mathnet-numerics/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs

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namespace MathNet.Numerics.LinearAlgebra.Complex32
{
    using System;
    using Algorithms.LinearAlgebra;
    using Generic;
    using Numerics;
    using Properties;
    using Storage;

    /// <summary>
    /// A Matrix class with dense storage. The underlying storage is a one dimensional array in column-major order.
    /// </summary>
    [Serializable]
    public class DenseMatrix : Matrix
    {
        readonly DenseColumnMajorMatrixStorage<Complex32> _storage;

        /// <summary>
        /// Number of rows.
        /// </summary>
        /// <remarks>Using this instead of the RowCount property to speed up calculating
        /// a matrix index in the data array.</remarks>
        private readonly int _rowCount;

        /// <summary>
        /// Number of columns.
        /// </summary>
        /// <remarks>Using this instead of the ColumnCount property to speed up calculating
        /// a matrix index in the data array.</remarks>
        private readonly int _columnCount;

        /// <summary>
        /// Gets the matrix's data.
        /// </summary>
        /// <value>The matrix's data.</value>
        readonly Complex32[] _data;

        /// <summary>
        /// Initializes a new instance of the <see cref="DenseMatrix"/> class. This matrix is square with a given size.
        /// </summary>
        /// <param name="order">the size of the square matrix.</param>
        /// <exception cref="ArgumentException">
        /// If <paramref name="order"/> is less than one.
        /// </exception>
        public DenseMatrix(int order)
            : base(order)
        {
            _storage = new DenseColumnMajorMatrixStorage<Complex32>(order, order);

            _rowCount = _storage.RowCount;
            _columnCount = _storage.ColumnCount;
            _data = _storage.Data;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="DenseMatrix"/> class.
        /// </summary>
        /// <param name="rows">
        /// The number of rows.
        /// </param>
        /// <param name="columns">
        /// The number of columns.
        /// </param>
        public DenseMatrix(int rows, int columns)
            : base(rows, columns)
        {
            _storage = new DenseColumnMajorMatrixStorage<Complex32>(rows, columns);

            _rowCount = _storage.RowCount;
            _columnCount = _storage.ColumnCount;
            _data = _storage.Data;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="DenseMatrix"/> class with all entries set to a particular value.
        /// </summary>
        /// <param name="rows">
        /// The number of rows.
        /// </param>
        /// <param name="columns">
        /// The number of columns.
        /// </param>
        /// <param name="value">The value which we assign to each element of the matrix.</param>
        public DenseMatrix(int rows, int columns, Complex32 value)
            : base(rows, columns)
        {
            _storage = new DenseColumnMajorMatrixStorage<Complex32>(rows, columns);

            _rowCount = _storage.RowCount;
            _columnCount = _storage.ColumnCount;
            _data = _storage.Data;

            for (var i = 0; i < _data.Length; i++)
            {
                _data[i] = value;
            }
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="DenseMatrix"/> class from a one dimensional array. This constructor
        /// will reference the one dimensional array and not copy it.
        /// </summary>
        /// <param name="rows">The number of rows.</param>
        /// <param name="columns">The number of columns.</param>
        /// <param name="array">The one dimensional array to create this matrix from. This array should store the matrix in column-major order. see: http://en.wikipedia.org/wiki/Row-major_order </param>
        public DenseMatrix(int rows, int columns, Complex32[] array)
            : base(rows, columns)
        {
            _storage = new DenseColumnMajorMatrixStorage<Complex32>(rows, columns, array);

            _rowCount = _storage.RowCount;
            _columnCount = _storage.ColumnCount;
            _data = _storage.Data;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="DenseMatrix"/> class from a 2D array. This constructor
        /// will allocate a completely new memory block for storing the dense matrix.
        /// </summary>
        /// <param name="array">The 2D array to create this matrix from.</param>
        public DenseMatrix(Complex32[,] array)
            : base(array.GetLength(0), array.GetLength(1))
        {
            _storage = new DenseColumnMajorMatrixStorage<Complex32>(array.GetLength(0), array.GetLength(1));

            _rowCount = _storage.RowCount;
            _columnCount = _storage.ColumnCount;
            _data = _storage.Data;

            for (var i = 0; i < _rowCount; i++)
            {
                for (var j = 0; j < _columnCount; j++)
                {
                    _data[(j * _rowCount) + i] = array[i, j];
                }
            }
        }

        internal DenseColumnMajorMatrixStorage<Complex32> Storage
        {
            get { return _storage; }
        }

