libMesh
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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 >:
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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
 
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< T > 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
 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...
 
Real size () const
 
Real norm () const
 
Real size_sq () const
 
Real norm_sq () 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, const bool newline=true) const
 Unformatted print to the stream out. More...
 

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 32 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 121 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 116 of file type_tensor.h.

Constructor & Destructor Documentation

◆ TypeTensor() [1/7]

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

Empty constructor.

Gives the tensor 0 in LIBMESH_DIM dimensions.

Definition at line 504 of file type_tensor.h.

505 {
506  _coords[0] = 0;
507 
508 #if LIBMESH_DIM > 1
509  _coords[1] = 0;
510  _coords[2] = 0;
511  _coords[3] = 0;
512 #endif
513 
514 #if LIBMESH_DIM > 2
515  _coords[4] = 0;
516  _coords[5] = 0;
517  _coords[6] = 0;
518  _coords[7] = 0;
519  _coords[8] = 0;
520 #endif
521 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ 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 
)
explicitprotected

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 527 of file type_tensor.h.

536 {
537  _coords[0] = xx;
538 
539 #if LIBMESH_DIM == 2
540  _coords[1] = xy;
541  _coords[2] = yx;
542  _coords[3] = yy;
543 #endif
544 
545 #if LIBMESH_DIM == 3
546  _coords[1] = xy;
547  _coords[2] = xz;
548  _coords[3] = yx;
549  _coords[4] = yy;
550  _coords[5] = yz;
551  _coords[6] = zx;
552  _coords[7] = zy;
553  _coords[8] = zz;
554 #endif
555 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ 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 
)
explicitprotected

Constructor-from-Scalar.

Definition at line 561 of file type_tensor.h.

572 {
573  _coords[0] = xx;
574 
575 #if LIBMESH_DIM == 2
576  _coords[1] = xy;
577  _coords[2] = yx;
578  _coords[3] = yy;
579 #endif
580 
581 #if LIBMESH_DIM == 3
582  _coords[1] = xy;
583  _coords[2] = xz;
584  _coords[3] = yx;
585  _coords[4] = yy;
586  _coords[5] = yz;
587  _coords[6] = zx;
588  _coords[7] = zy;
589  _coords[8] = zz;
590 #endif
591 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ 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 608 of file type_tensor.h.

609 {
610  libmesh_assert_equal_to (LIBMESH_DIM, 1);
611  _coords[0] = vx(0);
612 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ 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 616 of file type_tensor.h.

618 {
619  libmesh_assert_equal_to (LIBMESH_DIM, 2);
620  _coords[0] = vx(0);
621  _coords[1] = vx(1);
622  _coords[2] = vy(0);
623  _coords[3] = vy(1);
624 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ 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 628 of file type_tensor.h.

631 {
632  libmesh_assert_equal_to (LIBMESH_DIM, 3);
633  _coords[0] = vx(0);
634  _coords[1] = vx(1);
635  _coords[2] = vx(2);
636  _coords[3] = vy(0);
637  _coords[4] = vy(1);
638  _coords[5] = vy(2);
639  _coords[6] = vz(0);
640  _coords[7] = vz(1);
641  _coords[8] = vz(2);
642 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ TypeTensor() [7/7]

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

Copy-constructor.

Definition at line 598 of file type_tensor.h.

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

599 {
600  // copy the nodes from vector p to me
601  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
602  _coords[i] = p._coords[i];
603 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ ~TypeTensor()

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

Destructor.

Definition at line 649 of file type_tensor.h.

650 {
651 }

Member Function Documentation

◆ add()

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

Add to this tensor without creating a temporary.

Definition at line 787 of file type_tensor.h.

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

788 {
789  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
790  _coords[i] += p._coords[i];
791 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ add_scaled()

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

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

Definition at line 798 of file type_tensor.h.

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

799 {
800  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
801  _coords[i] += factor*p._coords[i];
802 
803 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ assign()

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

Assign to this tensor without creating a temporary.

Definition at line 658 of file type_tensor.h.

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

659 {
660  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
661  _coords[i] = p._coords[i];
662 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ contract()

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

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 1194 of file type_tensor.h.

