/*
 * 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.MathIllegalArgumentException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.ode.sampling.StepHandler;
import org.apache.commons.math3.ode.sampling.StepInterpolator;
import org.apache.commons.math3.util.FastMath;

import java.io.Serializable;
import java.util.ArrayList;
import java.util.List;

/**
 * This class stores all information provided by an ODE integrator during the integration process
 * and build a continuous model of the solution from this.
 *
 * <p>This class act as a step handler from the integrator point of view. It is called iteratively
 * during the integration process and stores a copy of all steps information in a sorted collection
 * for later use. Once the integration process is over, the user can use the {@link
 * #setInterpolatedTime setInterpolatedTime} and {@link #getInterpolatedState getInterpolatedState}
 * to retrieve this information at any time. It is important to wait for the integration to be over
 * before attempting to call {@link #setInterpolatedTime setInterpolatedTime} because some internal
 * variables are set only once the last step has been handled.
 *
 * <p>This is useful for example if the main loop of the user application should remain independent
 * from the integration process or if one needs to mimic the behaviour of an analytical model
 * despite a numerical model is used (i.e. one needs the ability to get the model value at any time
 * or to navigate through the data).
 *
 * <p>If problem modeling is done with several separate integration phases for contiguous intervals,
 * the same ContinuousOutputModel can be used as step handler for all integration phases as long as
 * they are performed in order and in the same direction. As an example, one can extrapolate the
 * trajectory of a satellite with one model (i.e. one set of differential equations) up to the
 * beginning of a maneuver, use another more complex model including thrusters modeling and accurate
 * attitude control during the maneuver, and revert to the first model after the end of the
 * maneuver. If the same continuous output model handles the steps of all integration phases, the
 * user do not need to bother when the maneuver begins or ends, he has all the data available in a
 * transparent manner.
 *
 * <p>An important feature of this class is that it implements the <code>Serializable</code>
 * interface. This means that the result of an integration can be serialized and reused later (if
 * stored into a persistent medium like a filesystem or a database) or elsewhere (if sent to another
 * application). Only the result of the integration is stored, there is no reference to the
 * integrated problem by itself.
 *
 * <p>One should be aware that the amount of data stored in a ContinuousOutputModel instance can be
 * important if the state vector is large, if the integration interval is long or if the steps are
 * small (which can result from small tolerance settings in {@link
 * org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator adaptive step size
 * integrators}).
 *
 * @see StepHandler
 * @see StepInterpolator
 * @since 1.2
 */
public class ContinuousOutputModel implements StepHandler, Serializable {

    /** Serializable version identifier */
    private static final long serialVersionUID = -1417964919405031606L;

    /** Initial integration time. */
    private double initialTime;

    /** Final integration time. */
    private double finalTime;

    /** Integration direction indicator. */
    private boolean forward;

    /** Current interpolator index. */
    private int index;

    /** Steps table. */
    private List<StepInterpolator> steps;

    /** Simple constructor. Build an empty continuous output model. */
    public ContinuousOutputModel() {
        steps = new ArrayList<StepInterpolator>();
        initialTime = Double.NaN;
        finalTime = Double.NaN;
        forward = true;
        index = 0;
    }

    /**
     * Append another model at the end of the instance.
     *
     * @param model model to add at the end of the instance
     * @exception MathIllegalArgumentException if the model to append is not compatible with the
     *     instance (dimension of the state vector, propagation direction, hole between the dates)
     * @exception MaxCountExceededException if the number of functions evaluations is exceeded
     *     during step finalization
     */
    public void append(final ContinuousOutputModel model)
            throws MathIllegalArgumentException, MaxCountExceededException {

        if (model.steps.size() == 0) {
            return;
        }

        if (steps.size() == 0) {
            initialTime = model.initialTime;
            forward = model.forward;
        } else {

            if (getInterpolatedState().length != model.getInterpolatedState().length) {
                throw new DimensionMismatchException(
                        model.getInterpolatedState().length, getInterpolatedState().length);
            }

            if (forward ^ model.forward) {
                throw new MathIllegalArgumentException(
                        LocalizedFormats.PROPAGATION_DIRECTION_MISMATCH);
            }

            final StepInterpolator lastInterpolator = steps.get(index);
            final double current = lastInterpolator.getCurrentTime();
            final double previous = lastInterpolator.getPreviousTime();
            final double step = current - previous;
            final double gap = model.getInitialTime() - current;
            if (FastMath.abs(gap) > 1.0e-3 * FastMath.abs(step)) {
                throw new MathIllegalArgumentException(
                        LocalizedFormats.HOLE_BETWEEN_MODELS_TIME_RANGES, FastMath.abs(gap));
            }
        }

        for (StepInterpolator interpolator : model.steps) {
            steps.add(interpolator.copy());
        }

        index = steps.size() - 1;
        finalTime = (steps.get(index)).getCurrentTime();
    }

    /** {@inheritDoc} */
    public void init(double t0, double[] y0, double t) {
        initialTime = Double.NaN;
        finalTime = Double.NaN;
        forward = true;
        index = 0;
        steps.clear();
    }

