FactorizedRankTwoTensorTempl< T > Class Template Reference

FactorizedRankTwoTensorTempl is designed to perform the spectral decomposition of an underlying symmetric second order tensor and reuse its bases for future operations if possible. More...

#include <FactorizedRankTwoTensor.h>

Public Types
typedef T::value_type	value_type
	For generic programming. More...

Public Member Functions
	FactorizedRankTwoTensorTempl ()=delete
	No default constructor. More...
	FactorizedRankTwoTensorTempl (const FactorizedRankTwoTensorTempl< T > &A)=default
	Copy constructor. More...
	FactorizedRankTwoTensorTempl (const T &A)
	Constructor if the factorization isn't known a priori. More...
	FactorizedRankTwoTensorTempl (const std::vector< typename T::value_type > &eigvals, const RankTwoTensorTempl< typename T::value_type > &eigvecs)
void	print (std::ostream &stm=Moose::out) const
FactorizedRankTwoTensorTempl< T >	rotated (const RankTwoTensorTempl< typename T::value_type > &R) const
FactorizedRankTwoTensorTempl< T >	transpose () const
	Returns the transpose of _A. More...
FactorizedRankTwoTensorTempl< T > &	operator*= (const typename T::value_type &a)
	performs _A *= a in place, also updates eigen values More...
template<typename T2 >
FactorizedRankTwoTensorTempl< T >	operator* (const T2 &a) const
	returns _A * a, also updates eigen values More...
FactorizedRankTwoTensorTempl< T > &	operator/= (const typename T::value_type &a)
	performs _A /= a in place, also updates eigen values More...
template<typename T2 >
FactorizedRankTwoTensorTempl< T >	operator/ (const T2 &a) const
	returns _A / a, also updates eigen values More...
bool	operator== (const T &A) const
	Defines logical equality with another second order tensor. More...
bool	operator== (const FactorizedRankTwoTensorTempl< T > &A) const
	Defines logical equality with another FactorizedRankTwoTensorTempl<T> More...
FactorizedRankTwoTensorTempl< T >	inverse () const
	inverse of _A More...
void	addIa (const typename T::value_type &a)
	add identity times a to _A More...
T::value_type	trace () const
	trace of _A More...
T::value_type	det () const
	determinant of _A More...
template<typename T2 = T>
T2	get () const
template<typename T2 = T>
T2	get ()
const std::vector< typename T::value_type > &	eigvals () const
std::vector< typename T::value_type >	eigvals ()
const RankTwoTensorTempl< typename T::value_type > &	eigvecs () const
RankTwoTensorTempl< typename T::value_type >	eigvecs ()
FactorizedRankTwoTensorTempl< T > &	operator= (const FactorizedRankTwoTensorTempl< T > &A)
FactorizedRankTwoTensorTempl< T > &	operator= (const T &A)

Private Member Functions
RankTwoTensorTempl< typename T::value_type >	assemble () const

Private Attributes
std::vector< typename T::value_type >	_eigvals
RankTwoTensorTempl< typename T::value_type >	_eigvecs

Detailed Description

template<typename T>
class FactorizedRankTwoTensorTempl< T >

FactorizedRankTwoTensorTempl is designed to perform the spectral decomposition of an underlying symmetric second order tensor and reuse its bases for future operations if possible.

FactorizedRankTwoTensorTempl templates on the underlying second order tensor. IMPORTANT: the underlying second order tensor must be symmetric. A check is only performed in debug mode.

Only operations that reuses the known factorization are provided. Otherwise, you will need to first retrieve the underlying RankTwoTensorTempl to perform the operation.

TODO? Although I am calling it factorization, it only really refers to eigenvalue decompositon at this point. I am not sure if in the future we need to add other types of similarity transformation.

Definition at line 17 of file FactorizedRankTwoTensor.h.

Member Typedef Documentation

value_type

template<typename T>

typedef T::value_type FactorizedRankTwoTensorTempl< T >::value_type

For generic programming.

Definition at line 39 of file FactorizedRankTwoTensor.h.

Constructor & Destructor Documentation

FactorizedRankTwoTensorTempl() [1/4]

template<typename T>

FactorizedRankTwoTensorTempl< T >::FactorizedRankTwoTensorTempl ( )

delete

No default constructor.

FactorizedRankTwoTensorTempl() [2/4]

template<typename T>

FactorizedRankTwoTensorTempl< T >::FactorizedRankTwoTensorTempl ( const FactorizedRankTwoTensorTempl< T > &  A )

default

Copy constructor.

FactorizedRankTwoTensorTempl() [3/4]

template<typename T>

FactorizedRankTwoTensorTempl< T >::FactorizedRankTwoTensorTempl ( const T &  A )

inline

Constructor if the factorization isn't known a priori.

Definition at line 48 of file FactorizedRankTwoTensor.h.

