libMesh::TypeTensor< T > Class Template Reference

This class defines a tensor in LIBMESH_DIM dimensional space of type T. More...

#include <tensor_tools.h>

Inheritance diagram for libMesh::TypeTensor< T >:

Public Types
typedef T	value_type
	Helper typedef for C++98 generic programming. More...
typedef std::tuple< unsigned int, unsigned int >	index_type
	Helper typedef for generic index programming. More...

Public Member Functions
	TypeTensor ()
	Empty constructor. More...
template<typename T2 >
	TypeTensor (const TypeTensor< T2 > &p)
	Copy-constructor. More...
	~TypeTensor ()
	Destructor. More...
template<typename T2 >
void	assign (const TypeTensor< T2 > &)
	Assign to this tensor without creating a temporary. More...
template<typename Scalar >
boostcopy::enable_if_c< ScalarTraits< Scalar >::value, TypeTensor & >::type	operator= (const Scalar &libmesh_dbg_var(p))
	Assignment-from-scalar operator. More...
const T &	operator() (const unsigned int i, const unsigned int j) const
T &	operator() (const unsigned int i, const unsigned int j)
ConstTypeTensorColumn< T >	slice (const unsigned int i) const
TypeTensorColumn< T >	slice (const unsigned int i)
TypeVector< T >	row (const unsigned int r) const
TypeVector< T >	column (const unsigned int r) const
template<typename T2 >
TypeTensor< typename CompareTypes< T, T2 >::supertype >	operator+ (const TypeTensor< T2 > &) const
	Add another tensor to this tensor. More...
template<typename T2 >
const TypeTensor< T > &	operator+= (const TypeTensor< T2 > &)
	Add to this tensor. More...
template<typename T2 >
void	add (const TypeTensor< T2 > &)
	Add to this tensor without creating a temporary. More...
template<typename T2 >
void	add_scaled (const TypeTensor< T2 > &, const T &)
	Add a scaled tensor to this tensor without creating a temporary. More...
template<typename T2 >
TypeTensor< typename CompareTypes< T, T2 >::supertype >	operator- (const TypeTensor< T2 > &) const
	Subtract a tensor from this tensor. More...
template<typename T2 >
const TypeTensor< T > &	operator-= (const TypeTensor< T2 > &)
	Subtract from this tensor. More...
template<typename T2 >
void	subtract (const TypeTensor< T2 > &)
	Subtract from this tensor without creating a temporary. More...
template<typename T2 >
void	subtract_scaled (const TypeTensor< T2 > &, const T &)
	Subtract a scaled value from this tensor without creating a temporary. More...
TypeTensor< T >	operator- () const
template<typename Scalar >
auto	operator* (const Scalar &scalar) const -> typename boostcopy::enable_if_c< ScalarTraits< Scalar >::value, TypeTensor< decltype(T() *scalar)>>::type
	Multiply this tensor by a scalar value. More...
template<typename Scalar , typename boostcopy::enable_if_c< ScalarTraits< Scalar >::value, int >::type = 0>
const TypeTensor< T > &	operator*= (const Scalar &factor)
	Multiply this tensor by a scalar value in place. More...
template<typename Scalar >
boostcopy::enable_if_c< ScalarTraits< Scalar >::value, TypeTensor< typename CompareTypes< T, Scalar >::supertype > >::type	operator/ (const Scalar &) const
	Divide each entry of this tensor by a scalar value. More...
const TypeTensor< T > &	operator/= (const T &)
	Divide each entry of this tensor by a scalar value. More...
template<typename T2 >
TypeTensor< typename CompareTypes< T, T2 >::supertype >	operator* (const TypeTensor< T2 > &) const
	Multiply 2 tensors together, i.e. More...
template<typename T2 >
const TypeTensor< T > &	operator*= (const TypeTensor< T2 > &)
	Multiply this tensor by a tensor value in place. More...
template<typename T2 >
CompareTypes< T, T2 >::supertype	contract (const TypeTensor< T2 > &) const
	Multiply 2 tensors together to return a scalar, i.e. More...
template<typename T2 >
TypeVector< typename CompareTypes< T, T2 >::supertype >	operator* (const TypeVector< T2 > &) const
	Right-multiply this tensor by a vector, i.e. More...
template<typename T2 >
TypeVector< typename CompareTypes< T, T2 >::supertype >	left_multiply (const TypeVector< T2 > &p) const
	Left-multiply this tensor by a vector, i.e. More...
TypeTensor< T >	transpose () const
TypeTensor< T >	inverse () const
void	solve (const TypeVector< T > &b, TypeVector< T > &x) const
	Solve the 2x2 or 3x3 system of equations A*x = b for x by directly inverting A and multiplying it by b. More...
auto	norm () const -> decltype(std::norm(T()))
auto	norm_sq () const -> decltype(std::norm(T()))
bool	is_zero () const
T	det () const
T	tr () const
void	zero ()
	Set all entries of the tensor to 0. More...
bool	operator== (const TypeTensor< T > &rhs) const
bool	operator< (const TypeTensor< T > &rhs) const
bool	operator> (const TypeTensor< T > &rhs) const
void	print (std::ostream &os=libMesh::out) const
	Formatted print to a stream which defaults to libMesh::out. More...
void	write_unformatted (std::ostream &out_stream, const bool newline=true) const
	Unformatted print to the stream out. More...
template<>
bool	operator< (const TypeTensor< Real > &rhs) const
template<>
bool	operator> (const TypeTensor< Real > &rhs) const
template<>
bool	operator< (const TypeTensor< Complex > &rhs) const
template<>
bool	operator> (const TypeTensor< Complex > &rhs) const

Protected Member Functions
	TypeTensor (const T &xx, const T &xy=0, const T &xz=0, const T &yx=0, const T &yy=0, const T &yz=0, const T &zx=0, const T &zy=0, const T &zz=0)
	Constructor-from-T. More...
template<typename Scalar >
	TypeTensor (const Scalar &xx, const Scalar &xy=0, const Scalar &xz=0, const Scalar &yx=0, const Scalar &yy=0, const Scalar &yz=0, const Scalar &zx=0, const Scalar &zy=0, typename boostcopy::enable_if_c< ScalarTraits< Scalar >::value, const Scalar >::type &zz=0)
	Constructor-from-Scalar. More...
template<typename T2 >
	TypeTensor (const TypeVector< T2 > &vx)
	Constructor. More...
template<typename T2 >
	TypeTensor (const TypeVector< T2 > &vx, const TypeVector< T2 > &vy)
template<typename T2 >
	TypeTensor (const TypeVector< T2 > &vx, const TypeVector< T2 > &vy, const TypeVector< T2 > &vz)

Protected Attributes
T	_coords [LIBMESH_DIM *LIBMESH_DIM]
	The coordinates of the TypeTensor. More...

