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libMesh::TensorValue< T > Class Template Reference

#include <tensor_value.h>

Inheritance diagram for libMesh::TensorValue< T >:
Inheritance graph
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List of all members.

Public Member Functions

 TensorValue ()
 TensorValue (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)
template<typename Scalar >
 TensorValue (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)
template<typename T2 >
 TensorValue (const TypeVector< T2 > &vx)
template<typename T2 >
 TensorValue (const TypeVector< T2 > &vx, const TypeVector< T2 > &vy)
template<typename T2 >
 TensorValue (const TypeVector< T2 > &vx, const TypeVector< T2 > &vy, const TypeVector< T2 > &vz)
template<typename T2 >
 TensorValue (const TensorValue< T2 > &p)
template<typename T2 >
 TensorValue (const TypeTensor< T2 > &p)
 TensorValue (const TypeTensor< Real > &p_re, const TypeTensor< Real > &p_im)
template<typename Scalar >
boostcopy::enable_if_c
< ScalarTraits< Scalar >
::value, TensorValue & >::type 		operator= (const Scalar &libmesh_dbg_var(p))
template<typename T2 >
void assign (const TypeTensor< T2 > &)
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)
template<typename T2 >
TypeTensor< typename
CompareTypes< T, T2 >
::supertype > 		operator+ (const TypeTensor< T2 > &) const
template<typename T2 >
const TypeTensor< T > & operator+= (const TypeTensor< T2 > &)
template<typename T2 >
void add (const TypeTensor< T2 > &)
template<typename T2 >
void add_scaled (const TypeTensor< T2 > &, const T)
template<typename T2 >
TypeTensor< typename
CompareTypes< T, T2 >
::supertype > 		operator- (const TypeTensor< T2 > &) const
TypeTensor< T > operator- () const
template<typename T2 >
const TypeTensor< T > & operator-= (const TypeTensor< T2 > &)
template<typename T2 >
void subtract (const TypeTensor< T2 > &)
template<typename T2 >
void subtract_scaled (const TypeTensor< T2 > &, const T)
template<typename Scalar >
boostcopy::enable_if_c
< ScalarTraits< Scalar >
::value, TypeTensor< typename
CompareTypes< T, Scalar >
::supertype > >::type 		operator* (const Scalar) const
template<typename T2 >
TypeTensor< T > operator* (const TypeTensor< T2 > &) const
template<typename T2 >
TypeVector< typename
CompareTypes< T, T2 >
::supertype > 		operator* (const TypeVector< T2 > &) const
template<typename Scalar >
const TypeTensor< T > & operator*= (const Scalar)
template<typename Scalar >
boostcopy::enable_if_c
< ScalarTraits< Scalar >
::value, TypeTensor< typename
CompareTypes< T, Scalar >
::supertype > >::type 		operator/ (const Scalar) const
const TypeTensor< T > & operator/= (const T)
template<typename T2 >
CompareTypes< T, T2 >::supertype contract (const TypeTensor< T2 > &) const
TypeTensor< T > transpose () const
TypeTensor< T > inverse () const
Real size () const
Real size_sq () const
T det () const
T tr () const
void zero ()
bool operator== (const TypeTensor< T > &rhs) const
bool operator< (const TypeTensor< T > &rhs) const
template<>
bool operator< (const TypeTensor< Real > &rhs) const
template<>
bool operator< (const TypeTensor< Complex > &rhs) const
bool operator> (const TypeTensor< T > &rhs) const
template<>
bool operator> (const TypeTensor< Real > &rhs) const
template<>
bool operator> (const TypeTensor< Complex > &rhs) const
void print (std::ostream &os=libMesh::out) const
void write_unformatted (std::ostream &out, const bool newline=true) const

Public Attributes

T _coords [LIBMESH_DIM *LIBMESH_DIM]

Friends

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

Detailed Description

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

This class defines a tensor in LIBMESH_DIM dimensional Real or Complex space. The typedef RealTensorValue always defines a real-valued tensor, and NumberTensorValue defines a real or complex-valued tensor depending on how the library was configured.

Author:
Roy H. Stogner 2004

Definition at line 40 of file tensor_value.h.

Constructor & Destructor Documentation

template<typename T >
libMesh::TensorValue< T >::TensorValue ( ) [inline]

Empty constructor. Gives the tensor 0 in LIBMESH_DIM dimensional T space.

Definition at line 157 of file tensor_value.h.

                             :
  TypeTensor<T> ()
{
}
template<typename T >
libMesh::TensorValue< T >::TensorValue ( 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 
) [inline, explicit]

Constructor-from-T. By default sets higher dimensional entries to 0.

Definition at line 167 of file tensor_value.h.