  {
    if (!A.isSymmetric())
      mooseError("The tensor is not symmetric.");
    A.symmetricEigenvaluesEigenvectors(_eigvals, _eigvecs);
  }

FactorizedRankTwoTensorTempl() [4/4]

template<typename T>

FactorizedRankTwoTensorTempl< T >::FactorizedRankTwoTensorTempl ( const std::vector< typename T::value_type > &  eigvals, const RankTwoTensorTempl< typename T::value_type > &  eigvecs  )

inline

Definition at line 59 of file FactorizedRankTwoTensor.h.

    : _eigvals(eigvals), _eigvecs(eigvecs)
  {
  }

Member Function Documentation

addIa()

template<typename T >

void FactorizedRankTwoTensorTempl< T >::addIa

(

const typename T::value_type &

a

)

add identity times a to _A

Definition at line 97 of file FactorizedRankTwoTensor.C.

{
  for (auto & eigval : _eigvals)
    eigval += a;
}

assemble()

template<typename T>

RankTwoTensorTempl<typename T::value_type> FactorizedRankTwoTensorTempl< T >::assemble ( ) const

inlineprivate

Definition at line 130 of file FactorizedRankTwoTensor.h.

Referenced by FactorizedRankTwoTensorTempl< T >::get().

  {
    typedef RankTwoTensorTempl<typename T::value_type> R2T;
    return _eigvals[0] * R2T::selfOuterProduct(_eigvecs.column(0)) +
           _eigvals[1] * R2T::selfOuterProduct(_eigvecs.column(1)) +
           _eigvals[2] * R2T::selfOuterProduct(_eigvecs.column(2));
  }

det()

template<typename T >

T::value_type FactorizedRankTwoTensorTempl< T >::det

(

)

const

determinant of _A

Definition at line 112 of file FactorizedRankTwoTensor.C.

{
  return _eigvals[0] * _eigvals[1] * _eigvals[2];
}

eigvals() [1/2]

template<typename T>

const std::vector<typename T::value_type>& FactorizedRankTwoTensorTempl< T >::eigvals ( ) const

inline

Definition at line 76 of file FactorizedRankTwoTensor.h.

{ return _eigvals; }

eigvals() [2/2]

template<typename T>

std::vector<typename T::value_type> FactorizedRankTwoTensorTempl< T >::eigvals ( )

inline

Definition at line 77 of file FactorizedRankTwoTensor.h.

{ return _eigvals; }

eigvecs() [1/2]

template<typename T>

const RankTwoTensorTempl<typename T::value_type>& FactorizedRankTwoTensorTempl< T >::eigvecs ( ) const

inline

Definition at line 78 of file FactorizedRankTwoTensor.h.

{ return _eigvecs; }

eigvecs() [2/2]

template<typename T>

RankTwoTensorTempl<typename T::value_type> FactorizedRankTwoTensorTempl< T >::eigvecs ( )

inline

Definition at line 79 of file FactorizedRankTwoTensor.h.

{ return _eigvecs; }

get() [1/2]

template<typename T>

template<typename T2 = T>

T2 FactorizedRankTwoTensorTempl< T >::get ( ) const

inline

Definition at line 67 of file FactorizedRankTwoTensor.h.

Referenced by FactorizedRankTwoTensorTempl< T >::operator==().

  {
    return static_cast<T2>(assemble());
  }

get() [2/2]

template<typename T>

template<typename T2 = T>

T2 FactorizedRankTwoTensorTempl< T >::get ( )

inline

Definition at line 72 of file FactorizedRankTwoTensor.h.

  {
    return static_cast<T2>(assemble());
  }

inverse()

template<typename T >

FactorizedRankTwoTensorTempl< T > FactorizedRankTwoTensorTempl< T >::inverse

(

)

const

inverse of _A

Definition at line 89 of file FactorizedRankTwoTensor.C.

{
  return FactorizedRankTwoTensorTempl<T>({1 / _eigvals[0], 1 / _eigvals[1], 1 / _eigvals[2]},
                                         _eigvecs);
}

operator*()

template<typename T >

template<typename T2 >

FactorizedRankTwoTensorTempl< T > FactorizedRankTwoTensorTempl< T >::operator*

(

const T2 &

a

)

const

returns _A * a, also updates eigen values

Definition at line 264 of file FactorizedRankTwoTensor.h.

{
  if constexpr (libMesh::ScalarTraits<T2>::value)
  {
    FactorizedRankTwoTensorTempl<T> A = *this;
    for (auto & eigval : A._eigvals)
      eigval *= a;
    return A;
  }
}

operator*=()

template<typename T >

FactorizedRankTwoTensorTempl< T > & FactorizedRankTwoTensorTempl< T >::operator*=

(

const typename T::value_type &

a

)

performs _A *= a in place, also updates eigen values

Definition at line 54 of file FactorizedRankTwoTensor.C.