        /// <summary>
        /// Gets the matrix's data.
        /// </summary>
        /// <value>The matrix's data.</value>
        public Complex32[] Data
        {
            get { return _data; }
        }

        /// <summary>
        /// Creates a <c>DenseMatrix</c> for the given number of rows and columns.
        /// </summary>
        /// <param name="numberOfRows">
        /// The number of rows.
        /// </param>
        /// <param name="numberOfColumns">
        /// The number of columns.
        /// </param>
        /// <returns>
        /// A <c>DenseMatrix</c> with the given dimensions.
        /// </returns>
        public override Matrix<Complex32> CreateMatrix(int numberOfRows, int numberOfColumns)
        {
            return new DenseMatrix(numberOfRows, numberOfColumns);
        }

        /// <summary>
        /// Creates a <see cref="Vector{T}"/> with a the given dimension.
        /// </summary>
        /// <param name="size">The size of the vector.</param>
        /// <returns>
        /// A <see cref="Vector{T}"/> with the given dimension.
        /// </returns>
        public override Vector<Complex32> CreateVector(int size)
        {
            return new DenseVector(size);
        }

        /// <summary>
        /// Copies the elements of this matrix to the given matrix.
        /// </summary>
        /// <param name="target">
        /// The matrix to copy values into.
        /// </param>
        /// <exception cref="ArgumentNullException">
        /// If target is <see langword="null"/>.
        /// </exception>
        /// <exception cref="ArgumentException">
        /// If this and the target matrix do not have the same dimensions..
        /// </exception>
        public override void CopyTo(Matrix<Complex32> target)
        {
            var denseTarget = target as DenseMatrix;
            if (denseTarget != null)
            {
                _storage.CopyTo(denseTarget.Storage);
                return;
            }

            base.CopyTo(target);
        }

        /// <summary>
        /// Creates a matrix that contains the values from the requested sub-matrix.
        /// </summary>
        /// <param name="rowIndex">The row to start copying from.</param>
        /// <param name="rowCount">The number of rows to copy. Must be positive.</param>
        /// <param name="columnIndex">The column to start copying from.</param>
        /// <param name="columnCount">The number of columns to copy. Must be positive.</param>
        /// <returns>The requested sub-matrix.</returns>
        /// <exception cref="ArgumentOutOfRangeException">If: <list><item><paramref name="rowIndex"/> is
        /// negative, or greater than or equal to the number of rows.</item>
        /// <item><paramref name="columnIndex"/> is negative, or greater than or equal to the number 
        /// of columns.</item>
        /// <item><c>(columnIndex + columnLength) &gt;= Columns</c></item>
        /// <item><c>(rowIndex + rowLength) &gt;= Rows</c></item></list></exception>        
        /// <exception cref="ArgumentException">If <paramref name="rowCount"/> or <paramref name="columnCount"/>
        /// is not positive.</exception>
        public override Matrix<Complex32> SubMatrix(int rowIndex, int rowCount, int columnIndex, int columnCount)
        {
            var storage = new DenseColumnMajorMatrixStorage<Complex32>(rowCount, columnCount);
            _storage.CopySubMatrixTo(storage, rowIndex, 0, rowCount, columnIndex, 0, columnCount);
            return new DenseMatrix(storage.RowCount, storage.ColumnCount, storage.Data);
        }

        /// <summary>
        /// Copies the values of a given matrix into a region in this matrix.
        /// </summary>
        /// <param name="rowIndex">The row to start copying to.</param>
        /// <param name="rowCount">The number of rows to copy. Must be positive.</param>
        /// <param name="columnIndex">The column to start copying to.</param>
        /// <param name="columnCount">The number of columns to copy. Must be positive.</param>
        /// <param name="subMatrix">The sub-matrix to copy from.</param>
        /// <exception cref="ArgumentOutOfRangeException">If: <list><item><paramref name="rowIndex"/> is
        /// negative, or greater than or equal to the number of rows.</item>
        /// <item><paramref name="columnIndex"/> is negative, or greater than or equal to the number 
        /// of columns.</item>
        /// <item><c>(columnIndex + columnLength) &gt;= Columns</c></item>
        /// <item><c>(rowIndex + rowLength) &gt;= Rows</c></item></list></exception> 
        /// <exception cref="ArgumentNullException">If <paramref name="subMatrix"/> is <see langword="null" /></exception>
        /// <item>the size of <paramref name="subMatrix"/> is not at least <paramref name="rowCount"/> x <paramref name="columnCount"/>.</item>
        /// <exception cref="ArgumentException">If <paramref name="rowCount"/> or <paramref name="columnCount"/>
        /// is not positive.</exception>
        public override void SetSubMatrix(int rowIndex, int rowCount, int columnIndex, int columnCount, Matrix<Complex32> subMatrix)
        {
            var denseSubMatrix = subMatrix as DenseMatrix;
            if (denseSubMatrix != null)
            {
                denseSubMatrix._storage.CopySubMatrixTo(_storage, 0, rowIndex, rowCount, 0, columnIndex, columnCount);
                return;
            }

