The class ISymEigen is an interface class for the method computing the eigenvalue Decomposition of a symmetric ArrayXX. More...

#include <STK_ISymEigen.h>

Inheritance diagram for STK::ISymEigen< Derived >:

Public Member Functions
	~ISymEigen ()
	virtual destructor

ISymEigen &	operator= (ISymEigen const &eigen)
	Operator = : overwrite the ISymEigen with eigen.

Range const &	range () const

Type const &	norm () const

int const &	rank () const

Type const &	det () const

Type const &	trace () const

CArraySquare< Type, size_ > const &	rotation () const

CArraySquare< Type, size_ > const &	eigenVectors () const

CArrayVector< Type, size_ > const &	eigenValues () const

template<class OtherDerived >
void	setData (ExprBase< OtherDerived > const &data)
	overloading of setData.

template<class ArraySquare >
ArraySquare &	ginv (ArraySquare &res) const
	Compute the generalized inverse of the symmetric matrix and put the result in res.

template<class ArraySquare >
ArraySquare &	ginvsqrt (ArraySquare &res) const
	Compute the generalized square root inverse of the symmetric matrix and put the result in res.

template<class ArraySquare >
ArraySquare &	gsqrt (ArraySquare &res) const
	Compute the square root of the symmetric matrix and put the result in res.

virtual bool	run ()
	Find the eigenvalues and eigenvectors of the matrix.

Public Member Functions inherited from STK::IRunnerBase
String const &	error () const
	get the last error message.

Public Member Functions inherited from STK::IRecursiveTemplate< Derived >
Derived &	asDerived ()
	static cast : return a reference of this with a cast to the derived class.

Derived const &	asDerived () const
	static cast : return a const reference of this with a cast to the derived class.

Derived *	asPtrDerived ()
	static cast : return a ptr on a `Derived` of this with a cast to the derived class.

Derived const *	asPtrDerived () const
	static cast : return a ptr on a constant `Derived` of this with a cast to the derived class.

Derived *	clone () const
	create a leaf using the copy constructor of the Derived class.

Derived *	clone (bool isRef) const
	create a leaf using the copy constructor of the Derived class and a flag determining if the clone is a reference or not.

Protected Types
enum	{ structure_ = hidden::Traits< SquareArray >::structure_ , orient_ = hidden::Traits< SquareArray >::orient_ , sizeRows_ = hidden::Traits< SquareArray >::sizeRows_ , sizeCols_ = hidden::Traits< SquareArray >::sizeCols_ , size_ = (sizeRows_<sizeCols_) ? sizeRows_ : sizeCols_ }

typedef IRunnerBase	Base

typedef hidden::AlgebraTraits< Derived >::SquareArray	SquareArray

typedef hidden::Traits< SquareArray >::Type	Type

Protected Member Functions
	ISymEigen ()
	Default constructor.

	ISymEigen (SquareArray const &data, bool ref=false)
	Constructor The original data set can be overwritten by the eigenvectors if it is stored in a CSquareXd.

template<class OtherDerived >
	ISymEigen (ExprBase< OtherDerived > const &data)
	template constructor

	ISymEigen (ISymEigen const &eigen)
	Copy constructor.

void	finalizeStep ()
	finalize the computation by computing the trace, rank, trace norm and determinant of the matrix.

Protected Member Functions inherited from STK::IRunnerBase
	IRunnerBase ()
	default constructor

	IRunnerBase (IRunnerBase const &runner)
	copy constructor

virtual	~IRunnerBase ()
	destructor

virtual void	update ()
	update the runner.

Protected Member Functions inherited from STK::IRecursiveTemplate< Derived >
	IRecursiveTemplate ()
	constructor.

	~IRecursiveTemplate ()
	destructor.

Protected Attributes
Range	range_
	range of the original data set.

Type	trace_
	trace norm

Type	norm_
	trace norm

int	rank_
	rank

Type	det_
	determinant

CArraySquare< Type, size_ >	eigenVectors_
	Square matrix or the eigenvectors.

CArrayVector< Type, size_ >	eigenValues_
	Array of the eigenvalues.

CVectorXi	SupportEigenVectors_
	Array for the support of the eigenvectors.

Protected Attributes inherited from STK::IRunnerBase
String	msg_error_
	String with the last error message.

bool	hasRun_
	`true` if run has been used, `false` otherwise

Detailed Description

template<class Derived>
class STK::ISymEigen< Derived >

The class ISymEigen is an interface class for the method computing the eigenvalue Decomposition of a symmetric ArrayXX.

