BracketedRealFieldUnivariateSolver.java
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* 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
*
* https://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,
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/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.analysis.solvers;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.analysis.CalculusFieldUnivariateFunction;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.MathIllegalStateException;
import org.hipparchus.exception.MathRuntimeException;
/** Interface for {@link UnivariateSolver (univariate real) root-finding
* algorithms} that maintain a bracketed solution. There are several advantages
* to having such root-finding algorithms:
* <ul>
* <li>The bracketed solution guarantees that the root is kept within the
* interval. As such, these algorithms generally also guarantee
* convergence.</li>
* <li>The bracketed solution means that we have the opportunity to only
* return roots that are greater than or equal to the actual root, or
* are less than or equal to the actual root. That is, we can control
* whether under-approximations and over-approximations are
* {@link AllowedSolution allowed solutions}. Other root-finding
* algorithms can usually only guarantee that the solution (the root that
* was found) is around the actual root.</li>
* </ul>
*
* <p>For backwards compatibility, all root-finding algorithms must have
* {@link AllowedSolution#ANY_SIDE ANY_SIDE} as default for the allowed
* solutions.</p>
*
* @see AllowedSolution
* @param <T> the type of the field elements
*/
public interface BracketedRealFieldUnivariateSolver<T extends CalculusFieldElement<T>> {
/**
* Get the maximum number of function evaluations.
*
* @return the maximum number of function evaluations.
*/
int getMaxEvaluations();
/**
* Get the number of evaluations of the objective function.
* The number of evaluations corresponds to the last call to the
* {@code optimize} method. It is 0 if the method has not been
* called yet.
*
* @return the number of evaluations of the objective function.
*/
int getEvaluations();
/**
* Get the absolute accuracy of the solver. Solutions returned by the
* solver should be accurate to this tolerance, i.e., if ε is the
* absolute accuracy of the solver and {@code v} is a value returned by
* one of the {@code solve} methods, then a root of the function should
* exist somewhere in the interval ({@code v} - ε, {@code v} + ε).
*
* @return the absolute accuracy.
*/
T getAbsoluteAccuracy();
/**
* Get the relative accuracy of the solver. The contract for relative
* accuracy is the same as {@link #getAbsoluteAccuracy()}, but using
* relative, rather than absolute error. If ρ is the relative accuracy
* configured for a solver and {@code v} is a value returned, then a root
* of the function should exist somewhere in the interval
* ({@code v} - ρ {@code v}, {@code v} + ρ {@code v}).
*
* @return the relative accuracy.
*/
T getRelativeAccuracy();
/**
* Get the function value accuracy of the solver. If {@code v} is
* a value returned by the solver for a function {@code f},
* then by contract, {@code |f(v)|} should be less than or equal to
* the function value accuracy configured for the solver.
*
* @return the function value accuracy.
*/
T getFunctionValueAccuracy();
/**
* Solve for a zero in the given interval.
* A solver may require that the interval brackets a single zero root.
* Solvers that do require bracketing should be able to handle the case
* where one of the endpoints is itself a root.
*
* @param maxEval Maximum number of evaluations.
* @param f Function to solve.
* @param min Lower bound for the interval.
* @param max Upper bound for the interval.
* @param allowedSolution The kind of solutions that the root-finding algorithm may
* accept as solutions.
* @return A value where the function is zero.
* @throws org.hipparchus.exception.MathIllegalArgumentException
* if the arguments do not satisfy the requirements specified by the solver.
* @throws org.hipparchus.exception.MathIllegalStateException if
* the allowed number of evaluations is exceeded.
*/
T solve(int maxEval, CalculusFieldUnivariateFunction<T> f, T min, T max,
AllowedSolution allowedSolution);
/**
* Solve for a zero in the given interval, start at {@code startValue}.
* A solver may require that the interval brackets a single zero root.
* Solvers that do require bracketing should be able to handle the case
* where one of the endpoints is itself a root.
*
* @param maxEval Maximum number of evaluations.
* @param f Function to solve.
* @param min Lower bound for the interval.
* @param max Upper bound for the interval.
* @param startValue Start value to use.
* @param allowedSolution The kind of solutions that the root-finding algorithm may
* accept as solutions.
* @return A value where the function is zero.
* @throws org.hipparchus.exception.MathIllegalArgumentException
* if the arguments do not satisfy the requirements specified by the solver.
* @throws org.hipparchus.exception.MathIllegalStateException if
* the allowed number of evaluations is exceeded.
*/
T solve(int maxEval, CalculusFieldUnivariateFunction<T> f, T min, T max, T startValue,
AllowedSolution allowedSolution);
/**
* Solve for a zero in the given interval and return a tolerance interval surrounding
* the root.
*
* <p> It is required that the starting interval brackets a root.
*
* @param maxEval Maximum number of evaluations.
* @param f Function to solve.
* @param min Lower bound for the interval. f(min) != 0.0.
* @param max Upper bound for the interval. f(max) != 0.0.
