A linear Nth-order generalised eigensystem base class. More...

#include <LinearEigenSystem_base.h>

Inheritance diagram for CppNoddy::LinearEigenSystem_base:

Public Member Functions
	LinearEigenSystem_base ()
	Constructor for a linear system object. More...

virtual	~LinearEigenSystem_base ()
	Destructor for a linear system object. More...

virtual void	eigensolve ()
	Solve the matrix linear eigensystem. More...

void	set_calc_eigenvectors (bool flag)
	Compute the eigenvectors in any eigenvalue computation. More...

void	set_shift (const D_complex &z)
	Set the shift value to be used in tagging. More...

D_complex	get_shift () const
	Get the shift value associated with this class (used for tagging) and eigenvalue tagging. More...

virtual void	tag_eigenvalues_right (const int &val)
	Tag those eigenvalues that are to the right of a specified shft point. More...

virtual void	tag_eigenvalues_left (const int &val)
	Tag those eigenvalues that are to the left of a specified point. More...

virtual void	tag_eigenvalues_upper (const int &val)
	Tag those eigenvalues that are in the upper half-plane above a specified point. More...

virtual void	tag_eigenvalues_lower (const int &val)
	Tag those eigenvalues that are in the lower half-plane below a specified point. More...

virtual void	tag_eigenvalues_disc (const int &val, const double &radius)
	Tag those eigenvalues that are within a disc centred at a point in the complex plane. More...

virtual void	tag_eigenvalues_all ()
	Tag all the eigenvalues returned from the ARPACK routine. More...

virtual void	clear_all_tags ()

virtual DenseVector< D_complex >	get_tagged_eigenvalues () const
	Get the the tagged eigenvalues. More...

virtual DenseMatrix< D_complex >	get_tagged_eigenvectors () const
	Get the the tagged eigenvectors. More...

Protected Types
typedef std::set< unsigned, std::less< unsigned > >::iterator	iter

typedef std::set< unsigned, std::less< unsigned > >::const_iterator	citer

Protected Attributes
DenseVector< D_complex >	m_all_eigenvalues
	storage for eigenvectors and eigenvalues More...

DenseMatrix< D_complex >	m_all_eigenvectors

std::set< unsigned, std::less< unsigned > >	m_tagged_indices
	a set of tagged eigenvalue indices More...

D_complex	m_shift
	The complex shift value. More...

bool	m_calc_eigenvectors
	calculate the eigenvectors in any eigenvalue computation More...

Detailed Description

A linear Nth-order generalised eigensystem base class.

Here we can construct a linear eigenproblem in the form

$A_{NxN} \,{\underline x}_i = \lambda_i\, B_{NxN}\, {\underline x}_i$

for matrices and . The eigenvalues and eigenvectors can be tagged and retrieved as required.

Definition at line 18 of file LinearEigenSystem_base.h.

Member Typedef Documentation

◆ citer

typedef std::set<unsigned,std::less<unsigned>>::const_iterator CppNoddy::LinearEigenSystem_base::citer

protected

Definition at line 25 of file LinearEigenSystem_base.h.

◆ iter

typedef std::set<unsigned,std::less<unsigned>>::iterator CppNoddy::LinearEigenSystem_base::iter

protected

Definition at line 23 of file LinearEigenSystem_base.h.

Constructor & Destructor Documentation

◆ LinearEigenSystem_base()

CppNoddy::LinearEigenSystem_base::LinearEigenSystem_base ( )

Constructor for a linear system object.

Definition at line 14 of file LinearEigenSystem_base.cpp.

                                                 :
    m_shift(D_complex(0., 0.)),
    m_calc_eigenvectors(true) {
  }

◆ ~LinearEigenSystem_base()

CppNoddy::LinearEigenSystem_base::~LinearEigenSystem_base ( )

virtual

Destructor for a linear system object.

Definition at line 20 of file LinearEigenSystem_base.cpp.

21 {}

Member Function Documentation

◆ clear_all_tags()

virtual void CppNoddy::LinearEigenSystem_base::clear_all_tags ( )

inlinevirtual

Definition at line 79 of file LinearEigenSystem_base.h.

                                  {
      m_tagged_indices.clear();
    }

References m_tagged_indices.

◆ eigensolve()

void CppNoddy::LinearEigenSystem_base::eigensolve ( )

virtual

Solve the matrix linear eigensystem.

Reimplemented in CppNoddy::DenseLinearEigenSystem< _Type >.

Definition at line 34 of file LinearEigenSystem_base.cpp.

