| /* |
| * 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; |
| |
| /** |
| * 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 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(boolean fsal, |
| double[] c, double[][] a, double[] b, |
| RungeKuttaStepInterpolator prototype, |
| double minStep, double maxStep, |
| double scalAbsoluteTolerance, |
| double scalRelativeTolerance) { |
| |
| super(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 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(boolean fsal, |
| double[] c, double[][] a, double[] b, |
| RungeKuttaStepInterpolator prototype, |
| double minStep, double maxStep, |
| double[] vecAbsoluteTolerance, |
| double[] vecRelativeTolerance) { |
| |
| super(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 name of the method. |
| * @return name of the method |
| */ |
| public abstract String getName(); |
| |
| /** 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(double safety) { |
| this.safety = safety; |
| } |
| |
| /** Integrate the differential equations up to the given time. |
| * <p>This method solves an Initial Value Problem (IVP).</p> |
| * <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.</p> |
| * @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 |
| * @throws IntegratorException if the integrator cannot perform integration |
| * @throws DerivativeException this exception is propagated to the caller if |
| * the underlying user function triggers one |
| */ |
| public void integrate(FirstOrderDifferentialEquations equations, |
| double t0, double[] y0, |
| double t, double[] y) |
| throws DerivativeException, IntegratorException { |
| |
| sanityChecks(equations, t0, y0, t, y); |
| boolean forward = (t > t0); |
| |
| // create some internal working arrays |
| int stages = c.length + 1; |
| if (y != y0) { |
| System.arraycopy(y0, 0, y, 0, y0.length); |
| } |
| double[][] yDotK = new double[stages][]; |
| for (int i = 0; i < stages; ++i) { |
| yDotK [i] = new double[y0.length]; |
| } |
| double[] yTmp = new double[y0.length]; |
| |
| // set up an interpolator sharing the integrator arrays |
| AbstractStepInterpolator interpolator; |
| if (handler.requiresDenseOutput() || (! switchesHandler.isEmpty())) { |
| RungeKuttaStepInterpolator rki = (RungeKuttaStepInterpolator) prototype.copy(); |
| rki.reinitialize(equations, yTmp, yDotK, forward); |
| interpolator = rki; |
| } else { |
| interpolator = new DummyStepInterpolator(yTmp, forward); |
| } |
| interpolator.storeTime(t0); |
| |
| stepStart = t0; |
| double hNew = 0; |
| boolean firstTime = true; |
| boolean lastStep; |
| handler.reset(); |
| do { |
| |
| interpolator.shift(); |
| |
| double error = 0; |
| for (boolean loop = true; loop;) { |
| |
| if (firstTime || !fsal) { |
| // first stage |
| equations.computeDerivatives(stepStart, y, yDotK[0]); |
| } |
| |
| if (firstTime) { |
| double[] scale; |
| if (vecAbsoluteTolerance != null) { |
| scale = vecAbsoluteTolerance; |
| } else { |
| scale = new double[y0.length]; |
| for (int i = 0; i < scale.length; ++i) { |
| scale[i] = scalAbsoluteTolerance; |
| } |
| } |
| hNew = initializeStep(equations, forward, getOrder(), scale, |
| stepStart, y, yDotK[0], yTmp, yDotK[1]); |
| firstTime = false; |
| } |
| |
| stepSize = hNew; |
| |
| // step adjustment near bounds |
| if ((forward && (stepStart + stepSize > t)) || |
| ((! forward) && (stepStart + stepSize < t))) { |
| stepSize = t - stepStart; |
| } |
| |
| // 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; |
| } |
| |
| equations.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) { |
| |
| // Switching functions handling |
| interpolator.storeTime(stepStart + stepSize); |
| if (switchesHandler.evaluateStep(interpolator)) { |
| // reject the step to match exactly the next switch time |
| hNew = switchesHandler.getEventTime() - stepStart; |
| } else { |
| // accept the step |
| loop = false; |
| } |
| |
| } else { |
| // reject the step and attempt to reduce error by stepsize control |
| double factor = Math.min(maxGrowth, |
| Math.max(minReduction, |
| safety * Math.pow(error, exp))); |
| hNew = filterStep(stepSize * factor, false); |
| } |
| |
| } |
| |
| // the step has been accepted |
| double nextStep = stepStart + stepSize; |
| System.arraycopy(yTmp, 0, y, 0, y0.length); |
| switchesHandler.stepAccepted(nextStep, y); |
| if (switchesHandler.stop()) { |
| lastStep = true; |
| } else { |
| lastStep = forward ? (nextStep >= t) : (nextStep <= t); |
| } |
| |
| // provide the step data to the step handler |
| interpolator.storeTime(nextStep); |
| 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 (switchesHandler.reset(stepStart, y) && ! lastStep) { |
| // some switching function has triggered changes that |
| // invalidate the derivatives, we need to recompute them |
| equations.computeDerivatives(stepStart, y, yDotK[0]); |
| } |
| |
| if (! lastStep) { |
| // stepsize control for next step |
| double factor = Math.min(maxGrowth, |
| Math.max(minReduction, |
| safety * Math.pow(error, exp))); |
| double scaledH = stepSize * factor; |
| double nextT = stepStart + scaledH; |
| boolean nextIsLast = forward ? (nextT >= t) : (nextT <= t); |
| hNew = filterStep(scaledH, nextIsLast); |
| } |
| |
| } while (! lastStep); |
| |
| resetInternalState(); |
| |
| } |
| |
| /** 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(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(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; |
| |
| } |
