/*
 * 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.math.ode.nonstiff;

import java.util.Arrays;

import org.apache.commons.math.ode.DerivativeException;
import org.apache.commons.math.ode.FirstOrderDifferentialEquations;
import org.apache.commons.math.ode.IntegratorException;
import org.apache.commons.math.ode.events.CombinedEventsManager;
import org.apache.commons.math.ode.sampling.AbstractStepInterpolator;
import org.apache.commons.math.ode.sampling.DummyStepInterpolator;
import org.apache.commons.math.ode.sampling.StepHandler;

/**
 * This class implements the common part of all embedded Runge-Kutta
 * integrators for Ordinary Differential Equations.
 *
 * <p>These methods are embedded explicit Runge-Kutta methods with two
 * sets of coefficients allowing to estimate the error, their Butcher
 * arrays are as follows :
 * <pre>
 *    0  |
 *   c2  | a21
 *   c3  | a31  a32
 *   ... |        ...
 *   cs  | as1  as2  ...  ass-1
 *       |--------------------------
 *       |  b1   b2  ...   bs-1  bs
 *       |  b'1  b'2 ...   b's-1 b's
 * </pre>
 * </p>
 *
 * <p>In fact, we rather use the array defined by ej = bj - b'j to
 * compute directly the error rather than computing two estimates and
 * then comparing them.</p>
 *
 * <p>Some methods are qualified as <i>fsal</i> (first same as last)
 * methods. This means the last evaluation of the derivatives in one
 * step is the same as the first in the next step. Then, this
 * evaluation can be reused from one step to the next one and the cost
 * of such a method is really s-1 evaluations despite the method still
 * has s stages. This behaviour is true only for successful steps, if
 * the step is rejected after the error estimation phase, no
 * evaluation is saved. For an <i>fsal</i> method, we have cs = 1 and
 * asi = bi for all i.</p>
 *
 * @version $Revision$ $Date$
 * @since 1.2
 */

public abstract class EmbeddedRungeKuttaIntegrator
  extends AdaptiveStepsizeIntegrator {

  /** Build a Runge-Kutta integrator with the given Butcher array.
   * @param name name of the method
   * @param fsal indicate that the method is an <i>fsal</i>
   * @param c time steps from Butcher array (without the first zero)
   * @param a internal weights from Butcher array (without the first empty row)
   * @param b propagation weights for the high order method from Butcher array
   * @param prototype prototype of the step interpolator to use
   * @param minStep minimal step (must be positive even for backward
   * integration), the last step can be smaller than this
   * @param maxStep maximal step (must be positive even for backward
   * integration)
   * @param scalAbsoluteTolerance allowed absolute error
   * @param scalRelativeTolerance allowed relative error
   */
  protected EmbeddedRungeKuttaIntegrator(final String name, final boolean fsal,
                                         final double[] c, final double[][] a, final double[] b,
                                         final RungeKuttaStepInterpolator prototype,
                                         final double minStep, final double maxStep,
                                         final double scalAbsoluteTolerance,
                                         final double scalRelativeTolerance) {

    super(name, minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);

    this.fsal      = fsal;
    this.c         = c;
    this.a         = a;
    this.b         = b;
    this.prototype = prototype;

    exp = -1.0 / getOrder();

    // set the default values of the algorithm control parameters
    setSafety(0.9);
    setMinReduction(0.2);
    setMaxGrowth(10.0);

  }

  /** Build a Runge-Kutta integrator with the given Butcher array.
   * @param name name of the method
   * @param fsal indicate that the method is an <i>fsal</i>
   * @param c time steps from Butcher array (without the first zero)
   * @param a internal weights from Butcher array (without the first empty row)
   * @param b propagation weights for the high order method from Butcher array
   * @param prototype prototype of the step interpolator to use
   * @param minStep minimal step (must be positive even for backward
   * integration), the last step can be smaller than this
   * @param maxStep maximal step (must be positive even for backward
   * integration)
   * @param vecAbsoluteTolerance allowed absolute error
   * @param vecRelativeTolerance allowed relative error
   */
  protected EmbeddedRungeKuttaIntegrator(final String name, final boolean fsal,
                                         final double[] c, final double[][] a, final double[] b,
                                         final RungeKuttaStepInterpolator prototype,
                                         final double   minStep, final double maxStep,
                                         final double[] vecAbsoluteTolerance,
                                         final double[] vecRelativeTolerance) {

    super(name, minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);

    this.fsal      = fsal;
    this.c         = c;
    this.a         = a;
    this.b         = b;
    this.prototype = prototype;

    exp = -1.0 / getOrder();

