FalsePositionSingleRootEstimator.java
/*
* Copyright (C) 2012 Alberto Irurueta Carro (alberto@irurueta.com)
*
* Licensed 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 com.irurueta.numerical.roots;
import com.irurueta.numerical.EvaluationException;
import com.irurueta.numerical.InvalidBracketRangeException;
import com.irurueta.numerical.LockedException;
import com.irurueta.numerical.NotReadyException;
import com.irurueta.numerical.SingleDimensionFunctionEvaluatorListener;
/**
* Computes a root for a single dimension function inside a given bracket of
* values, in other words, root will only be searched within provided minimum
* and maximum evaluation points.
* This class is based on the false position algorithm.
* This implementation is based on Numerical Recipes 3rd ed. Section 9.2
* page 451.
*/
public class FalsePositionSingleRootEstimator extends BracketedSingleRootEstimator {
/**
* Maximum allowed number of iterations.
*/
public static final int MAXIT = 30;
/**
* Constant defining default tolerance to find a root.
*/
public static final double DEFAULT_TOLERANCE = 1e-6;
/**
* Minimum allowed tolerance that can be set.
*/
public static final double MIN_TOLERANCE = 0.0;
/**
* Tolerance to find a root. Whenever the variation of the estimated root is
* smaller than the provided tolerance, then the algorithm is assumed to be
* converged.
*/
private double tolerance;
/**
* Empty constructor.
*/
public FalsePositionSingleRootEstimator() {
super();
tolerance = DEFAULT_TOLERANCE;
}
/**
* Constructor.
*
* @param listener Listener to evaluate a single dimension function f(x)
* to find its roots.
* @param minEvalPoint Smallest value inside the bracket of values where the
* root will be searched.
* @param maxEvalPoint Largest value inside the bracket of values where the
* root will be searched.
* @param tolerance Tolerance to find a root. During the estimation of a
* root, if the variation of the estimated root is smaller than the provided
* tolerance, then the algorithm is assumed to be converged, and the root
* is ensured to have an accuracy that equals tolerance.
* @throws InvalidBracketRangeException Raised if minEvalPoint <
* maxEvalPoint.
* @throws IllegalArgumentException Raised if provided tolerance is negative.
*/
public FalsePositionSingleRootEstimator(
final SingleDimensionFunctionEvaluatorListener listener, final double minEvalPoint,
final double maxEvalPoint, final double tolerance) throws InvalidBracketRangeException {
super(listener, minEvalPoint, maxEvalPoint);
internalSetTolerance(tolerance);
}
/**
* Returns tolerance to find a root. Whenever the variation of the estimated
* root is smaller than returned tolerance, then the algorithm is assumed to
* be converged, and the estimated root is ensured to have an accuracy that
* equals the returned tolerance.
*
* @return Tolerance to find a root.
*/
public double getTolerance() {
return tolerance;
}
/**
* Sets tolerance to find a root. Whenever the variation of the estimated
* root is smaller than provided tolerance, then the algorithm is assumed to
* be converged, and the estimated root is ensured to have an accuracy that
* equals provided tolerance.
*
* @param tolerance Tolerance to find a root.
* @throws LockedException Raised if this instance is locked while doing
* some computations.
* @throws IllegalArgumentException Raised if provided tolerance is negative.
*/
public void setTolerance(final double tolerance) throws LockedException {
if (isLocked()) {
throw new LockedException();
}
internalSetTolerance(tolerance);
}
/**
* Estimates a single root of the provided single dimension function
* contained within a given bracket of values.
*
* @throws LockedException Exception raised if this instance is already
* locked.
* @throws NotReadyException Exception raised if not enough parameters have
* been provided in order to start the estimation.
* @throws RootEstimationException Raised if the root estimation failed for
* some other reason (usually inability to evaluate the function,
* numerical instability or convergence problems, or no roots are found).
*/
@Override
public void estimate() throws LockedException, NotReadyException, RootEstimationException {
if (isLocked()) {
throw new LockedException();
}
if (!isReady()) {
throw new NotReadyException();
}
locked = true;
rootAvailable = false;
try {
final var v1 = new double[1];
final var v2 = new double[1];
final var x1 = minEvalPoint;
final var x2 = maxEvalPoint;
final var xacc = tolerance;
double xl;
double xh;
double del;
var fl = listener.evaluate(x1);
var fh = listener.evaluate(x2);
if (fl * fh > 0.0) {
// root must be bracketed
locked = false;
throw new RootEstimationException();
}
if (fl < 0.0) {
xl = x1;
xh = x2;
} else {
xl = x2;
xh = x1;
v1[0] = fl;
v2[0] = fh;
swap(v1, v2);
fl = v1[0];
fh = v2[0];
}
var dx = xh - xl;
for (var j = 0; j < MAXIT; j++) {
final var rtf = xl + dx * fl / (fl - fh);
final var f = listener.evaluate(rtf);
if (f < 0.0) {
del = xl - rtf;
xl = rtf;
fl = f;
} else {
del = xh - rtf;
xh = rtf;
fh = f;
}
dx = xh - xl;
if (Math.abs(del) < xacc || f == 0.0) {
// result obtained
root = rtf;
rootAvailable = true;
locked = false;
return;
}
}
} catch (final EvaluationException e) {
throw new RootEstimationException(e);
}
// too many iterations and error exceeds desired tolerance
locked = false;
throw new RootEstimationException();
}
/**
* Returns boolean indicating whether this instance is ready to compute a
* root.
* This instance is ready as soon as a listener is provided and a bracket
* is provided or computed.
*
* @return True if instance is ready, false otherwise
*/
@Override
public boolean isReady() {
return isListenerAvailable() && isBracketAvailable();
}
/**
* Internal method to set tolerance to find a root. This method does not
* check whether this instance is locked.
* Whenever the variation of the estimated root is smaller than provided
* tolerance, then the algorithm is assumed to be converged, and the
* estimated root is ensured to have an accuracy that equals provided
* tolerance.
*
* @param tolerance Tolerance to find a root.
* @throws IllegalArgumentException Raised if provided tolerance is negative.
*/
private void internalSetTolerance(final double tolerance) {
if (tolerance < MIN_TOLERANCE) {
throw new IllegalArgumentException();
}
this.tolerance = tolerance;
}
}