001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math.ode.nonstiff;
019
020
021 import org.apache.commons.math.ode.AbstractIntegrator;
022 import org.apache.commons.math.ode.DerivativeException;
023 import org.apache.commons.math.ode.FirstOrderDifferentialEquations;
024 import org.apache.commons.math.ode.IntegratorException;
025 import org.apache.commons.math.ode.sampling.AbstractStepInterpolator;
026 import org.apache.commons.math.ode.sampling.DummyStepInterpolator;
027 import org.apache.commons.math.ode.sampling.StepHandler;
028 import org.apache.commons.math.util.FastMath;
029
030 /**
031 * This class implements the common part of all fixed step Runge-Kutta
032 * integrators for Ordinary Differential Equations.
033 *
034 * <p>These methods are explicit Runge-Kutta methods, their Butcher
035 * arrays are as follows :
036 * <pre>
037 * 0 |
038 * c2 | a21
039 * c3 | a31 a32
040 * ... | ...
041 * cs | as1 as2 ... ass-1
042 * |--------------------------
043 * | b1 b2 ... bs-1 bs
044 * </pre>
045 * </p>
046 *
047 * @see EulerIntegrator
048 * @see ClassicalRungeKuttaIntegrator
049 * @see GillIntegrator
050 * @see MidpointIntegrator
051 * @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 f??vr. 2011) $
052 * @since 1.2
053 */
054
055 public abstract class RungeKuttaIntegrator extends AbstractIntegrator {
056
057 /** Time steps from Butcher array (without the first zero). */
058 private final double[] c;
059
060 /** Internal weights from Butcher array (without the first empty row). */
061 private final double[][] a;
062
063 /** External weights for the high order method from Butcher array. */
064 private final double[] b;
065
066 /** Prototype of the step interpolator. */
067 private final RungeKuttaStepInterpolator prototype;
068
069 /** Integration step. */
070 private final double step;
071
072 /** Simple constructor.
073 * Build a Runge-Kutta integrator with the given
074 * step. The default step handler does nothing.
075 * @param name name of the method
076 * @param c time steps from Butcher array (without the first zero)
077 * @param a internal weights from Butcher array (without the first empty row)
078 * @param b propagation weights for the high order method from Butcher array
079 * @param prototype prototype of the step interpolator to use
080 * @param step integration step
081 */
082 protected RungeKuttaIntegrator(final String name,
083 final double[] c, final double[][] a, final double[] b,
084 final RungeKuttaStepInterpolator prototype,
085 final double step) {
086 super(name);
087 this.c = c;
088 this.a = a;
089 this.b = b;
090 this.prototype = prototype;
091 this.step = FastMath.abs(step);
092 }
093
094 /** {@inheritDoc} */
095 public double integrate(final FirstOrderDifferentialEquations equations,
096 final double t0, final double[] y0,
097 final double t, final double[] y)
098 throws DerivativeException, IntegratorException {
099
100 sanityChecks(equations, t0, y0, t, y);
101 setEquations(equations);
102 resetEvaluations();
103 final boolean forward = t > t0;
104
105 // create some internal working arrays
106 final int stages = c.length + 1;
107 if (y != y0) {
108 System.arraycopy(y0, 0, y, 0, y0.length);
109 }
110 final double[][] yDotK = new double[stages][];
111 for (int i = 0; i < stages; ++i) {
112 yDotK [i] = new double[y0.length];
113 }
114 final double[] yTmp = new double[y0.length];
115 final double[] yDotTmp = new double[y0.length];
116
117 // set up an interpolator sharing the integrator arrays
118 AbstractStepInterpolator interpolator;
119 if (requiresDenseOutput()) {
120 final RungeKuttaStepInterpolator rki = (RungeKuttaStepInterpolator) prototype.copy();
121 rki.reinitialize(this, yTmp, yDotK, forward);
122 interpolator = rki;
123 } else {
124 interpolator = new DummyStepInterpolator(yTmp, yDotK[stages - 1], forward);
125 }
126 interpolator.storeTime(t0);
127
128 // set up integration control objects
129 stepStart = t0;
130 stepSize = forward ? step : -step;
131 for (StepHandler handler : stepHandlers) {
132 handler.reset();
133 }
134 setStateInitialized(false);
135
136 // main integration loop
137 isLastStep = false;
138 do {
139
140 interpolator.shift();
141
142 // first stage
143 computeDerivatives(stepStart, y, yDotK[0]);
144
145 // next stages
146 for (int k = 1; k < stages; ++k) {
147
148 for (int j = 0; j < y0.length; ++j) {
149 double sum = a[k-1][0] * yDotK[0][j];
150 for (int l = 1; l < k; ++l) {
151 sum += a[k-1][l] * yDotK[l][j];
152 }
153 yTmp[j] = y[j] + stepSize * sum;
154 }
155
156 computeDerivatives(stepStart + c[k-1] * stepSize, yTmp, yDotK[k]);
157
158 }
159
160 // estimate the state at the end of the step
161 for (int j = 0; j < y0.length; ++j) {
162 double sum = b[0] * yDotK[0][j];
163 for (int l = 1; l < stages; ++l) {
164 sum += b[l] * yDotK[l][j];
165 }
166 yTmp[j] = y[j] + stepSize * sum;
167 }
168
169 // discrete events handling
170 interpolator.storeTime(stepStart + stepSize);
171 System.arraycopy(yTmp, 0, y, 0, y0.length);
172 System.arraycopy(yDotK[stages - 1], 0, yDotTmp, 0, y0.length);
173 stepStart = acceptStep(interpolator, y, yDotTmp, t);
174
175 if (!isLastStep) {
176
177 // prepare next step
178 interpolator.storeTime(stepStart);
179
180 // stepsize control for next step
181 final double nextT = stepStart + stepSize;
182 final boolean nextIsLast = forward ? (nextT >= t) : (nextT <= t);
183 if (nextIsLast) {
184 stepSize = t - stepStart;
185 }
186 }
187
188 } while (!isLastStep);
189
190 final double stopTime = stepStart;
191 stepStart = Double.NaN;
192 stepSize = Double.NaN;
193 return stopTime;
194
195 }
196
197 }