using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Azimuth.DenseLinearAlgebra;

namespace Azimuth.UnitTests.DenseLinearAlgebra
{
    public class UpperHessenberMatrixTests : UnitTestSharp.TestFixture
    {
        public class Ctor : UnitTestSharp.TestFixture
        {
            public void BasicMat()
            {
                var expected = new SquareMatrix(new Scalar[,]
                {
                    {1, 2, 3, },
                    {4, 5, 6, },
                    {0, 7, 8, },
                });

                var mat = new UpperHessenbergMatrix(expected);

                CheckEqual(expected, mat);
                CheckEqual(3, mat.Size);
                CheckEqual(3, mat.ColumnCount);
                CheckEqual(3, mat.RowCount);
            }

            public void BasicArray()
            {
                var entries = new Scalar[,]
                {
                    {1, 2, 3, },
                    {4, 5, 6, },
                    {0, 7, 8, },
                };

                var mat = new UpperHessenbergMatrix(entries);
                var expected = new SquareMatrix(entries);

                CheckEqual(expected, mat);
                CheckEqual(3, mat.Size);
                CheckEqual(3, mat.ColumnCount);
                CheckEqual(3, mat.RowCount);
            }
        }

        public class Accessor : UnitTestSharp.TestFixture
        {
            public void AccessBasic()
            {
                var entries = new Scalar[,]
                {
                    {1, 2, 3, },
                    {4, 5, 6, },
                    {0, 7, 8, },
                };

                var mat = new UpperHessenbergMatrix(entries);
                var expected = new SquareMatrix(entries);

                CheckEqual(1, mat[0, 0]);
                CheckEqual(2, mat[0, 1]);
                CheckEqual(3, mat[0, 2]);

                CheckEqual(4, mat[1, 0]);
                CheckEqual(5, mat[1, 1]);
                CheckEqual(6, mat[1, 2]);

                CheckEqual(0, mat[2, 0]);
                CheckEqual(7, mat[2, 1]);
                CheckEqual(8, mat[2, 2]);
            }

            public void SetOnBand()
            {
                var entries = new Scalar[,]
                {
                    {1, 2, 3, },
                    {4, 5, 6, },
                    {0, 7, 8, },
                };

                var mat = new UpperHessenbergMatrix(entries);

                mat[1, 2] = 3;

                CheckEqual(3, mat[1, 2]);
            }

            public void SetOffBand_Zero()
            {
                var entries = new Scalar[,]
                {
                    {1, 2, 3, },
                    {4, 5, 6, },
                    {0, 7, 8, },
                };

                var mat = new UpperHessenbergMatrix(entries);
                var expected = new SquareMatrix(entries);

                mat[2, 0] = 0;
            }

            public void SetOffBand_Nonzero()
            {
                var entries = new Scalar[,]
                {
                    {1, 2, 3, },
                    {4, 5, 6, },
                    {0, 7, 8, },
                };

                var mat = new UpperHessenbergMatrix(entries);
                var expected = new SquareMatrix(entries);

                CheckThrow(typeof(Exception));
                mat[2, 0] = 1;
            }
        }

        public class CalculateEigenvalues : UnitTestSharp.TestFixture
        {
            public void Identity()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,]
                {
                    {1, 0, 0, 0, },
                    {0, 1, 0, 0, },
                    {0, 0, 1, 0, },
                    {0, 0, 0, 1, },
                });

                var eigenvalues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { 1, 1, 1, 1, };
                CheckEqualCommutative(expected, eigenvalues);
            }

            public void Diagonal()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,]
                {
                    {1, 0, 0, 0, },
                    {0, 2, 0, 0, },
                    {0, 0, -3, 0, },
                    {0, 0, 0, -1, },
                });

                var eigenvalues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { -3, -1, 1, 2 };
                CheckEqualCommutative(expected, eigenvalues);
            }

            public void ZeroMatrix()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,]
                {
                    { 0, 0, 0, 0, },
                    { 0, 0, 0, 0, },
                    { 0, 0, 0, 0, },
                    { 0, 0, 0, 0, },
                });

                var eigenvalues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { 0, 0, 0, 0 };
                CheckEqualCommutative(expected, eigenvalues);
            }

            public void NoReal()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,]
                {
                    { 0.8, -0.6, 0, 0, },
                    { 0.6, 0.8, 0, 0, },
                    { 0, 0, 0.8, -0.6, },
                    { 0, 0, 0.6, 0.8, },
                });

                var eigenvalues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { };
                CheckEqualCommutative(expected, eigenvalues);
            }

            public void x00()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,]
                {
                    
