libMesh::QJacobi Class Reference

This class implements two (for now) Jacobi-Gauss quadrature rules. More...

#include <quadrature_jacobi.h>

Inheritance diagram for libMesh::QJacobi:

Public Member Functions
	QJacobi (unsigned int dim, Order order=INVALID_ORDER, unsigned int a=1, unsigned int b=0)
	Constructor. More...
	QJacobi (const QJacobi &)=default
	Copy/move ctor, copy/move assignment operator, and destructor are all explicitly defaulted for this simple class. More...
	QJacobi (QJacobi &&)=default
QJacobi &	operator= (const QJacobi &)=default
QJacobi &	operator= (QJacobi &&)=default
virtual	~QJacobi ()=default
virtual QuadratureType	type () const override
virtual std::unique_ptr< QBase >	clone () const override
ElemType	get_elem_type () const
unsigned int	get_p_level () const
unsigned int	n_points () const
unsigned int	size () const
	Alias for n_points() to enable use in index_range. More...
unsigned int	get_dim () const
const std::vector< Point > &	get_points () const
std::vector< Point > &	get_points ()
const std::vector< Real > &	get_weights () const
std::vector< Real > &	get_weights ()
Point	qp (const unsigned int i) const
Real	w (const unsigned int i) const
virtual void	init (const Elem &e, unsigned int p_level=invalid_uint)
	Initializes the data structures for a quadrature rule for the element e. More...
virtual void	init (const ElemType type=INVALID_ELEM, unsigned int p_level=0, bool simple_type_only=false)
	Initializes the data structures for a quadrature rule for an element of type type. More...
virtual void	init (const QBase &other_rule)
	Initializes the data structures for a quadrature rule based on the element, element type, and p_level settings of other_rule. More...
virtual void	init (const Elem &elem, const std::vector< Real > &vertex_distance_func, unsigned int p_level=0)
	Initializes the data structures for an element potentially "cut" by a signed distance function. More...
Order	get_order () const
Order	get_base_order () const
void	print_info (std::ostream &os=libMesh::out) const
	Prints information relevant to the quadrature rule, by default to libMesh::out. More...
void	scale (std::pair< Real, Real > old_range, std::pair< Real, Real > new_range)
	Maps the points of a 1D quadrature rule defined by "old_range" to another 1D interval defined by "new_range" and scales the weights accordingly. More...
virtual bool	shapes_need_reinit ()

Static Public Member Functions
static std::unique_ptr< QBase >	build (std::string_view name, const unsigned int dim, const Order order=INVALID_ORDER)
	Builds a specific quadrature rule based on the name string. More...
static std::unique_ptr< QBase >	build (const QuadratureType qt, const unsigned int dim, const Order order=INVALID_ORDER)
	Builds a specific quadrature rule based on the QuadratureType. More...
static void	print_info (std::ostream &out_stream=libMesh::out)
	Prints the reference information, by default to libMesh::out. More...
static std::string	get_info ()
	Gets a string containing the reference information. More...
static unsigned int	n_objects ()
	Prints the number of outstanding (created, but not yet destroyed) objects. More...
static void	enable_print_counter_info ()
	Methods to enable/disable the reference counter output from print_info() More...
static void	disable_print_counter_info ()

Public Attributes
bool	allow_rules_with_negative_weights
	Flag (default true) controlling the use of quadrature rules with negative weights. More...
bool	allow_nodal_pyramid_quadrature
	The flag's value defaults to false so that one does not accidentally use a nodal quadrature rule on Pyramid elements, since evaluating the inverse element Jacobian (e.g. More...

Protected Types
typedef std::map< std::string, std::pair< unsigned int, unsigned int > >	Counts
	Data structure to log the information. More...

Protected Member Functions
virtual void	init_0D ()
	Initializes the 0D quadrature rule by filling the points and weights vectors with the appropriate values. More...
virtual void	init_2D ()
	Initializes the 2D quadrature rule by filling the points and weights vectors with the appropriate values. More...
virtual void	init_3D ()
	Initializes the 3D quadrature rule by filling the points and weights vectors with the appropriate values. More...
void	tensor_product_quad (const QBase &q1D)
	Constructs a 2D rule from the tensor product of q1D with itself. More...
void	tensor_product_hex (const QBase &q1D)
	Computes the tensor product quadrature rule [q1D x q1D x q1D] from the 1D rule q1D. More...
void	tensor_product_prism (const QBase &q1D, const QBase &q2D)
	Computes the tensor product of a 1D quadrature rule and a 2D quadrature rule. More...
void	increment_constructor_count (const std::string &name) noexcept
	Increments the construction counter. More...
void	increment_destructor_count (const std::string &name) noexcept
	Increments the destruction counter. More...

Protected Attributes
unsigned int	_dim
	The spatial dimension of the quadrature rule. More...
Order	_order
	The polynomial order which the quadrature rule is capable of integrating exactly. More...
ElemType	_type
	The type of element for which the current values have been computed. More...
const Elem *	_elem
	The element for which the current values were computed, or nullptr if values were computed without a specific element. More...
unsigned int	_p_level
	The p-level of the element for which the current values have been computed. More...
std::vector< Point >	_points
	The locations of the quadrature points in reference element space. More...
std::vector< Real >	_weights
	The quadrature weights. More...

Static Protected Attributes
static Counts	_counts
	Actually holds the data. More...
static Threads::atomic< unsigned int >	_n_objects
	The number of objects. More...
static Threads::spin_mutex	_mutex
	Mutual exclusion object to enable thread-safe reference counting. More...
static bool	_enable_print_counter = true
	Flag to control whether reference count information is printed when print_info is called. More...

Private Member Functions
virtual void	init_1D () override
	Initializes the 1D quadrature rule by filling the points and weights vectors with the appropriate values. More...

Private Attributes
unsigned int	_alpha
unsigned int	_beta

Detailed Description

This class implements two (for now) Jacobi-Gauss quadrature rules.

These rules have the same order of accuracy as the normal Gauss quadrature rules, but instead of integrating a weight function w(x)=1, they integrate w(x)=(1-x)^alpha * (1+x)^beta. The reason that they are useful is that they allow you to implement conical product rules for triangles and tetrahedra. Although these product rules are non-optimal (use more points than necessary) they are automatically constructable for high orders of accuracy where other formulae may not exist.

There is not much sense in using this class directly, since it only provides 1D rules, weighted, as described before. Still, this class is particularly helpful: check QGauss for triangles and tetrahedra, with orders beyond THIRTIETH.

Author

John W. Peterson

Date

2003 Implements 1D Gauss-Jacobi quadrature rules of various orders.

Definition at line 49 of file quadrature_jacobi.h.

Member Typedef Documentation

Counts

typedef std::map<std::string, std::pair<unsigned int, unsigned int> > libMesh::ReferenceCounter::Counts

protectedinherited

Data structure to log the information.

The log is identified by the class name.

Definition at line 119 of file reference_counter.h.

Constructor & Destructor Documentation

QJacobi() [1/3]

libMesh::QJacobi::QJacobi ( unsigned int  dim, Order  order = INVALID_ORDER, unsigned int  a = 1, unsigned int  b = 0  )

inline

Constructor.

Currently, only one-dimensional rules provided.

Definition at line 56 of file quadrature_jacobi.h.

References libMesh::QBase::_dim, libMesh::EDGE2, and libMesh::QBase::init().

                             :
    QBase(dim, order),
    _alpha(a),
    _beta(b)
  {
    if (_dim == 1)
      init(EDGE2);
  }

QJacobi() [2/3]

libMesh::QJacobi::QJacobi ( const QJacobi &  )

default

Copy/move ctor, copy/move assignment operator, and destructor are all explicitly defaulted for this simple class.

QJacobi() [3/3]

libMesh::QJacobi::QJacobi ( QJacobi &&  )

default

~QJacobi()

virtual libMesh::QJacobi::~QJacobi ( )

virtualdefault

Member Function Documentation

build() [1/2]

std::unique_ptr< QBase > libMesh::QBase::build ( std::string_view  name, const unsigned int  dim, const Order  order = INVALID_ORDER  )

staticinherited

Builds a specific quadrature rule based on the name string.

