MathNet.Numerics.LinearAlgebra.Double.DenseMatrix.LU C# (CSharp) Method

        public override LU<double> LU()
        {
            return DenseLU.Create(this);
        }

        /// <summary>
        /// Run example
        /// </summary>
        public void Run()
        {
            // Format matrix output to console
            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
            formatProvider.TextInfo.ListSeparator = " ";

            // Solve next system of linear equations (Ax=b):
            // 5*x + 2*y - 4*z = -7
            // 3*x - 7*y + 6*z = 38
            // 4*x + 1*y + 5*z = 43

            // Create matrix "A" with coefficients
            var matrixA = new DenseMatrix(new[,] { { 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 } });
            Console.WriteLine(@"Matrix 'A' with coefficients");
            Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // Create vector "b" with the constant terms.
            var vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
            Console.WriteLine(@"Vector 'b' with the constant terms");
            Console.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 1. Solve linear equations using LU decomposition
            var resultX = matrixA.LU().Solve(vectorB);
            Console.WriteLine(@"1. Solution using LU decomposition");
            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 2. Solve linear equations using QR decomposition
            resultX = matrixA.QR().Solve(vectorB);
            Console.WriteLine(@"2. Solution using QR decomposition");
            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 3. Solve linear equations using SVD decomposition
            matrixA.Svd(true).Solve(vectorB, resultX);
            Console.WriteLine(@"3. Solution using SVD decomposition");
            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 4. Solve linear equations using Gram-Shmidt decomposition
            matrixA.GramSchmidt().Solve(vectorB, resultX);
            Console.WriteLine(@"4. Solution using Gram-Shmidt decomposition");
            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 5. Verify result. Multiply coefficient matrix "A" by result vector "x"
            var reconstructVecorB = matrixA * resultX;
            Console.WriteLine(@"5. Multiply coefficient matrix 'A' by result vector 'x'");
            Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // To use Cholesky or Eigenvalue decomposition coefficient matrix must be
            // symmetric (for Evd and Cholesky) and positive definite (for Cholesky)
            // Multipy matrix "A" by its transpose - the result will be symmetric and positive definite matrix
            var newMatrixA = matrixA.TransposeAndMultiply(matrixA);
            Console.WriteLine(@"Symmetric positive definite matrix");
            Console.WriteLine(newMatrixA.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 6. Solve linear equations using Cholesky decomposition
            newMatrixA.Cholesky().Solve(vectorB, resultX);
            Console.WriteLine(@"6. Solution using Cholesky decomposition");
            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 7. Solve linear equations using eigen value decomposition
            newMatrixA.Evd().Solve(vectorB, resultX);
            Console.WriteLine(@"7. Solution using eigen value decomposition");
            Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 8. Verify result. Multiply new coefficient matrix "A" by result vector "x"
            reconstructVecorB = newMatrixA * resultX;
            Console.WriteLine(@"8. Multiply new coefficient matrix 'A' by result vector 'x'");
            Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
            Console.WriteLine();
        }