libMesh::DenseSubMatrix< T > Class Template Reference

Defines a dense submatrix for use in Finite Element-type computations. More...

#include <dense_submatrix.h>

Inheritance diagram for libMesh::DenseSubMatrix< T >:

Public Member Functions
	DenseSubMatrix (DenseMatrix< T > &new_parent, const unsigned int ioff=0, const unsigned int joff=0, const unsigned int m=0, const unsigned int n=0)
	Constructor.
	DenseSubMatrix (DenseSubMatrix &&)=default
	The 5 special functions can be defaulted for this class, as it does not manage any memory itself.
	DenseSubMatrix (const DenseSubMatrix &)=default
DenseSubMatrix &	operator= (const DenseSubMatrix &)=default
DenseSubMatrix &	operator= (DenseSubMatrix &&)=default
virtual	~DenseSubMatrix ()=default
DenseMatrix< T > &	parent ()
virtual void	zero () override final
	Set every element in the matrix to 0.
T	operator() (const unsigned int i, const unsigned int j) const
T &	operator() (const unsigned int i, const unsigned int j)
virtual T	el (const unsigned int i, const unsigned int j) const override final
virtual T &	el (const unsigned int i, const unsigned int j) override final
virtual void	left_multiply (const DenseMatrixBase< T > &M2) override final
	Performs the operation: (*this) <- M2 * (*this)
virtual void	right_multiply (const DenseMatrixBase< T > &M3) override final
	Performs the operation: (*this) <- (*this) * M3.
void	reposition (const unsigned int ioff, const unsigned int joff, const unsigned int new_m, const unsigned int new_n)
	Changes the location of the submatrix in the parent matrix.
unsigned int	i_off () const
unsigned int	j_off () const
void	condense (const unsigned int i, const unsigned int j, const T val, DenseSubVector< T > &rhs)
	Condense-out the (i,j) entry of the matrix, forcing it to take on the value val.
unsigned int	m () const
unsigned int	n () const
void	print (std::ostream &os=libMesh::out) const
	Pretty-print the matrix, by default to libMesh::out.
void	print_scientific (std::ostream &os, unsigned precision=8) const
	Prints the matrix entries with more decimal places in scientific notation.
template<typename T2 , typename T3 >
std::enable_if< ScalarTraits< T2 >::value, void >::type	add (const T2 factor, const DenseMatrixBase< T3 > &mat)
	Adds factor to every element in the matrix.
DenseVector< T >	diagonal () const
	Return the matrix diagonal.

Protected Member Functions
void	condense (const unsigned int i, const unsigned int j, const T val, DenseVectorBase< T > &rhs)
	Condense-out the (i,j) entry of the matrix, forcing it to take on the value val.

Static Protected Member Functions
static void	multiply (DenseMatrixBase< T > &M1, const DenseMatrixBase< T > &M2, const DenseMatrixBase< T > &M3)
	Helper function - Performs the computation M1 = M2 * M3 where: M1 = (m x n) M2 = (m x p) M3 = (p x n)

Protected Attributes
unsigned int	_m
	The row dimension.
unsigned int	_n
	The column dimension.

Private Attributes
DenseMatrix< T > &	_parent_matrix
	The parent matrix that contains this submatrix.
unsigned int	_i_off
	The row offset into the parent matrix.
unsigned int	_j_off
	The column offset into the parent matrix.

Detailed Description

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

Defines a dense submatrix for use in Finite Element-type computations.

Useful for storing element stiffness matrices before summation into a global matrix, particularly when you have systems of equations. All overridden virtual functions are documented in dense_matrix_base.h.

Author

Benjamin S. Kirk

Date

2003

Definition at line 45 of file dense_submatrix.h.

Constructor & Destructor Documentation

DenseSubMatrix() [1/3]

template<typename T >

libMesh::DenseSubMatrix< T >::DenseSubMatrix ( DenseMatrix< T > &  new_parent, const unsigned int  ioff = 0, const unsigned int  joff = 0, const unsigned int  m = 0, const unsigned int  n = 0  )

inline

Constructor.