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

Referenced by libMesh::TensorTools::inner_product().

1195 {
1196  typename CompareTypes<T,T2>::supertype sum = 0.;
1197  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
1198  sum += _coords[i]*t._coords[i];
1199  return sum;
1200 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ det()

template<typename T >
T libMesh::TypeTensor< T >::det ( ) const
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 1227 of file type_tensor.h.

1228 {
1229 #if LIBMESH_DIM == 1
1230  return _coords[0];
1231 #endif
1232 
1233 #if LIBMESH_DIM == 2
1234  return (_coords[0] * _coords[3]
1235  - _coords[1] * _coords[2]);
1236 #endif
1237 
1238 #if LIBMESH_DIM == 3
1239  return (_coords[0] * _coords[4] * _coords[8]
1240  + _coords[1] * _coords[5] * _coords[6]
1241  + _coords[2] * _coords[3] * _coords[7]
1242  - _coords[0] * _coords[5] * _coords[7]
1243  - _coords[1] * _coords[3] * _coords[8]
1244  - _coords[2] * _coords[4] * _coords[6]);
1245 #endif
1246 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ inverse()

template<typename T >
TypeTensor< T > libMesh::TypeTensor< T >::inverse ( ) const
Returns
The inverse of this tensor as an independent object.

Definition at line 1027 of file type_tensor.h.

1028 {
1029 #if LIBMESH_DIM == 1
1030  if (_coords[0] == static_cast<T>(0.))
1031  libmesh_convergence_failure();
1032  return TypeTensor(1. / _coords[0]);
1033 #endif
1034 
1035 #if LIBMESH_DIM == 2
1036  // Get convenient reference to this.
1037  const TypeTensor<T> & A = *this;
1038 
1039  // Use temporary variables, avoid multiple accesses
1040  T a = A(0,0), b = A(0,1),
1041  c = A(1,0), d = A(1,1);
1042 
1043  // Make sure det = ad - bc is not zero
1044  T my_det = a*d - b*c;
1045 
1046  if (my_det == static_cast<T>(0.))
1047  libmesh_convergence_failure();
1048 
1049  return TypeTensor(d/my_det, -b/my_det, -c/my_det, a/my_det);
1050 #endif
1051 
1052 #if LIBMESH_DIM == 3
1053  // Get convenient reference to this.
1054  const TypeTensor<T> & A = *this;
1055 
1056  T a11 = A(0,0), a12 = A(0,1), a13 = A(0,2),
1057  a21 = A(1,0), a22 = A(1,1), a23 = A(1,2),
1058  a31 = A(2,0), a32 = A(2,1), a33 = A(2,2);
1059 
1060  T my_det = a11*(a33*a22-a32*a23) - a21*(a33*a12-a32*a13) + a31*(a23*a12-a22*a13);
1061 
1062  if (my_det == static_cast<T>(0.))
1063  libmesh_convergence_failure();
1064 
1065  // Inline comment characters are for lining up columns.
1066  return TypeTensor( (a33*a22-a32*a23)/my_det, -(a33*a12-a32*a13)/my_det, (a23*a12-a22*a13)/my_det,
1067  -(a33*a21-a31*a23)/my_det, (a33*a11-a31*a13)/my_det, -(a23*a11-a21*a13)/my_det,
1068  (a32*a21-a31*a22)/my_det, -(a32*a11-a31*a12)/my_det, (a22*a11-a21*a12)/my_det);
1069 #endif
1070 }
libMesh::TypeTensor::TypeTensor
TypeTensor()
Empty constructor.
Definition: type_tensor.h:504
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ norm()

template<typename T >
Real libMesh::TypeTensor< T >::norm ( ) const
Returns
The Frobenius norm of the tensor, i.e. the square-root of the sum of the elements squared.

Definition at line 1218 of file type_tensor.h.

References libMesh::TensorTools::norm_sq().

