using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using L = Science.Mathematics.LinearAlgebra;

namespace Strang3Ed.Chapter10.Section2
{
    public class Example03
    {
        public Example03()
        {
        }
        private string result;
        public string Result
        {
            get { return result; }
        }
        public void Compute()
        {
            Science.Mathematics.Complex[,] x 
                = new Science.Mathematics.Complex[3,3];
            x[0, 0] = new Science.Mathematics.Complex(1.0, 0.0);
            x[0, 1] = new Science.Mathematics.Complex(1.0, 0.0);
            x[0, 2] = new Science.Mathematics.Complex(1.0, 0.0);

            x[1, 0] = new Science.Mathematics.Complex(1.0, 0.0);
            x[1, 1] = new Science.Mathematics.Complex();
            x[1, 1].Abs = 1.0;
            x[1, 1].Arg = 2.0 * Math.PI / 3.0;
            x[1, 2] = new Science.Mathematics.Complex();
            x[1, 2].Abs = 1.0;
            x[1, 2].Arg = 4.0 * Math.PI / 3.0;

            x[2, 0] = new Science.Mathematics.Complex(1.0, 0.0);
            x[2, 1] = new Science.Mathematics.Complex();
            x[2, 1].Abs = 1.0;
            x[2, 1].Arg = 4.0 * Math.PI / 3.0;
            x[2, 2] = new Science.Mathematics.Complex();
            x[2, 2].Abs = 1.0;
            x[2, 2].Arg = 2.0 * Math.PI / 3.0;
      
            L.MatrixComplex FF = new L.MatrixComplex(x);
            L.MatrixComplex F = FF *(1.0 / Math.Sqrt(3.0));

            L.MatrixComplex HQ = F.ConjugateTranspose - F;

            result += HQ.ToString() + "\r\n";

            L.MatrixComplex IQ = F.ConjugateTranspose * F;
            IQ.Chop();

            result += IQ.ToString() + "\r\n";

            L.MatrixComplex UQ = F.ConjugateTranspose - F.Inverse;
            UQ.Chop();

            result += UQ.ToString() + "\r\n";

            L.MatrixComplex IIQ = F * F.Inverse;
            IIQ.Chop();

            result += IIQ.ToString() + "\r\n";
        }
    }
}
/*
0     0     0     
0     0 -I 1     0 +I 1     
0     0 +I 1     0 -I 1     


1     0     0     
0     1     0     
0     0     1     


0     0     0     
0     0     0     
0     0     0     


1     0     0     
0     1     0     
0     0     1       
*/