    /**
     * Handle the last accepted step. A copy of the information provided by the last step is stored
     * in the instance for later use.
     *
     * @param interpolator interpolator for the last accepted step.
     * @param isLast true if the step is the last one
     * @exception MaxCountExceededException if the number of functions evaluations is exceeded
     *     during step finalization
     */
    public void handleStep(final StepInterpolator interpolator, final boolean isLast)
            throws MaxCountExceededException {

        if (steps.size() == 0) {
            initialTime = interpolator.getPreviousTime();
            forward = interpolator.isForward();
        }

        steps.add(interpolator.copy());

        if (isLast) {
            finalTime = interpolator.getCurrentTime();
            index = steps.size() - 1;
        }
    }

    /**
     * Get the initial integration time.
     *
     * @return initial integration time
     */
    public double getInitialTime() {
        return initialTime;
    }

    /**
     * Get the final integration time.
     *
     * @return final integration time
     */
    public double getFinalTime() {
        return finalTime;
    }

    /**
     * Get the time of the interpolated point. If {@link #setInterpolatedTime} has not been called,
     * it returns the final integration time.
     *
     * @return interpolation point time
     */
    public double getInterpolatedTime() {
        return steps.get(index).getInterpolatedTime();
    }

    /**
     * Set the time of the interpolated point.
     *
     * <p>This method should <strong>not</strong> be called before the integration is over because
     * some internal variables are set only once the last step has been handled.
     *
     * <p>Setting the time outside of the integration interval is now allowed, but should be used
     * with care since the accuracy of the interpolator will probably be very poor far from this
     * interval. This allowance has been added to simplify implementation of search algorithms near
     * the interval endpoints.
     *
     * <p>Note that each time this method is called, the internal arrays returned in {@link
     * #getInterpolatedState()}, {@link #getInterpolatedDerivatives()} and {@link
     * #getInterpolatedSecondaryState(int)} <em>will</em> be overwritten. So if their content must
     * be preserved across several calls, user must copy them.
     *
     * @param time time of the interpolated point
     * @see #getInterpolatedState()
     * @see #getInterpolatedDerivatives()
     * @see #getInterpolatedSecondaryState(int)
     */
    public void setInterpolatedTime(final double time) {

        // initialize the search with the complete steps table
        int iMin = 0;
        final StepInterpolator sMin = steps.get(iMin);
        double tMin = 0.5 * (sMin.getPreviousTime() + sMin.getCurrentTime());

        int iMax = steps.size() - 1;
        final StepInterpolator sMax = steps.get(iMax);
        double tMax = 0.5 * (sMax.getPreviousTime() + sMax.getCurrentTime());

        // handle points outside of the integration interval
        // or in the first and last step
        if (locatePoint(time, sMin) <= 0) {
            index = iMin;
            sMin.setInterpolatedTime(time);
            return;
        }
        if (locatePoint(time, sMax) >= 0) {
            index = iMax;
            sMax.setInterpolatedTime(time);
            return;
        }

        // reduction of the table slice size
        while (iMax - iMin > 5) {

            // use the last estimated index as the splitting index
            final StepInterpolator si = steps.get(index);
            final int location = locatePoint(time, si);
            if (location < 0) {
                iMax = index;
                tMax = 0.5 * (si.getPreviousTime() + si.getCurrentTime());
            } else if (location > 0) {
                iMin = index;
                tMin = 0.5 * (si.getPreviousTime() + si.getCurrentTime());
            } else {
                // we have found the target step, no need to continue searching
                si.setInterpolatedTime(time);
                return;
            }

            // compute a new estimate of the index in the reduced table slice
            final int iMed = (iMin + iMax) / 2;
            final StepInterpolator sMed = steps.get(iMed);
            final double tMed = 0.5 * (sMed.getPreviousTime() + sMed.getCurrentTime());

            if ((FastMath.abs(tMed - tMin) < 1e-6) || (FastMath.abs(tMax - tMed) < 1e-6)) {
                // too close to the bounds, we estimate using a simple dichotomy
                index = iMed;
            } else {
                // estimate the index using a reverse quadratic polynom
                // (reverse means we have i = P(t), thus allowing to simply
                // compute index = P(time) rather than solving a quadratic equation)
                final double d12 = tMax - tMed;
                final double d23 = tMed - tMin;
                final double d13 = tMax - tMin;
                final double dt1 = time - tMax;
                final double dt2 = time - tMed;
                final double dt3 = time - tMin;
                final double iLagrange =
                        ((dt2 * dt3 * d23) * iMax
                                        - (dt1 * dt3 * d13) * iMed
                                        + (dt1 * dt2 * d12) * iMin)
                                / (d12 * d23 * d13);
                index = (int) FastMath.rint(iLagrange);
            }