Creates a dense submatrix of the matrix parent. The submatrix has dimensions \((m \times n)\), and the \((0,0)\) entry of the submatrix is located at the \((ioff,joff)\) location in the parent matrix.

Definition at line 159 of file dense_submatrix.h.

                                                            :
  DenseMatrixBase<T>(new_m,new_n),
  _parent_matrix(new_parent)
{
  this->reposition (ioff, joff, new_m, new_n);
}

References libMesh::DenseSubMatrix< T >::reposition().

DenseSubMatrix() [2/3]

template<typename T >

libMesh::DenseSubMatrix< T >::DenseSubMatrix ( DenseSubMatrix< T > &&  )

default

The 5 special functions can be defaulted for this class, as it does not manage any memory itself.

DenseSubMatrix() [3/3]

template<typename T >

libMesh::DenseSubMatrix< T >::DenseSubMatrix ( const DenseSubMatrix< T > &  )

default

~DenseSubMatrix()

template<typename T >

virtual libMesh::DenseSubMatrix< T >::~DenseSubMatrix ( )

virtualdefault

Member Function Documentation

add()

template<typename T >

template<typename T2 , typename T3 >

std::enable_if< ScalarTraits< T2 >::value, void >::type libMesh::DenseMatrixBase< T >::add ( const T2  factor, const DenseMatrixBase< T3 > &  mat  )

inlineinherited

Adds factor to every element in the matrix.

This should only work if T += T2 * T3 is valid C++ and if T2 is scalar. Return type is void

Definition at line 195 of file dense_matrix_base.h.

{
  libmesh_assert_equal_to (this->m(), mat.m());
  libmesh_assert_equal_to (this->n(), mat.n());
 
  for (auto j : make_range(this->n()))
    for (auto i : make_range(this->m()))
      this->el(i,j) += factor*mat.el(i,j);
}

References libMesh::DenseMatrixBase< T >::el(), libMesh::DenseMatrixBase< T >::m(), libMesh::make_range(), and libMesh::DenseMatrixBase< T >::n().

condense() [1/2]

template<typename T >

void libMesh::DenseSubMatrix< T >::condense ( const unsigned int  i, const unsigned int  j, const T  val, DenseSubVector< T > &  rhs  )

inline

Condense-out the (i,j) entry of the matrix, forcing it to take on the value val.

This is useful in numerical simulations for applying boundary conditions. Preserves the symmetry of the matrix.

Definition at line 126 of file dense_submatrix.h.

  {
    this->parent().condense(this->i_off()+i,
                            this->j_off()+j,
                            val, rhs.parent());
  }

References libMesh::DenseSubMatrix< T >::i_off(), libMesh::DenseSubMatrix< T >::j_off(), libMesh::DenseSubMatrix< T >::parent(), and libMesh::DenseSubVector< T >::parent().

condense() [2/2]

template<typename T >

void libMesh::DenseMatrixBase< T >::condense ( const unsigned int  i, const unsigned int  j, const T  val, DenseVectorBase< T > &  rhs  )

protectedinherited

Condense-out the (i,j) entry of the matrix, forcing it to take on the value val.

This is useful in numerical simulations for applying boundary conditions. Preserves the symmetry of the matrix.

Definition at line 73 of file dense_matrix_base_impl.h.

  {
    libmesh_assert_equal_to (this->_m, rhs.size());
    libmesh_assert_equal_to (iv, jv);
 
 
    // move the known value into the RHS
    // and zero the column
    for (auto i : make_range(this->m()))
      {
        rhs.el(i) -= this->el(i,jv)*val;
        this->el(i,jv) = 0.;
      }
 
    // zero the row
    for (auto j : make_range(this->n()))
      this->el(iv,j) = 0.;
 
    this->el(iv,jv) = 1.;
    rhs.el(iv) = val;
 
  }

References libMesh::DenseVectorBase< T >::el(), libMesh::make_range(), and libMesh::DenseVectorBase< T >::size().