    // set the default values of the algorithm control parameters
    setSafety(0.9);
    setMinReduction(0.2);
    setMaxGrowth(10.0);

  }

  /** Get the order of the method.
   * @return order of the method
   */
  public abstract int getOrder();

  /** Get the safety factor for stepsize control.
   * @return safety factor
   */
  public double getSafety() {
    return safety;
  }

  /** Set the safety factor for stepsize control.
   * @param safety safety factor
   */
  public void setSafety(final double safety) {
    this.safety = safety;
  }

  /** {@inheritDoc} */
  @Override
  public double integrate(final FirstOrderDifferentialEquations equations,
                          final double t0, final double[] y0,
                          final double t, final double[] y)
  throws DerivativeException, IntegratorException {

    sanityChecks(equations, t0, y0, t, y);
    setEquations(equations);
    resetEvaluations();
    final boolean forward = (t > t0);

    // create some internal working arrays
    final int stages = c.length + 1;
    if (y != y0) {
      System.arraycopy(y0, 0, y, 0, y0.length);
    }
    final double[][] yDotK = new double[stages][y0.length];
    final double[] yTmp = new double[y0.length];

    // set up an interpolator sharing the integrator arrays
    AbstractStepInterpolator interpolator;
    if (requiresDenseOutput() || (! eventsHandlersManager.isEmpty())) {
      final RungeKuttaStepInterpolator rki = (RungeKuttaStepInterpolator) prototype.copy();
      rki.reinitialize(this, yTmp, yDotK, forward);
      interpolator = rki;
    } else {
      interpolator = new DummyStepInterpolator(yTmp, forward);
    }
    interpolator.storeTime(t0);

    // set up integration control objects
    stepStart         = t0;
    double  hNew      = 0;
    boolean firstTime = true;
    for (StepHandler handler : stepHandlers) {
        handler.reset();
    }
    CombinedEventsManager manager = addEndTimeChecker(t0, t, eventsHandlersManager);
    boolean lastStep = false;

    // main integration loop
    while (!lastStep) {

      interpolator.shift();

      double error = 0;
      for (boolean loop = true; loop;) {

        if (firstTime || !fsal) {
          // first stage
          computeDerivatives(stepStart, y, yDotK[0]);
        }

        if (firstTime) {
          final double[] scale;
          if (vecAbsoluteTolerance != null) {
            scale = vecAbsoluteTolerance;
          } else {
            scale = new double[y0.length];
            Arrays.fill(scale, scalAbsoluteTolerance);
          }
          hNew = initializeStep(equations, forward, getOrder(), scale,
                                stepStart, y, yDotK[0], yTmp, yDotK[1]);
          firstTime = false;
        }

        stepSize = hNew;

        // next stages
        for (int k = 1; k < stages; ++k) {

          for (int j = 0; j < y0.length; ++j) {
            double sum = a[k-1][0] * yDotK[0][j];
            for (int l = 1; l < k; ++l) {
              sum += a[k-1][l] * yDotK[l][j];
            }
            yTmp[j] = y[j] + stepSize * sum;
          }

          computeDerivatives(stepStart + c[k-1] * stepSize, yTmp, yDotK[k]);

        }

        // estimate the state at the end of the step
        for (int j = 0; j < y0.length; ++j) {
          double sum    = b[0] * yDotK[0][j];
          for (int l = 1; l < stages; ++l) {
            sum    += b[l] * yDotK[l][j];
          }
          yTmp[j] = y[j] + stepSize * sum;
        }

        // estimate the error at the end of the step
        error = estimateError(yDotK, y, yTmp, stepSize);
        if (error <= 1.0) {

