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With inspiration from other libraries
/*
* 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) Higham and Hall integrator for
* Ordinary Differential Equations.
*
* 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.
*
* @param the type of the field elements
* @since 3.6
*/
public class HighamHall54FieldIntegrator>
extends EmbeddedRungeKuttaFieldIntegrator {
/** Integrator method name. */
private static final String METHOD_NAME = "Higham-Hall 5(4)";
/** Error weights Butcher array. */
private final T[] e ;
/** Simple constructor.
* Build a fifth order Higham and Hall 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 HighamHall54FieldIntegrator(final Field field,
final double minStep, final double maxStep,
final double scalAbsoluteTolerance,
final double scalRelativeTolerance) {
super(field, METHOD_NAME, -1,
minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
e = MathArrays.buildArray(field, 7);
e[0] = fraction(-1, 20);
e[1] = field.getZero();
e[2] = fraction(81, 160);
e[3] = fraction(-6, 5);
e[4] = fraction(25, 32);
e[5] = fraction( 1, 16);
e[6] = fraction(-1, 10);
}
/** Simple constructor.
* Build a fifth order Higham and Hall 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 HighamHall54FieldIntegrator(final Field field,
final double minStep, final double maxStep,
final double[] vecAbsoluteTolerance,
final double[] vecRelativeTolerance) {
super(field, METHOD_NAME, -1,
minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
e = MathArrays.buildArray(field, 7);
e[0] = fraction(-1, 20);
e[1] = field.getZero();
e[2] = fraction(81, 160);
e[3] = fraction(-6, 5);
e[4] = fraction(25, 32);
e[5] = fraction( 1, 16);
e[6] = fraction(-1, 10);
}
/** {@inheritDoc} */
public T[] getC() {
final T[] c = MathArrays.buildArray(getField(), 6);
c[0] = fraction(2, 9);
c[1] = fraction(1, 3);
c[2] = fraction(1, 2);
c[3] = fraction(3, 5);
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( 2, 9);
a[1][0] = fraction( 1, 12);
a[1][1] = fraction( 1, 4);
a[2][0] = fraction( 1, 8);
a[2][1] = getField().getZero();
a[2][2] = fraction( 3, 8);
a[3][0] = fraction( 91, 500);
a[3][1] = fraction( -27, 100);
a[3][2] = fraction( 78, 125);
a[3][3] = fraction( 8, 125);
a[4][0] = fraction( -11, 20);
a[4][1] = fraction( 27, 20);
a[4][2] = fraction( 12, 5);
a[4][3] = fraction( -36, 5);
a[4][4] = fraction( 5, 1);
a[5][0] = fraction( 1, 12);
a[5][1] = getField().getZero();
a[5][2] = fraction( 27, 32);
a[5][3] = fraction( -4, 3);
a[5][4] = fraction( 125, 96);
a[5][5] = fraction( 5, 48);
return a;
}
/** {@inheritDoc} */
public T[] getB() {
final T[] b = MathArrays.buildArray(getField(), 7);
b[0] = fraction( 1, 12);
b[1] = getField().getZero();
b[2] = fraction( 27, 32);
b[3] = fraction( -4, 3);
b[4] = fraction(125, 96);
b[5] = fraction( 5, 48);
b[6] = getField().getZero();
return b;
}
/** {@inheritDoc} */
@Override
protected HighamHall54FieldStepInterpolator
createInterpolator(final boolean forward, T[][] yDotK,
final FieldODEStateAndDerivative globalPreviousState,
final FieldODEStateAndDerivative globalCurrentState, final FieldEquationsMapper mapper) {
return new HighamHall54FieldStepInterpolator(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) {
T errSum = yDotK[0][j].multiply(e[0]);
for (int l = 1; l < e.length; ++l) {
errSum = errSum.add(yDotK[l][j].multiply(e[l]));
}
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();
}
}