mathnet-numerics/src/Numerics/LinearAlgebra/Double/Matrix.cs

// <copyright file="Matrix.cs" company="Math.NET">
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namespace MathNet.Numerics.LinearAlgebra.Double
{
    using System;
    using Generic;
    using Properties;
    using Storage;

    /// <summary>
    /// <c>double</c> version of the <see cref="Matrix{T}"/> class.
    /// </summary>
    [Serializable]
    public abstract class Matrix : Matrix<double>
    {        
        /// <summary>
        /// Initializes a new instance of the Matrix class.
        /// </summary>
        protected Matrix(MatrixStorage<double> storage)
            : base(storage)
        {
        }

        /// <summary>Calculates the L1 norm.</summary>
        /// <returns>The L1 norm of the matrix.</returns>
        public override double L1Norm()
        {
            var norm = 0.0;
            for (var j = 0; j < ColumnCount; j++)
            {
                var s = 0.0;
                for (var i = 0; i < RowCount; i++)
                {
                    s += Math.Abs(At(i, j));
                }

                norm = Math.Max(norm, s);
            }

            return norm;
        }

        /// <summary>
        /// Returns the conjugate transpose of this matrix.
        /// </summary>        
        /// <returns>The conjugate transpose of this matrix.</returns>
        public override sealed Matrix<double> ConjugateTranspose()
        {
            return Transpose();
        }

        /// <summary>Calculates the Frobenius norm of this matrix.</summary>
        /// <returns>The Frobenius norm of this matrix.</returns>
        public override double FrobeniusNorm()
        {
            var transpose = Transpose();
            var aat = this * transpose;

            var norm = 0.0;
            for (var i = 0; i < RowCount; i++)
            {
                norm += aat.At(i, i);
            }

            norm = Math.Sqrt(norm);

            return norm;
        }

        /// <summary>Calculates the infinity norm of this matrix.</summary>
        /// <returns>The infinity norm of this matrix.</returns>   
        public override double InfinityNorm()
        {
            var norm = 0.0;
            for (var i = 0; i < RowCount; i++)
            {
                var s = 0.0;
                for (var j = 0; j < ColumnCount; j++)
                {
                    s += Math.Abs(At(i, j));
                }

                norm = Math.Max(norm, s);
            }

            return norm;
        }

        /// <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 the addition.</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<double> other, Matrix<double> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j < ColumnCount; j++)
                {
                    result.At(i, j, At(i, j) + other.At(i, j));
                }
            }
        }
    
        /// <summary>
        /// Subtracts another matrix from this matrix.
        /// </summary>
        /// <param name="other">The matrix to subtract to this matrix.</param>
        /// <param name="result">The matrix to store the result of subtraction.</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 DoSubtract(Matrix<double> other, Matrix<double> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j < ColumnCount; j++)
                {
                    result.At(i, j, At(i, j) - other.At(i, j));
                }
            }
        }

        /// <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(double scalar, Matrix<double> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j < ColumnCount; j++)
                {
                    result.At(i, j, At(i, j) * scalar);
                }
            }
        }

        /// <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<double> rightSide, Vector<double> result)
         {
             for (var i = 0; i < RowCount; i++)
             {
                 var s = 0.0;
                 for (var j = 0; j != ColumnCount; j++)
                 {
                     s += At(i, j) * rightSide[j];
                 }

                 result[i] = s;
             }
         }

        /// <summary>
        /// Divides each element of the matrix by a scalar and places results into the result matrix.
        /// </summary>
        /// <param name="scalar">The scalar to divide the matrix with.</param>
        /// <param name="result">The matrix to store the result of the division.</param>
        protected override void DoDivide(double scalar, Matrix<double> result)
        {
            DoMultiply(1.0 / scalar, result);
        }

        /// <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<double> other, Matrix<double> result)
        {
            for (var j = 0; j < RowCount; j++)
            {
                for (var i = 0; i != other.ColumnCount; i++)
                {
                    var s = 0.0;
                    for (var l = 0; l < ColumnCount; l++)
                    {
                        s += At(j, l) * other.At(l, i);
                    }

                    result.At(j, i, s);
                }
            }
        }

        /// <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<double> other, Matrix<double> result)
        {
            for (var j = 0; j < other.RowCount; j++)
            {
                for (var i = 0; i < RowCount; i++)
                {
                    var s = 0.0;
                    for (var l = 0; l < ColumnCount; l++)
                    {
                        s += At(i, l) * other.At(j, l);
                    }

                    result.At(i, j, s);
                }
            }
        }

        /// <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<double> other, Matrix<double> result)
        {
            for (var j = 0; j < other.ColumnCount; j++)
            {
                for (var i = 0; i < ColumnCount; i++)
                {
                    var s = 0.0;
                    for (var l = 0; l < RowCount; l++)
                    {
                        s += At(l, i) * other.At(l, j);
                    }

                    result.At(i, j, s);
                }
            }
        }

        /// <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<double> rightSide, Vector<double> result)
        {
            for (var i = 0; i < ColumnCount; i++)
            {
                var s = 0.0;
                for (var j = 0; j != RowCount; j++)
                {
                    s += At(j, i) * rightSide[j];
                }

                result[i] = s;
            }
        }

        /// <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<double> result)
        {
            for (var i = 0; i < RowCount; i++)
            {
                for (var j = 0; j != ColumnCount; j++)
                {
                    result.At(i, j, -At(i, j));
                }
            }
        }

        /// <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<double> other, Matrix<double> result)
        {
            for (var j = 0; j < ColumnCount; j++)
            {
                for (var i = 0; i < RowCount; i++)
                {
                    result.At(i, j, At(i, j) * other.At(i, j));
                }
            }
        }

        /// <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<double> other, Matrix<double> result)
        {
            for (var j = 0; j < ColumnCount; j++)
            {
                for (var i = 0; i < RowCount; i++)
                {
                    result.At(i, j, At(i, j) / other.At(i, j));
                }
            }
        }

        /// <summary>
        /// Computes the modulus for each element of the matrix.
        /// </summary>
        /// <param name="divisor">The divisor to use.</param>
        /// <param name="result">Matrix to store the results in.</param>
        protected override void DoModulus(double divisor, Matrix<double> result)
        {
            for (var row = 0; row < RowCount; row++)
            {
                for (var column = 0; column < ColumnCount; column++)
                {
                    result.At(row, column, At(row, column) % divisor);
                }
            }
        }

        /// <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 double Trace()
        {
            if (RowCount != ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSquare);
            }

            var sum = 0.0;
            for (var i = 0; i < RowCount; i++)
            {
                sum += At(i, i);
            }

            return sum;
        }
    }
}