/*
 * 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;

import org.apache.commons.math3.RealFieldElement;

/**
 * This interface represents a first order differential equations set.
 *
 * <p>This interface should be implemented by all real first order differential equation problems
 * before they can be handled by the integrators {@link FirstOrderIntegrator#integrate} method.
 *
 * <p>A first order differential equations problem, as seen by an integrator is the time derivative
 * <code>dY/dt</code> of a state vector <code>Y</code>, both being one dimensional arrays. From the
 * integrator point of view, this derivative depends only on the current time <code>t</code> and on
 * the state vector <code>Y</code>.
 *
 * <p>For real problems, the derivative depends also on parameters that do not belong to the state
 * vector (dynamical model constants for example). These constants are completely outside of the
 * scope of this interface, the classes that implement it are allowed to handle them as they want.
 *
 * @see FirstOrderFieldIntegrator
 * @param <T> the type of the field elements
 * @since 3.6
 */
public interface FirstOrderFieldDifferentialEquations<T extends RealFieldElement<T>> {

    /**
     * Get the dimension of the problem.
     *
     * @return dimension of the problem
     */
    int getDimension();

    /**
     * Initialize equations at the start of an ODE integration.
     *
     * <p>This method is called once at the start of the integration. It may be used by the
     * equations to initialize some internal data if needed.
     *
     * @param t0 value of the independent <I>time</I> variable at integration start
     * @param y0 array containing the value of the state vector at integration start
     * @param finalTime target time for the integration
     */
    void init(T t0, T[] y0, T finalTime);

    /**
     * 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
     * @return time derivative of the state vector
     */
    T[] computeDerivatives(T t, T[] y);
}