Referenced by libMesh::DenseMatrix< T >::condense().

diagonal()

template<typename T >

DenseVector< T > libMesh::DenseMatrixBase< T >::diagonal ( ) const

inherited

Return the matrix diagonal.

Definition at line 37 of file dense_matrix_base_impl.h.

  {
    DenseVector<T> ret(_m);
    for (decltype(_m) i = 0; i < _m; ++i)
      ret(i) = el(i, i);
    return ret;
  }

Referenced by libMesh::DiagonalMatrix< T >::add_matrix().

el() [1/2]

template<typename T >

virtual T libMesh::DenseSubMatrix< T >::el ( const unsigned int  i, const unsigned int  j  ) const

inlinefinaloverridevirtual

Returns

The (i,j) element of the matrix. Since internal data representations may differ, you must redefine this function.

Implements libMesh::DenseMatrixBase< T >.

Definition at line 90 of file dense_submatrix.h.

  { return (*this)(i,j); }

el() [2/2]

template<typename T >

virtual T & libMesh::DenseSubMatrix< T >::el ( const unsigned int  i, const unsigned int  j  )

inlinefinaloverridevirtual

Returns

The (i,j) element of the matrix as a writable reference. Since internal data representations may differ, you must redefine this function.

Implements libMesh::DenseMatrixBase< T >.

Definition at line 94 of file dense_submatrix.h.

  { return (*this)(i,j); }

i_off()

template<typename T >

unsigned int libMesh::DenseSubMatrix< T >::i_off ( ) const

inline

Returns

The row offset into the parent matrix.

Definition at line 113 of file dense_submatrix.h.

{ return _i_off; }

References libMesh::DenseSubMatrix< T >::_i_off.

Referenced by libMesh::DenseSubMatrix< T >::condense().

j_off()

template<typename T >

unsigned int libMesh::DenseSubMatrix< T >::j_off ( ) const

inline

Returns

The column offset into the parent matrix.

Definition at line 118 of file dense_submatrix.h.

{ return _j_off; }

References libMesh::DenseSubMatrix< T >::_j_off.

Referenced by libMesh::DenseSubMatrix< T >::condense().

left_multiply()

template<typename T >

void libMesh::DenseSubMatrix< T >::left_multiply ( const DenseMatrixBase< T > &  M2 )

finaloverridevirtual

Performs the operation: (*this) <- M2 * (*this)

Implements libMesh::DenseMatrixBase< T >.

Definition at line 31 of file dense_submatrix.C.

{
  // (*this) <- M2 * M3
  // Where:
  // (*this) = (m x n),
  // M2      = (m x p),
  // M3      = (p x n)
 
  // M3 is a simply a copy of *this
  DenseSubMatrix<T> M3(*this);
 
  // Call the multiply function in the base class
  this->multiply(*this, M2, M3);
}

m()

template<typename T >

unsigned int libMesh::DenseMatrixBase< T >::m ( ) const

inlineinherited

Returns

The row-dimension of the matrix.

Definition at line 104 of file dense_matrix_base.h.

{ return _m; }

References libMesh::DenseMatrixBase< T >::_m.