Friends
template<typename T2 >
class	TypeTensor
std::ostream &	operator<< (std::ostream &os, const TypeTensor< T > &t)
	Formatted print as above but supports the syntax: More...

Detailed Description

template<typename T>
class libMesh::TypeTensor< T >

This class defines a tensor in LIBMESH_DIM dimensional space of type T.

T may either be Real or Complex.

Author

Roy Stogner

Date

2004

Definition at line 36 of file tensor_tools.h.

Member Typedef Documentation

index_type

template<typename T>

typedef std::tuple<unsigned int, unsigned int> libMesh::TypeTensor< T >::index_type

Helper typedef for generic index programming.

Definition at line 125 of file type_tensor.h.

value_type

template<typename T>

typedef T libMesh::TypeTensor< T >::value_type

Helper typedef for C++98 generic programming.

Definition at line 120 of file type_tensor.h.

Constructor & Destructor Documentation

TypeTensor() [1/7]

template<typename T >

libMesh::TypeTensor< T >::TypeTensor ( )

inline

Empty constructor.

Gives the tensor 0 in LIBMESH_DIM dimensions.

Definition at line 510 of file type_tensor.h.

{
  _coords[0] = {};

#if LIBMESH_DIM > 1
  _coords[1] = {};
  _coords[2] = {};
  _coords[3] = {};
#endif

#if LIBMESH_DIM > 2
  _coords[4] = {};
  _coords[5] = {};
  _coords[6] = {};
  _coords[7] = {};
  _coords[8] = {};
#endif
}

TypeTensor() [2/7]

template<typename T >

libMesh::TypeTensor< T >::TypeTensor ( const T &  xx, const T &  xy = 0, const T &  xz = 0, const T &  yx = 0, const T &  yy = 0, const T &  yz = 0, const T &  zx = 0, const T &  zy = 0, const T &  zz = 0  )

inlineexplicitprotected

Constructor-from-T.

By default sets higher dimensional entries to 0. This is a poor constructor for 2D tensors - if the default arguments are to be overridden it requires that the "xz = 0." etc. arguments also be given explicitly.

Definition at line 533 of file type_tensor.h.

References libMesh::libmesh_ignore().

{
  _coords[0] = xx;

#if LIBMESH_DIM == 2
  _coords[1] = xy;
  _coords[2] = yx;
  _coords[3] = yy;
#elif LIBMESH_DIM == 1
  libmesh_assert_equal_to (xy, 0);
  libmesh_assert_equal_to (yx, 0);
  libmesh_assert_equal_to (yy, 0);
  libmesh_ignore(xy, yx, yy);
#endif

#if LIBMESH_DIM == 3
  _coords[1] = xy;
  _coords[2] = xz;
  _coords[3] = yx;
  _coords[4] = yy;
  _coords[5] = yz;
  _coords[6] = zx;
  _coords[7] = zy;
  _coords[8] = zz;
#else
  libmesh_assert_equal_to (xz, 0);
  libmesh_assert_equal_to (yz, 0);
  libmesh_assert_equal_to (zx, 0);
  libmesh_assert_equal_to (zy, 0);
  libmesh_assert_equal_to (zz, 0);
  libmesh_ignore(xz, yz, zx, zy, zz);
#endif
}

TypeTensor() [3/7]

template<typename T >

template<typename Scalar >

libMesh::TypeTensor< T >::TypeTensor ( const Scalar &  xx, const Scalar &  xy = 0, const Scalar &  xz = 0, const Scalar &  yx = 0, const Scalar &  yy = 0, const Scalar &  yz = 0, const Scalar &  zx = 0, const Scalar &  zy = 0, typename boostcopy::enable_if_c< ScalarTraits< Scalar >::value, const Scalar >::type &  zz = 0  )

inlineexplicitprotected

Constructor-from-Scalar.

Definition at line 579 of file type_tensor.h.

References libMesh::libmesh_ignore().

{
  _coords[0] = xx;

#if LIBMESH_DIM == 2
  _coords[1] = xy;
  _coords[2] = yx;
  _coords[3] = yy;
#elif LIBMESH_DIM == 1
  libmesh_assert_equal_to (xy, 0);
  libmesh_assert_equal_to (yx, 0);
  libmesh_assert_equal_to (yy, 0);
  libmesh_ignore(xy, yx, yy);
#endif

#if LIBMESH_DIM == 3
  _coords[1] = xy;
  _coords[2] = xz;
  _coords[3] = yx;
  _coords[4] = yy;
  _coords[5] = yz;
  _coords[6] = zx;
  _coords[7] = zy;
  _coords[8] = zz;
#else
  libmesh_assert_equal_to (xz, 0);
  libmesh_assert_equal_to (yz, 0);
  libmesh_assert_equal_to (zx, 0);
  libmesh_assert_equal_to (zy, 0);
  libmesh_assert_equal_to (zz, 0);
  libmesh_ignore(xz, yz, zx, zy, zz);
#endif
}

TypeTensor() [4/7]

template<typename T >

template<typename T2 >

libMesh::TypeTensor< T >::TypeTensor ( const TypeVector< T2 > &  vx )

protected

Constructor.

Assigns each vector to a different row of the tensor. We're in LIBMESH_DIM space dimensions and so LIBMESH_DIM many vectors are needed.

Definition at line 638 of file type_tensor.h.

{
  libmesh_assert_equal_to (LIBMESH_DIM, 1);
  _coords[0] = vx(0);
}

TypeTensor() [5/7]

template<typename T >

template<typename T2 >

libMesh::TypeTensor< T >::TypeTensor ( const TypeVector< T2 > &  vx, const TypeVector< T2 > &  vy  )

protected

Definition at line 646 of file type_tensor.h.

