Accord.Math.Decompositions.LuDecomposition.Solve C# (CSharp) Method

        public double[,] Solve(double[,] value)
        {
            if (value == null)
            {
                throw new ArgumentNullException("value");
            }

            if (value.GetLength(0) != lu.GetLength(0))
            {
                throw new ArgumentException("Invalid matrix dimensions.", "value");
            }

            if (!Nonsingular)
            {
                throw new InvalidOperationException("Matrix is singular");
            }

            // Copy right hand side with pivoting
            int count = value.GetLength(1);
            double[,] X = value.Submatrix(pivotVector, null);

            int columns = lu.GetLength(1);

            // Solve L*Y = B(piv,:)
            for (int k = 0; k < columns; k++)
                for (int i = k + 1; i < columns; i++)
                    for (int j = 0; j < count; j++)
                        X[i, j] -= X[k, j]*lu[i, k];

            // Solve U*X = Y;
            for (int k = columns - 1; k >= 0; k--)
            {
                for (int j = 0; j < count; j++)
                    X[k, j] /= lu[k, k];

                for (int i = 0; i < k; i++)
                    for (int j = 0; j < count; j++)
                        X[i, j] -= X[k, j]*lu[i, k];
            }

            return X;
        }

        public void SolveTest1()
        {
            double[,] value =
            {
               {  2,  3,  0 },
               { -1,  2,  1 },
               {  0, -1,  3 }
            };

            double[] rhs = { 5, 0, 1 };

            double[] expected =
            {
                1.6522,
                0.5652,
                0.5217,
            };

            var target = new LuDecomposition(value);
            double[] actual = target.Solve(rhs);
            Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-3));
            Assert.IsTrue(Matrix.IsEqual(value, target.Reverse()));

            var target2 = new JaggedLuDecomposition(value.ToJagged());
            actual = target2.Solve(rhs);
            Assert.IsTrue(Matrix.IsEqual(expected, actual, 1e-3));
            Assert.IsTrue(Matrix.IsEqual(value, target2.Reverse()));
        }