This enables selection of the quadrature rule at run-time. The input parameter name must be mappable through the Utility::string_to_enum<>() function.

This function allocates memory, therefore a std::unique_ptr<QBase> is returned so that the user does not accidentally leak it.

Definition at line 43 of file quadrature_build.C.

References libMesh::QBase::_dim, libMesh::QBase::_order, and libMesh::QBase::type().

Referenced by assemble_poisson(), libMesh::InfFE< Dim, T_radial, T_map >::attach_quadrature_rule(), libMesh::QBase::clone(), main(), libMesh::OverlapCoupling::OverlapCoupling(), libMesh::InfFE< Dim, T_radial, T_map >::reinit(), QuadratureTest::testBuild(), QuadratureTest::testJacobi(), and QuadratureTest::testPolynomials().

{
  return QBase::build (Utility::string_to_enum<QuadratureType> (type),
                       _dim,
                       _order);
}

build() [2/2]

std::unique_ptr< QBase > libMesh::QBase::build ( const QuadratureType  qt, const unsigned int  dim, const Order  order = INVALID_ORDER  )

staticinherited

Builds a specific quadrature rule based on the QuadratureType.

This enables selection of the quadrature rule at run-time.

This function allocates memory, therefore a std::unique_ptr<QBase> is returned so that the user does not accidentally leak it.

Definition at line 54 of file quadrature_build.C.

References libMesh::QBase::_dim, libMesh::QBase::_order, libMesh::FIRST, libMesh::FORTYTHIRD, libMesh::out, libMesh::QCLOUGH, libMesh::QCONICAL, libMesh::QGAUSS, libMesh::QGAUSS_LOBATTO, libMesh::QGRID, libMesh::QGRUNDMANN_MOLLER, libMesh::QJACOBI_1_0, libMesh::QJACOBI_2_0, libMesh::QMONOMIAL, libMesh::QNODAL, libMesh::QSIMPSON, libMesh::QTRAP, libMesh::THIRD, and libMesh::TWENTYTHIRD.

{
  switch (_qt)
    {

    case QCLOUGH:
      {
#ifdef DEBUG
        if (_order > TWENTYTHIRD)
          {
            libMesh::out << "WARNING: Clough quadrature implemented" << std::endl
                         << " up to TWENTYTHIRD order." << std::endl;
          }
#endif

        return std::make_unique<QClough>(_dim, _order);
      }

    case QGAUSS:
      {

#ifdef DEBUG
        if (_order > FORTYTHIRD)
          {
            libMesh::out << "WARNING: Gauss quadrature implemented" << std::endl
                         << " up to FORTYTHIRD order." << std::endl;
          }
#endif

        return std::make_unique<QGauss>(_dim, _order);
      }

    case QJACOBI_1_0:
      {

#ifdef DEBUG
        if (_order > FORTYTHIRD)
          {
            libMesh::out << "WARNING: Jacobi(1,0) quadrature implemented" << std::endl
                         << " up to FORTYTHIRD order." << std::endl;
          }

        if (_dim > 1)
          {
            libMesh::out << "WARNING: Jacobi(1,0) quadrature implemented" << std::endl
                         << " in 1D only." << std::endl;
          }
#endif

        return std::make_unique<QJacobi>(_dim, _order, 1, 0);
      }

    case QJACOBI_2_0:
      {

#ifdef DEBUG
        if (_order > FORTYTHIRD)
          {
            libMesh::out << "WARNING: Jacobi(2,0) quadrature implemented" << std::endl
                         << " up to FORTYTHIRD order." << std::endl;
          }

        if (_dim > 1)
          {
            libMesh::out << "WARNING: Jacobi(2,0) quadrature implemented" << std::endl
                         << " in 1D only." << std::endl;
          }
#endif

        return std::make_unique<QJacobi>(_dim, _order, 2, 0);
      }

    case QSIMPSON:
      {

#ifdef DEBUG
        if (_order > THIRD)
          {
            libMesh::out << "WARNING: Simpson rule provides only" << std::endl
                         << " THIRD order!" << std::endl;
          }
#endif

        return std::make_unique<QSimpson>(_dim);
      }

    case QTRAP:
      {

#ifdef DEBUG
        if (_order > FIRST)
          {
            libMesh::out << "WARNING: Trapezoidal rule provides only" << std::endl
                         << " FIRST order!" << std::endl;
          }
#endif

        return std::make_unique<QTrap>(_dim);
      }

    case QGRID:
      return std::make_unique<QGrid>(_dim, _order);

    case QGRUNDMANN_MOLLER:
      return std::make_unique<QGrundmann_Moller>(_dim, _order);

    case QMONOMIAL:
      return std::make_unique<QMonomial>(_dim, _order);

    case QGAUSS_LOBATTO:
      return std::make_unique<QGaussLobatto>(_dim, _order);

    case QCONICAL:
      return std::make_unique<QConical>(_dim, _order);

    case QNODAL:
      return std::make_unique<QNodal>(_dim, _order);

    default:
      libmesh_error_msg("ERROR: Bad qt=" << _qt);
    }
}

clone()

std::unique_ptr< QBase > libMesh::QJacobi::clone ( ) const

overridevirtual

Returns

A copy of this quadrature rule wrapped in a smart pointer.

Reimplemented from libMesh::QBase.

Definition at line 42 of file quadrature_jacobi.C.

{
  return std::make_unique<QJacobi>(*this);
}

disable_print_counter_info()

void libMesh::ReferenceCounter::disable_print_counter_info ( )

staticinherited

Definition at line 100 of file reference_counter.C.

References libMesh::ReferenceCounter::_enable_print_counter.

{
  _enable_print_counter = false;
  return;
}

enable_print_counter_info()

void libMesh::ReferenceCounter::enable_print_counter_info ( )

staticinherited

Methods to enable/disable the reference counter output from print_info()

Definition at line 94 of file reference_counter.C.

References libMesh::ReferenceCounter::_enable_print_counter.

{
  _enable_print_counter = true;
  return;
}

get_base_order()

Order libMesh::QBase::get_base_order ( ) const

inlineinherited

Returns

The "base" order of the quadrature rule, independent of element.

This function should be used when comparing quadrature objects independently of their last initialization.

Definition at line 258 of file quadrature.h.

References libMesh::QBase::_order.

{ return static_cast<Order>(_order); }

get_dim()

unsigned int libMesh::QBase::get_dim ( ) const

inlineinherited

Returns

The spatial dimension of the quadrature rule.

Definition at line 150 of file quadrature.h.

References libMesh::QBase::_dim.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::attach_quadrature_rule(), libMesh::QBase::clone(), libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), and QuadratureTest::testPolynomial().

{ return _dim; }

get_elem_type()

ElemType libMesh::QBase::get_elem_type ( ) const

inlineinherited

Returns

The element type we're currently using.

Definition at line 121 of file quadrature.h.

References libMesh::QBase::_type.

{ return _type; }

get_info()

std::string libMesh::ReferenceCounter::get_info ( )

staticinherited

Gets a string containing the reference information.

Definition at line 47 of file reference_counter.C.

References libMesh::ReferenceCounter::_counts, and libMesh::Quality::name().

Referenced by libMesh::ReferenceCounter::print_info().

{
#if defined(LIBMESH_ENABLE_REFERENCE_COUNTING) && defined(DEBUG)

  std::ostringstream oss;

  oss << '\n'
      << " ---------------------------------------------------------------------------- \n"
      << "| Reference count information                                                |\n"
      << " ---------------------------------------------------------------------------- \n";

  for (const auto & [name, cd] : _counts)
    oss << "| " << name << " reference count information:\n"
        << "|  Creations:    " << cd.first    << '\n'
        << "|  Destructions: " << cd.second << '\n';

  oss << " ---------------------------------------------------------------------------- \n";

  return oss.str();

#else

  return "";

#endif
}

get_order()

Order libMesh::QBase::get_order ( ) const

inlineinherited

Returns

The current "total" order of the quadrature rule which can vary element by element, depending on the Elem::p_level(), which gets passed to us during init().

Each additional power of p increases the quadrature order required to integrate the mass matrix by 2, hence the formula below.

Todo:

This function should also be used in all of the Order switch statements in the rules themselves.

Definition at line 249 of file quadrature.h.