                });

                var eigenvalues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { };
                CheckEqualCommutative(expected, eigenvalues);
            }

            public void x11()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,]
                {
                    { 7, },
                });

                var eigenvalues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { 7, };
                CheckEqualCommutative(expected, eigenvalues);
            }

            public void x22()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,]
                {
                    { 4, 3, },
                    { 3, 4, },
                });

                var eigenvalues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { 1, 7, };
                CheckEqualCommutative(expected, eigenvalues);
            }
            
            public void x33()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,]
                {
                    { 1, 2, 3, },
                    { 4, 5, 6, },
                    { 0, 8, 9, },
                });

                var eigenvalues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { 14.893242553325800, };
                CheckEqualCommutative(expected, eigenvalues);
            }

            public void x55()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,]
                {
                    { 1,  2,   3,   4,   5 },
                    { 2,  2,   3,   2,   1 },
                    { 0,  1,   2,   1,   1 },
                    { 0,  0,   2,   2,   1 },
                    { 0,  0,   0,   1,   1 },
                });

                var eigenvalues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { 5.485788536193147, };
                CheckEqualCommutative(expected, eigenvalues);   
            }

            public void x66()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,]
                {
                    {  7.000000000000000,  7.276068751089988,  5.812049373662239, -0.139700852436428,  9.015200635240408,   7.936343414048666, }, 
                    { 12.369316876852983,  4.130718954248365, 18.968509239938548, -1.207072582996759, 10.683308983004862,   2.415951310656580, },
                    {  0.000000000000000, -7.160341769381306,  2.447764803753486, -0.565593838239241, -4.181395925572754,  -3.250955159201561, },
                    {  0.000000000000000,  0.000000000000000, -8.598770629747584,  2.915100285023692, -3.416857533555016,   5.722969260736876, },
                    {  0.000000000000000,  0.000000000000000,  0.000000000000000,  1.046436231879865, -2.835100738826459, -10.979177930043305, },
                    {  0.000000000000000,  0.000000000000000,  0.000000000000000,  0.000000000000000,  1.414293337412555,   5.341516695800912, },
                });

                var eigenValues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { 4, 3, };
                CheckEqualCommutative(expected, eigenValues);
            }

            public void x1616()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,] 
                {
                    { 6, -7, -9, 7, -7, 3, 3, 9, 4, -7, -6, 1, 0, -3, 6, -2 },
                    { 2, 1, 0, 0, -1, -4, -1, 1, -7, 0, 3, -4, -2, -1, -10, -4 },
                    { 0, -4, -6, -6, 9, -8, 8, 8, -1, -1, -1, -2, 8, -8, -4, 5 },
                    { 0, 0, 8, -7, 3, -10, -8, 0, 8, -7, 7, -1, -7, -9, 8, 6 },
                    { 0, 0, 0, -2, -9, 1, -5, -9, 0, 9, -7, -2, -4, -4, 7, 9 },
                    { 0, 0, 0, 0, -9, 9, 0, -5, -5, -3, 7, -8, -1, -2, 2, 5 },
                    { 0, 0, 0, 0, 0, -4, 4, 9, 0, 4, -9, -7, -7, 2, -1, -8 },
                    { 0, 0, 0, 0, 0, 0, 1, -2, -5, 6, -8, -2, -2, 7, -8, -10 },
                    { 0, 0, 0, 0, 0, 0, 0, 1, -9, 5, -10, 7, 7, 7, 9, -8 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, -7, -10, 6, -7, -1, 1, 4, -3 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -3, -1, 8, -4, 2 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 1, -10, -4, 0, 0 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -9, 3, -1, -4 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 1, 4, -6 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 9 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 5 },
                });

                var eigenValues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { 
                    -14.15303053628267,
                    -10.66884376190023,
                    13.97123505511950,
                    4.63339810648546,
                    -4.02542691649254,
                    -3.81575486956688,
                };
                CheckEqualCommutative(expected, eigenValues);
            }

