using System;

namespace Science.Mathematics.VectorCalculus
{
    public class TaylorFormula
    {
        private Function.ToLastType<double[], double> dela;
        public TaylorFormula(Function.ToLastType<double[], double> func, double[] at, double[] smallDeviation)
        {
            dela = func;
            this.at = at;
            this.h = smallDeviation;
        }
        public void Compute()
        {
            PartialDerivative obj = new PartialDerivative(dela,at);
            int n = at.Length;
            double sum = 0.0;
            sum += dela(at);
            for(int i = 0; i < n; i++)
            {
                obj.WithRespectTo = i;
                obj.Compute();
                sum += obj.Result*h[i];
            }
            IteratedPartialDerivative obj2 = new IteratedPartialDerivative(dela, at, 2);
            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < n; j++)
                {
                    obj2.WithRespectToFirst = i;
                    obj2.WithRespectToSecond = j;
                    obj2.Compute();
                    sum += 1.0/ 2.0 * h[i] * obj2.Result * h[j];
                }
            }
            result = sum;
        }
        private double result;
        private double[] at;
        private double[] h;
        public double[] At
        {
            set { at = value; }
        }
        public double[] SmallDeviation
        {
            set { h = value; }
        }
        public double Result
        {
            get { return result; }
        }  	
    }
}