mathnet-numerics/src/Numerics/LinearAlgebra/Complex/Solvers/Preconditioners/Diagonal.cs

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namespace MathNet.Numerics.LinearAlgebra.Complex.Solvers.Preconditioners
{
    using System;
    using Properties;

#if NOSYSNUMERICS
    using Complex = Numerics.Complex;
#else
    using Complex = System.Numerics.Complex;
#endif

    /// <summary>
    /// A diagonal preconditioner. The preconditioner uses the inverse
    /// of the matrix diagonal as preconditioning values.
    /// </summary>
    public sealed class Diagonal : IPreConditioner
    {
        /// <summary>
        /// The inverse of the matrix diagonal.
        /// </summary>
        private Complex[] _inverseDiagonals;

        /// <summary>
        /// Returns the decomposed matrix diagonal.
        /// </summary>
        /// <returns>The matrix diagonal.</returns>
        internal DiagonalMatrix DiagonalEntries()
        {
            var result = new DiagonalMatrix(_inverseDiagonals.Length);
            for (var i = 0; i < _inverseDiagonals.Length; i++)
            {
                result.At(i, i, 1 / _inverseDiagonals[i]);
            }

            return result;
        }

        /// <summary>
        /// Initializes the preconditioner and loads the internal data structures.
        /// </summary>
        /// <param name="matrix">
        /// The <see cref="Matrix"/> upon which this preconditioner is based.</param>
        /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <see langword="null" />. </exception>
        /// <exception cref="ArgumentException">If <paramref name="matrix"/> is not a square matrix.</exception>
        public void Initialize(Matrix<Complex> matrix)
        {
            if (matrix == null)
            {
                throw new ArgumentNullException("matrix");
            }

            if (matrix.RowCount != matrix.ColumnCount)
            {
                throw new ArgumentException(Resources.ArgumentMatrixSquare, "matrix");
            }

            _inverseDiagonals = new Complex[matrix.RowCount];
            for (var i = 0; i < matrix.RowCount; i++)
            {
                _inverseDiagonals[i] = 1 / matrix.At(i, i);
            }
        }

        /// <summary>
        /// Approximates the solution to the matrix equation <b>Ax = b</b>.
        /// </summary>
        /// <param name="rhs">The right hand side vector.</param>
        /// <returns>The left hand side vector.</returns>
        public Vector<Complex> Approximate(Vector<Complex> rhs)
        {
            if (rhs == null)
            {
                throw new ArgumentNullException("rhs");
            }

            if (_inverseDiagonals == null)
            {
                throw new ArgumentException(Resources.ArgumentMatrixDoesNotExist);
            }

            if (rhs.Count != _inverseDiagonals.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength, "rhs");
            }

            var result = new DenseVector(rhs.Count);
            Approximate(rhs, result);
            return result;
        }

        /// <summary>
        /// Approximates the solution to the matrix equation <b>Ax = b</b>.
        /// </summary>
        /// <param name="rhs">The right hand side vector.</param>
        /// <param name="lhs">The left hand side vector. Also known as the result vector.</param>
        public void Approximate(Vector<Complex> rhs, Vector<Complex> lhs)
        {
            if (rhs == null)
            {
                throw new ArgumentNullException("rhs");
            }

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

            if (_inverseDiagonals == null)
            {
                throw new ArgumentException(Resources.ArgumentMatrixDoesNotExist);
            }

            if ((lhs.Count != rhs.Count) || (lhs.Count != _inverseDiagonals.Length))
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength, "rhs");
            }

            for (var i = 0; i < _inverseDiagonals.Length; i++)
            {
                lhs[i] = rhs[i] * _inverseDiagonals[i];
            }
        }
    }
}