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

namespace Strang3Ed.Chapter04.Section4
{
    public class Example05
    {
        public Example05()
        {
        }
        private string result;
        public string Result
        {
            get { return result; }
        }
        public void Compute()
        {
            L.Vector[] a = new L.Vector[3];
            a[0] = new L.Vector(3);
            a[0][0] = 1.0;
            a[0][1] = -1.0;
            a[0][2] = 0.0;

            a[1] = new L.Vector(3);
            a[1][0] = 2.0;
            a[1][1] = 0.0;
            a[1][2] = -2.0;

            a[2] = new L.Vector(3);
            a[2][0] = 3.0;
            a[2][1] = -3.0;
            a[2][2] = 3.0;

            L.Matrix A = new L.Matrix(a);

            L.FactorizationAeqQR obj = new L.FactorizationAeqQR(A);
            obj.Compute();

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

            L.Vector[] q = new L.Vector[3];
            q[0] = new L.Vector(3);
            q[0][0] = 1.0/Math.Sqrt(2.0);
            q[0][1] = -1.0 / Math.Sqrt(2.0); 
            q[0][2] = 0.0;

            q[1] = new L.Vector(3);
            q[1][0] = 1.0 / Math.Sqrt(6.0); 
            q[1][1] = 1.0 / Math.Sqrt(6.0); 
            q[1][2] = -2.0 / Math.Sqrt(6.0); 

            q[2] = new L.Vector(3);
            q[2][0] = 1.0 / Math.Sqrt(3.0); 
            q[2][1] = 1.0 / Math.Sqrt(3.0); 
            q[2][2] = 1.0 / Math.Sqrt(3.0);

            L.Matrix Q = new L.Matrix(q);

            result += Q.ToString() + "\r\n"; 
        }
    }
}
/*
-0.707106781186547     -0.408248290463863     0.577350269189626     
0.707106781186547     -0.408248290463863     0.577350269189626     
0     0.816496580927726     0.577350269189626     


0.707106781186547     0.408248290463863     0.577350269189626     
-0.707106781186547     0.408248290463863     0.577350269189626     
0     -0.816496580927726     0.577350269189626     
*/