References libMesh::libmesh_ignore().

{
  libmesh_assert_equal_to (LIBMESH_DIM, 2);
#if LIBMESH_DIM > 1
  _coords[0] = vx(0);
  _coords[1] = vx(1);
  _coords[2] = vy(0);
  _coords[3] = vy(1);
#else
  libmesh_ignore(vx, vy);
#endif
}

TypeTensor() [6/7]

template<typename T >

template<typename T2 >

libMesh::TypeTensor< T >::TypeTensor ( const TypeVector< T2 > &  vx, const TypeVector< T2 > &  vy, const TypeVector< T2 > &  vz  )

protected

Definition at line 662 of file type_tensor.h.

References libMesh::libmesh_ignore().

{
  libmesh_assert_equal_to (LIBMESH_DIM, 3);
#if LIBMESH_DIM > 2
  _coords[0] = vx(0);
  _coords[1] = vx(1);
  _coords[2] = vx(2);
  _coords[3] = vy(0);
  _coords[4] = vy(1);
  _coords[5] = vy(2);
  _coords[6] = vz(0);
  _coords[7] = vz(1);
  _coords[8] = vz(2);
#else
  libmesh_ignore(vx, vy, vz);
#endif
}

TypeTensor() [7/7]

template<typename T >

template<typename T2 >

libMesh::TypeTensor< T >::TypeTensor ( const TypeTensor< T2 > &  p )

inline

Copy-constructor.

Definition at line 628 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords.

{
  // copy the nodes from vector p to me
  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
    _coords[i] = p._coords[i];
}

~TypeTensor()

template<typename T >

libMesh::TypeTensor< T >::~TypeTensor ( )

inline

Destructor.

Definition at line 687 of file type_tensor.h.

{
}

Member Function Documentation

add()

template<typename T >

template<typename T2 >

void libMesh::TypeTensor< T >::add ( const TypeTensor< T2 > &  p )

inline

Add to this tensor without creating a temporary.

Definition at line 840 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords.

{
  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
    _coords[i] += p._coords[i];
}

add_scaled()

template<typename T >

template<typename T2 >

void libMesh::TypeTensor< T >::add_scaled ( const TypeTensor< T2 > &  p, const T &  factor  )

inline

Add a scaled tensor to this tensor without creating a temporary.

Definition at line 851 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords.

Referenced by libMesh::HPCoarsenTest::add_projection(), LinearElasticityWithContact::compute_stresses(), LargeDeformationElasticity::compute_stresses(), libMesh::MeshFunction::hessian(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::System::point_hessian(), and libMesh::HPCoarsenTest::select_refinement().

{
  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
    _coords[i] += factor*p._coords[i];

}

assign()

template<typename T >

template<typename T2 >

void libMesh::TypeTensor< T >::assign ( const TypeTensor< T2 > &  p )

inline

Assign to this tensor without creating a temporary.

Definition at line 696 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords.

{
  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
    _coords[i] = p._coords[i];
}

column()

template<typename T >

TypeVector< T > libMesh::TypeTensor< T >::column ( const unsigned int  r ) const

inline

Returns

A copy of one column of the tensor as a TypeVector.

Definition at line 779 of file type_tensor.h.

References libMesh::TypeVector< T >::_coords.

Referenced by TypeTensorTest::testRowCol().

{
  TypeVector<T> return_vector;

  for (unsigned int i=0; i<LIBMESH_DIM; i++)
    return_vector._coords[i] = _coords[i*LIBMESH_DIM + r];

  return return_vector;
}

contract()

template<typename T >

template<typename T2 >

CompareTypes< T, T2 >::supertype libMesh::TypeTensor< T >::contract ( const TypeTensor< T2 > &  t ) const

inline

Multiply 2 tensors together to return a scalar, i.e.

Multiply 2 tensors together, i.e.

\( \sum_{ij} A_{ij} B_{ij} \) The tensors may contain different numeric types. Also known as the "double inner product" or "double dot product" of tensors.

Returns

The scalar-valued result, this tensor is unchanged.

sum Aij*Bij. The tensors may be of different types.

Definition at line 1268 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords.

Referenced by libMesh::HPCoarsenTest::add_projection(), libMesh::VariationalSmootherSystem::element_time_derivative(), libMesh::TensorTools::inner_product(), and libMesh::HPCoarsenTest::select_refinement().

{
  typename CompareTypes<T,T2>::supertype sum = 0.;
  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
    sum += _coords[i]*t._coords[i];
  return sum;
}

det()

template<typename T >

T libMesh::TypeTensor< T >::det ( ) const

inline

Returns

The determinant of the tensor.

Because these are 3x3 tensors at most, we don't do an LU decomposition like DenseMatrix does.

Definition at line 1298 of file type_tensor.h.

Referenced by libMesh::VariationalSmootherSystem::compute_mesh_quality_info(), LargeDeformationElasticity::compute_stresses(), libMesh::VariationalSmootherSystem::element_time_derivative(), libMesh::Hex::quality(), and libMesh::Sphere::Sphere().

{
#if LIBMESH_DIM == 1
  return _coords[0];
#endif

#if LIBMESH_DIM == 2
  return (_coords[0] * _coords[3]
          - _coords[1] * _coords[2]);
#endif

#if LIBMESH_DIM == 3
  return (_coords[0] * _coords[4] * _coords[8]
          + _coords[1] * _coords[5] * _coords[6]
          + _coords[2] * _coords[3] * _coords[7]
          - _coords[0] * _coords[5] * _coords[7]
          - _coords[1] * _coords[3] * _coords[8]
          - _coords[2] * _coords[4] * _coords[6]);
#endif
}

inverse()

template<typename T >

TypeTensor< T > libMesh::TypeTensor< T >::inverse ( ) const

inline

Returns

The inverse of this tensor as an independent object.

Definition at line 1080 of file type_tensor.h.

Referenced by NonlinearNeoHookeCurrentConfig::calculate_stress(), libMesh::VariationalSmootherSystem::element_time_derivative(), libMesh::VariationalSmootherSystem::get_target_to_reference_jacobian(), and TypeTensorTest::testInverse().

