// <copyright file="GoldenSectionMinimizer.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
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//
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using System;

namespace IStation.Numerics.Optimization
{
    public class GoldenSectionMinimizer
    {
        public double XTolerance { get; set; }
        public int MaximumIterations { get; set; }
        public int MaximumExpansionSteps { get; set; }
        public double LowerExpansionFactor { get; set; }
        public double UpperExpansionFactor { get; set; }

        public GoldenSectionMinimizer(double xTolerance=1e-5, int maxIterations=1000, int maxExpansionSteps=10, double lowerExpansionFactor=2.0, double upperExpansionFactor=2.0)
        {
            XTolerance = xTolerance;
            MaximumIterations = maxIterations;
            MaximumExpansionSteps = maxExpansionSteps;
            LowerExpansionFactor = lowerExpansionFactor;
            UpperExpansionFactor = upperExpansionFactor;
        }

        public ScalarMinimizationResult FindMinimum(IScalarObjectiveFunction objective, double lowerBound, double upperBound)
        {
            return Minimum(objective, lowerBound, upperBound, XTolerance, MaximumIterations, MaximumExpansionSteps, LowerExpansionFactor, UpperExpansionFactor);
        }

        public static ScalarMinimizationResult Minimum(IScalarObjectiveFunction objective, double lowerBound, double upperBound, double xTolerance=1e-5, int maxIterations=1000, int maxExpansionSteps=10, double lowerExpansionFactor=2.0, double upperExpansionFactor=2.0)
        {
            if (upperBound <= lowerBound)
            {
                throw new OptimizationException("Lower bound must be lower than upper bound.");
            }

            double middlePointX = lowerBound + (upperBound - lowerBound)/(1 + Constants.GoldenRatio);
            IScalarObjectiveFunctionEvaluation lower = objective.Evaluate(lowerBound);
            IScalarObjectiveFunctionEvaluation middle = objective.Evaluate(middlePointX);
            IScalarObjectiveFunctionEvaluation upper = objective.Evaluate(upperBound);

            ValueChecker(lower.Value, lowerBound);
            ValueChecker(middle.Value, middlePointX);
            ValueChecker(upper.Value, upperBound);

            int expansion_steps = 0;
            while ((expansion_steps < maxExpansionSteps) && (upper.Value < middle.Value || lower.Value < middle.Value))
            {
                if (lower.Value < middle.Value)
                {
                    lowerBound = 0.5*(upperBound + lowerBound) - lowerExpansionFactor*0.5*(upperBound - lowerBound);
                    lower = objective.Evaluate(lowerBound);
                }

                if (upper.Value < middle.Value)
                {
                    upperBound = 0.5*(upperBound + lowerBound) + upperExpansionFactor*0.5*(upperBound - lowerBound);
                    upper = objective.Evaluate(upperBound);
                }

                middlePointX = lowerBound + (upperBound - lowerBound)/(1 + Constants.GoldenRatio);
                middle = objective.Evaluate(middlePointX);

                expansion_steps += 1;
            }

            if (upper.Value < middle.Value || lower.Value < middle.Value)
            {
                throw new OptimizationException("Lower and upper bounds do not necessarily bound a minimum.");
            }

            int iterations = 0;
            while (Math.Abs(upper.Point - lower.Point) > xTolerance && iterations < maxIterations)
            {
                // Recompute middle point on each iteration to avoid loss of precision
                middlePointX = lower.Point + (upper.Point - lower.Point)/(1 + Constants.GoldenRatio);
                middle = objective.Evaluate(middlePointX);
                ValueChecker(middle.Value, middlePointX);

                double testX = lower.Point + (upper.Point - middle.Point);
                var test = objective.Evaluate(testX);
                ValueChecker(test.Value, testX);

                if (test.Point < middle.Point)
                {
                    if (test.Value > middle.Value)
                    {
                        lower = test;
                    }
                    else
                    {
                        upper = middle;
                    }
                }
                else
                {
                    if (test.Value > middle.Value)
                    {
                        upper = test;
                    }
                    else
                    {
                        lower = middle;
                    }
                }

                iterations += 1;
            }

            if (iterations == maxIterations)
            {
                throw new MaximumIterationsException("Max iterations reached.");
            }

            return new ScalarMinimizationResult(middle, iterations, ExitCondition.BoundTolerance);
        }

        static void ValueChecker(double value, double point)
        {
            if (Double.IsNaN(value) || Double.IsInfinity(value))
            {
                throw new Exception("Objective function returned non-finite value.");
            }
        }
    }
}