The decomposition of a symmetric matrix require

Input: A symmetric matrix A of size (n,n)
Output:
1. P Array of size (n,n).
2. D Vector of dimension n
3. The matrix A can be copied or overwritten by the class.

The 2-norm (operator norm) of the matrix is given. if the 2-norm is less than the arithmetic precision of the type Real, the rank is not full. Thus the user can be faced with a deficient rank matrix and with a norm very small (i.e. not exactly 0.0).

Definition at line 64 of file STK_ISymEigen.h.

Member Typedef Documentation

◆ Base

template<class Derived >

typedef IRunnerBase STK::ISymEigen< Derived >::Base

protected

Definition at line 67 of file STK_ISymEigen.h.

◆ SquareArray

template<class Derived >

typedef hidden::AlgebraTraits<Derived>::SquareArray STK::ISymEigen< Derived >::SquareArray

protected

Definition at line 68 of file STK_ISymEigen.h.

◆ Type

template<class Derived >

typedef hidden::Traits<SquareArray>::Type STK::ISymEigen< Derived >::Type

protected

Definition at line 70 of file STK_ISymEigen.h.

Member Enumeration Documentation

◆ anonymous enum

template<class Derived >

anonymous enum

protected

Enumerator
structure_
orient_
sizeRows_
sizeCols_
size_

Definition at line 71 of file STK_ISymEigen.h.

    {
      structure_ = hidden::Traits< SquareArray >::structure_,
      orient_    = hidden::Traits< SquareArray >::orient_,
      sizeRows_  = hidden::Traits< SquareArray >::sizeRows_,
      sizeCols_  = hidden::Traits< SquareArray >::sizeCols_,
      size_ = (sizeRows_<sizeCols_) ? sizeRows_ : sizeCols_
 
    };

Constructor & Destructor Documentation

◆ ISymEigen() [1/4]

template<class Derived >

STK::ISymEigen< Derived >::ISymEigen ( )

protected

Default constructor.

Definition at line 220 of file STK_ISymEigen.h.

                             : Base()
                             , range_(), trace_(Type(0)), norm_(Type(0)), rank_(Type(0)), det_(Type(0))
                             , eigenVectors_()
                             , eigenValues_()
                             , SupportEigenVectors_()
{
  STK_STATIC_ASSERT(   SquareArray::structure_==(int)Arrays::square_
                    || SquareArray::structure_==(int)Arrays::symmetric_
                    || SquareArray::structure_==(int)Arrays::upper_symmetric_
                    || SquareArray::structure_==(int)Arrays::lower_symmetric_
                   ,YOU_HAVE_TO_USE_A_SQUARE_MATRIX_IN_THIS_METHOD)
}

References STK::Arrays::lower_symmetric_, STK::Arrays::square_, STK_STATIC_ASSERT, STK::Arrays::symmetric_, and STK::Arrays::upper_symmetric_.

◆ ISymEigen() [2/4]

template<class Derived >

STK::ISymEigen< Derived >::ISymEigen	(	SquareArray const &	data,
		bool	ref = `false`
	)

protected

Constructor The original data set can be overwritten by the eigenvectors if it is stored in a CSquareXd.

Observe that in this case the base index have to be 0.

Parameters

data	reference on a symmetric square matrix
ref	`true` if we overwrite the data set, `false` otherwise

Definition at line 241 of file STK_ISymEigen.h.

                             : Base()
                             , range_(data.range()), trace_(Type(0)), norm_(Type(0)), rank_(Type(0)), det_(Type(0))
                             , eigenVectors_(data, ref)
                             , eigenValues_(data.size(), 0.)
                             , SupportEigenVectors_(2*data.size(), 0)
{
    STK_STATIC_ASSERT(   SquareArray::structure_==(int)Arrays::square_
                      || SquareArray::structure_==(int)Arrays::symmetric_
                      || SquareArray::structure_==(int)Arrays::upper_symmetric_
                      || SquareArray::structure_==(int)Arrays::lower_symmetric_
                     ,YOU_HAVE_TO_USE_A_SQUARE_MATRIX_IN_THIS_METHOD)
}

References STK::Arrays::lower_symmetric_, STK::Arrays::square_, STK_STATIC_ASSERT, STK::Arrays::symmetric_, and STK::Arrays::upper_symmetric_.