{
#if LIBMESH_DIM == 1
  if (_coords[0] == static_cast<T>(0.))
    libmesh_convergence_failure();
  return TypeTensor(1. / _coords[0]);
#endif

#if LIBMESH_DIM == 2
  // Get convenient reference to this.
  const TypeTensor<T> & A = *this;

  // Use temporary variables, avoid multiple accesses
  T a = A(0,0), b = A(0,1),
    c = A(1,0), d = A(1,1);

  // Make sure det = ad - bc is not zero
  T my_det = a*d - b*c;

  if (my_det == static_cast<T>(0.))
    libmesh_convergence_failure();

  return TypeTensor(d/my_det, -b/my_det, -c/my_det, a/my_det);
#endif

#if LIBMESH_DIM == 3
  // Get convenient reference to this.
  const TypeTensor<T> & A = *this;

  T a11 = A(0,0), a12 = A(0,1), a13 = A(0,2),
    a21 = A(1,0), a22 = A(1,1), a23 = A(1,2),
    a31 = A(2,0), a32 = A(2,1), a33 = A(2,2);

  T my_det = a11*(a33*a22-a32*a23) - a21*(a33*a12-a32*a13) + a31*(a23*a12-a22*a13);

  if (my_det == static_cast<T>(0.))
    libmesh_convergence_failure();

  // Inline comment characters are for lining up columns.
  return TypeTensor(  (a33*a22-a32*a23)/my_det, -(a33*a12-a32*a13)/my_det,  (a23*a12-a22*a13)/my_det,
                     -(a33*a21-a31*a23)/my_det,  (a33*a11-a31*a13)/my_det, -(a23*a11-a21*a13)/my_det,
                      (a32*a21-a31*a22)/my_det, -(a32*a11-a31*a12)/my_det,  (a22*a11-a21*a12)/my_det);
#endif
}

is_zero()

template<typename T >

bool libMesh::TypeTensor< T >::is_zero ( ) const

inline

Returns

True if all values in the tensor are zero

Definition at line 1288 of file type_tensor.h.

Referenced by TypeTensorTest::testIsZero().

{
  for (const auto & val : _coords)
    if (val != T(0))
      return false;
  return true;
}

left_multiply()

template<typename T >

template<typename T2 >

TypeVector< typename CompareTypes< T, T2 >::supertype > libMesh::TypeTensor< T >::left_multiply ( const TypeVector< T2 > &  p ) const

inline

Left-multiply this tensor by a vector, i.e.

matrix-vector product. The tensor and vector may contain different numeric types.

Returns

A copy of the result vector, this tensor is unchanged.

Definition at line 1211 of file type_tensor.h.

Referenced by libMesh::operator*().

{
  TypeVector<typename CompareTypes<T,T2>::supertype> returnval;
  for (unsigned int i=0; i<LIBMESH_DIM; i++)
    for (unsigned int j=0; j<LIBMESH_DIM; j++)
      returnval(i) += p(j)*(*this)(j,i);

  return returnval;
}

norm()

template<typename T >

auto libMesh::TypeTensor< T >::norm ( ) const -> decltype(std::norm(T()))

inline

Returns

The Frobenius norm of the tensor, i.e. the square-root of the sum of the elements squared.

Definition at line 1280 of file type_tensor.h.

References libMesh::TensorTools::norm_sq().

{
  return std::sqrt(this->norm_sq());
}

norm_sq()

template<typename T >

auto libMesh::TypeTensor< T >::norm_sq ( ) const -> decltype(std::norm(T()))

inline

Returns

The Frobenius norm of the tensor squared, i.e. sum of the element magnitudes squared.

Definition at line 1348 of file type_tensor.h.

References libMesh::TensorTools::norm_sq(), and libMesh::Real.

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::ExactErrorEstimator::find_squared_element_error(), and libMesh::HPCoarsenTest::select_refinement().

{
  Real sum = 0.;
  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
    sum += TensorTools::norm_sq(_coords[i]);
  return sum;
}

operator()() [1/2]

template<typename T >

const T & libMesh::TypeTensor< T >::operator() ( const unsigned int  i, const unsigned int  j  ) const

inline

Returns

A const reference to the (i,j) entry of the tensor.

Definition at line 706 of file type_tensor.h.

{
  libmesh_assert_less (i, 3);
  libmesh_assert_less (j, 3);

#if LIBMESH_DIM < 3
  const static T my_zero = 0;
  if (i >= LIBMESH_DIM || j >= LIBMESH_DIM)
    return my_zero;
#endif

  return _coords[i*LIBMESH_DIM+j];
}

operator()() [2/2]

template<typename T >

T & libMesh::TypeTensor< T >::operator() ( const unsigned int  i, const unsigned int  j  )

inline

Returns

A writable reference to the (i,j) entry of the tensor.

Definition at line 725 of file type_tensor.h.

{
#if LIBMESH_DIM < 3

  libmesh_error_msg_if(i >= LIBMESH_DIM || j >= LIBMESH_DIM,
                       "ERROR:  You are assigning to a tensor component that is out of range for the compiled LIBMESH_DIM!");

#endif

  libmesh_assert_less (i, LIBMESH_DIM);
  libmesh_assert_less (j, LIBMESH_DIM);

  return _coords[i*LIBMESH_DIM+j];
}

operator*() [1/3]

template<typename T >

template<typename Scalar >

auto libMesh::TypeTensor< T >::operator* ( const Scalar &  scalar ) const -> typename boostcopy::enable_if_c< ScalarTraits<Scalar>::value, TypeTensor<decltype(T() * scalar)>>::type

inline

Multiply this tensor by a scalar value.

Returns

A copy of the result, this tensor is unchanged.

Definition at line 965 of file type_tensor.h.

