using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using V = Science.Mathematics.VectorCalculus;

namespace VectorCalculus5Ed.Chapter6.Section2
{
    public class Example06
    {
        public Example06()
		{
		}
		private string result;
		public string Result
		{
			get{return result;}
		}
        public void Compute()
        {
            Science.Mathematics.Function.ToLastType<double[], double> f
                = new Science.Mathematics.Function.ToLastType<double[], double>(func);
            double[] from = { 0.0, 0.0, 0.0 };
            double[] to = { 1.0, Math.PI, 2.0*Math.PI };
            V.IntegrationMultiD obj = new V.IntegrationMultiD(f, from, to);
            obj.NumberOfCall = 1000000;
            obj.Compute();
            result += obj.BestEstimation.ToString() + "\r\n";
            result += (4.0/3.0*Math.PI*(Math.E - 1.0)).ToString() + "\r\n";
        }
        private double func(double[] u)
        {
            return Math.Abs(jac(u)) * funcxy(funcT(u));
        }
        private double[] funcT(double[] u)
        {
            double[] x = new double[3];
            x[0] = u[0] * Math.Sin(u[1]) * Math.Cos(u[2]);
            x[1] = u[0] * Math.Sin(u[1]) * Math.Sin(u[2]);
            x[2] = u[0] * Math.Cos(u[1]);
            return x;
        }
        private double jac(double[] u)
        {
            double[] at = { u[0], u[1], u[2] };
            Science.Mathematics.Function.ToLastType<double[], double[]> f
                = new Science.Mathematics.Function.ToLastType<double[], double[]>(funcT);
            V.JacobianDeterminant obj = new V.JacobianDeterminant(f, at);
            obj.Compute();
            return obj.Result;
        }
        private double funcxy(double[] x)
        {
            return Math.Exp(Math.Pow(x[0] * x[0] + x[1] * x[1] + x[2] * x[2],1.5));
        }
    }
}
/* 
7.19752429792026
7.1975220921117
*/