{
  for (auto & eigval : _eigvals)
    eigval *= a;
  return *this;
}

operator/()

template<typename T >

template<typename T2 >

FactorizedRankTwoTensorTempl< T > FactorizedRankTwoTensorTempl< T >::operator/

(

const T2 &

a

)

const

returns _A / a, also updates eigen values

Definition at line 278 of file FactorizedRankTwoTensor.h.

{
  if constexpr (libMesh::ScalarTraits<T2>::value)
  {
    FactorizedRankTwoTensorTempl<T> A = *this;
    for (auto & eigval : A._eigvals)
      eigval /= a;
    return A;
  }
}

operator/=()

template<typename T >

FactorizedRankTwoTensorTempl< T > & FactorizedRankTwoTensorTempl< T >::operator/=

(

const typename T::value_type &

a

)

performs _A /= a in place, also updates eigen values

Definition at line 63 of file FactorizedRankTwoTensor.C.

{
  for (auto & eigval : _eigvals)
    eigval /= a;
  return *this;
}

operator=() [1/2]

template<typename T >

FactorizedRankTwoTensorTempl< T > & FactorizedRankTwoTensorTempl< T >::operator=

(

const FactorizedRankTwoTensorTempl< T > &

A

)

Definition at line 37 of file FactorizedRankTwoTensor.C.

{
  _eigvals = A._eigvals;
  _eigvecs = A._eigvecs;
  return *this;
}

operator=() [2/2]

template<typename T >

FactorizedRankTwoTensorTempl< T > & FactorizedRankTwoTensorTempl< T >::operator=

(

const T &

A

)

Definition at line 46 of file FactorizedRankTwoTensor.C.

{
  A.symmetricEigenvaluesEigenvectors(_eigvals, _eigvecs);
  return *this;
}

operator==() [1/2]

template<typename T >

bool FactorizedRankTwoTensorTempl< T >::operator==

(

const T &

A

)

const

Defines logical equality with another second order tensor.

Definition at line 72 of file FactorizedRankTwoTensor.C.

{
  T me = get();
  return me == A;
}

operator==() [2/2]

template<typename T >

bool FactorizedRankTwoTensorTempl< T >::operator==

(

const FactorizedRankTwoTensorTempl< T > &

A

)

const

Defines logical equality with another FactorizedRankTwoTensorTempl<T>

Definition at line 80 of file FactorizedRankTwoTensor.C.

{
  T me = get();
  T you = A.get();
  return me == you;
}

print()

template<typename T >

void FactorizedRankTwoTensorTempl< T >::print

(

std::ostream &

stm = Moose::out

)

const

Definition at line 16 of file FactorizedRankTwoTensor.C.

{
  this->get().print(stm);
}

rotated()

template<typename T >

FactorizedRankTwoTensorTempl< T > FactorizedRankTwoTensorTempl< T >::rotated

(

const RankTwoTensorTempl< typename T::value_type > &

R

)

const

Definition at line 23 of file FactorizedRankTwoTensor.C.

{
  return FactorizedRankTwoTensorTempl<T>(_eigvals, R * _eigvecs);
}

trace()

template<typename T >

T::value_type FactorizedRankTwoTensorTempl< T >::trace

(

)

const

trace of _A

Definition at line 105 of file FactorizedRankTwoTensor.C.

{
  return _eigvals[0] + _eigvals[1] + _eigvals[2];
}

transpose()

template<typename T >

FactorizedRankTwoTensorTempl< T > FactorizedRankTwoTensorTempl< T >::transpose

(

)

const

Returns the transpose of _A.

Definition at line 30 of file FactorizedRankTwoTensor.C.

{
  return *this;
}

Member Data Documentation

_eigvals

template<typename T>

std::vector<typename T::value_type> FactorizedRankTwoTensorTempl< T >::_eigvals

private

Definition at line 139 of file FactorizedRankTwoTensor.h.

Referenced by FactorizedRankTwoTensorTempl< T >::assemble(), FactorizedRankTwoTensorTempl< T >::eigvals(), FactorizedRankTwoTensorTempl< T >::FactorizedRankTwoTensorTempl(), FactorizedRankTwoTensorTempl< T >::operator*(), FactorizedRankTwoTensorTempl< T >::operator/(), and FactorizedRankTwoTensorTempl< T >::operator=().

_eigvecs

template<typename T>

RankTwoTensorTempl<typename T::value_type> FactorizedRankTwoTensorTempl< T >::_eigvecs

private

Definition at line 142 of file FactorizedRankTwoTensor.h.

Referenced by FactorizedRankTwoTensorTempl< T >::assemble(), FactorizedRankTwoTensorTempl< T >::eigvecs(), FactorizedRankTwoTensorTempl< T >::FactorizedRankTwoTensorTempl(), and FactorizedRankTwoTensorTempl< T >::operator=().

---

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

• include/utils/FactorizedRankTwoTensor.h
• src/utils/FactorizedRankTwoTensor.C