References libMesh::QBase::_order, and libMesh::QBase::_p_level.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::attach_quadrature_rule(), libMesh::QBase::clone(), libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::RBEIMConstruction::enrich_eim_approximation_on_interiors(), libMesh::QGaussLobatto::init_1D(), libMesh::QGauss::init_1D(), libMesh::QConical::init_1D(), init_1D(), libMesh::QGrundmann_Moller::init_1D(), libMesh::QGaussLobatto::init_2D(), libMesh::QGauss::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGrundmann_Moller::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGauss::init_3D(), libMesh::QMonomial::init_3D(), libMesh::QGrundmann_Moller::init_3D(), and libMesh::RBParametrizedFunction::preevaluate_parametrized_function_on_mesh().

{ return static_cast<Order>(_order + 2 * _p_level); }

get_p_level()

unsigned int libMesh::QBase::get_p_level ( ) const

inlineinherited

Returns

The p-refinement level we're currently using.

Definition at line 126 of file quadrature.h.

References libMesh::QBase::_p_level.

{ return _p_level; }

get_points() [1/2]

const std::vector<Point>& libMesh::QBase::get_points ( ) const

inlineinherited

Returns

A std::vector containing the quadrature point locations in reference element space.

Definition at line 156 of file quadrature.h.

References libMesh::QBase::_points.

Referenced by assemble_ellipticdg(), libMesh::QClough::init_1D(), libMesh::QConical::init_1D(), libMesh::QNodal::init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGrundmann_Moller::init_1D(), libMesh::QGaussLobatto::init_2D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGauss::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), and libMesh::OverlapCoupling::operator()().

{ return _points; }

get_points() [2/2]

std::vector<Point>& libMesh::QBase::get_points ( )

inlineinherited

Returns

A std::vector containing the quadrature point locations in reference element space as a writable reference.

Definition at line 162 of file quadrature.h.

References libMesh::QBase::_points.

{ return _points; }

get_weights() [1/2]

const std::vector<Real>& libMesh::QBase::get_weights ( ) const

inlineinherited

Returns

A constant reference to a std::vector containing the quadrature weights.

Definition at line 168 of file quadrature.h.

References libMesh::QBase::_weights.

Referenced by libMesh::VariationalSmootherSystem::element_time_derivative(), libMesh::QClough::init_1D(), libMesh::QConical::init_1D(), libMesh::QNodal::init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGrundmann_Moller::init_1D(), libMesh::QGaussLobatto::init_2D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGauss::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), and libMesh::OverlapCoupling::operator()().

{ return _weights; }

get_weights() [2/2]

std::vector<Real>& libMesh::QBase::get_weights ( )

inlineinherited

Returns

A writable references to a std::vector containing the quadrature weights.

Definition at line 174 of file quadrature.h.

References libMesh::QBase::_weights.

{ return _weights; }

increment_constructor_count()

void libMesh::ReferenceCounter::increment_constructor_count ( const std::string &  name )

inlineprotectednoexceptinherited

Increments the construction counter.

Should be called in the constructor of any derived class that will be reference counted.

Definition at line 183 of file reference_counter.h.

References libMesh::err, libMesh::BasicOStreamProxy< charT, traits >::get(), libMesh::Quality::name(), and libMesh::Threads::spin_mtx.

Referenced by libMesh::ReferenceCountedObject< RBParametrized >::ReferenceCountedObject().

{
  libmesh_try
  {
    Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
    std::pair<unsigned int, unsigned int> & p = _counts[name];
    p.first++;
  }
  libmesh_catch (...)
  {
    auto stream = libMesh::err.get();
    stream->exceptions(stream->goodbit); // stream must not throw
    libMesh::err << "Encountered unrecoverable error while calling "
                 << "ReferenceCounter::increment_constructor_count() "
                 << "for a(n) " << name << " object." << std::endl;
    std::terminate();
  }
}

increment_destructor_count()

void libMesh::ReferenceCounter::increment_destructor_count ( const std::string &  name )

inlineprotectednoexceptinherited

Increments the destruction counter.

Should be called in the destructor of any derived class that will be reference counted.

Definition at line 207 of file reference_counter.h.

References libMesh::err, libMesh::BasicOStreamProxy< charT, traits >::get(), libMesh::Quality::name(), and libMesh::Threads::spin_mtx.

Referenced by libMesh::ReferenceCountedObject< RBParametrized >::~ReferenceCountedObject().

{
  libmesh_try
  {
    Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
    std::pair<unsigned int, unsigned int> & p = _counts[name];
    p.second++;
  }
  libmesh_catch (...)
  {
    auto stream = libMesh::err.get();
    stream->exceptions(stream->goodbit); // stream must not throw
    libMesh::err << "Encountered unrecoverable error while calling "
                 << "ReferenceCounter::increment_destructor_count() "
                 << "for a(n) " << name << " object." << std::endl;
    std::terminate();
  }
}

init() [1/4]

void libMesh::QBase::init ( const Elem &  e, unsigned int  p_level = invalid_uint  )

virtualinherited

Initializes the data structures for a quadrature rule for the element e.

If p_level is specified it overrides the element p_level() elevation to use.

Definition at line 65 of file quadrature.C.

References libMesh::QBase::_dim, libMesh::QBase::_elem, libMesh::QBase::_p_level, libMesh::QBase::_type, libMesh::Elem::dim(), libMesh::QBase::init_0D(), libMesh::QBase::init_1D(), libMesh::QBase::init_2D(), libMesh::QBase::init_3D(), libMesh::invalid_uint, libMesh::Elem::p_level(), libMesh::Elem::runtime_topology(), and libMesh::Elem::type().

Referenced by libMesh::QBase::init(), libMesh::QClough::init_1D(), libMesh::QConical::init_1D(), libMesh::QNodal::init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGaussLobatto::init_2D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGauss::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QTrap::init_3D(), libMesh::QGrid::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), libMesh::OverlapCoupling::operator()(), libMesh::QClough::QClough(), libMesh::QConical::QConical(), libMesh::QGauss::QGauss(), libMesh::QGaussLobatto::QGaussLobatto(), libMesh::QGrid::QGrid(), libMesh::QGrundmann_Moller::QGrundmann_Moller(), QJacobi(), libMesh::QMonomial::QMonomial(), libMesh::QNodal::QNodal(), libMesh::QSimpson::QSimpson(), libMesh::QTrap::QTrap(), and libMesh::FE< Dim, LAGRANGE_VEC >::reinit_default_dual_shape_coeffs().

{
  libmesh_assert_equal_to(elem.dim(), _dim);

  // Default to the element p_level() value
  if (p == invalid_uint)
    p = elem.p_level();

  ElemType t = elem.type();

  // check to see if we have already
  // done the work for this quadrature rule
  //
  // If we have something like a Polygon subclass then we're going to
  // need to recompute to be safe; even if we're using the same
  // element, it might have been distorted enough that its subtriangle
  // triangulation has been changed.
  if (t == _type && p == _p_level && !elem.runtime_topology())
    return;
  else
    {
      _elem = &elem;
      _type = t;
      _p_level = p;
    }

  switch(_elem->dim())
    {
    case 0:
      this->init_0D();

      return;

    case 1:
      this->init_1D();

      return;

    case 2:
      this->init_2D();

      return;

    case 3:
      this->init_3D();

      return;

    default:
      libmesh_error_msg("Invalid dimension _dim = " << _dim);
    }
}

init() [2/4]

void libMesh::QBase::init ( const ElemType  type = INVALID_ELEM, unsigned int  p_level = 0, bool  simple_type_only = false  )

virtualinherited

Initializes the data structures for a quadrature rule for an element of type type.

Some types, such as Polygon subclasses, might require more detailed element information and so might not be compatible with this API.

New code should use the Elem-based API for most use cases, but some code may initialize quadrature rules with simple ElemType values like triangles and edges for use in tensor product or conical product constructions; this code can set the simple_type_only flag to avoid being identified as deprecated.

Definition at line 121 of file quadrature.C.

References libMesh::QBase::_dim, libMesh::QBase::_elem, libMesh::QBase::_p_level, libMesh::QBase::_type, libMesh::C0POLYGON, libMesh::C0POLYHEDRON, libMesh::EDGE2, libMesh::QBase::init_0D(), libMesh::QBase::init_1D(), libMesh::QBase::init_2D(), and libMesh::QBase::init_3D().

