public void HeapSortWithDecreasingDoubleArray()
        {
            var sortedIndices = new int[10];
            Vector<Complex> values = new DenseVector(10);
            values[0] = 9;
            values[1] = 8;
            values[2] = 7;
            values[3] = 6;
            values[4] = 5;
            values[5] = 4;
            values[6] = 3;
            values[7] = 2;
            values[8] = 1;
            values[9] = 0;
            for (var i = 0; i < sortedIndices.Length; i++)
            {
                sortedIndices[i] = i;
            }

            ILUTPElementSorter.SortDoubleIndicesDecreasing(0, sortedIndices.Length - 1, sortedIndices, values);
            for (var i = 0; i < sortedIndices.Length; i++)
            {
                Assert.AreEqual(i, sortedIndices[i], "#01-" + i);
            }
        }

        public void SolveWideMatrixThrowsArgumentException()
        {
            var matrix = new SparseMatrix(2, 3);
            var input = new DenseVector(2);

            var solver = new TFQMR();
            Assert.That(() => matrix.SolveIterative(input, solver), Throws.ArgumentException);
        }

        public void SolveLongMatrixThrowsArgumentException()
        {
            var matrix = new SparseMatrix(3, 2);
            var input = new DenseVector(3);

            var solver = new BiCgStab();
            Assert.That(() => matrix.SolveIterative(input, solver), Throws.ArgumentException);
        }

        public void SolveLongMatrixThrowsArgumentException()
        {
            var matrix = new SparseMatrix(3, 2);
            var input = new DenseVector(3);

            var solver = new TFQMR();
            Assert.Throws<ArgumentException>(() => matrix.SolveIterative(input, solver));
        }

        public void SolveWideMatrixThrowsArgumentException()
        {
            var matrix = new SparseMatrix(2, 3);
            var input = new DenseVector(2);

            var solver = new GpBiCg();
            Assert.Throws<ArgumentException>(() => matrix.SolveIterative(input, solver));
        }

        /// <summary>
        /// Create standard vector.
        /// </summary>
        /// <param name="size">Size of the vector.</param>
        /// <returns>New vector.</returns>
        protected DenseVector CreateStandardBcVector(int size)
        {
            var vector = new DenseVector(size);
            for (var i = 0; i < size; i++)
            {
                vector[i] = i + 1;
            }

            return vector;
        }

        /// <summary>
        /// Creates a new instance of the Vector class.
        /// </summary>
        /// <param name="data">The array to create this vector from.</param>
        /// <returns>The new <c>Vector</c>.</returns>
        protected override Vector<Complex> CreateVector(IList<Complex> data)
        {
            var vector = new DenseVector(data.Count);
            for (var index = 0; index < data.Count; index++)
            {
                vector[index] = data[index];
            }

            return vector;
        }

        public void DetermineStatus()
        {
            var criterium = new FailureStopCriterium();
            Assert.IsNotNull(criterium, "There should be a criterium");

            var solution = new DenseVector(new[] {new Complex(3.0, 0), new Complex(2.0, 0), new Complex(1, 0)});
            var source = new DenseVector(new[] {new Complex(1001.0, 0), Complex.Zero, new Complex(2003.0, 0)});
            var residual = new DenseVector(new[] {new Complex(1.0, 0), new Complex(2.0, 0), new Complex(3, 0)});

            var status = criterium.DetermineStatus(5, solution, source, residual);
            Assert.AreEqual(IterationStatus.Continue, status, "Should be running");
        }

        public void CanAddTwoDenseVectorsUsingOperator()
        {
            var vector = new DenseVector(Data);
            var other = new DenseVector(Data);
            var result = vector + other;
            CollectionAssert.AreEqual(Data, vector, "Making sure the original vector wasn't modified.");
            CollectionAssert.AreEqual(Data, other, "Making sure the original vector wasn't modified.");

            for (var i = 0; i < Data.Length; i++)
            {
                Assert.AreEqual(Data[i]*2.0, result[i]);
            }
        }

        public void ApproximateReturningOldVector()
        {
            const int Size = 10;
            var newMatrix = CreateUnitMatrix(Size);
            var vector = CreateStandardBcVector(Size);

            var preconditioner = CreatePreconditioner();
            preconditioner.Initialize(newMatrix);

            var result = new DenseVector(vector.Count);
            preconditioner.Approximate(vector, result);

            CheckResult(preconditioner, newMatrix, vector, result);
        }

        public void CanCreateDenseVectorFromArray()
        {
            var data = new Complex[Data.Length];
            Array.Copy(Data, data, Data.Length);
            var vector = new DenseVector(data);

            for (var i = 0; i < data.Length; i++)
            {
                Assert.AreEqual(data[i], vector[i]);
            }

            vector[0] = new Complex(10.0, 1);
            Assert.AreEqual(new Complex(10.0, 1), data[0]);
        }

        public void CanMultiplyWithVector()
        {
            var matrix = TestMatrices["Singular3x3"];
            var x = new DenseVector(new[] { new Complex(1, 1), new Complex(2, 1), new Complex(3, 1) });
            var y = matrix * x;