{
  typedef decltype((*this)(0, 0) * factor) TS;


#if LIBMESH_DIM == 1
  return TypeTensor<TS>(_coords[0]*factor);
#endif

#if LIBMESH_DIM == 2
  return TypeTensor<TS>(_coords[0]*factor,
                        _coords[1]*factor,
                        _coords[2]*factor,
                        _coords[3]*factor);
#endif

#if LIBMESH_DIM == 3
  return TypeTensor<TS>(_coords[0]*factor,
                        _coords[1]*factor,
                        _coords[2]*factor,
                        _coords[3]*factor,
                        _coords[4]*factor,
                        _coords[5]*factor,
                        _coords[6]*factor,
                        _coords[7]*factor,
                        _coords[8]*factor);
#endif
}

operator*() [2/3]

template<typename T >

template<typename T2 >

TypeTensor< typename CompareTypes< T, T2 >::supertype > libMesh::TypeTensor< T >::operator* ( const TypeTensor< T2 > &  p ) const

inline

Multiply 2 tensors together, i.e.

matrix-matrix product. The tensors may contain different numeric types.

Returns

A copy of the result, this tensor is unchanged.

Definition at line 1233 of file type_tensor.h.

{
  TypeTensor<typename CompareTypes<T, T2>::supertype> returnval;
  for (unsigned int i=0; i<LIBMESH_DIM; i++)
    for (unsigned int j=0; j<LIBMESH_DIM; j++)
      for (unsigned int k=0; k<LIBMESH_DIM; k++)
        returnval(i,j) += (*this)(i,k)*p(k,j);

  return returnval;
}

operator*() [3/3]

template<typename T >

template<typename T2 >

TypeVector< typename CompareTypes< T, T2 >::supertype > libMesh::TypeTensor< T >::operator* ( const TypeVector< T2 > &  p ) const

inline

Right-multiply this tensor by a vector, i.e.

matrix-vector product. The tensor and vector may contain different numeric types.

Returns

A copy of the result vector, this tensor is unchanged.

Definition at line 1197 of file type_tensor.h.

{
  TypeVector<typename CompareTypes<T,T2>::supertype> returnval;
  for (unsigned int i=0; i<LIBMESH_DIM; i++)
    for (unsigned int j=0; j<LIBMESH_DIM; j++)
      returnval(i) += (*this)(i,j)*p(j);

  return returnval;
}

operator*=() [1/2]

template<typename T>

template<typename Scalar , typename boostcopy::enable_if_c< ScalarTraits< Scalar >::value, int >::type = 0>

const TypeTensor<T>& libMesh::TypeTensor< T >::operator*= ( const Scalar &  factor )

inline

Multiply this tensor by a scalar value in place.

Returns

A reference to *this.

Definition at line 268 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords.

    {
      for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
        _coords[i] *= factor;

      return *this;
    }

operator*=() [2/2]

template<typename T >

template<typename T2 >

const TypeTensor< T > & libMesh::TypeTensor< T >::operator*= ( const TypeTensor< T2 > &  p )

inline

Multiply this tensor by a tensor value in place.

Returns

A reference to *this

Definition at line 1247 of file type_tensor.h.

{
  TypeTensor<T> temp;
  for (unsigned int i=0; i<LIBMESH_DIM; i++)
    for (unsigned int j=0; j<LIBMESH_DIM; j++)
      for (unsigned int k=0; k<LIBMESH_DIM; k++)
        temp(i,j) += (*this)(i,k)*p(k,j);

  this->assign(temp);
  return *this;
}

operator+()

template<typename T >

template<typename T2 >

TypeTensor< typename CompareTypes< T, T2 >::supertype > libMesh::TypeTensor< T >::operator+ ( const TypeTensor< T2 > &  p ) const

inline

Add another tensor to this tensor.

Returns

A copy of the result, this tensor is unchanged.

Definition at line 794 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords.

{

#if LIBMESH_DIM == 1
  return TypeTensor<typename CompareTypes<T, T2>::supertype>(_coords[0] + p._coords[0]);
#endif

#if LIBMESH_DIM == 2
  return TypeTensor<typename CompareTypes<T, T2>::supertype>(_coords[0] + p._coords[0],
                                                             _coords[1] + p._coords[1],
                                                             0.,
                                                             _coords[2] + p._coords[2],
                                                             _coords[3] + p._coords[3]);
#endif

#if LIBMESH_DIM == 3
  return TypeTensor<typename CompareTypes<T, T2>::supertype>(_coords[0] + p._coords[0],
                                                             _coords[1] + p._coords[1],
                                                             _coords[2] + p._coords[2],
                                                             _coords[3] + p._coords[3],
                                                             _coords[4] + p._coords[4],
                                                             _coords[5] + p._coords[5],
                                                             _coords[6] + p._coords[6],
                                                             _coords[7] + p._coords[7],
                                                             _coords[8] + p._coords[8]);
#endif

}

operator+=()

template<typename T >

template<typename T2 >

const TypeTensor< T > & libMesh::TypeTensor< T >::operator+= ( const TypeTensor< T2 > &  p )

inline

Add to this tensor.

Returns

A reference to *this.

Definition at line 828 of file type_tensor.h.

{
  this->add (p);

  return *this;
}

operator-() [1/2]

template<typename T >

template<typename T2 >

TypeTensor< typename CompareTypes< T, T2 >::supertype > libMesh::TypeTensor< T >::operator- ( const TypeTensor< T2 > &  p ) const

inline

Subtract a tensor from this tensor.

Returns

A copy of the result, this tensor is unchanged.

Definition at line 864 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords.

{

#if LIBMESH_DIM == 1
  return TypeTensor<typename CompareTypes<T, T2>::supertype>(_coords[0] - p._coords[0]);
#endif

#if LIBMESH_DIM == 2
  return TypeTensor<typename CompareTypes<T, T2>::supertype>(_coords[0] - p._coords[0],
                                                             _coords[1] - p._coords[1],
                                                             0.,
                                                             _coords[2] - p._coords[2],
                                                             _coords[3] - p._coords[3]);
#endif

#if LIBMESH_DIM == 3
  return TypeTensor<typename CompareTypes<T, T2>::supertype>(_coords[0] - p._coords[0],
                                                             _coords[1] - p._coords[1],
                                                             _coords[2] - p._coords[2],
                                                             _coords[3] - p._coords[3],
                                                             _coords[4] - p._coords[4],
                                                             _coords[5] - p._coords[5],
                                                             _coords[6] - p._coords[6],
                                                             _coords[7] - p._coords[7],
                                                             _coords[8] - p._coords[8]);
#endif

}

operator-() [2/2]

template<typename T >

TypeTensor< T > libMesh::TypeTensor< T >::operator- ( ) const

inline

Returns

The negative of this tensor in a separate copy.