1219 {
1220  return std::sqrt(this->norm_sq());
1221 }
libMesh::TypeTensor::norm_sq
Real norm_sq() const
Definition: type_tensor.h:1289

◆ norm_sq()

template<typename T >
Real libMesh::TypeTensor< T >::norm_sq ( ) const
Returns
The Frobenius norm of the tensor squared, i.e. sum of the element magnitudes squared.

Definition at line 1289 of file type_tensor.h.

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

1290 {
1291  Real sum = 0.;
1292  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
1293  sum += TensorTools::norm_sq(_coords[i]);
1294  return sum;
1295 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:131

◆ operator()() [1/2]

template<typename T >
const T & libMesh::TypeTensor< T >::operator() ( const unsigned int  i,
const unsigned int  j 
) const
Returns
A const reference to the (i,j) entry of the tensor.

Definition at line 668 of file type_tensor.h.

670 {
671  libmesh_assert_less (i, 3);
672  libmesh_assert_less (j, 3);
673 
674 #if LIBMESH_DIM < 3
675  const static T my_zero = 0;
676  if (i >= LIBMESH_DIM || j >= LIBMESH_DIM)
677  return my_zero;
678 #endif
679 
680  return _coords[i*LIBMESH_DIM+j];
681 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ operator()() [2/2]

template<typename T >
T & libMesh::TypeTensor< T >::operator() ( const unsigned int  i,
const unsigned int  j 
)
Returns
A writable reference to the (i,j) entry of the tensor.

Definition at line 687 of file type_tensor.h.

689 {
690 #if LIBMESH_DIM < 3
691 
692  if (i >= LIBMESH_DIM || j >= LIBMESH_DIM)
693  libmesh_error_msg("ERROR: You are assigning to a tensor component that is out of range for the compiled LIBMESH_DIM!");
694 
695 #endif
696 
697  libmesh_assert_less (i, LIBMESH_DIM);
698  libmesh_assert_less (j, LIBMESH_DIM);
699 
700  return _coords[i*LIBMESH_DIM+j];
701 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ 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

Multiply this tensor by a scalar value.

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

Definition at line 912 of file type_tensor.h.

915 {
916  typedef decltype((*this)(0, 0) * factor) TS;
917 
918 
919 #if LIBMESH_DIM == 1
920  return TypeTensor<TS>(_coords[0]*factor);
921 #endif
922 
923 #if LIBMESH_DIM == 2
924  return TypeTensor<TS>(_coords[0]*factor,
925  _coords[1]*factor,
926  _coords[2]*factor,
927  _coords[3]*factor);
928 #endif
929 
930 #if LIBMESH_DIM == 3
931  return TypeTensor<TS>(_coords[0]*factor,
932  _coords[1]*factor,
933  _coords[2]*factor,
934  _coords[3]*factor,
935  _coords[4]*factor,
936  _coords[5]*factor,
937  _coords[6]*factor,
938  _coords[7]*factor,
939  _coords[8]*factor);
940 #endif
941 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ operator*() [2/3]

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

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 1159 of file type_tensor.h.

1160 {
1161  TypeTensor<T> returnval;
1162  for (unsigned int i=0; i<LIBMESH_DIM; i++)
1163  for (unsigned int j=0; j<LIBMESH_DIM; j++)
1164  for (unsigned int k=0; k<LIBMESH_DIM; k++)
1165  returnval(i,j) += (*this)(i,k)*p(k,j);
1166 
1167  return returnval;
1168 }

◆ operator*() [3/3]

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

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 1144 of file type_tensor.h.

1145 {
1146  TypeVector<typename CompareTypes<T,T2>::supertype> returnval;
1147  for (unsigned int i=0; i<LIBMESH_DIM; i++)
1148  for (unsigned int j=0; j<LIBMESH_DIM; j++)
1149  returnval(i) += (*this)(i,j)*p(j);
1150 
1151  return returnval;
1152 }

◆ 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)

Multiply this tensor by a scalar value in place.

Returns
A reference to *this.

Definition at line 259 of file type_tensor.h.

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

260  {
261  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
262  _coords[i] *= factor;
263 
264  return *this;
265  }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ operator*=() [2/2]

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

Multiply this tensor by a tensor value in place.