{
  // Some element types require data from a specific element, so can
  // only be used with newer APIs.
  if (t == C0POLYGON || t == C0POLYHEDRON)
    libmesh_error_msg("Code (see stack trace) used an outdated quadrature function overload.\n"
                      "Quadrature rules on a C0Polygon are not defined by its ElemType alone.");

  // This API is dangerous to use on general meshes, which may include
  // element types where the desired quadrature depends on the
  // physical element, but we still want to be able to initialize
  // based on only a type for certain simple cases
  if (t != EDGE2 && !simple_type_only)
    libmesh_deprecated();

  // check to see if we have already
  // done the work for this quadrature rule
  if (t == _type && p == _p_level)
    return;
  else
    {
      _elem = nullptr;
      _type = t;
      _p_level = p;
    }

  switch(_dim)
    {
    case 0:
      this->init_0D();

      return;

    case 1:
      this->init_1D();

      return;

    case 2:
      this->init_2D();

      return;

    case 3:
      this->init_3D();

      return;

    default:
      libmesh_error_msg("Invalid dimension _dim = " << _dim);
    }
}

init() [3/4]

void libMesh::QBase::init ( const QBase &  other_rule )

virtualinherited

Initializes the data structures for a quadrature rule based on the element, element type, and p_level settings of other_rule.

Definition at line 178 of file quadrature.C.

References libMesh::QBase::_elem, libMesh::QBase::_p_level, libMesh::QBase::_type, and libMesh::QBase::init().

{
  if (other_rule._elem)
    this->init(*other_rule._elem, other_rule._p_level);
  else
    this->init(other_rule._type, other_rule._p_level, true);
}

init() [4/4]

void libMesh::QBase::init ( const Elem &  elem, const std::vector< Real > &  vertex_distance_func, unsigned int  p_level = 0  )

virtualinherited

Initializes the data structures for an element potentially "cut" by a signed distance function.

The array vertex_distance_func contains vertex values of the signed distance function. If the signed distance function changes sign on the vertices, then the element is considered to be cut.) This interface can be extended by derived classes in order to subdivide the element and construct a composite quadrature rule.

Definition at line 188 of file quadrature.C.

References libMesh::QBase::init(), and libMesh::Elem::type().

{
  // dispatch generic implementation
  this->init(elem.type(), p_level);
}

init_0D()

void libMesh::QBase::init_0D ( )

protectedvirtualinherited

Initializes the 0D quadrature rule by filling the points and weights vectors with the appropriate values.

Generally this is just one point with weight 1.

Definition at line 198 of file quadrature.C.

References libMesh::QBase::_points, and libMesh::QBase::_weights.

Referenced by libMesh::QBase::init().

{
  _points.resize(1);
  _weights.resize(1);
  _points[0] = Point(0.);
  _weights[0] = 1.0;
}

init_1D()

void libMesh::QJacobi::init_1D ( )

overrideprivatevirtual

Initializes the 1D quadrature rule by filling the points and weights vectors with the appropriate values.

The order of the rule will be defined by the implementing class. It is assumed that derived quadrature rules will at least define the init_1D function, therefore it is pure virtual.

Implements libMesh::QBase.

Definition at line 26 of file quadrature_jacobi_1D.C.

References _alpha, _beta, libMesh::QBase::_order, libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::CONSTANT, libMesh::EIGHTH, libMesh::EIGHTTEENTH, libMesh::ELEVENTH, libMesh::err, libMesh::FIFTEENTH, libMesh::FIFTH, libMesh::FIRST, libMesh::FORTIETH, libMesh::FORTYFIRST, libMesh::FORTYSECOND, libMesh::FORTYTHIRD, libMesh::FOURTEENTH, libMesh::FOURTH, libMesh::QBase::get_order(), libMesh::NINETEENTH, libMesh::NINTH, libMesh::Real, libMesh::SECOND, libMesh::SEVENTEENTH, libMesh::SEVENTH, libMesh::SIXTEENTH, libMesh::SIXTH, libMesh::TENTH, libMesh::THIRD, libMesh::THIRTEENTH, libMesh::THIRTIETH, libMesh::THIRTYEIGHTH, libMesh::THIRTYFIFTH, libMesh::THIRTYFIRST, libMesh::THIRTYFOURTH, libMesh::THIRTYNINTH, libMesh::THIRTYSECOND, libMesh::THIRTYSEVENTH, libMesh::THIRTYSIXTH, libMesh::THIRTYTHIRD, libMesh::TWELFTH, libMesh::TWENTIETH, libMesh::TWENTYEIGHTH, libMesh::TWENTYFIFTH, libMesh::TWENTYFIRST, libMesh::TWENTYFOURTH, libMesh::TWENTYNINTH, libMesh::TWENTYSECOND, libMesh::TWENTYSEVENTH, libMesh::TWENTYSIXTH, and libMesh::TWENTYTHIRD.

{
  //----------------------------------------------------------------------
  // 1D quadrature rules
  // Note that we need to check _alpha and _beta
  // to determine which quadrature rule to implement.
  // These rules have been pre-scaled based on their
  // intended use.  The weights of the (alpha=1,beta=0)
  // rule sum to 0.5.  The weights of the (alpha=2,beta=0)
  // rule sum to 0.333333333333.

  if ((_alpha == 1) && (_beta == 0))
    {
      switch(get_order())
        {
        case CONSTANT:
        case FIRST:
          {
            _points.resize (1);
            _weights.resize(1);

            _points[0](0)  = 1/Real(3);

            _weights[0]    = 0.5;

            return;
          }
        case SECOND:
        case THIRD:
          {
            _points.resize (2);
            _weights.resize(2);

            _points[ 0](0)=1.5505102572168219018027159252941e-01_R;
            _points[ 1](0)=6.4494897427831780981972840747059e-01_R;

            _weights[ 0]=3.1804138174397716939436900207516e-01_R;
            _weights[ 1]=1.8195861825602283060563099792484e-01_R;

            return;
          }
        case FOURTH:
        case FIFTH:
          {
            _points.resize (3);
            _weights.resize(3);

            _points[ 0](0)=8.8587959512703947395546143769456e-02_R;
            _points[ 1](0)=4.0946686444073471086492625206883e-01_R;
            _points[ 2](0)=7.8765946176084705602524188987600e-01_R;

            _weights[ 0]=2.0093191373895963077219813326460e-01_R;
            _weights[ 1]=2.2924110635958624669392059455632e-01_R;
            _weights[ 2]=6.9826979901454122533881272179077e-02_R;

            return;
          }
        case SIXTH:
        case SEVENTH:
          {
            _points.resize (4);
            _weights.resize(4);

            _points[ 0](0)=5.7104196114517682193121192554116e-02_R;
            _points[ 1](0)=2.7684301363812382768004599768563e-01_R;
            _points[ 2](0)=5.8359043236891682005669766866292e-01_R;
            _points[ 3](0)=8.6024013565621944784791291887512e-01_R;

            _weights[ 0]=1.3550691343148811620826417407794e-01_R;
            _weights[ 1]=2.0346456801027136079140447593585e-01_R;
            _weights[ 2]=1.2984754760823244082645620288963e-01_R;
            _weights[ 3]=3.1180970950008082173875147096575e-02_R;

            return;
          }
        case EIGHTH:
        case NINTH:
          {
            _points.resize (5);
            _weights.resize(5);

            _points[ 0](0)=3.9809857051468742340806690093333e-02_R;
            _points[ 1](0)=1.9801341787360817253579213679530e-01_R;
            _points[ 2](0)=4.3797481024738614400501252000523e-01_R;
            _points[ 3](0)=6.9546427335363609451461482372117e-01_R;
            _points[ 4](0)=9.0146491420117357387650110211225e-01_R;

            _weights[ 0]=9.6781590226651679274360971636151e-02_R;
            _weights[ 1]=1.6717463809436956549167562309770e-01_R;
            _weights[ 2]=1.4638698708466980869803786935596e-01_R;
            _weights[ 3]=7.3908870072616670350633219341704e-02_R;
            _weights[ 4]=1.5747914521692276185292316568488e-02_R;

            return;
          }
        case TENTH:
        case ELEVENTH:
          {

            _points.resize (6);
            _weights.resize(6);