            base.SetSubMatrix(rowIndex, rowCount, columnIndex, columnCount, subMatrix);
        }

        /// <summary>
        /// Gets or sets the value at the given row and column, with range checking.
        /// </summary>
        /// <param name="row">
        /// The row of the element.
        /// </param>
        /// <param name="column">
        /// The column of the element.
        /// </param>
        /// <value>The value to get or set.</value>
        /// <remarks>This method is ranged checked. <see cref="At(int,int)"/> and <see cref="At(int,int,Complex32)"/>
        /// to get and set values without range checking.</remarks>
        public override Complex32 this[int row, int column]
        {
            get { return _storage[row, column]; }
            set { _storage[row, column] = value; }
        }

        /// <summary>
        /// Retrieves the requested element without range checking.
        /// </summary>
        /// <param name="row">
        /// The row of the element.
        /// </param>
        /// <param name="column">
        /// The column of the element.
        /// </param>
        /// <returns>
        /// The requested element.
        /// </returns>
        public override Complex32 At(int row, int column)
        {
            return _storage.At(row, column);
        }

        /// <summary>
        /// Sets the value of the given element.
        /// </summary>
        /// <param name="row">
        /// The row of the element.
        /// </param>
        /// <param name="column">
        /// The column of the element.
        /// </param>
        /// <param name="value">
        /// The value to set the element to.
        /// </param>
        public override void At(int row, int column, Complex32 value)
        {
            _storage.At(row, column, value);
        }

        /// <summary>
        /// Sets all values to zero.
        /// </summary>
        public override void Clear()
        {
            _storage.Clear();
        }

        /// <summary>
        /// Returns the transpose of this matrix.
        /// </summary>        
        /// <returns>The transpose of this matrix.</returns>
        public override Matrix<Complex32> Transpose()
        {
            var ret = new DenseMatrix(_columnCount, _rowCount);
            for (var j = 0; j < _columnCount; j++)
            {
                var index = j * _rowCount;
                for (var i = 0; i < _rowCount; i++)
                {
                    ret._data[(i * _columnCount) + j] = _data[index + i];
                }
            }

            return ret;
        }

        /// <summary>Calculates the L1 norm.</summary>
        /// <returns>The L1 norm of the matrix.</returns>
        public override Complex32 L1Norm()
        {
            return Control.LinearAlgebraProvider.MatrixNorm(Norm.OneNorm, _rowCount, _columnCount, _data);
        }

        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
        /// <returns>The Frobenius norm of this matrix.</returns>
        public override Complex32 FrobeniusNorm()
        {
            return Control.LinearAlgebraProvider.MatrixNorm(Norm.FrobeniusNorm, _rowCount, _columnCount, _data);
        }

        /// <summary>Calculates the infinity norm of this matrix.</summary>
        /// <returns>The infinity norm of this matrix.</returns>  
        public override Complex32 InfinityNorm()
        {
            return Control.LinearAlgebraProvider.MatrixNorm(Norm.InfinityNorm, _rowCount, _columnCount, _data);
        }

        #region Static constructors for special matrices.

