Accord.Tests.Math.GeneralizedEigenvalueDecompositionTest.GeneralizedEigenvalueDecompositionConstructorTest C# (CSharp) Method

        public void GeneralizedEigenvalueDecompositionConstructorTest()
        {
            // Suppose we have the following 
            // matrices A and B shown below:

            double[,] A = 
            {
                { 1, 2, 3},
                { 8, 1, 4},
                { 3, 2, 3}
            };

            double[,] B = 
            {
                { 5, 1, 1},
                { 1, 5, 1},
                { 1, 1, 5}
            };

            // Now, suppose we would like to find values for λ 
            // that are solutions for the equation det(A - λB) = 0

            // For this, we can use a Generalized Eigendecomposition
            var gevd = new GeneralizedEigenvalueDecomposition(A, B);

            // Now, if A and B are Hermitian and B is positive
            // -definite, then the eigenvalues λ will be real:
            double[] lambda = gevd.RealEigenvalues;

            // Check if they are indeed a solution:
            for (int i = 0; i < lambda.Length; i++)
            {
                // Compute the determinant equation show above
                double det = Matrix.Determinant(A.Subtract(lambda[i].Multiply(B))); // almost zero

                Assert.IsTrue(det < 1e-6);
            }


            double[,] expectedVectors =
            {               
                { 0.427490473174445, -0.459244062074000, -0.206685960405416 },
                { 1,	1,	-1},
                { 0.615202547759401,	-0.152331764458173, 0.779372135871111}
            };

            double[,] expectedValues =
            {
              {1.13868666711946,	0,	0 },
              {0, -0.748168231839396,	0},
              {0,	0,	-0.104804149565775}
            };


            Assert.IsTrue(Matrix.IsEqual(gevd.Eigenvectors, expectedVectors, 0.00000000001));
            Assert.IsTrue(Matrix.IsEqual(gevd.DiagonalMatrix, expectedValues, 0.00000000001));
        }