            _points[ 0](0)=2.9316427159784891972050276913165e-02_R;
            _points[ 1](0)=1.4807859966848429184997685249598e-01_R;
            _points[ 2](0)=3.3698469028115429909705297208078e-01_R;
            _points[ 3](0)=5.5867151877155013208139334180552e-01_R;
            _points[ 4](0)=7.6923386203005450091688336011565e-01_R;
            _points[ 5](0)=9.2694567131974111485187396581968e-01_R;

            _weights[ 0]=7.2310330725508683655454326124832e-02_R;
            _weights[ 1]=1.3554249723151861684069039663805e-01_R;
            _weights[ 2]=1.4079255378819892811907683907093e-01_R;
            _weights[ 3]=9.8661150890655264120584510548360e-02_R;
            _weights[ 4]=4.3955165550508975508176624305430e-02_R;
            _weights[ 5]=8.7383018136095317560173033123989e-03_R;

            return;
          }
        case TWELFTH:
        case THIRTEENTH:
          {
            _points.resize (7);
            _weights.resize(7);

            _points[ 0](0)=2.2479386438712498108825499570845e-02_R;
            _points[ 1](0)=1.1467905316090423190964023706751e-01_R;
            _points[ 2](0)=2.6578982278458946847678939169339e-01_R;
            _points[ 3](0)=4.5284637366944461699855144234765e-01_R;
            _points[ 4](0)=6.4737528288683036262609222982876e-01_R;
            _points[ 5](0)=8.1975930826310763501242005719082e-01_R;
            _points[ 6](0)=9.4373743946307785353434780896769e-01_R;

            _weights[ 0]=5.5967363423491051151562113429926e-02_R;
            _weights[ 1]=1.1050925819087460242112073636961e-01_R;
            _weights[ 2]=1.2739089729958832691873448577496e-01_R;
            _weights[ 3]=1.0712506569587366999091225299986e-01_R;
            _weights[ 4]=6.6384696465491469983647988763640e-02_R;
            _weights[ 5]=2.7408356721873475444331048358226e-02_R;
            _weights[ 6]=5.2143622028074040896913743037830e-03_R;

            return;
          }
        case FOURTEENTH:
        case FIFTEENTH:
          {
            _points.resize (8);
            _weights.resize(8);

            _points[ 0](0)=1.7779915147363451813205101037679e-02_R;
            _points[ 1](0)=9.1323607899793956003741458074541e-02_R;
            _points[ 2](0)=2.1430847939563075835754126758167e-01_R;
            _points[ 3](0)=3.7193216458327230243085396048263e-01_R;
            _points[ 4](0)=5.4518668480342664903227222995321e-01_R;
            _points[ 5](0)=7.1317524285556948105131376025091e-01_R;
            _points[ 6](0)=8.5563374295785442851478147977179e-01_R;
            _points[ 7](0)=9.5536604471003014926687897814169e-01_R;

            _weights[ 0]=4.4550804361555931326215619533963e-02_R;
            _weights[ 1]=9.1119023636373626345722461782880e-02_R;
            _weights[ 2]=1.1250579947088736617177209860428e-01_R;
            _weights[ 3]=1.0604735943593001070453109641116e-01_R;
            _weights[ 4]=7.9199599492319160120408189359892e-02_R;
            _weights[ 5]=4.5439319504698898083055421095694e-02_R;
            _weights[ 6]=1.7842902655986208393552797201042e-02_R;
            _weights[ 7]=3.2951914422487988547423160110891e-03_R;

            return;
          }
        case SIXTEENTH:
        case SEVENTEENTH:
          {
            _points.resize (9);
            _weights.resize(9);

            _points[ 0](0)=1.4412409648876548632826740810813e-02_R;
            _points[ 1](0)=7.4387389709196044635918185955999e-02_R;
            _points[ 2](0)=1.7611665616299528186317574607257e-01_R;
            _points[ 3](0)=3.0966757992763781705962046722948e-01_R;
            _points[ 4](0)=4.6197040108101093488314310868056e-01_R;
            _points[ 5](0)=6.1811723469529402463922975160350e-01_R;
            _points[ 6](0)=7.6282301518503961468269330714673e-01_R;
            _points[ 7](0)=8.8192102121000129980771488800526e-01_R;
            _points[ 8](0)=9.6374218711679053905883569923192e-01_R;

            _weights[ 0]=3.6278003523279871459649597941160e-02_R;
            _weights[ 1]=7.6074255109308162580079303753964e-02_R;
            _weights[ 2]=9.8533742172345705160173020369274e-02_R;
            _weights[ 3]=1.0030880919336828965415022473259e-01_R;
            _weights[ 4]=8.4358321844920349394250019958587e-02_R;
            _weights[ 5]=5.8401195295165110565731522901640e-02_R;
            _weights[ 6]=3.1804821491054001261690106935870e-02_R;
            _weights[ 7]=1.2060004284785379051727152286900e-02_R;
            _weights[ 8]=2.1808470857731308725490511200170e-03_R;

            return;
          }
        case EIGHTTEENTH:
        case NINETEENTH:
          {
            _points.resize (10);
            _weights.resize(10);

            _points[ 0](0)=1.1917613432415596909745586958986e-02_R;
            _points[ 1](0)=6.1732071877148125522629367194250e-02_R;
            _points[ 2](0)=1.4711144964307024042759943557982e-01_R;
            _points[ 3](0)=2.6115967600845624026605165805485e-01_R;
            _points[ 4](0)=3.9463984688578684296195210507761e-01_R;
            _points[ 5](0)=5.3673876571566063287309517771189e-01_R;
            _points[ 6](0)=6.7594446167666510735715050893476e-01_R;
            _points[ 7](0)=8.0097892103689884513794630161724e-01_R;
            _points[ 8](0)=9.0171098779014677034879897840977e-01_R;
            _points[ 9](0)=9.6997096783851350295693564236559e-01_R;

            _weights[ 0]=3.0099508024037023300654755523879e-02_R;
            _weights[ 1]=6.4287154509082572874826538628865e-02_R;
            _weights[ 2]=8.6211300289176036428333360711914e-02_R;
            _weights[ 3]=9.2696893677723415844756991929711e-02_R;
            _weights[ 4]=8.4557109690827332430645582165501e-02_R;
            _weights[ 5]=6.6053075563350379166074502504878e-02_R;
            _weights[ 6]=4.3401906407150625922456117586384e-02_R;
            _weights[ 7]=2.2774591453263032586487649426060e-02_R;
            _weights[ 8]=8.4193197829831874175163655187011e-03_R;
            _weights[ 9]=1.4991406024063940282481360041064e-03_R;

            return;
          }
        case TWENTIETH:
        case TWENTYFIRST:
          {
            _points.resize (11);
            _weights.resize(11);

            _points[ 0](0)=1.0018280461680405843024729867805e-02_R;
            _points[ 1](0)=5.2035451127180552583542695772964e-02_R;
            _points[ 2](0)=1.2461922514444307373529958726391e-01_R;
            _points[ 3](0)=2.2284060704383785550783145345736e-01_R;
            _points[ 4](0)=3.4000815791466518823360523389702e-01_R;
            _points[ 5](0)=4.6813761308958404208311038075775e-01_R;
            _points[ 6](0)=5.9849727976713918322772071367304e-01_R;
            _points[ 7](0)=7.2220328489096792556332130780461e-01_R;
            _points[ 8](0)=8.3082489962281857403056654390566e-01_R;
            _points[ 9](0)=9.1695838655259485329313462701803e-01_R;
            _points[10](0)=9.7472637960247965024666881353837e-01_R;