            // force the next size reduction to be at least one tenth
            final int low = FastMath.max(iMin + 1, (9 * iMin + iMax) / 10);
            final int high = FastMath.min(iMax - 1, (iMin + 9 * iMax) / 10);
            if (index < low) {
                index = low;
            } else if (index > high) {
                index = high;
            }
        }

        // now the table slice is very small, we perform an iterative search
        index = iMin;
        while ((index <= iMax) && (locatePoint(time, steps.get(index)) > 0)) {
            ++index;
        }

        steps.get(index).setInterpolatedTime(time);
    }

    /**
     * Get the state vector of the interpolated point.
     *
     * <p>The returned vector is a reference to a reused array, so it should not be modified and it
     * should be copied if it needs to be preserved across several calls to the associated {@link
     * #setInterpolatedTime(double)} method.
     *
     * @return state vector at time {@link #getInterpolatedTime}
     * @exception MaxCountExceededException if the number of functions evaluations is exceeded
     * @see #setInterpolatedTime(double)
     * @see #getInterpolatedDerivatives()
     * @see #getInterpolatedSecondaryState(int)
     * @see #getInterpolatedSecondaryDerivatives(int)
     */
    public double[] getInterpolatedState() throws MaxCountExceededException {
        return steps.get(index).getInterpolatedState();
    }

    /**
     * Get the derivatives of the state vector of the interpolated point.
     *
     * <p>The returned vector is a reference to a reused array, so it should not be modified and it
     * should be copied if it needs to be preserved across several calls to the associated {@link
     * #setInterpolatedTime(double)} method.
     *
     * @return derivatives of the state vector at time {@link #getInterpolatedTime}
     * @exception MaxCountExceededException if the number of functions evaluations is exceeded
     * @see #setInterpolatedTime(double)
     * @see #getInterpolatedState()
     * @see #getInterpolatedSecondaryState(int)
     * @see #getInterpolatedSecondaryDerivatives(int)
     * @since 3.4
     */
    public double[] getInterpolatedDerivatives() throws MaxCountExceededException {
        return steps.get(index).getInterpolatedDerivatives();
    }

    /**
     * Get the interpolated secondary state corresponding to the secondary equations.
     *
     * <p>The returned vector is a reference to a reused array, so it should not be modified and it
     * should be copied if it needs to be preserved across several calls to the associated {@link
     * #setInterpolatedTime(double)} method.
     *
     * @param secondaryStateIndex index of the secondary set, as returned by {@link
     *     org.apache.commons.math3.ode.ExpandableStatefulODE#addSecondaryEquations(
     *     org.apache.commons.math3.ode.SecondaryEquations)
     *     ExpandableStatefulODE.addSecondaryEquations(SecondaryEquations)}
     * @return interpolated secondary state at the current interpolation date
     * @see #setInterpolatedTime(double)
     * @see #getInterpolatedState()
     * @see #getInterpolatedDerivatives()
     * @see #getInterpolatedSecondaryDerivatives(int)
     * @since 3.2
     * @exception MaxCountExceededException if the number of functions evaluations is exceeded
     */
    public double[] getInterpolatedSecondaryState(final int secondaryStateIndex)
            throws MaxCountExceededException {
        return steps.get(index).getInterpolatedSecondaryState(secondaryStateIndex);
    }

    /**
     * Get the interpolated secondary derivatives corresponding to the secondary equations.
     *
     * <p>The returned vector is a reference to a reused array, so it should not be modified and it
     * should be copied if it needs to be preserved across several calls to the associated {@link
     * #setInterpolatedTime(double)} method.
     *
     * @param secondaryStateIndex index of the secondary set, as returned by {@link
     *     org.apache.commons.math3.ode.ExpandableStatefulODE#addSecondaryEquations(
     *     org.apache.commons.math3.ode.SecondaryEquations)
     *     ExpandableStatefulODE.addSecondaryEquations(SecondaryEquations)}
     * @return interpolated secondary derivatives at the current interpolation date
     * @see #setInterpolatedTime(double)
     * @see #getInterpolatedState()
     * @see #getInterpolatedDerivatives()
     * @see #getInterpolatedSecondaryState(int)
     * @since 3.4
     * @exception MaxCountExceededException if the number of functions evaluations is exceeded
     */
    public double[] getInterpolatedSecondaryDerivatives(final int secondaryStateIndex)
            throws MaxCountExceededException {
        return steps.get(index).getInterpolatedSecondaryDerivatives(secondaryStateIndex);
    }

    /**
     * Compare a step interval and a double.
     *
     * @param time point to locate
     * @param interval step interval
     * @return -1 if the double is before the interval, 0 if it is in the interval, and +1 if it is
     *     after the interval, according to the interval direction
     */
    private int locatePoint(final double time, final StepInterpolator interval) {
        if (forward) {
            if (time < interval.getPreviousTime()) {
                return -1;
            } else if (time > interval.getCurrentTime()) {
                return +1;
            } else {
                return 0;
            }
        }
        if (time > interval.getPreviousTime()) {
            return -1;
        } else if (time < interval.getCurrentTime()) {
            return +1;
        } else {
            return 0;
        }
    }
}