libMesh::SystemNorm Class Reference

#include <system_norm.h>

List of all members.

Public Member Functions
	SystemNorm ()
	SystemNorm (const FEMNormType &t)
	SystemNorm (const std::vector< FEMNormType > &norms)
	SystemNorm (const std::vector< FEMNormType > &norms, std::vector< Real > &weights)
	SystemNorm (const std::vector< FEMNormType > &norms, std::vector< std::vector< Real > > &weights)
	SystemNorm (const SystemNorm &s)
bool	is_discrete () const
Real	calculate_norm (const std::vector< Real > &v)
Real	calculate_norm (const std::vector< Real > &v1, const std::vector< Real > &v2)
bool	is_identity ()
FEMNormType	type (unsigned int var) const
void	set_type (unsigned int var, const FEMNormType &t)
Real	weight (unsigned int var) const
void	set_weight (unsigned int var, Real w)
void	set_off_diagonal_weight (unsigned int i, unsigned int j, Real w)
Real	weight_sq (unsigned int var) const
Private Attributes
std::vector< FEMNormType >	_norms
std::vector< Real >	_weights
std::vector< Real >	_weights_sq
std::vector< std::vector< Real > >	_off_diagonal_weights

---

Detailed Description

This class defines a norm/seminorm to be applied to a NumericVector which contains coefficients in a finite element space.

Discrete vector norms and weighted l2 combinations of Sobolev norms and seminorms are representable.

Author:

Roy H. Stogner 2008

Definition at line 48 of file system_norm.h.

---

Constructor & Destructor Documentation

libMesh::SystemNorm::SystemNorm

(

)

[inline]

Constructor, defaults to DISCRETE_L2

Definition at line 173 of file system_norm.h.

                       :
    _norms(1, DISCRETE_L2), _weights(1, 1.0), _weights_sq(1, 1.0)
{
}

libMesh::SystemNorm::SystemNorm

(

const FEMNormType &

t

)

[inline]

Constructor, for discrete vector norms, systems with one variable, and systems for which the same norm type should be used with a weight of one on each variable.

This is deliberately an implicit constructor; we want user code to be able to include lines like "error_norm = L2"

Definition at line 180 of file system_norm.h.

                                           :
    _norms(1, t), _weights(1, 1.0), _weights_sq(1, 1.0)
{
}

libMesh::SystemNorm::SystemNorm

(

const std::vector< FEMNormType > &

norms

)

[inline, explicit]

Constructor, for unweighted sobolev norms on systems with multiple variables.

For a system with n variables, the final norm will be the l2 norm of the n-vector of the norms in each variable.

Definition at line 187 of file system_norm.h.

References _norms, and libMeshEnums::DISCRETE_L2.

                                                          :
    _norms(norms), _weights(1, 1.0), _weights_sq(1, 1.0)
{
  if (_norms.empty())
    _norms.push_back(DISCRETE_L2);
}

libMesh::SystemNorm::SystemNorm	(	const std::vector< FEMNormType > &	norms,
		std::vector< Real > &	weights
	)			[inline]

Constructor, for weighted sobolev norms on systems with multiple variables.

For a system with n variables, the final norm will be the l2 norm of the n-vector of the norms in each variable, each multiplied by weight.

Definition at line 196 of file system_norm.h.

References _norms, _weights, _weights_sq, and libMeshEnums::DISCRETE_L2.

                                                 :
    _norms(norms), _weights(weights), _weights_sq(_weights.size(), 0.0)
{
  if (_norms.empty())
    _norms.push_back(DISCRETE_L2);

  if (_weights.empty())
    {
      _weights.push_back(1.0);
      _weights_sq.push_back(1.0);
    }
  else
    for (std::size_t i=0; i != _weights.size(); ++i)
      _weights_sq[i] = _weights[i] * _weights[i];
}

libMesh::SystemNorm::SystemNorm	(	const std::vector< FEMNormType > &	norms,
		std::vector< std::vector< Real > > &	weights
	)			[inline]

Constructor, for weighted sobolev norms on systems with multiple variables and their adjoints

For a system with n variables, the final norm computed will be of the form norm_u^T*R*norm_z where R is a scaling matrix

Definition at line 214 of file system_norm.h.

References _norms, _off_diagonal_weights, _weights, _weights_sq, and libMeshEnums::DISCRETE_L2.