            _weights[ 0]=2.5367340688141426184944658517383e-02_R;
            _weights[ 1]=5.4938091132871498258746681665651e-02_R;
            _weights[ 2]=7.5620048057186998321377054841660e-02_R;
            _weights[ 3]=8.4659422884017621219239388551910e-02_R;
            _weights[ 4]=8.1879102988063470389586851943461e-02_R;
            _weights[ 5]=6.9531875158183049799050889633934e-02_R;
            _weights[ 6]=5.1591360672297580193086641744608e-02_R;
            _weights[ 7]=3.2641546713833346017953865389764e-02_R;
            _weights[ 8]=1.6663623451680692415747124573826e-02_R;
            _weights[ 9]=6.0439209604797757927329621765769e-03_R;
            _weights[10]=1.0636672932445414075338809612253e-03_R;

            return;
          }
        case TWENTYSECOND:
        case TWENTYTHIRD:
          {
            _points.resize (12);
            _weights.resize(12);

            _points[ 0](0)=8.5390549884274193686644608778398e-03_R;
            _points[ 1](0)=4.4446463155407723025466798785553e-02_R;
            _points[ 2](0)=1.0685449088347665763410677043250e-01_R;
            _points[ 3](0)=1.9215105452985404099105725622861e-01_R;
            _points[ 4](0)=2.9538088426258022162291683437601e-01_R;
            _points[ 5](0)=4.1054508120145768248903435055933e-01_R;
            _points[ 6](0)=5.3095084931281767062893024289682e-01_R;
            _points[ 7](0)=6.4960065027725499276629172334298e-01_R;
            _points[ 8](0)=7.5959888952522705374260257404342e-01_R;
            _points[ 9](0)=8.5455254376493588079021191640562e-01_R;
            _points[10](0)=9.2894210126441101784881015513432e-01_R;
            _points[11](0)=9.7843793683414963909190691691700e-01_R;

            _weights[ 0]=2.1664860886871767324583472077976e-02_R;
            _weights[ 1]=4.7427851980377470134309182197087e-02_R;
            _weights[ 2]=6.6606750626673198130834485351975e-02_R;
            _weights[ 3]=7.6896602680041006281204469112373e-02_R;
            _weights[ 4]=7.7696316815531026628765631099760e-02_R;
            _weights[ 5]=7.0109339997630094495921805029671e-02_R;
            _weights[ 6]=5.6613843713667631943701105156121e-02_R;
            _weights[ 7]=4.0451653706913616760646424250646e-02_R;
            _weights[ 8]=2.4876780409265432012508172290016e-02_R;
            _weights[ 9]=1.2436009166422265607483293056674e-02_R;
            _weights[10]=4.4448077956684623227961458658283e-03_R;
            _weights[11]=7.7518222093802835724581451187414e-04_R;

            return;
          }

        case TWENTYFOURTH:
        case TWENTYFIFTH:
          {
            _points.resize (13);
            _weights.resize(13);

            _points[ 0](0)=7.3646510260893216506914984138223e-03_R;
            _points[ 1](0)=3.8398138739678350376832524864142e-02_R;
            _points[ 2](0)=9.2595224699002635282891375438616e-02_R;
            _points[ 3](0)=1.6725101139155773149552247875936e-01_R;
            _points[ 4](0)=2.5862354070576251658979073282269e-01_R;
            _points[ 5](0)=3.6213139728223880040868129822732e-01_R;
            _points[ 6](0)=4.7258438600411772517509464267860e-01_R;
            _points[ 7](0)=5.8444396402134045550422084781091e-01_R;
            _points[ 8](0)=6.9210100171960165689704195168767e-01_R;
            _points[ 9](0)=7.9015702827343748555286333249938e-01_R;
            _points[10](0)=8.7369482130668941936771456713174e-01_R;
            _points[11](0)=9.3852445910073101239763338676530e-01_R;
            _points[12](0)=9.8138963498901214856028062215971e-01_R;

            _weights[ 0]=1.8714731585615175193374408664994e-02_R;
            _weights[ 1]=4.1320289419839298476611706952624e-02_R;
            _weights[ 2]=5.8953937956647082536161503261961e-02_R;
            _weights[ 3]=6.9713468282144398251416629950427e-02_R;
            _weights[ 4]=7.2849696515818223079384033843973e-02_R;
            _weights[ 5]=6.8815529487565417217837889436694e-02_R;
            _weights[ 6]=5.9120481314092327419290155953032e-02_R;
            _weights[ 7]=4.5995780676052393313259784530213e-02_R;
            _weights[ 8]=3.1936787162203148842381371158461e-02_R;
            _weights[ 9]=1.9213957164719820645895497863743e-02_R;
            _weights[10]=9.4489244795927503661800865492413e-03_R;
            _weights[11]=3.3383592507737718066104206420419e-03_R;
            _weights[12]=5.7805670493619285159651119259460e-04_R;

            return;
          }

        case TWENTYSIXTH:
        case TWENTYSEVENTH:
          {
            _points.resize (14);
            _weights.resize(14);

            _points[ 0](0)=6.4167607928184568108204640945072e-03_R;
            _points[ 1](0)=3.3501404532013140035963928570572e-02_R;
            _points[ 2](0)=8.0985499681955184392451307739982e-02_R;
            _points[ 3](0)=1.4680486768121372992366016526080e-01_R;
            _points[ 4](0)=2.2808427064925799153464409861994e-01_R;
            _points[ 5](0)=3.2127174398893617440234039741304e-01_R;
            _points[ 6](0)=4.2229465730757025784040898751810e-01_R;
            _points[ 7](0)=5.2673786133987303205372694481288e-01_R;
            _points[ 8](0)=6.3003668837040395788448059413143e-01_R;
            _points[ 9](0)=7.2767645288926468543602672799033e-01_R;
            _points[10](0)=8.1538973944347464197307421861206e-01_R;
            _points[11](0)=8.8934280881951553969087166094649e-01_R;
            _points[12](0)=9.4630270006027538353340594342472e-01_R;
            _points[13](0)=9.8377523409860023828122800914100e-01_R;

            _weights[ 0]=1.6326754322596839819449429350767e-02_R;
            _weights[ 1]=3.6296078055443693187652118821852e-02_R;
            _weights[ 2]=5.2445953501916745591081806162678e-02_R;
            _weights[ 3]=6.3213025574329203442529115357932e-02_R;
            _weights[ 4]=6.7831659604182837102347339834146e-02_R;
            _weights[ 5]=6.6392350626085425132821358651277e-02_R;
            _weights[ 6]=5.9785559022531584222614059168587e-02_R;
            _weights[ 7]=4.9519454523203004580936179335753e-02_R;
            _weights[ 8]=3.7443096458985826655938301826886e-02_R;
            _weights[ 9]=2.5423465407148762115069898757459e-02_R;
            _weights[10]=1.5032303743928643503408714751315e-02_R;
            _weights[11]=7.2964841332126214434099222674776e-03_R;
            _weights[12]=2.5541013176876539479794996099427e-03_R;
            _weights[13]=4.3971370874715925476225610392609e-04_R;

            return;
          }

        case TWENTYEIGHTH:
        case TWENTYNINTH:
          {
            _points.resize (15);
            _weights.resize(15);

            _points[ 0](0)=5.6406889725117097575064665794442e-03_R;
            _points[ 1](0)=2.9482298647942486631640984718004e-02_R;
            _points[ 2](0)=7.1412953115158840054783901746735e-02_R;
            _points[ 3](0)=1.2983102555359105597125453809429e-01_R;
            _points[ 4](0)=2.0249275505010404756821998832023e-01_R;
            _points[ 5](0)=2.8660608625752705998402604548440e-01_R;
            _points[ 6](0)=3.7893868864697803810652900914277e-01_R;
            _points[ 7](0)=4.7594230846323486057258899201585e-01_R;
            _points[ 8](0)=5.7388916090668588067145385523753e-01_R;
            _points[ 9](0)=6.6901519502995987653869563905314e-01_R;
            _points[10](0)=7.5766473903134271199707427774029e-01_R;
            _points[11](0)=8.3643096060561012397555908565418e-01_R;
            _points[12](0)=9.0228670067937802663123850466201e-01_R;
            _points[13](0)=9.5270040990583331433804420752426e-01_R;
            _points[14](0)=9.8573054526317422526590063305913e-01_R;

