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Dwsim / data /DWSIM.Math.DotNumerics /LinearAlgebra /EigenSystem.cs
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#region Copyright © 2009, De Santiago-Castillo JA. All rights reserved.
//Copyright © 2009 Jose Antonio De Santiago-Castillo
//E-mail:JAntonioDeSantiago@gmail.com
//Web: www.DotNumerics.com
//
#endregion
using System;
using System.Collections.Generic;
using System.Text;
using System.ComponentModel;
using DotNumerics.LinearAlgebra.CSLapack;
using DotNumerics.LinearAlgebra.CSEispack;
using DotNumerics.FortranLibrary;
namespace DotNumerics.LinearAlgebra
{
/// <summary>
/// Computes the eigenvalues and the eigenvectors of a square matrix.
/// </summary>
public sealed class EigenSystem
{
#region Fields
DGEEV _dgeev;
DSYEV _dsyev;
DSBEV _dsbev;
CG _cg;
#endregion
/// <summary>
/// Initializes a new instance of the EigenSystem class.
/// </summary>
public EigenSystem()
{
}
#region General matrix
/// <summary>
/// Computes the eigenvalues for an N-by-N real nonsymmetric matrix A.
/// </summary>
/// <param name="A">N-by-N real nonsymmetric matrix A.</param>
/// <returns>The eigenvalues.</returns>
public ComplexMatrix GetEigenvalues(Matrix A)
{
if (this._dgeev == null) this._dgeev = new DGEEV();
this.CheckDimensions(A);
Matrix ACopy = A.Clone();
double[] ACopyData = ACopy.Data;
Matrix RealEVectors = new Matrix(1, 1);
double[] EigenVectsData = RealEVectors.Data;
ComplexMatrix EigenVals = new ComplexMatrix(A.RowCount, 1);
double[] REigVal = new double[A.RowCount];
double[] IEigVal = new double[A.RowCount];
//double[] EigenValsData = EigenVals.Data;
int Info = 0;
double[] VL = new double[A.RowCount];
double[] Work = new double[1];
int LWork = -1;
//Calculamos LWORK
_dgeev.Run("N", "N", A.RowCount, ref ACopyData, 0, ACopy.RowCount, ref REigVal, 0, ref IEigVal, 0, ref VL, 0, 1, ref EigenVectsData, 0, A.RowCount, ref Work, 0, LWork, ref Info);
LWork = Convert.ToInt32(Work[0]);
if (LWork > 0)
{
Work = new double[LWork];
_dgeev.Run("N", "N", A.RowCount, ref ACopyData, 0, ACopy.RowCount, ref REigVal, 0, ref IEigVal, 0, ref VL, 0, 1, ref EigenVectsData, 0, A.RowCount, ref Work, 0, LWork, ref Info);
}
else
{
//Error
}
#region Error
//= 0: successful exit
//.LT. 0: if INFO = -i, the i-th argument had an illegal value.
//.GT. 0: if INFO = i, the QR algorithm failed to compute all the
// eigenvalues, and no eigenvectors have been computed;
// elements i+1:N of WR and WI contain eigenvalues which
// have converged.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("The QR algorithm failed to compute all the eigenvalues.");
}
#endregion
for (int i = 0; i < EigenVals.RowCount; i++)
{
EigenVals[i, 0] = new Complex(REigVal[i], IEigVal[i]);
}
return EigenVals;
}
/// <summary>
/// Computes for an N-by-N real nonsymmetric matrix A, the
/// eigenvalues and eigenvectors.
