RidderSingleRootEstimator.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 searches for REAL roots only!
* This implementation is based on Numerical Recipes 3rd ed. Section 9.2.1, page
* 452.
*/
public class RidderSingleRootEstimator extends BracketedSingleRootEstimator {
/**
* Maximum number of iterations.
*/
public static final int MAXIT = 60;
/**
* Constant defining default accuracy of the estimated root.
*/
public static final double DEFAULT_TOLERANCE = 1e-6;
/**
* Constant defining minimum allowed tolerance.
*/
public static final double MIN_TOLERANCE = 0.0;
/**
* Tolerance value. The algorithm will iterate until the result converges
* below this value of accuracy or until the maximum number of iterations is
* achieved (and in such case, convergence will be assumed to have failed).
*/
private double tolerance;
/**
* Empty constructor.
*/
public RidderSingleRootEstimator() {
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 be achieved in the estimated root.
* @throws InvalidBracketRangeException Raised if minEvalPoint <
* maxEvalPoint.
* @throws IllegalArgumentException Raised if tolerance is negative.
*/
public RidderSingleRootEstimator(
final SingleDimensionFunctionEvaluatorListener listener, final double minEvalPoint,
final double maxEvalPoint, final double tolerance) throws InvalidBracketRangeException {
super(listener, minEvalPoint, maxEvalPoint);
internalSetTolerance(tolerance);
}
/**
* Returns tolerance value.
* Tolerance is the accuracy to be achieved when estimating a root.
* If a root is found by this class, it is ensured to have an accuracy below
* the tolerance value.
*
* @return Tolerance value.
*/
public double getTolerance() {
return tolerance;
}
/**
* Internal method to set tolerance value.
* Tolerance is the accuracy to be achieved when estimating a root.
* If a root is found by this class, it is ensured to have an accuracy below
* provided tolerance value.
* This method does not check whether this instance is locked or not.
*
* @param tolerance Tolerance value.
* @throws IllegalArgumentException Raised if provided tolerance value is
* negative.
*/
private void internalSetTolerance(final double tolerance) {
if (tolerance < MIN_TOLERANCE) {
throw new IllegalArgumentException();
}
this.tolerance = tolerance;
}
/**
* Sets tolerance value.
* Tolerance is the accuracy to be achieved when estimating a root.
* If a root is found by this class, it is ensured to have an accuracy below
* provided tolerance value.
*
* @param tolerance Tolerance value.
* @throws LockedException Raised if this instance is locked.
* @throws IllegalArgumentException Raised if provided tolerance value is
* negative.
*/
public void setTolerance(final double tolerance) throws LockedException {
if (isLocked()) {
throw new LockedException();
}
internalSetTolerance(tolerance);
}
/**
* Estimates a local root for a given single dimension function being
* evaluated by provided listener.
*
* @throws LockedException Exception raised if this instance is already
* locked.
* @throws NotReadyException Exception raised if either a listener has not
* yet been provided or a bracket has not been provided or computed.
* @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
@SuppressWarnings("Duplicates")
public void estimate() throws LockedException, NotReadyException, RootEstimationException {
if (isLocked()) {
throw new LockedException();
}
if (!isReady()) {
throw new NotReadyException();
}
locked = true;
final var x1 = minEvalPoint;
final var x2 = maxEvalPoint;
final var xacc = tolerance;
double fl;
double fh;
try {
fl = listener.evaluate(x1);
fh = listener.evaluate(x2);
} catch (final EvaluationException e) {
throw new RootEstimationException(e);
}
double ans;
var found = false;
if ((fl > 0.0 && fh < 0.0) || (fl < 0.0 && fh > 0.0)) {
var xl = x1;
var xh = x2;
ans = -9.99e99;
try {
for (var j = 0; j < MAXIT; j++) {
final var xm = 0.5 * (xl + xh);
final var fm = listener.evaluate(xm);
final var s = Math.sqrt(fm * fm - fl * fh);
if (s == 0.0) {
found = true;
break;
}
final var xnew = xm + (xm - xl) * ((fl >= fh ? 1.0 : -1.0) * fm / s);
if (Math.abs(xnew - ans) <= xacc) {
// result found
found = true;
break;
}
ans = xnew;
final var fnew = listener.evaluate(ans);
if (sign(fm, fnew) != fm) {
xl = xm;
fl = fm;
xh = ans;
fh = fnew;
} else if (sign(fl, fnew) != fl) {
xh = ans;
fh = fnew;
} else if (sign(fh, fnew) != fh) {
xl = ans;
fl = fnew;
} else {
// never get here
locked = false;
throw new RootEstimationException();
}
if (Math.abs(xh - xl) <= xacc) {
// result found
found = true;
break;
}
}
} catch (final EvaluationException e) {
throw new RootEstimationException(e);
}
if (!found) {
// too many iterations and error exceeds desired tolerance
locked = false;
throw new RootEstimationException();
}
} else {
if (fl == 0.0) {
// result found
ans = x1;
} else if (fh == 0.0) {
// result found
ans = x2;
} else {
locked = false;
throw new RootEstimationException();
}
}
// result found
root = ans;
rootAvailable = true;
locked = false;
}
/**
* Returns boolean indicating whether this instance is ready to start
* estimating a root.
* This class will be ready once a listener is provided and a bracket is
* either provided or computed.
*
* @return True if this instance is ready, false otherwise.
*/
@Override
public boolean isReady() {
return isListenerAvailable() && isBracketAvailable();
}
}