/// <summary>
        /// Check the result.
        /// </summary>
        /// <param name="preconditioner">Specific preconditioner.</param>
        /// <param name="matrix">Source matrix.</param>
        /// <param name="vector">Initial vector.</param>
        /// <param name="result">Result vector.</param>
        protected override void CheckResult(IPreconditioner<Complex> preconditioner, SparseMatrix matrix, Vector<Complex> vector, Vector<Complex> result)
        {
            Assert.AreEqual(typeof(Diagonal), preconditioner.GetType(), "#01");

            // Compute M * result = product
            // compare vector and product. Should be equal
            var product = new DenseVector(result.Count);
            matrix.Multiply(result, product);

            for (var i = 0; i < product.Count; i++)
            {
                Assert.IsTrue(vector[i].Real.AlmostEqual(product[i].Real, -Epsilon.Magnitude()), "#02-" + i);
                Assert.IsTrue(vector[i].Imaginary.AlmostEqual(product[i].Imaginary, -Epsilon.Magnitude()), "#03-" + i);
            }
        }
        public void SolvePoissonMatrixAndBackMultiply()
        {
            // Create the matrix
            var matrix = new SparseMatrix(100);

            // Assemble the matrix. We assume we're solving the Poisson equation
            // on a rectangular 10 x 10 grid
            const int GridSize = 10;

            // The pattern is:
            // 0 .... 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 ... 0
            for (var i = 0; i < matrix.RowCount; i++)
            {
                // Insert the first set of -1's
                if (i > (GridSize - 1))
                {
                    matrix[i, i - GridSize] = -1;
                }

                // Insert the second set of -1's
                if (i > 0)
                {
                    matrix[i, i - 1] = -1;
                }

                // Insert the centerline values
                matrix[i, i] = 4;

                // Insert the first trailing set of -1's
                if (i < matrix.RowCount - 1)
                {
                    matrix[i, i + 1] = -1;
                }

                // Insert the second trailing set of -1's
                if (i < matrix.RowCount - GridSize)
                {
                    matrix[i, i + GridSize] = -1;
                }
            }

            // Create the y vector
            var y = Vector<Complex>.Build.Dense(matrix.RowCount, 1);

            // Create an iteration monitor which will keep track of iterative convergence
            var monitor = new Iterator<Complex>(
                new IterationCountStopCriterium<Complex>(MaximumIterations),
                new ResidualStopCriterium<Complex>(ConvergenceBoundary),
                new DivergenceStopCriterium<Complex>(),
                new FailureStopCriterium<Complex>());

            var solver = new TFQMR();

            // Solve equation Ax = y
            var x = matrix.SolveIterative(y, solver, monitor);

            // Now compare the results
            Assert.IsNotNull(x, "#02");
            Assert.AreEqual(y.Count, x.Count, "#03");

            // Back multiply the vector
            var z = matrix.Multiply(x);

            // Check that the solution converged
            Assert.IsTrue(monitor.Status == IterationStatus.Converged, "#04");

            // Now compare the vectors
            Assert.LessOrEqual(Distance.Chebyshev(y, z), 2*ConvergenceBoundary);
        }
        public void SolvePoissonMatrixAndBackMultiply()
        {
            // Create the matrix
            var matrix = new SparseMatrix(100);

            // Assemble the matrix. We assume we're solving the Poisson equation
            // on a rectangular 10 x 10 grid
            const int GridSize = 10;

            // The pattern is:
            // 0 .... 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 ... 0
            for (var i = 0; i < matrix.RowCount; i++)
            {
                // Insert the first set of -1's
                if (i > (GridSize - 1))
                {
                    matrix[i, i - GridSize] = -1;
                }

                // Insert the second set of -1's
                if (i > 0)
                {
                    matrix[i, i - 1] = -1;
                }

                // Insert the centerline values
                matrix[i, i] = 4;

                // Insert the first trailing set of -1's
                if (i < matrix.RowCount - 1)
                {
                    matrix[i, i + 1] = -1;
                }

                // Insert the second trailing set of -1's
                if (i < matrix.RowCount - GridSize)
                {
                    matrix[i, i + GridSize] = -1;
                }
            }

            // Create the y vector
            var y = DenseVector.Create(matrix.RowCount, i => 1);

            // Create an iteration monitor which will keep track of iterative convergence
            var monitor = new Iterator<Complex>(new IIterationStopCriterium<Complex>[]
                {
                    new IterationCountStopCriterium<Complex>(MaximumIterations),
                    new ResidualStopCriterium(ConvergenceBoundary),
                    new DivergenceStopCriterium(),
                    new FailureStopCriterium()
                });
            var solver = new MlkBiCgStab(monitor);

            // Solve equation Ax = y
            var x = solver.Solve(matrix, y);

            // Now compare the results
            Assert.IsNotNull(x, "#02");
            Assert.AreEqual(y.Count, x.Count, "#03");

            // Back multiply the vector
            var z = matrix.Multiply(x);

            // Check that the solution converged
            Assert.IsTrue(monitor.HasConverged, "#04");

            // Now compare the vectors
            for (var i = 0; i < y.Count; i++)
            {
                Assert.IsTrue((y[i] - z[i]).Magnitude.IsSmaller(ConvergenceBoundary, 1), "#05-" + i);
            }
        }