                                                              :
  _norms(norms), _weights(weights.size()), _off_diagonal_weights(weights)
{
  if(_norms.empty())
    _norms.push_back(DISCRETE_L2);

  if (_weights.empty())
    {
      _weights.push_back(1.0);
      _weights_sq.push_back(1.0);
    }
  else
    {
      // Loop over the entries of the user provided matrix and store its entries in
      // the _off_diagonal_weights or _diagonal_weights
      for(std::size_t i=0; i!=_off_diagonal_weights.size(); ++i)
        {
          if(_off_diagonal_weights[i].size() > i)
            {
              _weights[i] = _off_diagonal_weights[i][i];
              _off_diagonal_weights[i][i] = 0;
            }
          else
            _weights[i] = 1.0;
        }
      for (std::size_t i=0; i != _weights.size(); ++i)
        _weights_sq[i] = _weights[i] * _weights[i];
    }
}

libMesh::SystemNorm::SystemNorm

(

const SystemNorm &

s

)

[inline]

Copy Constructor

Definition at line 246 of file system_norm.h.

                                          :
    _norms(s._norms), _weights(s._weights), _weights_sq(s._weights_sq)
{
}

---

Member Function Documentation

Real libMesh::SystemNorm::calculate_norm	(	const std::vector< Real > &	v1,
		const std::vector< Real > &	v2
	)			[inline]

Returns the weighted inner product v1^T*W*v2 where R is our weights

Definition at line 344 of file system_norm.h.

References _off_diagonal_weights, _weights, and libMesh::Real.

{
  // The vectors are assumed to both be vectors of the (same number
  // of) components
  std::size_t vsize = v1.size();
  libmesh_assert_equal_to (vsize, v2.size());

  // We'll support implicitly defining weights, but if the user sets
  // more weights than he uses then something's probably wrong
  std::size_t diagsize = this->_weights.size();
  libmesh_assert_greater_equal (vsize, diagsize);

  // Initialize the variable val
  Real val = 0.;

  // Loop over all the components of the system with explicit
  // weights
  for(std::size_t i = 0; i != diagsize; i++)
    {
      val += this->_weights[i] * v1[i] * v2[i];
    }
  // Loop over all the components of the system with implicit
  // weights
  for(std::size_t i = diagsize; i < vsize; i++)
    {
      val += v1[i] * v2[i];
    }

  // Loop over the components of the system
  std::size_t nrows = this->_off_diagonal_weights.size();
  libmesh_assert_less_equal (vsize, nrows);

  for(std::size_t i = 0; i != nrows; i++)
    {
      std::size_t ncols = this->_off_diagonal_weights[i].size();
      for(std::size_t j=0; j != ncols; j++)
        {
          // Note that the diagonal weights here were set to zero
          // in the constructor
          val += this->_off_diagonal_weights[i][j] * v1[i] * v2[j];
        }
    }

    return(val);
  }

Real libMesh::SystemNorm::calculate_norm

(

const std::vector< Real > &

v

)

[inline]

Returns the weighted norm v^T*W*v where W represents our weights matrix or weights vector times identity matrix.

Definition at line 391 of file system_norm.h.

Referenced by libMesh::AdjointResidualErrorEstimator::estimate_error().

{
  return this->calculate_norm(v1,v1);
}

bool libMesh::SystemNorm::is_discrete

(

)

const [inline]

Returns true if this is purely a discrete norm

Definition at line 253 of file system_norm.h.

References _norms, libMeshEnums::DISCRETE_L1, libMeshEnums::DISCRETE_L2, and libMeshEnums::DISCRETE_L_INF.

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

{
  libmesh_assert (!_norms.empty());

  if (_norms[0] == DISCRETE_L1 ||
      _norms[0] == DISCRETE_L2 ||
      _norms[0] == DISCRETE_L_INF)
    return true;

  return false;
}

bool libMesh::SystemNorm::is_identity

(

)

[inline]

Returns true if no weight matrix W is specified or an identiy matrix is specified, otherwise returns false

Definition at line 397 of file system_norm.h.

References _off_diagonal_weights, and _weights.

Referenced by libMesh::AdjointResidualErrorEstimator::estimate_error().

{
  std::size_t nrows = this->_off_diagonal_weights.size();

  // If any of the off-diagonal elements is not 0, then we are in the non-identity case
  for(std::size_t i = 0; i != nrows; i++)
    {
      std::size_t ncols = this->_off_diagonal_weights[i].size();
      for(std::size_t j = 0; j != ncols; j++)
        {
          if(_off_diagonal_weights[i][j] != 0)
            {
              return(false);
            }
        }
    }

  // If any of the diagonal elements is not 1, then we are in the non-identity case
  nrows = this->_weights.size();
  for(std::size_t i = 0; i != nrows; i++)
    if(_weights[i] != 1)
      return(false);

  // If all the off-diagonals elements are 0, and diagonal elements 1, then we are in an identity case
  return(true);
}

void libMesh::SystemNorm::set_off_diagonal_weight	(	unsigned int	i,
		unsigned int	j,
		Real	w
	)			[inline]

Sets the weight corresponding to the norm from the variable pair v1(var1) coming from v2(var2). See calculate_norm

Definition at line 315 of file system_norm.h.