Returns
A reference to *this

Definition at line 1173 of file type_tensor.h.

1174 {
1175  TypeTensor<T> temp;
1176  for (unsigned int i=0; i<LIBMESH_DIM; i++)
1177  for (unsigned int j=0; j<LIBMESH_DIM; j++)
1178  for (unsigned int k=0; k<LIBMESH_DIM; k++)
1179  temp(i,j) += (*this)(i,k)*p(k,j);
1180 
1181  this->assign(temp);
1182  return *this;
1183 }
libMesh::TypeTensor::assign
void assign(const TypeTensor< T2 > &)
Assign to this tensor without creating a temporary.
Definition: type_tensor.h:658

◆ operator+()

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

Add another tensor to this tensor.

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

Definition at line 741 of file type_tensor.h.

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

742 {
743 
744 #if LIBMESH_DIM == 1
745  return TypeTensor(_coords[0] + p._coords[0]);
746 #endif
747 
748 #if LIBMESH_DIM == 2
749  return TypeTensor(_coords[0] + p._coords[0],
750  _coords[1] + p._coords[1],
751  0.,
752  _coords[2] + p._coords[2],
753  _coords[3] + p._coords[3]);
754 #endif
755 
756 #if LIBMESH_DIM == 3
757  return TypeTensor(_coords[0] + p._coords[0],
758  _coords[1] + p._coords[1],
759  _coords[2] + p._coords[2],
760  _coords[3] + p._coords[3],
761  _coords[4] + p._coords[4],
762  _coords[5] + p._coords[5],
763  _coords[6] + p._coords[6],
764  _coords[7] + p._coords[7],
765  _coords[8] + p._coords[8]);
766 #endif
767 
768 }
libMesh::TypeTensor::TypeTensor
TypeTensor()
Empty constructor.
Definition: type_tensor.h:504
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ operator+=()

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

Add to this tensor.

Returns
A reference to *this.

Definition at line 775 of file type_tensor.h.

776 {
777  this->add (p);
778 
779  return *this;
780 }
libMesh::TypeTensor::add
void add(const TypeTensor< T2 > &)
Add to this tensor without creating a temporary.
Definition: type_tensor.h:787

◆ operator-() [1/2]

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

Subtract a tensor from this tensor.

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

Definition at line 811 of file type_tensor.h.

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

812 {
813 
814 #if LIBMESH_DIM == 1
815  return TypeTensor(_coords[0] - p._coords[0]);
816 #endif
817 
818 #if LIBMESH_DIM == 2
819  return TypeTensor(_coords[0] - p._coords[0],
820  _coords[1] - p._coords[1],
821  0.,
822  _coords[2] - p._coords[2],
823  _coords[3] - p._coords[3]);
824 #endif
825 
826 #if LIBMESH_DIM == 3
827  return TypeTensor(_coords[0] - p._coords[0],
828  _coords[1] - p._coords[1],
829  _coords[2] - p._coords[2],
830  _coords[3] - p._coords[3],
831  _coords[4] - p._coords[4],
832  _coords[5] - p._coords[5],
833  _coords[6] - p._coords[6],
834  _coords[7] - p._coords[7],
835  _coords[8] - p._coords[8]);
836 #endif
837 
838 }
libMesh::TypeTensor::TypeTensor
TypeTensor()
Empty constructor.
Definition: type_tensor.h:504
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ operator-() [2/2]

template<typename T >
TypeTensor< T > libMesh::TypeTensor< T >::operator- ( ) const
Returns
The negative of this tensor in a separate copy.

Definition at line 878 of file type_tensor.h.

879 {
880 
881 #if LIBMESH_DIM == 1
882  return TypeTensor(-_coords[0]);
883 #endif
884 
885 #if LIBMESH_DIM == 2
886  return TypeTensor(-_coords[0],
887  -_coords[1],
888  -_coords[2],
889  -_coords[3]);
890 #endif
891 
892 #if LIBMESH_DIM == 3
893  return TypeTensor(-_coords[0],
894  -_coords[1],
895  -_coords[2],
896  -_coords[3],
897  -_coords[4],
898  -_coords[5],
899  -_coords[6],
900  -_coords[7],
901  -_coords[8]);
902 #endif
903 
904 }
libMesh::TypeTensor::TypeTensor
TypeTensor()
Empty constructor.
Definition: type_tensor.h:504
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ operator-=()

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

Subtract from this tensor.