            public void x1616_NullRow()
            {
                var mat = new UpperHessenbergMatrix(new Scalar[,] 
                {
                    { 8, -6, -9, 7, 7, 7, 6, -2, 0, 1, 0, -10, 6, 7, -2, -7 },
                    { 5, 7, 5, 6, 2, 3, -10, -8, 4, -5, -1, -9, -1, 3, 4, -5 },
                    { 0, 9, 4, 7, 7, -6, -7, 0, 2, 1, 8, 5, -7, 7, 4, 6 },
                    { 0, 0, -2, 6, -1, 1, 4, -4, -1, 2, -6, 6, 5, 6, 2, 6 },
                    { 0, 0, 0, 8, -7, -1, -5, 0, -6, -3, -1, 0, -2, -2, 5, 0 },
                    { 0, 0, 0, 0, -9, -2, -2, 7, -3, 0, 0, 1, 7, -3, 2, 7 },
                    { 0, 0, 0, 0, 0, -10, 7, 3, 9, -9, -4, 3, -10, 5, -10, 8 },
                    { 0, 0, 0, 0, 0, 0, 3, -6, -10, 9, -7, -6, 9, 0, -7, -4 },
                    { 0, 0, 0, 0, 0, 0, 0, -7, 0, 3, 3, 4, -10, 1, -3, 8 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 3, -6, -6, 5, 9, 2, -6, 2 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -7, 5, -5, 4, -3, -4 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -5, 3, 0, -7, 7 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -5, -3, -1, 1 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -10, -10, -9 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -9, 8 },
                    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
                });

                var eigenValues = mat.CalculateRealEigenvalues();

                var expected = new Scalar[] { 
                    -18.609437265080107,
                    -15.550183034148326,
                    -11.654703459672424,
                    -10.689362912011779,
                    -6.985319148966362,
                    -2.489085229048183,
                    1.463460687524856,
                    0.000000000000000,
                };
                CheckEqualCommutative(expected, eigenValues);
            }

            public void LargeBalancedProblem()
            {
                // Tests the shift in the QR implicit algorithm

                var mat = new UpperHessenbergMatrix(new Scalar[,] 
                {
                    {0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.5914642398}, 
                    {1, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
                    {0, 0.5, 0, 0.25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.6018803568}, 
                    {0, 0, 1, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
                    {0, 0, 0, 0.5, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5557374768}, 
                    {0, 0, 0, 0, 0.5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
                    {0, 0, 0, 0, 0, 0.25, 0, 0.25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.383746165}, 
                    {0, 0, 0, 0, 0, 0, 1, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
                    {0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0.25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.6733533656}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0.125, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.8593483656000001}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0.25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0.125, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.0372740352}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0.25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0.25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.8406088192}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0.25, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, -0.2466699264}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0.5, 0, 0, 0, 0, 0, 0, 0}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0.25, 0, 0, 0, 0, 0, 0.013773824}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0.125, 0, 0, 0, 0, 0}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0.0625, 0, 0, 0, -0.0048529408}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0.03125, 0, 0, 0}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0.015625, 0, 0.0222298112}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0.015625, 0}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, -0.6442450944}, 
                    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14.98620022491962, 9.490800000000001e-006}, 
                });

                var expectedEigenvalues = new Scalar[] { -.8, -.8, 0, 0, .8, .8 };

                var eigenValues = mat.CalculateRealEigenvalues();

                CheckEqualCommutative(expectedEigenvalues, eigenValues);
            }

            public void UnbalancedLargeSparseProblem()
            {
                // Tests the shift in the QR implicit algorithm

                var mat = new UpperHessenbergMatrix(new Scalar[,] 
                {
                    { 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.7957321199 },
                    { 1 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
                    { 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , -0.3009401784 },
                    { 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
                    { 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.1389343692 },
                    { 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
                    { 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.6918730825 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , -0.4183383414 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.1074185457 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , -0.0162074068 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.0016418141 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , -0.0001204443 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 , 0.0000067255 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , 0 , 0 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 , -0.0000002962 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0 , 0 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 , 0.0000000106 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , 0.5 , 0 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.5 , 0 , -0.0000000003 },
                    { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , -32182619928.6688 , 0.0000094908 },
                });

                var expectedEigenvalues = new Scalar[] { -.8, -.8, 0, 0, .8, .8 };

                var eigenValues = mat.CalculateRealEigenvalues();

                CheckEqualCommutative(expectedEigenvalues, eigenValues);
            }
        }
    }
}