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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
 *
 * 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.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;

/**
 * This interface represents a first order integrator for differential equations.
 *
 * <p>The classes which are devoted to solve first order differential equations should implement
 * this interface. The problems which can be handled should implement the {@link
 * FirstOrderDifferentialEquations} interface.
 *
 * @see FirstOrderDifferentialEquations
 * @see org.apache.commons.math3.ode.sampling.StepHandler
 * @see org.apache.commons.math3.ode.events.EventHandler
 * @since 1.2
 */
public interface FirstOrderIntegrator extends ODEIntegrator {

    /**
     * Integrate the differential equations up to the given time.
     *
     * <p>This method solves an Initial Value Problem (IVP).
     *
     * <p>Since this method stores some internal state variables made available in its public
     * interface during integration ({@link #getCurrentSignedStepsize()}), it is <em>not</em>
     * thread-safe.
     *
     * @param equations differential equations to integrate
     * @param t0 initial time
     * @param y0 initial value of the state vector at t0
     * @param t target time for the integration (can be set to a value smaller than <code>t0</code>
     *     for backward integration)
     * @param y placeholder where to put the state vector at each successful step (and hence at the
     *     end of integration), can be the same object as y0
     * @return stop time, will be the same as target time if integration reached its target, but may
     *     be different if some {@link org.apache.commons.math3.ode.events.EventHandler} stops it at
     *     some point.
     * @exception DimensionMismatchException if arrays dimension do not match equations settings
     * @exception NumberIsTooSmallException if integration step is too small
     * @exception MaxCountExceededException if the number of functions evaluations is exceeded
     * @exception NoBracketingException if the location of an event cannot be bracketed
     */
    double integrate(
            FirstOrderDifferentialEquations equations, double t0, double[] y0, double t, double[] y)
            throws DimensionMismatchException,
                    NumberIsTooSmallException,
                    MaxCountExceededException,
                    NoBracketingException;
}