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Diffstat (limited to 'src/main/java/org/apache/commons/math/ode/nonstiff/RungeKuttaIntegrator.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math/ode/nonstiff/RungeKuttaIntegrator.java | 197 |
1 files changed, 197 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/RungeKuttaIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/RungeKuttaIntegrator.java new file mode 100644 index 0000000..c550f90 --- /dev/null +++ b/src/main/java/org/apache/commons/math/ode/nonstiff/RungeKuttaIntegrator.java @@ -0,0 +1,197 @@ +/* + * 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. + * + * <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> + * </p> + * + * @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; + + } + +} |