// <copyright file="Diagonal.cs" company="Math.NET">
|
// Math.NET Numerics, part of the Math.NET Project
|
// http://numerics.mathdotnet.com
|
// http://github.com/mathnet/mathnet-numerics
|
//
|
// Copyright (c) 2009-2010 Math.NET
|
//
|
// Permission is hereby granted, free of charge, to any person
|
// obtaining a copy of this software and associated documentation
|
// files (the "Software"), to deal in the Software without
|
// restriction, including without limitation the rights to use,
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
// copies of the Software, and to permit persons to whom the
|
// Software is furnished to do so, subject to the following
|
// conditions:
|
//
|
// The above copyright notice and this permission notice shall be
|
// included in all copies or substantial portions of the Software.
|
//
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
// OTHER DEALINGS IN THE SOFTWARE.
|
// </copyright>
|
|
using System;
|
using IStation.Numerics.LinearAlgebra.Solvers;
|
|
namespace IStation.Numerics.LinearAlgebra.Complex.Solvers
|
{
|
using Complex = System.Numerics.Complex;
|
|
/// <summary>
|
/// A diagonal preconditioner. The preconditioner uses the inverse
|
/// of the matrix diagonal as preconditioning values.
|
/// </summary>
|
public sealed class DiagonalPreconditioner : IPreconditioner<Complex>
|
{
|
/// <summary>
|
/// The inverse of the matrix diagonal.
|
/// </summary>
|
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.RowCount != matrix.ColumnCount)
|
{
|
throw new ArgumentException("Matrix must be square.", nameof(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>
|
/// <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 (_inverseDiagonals == null)
|
{
|
throw new ArgumentException("The requested matrix does not exist.");
|
}
|
|
if ((lhs.Count != rhs.Count) || (lhs.Count != _inverseDiagonals.Length))
|
{
|
throw new ArgumentException("All vectors must have the same dimensionality.", nameof(rhs));
|
}
|
|
for (var i = 0; i < _inverseDiagonals.Length; i++)
|
{
|
lhs[i] = rhs[i]*_inverseDiagonals[i];
|
}
|
}
|
}
|
}
|
