> getMapper() {
        return mapper;
    }

    /** Add a set of secondary equations to be integrated along with the primary set.
     * @param secondary secondary equations set
     * @return index of the secondary equation in the expanded state, to be used
     * as the parameter to {@link FieldODEState#getSecondaryState(int)} and
     * {@link FieldODEStateAndDerivative#getSecondaryDerivative(int)} (beware index
     * 0 corresponds to primary state, secondary states start at 1)
     */
    public int addSecondaryEquations(final FieldSecondaryODE<T> secondary) {

        components.add(secondary);
        mapper = new FieldEquationsMapper<>(mapper, secondary.getDimension());

        return components.size();

    }

    /** Initialize equations at the start of an ODE integration.
     * @param s0 state at integration start
     * @param finalTime target time for the integration
     * @exception MathIllegalStateException if the number of functions evaluations is exceeded
     * @exception MathIllegalArgumentException if arrays dimensions do not match equations settings
     */
    public void init(final FieldODEState<T> s0, final T finalTime) {

        final T t0 = s0.getTime();

        // initialize primary equations
        final T[] primary0 = s0.getPrimaryState();
        primary.init(t0, primary0, finalTime);

        // initialize secondary equations
        for (int index = 1; index < mapper.getNumberOfEquations(); ++index) {
            final T[] secondary0 = s0.getSecondaryState(index);
            components.get(index - 1).init(t0, primary0, secondary0, finalTime);
        }

    }

    /** Get the current time derivative of the complete state vector.
     * @param t current value of the independent <I>time</I> variable
     * @param y array containing the current value of the complete state vector
     * @return time derivative of the complete state vector
     * @exception MathIllegalStateException if the number of functions evaluations is exceeded
     * @exception MathIllegalArgumentException if arrays dimensions do not match equations settings
     */
    public T[] computeDerivatives(final T t, final T[] y)
        throws MathIllegalArgumentException, MathIllegalStateException {

        final T[] yDot = MathArrays.buildArray(t.getField(), mapper.getTotalDimension());

        // compute derivatives of the primary equations
        final T[] primaryState    = mapper.extractEquationData(0, y);
        final T[] primaryStateDot = primary.computeDerivatives(t, primaryState);

        // Add contribution for secondary equations
        for (int index = 1; index < mapper.getNumberOfEquations(); ++index) {
            final T[] componentState    = mapper.extractEquationData(index, y);
            final T[] componentStateDot = components.get(index - 1).computeDerivatives(t, primaryState, primaryStateDot,
                                                                                       componentState);
            mapper.insertEquationData(index, componentStateDot, yDot);
        }

        // we retrieve the primaryStateDot array after the secondary equations have
        // been computed in case they change the main state derivatives; this happens
        // for example in optimal control when the secondary equations handle co-state,
        // which changes control, and the control changes the primary state
        mapper.insertEquationData(0, primaryStateDot, yDot);

        return yDot;

    }

}