            _weights[ 0]=1.4367069621712523019113300206269e-02_R;
            _weights[ 1]=3.2119044874965915878547666076448e-02_R;
            _weights[ 2]=4.6891639944059925679345570546797e-02_R;
            _weights[ 3]=5.7398825506941289374618916116414e-02_R;
            _weights[ 4]=6.2918106648596909592665349230551e-02_R;
            _weights[ 5]=6.3343955161511392519350738069297e-02_R;
            _weights[ 6]=5.9174192059712931565021168664588e-02_R;
            _weights[ 7]=5.1412362311886468530400169371359e-02_R;
            _weights[ 8]=4.1400735184422578228813150524935e-02_R;
            _weights[ 9]=3.0609769586468540804291808789747e-02_R;
            _weights[10]=2.0416309272619835691190995270654e-02_R;
            _weights[11]=1.1904190355097578843030186960250e-02_R;
            _weights[12]=5.7172223947211761716246502974268e-03_R;
            _weights[13]=1.9862346931450380410338051145760e-03_R;
            _weights[14]=3.4034238413789606095252476068833e-04_R;

            return;
          }


        case THIRTIETH:
        case THIRTYFIRST:
          {
            _points.resize (16);
            _weights.resize(16);

            _points[ 0](0)=4.9972996637719210426511496015207e-03_R;
            _points[ 1](0)=2.6143513681394051978549323380543e-02_R;
            _points[ 2](0)=6.3430945583836745492528222770701e-02_R;
            _points[ 3](0)=1.1559843757981594017892362824740e-01_R;
            _points[ 4](0)=1.8087055965788366624757339125570e-01_R;
            _points[ 5](0)=2.5702480784517085992294423955927e-01_R;
            _points[ 6](0)=3.4146792754782306862589929793869e-01_R;
            _points[ 7](0)=4.3132434359562537508359226958274e-01_R;
            _points[ 8](0)=5.2353411602516832051747016507566e-01_R;
            _points[ 9](0)=6.1495715187648951748964083381908e-01_R;
            _points[10](0)=7.0248013792504104445480697553762e-01_R;
            _points[11](0)=7.8312255396486808385218178256205e-01_R;
            _points[12](0)=8.5413814777521063366511368381932e-01_R;
            _points[13](0)=9.1310837653714127462958554670327e-01_R;
            _points[14](0)=9.5802441769047545454495934455429e-01_R;
            _points[15](0)=9.8735302062604161803115590316790e-01_R;

            _weights[ 0]=1.2739310657334184747549845879578e-02_R;
            _weights[ 1]=2.8612452590143149357558068987418e-02_R;
            _weights[ 2]=4.2129431157428284757515740541878e-02_R;
            _weights[ 3]=5.2228594403959147363509678893029e-02_R;
            _weights[ 4]=5.8254240209855835379301779422393e-02_R;
            _weights[ 5]=6.0000854888113507055385942002166e-02_R;
            _weights[ 6]=5.7718879609267823617681995467969e-02_R;
            _weights[ 7]=5.2064137843806583754973352189273e-02_R;
            _weights[ 8]=4.3997382189243923173481417304490e-02_R;
            _weights[ 9]=3.4647816579285799103084877873731e-02_R;
            _weights[10]=2.5159233106470040585653957496918e-02_R;
            _weights[11]=1.6539584355635793501225242083105e-02_R;
            _weights[12]=9.5341678846659366549669638207733e-03_R;
            _weights[13]=4.5392323861386350682211111786128e-03_R;
            _weights[14]=1.5671884735958197030724006964051e-03_R;
            _weights[15]=2.6749366505553617681762616226073e-04_R;

            return;
          }


        case THIRTYSECOND:
        case THIRTYTHIRD:
          {
            _points.resize (17);
            _weights.resize(17);

            _points[ 0](0)=4.4579935677873917545062291115464e-03_R;
            _points[ 1](0)=2.3340094123774273967021528207683e-02_R;
            _points[ 2](0)=5.6707968769078239532713331556521e-02_R;
            _points[ 3](0)=1.0355543293519706341349122696131e-01_R;
            _points[ 4](0)=1.6246000342813654998162954391410e-01_R;
            _points[ 5](0)=2.3163212577717218294679722573836e-01_R;
            _points[ 6](0)=3.0897011775219590331752426128626e-01_R;
            _points[ 7](0)=3.9212413472209565803361946333190e-01_R;
            _points[ 8](0)=4.7856759685307958878371046285937e-01_R;
            _points[ 9](0)=5.6567396688663433190330697600965e-01_R;
            _points[10](0)=6.5079655845338226473148740732315e-01_R;
            _points[11](0)=7.3134895273405138213302149556298e-01_R;
            _points[12](0)=8.0488357852496649199917770139703e-01_R;
            _points[13](0)=8.6916605956741361920444649801116e-01_R;
            _points[14](0)=9.2224303459229840848710732823038e-01_R;
            _points[15](0)=9.6250119782335004125046077538851e-01_R;
            _points[16](0)=9.8871404063224375141712140225296e-01_R;

            _weights[ 0]=1.1372703113196894148880104403419e-02_R;
            _weights[ 1]=2.5642427920205179185750205247311e-02_R;
            _weights[ 2]=3.8025728825742400201474917006665e-02_R;
            _weights[ 3]=4.7641869374618441920575209265709e-02_R;
            _weights[ 4]=5.3907931667527480191616020246527e-02_R;
            _weights[ 5]=5.6573611382471512986991034182850e-02_R;
            _weights[ 6]=5.5734917923560549577129019490753e-02_R;
            _weights[ 7]=5.1809741929296333255214704762820e-02_R;
            _weights[ 8]=4.5477790399142277497438924164211e-02_R;
            _weights[ 9]=3.7592325487112238031431998524319e-02_R;
            _weights[10]=2.9074524087705050563187355467924e-02_R;
            _weights[11]=2.0803278010295362060012866375773e-02_R;
            _weights[12]=1.3513697452300780909638958310491e-02_R;
            _weights[13]=7.7164222148059386958884227660543e-03_R;
            _weights[14]=3.6472304834214064450344565237838e-03_R;
            _weights[15]=1.2526834393912207489106525201067e-03_R;
            _weights[16]=2.1311628920693358082515074128342e-04_R;

            return;
          }

        case THIRTYFOURTH:
        case THIRTYFIFTH:
          {
            _points.resize (18);
            _weights.resize(18);

            _points[ 0](0)=4.0014793838673867970427199102708e-03_R;
            _points[ 1](0)=2.0963648393766477995135600986561e-02_R;
            _points[ 2](0)=5.0994041587890553966774921299853e-02_R;
            _points[ 3](0)=9.3280395928544950777609058826066e-02_R;
            _points[ 4](0)=1.4667010367761795715160882973461e-01_R;
            _points[ 5](0)=2.0970703958884296672188171145203e-01_R;
            _points[ 6](0)=2.8067179006017169910681926203455e-01_R;
            _points[ 7](0)=3.5762864997663462939832714298390e-01_R;
            _points[ 8](0)=4.3847844922413811765185426038741e-01_R;
            _points[ 9](0)=5.2101582087077614731981479158547e-01_R;
            _points[10](0)=6.0298936055983207213748070418747e-01_R;
            _points[11](0)=6.8216303911365156501882207998153e-01_R;
            _points[12](0)=7.5637719340615062679816733590978e-01_R;
            _points[13](0)=8.2360742977486956587394885462062e-01_R;
            _points[14](0)=8.8201982536207914673124120886230e-01_R;
            _points[15](0)=9.3002088969969321648195850472769e-01_R;
            _points[16](0)=9.6630075194563254241150674649068e-01_R;
            _points[17](0)=9.8986684820259713441676302277596e-01_R;

            _weights[ 0]=1.0214339435040633872267566728543e-02_R;
            _weights[ 1]=2.3106350163377066931289331193145e-02_R;
            _weights[ 2]=3.4471118921922024965038695158493e-02_R;
            _weights[ 3]=4.3573907074643088262181650935306e-02_R;
            _weights[ 4]=4.9902226917702713891102223856106e-02_R;
            _weights[ 5]=5.3192334631835660026223777017865e-02_R;
            _weights[ 6]=5.3445287802814027020361560753181e-02_R;
            _weights[ 7]=5.0916928856374093181562996165432e-02_R;
            _weights[ 8]=4.6082400990241280762086995392822e-02_R;
            _weights[ 9]=3.9579162288607878726422969126448e-02_R;
            _weights[10]=3.2134806127628549240737903166505e-02_R;
            _weights[11]=2.4487590001291716597869859208141e-02_R;
            _weights[12]=1.7308300480899289815470186505791e-02_R;
            _weights[13]=1.1131870097409362452892993478578e-02_R;
            _weights[14]=6.3060388823805337332782426625400e-03_R;
            _weights[15]=2.9624430644328375036535062298419e-03_R;
            _weights[16]=1.0130251793010471252471709101709e-03_R;
            _weights[17]=1.7186908409819589231237151109171e-04_R;

            return;
          }

        case THIRTYSIXTH:
        case THIRTYSEVENTH:
          {
            _points.resize (19);
            _weights.resize(19);

