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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.math.analysis.solvers;
import org.apache.commons.math.ConvergenceException;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.MaxIterationsExceededException;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.util.FastMath;
/**
* Implements a modified version of the
* <a href="http://mathworld.wolfram.com/SecantMethod.html">secant method</a>
* for approximating a zero of a real univariate function.
* <p>
* The algorithm is modified to maintain bracketing of a root by successive
* approximations. Because of forced bracketing, convergence may be slower than
* the unrestricted secant algorithm. However, this implementation should in
* general outperform the
* <a href="http://mathworld.wolfram.com/MethodofFalsePosition.html">
* regula falsi method.</a></p>
* <p>
* The function is assumed to be continuous but not necessarily smooth.</p>
*
* @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $
*/
public class SecantSolver extends UnivariateRealSolverImpl {
/**
* Construct a solver for the given function.
* @param f function to solve.
* @deprecated as of 2.0 the function to solve is passed as an argument
* to the {@link #solve(UnivariateRealFunction, double, double)} or
* {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)}
* method.
*/
@Deprecated
public SecantSolver(UnivariateRealFunction f) {
super(f, 100, 1E-6);
}
/**
* Construct a solver.
* @deprecated in 2.2 (to be removed in 3.0).
*/
@Deprecated
public SecantSolver() {
super(100, 1E-6);
}
/** {@inheritDoc} */
@Deprecated
public double solve(final double min, final double max)
throws ConvergenceException, FunctionEvaluationException {
return solve(f, min, max);
}
/** {@inheritDoc} */
@Deprecated
public double solve(final double min, final double max, final double initial)
throws ConvergenceException, FunctionEvaluationException {
return solve(f, min, max, initial);
}
/**
* Find a zero in the given interval.
*
* @param f the function to solve
* @param min the lower bound for the interval
* @param max the upper bound for the interval
* @param initial the start value to use (ignored)
* @param maxEval Maximum number of evaluations.
* @return the value where the function is zero
* @throws MaxIterationsExceededException if the maximum iteration count is exceeded
* @throws FunctionEvaluationException if an error occurs evaluating the function
* @throws IllegalArgumentException if min is not less than max or the
* signs of the values of the function at the endpoints are not opposites
*/
@Override
public double solve(int maxEval, final UnivariateRealFunction f,
final double min, final double max, final double initial)
throws MaxIterationsExceededException, FunctionEvaluationException {
setMaximalIterationCount(maxEval);
return solve(f, min, max, initial);
}
/**
* Find a zero in the given interval.
*
* @param f the function to solve
* @param min the lower bound for the interval
* @param max the upper bound for the interval
* @param initial the start value to use (ignored)
* @return the value where the function is zero
* @throws MaxIterationsExceededException if the maximum iteration count is exceeded
* @throws FunctionEvaluationException if an error occurs evaluating the function
* @throws IllegalArgumentException if min is not less than max or the
* signs of the values of the function at the endpoints are not opposites
* @deprecated in 2.2 (to be removed in 3.0).
*/
@Deprecated
public double solve(final UnivariateRealFunction f,
final double min, final double max, final double initial)
throws MaxIterationsExceededException, FunctionEvaluationException {
return solve(f, min, max);
}
/**
* Find a zero in the given interval.
* @param f the function to solve
* @param min the lower bound for the interval.
* @param max the upper bound for the interval.
* @param maxEval Maximum number of evaluations.
* @return the value where the function is zero
* @throws MaxIterationsExceededException if the maximum iteration count is exceeded
* @throws FunctionEvaluationException if an error occurs evaluating the function
* @throws IllegalArgumentException if min is not less than max or the
* signs of the values of the function at the endpoints are not opposites
*/
@Override
public double solve(int maxEval, final UnivariateRealFunction f,
final double min, final double max)
throws MaxIterationsExceededException, FunctionEvaluationException {
setMaximalIterationCount(maxEval);
return solve(f, min, max);
}
/**
* Find a zero in the given interval.
* @param f the function to solve
* @param min the lower bound for the interval.
* @param max the upper bound for the interval.
* @return the value where the function is zero
* @throws MaxIterationsExceededException if the maximum iteration count is exceeded
* @throws FunctionEvaluationException if an error occurs evaluating the function
* @throws IllegalArgumentException if min is not less than max or the
* signs of the values of the function at the endpoints are not opposites
* @deprecated in 2.2 (to be removed in 3.0).
*/
@Deprecated
public double solve(final UnivariateRealFunction f,
final double min, final double max)
throws MaxIterationsExceededException, FunctionEvaluationException {
clearResult();
verifyInterval(min, max);
// Index 0 is the old approximation for the root.
// Index 1 is the last calculated approximation for the root.
// Index 2 is a bracket for the root with respect to x0.
// OldDelta is the length of the bracketing interval of the last
// iteration.
double x0 = min;
double x1 = max;
double y0 = f.value(x0);
double y1 = f.value(x1);
// Verify bracketing
if (y0 * y1 >= 0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.SAME_SIGN_AT_ENDPOINTS, min, max, y0, y1);
}
double x2 = x0;
double y2 = y0;
double oldDelta = x2 - x1;
int i = 0;
while (i < maximalIterationCount) {
if (FastMath.abs(y2) < FastMath.abs(y1)) {
x0 = x1;
x1 = x2;
x2 = x0;
y0 = y1;
y1 = y2;
y2 = y0;
}
if (FastMath.abs(y1) <= functionValueAccuracy) {
setResult(x1, i);
return result;
}
if (FastMath.abs(oldDelta) <
FastMath.max(relativeAccuracy * FastMath.abs(x1), absoluteAccuracy)) {
setResult(x1, i);
return result;
}
double delta;
if (FastMath.abs(y1) > FastMath.abs(y0)) {
// Function value increased in last iteration. Force bisection.
delta = 0.5 * oldDelta;
} else {
delta = (x0 - x1) / (1 - y0 / y1);
if (delta / oldDelta > 1) {
// New approximation falls outside bracket.
// Fall back to bisection.
delta = 0.5 * oldDelta;
}
}
x0 = x1;
y0 = y1;
x1 = x1 + delta;
y1 = f.value(x1);
if ((y1 > 0) == (y2 > 0)) {
// New bracket is (x0,x1).
x2 = x0;
y2 = y0;
}
oldDelta = x2 - x1;
i++;
}
throw new MaxIterationsExceededException(maximalIterationCount);
}
}
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