/// </summary>
/// <param name="A">N-by-N real nonsymmetric matrix A.</param>
/// <param name="EigenVectors">The eigenvectors.</param>
/// <returns>The eigenvalues.</returns>
public ComplexMatrix GetEigenvalues(Matrix A, out ComplexMatrix EigenVectors)
{
if (this._dgeev == null) this._dgeev = new DGEEV();
this.CheckDimensions(A);
Matrix ACopy = A.Clone();
double[] ACopyData = ACopy.Data;
EigenVectors = new ComplexMatrix(A.RowCount, A.ColumnCount);
Matrix RealEVectors = new Matrix(A.RowCount, A.ColumnCount);
double[] EigenVectsData = RealEVectors.Data;
ComplexMatrix EigenVals = new ComplexMatrix(A.RowCount, 1);
double[] REigVal = new double[A.RowCount];
double[] IEigVal = new double[A.RowCount];
//double[] EigenValsData = EigenVals.Data;
int Info = 0;
double[] VL = new double[A.RowCount];
double[] Work = new double[1];
int LWork = -1;
//Calculamos LWORK
_dgeev.Run("N", "V", A.RowCount, ref ACopyData, 0, ACopy.RowCount, ref REigVal, 0, ref IEigVal, 0, ref VL, 0, 1, ref EigenVectsData, 0, A.RowCount, ref Work, 0, LWork, ref Info);
LWork = Convert.ToInt32(Work[0]);
if (LWork > 0)
{
Work = new double[LWork];
_dgeev.Run("N", "V", A.RowCount, ref ACopyData, 0, ACopy.RowCount, ref REigVal, 0, ref IEigVal, 0, ref VL, 0, 1, ref EigenVectsData, 0, A.RowCount, ref Work, 0, LWork, ref Info);
}
else
{
//Error
}
#region Error
//= 0: successful exit
//.LT. 0: if INFO = -i, the i-th argument had an illegal value.
//.GT. 0: if INFO = i, the QR algorithm failed to compute all the
// eigenvalues, and no eigenvectors have been computed;
// elements i+1:N of WR and WI contain eigenvalues which
// have converged.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("The QR algorithm failed to compute all the eigenvalues.");
}
#endregion
for (int i = 0; i < EigenVals.RowCount; i++)
{
EigenVals[i, 0] = new Complex(REigVal[i], IEigVal[i]);
}
for (int i = 0; i < EigenVals.RowCount; i++)
{
if (EigenVals[i, 0].Imaginary == 0.0)
{
for (int j = 0; j < EigenVectors.RowCount; j++)
{
EigenVectors[j, i] = new Complex(RealEVectors[j, i], 0.0);
}
}
else
{
if (EigenVals[i, 0].Imaginary > 0.0)
{
for (int j = 0; j < EigenVectors.RowCount; j++)
{
EigenVectors[j, i] = new Complex(RealEVectors[j, i], RealEVectors[j, i + 1]);
}
}
else
{
for (int j = 0; j < EigenVectors.RowCount; j++)
{
EigenVectors[j, i] = new Complex(RealEVectors[j, i - 1], -RealEVectors[j, i]);
}
}
}
}
return EigenVals;
}
#endregion
#region SymmetricMatrix
/// <summary>
/// Computes all eigenvalues of a real symmetric matrix A.
/// </summary>
/// <param name="A">The real symmetric matrix A.</param>
/// <returns>The eigenvalues.</returns>
public Matrix GetEigenvalues(SymmetricMatrix A)
{
if (this._dsyev == null) this._dsyev = new DSYEV();
this.CheckDimensions(A);
Matrix EigenVects = new Matrix(A.RowCount, A.ColumnCount, A.Data);
double[] EigenVectsData = EigenVects.Data;
Matrix EigenVals = new Matrix(A.RowCount, 1);
double[] EigenValsData = EigenVals.Data;
int Info = 0;
double[] Work = new double[1];
int LWork = -1;
//Calculamos LWORK ideal
_dsyev.Run("N", "U", A.RowCount, ref EigenVectsData, 0, A.RowCount, ref EigenValsData, 0, ref Work, 0, LWork, ref Info);
LWork = Convert.ToInt32(Work[0]);
if (LWork > 0)
{
Work = new double[LWork];
_dsyev.Run("N", "U", A.RowCount, ref EigenVectsData, 0, A.RowCount, ref EigenValsData, 0, ref Work, 0, LWork, ref Info);
}
else
{
//Error
}
#region Error
/// = 0: successful exit
/// .LT. 0: if INFO = -i, the i-th argument had an illegal value
/// .GT. 0: if INFO = i, the algorithm failed to converge; i
/// off-diagonal elements of an intermediate tridiagonal
/// form did not converge to zero.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("The algorithm failed to converge.");
}
#endregion
return EigenVals;
}
/// <summary>
/// Computes all eigenvalues and eigenvectors of a of a real symmetric matrix A.
