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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.math.ode.nonstiff;


import org.apache.commons.math.ode.AbstractIntegrator;
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.sampling.AbstractStepInterpolator;
import org.apache.commons.math.ode.sampling.DummyStepInterpolator;
import org.apache.commons.math.ode.sampling.StepHandler;
import org.apache.commons.math.util.FastMath;

/**
 * This class implements the common part of all fixed step Runge-Kutta
 * integrators for Ordinary Differential Equations.
 *
 * 

These methods are explicit Runge-Kutta methods, their Butcher * arrays are as follows : *

 *    0  |
 *   c2  | a21
 *   c3  | a31  a32
 *   ... |        ...
 *   cs  | as1  as2  ...  ass-1
 *       |--------------------------
 *       |  b1   b2  ...   bs-1  bs
 * 
*

* * @see EulerIntegrator * @see ClassicalRungeKuttaIntegrator * @see GillIntegrator * @see MidpointIntegrator * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $ * @since 1.2 */ public abstract class RungeKuttaIntegrator extends AbstractIntegrator { /** Time steps from Butcher array (without the first zero). */ private final double[] c; /** Internal weights from Butcher array (without the first empty row). */ private final double[][] a; /** External weights for the high order method from Butcher array. */ private final double[] b; /** Prototype of the step interpolator. */ private final RungeKuttaStepInterpolator prototype; /** Integration step. */ private final double step; /** Simple constructor. * Build a Runge-Kutta integrator with the given * step. The default step handler does nothing. * @param name name of the method * @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 step integration step */ protected RungeKuttaIntegrator(final String name, final double[] c, final double[][] a, final double[] b, final RungeKuttaStepInterpolator prototype, final double step) { super(name); this.c = c; this.a = a; this.b = b; this.prototype = prototype; this.step = FastMath.abs(step); } /** {@inheritDoc} */ 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][]; for (int i = 0; i < stages; ++i) { yDotK [i] = new double[y0.length]; } final double[] yTmp = new double[y0.length]; final double[] yDotTmp = new double[y0.length]; // set up an interpolator sharing the integrator arrays AbstractStepInterpolator interpolator; if (requiresDenseOutput()) { final RungeKuttaStepInterpolator rki = (RungeKuttaStepInterpolator) prototype.copy(); rki.reinitialize(this, yTmp, yDotK, forward); interpolator = rki; } else { interpolator = new DummyStepInterpolator(yTmp, yDotK[stages - 1], forward); } interpolator.storeTime(t0); // set up integration control objects stepStart = t0; stepSize = forward ? step : -step; for (StepHandler handler : stepHandlers) { handler.reset(); } setStateInitialized(false); // main integration loop isLastStep = false; do { interpolator.shift(); // first stage computeDerivatives(stepStart, y, yDotK[0]); // 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; } // discrete events handling interpolator.storeTime(stepStart + stepSize); System.arraycopy(yTmp, 0, y, 0, y0.length); System.arraycopy(yDotK[stages - 1], 0, yDotTmp, 0, y0.length); stepStart = acceptStep(interpolator, y, yDotTmp, t); if (!isLastStep) { // prepare next step interpolator.storeTime(stepStart); // stepsize control for next step final double nextT = stepStart + stepSize; final boolean nextIsLast = forward ? (nextT >= t) : (nextT <= t); if (nextIsLast) { stepSize = t - stepStart; } } } while (!isLastStep); final double stopTime = stepStart; stepStart = Double.NaN; stepSize = Double.NaN; return stopTime; } }




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