◆ ISymEigen() [3/4]

template<class Derived >

template<class OtherDerived >

STK::ISymEigen< Derived >::ISymEigen ( ExprBase< OtherDerived > const & data )

protected

template constructor

Parameters

data	reference on a symmetric square expression

Definition at line 259 of file STK_ISymEigen.h.

                             : Base()
                             , range_(data.range()), trace_(Type(0)), norm_(0.), rank_(0), det_(0.)
                             , eigenVectors_(data.asDerived())
                             , eigenValues_(data.size(), 0.)
                             , SupportEigenVectors_(2*data.size(), 0)
{
    STK_STATIC_ASSERT(   SquareArray::structure_==(int)Arrays::square_
                      || SquareArray::structure_==(int)Arrays::symmetric_
                      || SquareArray::structure_==(int)Arrays::upper_symmetric_
                      || SquareArray::structure_==(int)Arrays::lower_symmetric_
                     ,YOU_HAVE_TO_USE_A_SQUARE_MATRIX_IN_THIS_METHOD)
}

References STK::Arrays::lower_symmetric_, STK::Arrays::square_, STK_STATIC_ASSERT, STK::Arrays::symmetric_, and STK::Arrays::upper_symmetric_.

◆ ISymEigen() [4/4]

template<class Derived >

STK::ISymEigen< Derived >::ISymEigen ( ISymEigen< Derived > const & eigen )

protected

Copy constructor.

Parameters

eigen the EigenValue to copy

Definition at line 276 of file STK_ISymEigen.h.

                             : Base(eigen)
                             , range_(eigen.range_), trace_(eigen.trace_), norm_(eigen.norm_), rank_(eigen.rank_), det_(eigen.det_)
                             , eigenVectors_(eigen.eigenVectors_)
                             , eigenValues_(eigen.eigenValues_)
                             , SupportEigenVectors_(eigen.SupportEigenVectors_)
{
    STK_STATIC_ASSERT(   SquareArray::structure_==(int)Arrays::square_
                      || SquareArray::structure_==(int)Arrays::symmetric_
                      || SquareArray::structure_==(int)Arrays::upper_symmetric_
                      || SquareArray::structure_==(int)Arrays::lower_symmetric_
                     ,YOU_HAVE_TO_USE_A_SQUARE_MATRIX_IN_THIS_METHOD)
}

References STK::Arrays::lower_symmetric_, STK::Arrays::square_, STK_STATIC_ASSERT, STK::Arrays::symmetric_, and STK::Arrays::upper_symmetric_.

◆ ~ISymEigen()

template<class Derived >

STK::ISymEigen< Derived >::~ISymEigen ( )

inline

virtual destructor

Definition at line 102 of file STK_ISymEigen.h.

102{}

Member Function Documentation

◆ det()

template<class Derived >

Type const & STK::ISymEigen< Derived >::det ( ) const

inline

Returns: the determinant of the Array

Definition at line 127 of file STK_ISymEigen.h.

127{ return det_;}

References STK::ISymEigen< Derived >::det_.

Referenced by STK::hidden::InvertLowerSymMatrixImpl< Matrix, Size_ >::invertLowerSymMatrixXX(), STK::hidden::InvertSymImpl< Matrix, Size_ >::invertSymMatrixXX(), and STK::hidden::InvertUpperSymMatrixImpl< Matrix, Size_ >::invertUpperSymMatrixXX().

◆ eigenValues()

template<class Derived >

CArrayVector< Type, size_ > const & STK::ISymEigen< Derived >::eigenValues ( ) const

inline

Returns: the eigenvalues

Definition at line 135 of file STK_ISymEigen.h.

135{ return eigenValues_;}

References STK::ISymEigen< Derived >::eigenValues_.

Referenced by main().

◆ eigenVectors()

template<class Derived >

CArraySquare< Type, size_ > const & STK::ISymEigen< Derived >::eigenVectors ( ) const

inline

Returns: the rotation matrix

Definition at line 133 of file STK_ISymEigen.h.

133{ return eigenVectors_;}

References STK::ISymEigen< Derived >::eigenVectors_.

Referenced by main().

◆ finalizeStep()

template<class Derived >

void STK::ISymEigen< Derived >::finalizeStep ( )

protected

finalize the computation by computing the trace, rank, trace norm and determinant of the matrix.

Definition at line 294 of file STK_ISymEigen.h.