/// </summary>
/// <param name="A">The real symmetric matrix A.</param>
/// <param name="EigenVects">The eigenvectors.</param>
/// <returns>The eigenvalues.</returns>
public Matrix GetEigenvalues(SymmetricMatrix A, out Matrix EigenVects)
{
if (this._dsyev == null) this._dsyev = new DSYEV();
this.CheckDimensions(A);
EigenVects = new Matrix(A.RowCount, A.ColumnCount, A.Data);
double[] EigenVectsData = EigenVects.Data;
Matrix EigenVals = new Matrix(A.RowCount, 1);
double[] EigenValsData = EigenVals.Data;
int Info = 0;
double[] Work = new double[1];
int LWork = -1;
//Calculamos LWORK ideal
_dsyev.Run("V", "U", A.RowCount, ref EigenVectsData, 0, A.RowCount, ref EigenValsData, 0, ref Work, 0, LWork, ref Info);
LWork = Convert.ToInt32(Work[0]);
if (LWork > 0)
{
Work = new double[LWork];
_dsyev.Run("V", "U", A.RowCount, ref EigenVectsData, 0, A.RowCount, ref EigenValsData, 0, ref Work, 0, LWork, ref Info);
}
else
{
//Error
}
#region Error
/// = 0: successful exit
/// .LT. 0: if INFO = -i, the i-th argument had an illegal value
/// .GT. 0: if INFO = i, the algorithm failed to converge; i
/// off-diagonal elements of an intermediate tridiagonal
/// form did not converge to zero.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("The algorithm failed to converge.");
}
#endregion
return EigenVals;
}
#endregion
#region SymmetricBandMatrix
/// <summary>
///Computes all the eigenvalues of
/// a real symmetric band matrix A.
/// </summary>
/// <param name="A">The real symmetric band matrix A.</param>
/// <returns>The eigenvalues.</returns>
public Matrix GetEigenvalues(SymmetricBandMatrix A)
{
if (this._dsbev == null) this._dsbev = new DSBEV();
this.CheckDimensions(A);
Matrix SymmetricBand = A.GetSymmetricBandPackedMatrix();
double[] SymmetricBandData = SymmetricBand.Data;
Matrix EigenVects = new Matrix(1, 1); //Se pone (1,1) pues nos e usaran
double[] EigenVectsData = EigenVects.Data;
Matrix EigenVals = new Matrix(A.RowCount, 1);
double[] EigenValsData = EigenVals.Data;
int Info = 0;
double[] Work = new double[3 * A.RowCount - 2];
_dsbev.Run("N", "U", A.RowCount, A.UpperBandWidth, ref SymmetricBandData, 0, SymmetricBand.RowCount, ref EigenValsData, 0, ref EigenVectsData, 0, A.RowCount, ref Work, 0, ref Info);
#region Error
/// = 0: successful exit
/// .LT. 0: if INFO = -i, the i-th argument had an illegal value
/// .GT. 0: if INFO = i, the algorithm failed to converge; i
/// off-diagonal elements of an intermediate tridiagonal
/// form did not converge to zero.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("The algorithm failed to converge.");
}
#endregion
return EigenVals;
}
/// <summary>
///Computes all the eigenvalues and eigenvectors of
/// a real symmetric band matrix A.