             :
  TypeTensor<T> (xx,xy,xz,yx,yy,yz,zx,zy,zz)
{
}
template<typename T >
template<typename Scalar >
libMesh::TensorValue< T >::TensorValue ( 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 
) [inline, explicit]

Constructor-from-scalars. By default sets higher dimensional entries to 0.

Definition at line 185 of file tensor_value.h.

                       :
  TypeTensor<T> (xx,xy,xz,yx,yy,yz,zx,zy,zz)
{
}
template<typename T >
template<typename T2 >
libMesh::TensorValue< T >::TensorValue ( const TypeVector< T2 > &  vx) [inline]

Constructor. Takes 1 row vector for LIBMESH_DIM=1

Definition at line 215 of file tensor_value.h.

                                                     :
  TypeTensor<T> (vx)
{
}
template<typename T >
template<typename T2 >
libMesh::TensorValue< T >::TensorValue ( const TypeVector< T2 > &  vx,
const TypeVector< T2 > &  vy 
) [inline]

Constructor. Takes 2 row vectors for LIBMESH_DIM=2

Definition at line 225 of file tensor_value.h.

                                                       :
  TypeTensor<T> (vx, vy)
{
}
template<typename T >
template<typename T2 >
libMesh::TensorValue< T >::TensorValue ( const TypeVector< T2 > &  vx,
const TypeVector< T2 > &  vy,
const TypeVector< T2 > &  vz 
) [inline]

Constructor. Takes 3 row vectors for LIBMESH_DIM=3

Definition at line 236 of file tensor_value.h.

                                                       :
  TypeTensor<T> (vx, vy, vz)
{
}
template<typename T >
template<typename T2 >
libMesh::TensorValue< T >::TensorValue ( const TensorValue< T2 > &  p) [inline]

Copy-constructor.

Definition at line 205 of file tensor_value.h.

                                                     :
  TypeTensor<T> (p)
{
}
template<typename T >
template<typename T2 >
libMesh::TensorValue< T >::TensorValue ( const TypeTensor< T2 > &  p) [inline]

Copy-constructor.

Definition at line 248 of file tensor_value.h.

                                                    :
  TypeTensor<T> (p)
{
}
template<typename T >
libMesh::TensorValue< T >::TensorValue ( const TypeTensor< Real > &  p_re,
const TypeTensor< Real > &  p_im 
) [inline]

Constructor that takes two TypeTensor<Real> representing the real and imaginary part as arguments.

Definition at line 257 of file tensor_value.h.

                                                           :
  TypeTensor<T> (Complex (p_re(0,0), p_im(0,0)),
                 Complex (p_re(0,1), p_im(0,1)),
                 Complex (p_re(0,2), p_im(0,2)),
                 Complex (p_re(1,0), p_im(1,0)),
                 Complex (p_re(1,1), p_im(1,1)),
                 Complex (p_re(1,2), p_im(1,2)),
                 Complex (p_re(2,0), p_im(2,0)),
                 Complex (p_re(2,1), p_im(2,1)),
                 Complex (p_re(2,2), p_im(2,2)))
{
}

Member Function Documentation

template<typename T >
template<typename T2 >
void libMesh::TypeTensor< T >::add ( const TypeTensor< T2 > &  p) [inline, inherited]

Add to this tensor without creating a temporary.

Definition at line 706 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];
}
template<typename T >
template<typename T2 >
void libMesh::TypeTensor< T >::add_scaled ( const TypeTensor< T2 > &  p,
const T  factor 
) [inline, inherited]

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

Definition at line 717 of file type_tensor.h.

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

Referenced by libMesh::HPCoarsenTest::add_projection(), libMesh::System::calculate_norm(), 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];

}
template<typename T >
template<typename T2 >
void libMesh::TypeTensor< T >::assign ( const TypeTensor< T2 > &  p) [inline, inherited]

Assign to a tensor without creating a temporary.

Definition at line 577 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];
}
template<typename T >
template<typename T2 >
CompareTypes< T, T2 >::supertype libMesh::TypeTensor< T >::contract ( const TypeTensor< T2 > &  t) const [inline, inherited]

Multiply 2 tensors together, i.e. dyadic product sum_ij Aij*Bij. The tensors may be of different types.

Multiply 2 tensors together, i.e. sum Aij*Bij. The tensors may be of different types.

Definition at line 1059 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords, and libMesh::Parallel::sum().

Referenced by libMesh::HPCoarsenTest::add_projection(), 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;
}
template<typename T >
T libMesh::TypeTensor< T >::det ( ) const [inline, inherited]

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 1080 of file type_tensor.h.

Referenced by 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
}
template<typename T >
TypeTensor< T > libMesh::TypeTensor< T >::inverse ( ) const [inline, inherited]

Returns the inverse of the tensor.

Definition at line 962 of file type_tensor.h.

