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// Math.NET Numerics, part of the Math.NET Project
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using System;
using IStation.Numerics.LinearAlgebra;
using IStation.Numerics.Optimization.ObjectiveFunctions;

namespace IStation.Numerics.Optimization
{
    public static class ObjectiveFunction
    {
        /// <summary>
        /// Objective function where neither Gradient nor Hessian is available.
        /// </summary>
        public static IObjectiveFunction Value(Func<Vector<double>, double> function)
        {
            return new ValueObjectiveFunction(function);
        }

        /// <summary>
        /// Objective function where the Gradient is available. Greedy evaluation.
        /// </summary>
        public static IObjectiveFunction Gradient(Func<Vector<double>, Tuple<double, Vector<double>>> function)
        {
            return new GradientObjectiveFunction(function);
        }

        /// <summary>
        /// Objective function where the Gradient is available. Lazy evaluation.
        /// </summary>
        public static IObjectiveFunction Gradient(Func<Vector<double>, double> function, Func<Vector<double>, Vector<double>> gradient)
        {
            return new LazyObjectiveFunction(function, gradient: gradient);
        }

        /// <summary>
        /// Objective function where the Hessian is available. Greedy evaluation.
        /// </summary>
        public static IObjectiveFunction Hessian(Func<Vector<double>, Tuple<double, Matrix<double>>> function)
        {
            return new HessianObjectiveFunction(function);
        }

        /// <summary>
        /// Objective function where the Hessian is available. Lazy evaluation.
        /// </summary>
        public static IObjectiveFunction Hessian(Func<Vector<double>, double> function, Func<Vector<double>, Matrix<double>> hessian)
        {
            return new LazyObjectiveFunction(function, hessian: hessian);
        }

        /// <summary>
        /// Objective function where both Gradient and Hessian are available. Greedy evaluation.
        /// </summary>
        public static IObjectiveFunction GradientHessian(Func<Vector<double>, Tuple<double, Vector<double>, Matrix<double>>> function)
        {
            return new GradientHessianObjectiveFunction(function);
        }

        /// <summary>
        /// Objective function where both Gradient and Hessian are available. Lazy evaluation.
        /// </summary>
        public static IObjectiveFunction GradientHessian(Func<Vector<double>, double> function, Func<Vector<double>, Vector<double>> gradient, Func<Vector<double>, Matrix<double>> hessian)
        {
            return new LazyObjectiveFunction(function, gradient: gradient, hessian: hessian);
        }

        /// <summary>
        /// Objective function where neither first nor second derivative is available.
        /// </summary>
        public static IScalarObjectiveFunction ScalarValue(Func<double, double> function)
        {
            return new ScalarValueObjectiveFunction(function);
        }

        /// <summary>
        /// Objective function where the first derivative is available.
        /// </summary>
        public static IScalarObjectiveFunction ScalarDerivative(Func<double, double> function, Func<double, double> derivative)
        {
            return new ScalarObjectiveFunction(function, derivative);
        }

        /// <summary>
        /// Objective function where the first and second derivatives are available.
        /// </summary>
        public static IScalarObjectiveFunction ScalarSecondDerivative(Func<double, double> function, Func<double, double> derivative, Func<double,double> secondDerivative)
        {
            return new ScalarObjectiveFunction(function, derivative, secondDerivative);
        }

        /// <summary>
        /// objective model with a user supplied jacobian for non-linear least squares regression.
        /// </summary>
        public static IObjectiveModel NonlinearModel(Func<Vector<double>, Vector<double>, Vector<double>> function,
            Func<Vector<double>, Vector<double>, Matrix<double>> derivatives,
            Vector<double> observedX, Vector<double> observedY, Vector<double> weight = null)
        {
            var objective = new NonlinearObjectiveFunction(function, derivatives);
            objective.SetObserved(observedX, observedY, weight);
            return objective;
        }

        /// <summary>
        /// Objective model for non-linear least squares regression.
        /// </summary>
        public static IObjectiveModel NonlinearModel(Func<Vector<double>, Vector<double>, Vector<double>> function,
            Vector<double> observedX, Vector<double> observedY, Vector<double> weight = null,
            int accuracyOrder = 2)
        {
            var objective = new NonlinearObjectiveFunction(function, accuracyOrder: accuracyOrder);
            objective.SetObserved(observedX, observedY, weight);
            return objective;
        }

        /// <summary>
        /// Objective model with a user supplied jacobian for non-linear least squares regression.
        /// </summary>
        public static IObjectiveModel NonlinearModel(Func<Vector<double>, double, double> function,
            Func<Vector<double>, double, Vector<double>> derivatives,
            Vector<double> observedX, Vector<double> observedY, Vector<double> weight = null)
        {
            Vector<double> func(Vector<double> point, Vector<double> x)
            {
                var functionValues = CreateVector.Dense<double>(x.Count);
                for (int i = 0; i < x.Count; i++)
                {
                    functionValues[i] = function(point, x[i]);
                }

                return functionValues;
            }

            Matrix<double> prime(Vector<double> point, Vector<double> x)
            {
                var derivativeValues = CreateMatrix.Dense<double>(x.Count, point.Count);
                for (int i = 0; i < x.Count; i++)
                {
                    derivativeValues.SetRow(i, derivatives(point, x[i]));
                }

                return derivativeValues;
            }

            var objective = new NonlinearObjectiveFunction(func, prime);
            objective.SetObserved(observedX, observedY, weight);
            return objective;
        }

        /// <summary>
        /// Objective model for non-linear least squares regression.
        /// </summary>
        public static IObjectiveModel NonlinearModel(Func<Vector<double>, double, double> function,
            Vector<double> observedX, Vector<double> observedY, Vector<double> weight = null,
            int accuracyOrder = 2)
        {
            Vector<double> func(Vector<double> point, Vector<double> x)
            {
                var functionValues = CreateVector.Dense<double>(x.Count);
                for (int i = 0; i < x.Count; i++)
                {
                    functionValues[i] = function(point, x[i]);
                }

                return functionValues;
            }

            var objective = new NonlinearObjectiveFunction(func, accuracyOrder: accuracyOrder);
            objective.SetObserved(observedX, observedY, weight);
            return objective;
        }

        /// <summary>
        /// Objective function with a user supplied jacobian for nonlinear least squares regression.
        /// </summary>
        public static IObjectiveFunction NonlinearFunction(Func<Vector<double>, Vector<double>, Vector<double>> function,
            Func<Vector<double>, Vector<double>, Matrix<double>> derivatives,
            Vector<double> observedX, Vector<double> observedY, Vector<double> weight = null)
        {
            var objective = new NonlinearObjectiveFunction(function, derivatives);
            objective.SetObserved(observedX, observedY, weight);
            return objective.ToObjectiveFunction();
        }

        /// <summary>
        /// Objective function for nonlinear least squares regression.
        /// The numerical jacobian with accuracy order is used.
        /// </summary>
        public static IObjectiveFunction NonlinearFunction(Func<Vector<double>, Vector<double>, Vector<double>> function,
            Vector<double> observedX, Vector<double> observedY, Vector<double> weight = null,
            int accuracyOrder = 2)
        {
            var objective = new NonlinearObjectiveFunction(function, null, accuracyOrder: accuracyOrder);
            objective.SetObserved(observedX, observedY, weight);
            return objective.ToObjectiveFunction();
        }
    }
}