{
  // compute sign and trace
  trace_ = 0.;
  int s = 1;
  for (int i=eigenValues_.begin(); i< eigenValues_.end(); ++i )
  {
    Type value = eigenValues_[i];
    s *= sign(value);
    trace_ += value;
  }
 
  // compute norm_ (2-norm) and determinant
  norm_ = eigenValues_.maxElt();
  det_  = 0;
  if (eigenValues_.abs().minElt() > 0)
  { det_ = s * std::exp(eigenValues_.abs().log().sum());}
 
  // compute norm_ rank_
  rank_ = eigenValues_.size(); // full rank
  Type tol = norm_ * Arithmetic<Type>::epsilon();
  for (int i=eigenValues_.begin(); i< eigenValues_.end(); ++i )
  { if (std::abs(eigenValues_[i]) < tol) { rank_--;}}
}

References STK::sign().

◆ ginv()

template<class Derived >

template<class ArraySquare >

ArraySquare & STK::ISymEigen< Derived >::ginv ( ArraySquare & res ) const

inline

Compute the generalized inverse of the symmetric matrix and put the result in res.

Parameters

res	array with the result

Returns: the result

Definition at line 156 of file STK_ISymEigen.h.

    {
      Type tol = Arithmetic<Type>::epsilon() * norm_;
      if(tol==0) { tol = Arithmetic<Type>::min();}
      // compute and return PD^{-1}P'
      return (res = eigenVectors_ * eigenValues_.diagonalize().safeInverse(tol) * eigenVectors_.transpose());
    }

References STK::ArrayBase< Derived >::diagonalize(), STK::ISymEigen< Derived >::eigenValues_, STK::ISymEigen< Derived >::eigenVectors_, STK::ISymEigen< Derived >::norm_, and STK::ArrayBase< Derived >::transpose().

Referenced by STK::hidden::InvertLowerSymMatrixImpl< Matrix, Size_ >::invertLowerSymMatrixXX(), STK::hidden::InvertSymImpl< Matrix, Size_ >::invertSymMatrixXX(), and STK::hidden::InvertUpperSymMatrixImpl< Matrix, Size_ >::invertUpperSymMatrixXX().

◆ ginvsqrt()

template<class Derived >

template<class ArraySquare >

ArraySquare & STK::ISymEigen< Derived >::ginvsqrt ( ArraySquare & res ) const

inline

Compute the generalized square root inverse of the symmetric matrix and put the result in res.

Parameters

res	array with the result

Returns: the result

Definition at line 169 of file STK_ISymEigen.h.

    {
      Type tol = Arithmetic<Type>::epsilon() * norm_;
      if(tol==0) { tol = Arithmetic<Type>::min();}
      // compute and return PD^{-1/2}P'
      return(res = eigenVectors_ * eigenValues_.diagonalize().sqrt().safeInverse(tol) * eigenVectors_.transpose());
    }

References STK::ArrayBase< Derived >::diagonalize(), STK::ISymEigen< Derived >::eigenValues_, STK::ISymEigen< Derived >::eigenVectors_, STK::ISymEigen< Derived >::norm_, and STK::ArrayBase< Derived >::transpose().

◆ gsqrt()

template<class Derived >

template<class ArraySquare >

ArraySquare & STK::ISymEigen< Derived >::gsqrt ( ArraySquare & res ) const

inline

Compute the square root of the symmetric matrix and put the result in res.

Parameters

res	array with the result

Returns: the result

Definition at line 181 of file STK_ISymEigen.h.

    {
      Type tol = Arithmetic<Type>::epsilon() * norm_;
      if(tol==0) { tol = Arithmetic<Type>::min();}
      // compute and return PD^{1/2}P'
      return(res = eigenVectors_ * eigenValues_.diagonalize().sqrt() * eigenVectors_.transpose());
    }

References STK::ArrayBase< Derived >::diagonalize(), STK::ISymEigen< Derived >::eigenValues_, STK::ISymEigen< Derived >::eigenVectors_, STK::ISymEigen< Derived >::norm_, and STK::ArrayBase< Derived >::transpose().

◆ norm()

template<class Derived >

Type const & STK::ISymEigen< Derived >::norm ( ) const

inline

Returns: the trace norm of the matrix

Definition at line 123 of file STK_ISymEigen.h.

123{ return norm_;}

References STK::ISymEigen< Derived >::norm_.