{
#if LIBMESH_DIM == 1
  libmesh_assert_not_equal_to(_coords[0], static_cast<T>(0.));
  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;
  libmesh_assert_not_equal_to(my_det, static_cast<T>(0.));

  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);
  libmesh_assert_not_equal_to(my_det, static_cast<T>(0.));

  // 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
}
template<typename T >
const T & libMesh::TypeTensor< T >::operator() ( const unsigned int  i,
const unsigned int  j 
) const [inline, inherited]

Return the $ i,j^{th} $ element of the tensor.

Definition at line 587 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];
}
template<typename T >
T & libMesh::TypeTensor< T >::operator() ( const unsigned int  i,
const unsigned int  j 
) [inline, inherited]

Return a writeable reference to the $ i,j^{th} $ element of the tensor.

Definition at line 606 of file type_tensor.h.

{
#if LIBMESH_DIM < 3

  if (i >= LIBMESH_DIM || j >= LIBMESH_DIM)
    libmesh_error_msg("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];
}
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, inherited]

Multiply a tensor by a number, i.e. scale.

Definition at line 833 of file type_tensor.h.

{
  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
}
template<typename T >
template<typename T2 >
TypeTensor< T > libMesh::TypeTensor< T >::operator* ( const TypeTensor< T2 > &  p) const [inline, inherited]

Multiply 2 tensors together, i.e. matrix product. The tensors may be of different types.

Definition at line 1038 of file type_tensor.h.

{
  TypeTensor<T> 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;
}
template<typename T >
template<typename T2 >
TypeVector< typename CompareTypes< T, T2 >::supertype > libMesh::TypeTensor< T >::operator* ( const TypeVector< T2 > &  p) const [inline, inherited]

Multiply a tensor and vector together, i.e. matrix-vector product. The tensor and vector may be of different types.

Definition at line 1023 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;
}
template<typename T >
template<typename Scalar >
const TypeTensor< T > & libMesh::TypeTensor< T >::operator*= ( const Scalar  factor) [inline, inherited]

Multiply this tensor by a number, i.e. scale.

Definition at line 880 of file type_tensor.h.

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

  return *this;
}
template<typename T >
template<typename T2 >
TypeTensor< typename CompareTypes< T, T2 >::supertype > libMesh::TypeTensor< T >::operator+ ( const TypeTensor< T2 > &  p) const [inline, inherited]

Add two tensors.

Definition at line 660 of file type_tensor.h.

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

{

#if LIBMESH_DIM == 1
  return TypeTensor(_coords[0] + p._coords[0]);
#endif

#if LIBMESH_DIM == 2
  return TypeTensor(_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(_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

}
template<typename T >
template<typename T2 >
const TypeTensor< T > & libMesh::TypeTensor< T >::operator+= ( const TypeTensor< T2 > &  p) [inline, inherited]

Add to this tensor.

Definition at line 694 of file type_tensor.h.

{
  this->add (p);

  return *this;
}
template<typename T >
template<typename T2 >
TypeTensor< typename CompareTypes< T, T2 >::supertype > libMesh::TypeTensor< T >::operator- ( const TypeTensor< T2 > &  p) const [inline, inherited]

Subtract two tensors.

Definition at line 730 of file type_tensor.h.

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

{

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

#if LIBMESH_DIM == 2
  return TypeTensor(_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(_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

}
template<typename T >
TypeTensor< T > libMesh::TypeTensor< T >::operator- ( ) const [inline, inherited]

Return the opposite of a tensor

Definition at line 797 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

}
template<typename T >
template<typename T2 >
const TypeTensor< T > & libMesh::TypeTensor< T >::operator-= ( const TypeTensor< T2 > &  p) [inline, inherited]

Subtract from this tensor.

Definition at line 764 of file type_tensor.h.

{
  this->subtract (p);

  return *this;
}
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, inherited]

Divide a tensor by a number, i.e. scale.

Definition at line 897 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

}
template<typename T >
const TypeTensor< T > & libMesh::TypeTensor< T >::operator/= ( const T  factor) [inline, inherited]

Divide this tensor by a number, i.e. scale.

Definition at line 1006 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;
}
template<>
bool libMesh::TypeTensor< Real >::operator< ( const TypeTensor< Real > &  rhs) const [inherited]

Definition at line 113 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;
}
template<>
bool libMesh::TypeTensor< Complex >::operator< ( const TypeTensor< Complex > &  rhs) const [inherited]

Definition at line 146 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).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;
}
template<typename T>
bool libMesh::TypeTensor< T >::operator< ( const TypeTensor< T > &  rhs) const [inherited]
Returns:
true if this tensor is "less" than another. Useful for sorting.
template<typename T>
template<typename Scalar >
boostcopy::enable_if_c< ScalarTraits<Scalar>::value, TensorValue&>::type libMesh::TensorValue< T >::operator= ( const Scalar &  libmesh_dbg_varp) [inline]

Assignment-from-scalar operator. Used only to zero out tensors.

