/*
    * 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
    *
    *      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,
   * 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.
   */
  
  /*
   * 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 &epsilon; 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} - &epsilon;, {@code v} + &epsilon;).
       *
       * @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 &rho; 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} - &rho; {@code v}, {@code v} + &rho; {@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 | &lt;= {@link #getAbsoluteAccuracy() absolute}
      * accuracy + max(ta, tb) * {@link #getRelativeAccuracy() relative} accuracy) or (
      * max(|f(ta)|, |f(tb)|) &lt;= {@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 | &lt;= {@link #getAbsoluteAccuracy() absolute}
      * accuracy + max(ta, tb) * {@link #getRelativeAccuracy() relative} accuracy) or (
      * max(|f(ta)|, |f(tb)|) &lt;= {@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();
             }
         }
 
     }
 
 }