/// </summary>
/// <param name="A">The real symmetric band matrix A.</param>
/// <param name="EigenVects">The eigenvectors.</param>
/// <returns>The eigenvalues.</returns>
public Matrix GetEigenvalues(SymmetricBandMatrix A, out Matrix EigenVects)
{
if (this._dsbev == null) this._dsbev = new DSBEV();
this.CheckDimensions(A);
Matrix SymmetricBand = A.GetSymmetricBandPackedMatrix();
double[] SymmetricBandData = SymmetricBand.Data;
EigenVects = new Matrix(A.RowCount, A.ColumnCount);
double[] EigenVectsData = EigenVects.Data;
Matrix EigenVals = new Matrix(A.RowCount, 1);
double[] EigenValsData = EigenVals.Data;
int Info = 0;
double[] Work = new double[3 * A.RowCount - 2];
_dsbev.Run("V", "U", A.RowCount, A.UpperBandWidth, ref SymmetricBandData, 0, SymmetricBand.RowCount, ref EigenValsData, 0, ref EigenVectsData, 0, A.RowCount, ref Work, 0, ref Info);
#region Error
/// = 0: successful exit
/// .LT. 0: if INFO = -i, the i-th argument had an illegal value
/// .GT. 0: if INFO = i, the algorithm failed to converge; i
/// off-diagonal elements of an intermediate tridiagonal
/// form did not converge to zero.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("The algorithm failed to converge.");
}
#endregion
return EigenVals;
}
#endregion
#region Complex General matrix
/// <summary>
/// Computes the eigenvalues for an complex general matrix A.
/// </summary>
/// <param name="A">The complex general matrix A.</param>
/// <returns>The eigenvalues.</returns>
public ComplexMatrix GetEigenvalues(ComplexMatrix A)
{
//Fortran Ejemplo
//CG(NM,N,AR,AI,WR,WI,1,ZR,ZI,SCALE,ORTR,ORTI,ERROR)
//C
//C THIS DRIVER TESTS EISPACK FOR THE CLASS OF COMPLEX GENERAL
//C MATRICES SUMMARIZING THE FIGURES OF MERIT FOR ALL PATHS.
//C
//C THIS DRIVER IS CATALOGUED AS EISPDRV4(CGSUMARY).
//C
//C THE DIMENSION OF AR,AI,ZR,ZI,ASAVER,ASAVEI,RM1, AND RM2 SHOULD
//C BE NM BY NM.
//C THE DIMENSION OF WR,WI,WR1,WI1,SELECT,SLHOLD,INT,SCALE,ORTR,ORTI,
//C RV1 AND RV2 SHOULD BE NM.
//C THE DIMENSION OF ARHOLD AND AIHOLD SHOULD BE NM BY NM.
//C HERE NM = 20.
if (this._cg == null) this._cg = new CG();
this.CheckDimensions(A);
Matrix AReal = A.GetReal();
double[] ARealData = AReal.Data;
Matrix AImag = A.GetImag();
double[] AImagData = AImag.Data;
ComplexMatrix EigenVals = new ComplexMatrix(A.RowCount, 1);
Matrix RealEigenVals = new Matrix(A.RowCount, 1);
double[] RealEigenValsData = RealEigenVals.Data;
Matrix ImagEigenVals = new Matrix(A.RowCount, 1);
double[] ImagEigenValsData = ImagEigenVals.Data;
ComplexMatrix EigenVectors = new ComplexMatrix(1, 1);
Matrix RealEigVect = new Matrix(A.RowCount);
double[] RealEigVectData = RealEigVect.Data;
Matrix ImagEigVect = new Matrix(A.RowCount);
double[] ImagEigVectData = ImagEigVect.Data;
double[] SCALE = new double[A.RowCount];
double[] ORTR = new double[A.RowCount];
double[] ORTI = new double[A.RowCount];
int Info = 0;
int matz = 0; //No se calculan los eigenvectores
_cg.Run(A.RowCount, A.RowCount, ref ARealData, 0, ref AImagData, 0, ref RealEigenValsData, 0, ref ImagEigenValsData, 0,
matz, ref RealEigVectData, 0, ref ImagEigVectData, 0, ref SCALE, 0, ref ORTR, 0, ref ORTI, 0, ref Info);
#region Error
/// is set to
/// zero for normal return,
/// j if the limit of 30*n iterations is exhausted
/// while the j-th eigenvalue is being sought.
if (Info != 0)
{
throw new ArgumentException("The limit of 30*n iterations is exhausted");
}
#endregion
EigenVals.SetReal(RealEigenVals);
EigenVals.SetImag(ImagEigenVals);
EigenVectors.SetReal(RealEigVect);
EigenVectors.SetImag(ImagEigVect);
return EigenVals;
}
/// <summary>
/// Computes the eigenvalues and eigenvectors for an complex general matrix A.