        /// <summary>
        /// Initializes a square <see cref="DenseMatrix"/> with all zero's except for ones on the diagonal.
        /// </summary>
        /// <param name="order">the size of the square matrix.</param>
        /// <returns>A dense identity matrix.</returns>
        /// <exception cref="ArgumentException">
        /// If <paramref name="order"/> is less than one.
        /// </exception>
        public static DenseMatrix Identity(int order)
        {
            var m = new DenseMatrix(order);
            for (var i = 0; i < order; i++)
            {
                m._data[(i * order) + i] = 1.0f;
            }

            return m;
        }

        #endregion

        /// <summary>
        /// Multiplies each element of the matrix by a scalar and places results into the result matrix.
        /// </summary>
        /// <param name="scalar">The scalar to multiply the matrix with.</param>
        /// <param name="result">The matrix to store the result of the multiplication.</param>
        protected override void DoMultiply(Complex32 scalar, Matrix<Complex32> result)
        {
            var denseResult = result as DenseMatrix;
            if (denseResult == null)
            {
                base.DoMultiply(scalar, result);
            }
            else
            {
                Control.LinearAlgebraProvider.ScaleArray(scalar, _data, denseResult._data);
            }
        }

        /// <summary>
        /// Multiplies this matrix with a vector and places the results into the result vector.
        /// </summary>
        /// <param name="rightSide">The vector to multiply with.</param>
        /// <param name="result">The result of the multiplication.</param>
        protected override void DoMultiply(Vector<Complex32> rightSide, Vector<Complex32> result)
        {
            var denseRight = rightSide as DenseVector;
            var denseResult = result as DenseVector;

            if (denseRight == null || denseResult == null)
            {
                base.DoMultiply(rightSide, result);
            }
            else
            {
                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
                    Algorithms.LinearAlgebra.Transpose.DontTranspose,
                    Algorithms.LinearAlgebra.Transpose.DontTranspose,
                    1.0f,
                    _data,
                    _rowCount,
                    _columnCount,
                    denseRight.Data,
                    denseRight.Count,
                    1,
                    0.0f,
                    denseResult.Data);
            }
        }

        /// <summary>
        /// Multiplies this matrix with another matrix and places the results into the result matrix.
        /// </summary>
        /// <param name="other">The matrix to multiply with.</param>
        /// <param name="result">The result of the multiplication.</param>
        protected override void DoMultiply(Matrix<Complex32> other, Matrix<Complex32> result)
        {
            var denseOther = other as DenseMatrix;
            var denseResult = result as DenseMatrix;

            if (denseOther == null || denseResult == null)
            {
                base.DoMultiply(other, result);
            }
            else
            {
                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
                    Algorithms.LinearAlgebra.Transpose.DontTranspose,
                    Algorithms.LinearAlgebra.Transpose.DontTranspose,
                    1.0f,
                    _data,
                    _rowCount,
                    _columnCount,
                    denseOther._data,
                    denseOther._rowCount,
                    denseOther._columnCount,
                    0.0f,
                    denseResult._data);
            }
        }

        /// <summary>
        /// Multiplies this matrix with transpose of another matrix and places the results into the result matrix.
        /// </summary>
        /// <param name="other">The matrix to multiply with.</param>
        /// <param name="result">The result of the multiplication.</param>
        protected override void DoTransposeAndMultiply(Matrix<Complex32> other, Matrix<Complex32> result)
        {
             var denseOther = other as DenseMatrix;
            var denseResult = result as DenseMatrix;

            if (denseOther == null || denseResult == null)
            {
                base.DoTransposeAndMultiply(other, result);
            }
            else
            {
                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
                    Algorithms.LinearAlgebra.Transpose.DontTranspose,
                    Algorithms.LinearAlgebra.Transpose.Transpose,
                    1.0f,
                    _data,
                    _rowCount,
                    _columnCount,
                    denseOther._data,
                    denseOther._rowCount,
                    denseOther._columnCount,
                    0.0f,
                    denseResult._data);
            }
        }

        /// <summary>
        /// Multiplies the transpose of this matrix with a vector and places the results into the result vector.
        /// </summary>
        /// <param name="rightSide">The vector to multiply with.</param>
        /// <param name="result">The result of the multiplication.</param>
        protected override void DoTransposeThisAndMultiply(Vector<Complex32> rightSide, Vector<Complex32> result)
        {
            var denseRight = rightSide as DenseVector;
            var denseResult = result as DenseVector;

            if (denseRight == null || denseResult == null)
            {
                base.DoTransposeThisAndMultiply(rightSide, result);
            }
            else
            {
                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
                    Algorithms.LinearAlgebra.Transpose.Transpose,
                    Algorithms.LinearAlgebra.Transpose.DontTranspose,
                    1.0f,
                    _data,
                    _rowCount,
                    _columnCount,
                    denseRight.Data,
                    denseRight.Count,
                    1,
                    0.0f,
                    denseResult.Data);
            }
        }