◆ operator=()

template<class Derived >

ISymEigen & STK::ISymEigen< Derived >::operator= ( ISymEigen< Derived > const & eigen )

inline

Operator = : overwrite the ISymEigen with eigen.

Parameters

eigen ISymEigen to copy

Returns: a reference on this

Definition at line 107 of file STK_ISymEigen.h.

    {
      range_ = eigen.range_;
      trace_ = eigen.trace_;    // trace of the matrix
      norm_  = eigen.norm_;     // norm of the matrix
      rank_  = eigen.rank_;     // rank of the matrix
      det_   = eigen.det_;      // determinant of the matrix
      eigenVectors_        = eigen.eigenVectors_;
      eigenValues_         = eigen.eigenValues_;
      SupportEigenVectors_ = eigen.SupportEigenVectors_;
      return *this;
    }

References STK::ISymEigen< Derived >::det_, STK::ISymEigen< Derived >::eigenValues_, STK::ISymEigen< Derived >::eigenVectors_, STK::ISymEigen< Derived >::norm_, STK::ISymEigen< Derived >::range_, STK::ISymEigen< Derived >::rank_, STK::ISymEigen< Derived >::SupportEigenVectors_, and STK::ISymEigen< Derived >::trace_.

◆ range()

template<class Derived >

Range const & STK::ISymEigen< Derived >::range ( ) const

inline

Returns: the range of the matrix

Definition at line 121 of file STK_ISymEigen.h.

121{ return range_;}

References STK::ISymEigen< Derived >::range_.

◆ rank()

template<class Derived >

int const & STK::ISymEigen< Derived >::rank ( ) const

inline

Returns: the rank of the matrix

Definition at line 125 of file STK_ISymEigen.h.

125{ return rank_;}

References STK::ISymEigen< Derived >::rank_.

◆ rotation()

template<class Derived >

CArraySquare< Type, size_ > const & STK::ISymEigen< Derived >::rotation ( ) const

inline

Returns: the rotation matrix

Definition at line 131 of file STK_ISymEigen.h.

131{ return eigenVectors_;}

References STK::ISymEigen< Derived >::eigenVectors_.

◆ run()

template<class Derived >

virtual bool STK::ISymEigen< Derived >::run ( )

inlinevirtual

Find the eigenvalues and eigenvectors of the matrix.

Implements STK::IRunnerBase.

Definition at line 189 of file STK_ISymEigen.h.

    {
      if (eigenVectors_.empty()) { return true;}
      return this->asDerived().runImpl();
    }

References STK::IRecursiveTemplate< Derived >::asDerived(), STK::ISymEigen< Derived >::eigenVectors_, and STK::ICArray< Derived >::empty().

Referenced by STK::hidden::InvertLowerSymMatrixImpl< Matrix, Size_ >::invertLowerSymMatrixXX(), STK::hidden::InvertSymImpl< Matrix, Size_ >::invertSymMatrixXX(), STK::hidden::InvertUpperSymMatrixImpl< Matrix, Size_ >::invertUpperSymMatrixXX(), and main().

◆ setData()

template<class Derived >

template<class OtherDerived >

void STK::ISymEigen< Derived >::setData ( ExprBase< OtherDerived > const & data )

inline

overloading of setData.

Parameters

data	the data set to set.

Definition at line 141 of file STK_ISymEigen.h.

    {
      STK_STATIC_ASSERT(OtherDerived::structure_==(int)Arrays::square_,YOU_HAVE_TO_USE_A_SQUARE_MATRIX_IN_THIS_METHOD)
      range_ = data.range(); trace_ = 0; norm_ = 0.; rank_ = 0; det_ = 0.;
      eigenVectors_ = data;
      eigenValues_.resize(range_) = 0;
      SupportEigenVectors_.resize(2*data.size());
      this->hasRun_ = false;
    }

References STK::ISymEigen< Derived >::det_, STK::ISymEigen< Derived >::eigenValues_, STK::ISymEigen< Derived >::eigenVectors_, STK::IRunnerBase::hasRun_, STK::ISymEigen< Derived >::norm_, STK::ISymEigen< Derived >::range_, STK::ISymEigen< Derived >::rank_, STK::ICArray< Derived >::resize(), STK::Arrays::square_, STK_STATIC_ASSERT, STK::ISymEigen< Derived >::SupportEigenVectors_, and STK::ISymEigen< Derived >::trace_.