Referenced by libMesh::DenseMatrix< T >::_left_multiply_transpose(), libMesh::DenseMatrix< T >::_multiply_blas(), libMesh::DenseMatrix< T >::_right_multiply_transpose(), libMesh::DenseMatrix< T >::_svd_solve_lapack(), libMesh::DenseMatrix< T >::add(), libMesh::DenseMatrixBase< T >::add(), libMesh::PetscMatrix< T >::add_block_matrix(), libMesh::StaticCondensation::add_matrix(), libMesh::DiagonalMatrix< T >::add_matrix(), libMesh::EigenSparseMatrix< T >::add_matrix(), libMesh::LaspackMatrix< T >::add_matrix(), libMesh::PetscMatrix< T >::add_matrix(), libMesh::EpetraMatrix< T >::add_matrix(), libMesh::RBConstruction::add_scaled_matrix_and_vector(), libMesh::DofMap::build_constraint_matrix(), libMesh::DofMap::build_constraint_matrix_and_vector(), libMesh::DofMap::extract_local_vector(), libMesh::DenseMatrix< T >::get_transpose(), libMesh::DofMap::heterogeneously_constrain_element_jacobian_and_residual(), libMesh::DofMap::heterogeneously_constrain_element_residual(), libMesh::isfinite(), libMesh::isfinite(), libMesh::isinf(), libMesh::isinf(), libMesh::isnan(), libMesh::isnan(), libMesh::DenseMatrix< T >::left_multiply(), libMesh::DenseMatrix< T >::left_multiply(), libMesh::DofMap::max_constraint_error(), libMesh::DenseMatrixBase< T >::multiply(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::DenseMatrix< T >::operator=(), libMesh::RBEIMEvaluation::set_interpolation_matrix_entry(), DualShapeTest::testEdge2Lagrange(), DenseMatrixTest::testEVD_helper(), DenseMatrixTest::testSVD(), and MetaPhysicL::RawType< libMesh::DenseMatrix< T > >::value().

multiply()

template<typename T >

void libMesh::DenseMatrixBase< T >::multiply ( DenseMatrixBase< T > &  M1, const DenseMatrixBase< T > &  M2, const DenseMatrixBase< T > &  M3  )

staticprotectedinherited

Helper function - Performs the computation M1 = M2 * M3 where: M1 = (m x n) M2 = (m x p) M3 = (p x n)

Definition at line 46 of file dense_matrix_base_impl.h.

  {
    // Assertions to make sure we have been
    // passed matrices of the correct dimension.
    libmesh_assert_equal_to (M1.m(), M2.m());
    libmesh_assert_equal_to (M1.n(), M3.n());
    libmesh_assert_equal_to (M2.n(), M3.m());
 
    const unsigned int m_s = M2.m();
    const unsigned int p_s = M2.n();
    const unsigned int n_s = M1.n();
 
    // Do it this way because there is a
    // decent chance (at least for constraint matrices)
    // that M3(k,j) = 0. when right-multiplying.
    for (unsigned int k=0; k<p_s; k++)
      for (unsigned int j=0; j<n_s; j++)
        if (M3.el(k,j) != 0.)
          for (unsigned int i=0; i<m_s; i++)
            M1.el(i,j) += M2.el(i,k) * M3.el(k,j);
  }

References libMesh::DenseMatrixBase< T >::el(), libMesh::DenseMatrixBase< T >::m(), and libMesh::DenseMatrixBase< T >::n().

n()

template<typename T >

unsigned int libMesh::DenseMatrixBase< T >::n ( ) const

inlineinherited

Returns

The column-dimension of the matrix.

Definition at line 109 of file dense_matrix_base.h.

{ return _n; }

References libMesh::DenseMatrixBase< T >::_n.