Returns
A reference to *this.

Definition at line 845 of file type_tensor.h.

846 {
847  this->subtract (p);
848 
849  return *this;
850 }
libMesh::TypeTensor::subtract
void subtract(const TypeTensor< T2 > &)
Subtract from this tensor without creating a temporary.
Definition: type_tensor.h:857

◆ 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

Divide each entry of this tensor by a scalar value.

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

Definition at line 962 of file type_tensor.h.

963 {
964  libmesh_assert_not_equal_to (factor, static_cast<T>(0.));
965 
966  typedef typename CompareTypes<T, Scalar>::supertype TS;
967 
968 #if LIBMESH_DIM == 1
969  return TypeTensor<TS>(_coords[0]/factor);
970 #endif
971 
972 #if LIBMESH_DIM == 2
973  return TypeTensor<TS>(_coords[0]/factor,
974  _coords[1]/factor,
975  _coords[2]/factor,
976  _coords[3]/factor);
977 #endif
978 
979 #if LIBMESH_DIM == 3
980  return TypeTensor<TS>(_coords[0]/factor,
981  _coords[1]/factor,
982  _coords[2]/factor,
983  _coords[3]/factor,
984  _coords[4]/factor,
985  _coords[5]/factor,
986  _coords[6]/factor,
987  _coords[7]/factor,
988  _coords[8]/factor);
989 #endif
990 
991 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ operator/=()

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

Divide each entry of this tensor by a scalar value.

Returns
A reference to *this.

Definition at line 1127 of file type_tensor.h.

1128 {
1129  libmesh_assert_not_equal_to (factor, static_cast<T>(0.));
1130 
1131  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
1132  _coords[i] /= factor;
1133 
1134  return *this;
1135 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ operator<()

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)

Assignment-from-scalar operator.

Used only to zero out vectors.

Returns
A reference to *this.

Definition at line 149 of file type_tensor.h.

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

150  { libmesh_assert_equal_to (p, Scalar(0)); this->zero(); return *this; }
libMesh::TypeTensor::zero
void zero()
Set all entries of the tensor to 0.
Definition: type_tensor.h:1267

◆ operator==()

template<typename T >
bool libMesh::TypeTensor< T >::operator== ( const TypeTensor< T > &  rhs) const
Returns
true if two tensors are equal, false otherwise.

Definition at line 1301 of file type_tensor.h.

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

1302 {
1303 #if LIBMESH_DIM == 1
1304  return (std::abs(_coords[0] - rhs._coords[0])
1305  < TOLERANCE);
1306 #endif
1307 
1308 #if LIBMESH_DIM == 2
1309  return ((std::abs(_coords[0] - rhs._coords[0]) +
1310  std::abs(_coords[1] - rhs._coords[1]) +
1311  std::abs(_coords[2] - rhs._coords[2]) +
1312  std::abs(_coords[3] - rhs._coords[3]))
1313  < 4.*TOLERANCE);
1314 #endif
1315 
1316 #if LIBMESH_DIM == 3
1317  return ((std::abs(_coords[0] - rhs._coords[0]) +
1318  std::abs(_coords[1] - rhs._coords[1]) +
1319  std::abs(_coords[2] - rhs._coords[2]) +
1320  std::abs(_coords[3] - rhs._coords[3]) +
1321  std::abs(_coords[4] - rhs._coords[4]) +
1322  std::abs(_coords[5] - rhs._coords[5]) +
1323  std::abs(_coords[6] - rhs._coords[6]) +
1324  std::abs(_coords[7] - rhs._coords[7]) +
1325  std::abs(_coords[8] - rhs._coords[8]))
1326  < 9.*TOLERANCE);
1327 #endif
1328 
1329 }
std::abs
double abs(double a)
Definition: libmesh_augment_std_namespace.h:59
libMesh::TOLERANCE
static const Real TOLERANCE
Definition: libmesh_common.h:139
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ operator>()

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.