Definition at line 931 of file type_tensor.h.

{

#if LIBMESH_DIM == 1
  return TypeTensor(-_coords[0]);
#endif

#if LIBMESH_DIM == 2
  return TypeTensor(-_coords[0],
                    -_coords[1],
                    -_coords[2],
                    -_coords[3]);
#endif

#if LIBMESH_DIM == 3
  return TypeTensor(-_coords[0],
                    -_coords[1],
                    -_coords[2],
                    -_coords[3],
                    -_coords[4],
                    -_coords[5],
                    -_coords[6],
                    -_coords[7],
                    -_coords[8]);
#endif

}

operator-=()

template<typename T >

template<typename T2 >

const TypeTensor< T > & libMesh::TypeTensor< T >::operator-= ( const TypeTensor< T2 > &  p )

inline

Subtract from this tensor.

Returns

A reference to *this.

Definition at line 898 of file type_tensor.h.

{
  this->subtract (p);

  return *this;
}

operator/()

template<typename T >

template<typename Scalar >

boostcopy::enable_if_c< ScalarTraits< Scalar >::value, TypeTensor< typename CompareTypes< T, Scalar >::supertype > >::type libMesh::TypeTensor< T >::operator/ ( const Scalar &  factor ) const

inline

Divide each entry of this tensor by a scalar value.

Returns

A copy of the result, this tensor is unchanged.

Definition at line 1015 of file type_tensor.h.

{
  libmesh_assert_not_equal_to (factor, static_cast<T>(0.));

  typedef typename CompareTypes<T, Scalar>::supertype TS;

#if LIBMESH_DIM == 1
  return TypeTensor<TS>(_coords[0]/factor);
#endif

#if LIBMESH_DIM == 2
  return TypeTensor<TS>(_coords[0]/factor,
                        _coords[1]/factor,
                        _coords[2]/factor,
                        _coords[3]/factor);
#endif

#if LIBMESH_DIM == 3
  return TypeTensor<TS>(_coords[0]/factor,
                        _coords[1]/factor,
                        _coords[2]/factor,
                        _coords[3]/factor,
                        _coords[4]/factor,
                        _coords[5]/factor,
                        _coords[6]/factor,
                        _coords[7]/factor,
                        _coords[8]/factor);
#endif

}

operator/=()

template<typename T >

const TypeTensor< T > & libMesh::TypeTensor< T >::operator/= ( const T &  factor )

inline

Divide each entry of this tensor by a scalar value.

Returns

A reference to *this.

Definition at line 1180 of file type_tensor.h.

{
  libmesh_assert_not_equal_to (factor, static_cast<T>(0.));

  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
    _coords[i] /= factor;

  return *this;
}

operator<() [1/3]

template<>

bool libMesh::TypeTensor< Real >::operator<

(

const TypeTensor< Real > &

rhs

)

const

Definition at line 69 of file type_tensor.C.

{
  for (unsigned int i=0; i<LIBMESH_DIM; i++)
    for (unsigned int j=0; j<LIBMESH_DIM; j++)
      {
        if ((*this)(i,j) < rhs(i,j))
          return true;
        if ((*this)(i,j) > rhs(i,j))
          return false;
      }
  return false;
}

operator<() [2/3]

template<>

bool libMesh::TypeTensor< Complex >::operator<

(

const TypeTensor< Complex > &

rhs

)

const

Definition at line 102 of file type_tensor.C.

References std::imag(), and std::real().

{
  for (unsigned int i=0; i<LIBMESH_DIM; i++)
    for (unsigned int j=0; j<LIBMESH_DIM; j++)
      {
        if ((*this)(i,j).real() < rhs(i,j).real())
          return true;
        if ((*this)(i,j).real() > rhs(i,j).real())
          return false;
        if ((*this)(i,j).imag() < rhs(i,j).imag())
          return true;
        if ((*this)(i,j).imag() > rhs(i,j).imag())
          return false;
      }
  return false;
}

operator<() [3/3]

template<typename T>

bool libMesh::TypeTensor< T >::operator<

(

const TypeTensor< T > &

rhs

)

const

Returns

true if this tensor is "less" than another. Useful for sorting.

operator=()

template<typename T>

template<typename Scalar >

boostcopy::enable_if_c< ScalarTraits<Scalar>::value, TypeTensor &>::type libMesh::TypeTensor< T >::operator= ( const Scalar &  libmesh_dbg_varp )

inline

Assignment-from-scalar operator.

Used only to zero out vectors.

Returns

A reference to *this.

Definition at line 153 of file type_tensor.h.

References libMesh::TypeTensor< T >::zero().

  { libmesh_assert_equal_to (p, Scalar(0)); this->zero(); return *this; }

operator==()

template<typename T >

bool libMesh::TypeTensor< T >::operator== ( const TypeTensor< T > &  rhs ) const

inline

Returns

true if two tensors are equal, false otherwise.

Definition at line 1360 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords, and libMesh::TOLERANCE.

{
#if LIBMESH_DIM == 1
  return (std::abs(_coords[0] - rhs._coords[0])
          < TOLERANCE);
#endif

#if LIBMESH_DIM == 2
  return ((std::abs(_coords[0] - rhs._coords[0]) +
           std::abs(_coords[1] - rhs._coords[1]) +
           std::abs(_coords[2] - rhs._coords[2]) +
           std::abs(_coords[3] - rhs._coords[3]))
          < 4.*TOLERANCE);
#endif

#if LIBMESH_DIM == 3
  return ((std::abs(_coords[0] - rhs._coords[0]) +
           std::abs(_coords[1] - rhs._coords[1]) +
           std::abs(_coords[2] - rhs._coords[2]) +
           std::abs(_coords[3] - rhs._coords[3]) +
           std::abs(_coords[4] - rhs._coords[4]) +
           std::abs(_coords[5] - rhs._coords[5]) +
           std::abs(_coords[6] - rhs._coords[6]) +
           std::abs(_coords[7] - rhs._coords[7]) +
           std::abs(_coords[8] - rhs._coords[8]))
          < 9.*TOLERANCE);
#endif

}

operator>() [1/3]

template<>

bool libMesh::TypeTensor< Real >::operator>

(

const TypeTensor< Real > &

rhs

)

const

Definition at line 85 of file type_tensor.C.