Referenced by libMesh::DenseMatrix< T >::_left_multiply_transpose(), libMesh::DenseMatrix< T >::_multiply_blas(), libMesh::DenseMatrix< T >::_right_multiply_transpose(), libMesh::DenseMatrix< T >::_svd_solve_lapack(), libMesh::DenseMatrix< T >::add(), libMesh::DenseMatrixBase< T >::add(), libMesh::PetscMatrix< T >::add_block_matrix(), libMesh::StaticCondensation::add_matrix(), libMesh::DiagonalMatrix< T >::add_matrix(), libMesh::EigenSparseMatrix< T >::add_matrix(), libMesh::LaspackMatrix< T >::add_matrix(), libMesh::PetscMatrix< T >::add_matrix(), libMesh::EpetraMatrix< T >::add_matrix(), libMesh::RBConstruction::add_scaled_matrix_and_vector(), libMesh::DofMap::build_constraint_matrix(), libMesh::DofMap::build_constraint_matrix_and_vector(), libMesh::DofMap::constrain_element_residual(), libMesh::DofMap::extract_local_vector(), libMesh::DenseMatrix< T >::get_transpose(), libMesh::DofMap::heterogeneously_constrain_element_jacobian_and_residual(), libMesh::DofMap::heterogeneously_constrain_element_residual(), libMesh::isfinite(), libMesh::isfinite(), libMesh::isinf(), libMesh::isinf(), libMesh::isnan(), libMesh::isnan(), libMesh::DenseMatrix< T >::left_multiply(), libMesh::DenseMatrix< T >::left_multiply(), libMesh::DofMap::max_constraint_error(), libMesh::DenseMatrixBase< T >::multiply(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::DenseMatrix< T >::operator=(), libMesh::DenseMatrix< Real >::right_multiply(), libMesh::RBEIMEvaluation::set_interpolation_matrix_entry(), DualShapeTest::testEdge2Lagrange(), DenseMatrixTest::testSVD(), and MetaPhysicL::RawType< libMesh::DenseMatrix< T > >::value().

operator()() [1/2]

template<typename T >

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

inline

Returns

The (i,j) element of the submatrix as a writable reference.

Definition at line 219 of file dense_submatrix.h.

{
  libmesh_assert_less (i, this->m());
  libmesh_assert_less (j, this->n());
  libmesh_assert_less (i + this->i_off(), _parent_matrix.m());
  libmesh_assert_less (j + this->j_off(), _parent_matrix.n());
 
  return _parent_matrix (i + this->i_off(),
                         j + this->j_off());
}

operator()() [2/2]

template<typename T >

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

inline

Returns

The (i,j) element of the submatrix.

Definition at line 204 of file dense_submatrix.h.

{
  libmesh_assert_less (i, this->m());
  libmesh_assert_less (j, this->n());
  libmesh_assert_less (i + this->i_off(), _parent_matrix.m());
  libmesh_assert_less (j + this->j_off(), _parent_matrix.n());
 
  return _parent_matrix (i + this->i_off(),
                         j + this->j_off());
}

operator=() [1/2]

template<typename T >

DenseSubMatrix & libMesh::DenseSubMatrix< T >::operator= ( const DenseSubMatrix< T > &  )

default

operator=() [2/2]

template<typename T >

DenseSubMatrix & libMesh::DenseSubMatrix< T >::operator= ( DenseSubMatrix< T > &&  )

default

parent()

template<typename T >

DenseMatrix< T > & libMesh::DenseSubMatrix< T >::parent ( )

inline

Returns

A reference to the parent matrix.

Definition at line 74 of file dense_submatrix.h.

{ return _parent_matrix; }

References libMesh::DenseSubMatrix< T >::_parent_matrix.

Referenced by libMesh::DenseSubMatrix< T >::condense().

print()

template<typename T >

void libMesh::DenseMatrixBase< T >::print ( std::ostream &  os = libMesh::out ) const

inherited

Pretty-print the matrix, by default to libMesh::out.

Definition at line 125 of file dense_matrix_base_impl.h.

  {
    for (auto i : make_range(this->m()))
      {
        for (auto j : make_range(this->n()))
          os << std::setw(8)
             << this->el(i,j) << " ";
 
        os << std::endl;
      }
 
    return;
  }

References libMesh::make_range().

print_scientific()

template<typename T >

void libMesh::DenseMatrixBase< T >::print_scientific ( std::ostream &  os, unsigned  precision = 8  ) const

inherited

Prints the matrix entries with more decimal places in scientific notation.

Definition at line 101 of file dense_matrix_base_impl.h.