◆ row()

template<typename T >
TypeVector< T > libMesh::TypeTensor< T >::row ( const unsigned int  r) const
Returns
A copy of one row of the tensor as a TypeVector.

Definition at line 727 of file type_tensor.h.

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

728 {
729  TypeVector<T> return_vector;
730 
731  for (unsigned int j=0; j<LIBMESH_DIM; j++)
732  return_vector._coords[j] = _coords[r*LIBMESH_DIM + j];
733 
734  return return_vector;
735 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ size()

template<typename T >
Real libMesh::TypeTensor< T >::size ( ) const
Returns
The Frobenius norm of the tensor, i.e. the square-root of the sum of the elements squared.
Deprecated:
Use the norm() function instead.

Definition at line 1207 of file type_tensor.h.

1208 {
1209  libmesh_deprecated();
1210  return this->norm();
1211 }
libMesh::TypeTensor::norm
Real norm() const
Definition: type_tensor.h:1218

◆ size_sq()

template<typename T >
Real libMesh::TypeTensor< T >::size_sq ( ) const
Returns
The Frobenius norm of the tensor squared, i.e. sum of the element magnitudes squared.
Deprecated:
Use the norm_sq() function instead.

Definition at line 1278 of file type_tensor.h.

References libMesh::TensorTools::norm_sq().

1279 {
1280  libmesh_deprecated();
1281  return this->norm_sq();
1282 }
libMesh::TypeTensor::norm_sq
Real norm_sq() const
Definition: type_tensor.h:1289

◆ slice() [1/2]

template<typename T >
ConstTypeTensorColumn< T > libMesh::TypeTensor< T >::slice ( const unsigned int  i) const
Returns
A proxy for the $ i^{th} $ column of the tensor.

Definition at line 707 of file type_tensor.h.

708 {
709  libmesh_assert_less (i, LIBMESH_DIM);
710  return ConstTypeTensorColumn<T>(*this, i);
711 }

◆ slice() [2/2]

template<typename T >
TypeTensorColumn< T > libMesh::TypeTensor< T >::slice ( const unsigned int  i)
Returns
A writable proxy for the $ i^{th} $ column of the tensor.

Definition at line 717 of file type_tensor.h.

718 {
719  libmesh_assert_less (i, LIBMESH_DIM);
720  return TypeTensorColumn<T>(*this, i);
721 }

◆ solve()

template<typename T >
void libMesh::TypeTensor< T >::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.

Returns
The solution in the x vector.

Definition at line 1076 of file type_tensor.h.

1077 {
1078 #if LIBMESH_DIM == 1
1079  if (_coords[0] == static_cast<T>(0.))
1080  libmesh_convergence_failure();
1081  x(0) = b(0) / _coords[0];
1082 #endif
1083 
1084 #if LIBMESH_DIM == 2
1085  T my_det = _coords[0]*_coords[3] - _coords[1]*_coords[2];
1086 
1087  if (my_det == static_cast<T>(0.))
1088  libmesh_convergence_failure();
1089 
1090  T my_det_inv = 1./my_det;
1091 
1092  x(0) = my_det_inv*( _coords[3]*b(0) - _coords[1]*b(1));
1093  x(1) = my_det_inv*(-_coords[2]*b(0) + _coords[0]*b(1));
1094 #endif
1095 
1096 #if LIBMESH_DIM == 3
1097  T my_det =
1098  // a11*(a33 *a22 - a32 *a23)
1099  _coords[0]*(_coords[8]*_coords[4] - _coords[7]*_coords[5])
1100  // -a21*(a33 *a12 - a32 *a13)
1101  -_coords[3]*(_coords[8]*_coords[1] - _coords[7]*_coords[2]) +
1102  // +a31*(a23 *a12 - a22 *a13)
1103  +_coords[6]*(_coords[5]*_coords[1] - _coords[4]*_coords[2]);
1104 
1105  if (my_det == static_cast<T>(0.))
1106  libmesh_convergence_failure();
1107 
1108  T my_det_inv = 1./my_det;
1109  x(0) = my_det_inv*((_coords[8]*_coords[4] - _coords[7]*_coords[5])*b(0) -
1110  (_coords[8]*_coords[1] - _coords[7]*_coords[2])*b(1) +
1111  (_coords[5]*_coords[1] - _coords[4]*_coords[2])*b(2));
1112 
1113  x(1) = my_det_inv*((_coords[6]*_coords[5] - _coords[8]*_coords[3])*b(0) +
1114  (_coords[8]*_coords[0] - _coords[6]*_coords[2])*b(1) -
1115  (_coords[5]*_coords[0] - _coords[3]*_coords[2])*b(2));
1116 
1117  x(2) = my_det_inv*((_coords[7]*_coords[3] - _coords[6]*_coords[4])*b(0) -
1118  (_coords[7]*_coords[0] - _coords[6]*_coords[1])*b(1) +
1119  (_coords[4]*_coords[0] - _coords[3]*_coords[1])*b(2));
1120 #endif
1121 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ subtract()