                                          {
    std::string problem;
    problem = "The LinearEigenSystem_base::eigensolve method has been called\n";
    problem += "but the method has not been implemented ... this should be \n";
    problem += "implemented in the sub-class.";
    throw ExceptionExternal(problem);
  }

◆ get_shift()

std::complex< double > CppNoddy::LinearEigenSystem_base::get_shift ( ) const

Get the shift value associated with this class (used for tagging) and eigenvalue tagging.

Definition at line 29 of file LinearEigenSystem_base.cpp.

                                                             {
    return m_shift;
  }

References m_shift.

◆ get_tagged_eigenvalues()

DenseVector< D_complex > CppNoddy::LinearEigenSystem_base::get_tagged_eigenvalues ( ) const

virtual

Get the the tagged eigenvalues.

All of the tagged eigenvalues are returned in a complex vector, with no ordering guaranteed.

Returns: The tagged eigenvalues as a complex vector

Reimplemented in CppNoddy::DenseLinearEigenSystem< _Type >.

Definition at line 48 of file LinearEigenSystem_base.cpp.

                                                                              {
    if(m_tagged_indices.size() == 0) {
      std::string problem;
      problem = "In LinearEigenSystem_base.get_tagged_eigenvalues() : there are\n";
      problem += "no eigenvalues that have been tagged. This set is empty.\n";
      throw ExceptionRuntime(problem);
    }
    // storage for the eigenvalues
    DenseVector<D_complex> evals;
    // loop through the tagged set
    for(iter p = m_tagged_indices.begin(); p != m_tagged_indices.end(); ++p) {
      // get the index of the relevant eigenvalue from the set
      std::size_t j = *p;
      std::cout << " number " << j << " is a tagged ev.\n";
      // work out the complex eigenvalue associated with this index
      // and add it to the vector
      evals.push_back(m_all_eigenvalues[ j ]);
    }
    // return the complex vector of eigenvalues
    return evals;
  }

References m_all_eigenvalues, m_tagged_indices, p, and CppNoddy::DenseVector< _Type >::push_back().

◆ get_tagged_eigenvectors()

DenseMatrix< D_complex > CppNoddy::LinearEigenSystem_base::get_tagged_eigenvectors ( ) const

virtual

Get the the tagged eigenvectors.

All of the eigenvectors associated with the tagged eigenvalues are returned, with the i-th eigenvector corresponding to the i-th eigenvalue as returned by the get_tagged_eigenvalues method. The i-th eigenvector is returned in row i of the complex dense matrix.

Returns: The tagged eigenvectors as a complex matrix

Reimplemented in CppNoddy::DenseLinearEigenSystem< _Type >.

Definition at line 71 of file LinearEigenSystem_base.cpp.

                                                                               {
    if(m_tagged_indices.size() == 0) {
      std::string problem;
      problem = "In LinearEigenSystem_base.get_tagged_eigenvectors() : there are\n";
      problem += "no eigenvalues that have been tagged. This set is empty.\n";
      throw ExceptionRuntime(problem);
    }
    // number of degrees of freedom in each eigenvector
    std::size_t n = m_all_eigenvectors[0].size();
    // eigenvector storage : size() eigenvectors each of length n
    DenseMatrix<D_complex> evecs(m_tagged_indices.size(), n, 0.0);
    std::size_t row = 0;
    // loop through the tagged set
    for(iter p = m_tagged_indices.begin(); p != m_tagged_indices.end(); ++p) {
      // get the index of the relevant eigenvalue from the set
      std::size_t j = *p;
      // put the eigenvector in the matrix
      evecs[ row ] = m_all_eigenvectors[ j ];
      // next row/eigenvector
      ++row;
    }
    return evecs;
  }

References m_all_eigenvectors, m_tagged_indices, and p.

◆ set_calc_eigenvectors()

void CppNoddy::LinearEigenSystem_base::set_calc_eigenvectors ( bool flag )

Compute the eigenvectors in any eigenvalue computation.

Parameters

flag	The boolean value to set.

Definition at line 43 of file LinearEigenSystem_base.cpp.

                                                              {
    m_calc_eigenvectors = flag;
  }

References m_calc_eigenvectors.

Referenced by main().

◆ set_shift()

void CppNoddy::LinearEigenSystem_base::set_shift ( const D_complex & z )

Set the shift value to be used in tagging.

Parameters

z	The shift value to be used

Definition at line 24 of file LinearEigenSystem_base.cpp.

                                                           {
    m_shift = z;
  }

References m_shift.

Referenced by CppNoddy::HST::Rayleigh< _Type >::global_evp(), and main().

