| /* |
| * 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.math4.legacy.ode.nonstiff; |
| |
| |
| import org.apache.commons.math4.legacy.exception.DimensionMismatchException; |
| import org.apache.commons.math4.legacy.exception.MaxCountExceededException; |
| import org.apache.commons.math4.legacy.exception.NoBracketingException; |
| import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException; |
| import org.apache.commons.math4.legacy.ode.AbstractIntegrator; |
| import org.apache.commons.math4.legacy.ode.ExpandableStatefulODE; |
| import org.apache.commons.math4.legacy.ode.FirstOrderDifferentialEquations; |
| import org.apache.commons.math4.legacy.core.jdkmath.AccurateMath; |
| |
| /** |
| * This class implements the common part of all fixed step Runge-Kutta |
| * integrators for Ordinary Differential Equations. |
| * |
| * <p>These methods are explicit Runge-Kutta methods, their Butcher |
| * arrays are as follows : |
| * <pre> |
| * 0 | |
| * c2 | a21 |
| * c3 | a31 a32 |
| * ... | ... |
| * cs | as1 as2 ... ass-1 |
| * |-------------------------- |
| * | b1 b2 ... bs-1 bs |
| * </pre> |
| * |
| * @see EulerIntegrator |
| * @see ClassicalRungeKuttaIntegrator |
| * @see GillIntegrator |
| * @see MidpointIntegrator |
| * @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 = AccurateMath.abs(step); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public void integrate(final ExpandableStatefulODE equations, final double t) |
| throws NumberIsTooSmallException, DimensionMismatchException, |
| MaxCountExceededException, NoBracketingException { |
| |
| sanityChecks(equations, t); |
| setEquations(equations); |
| final boolean forward = t > equations.getTime(); |
| |
| // create some internal working arrays |
| final double[] y0 = equations.getCompleteState(); |
| final double[] y = y0.clone(); |
| final int stages = c.length + 1; |
| final double[][] yDotK = new double[stages][]; |
| for (int i = 0; i < stages; ++i) { |
| yDotK [i] = new double[y0.length]; |
| } |
| final double[] yTmp = y0.clone(); |
| final double[] yDotTmp = new double[y0.length]; |
| |
| // set up an interpolator sharing the integrator arrays |
| final RungeKuttaStepInterpolator interpolator = (RungeKuttaStepInterpolator) prototype.copy(); |
| interpolator.reinitialize(this, yTmp, yDotK, forward, |
| equations.getPrimaryMapper(), equations.getSecondaryMappers()); |
| interpolator.storeTime(equations.getTime()); |
| |
| // set up integration control objects |
| stepStart = equations.getTime(); |
| if (forward) { |
| if (stepStart + step >= t) { |
| stepSize = t - stepStart; |
| } else { |
| stepSize = step; |
| } |
| } else { |
| if (stepStart - step <= t) { |
| stepSize = t - stepStart; |
| } else { |
| stepSize = -step; |
| } |
| } |
| initIntegration(equations.getTime(), y0, t); |
| |
| // 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); |
| |
| // dispatch results |
| equations.setTime(stepStart); |
| equations.setCompleteState(y); |
| |
| stepStart = Double.NaN; |
| stepSize = Double.NaN; |
| |
| } |
| |
| /** Fast computation of a single step of ODE integration. |
| * <p>This method is intended for the limited use case of |
| * very fast computation of only one step without using any of the |
| * rich features of general integrators that may take some time |
| * to set up (i.e. no step handlers, no events handlers, no additional |
| * states, no interpolators, no error control, no evaluations count, |
| * no sanity checks ...). It handles the strict minimum of computation, |
| * so it can be embedded in outer loops.</p> |
| * <p> |
| * This method is <em>not</em> used at all by the {@link #integrate(ExpandableStatefulODE, double)} |
| * method. It also completely ignores the step set at construction time, and |
| * uses only a single step to go from {@code t0} to {@code t}. |
| * </p> |
| * <p> |
| * As this method does not use any of the state-dependent features of the integrator, |
| * it should be reasonably thread-safe <em>if and only if</em> the provided differential |
| * equations are themselves 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} for backward integration) |
| * @return state vector at {@code t} |
| */ |
| public double[] singleStep(final FirstOrderDifferentialEquations equations, |
| final double t0, final double[] y0, final double t) { |
| |
| // create some internal working arrays |
| final double[] y = y0.clone(); |
| final int stages = c.length + 1; |
| final double[][] yDotK = new double[stages][]; |
| for (int i = 0; i < stages; ++i) { |
| yDotK [i] = new double[y0.length]; |
| } |
| final double[] yTmp = y0.clone(); |
| |
| // first stage |
| final double h = t - t0; |
| equations.computeDerivatives(t0, 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] + h * sum; |
| } |
| |
| equations.computeDerivatives(t0 + c[k-1] * h, 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]; |
| } |
| y[j] += h * sum; |
| } |
| |
| return y; |
| |
| } |
| |
| } |