* @return an interval [ta, tb] such that for some t in [ta, tb] f(t) == 0.0 or has a
* step wise discontinuity that crosses zero. Both end points also satisfy the
* convergence criteria so either one could be used as the root. That is the interval
* satisfies the condition (| tb - ta | <= {@link #getAbsoluteAccuracy() absolute}
* accuracy + max(ta, tb) * {@link #getRelativeAccuracy() relative} accuracy) or (
* max(|f(ta)|, |f(tb)|) <= {@link #getFunctionValueAccuracy()}) or there are no
* numbers in the field between ta and tb. The width of the interval (tb - ta) may be
* zero.
* @throws MathIllegalArgumentException if the arguments do not satisfy the
* requirements specified by the solver.
* @throws MathIllegalStateException if the allowed number of evaluations is
* exceeded.
*/
default Interval<T> solveInterval(int maxEval,
CalculusFieldUnivariateFunction<T> f,
T min,
T max)
throws MathIllegalArgumentException, MathIllegalStateException {
return this.solveInterval(maxEval, f, min, max, min.add(max.subtract(min).multiply(0.5)));
}
/**
* Solve for a zero in the given interval and return a tolerance interval surrounding
* the root.
*
* <p> It is required that the starting interval brackets a root.
*
* @param maxEval Maximum number of evaluations.
* @param startValue start value to use.
* @param f Function to solve.
* @param min Lower bound for the interval. f(min) != 0.0.
* @param max Upper bound for the interval. f(max) != 0.0.
* @return an interval [ta, tb] such that for some t in [ta, tb] f(t) == 0.0 or has a
* step wise discontinuity that crosses zero. Both end points also satisfy the
* convergence criteria so either one could be used as the root. That is the interval
* satisfies the condition (| tb - ta | <= {@link #getAbsoluteAccuracy() absolute}
* accuracy + max(ta, tb) * {@link #getRelativeAccuracy() relative} accuracy) or (
* max(|f(ta)|, |f(tb)|) <= {@link #getFunctionValueAccuracy()}) or numbers in the
* field between ta and tb. The width of the interval (tb - ta) may be zero.
* @throws MathIllegalArgumentException if the arguments do not satisfy the
* requirements specified by the solver.
* @throws MathIllegalStateException if the allowed number of evaluations is
* exceeded.
*/
Interval<T> solveInterval(int maxEval,
CalculusFieldUnivariateFunction<T> f,
T min,
T max,
T startValue)
throws MathIllegalArgumentException, MathIllegalStateException;
/**
* An interval of a function that brackets a root.
* <p>
* Contains two end points and the value of the function at the two end points.
*
* @see #solveInterval(int, CalculusFieldUnivariateFunction, CalculusFieldElement,
* CalculusFieldElement)
* @param <T> the element type
*/
class Interval<T extends CalculusFieldElement<T>> {
/** Abscissa on the left end of the interval. */
private final T leftAbscissa;
/** Function value at {@link #leftAbscissa}. */
private final T leftValue;
/** Abscissa on the right end of the interval, >= {@link #leftAbscissa}. */
private final T rightAbscissa;
/** Function value at {@link #rightAbscissa}. */
private final T rightValue;
/**
* Construct a new interval with the given end points.
*
* @param leftAbscissa is the abscissa value at the left side of the interval.
* @param leftValue is the function value at {@code leftAbscissa}.
* @param rightAbscissa is the abscissa value on the right side of the interval.
* Must be greater than or equal to {@code leftAbscissa}.
* @param rightValue is the function value at {@code rightAbscissa}.
*/
public Interval(final T leftAbscissa,
final T leftValue,
final T rightAbscissa,
final T rightValue) {
this.leftAbscissa = leftAbscissa;
this.leftValue = leftValue;
this.rightAbscissa = rightAbscissa;
this.rightValue = rightValue;
}
/**
* Get the left abscissa.
*
* @return abscissa of the start of the interval.
*/
public T getLeftAbscissa() {
return leftAbscissa;
}
/**
* Get the right abscissa.
*
* @return abscissa of the end of the interval.
*/
public T getRightAbscissa() {
return rightAbscissa;
}
/**
* Get the function value at {@link #getLeftAbscissa()}.
*
* @return value of the function at the start of the interval.
*/
public T getLeftValue() {
return leftValue;
}
/**
* Get the function value at {@link #getRightAbscissa()}.
*
* @return value of the function at the end of the interval.
*/
public T getRightValue() {
return rightValue;
}
/**
* Get the abscissa corresponding to the allowed side.
*
* @param allowed side of the root.
* @return the abscissa on the selected side of the root.
*/
public T getSide(final AllowedSolution allowed) {
final T xA = this.getLeftAbscissa();
final T yA = this.getLeftValue();
final T xB = this.getRightAbscissa();
switch (allowed) {
case ANY_SIDE:
final T absYA = this.getLeftValue().abs();
final T absYB = this.getRightValue().abs();
return absYA.subtract(absYB).getReal() < 0 ? xA : xB;
case LEFT_SIDE:
return xA;
case RIGHT_SIDE:
return xB;
case BELOW_SIDE:
return (yA.getReal() <= 0) ? xA : xB;
case ABOVE_SIDE:
return (yA.getReal() < 0) ? xB : xA;
default:
// this should never happen
throw MathRuntimeException.createInternalError();
}
}
}
}