◆ tag_eigenvalues_all()

void CppNoddy::LinearEigenSystem_base::tag_eigenvalues_all ( )

virtual

Tag all the eigenvalues returned from the ARPACK routine.

Definition at line 98 of file LinearEigenSystem_base.cpp.

                                                   {
    for(unsigned i = 0; i < m_all_eigenvalues.size(); ++i) {
      m_tagged_indices.insert(m_tagged_indices.end(), i);
    }
    std::cout << "** I have tagged " << m_all_eigenvalues.size() << " eigenvalues.\n";
  }

References m_all_eigenvalues, m_tagged_indices, and CppNoddy::DenseVector< _Type >::size().

◆ tag_eigenvalues_disc()

void CppNoddy::LinearEigenSystem_base::tag_eigenvalues_disc	(	const int &	val,
		const double &	radius
	)

virtual

Tag those eigenvalues that are within a disc centred at a point in the complex plane.

Parameters

val	Tags are added or removed for val +ve or -ve
radius	The radius of the disc to be considered

Reimplemented in CppNoddy::DenseLinearEigenSystem< _Type >.

Definition at line 106 of file LinearEigenSystem_base.cpp.

                                                                                        {
    // loop through all the eigenvalues
    for(std::size_t i = 0; i < m_all_eigenvalues.size(); ++i) {
      // if the eigenvalue is in the disc centred at shift then include it
      if(std::abs(m_all_eigenvalues[ i ] - m_shift) < radius) {
        if(val > 0) {
          // add it to our set of tagged eigenvalues
          m_tagged_indices.insert(m_tagged_indices.end(), i);
        } else {
          // remove it from the set if it exists
          m_tagged_indices.erase(i);
        }
      }
    }
  }

References m_all_eigenvalues, m_shift, m_tagged_indices, and CppNoddy::DenseVector< _Type >::size().

◆ tag_eigenvalues_left()

void CppNoddy::LinearEigenSystem_base::tag_eigenvalues_left ( const int & val )

virtual

Tag those eigenvalues that are to the left of a specified point.

Parameters

val	Tags are added or removed for val +ve or -ve

Reimplemented in CppNoddy::DenseLinearEigenSystem< _Type >.

Definition at line 140 of file LinearEigenSystem_base.cpp.

                                                                  {
    // loop through all the eigenvalues
    for(std::size_t i = 0; i < m_all_eigenvalues.size(); ++i) {
      // if the eigenvalue is in the disc centred at m_shift then include it
      if((m_all_eigenvalues[ i ] - m_shift).real() < 0.0) {
        if(val > 0) {
          // add it to our set of tagged eigenvalues
          m_tagged_indices.insert(m_tagged_indices.end(), i);
        } else {
          // remove it from the set if it exists
          m_tagged_indices.erase(i);
        }
      }
    }
  }

References m_all_eigenvalues, m_shift, m_tagged_indices, and CppNoddy::DenseVector< _Type >::size().

◆ tag_eigenvalues_lower()

void CppNoddy::LinearEigenSystem_base::tag_eigenvalues_lower ( const int & val )

virtual

Tag those eigenvalues that are in the lower half-plane below a specified point.

Parameters

val	Tags are added or removed for val +ve or -ve

Reimplemented in CppNoddy::DenseLinearEigenSystem< _Type >.

Definition at line 173 of file LinearEigenSystem_base.cpp.

                                                                   {
    // loop through all the eigenvalues
    for(std::size_t i = 0; i < m_all_eigenvalues.size(); ++i) {
      // if the eigenvalue is in the disc centred at m_shift then include it
      if((m_all_eigenvalues[ i ] - m_shift).imag() < 0.0) {
        if(val > 0) {
          // add it to our set of tagged eigenvalues
          m_tagged_indices.insert(m_tagged_indices.end(), i);
        } else {
          // remove it from the set if it exists
          m_tagged_indices.erase(i);
        }
      }
    }
  }

References m_all_eigenvalues, m_shift, m_tagged_indices, and CppNoddy::DenseVector< _Type >::size().

◆ tag_eigenvalues_right()

void CppNoddy::LinearEigenSystem_base::tag_eigenvalues_right ( const int & val )

virtual

Tag those eigenvalues that are to the right of a specified shft point.

Parameters

val	Tags are added or removed for val +ve or -ve

Reimplemented in CppNoddy::DenseLinearEigenSystem< _Type >.

Definition at line 123 of file LinearEigenSystem_base.cpp.

