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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.util.FastMath;
+import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.exception.ConvergenceException;
+import org.apache.commons.math.exception.MathInternalError;
+
+/**
+ * Base class for all bracketing <em>Secant</em>-based methods for root-finding
+ * (approximating a zero of a univariate real function).
+ *
+ * <p>Implementation of the {@link RegulaFalsiSolver <em>Regula Falsi</em>} and
+ * {@link IllinoisSolver <em>Illinois</em>} methods is based on the
+ * following article: M. Dowell and P. Jarratt,
+ * <em>A modified regula falsi method for computing the root of an
+ * equation</em>, BIT Numerical Mathematics, volume 11, number 2,
+ * pages 168-174, Springer, 1971.</p>
+ *
+ * <p>Implementation of the {@link PegasusSolver <em>Pegasus</em>} method is
+ * based on the following article: M. Dowell and P. Jarratt,
+ * <em>The "Pegasus" method for computing the root of an equation</em>,
+ * BIT Numerical Mathematics, volume 12, number 4, pages 503-508, Springer,
+ * 1972.</p>
+ *
+ * <p>The {@link SecantSolver <em>Secant</em>} method is <em>not</em> a
+ * bracketing method, so it is not implemented here. It has a separate
+ * implementation.</p>
+ *
+ * @since 3.0
+ * @version $Id$
+ */
+public abstract class BaseSecantSolver
+    extends AbstractUnivariateRealSolver
+    implements BracketedUnivariateRealSolver<UnivariateRealFunction> {
+
+    /** Default absolute accuracy. */
+    protected static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;
+
+    /** The kinds of solutions that the algorithm may accept. */
+    private AllowedSolution allowed;
+
+    /** The <em>Secant</em>-based root-finding method to use. */
+    private final Method method;
+
+    /**
+     * Construct a solver.
+     *
+     * @param absoluteAccuracy Absolute accuracy.
+     * @param method <em>Secant</em>-based root-finding method to use.
+     */
+    protected BaseSecantSolver(final double absoluteAccuracy, final Method method) {
+        super(absoluteAccuracy);
+        this.allowed = AllowedSolution.ANY_SIDE;
+        this.method = method;
+    }
+
+    /**
+     * Construct a solver.
+     *
+     * @param relativeAccuracy Relative accuracy.
+     * @param absoluteAccuracy Absolute accuracy.
+     * @param method <em>Secant</em>-based root-finding method to use.
+     */
+    protected BaseSecantSolver(final double relativeAccuracy,
+                               final double absoluteAccuracy,
+                               final Method method) {
+        super(relativeAccuracy, absoluteAccuracy);
+        this.allowed = AllowedSolution.ANY_SIDE;
+        this.method = method;
+    }
+
+    /**
+     * Construct a solver.
+     *
+     * @param relativeAccuracy Maximum relative error.
+     * @param absoluteAccuracy Maximum absolute error.
+     * @param functionValueAccuracy Maximum function value error.
+     * @param method <em>Secant</em>-based root-finding method to use
+     */
+    protected BaseSecantSolver(final double relativeAccuracy,
+                               final double absoluteAccuracy,
+                               final double functionValueAccuracy,
+                               final Method method) {
+        super(relativeAccuracy, absoluteAccuracy, functionValueAccuracy);
+        this.allowed = AllowedSolution.ANY_SIDE;
+        this.method = method;
+    }
+
+    /** {@inheritDoc} */
+    public double solve(final int maxEval, final UnivariateRealFunction f,
+                        final double min, final double max,
+                        final AllowedSolution allowedSolution) {
+        return solve(maxEval, f, min, max, min + 0.5 * (max - min), allowedSolution);
+    }
+
+    /** {@inheritDoc} */
+    public double solve(final int maxEval, final UnivariateRealFunction f,
+                        final double min, final double max, final double startValue,
+                        final AllowedSolution allowedSolution) {
+        this.allowed = allowedSolution;
+        return super.solve(maxEval, f, min, max, startValue);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double solve(final int maxEval, final UnivariateRealFunction f,
+                        final double min, final double max, final double startValue) {
+        return solve(maxEval, f, min, max, startValue, AllowedSolution.ANY_SIDE);
+    }
+
+    /** {@inheritDoc} */
+    protected final double doSolve() {
+        // Get initial solution
+        double x0 = getMin();
+        double x1 = getMax();
+        double f0 = computeObjectiveValue(x0);
+        double f1 = computeObjectiveValue(x1);
+
+        // If one of the bounds is the exact root, return it. Since these are
+        // not under-approximations or over-approximations, we can return them
+        // regardless of the allowed solutions.