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

Subtract from this tensor without creating a temporary.

Definition at line 857 of file type_tensor.h.

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

858 {
859  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
860  _coords[i] -= p._coords[i];
861 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ subtract_scaled()

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

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

Definition at line 868 of file type_tensor.h.

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

869 {
870  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
871  _coords[i] -= factor*p._coords[i];
872 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ tr()

template<typename T >
T libMesh::TypeTensor< T >::tr ( ) const
Returns
The trace of the tensor.

Definition at line 1250 of file type_tensor.h.

1251 {
1252 #if LIBMESH_DIM == 1
1253  return _coords[0];
1254 #endif
1255 
1256 #if LIBMESH_DIM == 2
1257  return _coords[0] + _coords[3];
1258 #endif
1259 
1260 #if LIBMESH_DIM == 3
1261  return _coords[0] + _coords[4] + _coords[8];
1262 #endif
1263 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ transpose()

template<typename T >
TypeTensor< T > libMesh::TypeTensor< T >::transpose ( ) const
Returns
The transpose of this tensor (with complex numbers not conjugated).

Definition at line 997 of file type_tensor.h.

998 {
999 #if LIBMESH_DIM == 1
1000  return TypeTensor(_coords[0]);
1001 #endif
1002 
1003 #if LIBMESH_DIM == 2
1004  return TypeTensor(_coords[0],
1005  _coords[2],
1006  _coords[1],
1007  _coords[3]);
1008 #endif
1009 
1010 #if LIBMESH_DIM == 3
1011  return TypeTensor(_coords[0],
1012  _coords[3],
1013  _coords[6],
1014  _coords[1],
1015  _coords[4],
1016  _coords[7],
1017  _coords[2],
1018  _coords[5],
1019  _coords[8]);
1020 #endif
1021 }
libMesh::TypeTensor::TypeTensor
TypeTensor()
Empty constructor.
Definition: type_tensor.h:504
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

◆ write_unformatted()

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

Unformatted print to the stream out.

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

◆ zero()

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

Set all entries of the tensor to 0.

Definition at line 1267 of file type_tensor.h.

Referenced by libMesh::TensorValue< T >::operator=(), and libMesh::TypeTensor< T >::operator=().

1268 {
1269  for (unsigned int i=0; i<LIBMESH_DIM*LIBMESH_DIM; i++)
1270  _coords[i] = 0.;
1271 }
libMesh::TypeTensor::_coords
T _coords[LIBMESH_DIM *LIBMESH_DIM]
The coordinates of the TypeTensor.
Definition: type_tensor.h:438

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 421 of file type_tensor.h.

422  {
423  t.print(os);
424  return os;
425  }

◆ TypeTensor

template<typename T>
template<typename T2 >
friend class TypeTensor
friend

Definition at line 51 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 438 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().

The documentation for this class was generated from the following files:
Generated on Thu Dec 13 2018 19:34:09 for libMesh by   doxygen 1.8.14