                                                                   {
    // loop through all the eigenvalues
    for(std::size_t i = 0; i < m_all_eigenvalues.size(); ++i) {
      // if the eigenvalue is in the disc centred at m_shift then include it
      if((m_all_eigenvalues[ i ] - m_shift).real() > 0.0) {
        if(val > 0) {
          // add it to our set of tagged eigenvalues
          m_tagged_indices.insert(m_tagged_indices.end(), i);
        } else {
          // remove it from the set if it exists
          m_tagged_indices.erase(i);
        }
      }
    }
  }

References m_all_eigenvalues, m_shift, m_tagged_indices, and CppNoddy::DenseVector< _Type >::size().

◆ tag_eigenvalues_upper()

void CppNoddy::LinearEigenSystem_base::tag_eigenvalues_upper ( const int & val )

virtual

Tag those eigenvalues that are in the upper half-plane above a specified point.

Parameters

val	Tags are added or removed for val +ve or -ve

Reimplemented in CppNoddy::DenseLinearEigenSystem< _Type >.

Definition at line 157 of file LinearEigenSystem_base.cpp.

                                                                   {
    // loop through all the eigenvalues
    for(std::size_t i = 0; i < m_all_eigenvalues.size(); ++i) {
      // if the eigenvalue is in the disc centred at m_shift then include it
      if((m_all_eigenvalues[ i ] - m_shift).imag() > 0.0) {
        if(val > 0) {
          // add it to our set of tagged eigenvalues
          m_tagged_indices.insert(m_tagged_indices.end(), i);
        } else {
          // remove it from the set if it exists
          m_tagged_indices.erase(i);
        }
      }
    }
  }

References m_all_eigenvalues, m_shift, m_tagged_indices, and CppNoddy::DenseVector< _Type >::size().

Member Data Documentation

◆ m_all_eigenvalues

DenseVector<D_complex> CppNoddy::LinearEigenSystem_base::m_all_eigenvalues

protected

storage for eigenvectors and eigenvalues

Definition at line 98 of file LinearEigenSystem_base.h.

Referenced by get_tagged_eigenvalues(), tag_eigenvalues_all(), tag_eigenvalues_disc(), tag_eigenvalues_left(), tag_eigenvalues_lower(), tag_eigenvalues_right(), and tag_eigenvalues_upper().

◆ m_all_eigenvectors

DenseMatrix<D_complex> CppNoddy::LinearEigenSystem_base::m_all_eigenvectors

protected

Definition at line 99 of file LinearEigenSystem_base.h.

Referenced by get_tagged_eigenvectors().

◆ m_calc_eigenvectors

bool CppNoddy::LinearEigenSystem_base::m_calc_eigenvectors

protected

calculate the eigenvectors in any eigenvalue computation

Definition at line 109 of file LinearEigenSystem_base.h.

Referenced by set_calc_eigenvectors().

◆ m_shift

D_complex CppNoddy::LinearEigenSystem_base::m_shift

protected

The complex shift value.

Definition at line 106 of file LinearEigenSystem_base.h.

Referenced by get_shift(), set_shift(), tag_eigenvalues_disc(), tag_eigenvalues_left(), tag_eigenvalues_lower(), tag_eigenvalues_right(), and tag_eigenvalues_upper().

◆ m_tagged_indices

std::set< unsigned, std::less<unsigned> > CppNoddy::LinearEigenSystem_base::m_tagged_indices

protected

a set of tagged eigenvalue indices

Definition at line 103 of file LinearEigenSystem_base.h.

Referenced by clear_all_tags(), get_tagged_eigenvalues(), get_tagged_eigenvectors(), tag_eigenvalues_all(), tag_eigenvalues_disc(), tag_eigenvalues_left(), tag_eigenvalues_lower(), tag_eigenvalues_right(), and tag_eigenvalues_upper().

The documentation for this class was generated from the following files:

include/LinearEigenSystem_base.h
src/LinearEigenSystem_base.cpp

Public Member Functions

Protected Types

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ citer

◆ iter

Constructor & Destructor Documentation

◆ LinearEigenSystem_base()

◆ ~LinearEigenSystem_base()

Member Function Documentation

◆ clear_all_tags()

◆ eigensolve()

◆ get_shift()

◆ get_tagged_eigenvalues()

◆ get_tagged_eigenvectors()

◆ set_calc_eigenvectors()

◆ set_shift()

◆ tag_eigenvalues_all()

◆ tag_eigenvalues_disc()

◆ tag_eigenvalues_left()

◆ tag_eigenvalues_lower()

◆ tag_eigenvalues_right()

◆ tag_eigenvalues_upper()

Member Data Documentation

◆ m_all_eigenvalues

◆ m_all_eigenvectors

◆ m_calc_eigenvectors

◆ m_shift

◆ m_tagged_indices