+        if (f0 == 0.0) {
+            return x0;
+        }
+        if (f1 == 0.0) {
+            return x1;
+        }
+
+        // Verify bracketing of initial solution.
+        verifyBracketing(x0, x1);
+
+        // Get accuracies.
+        final double ftol = getFunctionValueAccuracy();
+        final double atol = getAbsoluteAccuracy();
+        final double rtol = getRelativeAccuracy();
+
+        // Keep track of inverted intervals, meaning that the left bound is
+        // larger than the right bound.
+        boolean inverted = false;
+
+        // Keep finding better approximations.
+        while (true) {
+            // Calculate the next approximation.
+            final double x = x1 - ((f1 * (x1 - x0)) / (f1 - f0));
+            final double fx = computeObjectiveValue(x);
+
+            // If the new approximation is the exact root, return it. Since
+            // this is not an under-approximation or an over-approximation,
+            // we can return it regardless of the allowed solutions.
+            if (fx == 0.0) {
+                return x;
+            }
+
+            // Update the bounds with the new approximation.
+            if (f1 * fx < 0) {
+                // The value of x1 has switched to the other bound, thus inverting
+                // the interval.
+                x0 = x1;
+                f0 = f1;
+                inverted = !inverted;
+            } else {
+                switch (method) {
+                case ILLINOIS:
+                    f0 *= 0.5;
+                    break;
+                case PEGASUS:
+                    f0 *= f1 / (f1 + fx);
+                    break;
+                case REGULA_FALSI:
+                    // Detect early that algorithm is stuck, instead of waiting
+                    // for the maximum number of iterations to be exceeded.
+                    break;
+                default:
+                    // Should never happen.
+                    throw new MathInternalError();
+                }
+            }
+            // Update from [x0, x1] to [x0, x].
+            x1 = x;
+            f1 = fx;
+
+            // If the function value of the last approximation is too small,
+            // given the function value accuracy, then we can't get closer to
+            // the root than we already are.
+            if (FastMath.abs(f1) <= ftol) {
+                switch (allowed) {
+                case ANY_SIDE:
+                    return x1;
+                case LEFT_SIDE:
+                    if (inverted) {
+                        return x1;
+                    }
+                    break;
+                case RIGHT_SIDE:
+                    if (!inverted) {
+                        return x1;
+                    }
+                    break;
+                case BELOW_SIDE:
+                    if (f1 <= 0) {
+                        return x1;
+                    }
+                    break;
+                case ABOVE_SIDE:
+                    if (f1 >= 0) {
+                        return x1;
+                    }
+                    break;
+                default:
+                    throw new MathInternalError();
+                }
+            }
+
+            // If the current interval is within the given accuracies, we
+            // are satisfied with the current approximation.
+            if (FastMath.abs(x1 - x0) < FastMath.max(rtol * FastMath.abs(x1),
+                                                     atol)) {
+                switch (allowed) {
+                case ANY_SIDE:
+                    return x1;
+                case LEFT_SIDE:
+                    return inverted ? x1 : x0;
+                case RIGHT_SIDE:
+                    return inverted ? x0 : x1;
+                case BELOW_SIDE:
+                    return (f1 <= 0) ? x1 : x0;
+                case ABOVE_SIDE:
+                    return (f1 >= 0) ? x1 : x0;
+                default:
+                    throw new MathInternalError();
+                }
+            }
+        }
+    }
+
+    /** <em>Secant</em>-based root-finding methods. */
+    protected enum Method {
+
+        /**
+         * The {@link RegulaFalsiSolver <em>Regula Falsi</em>} or
+         * <em>False Position</em> method.
+         */
+        REGULA_FALSI,
+
+        /** The {@link IllinoisSolver <em>Illinois</em>} method. */
+        ILLINOIS,
+
+        /** The {@link PegasusSolver <em>Pegasus</em>} method. */
+        PEGASUS;
+
+    }
+}