/// </summary>
/// <param name="A">The complex general matrix A.</param>
/// <param name="EigenVectors">The eigenvectors.</param>
/// <returns>The eigenvalues.</returns>
public ComplexMatrix GetEigenvalues(ComplexMatrix A, out ComplexMatrix EigenVectors)
{
//Fortran Ejemplo
//CG(NM,N,AR,AI,WR,WI,1,ZR,ZI,SCALE,ORTR,ORTI,ERROR)
//C
//C THIS DRIVER TESTS EISPACK FOR THE CLASS OF COMPLEX GENERAL
//C MATRICES SUMMARIZING THE FIGURES OF MERIT FOR ALL PATHS.
//C
//C THIS DRIVER IS CATALOGUED AS EISPDRV4(CGSUMARY).
//C
//C THE DIMENSION OF AR,AI,ZR,ZI,ASAVER,ASAVEI,RM1, AND RM2 SHOULD
//C BE NM BY NM.
//C THE DIMENSION OF WR,WI,WR1,WI1,SELECT,SLHOLD,INT,SCALE,ORTR,ORTI,
//C RV1 AND RV2 SHOULD BE NM.
//C THE DIMENSION OF ARHOLD AND AIHOLD SHOULD BE NM BY NM.
//C HERE NM = 20.
if (this._cg == null) this._cg = new CG();
this.CheckDimensions(A);
Matrix AReal = A.GetReal();
double[] ARealData = AReal.Data;
Matrix AImag = A.GetImag();
double[] AImagData = AImag.Data;
ComplexMatrix EigenVals = new ComplexMatrix(A.RowCount, 1);
Matrix RealEigenVals = new Matrix(A.RowCount, 1);
double[] RealEigenValsData = RealEigenVals.Data;
Matrix ImagEigenVals = new Matrix(A.RowCount, 1);
double[] ImagEigenValsData = ImagEigenVals.Data;
EigenVectors = new ComplexMatrix(A.RowCount, A.ColumnCount);
Matrix RealEigVect = new Matrix(A.RowCount);
double[] RealEigVectData = RealEigVect.Data;
Matrix ImagEigVect = new Matrix(A.RowCount);
double[] ImagEigVectData = ImagEigVect.Data;
double[] SCALE = new double[A.RowCount];
double[] ORTR = new double[A.RowCount];
double[] ORTI = new double[A.RowCount];
int Info = 0;
int matz = 1; //Se calculan los eigenvalores y los eigenvectores
_cg.Run(A.RowCount, A.RowCount, ref ARealData, 0, ref AImagData, 0, ref RealEigenValsData, 0, ref ImagEigenValsData, 0,
matz, ref RealEigVectData, 0, ref ImagEigVectData, 0, ref SCALE, 0, ref ORTR, 0, ref ORTI, 0, ref Info);
#region Error
/// is set to
/// zero for normal return,
/// j if the limit of 30*n iterations is exhausted
/// while the j-th eigenvalue is being sought.
if (Info != 0)
{
throw new ArgumentException("The limit of 30*n iterations is exhausted");
}
#endregion
EigenVals.SetReal(RealEigenVals);
EigenVals.SetImag(ImagEigenVals);
EigenVectors.SetReal(RealEigVect);
EigenVectors.SetImag(ImagEigVect);
return EigenVals;
}
#endregion
#region Private methods
private void CheckDimensions(BaseMatrix matrixA)
{
if (matrixA.IsSquare != true)
{
throw new System.ArgumentException("Matrix A is not a square matrix.");
}
}
private void CheckDimensions(ComplexMatrix matrixA)
{
if (matrixA.IsSquare != true)
{
throw new System.ArgumentException("Matrix A is not a square matrix.");
}
}
#endregion
}
}