Definition at line 131 of file tensor_value.h.

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

  { libmesh_assert_equal_to (p, Scalar(0)); this->zero(); return *this; }
template<typename T >
bool libMesh::TypeTensor< T >::operator== ( const TypeTensor< T > &  rhs) const [inline, inherited]
Returns:
true if two tensors are equal valued.

Definition at line 1142 of file type_tensor.h.

References libMesh::TypeTensor< T >::_coords, std::abs(), 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

}
template<>
bool libMesh::TypeTensor< Real >::operator> ( const TypeTensor< Real > &  rhs) const [inherited]

Definition at line 129 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;
}
template<>
bool libMesh::TypeTensor< Complex >::operator> ( const TypeTensor< Complex > &  rhs) const [inherited]

Definition at line 166 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).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;
}
template<typename T>
bool libMesh::TypeTensor< T >::operator> ( const TypeTensor< T > &  rhs) const [inherited]
Returns:
true if this tensor is "greater" than another.
template<typename T >
void libMesh::TypeTensor< T >::print ( std::ostream &  os = libMesh::out) const [inherited]

Formatted print, by default to libMesh::out.

Definition at line 39 of file type_tensor.C.

{
#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
}
template<typename T >
TypeVector< T > libMesh::TypeTensor< T >::row ( const unsigned int  r) [inline, inherited]

Return one row of the tensor as a TypeVector.

Definition at line 646 of file type_tensor.h.

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

{
  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;
}
template<typename T >
Real libMesh::TypeTensor< T >::size ( ) const [inline, inherited]

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

Definition at line 1071 of file type_tensor.h.

Referenced by libMesh::System::calculate_norm().

{
  return std::sqrt(this->size_sq());
}
template<typename T >
Real libMesh::TypeTensor< T >::size_sq ( ) const [inline, inherited]

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

Definition at line 1130 of file type_tensor.h.

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

Referenced by libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::System::calculate_norm(), 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;
}
template<typename T >
ConstTypeTensorColumn< T > libMesh::TypeTensor< T >::slice ( const unsigned int  i) const [inline, inherited]

Return a proxy for the $ i^{th} $ column of the tensor.

Definition at line 626 of file type_tensor.h.

{
  libmesh_assert_less (i, LIBMESH_DIM);
  return ConstTypeTensorColumn<T>(*this, i);
}
template<typename T >
TypeTensorColumn< T > libMesh::TypeTensor< T >::slice ( const unsigned int  i) [inline, inherited]

Return a writeable proxy for the $ i^{th} $ column of the tensor.

Definition at line 636 of file type_tensor.h.

{
  libmesh_assert_less (i, LIBMESH_DIM);
  return TypeTensorColumn<T>(*this, i);
}
template<typename T >
template<typename T2 >
void libMesh::TypeTensor< T >::subtract ( const TypeTensor< T2 > &  p) [inline, inherited]

Subtract from this tensor without creating a temporary.

Definition at line 776 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];
}
template<typename T >
template<typename T2 >
void libMesh::TypeTensor< T >::subtract_scaled ( const TypeTensor< T2 > &  p,
const T  factor 
) [inline, inherited]

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

Definition at line 787 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];
}
template<typename T >
T libMesh::TypeTensor< T >::tr ( ) const [inline, inherited]

Returns the trace of the tensor.

Definition at line 1103 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
}
template<typename T >
TypeTensor< T > libMesh::TypeTensor< T >::transpose ( ) const [inline, inherited]

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

Definition at line 932 of file type_tensor.h.

{
#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
}
template<typename T >
void libMesh::TypeTensor< T >::write_unformatted ( std::ostream &  out,
const bool  newline = true 
) const [inherited]

Unformatted print to the stream out. Simply prints the elements of the tensor separated by spaces and newlines.

Definition at line 83 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';
}
template<typename T >
void libMesh::TypeTensor< T >::zero ( ) [inline, inherited]

Zero the tensor in any dimension.

Definition at line 1120 of file type_tensor.h.

Referenced by 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

template<typename T>
std::ostream& operator<< ( std::ostream &  os,
const TypeTensor< T > &  t 
) [friend, inherited]

Formatted print as above but allows you to do std::cout << t << std::endl;

Definition at line 341 of file type_tensor.h.

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

Member Data Documentation

template<typename T>
T libMesh::TypeTensor< T >::_coords[LIBMESH_DIM *LIBMESH_DIM] [inherited]

The coordinates of the TypeTensor

Definition at line 358 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 >::subtract(), libMesh::TypeTensor< T >::subtract_scaled(), and libMesh::TypeTensor< T >::TypeTensor().

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