// <copyright file="Evd.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) 2009-2013 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 IStation.Numerics.LinearAlgebra.Factorization;
|
|
namespace IStation.Numerics.LinearAlgebra.Complex.Factorization
|
{
|
using Complex = System.Numerics.Complex;
|
|
/// <summary>
|
/// Eigenvalues and eigenvectors of a real matrix.
|
/// </summary>
|
/// <remarks>
|
/// If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
|
/// diagonal and the eigenvector matrix V is orthogonal.
|
/// I.e. A = V*D*V' and V*VT=I.
|
/// If A is not symmetric, then the eigenvalue matrix D is block diagonal
|
/// with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
|
/// lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The
|
/// columns of V represent the eigenvectors in the sense that A*V = V*D,
|
/// i.e. A.Multiply(V) equals V.Multiply(D). The matrix V may be badly
|
/// conditioned, or even singular, so the validity of the equation
|
/// A = V*D*Inverse(V) depends upon V.Condition().
|
/// </remarks>
|
internal abstract class Evd : Evd<Complex>
|
{
|
protected Evd(Matrix<Complex> eigenVectors, Vector<Complex> eigenValues, Matrix<Complex> blockDiagonal, bool isSymmetric)
|
: base(eigenVectors, eigenValues, blockDiagonal, isSymmetric)
|
{
|
}
|
|
/// <summary>
|
/// Gets the absolute value of determinant of the square matrix for which the EVD was computed.
|
/// </summary>
|
public override Complex Determinant
|
{
|
get
|
{
|
var det = Complex.One;
|
for (var i = 0; i < EigenValues.Count; i++)
|
{
|
det *= EigenValues[i];
|
|
if (EigenValues[i].AlmostEqual(Complex.Zero))
|
{
|
return 0;
|
}
|
}
|
|
return det.Magnitude;
|
}
|
}
|
|
/// <summary>
|
/// Gets the effective numerical matrix rank.
|
/// </summary>
|
/// <value>The number of non-negligible singular values.</value>
|
public override int Rank
|
{
|
get
|
{
|
var rank = 0;
|
for (var i = 0; i < EigenValues.Count; i++)
|
{
|
if (EigenValues[i].AlmostEqual(Complex.Zero))
|
{
|
continue;
|
}
|
|
rank++;
|
}
|
|
return rank;
|
}
|
}
|
|
/// <summary>
|
/// Gets a value indicating whether the matrix is full rank or not.
|
/// </summary>
|
/// <value><c>true</c> if the matrix is full rank; otherwise <c>false</c>.</value>
|
public override bool IsFullRank
|
{
|
get
|
{
|
for (var i = 0; i < EigenValues.Count; i++)
|
{
|
if (EigenValues[i].AlmostEqual(Complex.Zero))
|
{
|
return false;
|
}
|
}
|
|
return true;
|
}
|
}
|
}
|
}
|