            Assert.AreEqual(matrix.RowCount, y.Count);

            for (var i = 0; i < matrix.RowCount; i++)
            {
                var ar = matrix.Row(i);
                var dot = ar * x;
                Assert.AreEqual(dot, y[i]);
            }
        }

        /// <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 CanSolveForRandomVectorWhenResultVectorGiven(int row, int column)
        {
            var matrixA = MatrixLoader.GenerateRandomDenseMatrix(row, column);
            var matrixACopy = matrixA.Clone();
            var factorSvd = matrixA.Svd();
            var vectorb = MatrixLoader.GenerateRandomDenseVector(row);
            var vectorbCopy = vectorb.Clone();
            var resultx = new DenseVector(column);
            factorSvd.Solve(vectorb, resultx);

            var matrixBReconstruct = matrixA*resultx;

            // Check the reconstruction.
            for (var i = 0; i < vectorb.Count; i++)
            {
                AssertHelpers.AlmostEqual(vectorb[i], matrixBReconstruct[i], 9);
            }

            // Make sure A didn't change.
            for (var i = 0; i < matrixA.RowCount; i++)
            {
                for (var j = 0; j < matrixA.ColumnCount; j++)
                {
                    Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
                }
            }

            // Make sure b didn't change.
            for (var i = 0; i < vectorb.Count; i++)
            {
                Assert.AreEqual(vectorbCopy[i], vectorb[i]);
            }
        }

 public void CanCallUnaryNegationOperatorOnDenseVector()
 {
     var vector = new DenseVector(Data);
     var other = -vector;
     for (var i = 0; i < Data.Length; i++)
     {
         Assert.AreEqual(-Data[i], other[i]);
     }
 }

        public void CanMultiplyDenseVectorByScalarUsingOperators()
        {
            var vector = new DenseVector(Data);
            vector = vector*new Complex(2.0, 1);

            for (var i = 0; i < Data.Length; i++)
            {
                Assert.AreEqual(Data[i]*new Complex(2.0, 1), vector[i]);
            }

            vector = vector*1.0;
            for (var i = 0; i < Data.Length; i++)
            {
                Assert.AreEqual(Data[i]*new Complex(2.0, 1), vector[i]);
            }

            vector = new DenseVector(Data);
            vector = new Complex(2.0, 1)*vector;

            for (var i = 0; i < Data.Length; i++)
            {
                Assert.AreEqual(Data[i]*new Complex(2.0, 1), vector[i]);
            }

            vector = 1.0*vector;
            for (var i = 0; i < Data.Length; i++)
            {
                Assert.AreEqual(Data[i]*new Complex(2.0, 1), vector[i]);
            }
        }

        public void CanDivideDenseVectorByComplexUsingOperators()
        {
            var vector = new DenseVector(Data);
            vector = vector/new Complex(2.0, 1);

            for (var i = 0; i < Data.Length; i++)
            {
                AssertHelpers.AlmostEqual(Data[i]/new Complex(2.0, 1), vector[i], 14);
            }

            vector = vector/1.0;
            for (var i = 0; i < Data.Length; i++)
            {
                AssertHelpers.AlmostEqual(Data[i]/new Complex(2.0, 1), vector[i], 14);
            }
        }

        public void CanCreateDenseVectorFromAnotherDenseVector()
        {
            var vector = new DenseVector(Data);
            var other = DenseVector.OfVector(vector);

            Assert.AreNotSame(vector, other);
            for (var i = 0; i < Data.Length; i++)
            {
                Assert.AreEqual(vector[i], other[i]);
            }
        }

 /// <summary>
 /// Converts the string representation of a complex dense vector to double-precision dense vector equivalent.
 /// A return value indicates whether the conversion succeeded or failed.
 /// </summary>
 /// <param name="value">
 /// A string containing a complex vector to convert.
 /// </param>
 /// <param name="result">
 /// The parsed value.
 /// </param>
 /// <returns>
 /// If the conversion succeeds, the result will contain a complex number equivalent to value.
 /// Otherwise the result will be <c>null</c>.
 /// </returns>
 public static bool TryParse(string value, out DenseVector result)
 {
     return TryParse(value, null, out result);
 }

        /// <summary>
        /// Outer product of two vectors
        /// </summary>
        /// <param name="u">First vector</param>
        /// <param name="v">Second vector</param>
        /// <returns>Matrix M[i,j] = u[i]*v[j] </returns>
        /// <exception cref="ArgumentNullException">If the u vector is <see langword="null" />.</exception> 
        /// <exception cref="ArgumentNullException">If the v vector is <see langword="null" />.</exception> 
        public static DenseMatrix OuterProduct(DenseVector u, DenseVector v)
        {
            if (u == null)
            {
                throw new ArgumentNullException("u");
            }

            if (v == null)
            {
                throw new ArgumentNullException("v");
            }

            var matrix = new DenseMatrix(u.Count, v.Count);
            CommonParallel.For(
                0, 
                u.Count, 
                i =>
                {
                    for (var j = 0; j < v.Count; j++)
                    {
                        matrix.At(i, j, u._values[i] * v._values[j]);
                    }
                });
            return matrix;
        }