{
  for (unsigned int i=0; i<LIBMESH_DIM; i++)
    for (unsigned int j=0; j<LIBMESH_DIM; j++)
      {
        if ((*this)(i,j) > rhs(i,j))
          return true;
        if ((*this)(i,j) < rhs(i,j))
          return false;
      }
  return false;
}

operator>() [2/3]

template<>

bool libMesh::TypeTensor< Complex >::operator>

(

const TypeTensor< Complex > &

rhs

)

const

Definition at line 122 of file type_tensor.C.

References std::imag(), and std::real().

{
  for (unsigned int i=0; i<LIBMESH_DIM; i++)
    for (unsigned int j=0; j<LIBMESH_DIM; j++)
      {
        if ((*this)(i,j).real() > rhs(i,j).real())
          return true;
        if ((*this)(i,j).real() < rhs(i,j).real())
          return false;
        if ((*this)(i,j).imag() > rhs(i,j).imag())
          return true;
        if ((*this)(i,j).imag() < rhs(i,j).imag())
          return false;
      }
  return false;
}

operator>() [3/3]

template<typename T>

bool libMesh::TypeTensor< T >::operator>

(

const TypeTensor< T > &

rhs

)

const

Returns

true if this tensor is "greater" than another.

print()

template<typename T >

void libMesh::TypeTensor< T >::print

(

std::ostream &

os = libMesh::out

)

const

Formatted print to a stream which defaults to libMesh::out.

Definition at line 1391 of file type_tensor.h.

{
#if LIBMESH_DIM == 1

  os << "x=" << (*this)(0,0) << std::endl;

#endif
#if LIBMESH_DIM == 2

  os << "(xx,xy)=("
     << std::setw(8) << (*this)(0,0) << ", "
     << std::setw(8) << (*this)(0,1) << ")"
     << std::endl;
  os << "(yx,yy)=("
     << std::setw(8) << (*this)(1,0) << ", "
     << std::setw(8) << (*this)(1,1) << ")"
     << std::endl;

#endif
#if LIBMESH_DIM == 3

  os <<  "(xx,xy,xz)=("
     << std::setw(8) << (*this)(0,0) << ", "
     << std::setw(8) << (*this)(0,1) << ", "
     << std::setw(8) << (*this)(0,2) << ")"
     << std::endl;
  os <<  "(yx,yy,yz)=("
     << std::setw(8) << (*this)(1,0) << ", "
     << std::setw(8) << (*this)(1,1) << ", "
     << std::setw(8) << (*this)(1,2) << ")"
     << std::endl;
  os <<  "(zx,zy,zz)=("
     << std::setw(8) << (*this)(2,0) << ", "
     << std::setw(8) << (*this)(2,1) << ", "
     << std::setw(8) << (*this)(2,2) << ")"
     << std::endl;
#endif
}

row()

template<typename T >

TypeVector< T > libMesh::TypeTensor< T >::row ( const unsigned int  r ) const

inline

Returns

A copy of one row of the tensor as a TypeVector.

Definition at line 765 of file type_tensor.h.

References libMesh::TypeVector< T >::_coords.

Referenced by TypeTensorTest::testRowCol().

{
  TypeVector<T> return_vector;

  for (unsigned int j=0; j<LIBMESH_DIM; j++)
    return_vector._coords[j] = _coords[r*LIBMESH_DIM + j];

  return return_vector;
}

slice() [1/2]

template<typename T >

ConstTypeTensorColumn< T > libMesh::TypeTensor< T >::slice ( const unsigned int  i ) const

inline

Returns

A proxy for the \( i^{th} \) column of the tensor.

Definition at line 745 of file type_tensor.h.

{
  libmesh_assert_less (i, LIBMESH_DIM);
  return ConstTypeTensorColumn<T>(*this, i);
}

slice() [2/2]

template<typename T >

TypeTensorColumn< T > libMesh::TypeTensor< T >::slice ( const unsigned int  i )

inline

Returns

A writable proxy for the \( i^{th} \) column of the tensor.

Definition at line 755 of file type_tensor.h.

{
  libmesh_assert_less (i, LIBMESH_DIM);
  return TypeTensorColumn<T>(*this, i);
}

solve()

template<typename T >

void libMesh::TypeTensor< T >::solve ( const TypeVector< T > &  b, TypeVector< T > &  x  ) const

inline

Solve the 2x2 or 3x3 system of equations A*x = b for x by directly inverting A and multiplying it by b.

Returns

The solution in the x vector.

Definition at line 1129 of file type_tensor.h.

Referenced by InfFERadialTest::base_point(), and libMesh::InfFEMap::inverse_map().

{
#if LIBMESH_DIM == 1
  if (_coords[0] == static_cast<T>(0.))
    libmesh_convergence_failure();
  x(0) = b(0) / _coords[0];
#endif

#if LIBMESH_DIM == 2
  T my_det = _coords[0]*_coords[3] - _coords[1]*_coords[2];

  if (my_det == static_cast<T>(0.))
    libmesh_convergence_failure();

  T my_det_inv = 1./my_det;

  x(0) = my_det_inv*( _coords[3]*b(0) - _coords[1]*b(1));
  x(1) = my_det_inv*(-_coords[2]*b(0) + _coords[0]*b(1));
#endif

#if LIBMESH_DIM == 3
  T my_det =
    //           a11*(a33       *a22        - a32       *a23)
      _coords[0]*(_coords[8]*_coords[4] - _coords[7]*_coords[5])
    //          -a21*(a33       *a12        - a32       *a13)
     -_coords[3]*(_coords[8]*_coords[1] - _coords[7]*_coords[2]) +
    //          +a31*(a23       *a12        - a22       *a13)
     +_coords[6]*(_coords[5]*_coords[1] - _coords[4]*_coords[2]);

  if (my_det == static_cast<T>(0.))
    libmesh_convergence_failure();