          // discrete events handling
          interpolator.storeTime(stepStart + stepSize);
          if (manager.evaluateStep(interpolator)) {
              final double dt = manager.getEventTime() - stepStart;
              if (Math.abs(dt) <= Math.ulp(stepStart)) {
                  // rejecting the step would lead to a too small next step, we accept it
                  loop = false;
              } else {
                  // reject the step to match exactly the next switch time
                  hNew = dt;
              }
          } else {
            // accept the step
            loop = false;
          }

        } else {
          // reject the step and attempt to reduce error by stepsize control
          final double factor =
              Math.min(maxGrowth,
                       Math.max(minReduction, safety * Math.pow(error, exp)));
          hNew = filterStep(stepSize * factor, forward, false);
        }

      }

      // the step has been accepted
      final double nextStep = stepStart + stepSize;
      System.arraycopy(yTmp, 0, y, 0, y0.length);
      manager.stepAccepted(nextStep, y);
      lastStep = manager.stop();

      // provide the step data to the step handler
      interpolator.storeTime(nextStep);
      for (StepHandler handler : stepHandlers) {
          handler.handleStep(interpolator, lastStep);
      }
      stepStart = nextStep;

      if (fsal) {
        // save the last evaluation for the next step
        System.arraycopy(yDotK[stages - 1], 0, yDotK[0], 0, y0.length);
      }

      if (manager.reset(stepStart, y) && ! lastStep) {
        // some event handler has triggered changes that
        // invalidate the derivatives, we need to recompute them
        computeDerivatives(stepStart, y, yDotK[0]);
      }

      if (! lastStep) {
        // in some rare cases we may get here with stepSize = 0, for example
        // when an event occurs at integration start, reducing the first step
        // to zero; we have to reset the step to some safe non zero value
          stepSize = filterStep(stepSize, forward, true);

        // stepsize control for next step
        final double factor = Math.min(maxGrowth,
                                       Math.max(minReduction,
                                                safety * Math.pow(error, exp)));
        final double  scaledH    = stepSize * factor;
        final double  nextT      = stepStart + scaledH;
        final boolean nextIsLast = forward ? (nextT >= t) : (nextT <= t);
        hNew = filterStep(scaledH, forward, nextIsLast);
      }

    }

    final double stopTime = stepStart;
    resetInternalState();
    return stopTime;

  }

  /** Get the minimal reduction factor for stepsize control.
   * @return minimal reduction factor
   */
  public double getMinReduction() {
    return minReduction;
  }

  /** Set the minimal reduction factor for stepsize control.
   * @param minReduction minimal reduction factor
   */
  public void setMinReduction(final double minReduction) {
    this.minReduction = minReduction;
  }

  /** Get the maximal growth factor for stepsize control.
   * @return maximal growth factor
   */
  public double getMaxGrowth() {
    return maxGrowth;
  }

  /** Set the maximal growth factor for stepsize control.
   * @param maxGrowth maximal growth factor
   */
  public void setMaxGrowth(final double maxGrowth) {
    this.maxGrowth = maxGrowth;
  }

  /** Compute the error ratio.
   * @param yDotK derivatives computed during the first stages
   * @param y0 estimate of the step at the start of the step
   * @param y1 estimate of the step at the end of the step
   * @param h  current step
   * @return error ratio, greater than 1 if step should be rejected
   */
  protected abstract double estimateError(double[][] yDotK,
                                          double[] y0, double[] y1,
                                          double h);

  /** Indicator for <i>fsal</i> methods. */
  private boolean fsal;

  /** Time steps from Butcher array (without the first zero). */
  private double[] c;

  /** Internal weights from Butcher array (without the first empty row). */
  private double[][] a;

  /** External weights for the high order method from Butcher array. */
  private double[] b;

  /** Prototype of the step interpolator. */
  private RungeKuttaStepInterpolator prototype;
                                         
  /** Stepsize control exponent. */
  private double exp;

  /** Safety factor for stepsize control. */
  private double safety;

  /** Minimal reduction factor for stepsize control. */
  private double minReduction;

  /** Maximal growth factor for stepsize control. */
  private double maxGrowth;

}