References _off_diagonal_weights, and _weights.

{
  libmesh_assert (!_weights.empty());

  if (i >= _off_diagonal_weights.size())
    {
      _off_diagonal_weights.resize(i+1);
    }

  if (j >= _off_diagonal_weights[i].size())
    {
      _off_diagonal_weights[i].resize(j+1, 0.);
    }

  _off_diagonal_weights[i][j] = w;

}

void libMesh::SystemNorm::set_type	(	unsigned int	var,
		const FEMNormType &	t
	)			[inline]

Sets the type of the norm in variable var

Definition at line 279 of file system_norm.h.

References _norms.

{
  libmesh_assert (!_norms.empty());

  if (var >= _norms.size())
    _norms.resize(var+1, t);

  _norms[var] = t;
}

void libMesh::SystemNorm::set_weight	(	unsigned int	var,
		Real	w
	)			[inline]

Sets the weight corresponding to the norm in variable var

Definition at line 300 of file system_norm.h.

References _weights, and _weights_sq.

{
  libmesh_assert (!_weights.empty());

  if (var >= _weights.size())
    {
      _weights.resize(var+1, 1.0);
      _weights_sq.resize(var+1, 1.0);
    }

  _weights[var] = w;
  _weights_sq[var] = w*w;
}

FEMNormType libMesh::SystemNorm::type

(

unsigned int

var

)

const [inline]

Returns the type of the norm in variable var

Definition at line 267 of file system_norm.h.

References _norms.

Referenced by libMesh::System::calculate_norm(), libMesh::ErrorEstimator::estimate_errors(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), and libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()().

{
  libmesh_assert (!_norms.empty());

  std::size_t i = (var < _norms.size()) ? var : _norms.size() - 1;

  return _norms[i];
}

Real libMesh::SystemNorm::weight

(

unsigned int

var

)

const [inline]

Returns the weight corresponding to the norm in variable var

Definition at line 291 of file system_norm.h.

References _weights.

Referenced by libMesh::KellyErrorEstimator::boundary_side_integration(), libMesh::DiscontinuityMeasure::boundary_side_integration(), libMesh::System::calculate_norm(), libMesh::JumpErrorEstimator::estimate_error(), libMesh::KellyErrorEstimator::internal_side_integration(), libMesh::LaplacianErrorEstimator::internal_side_integration(), libMesh::DiscontinuityMeasure::internal_side_integration(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), and libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()().

{
  libmesh_assert (!_weights.empty());

  return (var < _weights.size()) ? _weights[var] : 1.0;
}

Real libMesh::SystemNorm::weight_sq

(

unsigned int

var

)

const [inline]

Returns the squared weight corresponding to the norm in variable var. We cache that at construction time to save a few flops.

Definition at line 335 of file system_norm.h.

References _weights_sq.

Referenced by libMesh::System::calculate_norm(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), and libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()().

{
  libmesh_assert (!_weights_sq.empty());

  return (var < _weights_sq.size()) ? _weights_sq[var] : 1.0;
}

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Member Data Documentation

std::vector<FEMNormType> libMesh::SystemNorm::_norms [private]

Definition at line 155 of file system_norm.h.

Referenced by is_discrete(), set_type(), SystemNorm(), and type().

std::vector<std::vector<Real> > libMesh::SystemNorm::_off_diagonal_weights [private]

One more data structure needed to store the off diagonal components for the generalize SystemNorm case

Definition at line 164 of file system_norm.h.

Referenced by calculate_norm(), is_identity(), set_off_diagonal_weight(), and SystemNorm().

std::vector<Real> libMesh::SystemNorm::_weights [private]

Definition at line 157 of file system_norm.h.

Referenced by calculate_norm(), is_identity(), set_off_diagonal_weight(), set_weight(), SystemNorm(), and weight().

std::vector<Real> libMesh::SystemNorm::_weights_sq [private]

Definition at line 158 of file system_norm.h.

Referenced by set_weight(), SystemNorm(), and weight_sq().

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

• system_norm.h