  T my_det_inv = 1./my_det;
  x(0) = my_det_inv*((_coords[8]*_coords[4] - _coords[7]*_coords[5])*b(0) -
                     (_coords[8]*_coords[1] - _coords[7]*_coords[2])*b(1) +
                     (_coords[5]*_coords[1] - _coords[4]*_coords[2])*b(2));

  x(1) = my_det_inv*((_coords[6]*_coords[5] - _coords[8]*_coords[3])*b(0) +
                     (_coords[8]*_coords[0] - _coords[6]*_coords[2])*b(1) -
                     (_coords[5]*_coords[0] - _coords[3]*_coords[2])*b(2));

  x(2) = my_det_inv*((_coords[7]*_coords[3] - _coords[6]*_coords[4])*b(0) -
                     (_coords[7]*_coords[0] - _coords[6]*_coords[1])*b(1) +
                     (_coords[4]*_coords[0] - _coords[3]*_coords[1])*b(2));
#endif
}

subtract()

template<typename T >

template<typename T2 >

void libMesh::TypeTensor< T >::subtract ( const TypeTensor< T2 > &  p )

inline

Subtract from this tensor without creating a temporary.

Definition at line 910 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords.

{
  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
    _coords[i] -= p._coords[i];
}

subtract_scaled()

template<typename T >

template<typename T2 >

void libMesh::TypeTensor< T >::subtract_scaled ( const TypeTensor< T2 > &  p, const T &  factor  )

inline

Subtract a scaled value from this tensor without creating a temporary.

Definition at line 921 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords.

Referenced by libMesh::HPCoarsenTest::select_refinement().

{
  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
    _coords[i] -= factor*p._coords[i];
}

tr()

template<typename T >

T libMesh::TypeTensor< T >::tr ( ) const

inline

Returns

The trace of the tensor.

Definition at line 1321 of file type_tensor.h.

{
#if LIBMESH_DIM == 1
  return _coords[0];
#endif

#if LIBMESH_DIM == 2
  return _coords[0] + _coords[3];
#endif

#if LIBMESH_DIM == 3
  return _coords[0] + _coords[4] + _coords[8];
#endif
}

transpose()

template<typename T >

TypeTensor< T > libMesh::TypeTensor< T >::transpose ( ) const

inline

Returns

The transpose of this tensor (with complex numbers not conjugated).

Definition at line 1050 of file type_tensor.h.

Referenced by assemble_shell(), libMesh::VariationalSmootherSystem::compute_mesh_quality_info(), LargeDeformationElasticity::compute_stresses(), libMesh::VariationalSmootherSystem::element_time_derivative(), libMesh::get_jacobian_at_qp(), GradDivExactSolution::grad(), and CurlCurlExactSolution::grad().

{
#if LIBMESH_DIM == 1
  return TypeTensor(_coords[0]);
#endif

#if LIBMESH_DIM == 2
  return TypeTensor(_coords[0],
                    _coords[2],
                    _coords[1],
                    _coords[3]);
#endif

#if LIBMESH_DIM == 3
  return TypeTensor(_coords[0],
                    _coords[3],
                    _coords[6],
                    _coords[1],
                    _coords[4],
                    _coords[7],
                    _coords[2],
                    _coords[5],
                    _coords[8]);
#endif
}

write_unformatted()

template<typename T >

void libMesh::TypeTensor< T >::write_unformatted	(	std::ostream &	out_stream,
		const bool	newline = true
	)		const

Unformatted print to the stream out.

Simply prints the elements of the tensor separated by spaces and newlines.

Definition at line 39 of file type_tensor.C.

References libMesh::libmesh_assert().

{
  libmesh_assert (out_stream);

  out_stream << std::setiosflags(std::ios::showpoint)
             << (*this)(0,0) << " "
             << (*this)(0,1) << " "
             << (*this)(0,2) << " ";
  if (newline)
    out_stream << '\n';

  out_stream << std::setiosflags(std::ios::showpoint)
             << (*this)(1,0) << " "
             << (*this)(1,1) << " "
             << (*this)(1,2) << " ";
  if (newline)
    out_stream << '\n';

  out_stream << std::setiosflags(std::ios::showpoint)
             << (*this)(2,0) << " "
             << (*this)(2,1) << " "
             << (*this)(2,2) << " ";
  if (newline)
    out_stream << '\n';
}

zero()

template<typename T >

void libMesh::TypeTensor< T >::zero ( )

inline

Set all entries of the tensor to 0.

Definition at line 1338 of file type_tensor.h.

Referenced by LinearElasticityWithContact::compute_stresses(), LargeDeformationElasticity::compute_stresses(), NonlinearNeoHookeCurrentConfig::init_for_qp(), libMesh::TensorValue< T >::operator=(), and libMesh::TypeTensor< T >::operator=().

{
  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
    _coords[i] = 0.;
}

Friends And Related Function Documentation

operator<<

template<typename T>

std::ostream& operator<< ( std::ostream &  os, const TypeTensor< T > &  t  )

friend

Formatted print as above but supports the syntax:

std::cout << t << std::endl;

Definition at line 426 of file type_tensor.h.

  {
    t.print(os);
    return os;
  }

TypeTensor

template<typename T>

template<typename T2 >

friend class TypeTensor

friend

Definition at line 55 of file type_tensor.h.

Member Data Documentation

_coords

template<typename T>

T libMesh::TypeTensor< T >::_coords[LIBMESH_DIM *LIBMESH_DIM]

protected

The coordinates of the TypeTensor.

Definition at line 444 of file type_tensor.h.

Referenced by libMesh::TypeTensor< T >::add(), libMesh::TypeTensor< T >::add_scaled(), libMesh::TypeTensor< T >::assign(), libMesh::TypeTensor< T >::contract(), libMesh::TypeTensor< T >::operator*=(), libMesh::TypeTensor< T >::operator+(), libMesh::TypeTensor< T >::operator-(), libMesh::TypeTensor< T >::operator==(), libMesh::TypeTensor< T >::subtract(), libMesh::TypeTensor< T >::subtract_scaled(), and libMesh::TypeTensor< T >::TypeTensor().

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

• include/numerics/tensor_tools.h
• include/numerics/type_tensor.h
• src/numerics/type_tensor.C