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/*
* 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.analysis.solvers;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
/**
* Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html">
* Ridders' Method</a> for root finding of real univariate functions. For
* reference, see C. Ridders, <i>A new algorithm for computing a single root
* of a real continuous function </i>, IEEE Transactions on Circuits and
* Systems, 26 (1979), 979 - 980.
* <p>
* The function should be continuous but not necessarily smooth.</p>
*
* @since 1.2
*/
public class RiddersSolver extends AbstractUnivariateSolver {
/** Default absolute accuracy. */
private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;
/**
* Construct a solver with default accuracy (1e-6).
*/
public RiddersSolver() {
this(DEFAULT_ABSOLUTE_ACCURACY);
}
/**
* Construct a solver.
*
* @param absoluteAccuracy Absolute accuracy.
*/
public RiddersSolver(double absoluteAccuracy) {
super(absoluteAccuracy);
}
/**
* Construct a solver.
*
* @param relativeAccuracy Relative accuracy.
* @param absoluteAccuracy Absolute accuracy.
*/
public RiddersSolver(double relativeAccuracy,
double absoluteAccuracy) {
super(relativeAccuracy, absoluteAccuracy);
}
/**
* {@inheritDoc}
*/
@Override
protected double doSolve()
throws TooManyEvaluationsException,
NoBracketingException {
double min = getMin();
double max = getMax();
// [x1, x2] is the bracketing interval in each iteration
// x3 is the midpoint of [x1, x2]
// x is the new root approximation and an endpoint of the new interval
double x1 = min;
double y1 = computeObjectiveValue(x1);
double x2 = max;
double y2 = computeObjectiveValue(x2);
// check for zeros before verifying bracketing
if (y1 == 0) {
return min;
}
if (y2 == 0) {
return max;
}
verifyBracketing(min, max);
final double absoluteAccuracy = getAbsoluteAccuracy();
final double functionValueAccuracy = getFunctionValueAccuracy();
final double relativeAccuracy = getRelativeAccuracy();
double oldx = Double.POSITIVE_INFINITY;
while (true) {
// calculate the new root approximation
final double x3 = 0.5 * (x1 + x2);
final double y3 = computeObjectiveValue(x3);
if (FastMath.abs(y3) <= functionValueAccuracy) {
return x3;
}
final double delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing
final double correction = (FastMath.signum(y2) * FastMath.signum(y3)) *
(x3 - x1) / FastMath.sqrt(delta);
final double x = x3 - correction; // correction != 0
final double y = computeObjectiveValue(x);
// check for convergence
final double tolerance = FastMath.max(relativeAccuracy * FastMath.abs(x), absoluteAccuracy);
if (FastMath.abs(x - oldx) <= tolerance) {
return x;
}
if (FastMath.abs(y) <= functionValueAccuracy) {
return x;
}
// prepare the new interval for next iteration
// Ridders' method guarantees x1 < x < x2
if (correction > 0.0) { // x1 < x < x3
if (FastMath.signum(y1) + FastMath.signum(y) == 0.0) {
x2 = x;
y2 = y;
} else {
x1 = x;
x2 = x3;
y1 = y;
y2 = y3;
}
} else { // x3 < x < x2
if (FastMath.signum(y2) + FastMath.signum(y) == 0.0) {
x1 = x;
y1 = y;
} else {
x1 = x3;
x2 = x;
y1 = y3;
y2 = y;
}
}
oldx = x;
}
}
}
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