/*
* 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.math3.ode.nonstiff;
import org.apache.commons.math3.Field;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.MathUtils;
/**
* This class implements the 5(4) Dormand-Prince integrator for Ordinary
* Differential Equations.
* <p>This integrator is an embedded Runge-Kutta integrator
* of order 5(4) used in local extrapolation mode (i.e. the solution
* is computed using the high order formula) with stepsize control
* (and automatic step initialization) and continuous output. This
* method uses 7 functions evaluations per step. However, since this
* is an <i>fsal</i>, the last evaluation of one step is the same as
* the first evaluation of the next step and hence can be avoided. So
* the cost is really 6 functions evaluations per step.</p>
*
* <p>This method has been published (whithout the continuous output
* that was added by Shampine in 1986) in the following article :
* <pre>
* A family of embedded Runge-Kutta formulae
* J. R. Dormand and P. J. Prince
* Journal of Computational and Applied Mathematics
* volume 6, no 1, 1980, pp. 19-26
* </pre></p>
*
* @param <T> the type of the field elements
* @since 3.6
*/
public class DormandPrince54FieldIntegrator<T extends RealFieldElement<T>>
extends EmbeddedRungeKuttaFieldIntegrator<T> {
/** Integrator method name. */
private static final String METHOD_NAME = "Dormand-Prince 5(4)";
/** Error array, element 1. */
private final T e1;
// element 2 is zero, so it is neither stored nor used
/** Error array, element 3. */
private final T e3;
/** Error array, element 4. */
private final T e4;
/** Error array, element 5. */
private final T e5;
/** Error array, element 6. */
private final T e6;
/** Error array, element 7. */
private final T e7;
/** Simple constructor.
* Build a fifth order Dormand-Prince integrator with the given step bounds
* @param field field to which the time and state vector elements belong
* @param minStep minimal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param maxStep maximal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param scalAbsoluteTolerance allowed absolute error
* @param scalRelativeTolerance allowed relative error
*/
public DormandPrince54FieldIntegrator(final Field<T> field,
final double minStep, final double maxStep,
final double scalAbsoluteTolerance,
final double scalRelativeTolerance) {
super(field, METHOD_NAME, 6,
minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
e1 = fraction( 71, 57600);
e3 = fraction( -71, 16695);
e4 = fraction( 71, 1920);
e5 = fraction(-17253, 339200);
e6 = fraction( 22, 525);
e7 = fraction( -1, 40);
}
/** Simple constructor.
* Build a fifth order Dormand-Prince integrator with the given step bounds
* @param field field to which the time and state vector elements belong
* @param minStep minimal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param maxStep maximal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param vecAbsoluteTolerance allowed absolute error
* @param vecRelativeTolerance allowed relative error
*/
public DormandPrince54FieldIntegrator(final Field<T> field,
final double minStep, final double maxStep,
final double[] vecAbsoluteTolerance,
final double[] vecRelativeTolerance) {
super(field, METHOD_NAME, 6,
minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
e1 = fraction( 71, 57600);
e3 = fraction( -71, 16695);
e4 = fraction( 71, 1920);
e5 = fraction(-17253, 339200);
e6 = fraction( 22, 525);
e7 = fraction( -1, 40);
}
/** {@inheritDoc} */
public T[] getC() {
final T[] c = MathArrays.buildArray(getField(), 6);
c[0] = fraction(1, 5);
c[1] = fraction(3, 10);
c[2] = fraction(4, 5);
c[3] = fraction(8, 9);
c[4] = getField().getOne();
c[5] = getField().getOne();
return c;
}
/** {@inheritDoc} */
public T[][] getA() {
final T[][] a = MathArrays.buildArray(getField(), 6, -1);
for (int i = 0; i < a.length; ++i) {
a[i] = MathArrays.buildArray(getField(), i + 1);
}
a[0][0] = fraction( 1, 5);
a[1][0] = fraction( 3, 40);
a[1][1] = fraction( 9, 40);
a[2][0] = fraction( 44, 45);
a[2][1] = fraction( -56, 15);
a[2][2] = fraction( 32, 9);
a[3][0] = fraction( 19372, 6561);
a[3][1] = fraction(-25360, 2187);
a[3][2] = fraction( 64448, 6561);
a[3][3] = fraction( -212, 729);
a[4][0] = fraction( 9017, 3168);
a[4][1] = fraction( -355, 33);
a[4][2] = fraction( 46732, 5247);
a[4][3] = fraction( 49, 176);
a[4][4] = fraction( -5103, 18656);
a[5][0] = fraction( 35, 384);
a[5][1] = getField().getZero();
a[5][2] = fraction( 500, 1113);
a[5][3] = fraction( 125, 192);
a[5][4] = fraction( -2187, 6784);
a[5][5] = fraction( 11, 84);
return a;
}
/** {@inheritDoc} */
public T[] getB() {
final T[] b = MathArrays.buildArray(getField(), 7);
b[0] = fraction( 35, 384);
b[1] = getField().getZero();
b[2] = fraction( 500, 1113);
b[3] = fraction( 125, 192);
b[4] = fraction(-2187, 6784);
b[5] = fraction( 11, 84);
b[6] = getField().getZero();
return b;
}
/** {@inheritDoc} */
@Override
protected DormandPrince54FieldStepInterpolator<T>
createInterpolator(final boolean forward, T[][] yDotK,
final FieldODEStateAndDerivative<T> globalPreviousState,
final FieldODEStateAndDerivative<T> globalCurrentState, final FieldEquationsMapper<T> mapper) {
return new DormandPrince54FieldStepInterpolator<T>(getField(), forward, yDotK,
globalPreviousState, globalCurrentState,
globalPreviousState, globalCurrentState,
mapper);
}
/** {@inheritDoc} */
@Override
public int getOrder() {
return 5;
}
/** {@inheritDoc} */
@Override
protected T estimateError(final T[][] yDotK, final T[] y0, final T[] y1, final T h) {
T error = getField().getZero();
for (int j = 0; j < mainSetDimension; ++j) {
final T errSum = yDotK[0][j].multiply(e1).
add(yDotK[2][j].multiply(e3)).
add(yDotK[3][j].multiply(e4)).
add(yDotK[4][j].multiply(e5)).
add(yDotK[5][j].multiply(e6)).
add(yDotK[6][j].multiply(e7));
final T yScale = MathUtils.max(y0[j].abs(), y1[j].abs());
final T tol = (vecAbsoluteTolerance == null) ?
yScale.multiply(scalRelativeTolerance).add(scalAbsoluteTolerance) :
yScale.multiply(vecRelativeTolerance[j]).add(vecAbsoluteTolerance[j]);
final T ratio = h.multiply(errSum).divide(tol);
error = error.add(ratio.multiply(ratio));
}
return error.divide(mainSetDimension).sqrt();
}
}