        /// <summary>
        /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
        /// </summary>
        /// <param name="other">The matrix to multiply with.</param>
        /// <param name="result">The result of the multiplication.</param>
        protected override void DoTransposeThisAndMultiply(Matrix<Complex32> other, Matrix<Complex32> result)
        {
            var denseOther = other as DenseMatrix;
            var denseResult = result as DenseMatrix;

            if (denseOther == null || denseResult == null)
            {
                base.DoTransposeThisAndMultiply(other, result);
            }
            else
            {
                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
                    Algorithms.LinearAlgebra.Transpose.Transpose,
                    Algorithms.LinearAlgebra.Transpose.DontTranspose,
                    1.0f,
                    _data,
                    _rowCount,
                    _columnCount,
                    denseOther._data,
                    denseOther._rowCount,
                    denseOther._columnCount,
                    0.0f,
                    denseResult._data);
            }
        }

        /// <summary>
        /// Negate each element of this matrix and place the results into the result matrix.
        /// </summary>
        /// <param name="result">The result of the negation.</param>
        protected override void DoNegate(Matrix<Complex32> result)
        {
            var denseResult = result as DenseMatrix;

            if (denseResult == null)
            {
                base.DoNegate(result);
            }
            else
            {
                Control.LinearAlgebraProvider.ScaleArray(-1, _data, denseResult._data);
            }
        }

        /// <summary>
        /// Pointwise multiplies this matrix with another matrix and stores the result into the result matrix.
        /// </summary>
        /// <param name="other">The matrix to pointwise multiply with this one.</param>
        /// <param name="result">The matrix to store the result of the pointwise multiplication.</param>
        protected override void DoPointwiseMultiply(Matrix<Complex32> other, Matrix<Complex32> result)
        {
            var denseOther = other as DenseMatrix;
            var denseResult = result as DenseMatrix;

            if (denseOther == null || denseResult == null)
            {
                base.DoPointwiseMultiply(other, result);
            }
            else
            {
                Control.LinearAlgebraProvider.PointWiseMultiplyArrays(_data, denseOther._data, denseResult._data);
            }
        }

        /// <summary>
        /// Pointwise divide this matrix by another matrix and stores the result into the result matrix.
        /// </summary>
        /// <param name="other">The matrix to pointwise divide this one by.</param>
        /// <param name="result">The matrix to store the result of the pointwise division.</param>
        protected override void DoPointwiseDivide(Matrix<Complex32> other, Matrix<Complex32> result)
        {
            var denseOther = other as DenseMatrix;
            var denseResult = result as DenseMatrix;

            if (denseOther == null || denseResult == null)
            {
                base.DoPointwiseDivide(other, result);
            }
            else
            {
                Control.LinearAlgebraProvider.PointWiseDivideArrays(_data, denseOther._data, denseResult._data);
            }
        }

        /// <summary>
        /// Adds another matrix to this matrix.
        /// </summary>
        /// <param name="other">The matrix to add to this matrix.</param>
        /// <param name="result">The matrix to store the result of add</param>
        /// <exception cref="ArgumentNullException">If the other matrix is <see langword="null"/>.</exception>
        /// <exception cref="ArgumentOutOfRangeException">If the two matrices don't have the same dimensions.</exception>
        protected override void DoAdd(Matrix<Complex32> other, Matrix<Complex32> result)
        {
            var denseOther = other as DenseMatrix;
            var denseResult = result as DenseMatrix;
            if (denseOther == null || denseResult == null)
            {
                base.DoAdd(other, result);
            }
            else
            {
                Control.LinearAlgebraProvider.AddArrays(_data, denseOther._data, denseResult._data);
            }
        }

        /// <summary>
        /// Subtracts another matrix from this matrix.
        /// </summary>
        /// <param name="other">The matrix to subtract.</param>
        /// <param name="result">The matrix to store the result of the subtraction.</param>
        protected override void DoSubtract(Matrix<Complex32> other, Matrix<Complex32> result)
        {
            var denseOther = other as DenseMatrix;
            var denseResult = result as DenseMatrix;
            if (denseOther == null || denseResult == null)
            {
                base.DoSubtract(other, result);
            }
            else
            {
                Control.LinearAlgebraProvider.SubtractArrays(_data, denseOther._data, denseResult._data);
            }
        }