◆ trace()

template<class Derived >

Type const & STK::ISymEigen< Derived >::trace ( ) const

inline

Returns: the trace of the Array

Definition at line 129 of file STK_ISymEigen.h.

129{ return trace_;}

References STK::ISymEigen< Derived >::trace_.

Member Data Documentation

◆ det_

template<class Derived >

Type STK::ISymEigen< Derived >::det_

protected

determinant

Definition at line 205 of file STK_ISymEigen.h.

Referenced by STK::ISymEigen< Derived >::det(), STK::ISymEigen< Derived >::operator=(), and STK::ISymEigen< Derived >::setData().

◆ eigenValues_

template<class Derived >

CArrayVector<Type, size_> STK::ISymEigen< Derived >::eigenValues_

protected

Array of the eigenvalues.

Definition at line 209 of file STK_ISymEigen.h.

Referenced by STK::ISymEigen< Derived >::eigenValues(), STK::ISymEigen< Derived >::ginv(), STK::ISymEigen< Derived >::ginvsqrt(), STK::ISymEigen< Derived >::gsqrt(), STK::ISymEigen< Derived >::operator=(), and STK::ISymEigen< Derived >::setData().

◆ eigenVectors_

template<class Derived >

CArraySquare<Type, size_> STK::ISymEigen< Derived >::eigenVectors_

protected

Square matrix or the eigenvectors.

Definition at line 207 of file STK_ISymEigen.h.

Referenced by STK::ISymEigen< Derived >::eigenVectors(), STK::ISymEigen< Derived >::ginv(), STK::ISymEigen< Derived >::ginvsqrt(), STK::ISymEigen< Derived >::gsqrt(), STK::ISymEigen< Derived >::operator=(), STK::ISymEigen< Derived >::rotation(), STK::ISymEigen< Derived >::run(), and STK::ISymEigen< Derived >::setData().

◆ norm_

template<class Derived >

Type STK::ISymEigen< Derived >::norm_

protected

trace norm

Definition at line 201 of file STK_ISymEigen.h.

Referenced by STK::ISymEigen< Derived >::ginv(), STK::ISymEigen< Derived >::ginvsqrt(), STK::ISymEigen< Derived >::gsqrt(), STK::ISymEigen< Derived >::norm(), STK::ISymEigen< Derived >::operator=(), and STK::ISymEigen< Derived >::setData().

◆ range_

template<class Derived >

Range STK::ISymEigen< Derived >::range_

protected

range of the original data set.

Definition at line 197 of file STK_ISymEigen.h.

Referenced by STK::ISymEigen< Derived >::operator=(), STK::ISymEigen< Derived >::range(), and STK::ISymEigen< Derived >::setData().

◆ rank_

template<class Derived >

int STK::ISymEigen< Derived >::rank_

protected

rank

Definition at line 203 of file STK_ISymEigen.h.

Referenced by STK::ISymEigen< Derived >::operator=(), STK::ISymEigen< Derived >::rank(), and STK::ISymEigen< Derived >::setData().

◆ SupportEigenVectors_

template<class Derived >

CVectorXi STK::ISymEigen< Derived >::SupportEigenVectors_

protected

Array for the support of the eigenvectors.

Definition at line 211 of file STK_ISymEigen.h.

Referenced by STK::ISymEigen< Derived >::operator=(), and STK::ISymEigen< Derived >::setData().

◆ trace_

template<class Derived >

Type STK::ISymEigen< Derived >::trace_

protected

trace norm

Definition at line 199 of file STK_ISymEigen.h.

Referenced by STK::ISymEigen< Derived >::operator=(), STK::ISymEigen< Derived >::setData(), and STK::ISymEigen< Derived >::trace().

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

STK_ISymEigen.h

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Base

◆ SquareArray

◆ Type

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ ISymEigen() [1/4]

◆ ISymEigen() [2/4]

◆ ISymEigen() [3/4]

◆ ISymEigen() [4/4]

◆ ~ISymEigen()

Member Function Documentation

◆ det()

◆ eigenValues()

◆ eigenVectors()

◆ finalizeStep()

◆ ginv()

◆ ginvsqrt()

◆ gsqrt()

◆ norm()

◆ operator=()

◆ range()

◆ rank()

◆ rotation()

◆ run()

◆ setData()

◆ trace()

Member Data Documentation

◆ det_

◆ eigenValues_

◆ eigenVectors_

◆ norm_

◆ range_

◆ rank_

◆ SupportEigenVectors_

◆ trace_