  {
    // save the initial format flags
    std::ios_base::fmtflags os_flags = os.flags();
 
    // Print the matrix entries.
    for (auto i : make_range(this->m()))
      {
        for (auto j : make_range(this->n()))
          os << std::setw(15)
             << std::scientific
             << std::setprecision(precision)
             << this->el(i,j) << " ";
 
        os << std::endl;
      }
 
    // reset the original format flags
    os.flags(os_flags);
  }

References libMesh::make_range().

reposition()

template<typename T >

void libMesh::DenseSubMatrix< T >::reposition ( const unsigned int  ioff, const unsigned int  joff, const unsigned int  new_m, const unsigned int  new_n  )

inline

Changes the location of the submatrix in the parent matrix.

Definition at line 173 of file dense_submatrix.h.

{
  _i_off = ioff;
  _j_off = joff;
  this->_m = new_m;
  this->_n = new_n;
 
  // Make sure we still fit in the parent matrix.
  libmesh_assert_less_equal ((this->i_off() + this->m()), _parent_matrix.m());
  libmesh_assert_less_equal ((this->j_off() + this->n()), _parent_matrix.n());
}

Referenced by assemble_elasticity(), assemble_laplace(), assemble_shell(), assemble_stokes(), and libMesh::DenseSubMatrix< T >::DenseSubMatrix().

right_multiply()

template<typename T >

void libMesh::DenseSubMatrix< T >::right_multiply ( const DenseMatrixBase< T > &  M3 )

finaloverridevirtual

Performs the operation: (*this) <- (*this) * M3.

Implements libMesh::DenseMatrixBase< T >.

Definition at line 49 of file dense_submatrix.C.

{
  // (*this) <- M2 * M3
  // Where:
  // (*this) = (m x n),
  // M2      = (m x p),
  // M3      = (p x n)
 
  // M2 is simply a copy of *this
  DenseSubMatrix<T> M2(*this);
 
  // Call the multiply function in the base class
  this->multiply(*this, M2, M3);
}

zero()

template<typename T >

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

inlinefinaloverridevirtual

Set every element in the matrix to 0.

You must redefine what you mean by zeroing the matrix since it depends on how your values are stored.

Implements libMesh::DenseMatrixBase< T >.

Definition at line 192 of file dense_submatrix.h.

{
  for (auto i : make_range(this->m()))
    for (auto j : make_range(this->n()))
      _parent_matrix(i + this->i_off(),
                     j + this->j_off()) = 0.;
}

References libMesh::make_range().

Member Data Documentation

_i_off

template<typename T >

unsigned int libMesh::DenseSubMatrix< T >::_i_off

private

The row offset into the parent matrix.

Definition at line 146 of file dense_submatrix.h.

Referenced by libMesh::DenseSubMatrix< T >::i_off().

_j_off

template<typename T >

unsigned int libMesh::DenseSubMatrix< T >::_j_off

private

The column offset into the parent matrix.

Definition at line 151 of file dense_submatrix.h.

Referenced by libMesh::DenseSubMatrix< T >::j_off().

_m

template<typename T >

unsigned int libMesh::DenseMatrixBase< T >::_m

protectedinherited

The row dimension.

Definition at line 176 of file dense_matrix_base.h.

Referenced by libMesh::DenseMatrixBase< T >::m(), libMesh::DenseMatrix< T >::sub_matrix(), and libMesh::DenseMatrix< T >::swap().

_n

template<typename T >

unsigned int libMesh::DenseMatrixBase< T >::_n

protectedinherited

The column dimension.

Definition at line 181 of file dense_matrix_base.h.

Referenced by libMesh::DenseMatrixBase< T >::n(), libMesh::DenseMatrix< T >::sub_matrix(), and libMesh::DenseMatrix< T >::swap().

_parent_matrix

template<typename T >

DenseMatrix<T>& libMesh::DenseSubMatrix< T >::_parent_matrix

private

The parent matrix that contains this submatrix.

Definition at line 141 of file dense_submatrix.h.

Referenced by libMesh::DenseSubMatrix< T >::parent().

---

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

• include/numerics/dense_submatrix.h
• src/numerics/dense_submatrix.C