        /// <summary>
        /// Returns the conjugate transpose of this matrix.
        /// </summary>        
        /// <returns>The conjugate transpose of this matrix.</returns>
        public override Matrix<Complex32> ConjugateTranspose()
        {
            var ret = new DenseMatrix(_columnCount, _rowCount);
            for (var j = 0; j < _columnCount; j++)
            {
                var index = j * _rowCount;
                for (var i = 0; i < _rowCount; i++)
                {
                    ret._data[(i * _columnCount) + j] = _data[index + i].Conjugate();
                }
            }

            return ret;
        }
        
        /// <summary>
        /// Computes the trace of this matrix.
        /// </summary>
        /// <returns>The trace of this matrix</returns>
        /// <exception cref="ArgumentException">If the matrix is not square</exception>
        public override Complex32 Trace()
        {
            if (_rowCount != _columnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSquare);
            }

            var sum = Complex32.Zero;
            for (var i = 0; i < _rowCount; i++)
            {
                sum += _data[(i * _rowCount) + i];
            }

            return sum;
        }

        /// <summary>
        /// Adds two matrices together and returns the results.
        /// </summary>
        /// <remarks>This operator will allocate new memory for the result. It will
        /// choose the representation of either <paramref name="leftSide"/> or <paramref name="rightSide"/> depending on which
        /// is denser.</remarks>
        /// <param name="leftSide">The left matrix to add.</param>
        /// <param name="rightSide">The right matrix to add.</param>
        /// <returns>The result of the addition.</returns>
        /// <exception cref="ArgumentOutOfRangeException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> don't have the same dimensions.</exception>
        /// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
        public static DenseMatrix operator +(DenseMatrix leftSide, DenseMatrix rightSide)
        {
            if (rightSide == null)
            {
                throw new ArgumentNullException("rightSide");
            }

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

            if (leftSide._rowCount != rightSide._rowCount || leftSide._columnCount != rightSide._columnCount)
            {
                throw DimensionsDontMatch<ArgumentOutOfRangeException>(leftSide, rightSide);
            }

            return (DenseMatrix)leftSide.Add(rightSide);
        }

        /// <summary>
        /// Returns a <strong>Matrix</strong> containing the same values of <paramref name="rightSide"/>. 
        /// </summary>
        /// <param name="rightSide">The matrix to get the values from.</param>
        /// <returns>A matrix containing a the same values as <paramref name="rightSide"/>.</returns>
        /// <exception cref="ArgumentNullException">If <paramref name="rightSide"/> is <see langword="null" />.</exception>
        public static DenseMatrix operator +(DenseMatrix rightSide)
        {
            if (rightSide == null)
            {
                throw new ArgumentNullException("rightSide");
            }

            return (DenseMatrix)rightSide.Clone();
        }

        /// <summary>
        /// Subtracts two matrices together and returns the results.
        /// </summary>
        /// <remarks>This operator will allocate new memory for the result. It will
        /// choose the representation of either <paramref name="leftSide"/> or <paramref name="rightSide"/> depending on which
        /// is denser.</remarks>
        /// <param name="leftSide">The left matrix to subtract.</param>
        /// <param name="rightSide">The right matrix to subtract.</param>
        /// <returns>The result of the addition.</returns>
        /// <exception cref="ArgumentOutOfRangeException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> don't have the same dimensions.</exception>
        /// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
        public static DenseMatrix operator -(DenseMatrix leftSide, DenseMatrix rightSide)
        {
            if (rightSide == null)
            {
                throw new ArgumentNullException("rightSide");
            }

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

            if (leftSide._rowCount != rightSide._rowCount || leftSide._columnCount != rightSide._columnCount)
            {
                throw DimensionsDontMatch<ArgumentOutOfRangeException>(leftSide, rightSide);
            }

            return (DenseMatrix)leftSide.Subtract(rightSide);
        }

        /// <summary>
        /// Negates each element of the matrix.
        /// </summary>
        /// <param name="rightSide">The matrix to negate.</param>
        /// <returns>A matrix containing the negated values.</returns>
        /// <exception cref="ArgumentNullException">If <paramref name="rightSide"/> is <see langword="null" />.</exception>
        public static DenseMatrix operator -(DenseMatrix rightSide)
        {
            if (rightSide == null)
            {
                throw new ArgumentNullException("rightSide");
            }

            return (DenseMatrix)rightSide.Negate();
        }

        /// <summary>
        /// Multiplies a <strong>Matrix</strong> by a constant and returns the result.
        /// </summary>
        /// <param name="leftSide">The matrix to multiply.</param>
        /// <param name="rightSide">The constant to multiply the matrix by.</param>
        /// <returns>The result of the multiplication.</returns>
        /// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> is <see langword="null" />.</exception>
        public static DenseMatrix operator *(DenseMatrix leftSide, Complex32 rightSide)
        {
            if (leftSide == null)
            {
                throw new ArgumentNullException("leftSide");
            }

            return (DenseMatrix)leftSide.Multiply(rightSide);
        }

        /// <summary>
        /// Multiplies a <strong>Matrix</strong> by a constant and returns the result.
        /// </summary>
        /// <param name="leftSide">The matrix to multiply.</param>
        /// <param name="rightSide">The constant to multiply the matrix by.</param>
        /// <returns>The result of the multiplication.</returns>
        /// <exception cref="ArgumentNullException">If <paramref name="rightSide"/> is <see langword="null" />.</exception>
        public static DenseMatrix operator *(Complex32 leftSide, DenseMatrix rightSide)
        {
            if (rightSide == null)
            {
                throw new ArgumentNullException("rightSide");
            }

            return (DenseMatrix)rightSide.Multiply(leftSide);
        }

        /// <summary>
        /// Multiplies two matrices.
        /// </summary>
        /// <remarks>This operator will allocate new memory for the result. It will
        /// choose the representation of either <paramref name="leftSide"/> or <paramref name="rightSide"/> depending on which
        /// is denser.</remarks>
        /// <param name="leftSide">The left matrix to multiply.</param>
        /// <param name="rightSide">The right matrix to multiply.</param>
        /// <returns>The result of multiplication.</returns>
        /// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
        /// <exception cref="ArgumentException">If the dimensions of <paramref name="leftSide"/> or <paramref name="rightSide"/> don't conform.</exception>
        public static DenseMatrix operator *(DenseMatrix leftSide, DenseMatrix rightSide)
        {
            if (leftSide == null)
            {
                throw new ArgumentNullException("leftSide");
            }

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

            if (leftSide._columnCount != rightSide._rowCount)
            {
                throw DimensionsDontMatch<ArgumentException>(leftSide, rightSide);
            }

            return (DenseMatrix)leftSide.Multiply(rightSide);
        }

        /// <summary>
        /// Multiplies a <strong>Matrix</strong> and a Vector.
        /// </summary>
        /// <param name="leftSide">The matrix to multiply.</param>
        /// <param name="rightSide">The vector to multiply.</param>
        /// <returns>The result of multiplication.</returns>
        /// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
        public static DenseVector operator *(DenseMatrix leftSide, DenseVector rightSide)
        {
            if (leftSide == null)
            {
                throw new ArgumentNullException("leftSide");
            }

            return (DenseVector)leftSide.Multiply(rightSide);
        }

        /// <summary>
        /// Multiplies a Vector and a <strong>Matrix</strong>.
        /// </summary>
        /// <param name="leftSide">The vector to multiply.</param>
        /// <param name="rightSide">The matrix to multiply.</param>
        /// <returns>The result of multiplication.</returns>
        /// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
        public static DenseVector operator *(DenseVector leftSide, DenseMatrix rightSide)
        {
            if (rightSide == null)
            {
                throw new ArgumentNullException("rightSide");
            }

            return (DenseVector)rightSide.LeftMultiply(leftSide);
        }

        /// <summary>
        /// Multiplies a <strong>Matrix</strong> by a constant and returns the result.
        /// </summary>
        /// <param name="leftSide">The matrix to multiply.</param>
        /// <param name="rightSide">The constant to multiply the matrix by.</param>
        /// <returns>The result of the multiplication.</returns>
        /// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> is <see langword="null" />.</exception>
        public static DenseMatrix operator %(DenseMatrix leftSide, Complex32 rightSide)
        {
            if (leftSide == null)
            {
                throw new ArgumentNullException("leftSide");
            }

            return (DenseMatrix)leftSide.Modulus(rightSide);
        }
    }
}