            _points[ 0](0)=3.6116428185568930344532101262520e-03_R;
            _points[ 1](0)=1.8931837031588217250264524316949e-02_R;
            _points[ 2](0)=4.6097933048431083573924770835459e-02_R;
            _points[ 3](0)=8.4447222784209820599847900451170e-02_R;
            _points[ 4](0)=1.3303618855809877542408742397522e-01_R;
            _points[ 5](0)=1.9066859490476335108747466488719e-01_R;
            _points[ 6](0)=2.5592540348210296025204739729528e-01_R;
            _points[ 7](0)=3.2719980076381171572842996527566e-01_R;
            _points[ 8](0)=4.0273678616507709512304701110488e-01_R;
            _points[ 9](0)=4.8067639357855190263322135248271e-01_R;
            _points[10](0)=5.5909949264903198784692797587908e-01_R;
            _points[11](0)=6.3607504487927089469109105709816e-01_R;
            _points[12](0)=7.0970765165390239884374678311164e-01_R;
            _points[13](0)=7.7818422297676161420929964704208e-01_R;
            _points[14](0)=8.3981861570871107783863629442929e-01_R;
            _points[15](0)=8.9309313498184497075098115456491e-01_R;
            _points[16](0)=9.3669584807436508054390550208195e-01_R;
            _points[17](0)=9.6955263708022088547192878623227e-01_R;
            _points[18](0)=9.9085180527095568535309483522012e-01_R;

            _weights[ 0]=9.2240377250330766917668248692203e-03_R;
            _weights[ 1]=2.0924651751979890481445228332988e-02_R;
            _weights[ 2]=3.1376275285732898854356814457609e-02_R;
            _weights[ 3]=3.9962370048991741940293076442317e-02_R;
            _weights[ 4]=4.6234928168578411765380785132191e-02_R;
            _weights[ 5]=4.9934138240419379553284105838773e-02_R;
            _weights[ 6]=5.1004186626719396295755229568486e-02_R;
            _weights[ 7]=4.9591046468706580141316052533532e-02_R;
            _weights[ 8]=4.6021985716138412908362881060678e-02_R;
            _weights[ 9]=4.0768870871836685572301729841664e-02_R;
            _weights[10]=3.4398957951907391429559705435925e-02_R;
            _weights[11]=2.7518058144347978141481142479516e-02_R;
            _weights[12]=2.0711672562757804879837159838775e-02_R;
            _weights[13]=1.4489847112109724657001233005036e-02_R;
            _weights[14]=9.2410919293165977626976877702861e-03_R;
            _weights[15]=5.1997813282783796868055465441831e-03_R;
            _weights[16]=2.4300917120432807075681660438661e-03_R;
            _weights[17]=8.2788076092398219334600301771448e-04_R;
            _weights[18]=1.4012759417838633744062778723898e-04_R;

            return;
          }

        case THIRTYEIGHTH:
        case THIRTYNINTH:
          {
            _points.resize (20);
            _weights.resize(20);

            _points[ 0](0)=3.2761066690500989752646761128711e-03_R;
            _points[ 1](0)=1.7181218145255713738247704631582e-02_R;
            _points[ 2](0)=4.1871431117765195244234634143709e-02_R;
            _points[ 3](0)=7.6800837089621970481870523019947e-02_R;
            _points[ 4](0)=1.2118986732367606561768615229454e-01_R;
            _points[ 5](0)=1.7404711263554216522415793419966e-01_R;
            _points[ 6](0)=2.3419188631359219089445571283230e-01_R;
            _points[ 7](0)=3.0028067683595016436625841871717e-01_R;
            _points[ 8](0)=3.7083718058439689644532207953771e-01_R;
            _points[ 9](0)=4.4428528696301116212882391783598e-01_R;
            _points[10](0)=5.1898428870357372961841176083024e-01_R;
            _points[11](0)=5.9326553348350648796739308654437e-01_R;
            _points[12](0)=6.6546969890551364795372958813385e-01_R;
            _points[13](0)=7.3398385823565944973202719329584e-01_R;
            _points[14](0)=7.9727750833659468770218885137527e-01_R;
            _points[15](0)=8.5393675303589045708900439161802e-01_R;
            _points[16](0)=9.0269587179345369227634694169967e-01_R;
            _points[17](0)=9.4246554236318633869089187742766e-01_R;
            _points[18](0)=9.7235694664743691118470187166465e-01_R;
            _points[19](0)=9.9169995579293273076654365969470e-01_R;

            _weights[ 0]=8.3708441762725569742347797346057e-03_R;
            _weights[ 1]=1.9034969463701666952317752319364e-02_R;
            _weights[ 2]=2.8668237379130596303519483134423e-02_R;
            _weights[ 3]=3.6750239836647855880170014918540e-02_R;
            _weights[ 4]=4.2890295837978204214146023790200e-02_R;
            _weights[ 5]=4.6841691862557827847492882468251e-02_R;
            _weights[ 6]=4.8516105059854090810181874268668e-02_R;
            _weights[ 7]=4.7985461609943912515256158210751e-02_R;
            _weights[ 8]=4.5470588941353475125260875269943e-02_R;
            _weights[ 9]=4.1317706816665737825832945172262e-02_R;
            _weights[10]=3.5964919153862747854063187859799e-02_R;
            _weights[11]=2.9901741842629013049082489189589e-02_R;
            _weights[12]=2.3625296173548892813066360441583e-02_R;
            _weights[13]=1.7597066879206016267686128655074e-02_R;
            _weights[14]=1.2204046126680104278798703245791e-02_R;
            _weights[15]=7.7276679300514628735780671415898e-03_R;
            _weights[16]=4.3232191126901531337390520742896e-03_R;
            _weights[17]=2.0114576139640780069071394684122e-03_R;
            _weights[18]=6.8306227608592198451771987553801e-04_R;
            _weights[19]=1.1538190717568529014836276132844e-04_R;

            return;
          }

        case FORTIETH:
        case FORTYFIRST:
          {
            _points.resize (21);
            _weights.resize(21);

            _points[ 0](0)=2.9852372832130627418887840757498e-03_R;
            _points[ 1](0)=1.5662280557573547332895610655678e-02_R;
            _points[ 2](0)=3.8198288245073553344832819395658e-02_R;
            _points[ 3](0)=7.0139619062325798139842656763758e-02_R;
            _points[ 4](0)=1.1083667332036350223762530758616e-01_R;
            _points[ 5](0)=1.5946112944406525026381380836555e-01_R;
            _points[ 6](0)=2.1502318535802028508091216764592e-01_R;
            _points[ 7](0)=2.7639177909378317240968620976306e-01_R;
            _points[ 8](0)=3.4231763295873079372348132371246e-01_R;
            _points[ 9](0)=4.1145869156190519892697533612651e-01_R;
            _points[10](0)=4.8240744461243888053531852185958e-01_R;
            _points[11](0)=5.5371958072829359140036561243486e-01_R;
            _points[12](0)=6.2394338972128194749630581474409e-01_R;
            _points[13](0)=6.9164931501296225721944667896925e-01_R;
            _points[14](0)=7.5545905444968698626584997281486e-01_R;
            _points[15](0)=8.1407361651269741678894410957934e-01_R;
            _points[16](0)=8.6629975897095659707636330435792e-01_R;
            _points[17](0)=9.1107426580261577477966643276619e-01_R;
            _points[18](0)=9.4748554440639734668609897166113e-01_R;
            _points[19](0)=9.7479197566036565307915209128675e-01_R;
            _points[20](0)=9.9243549072562147749379027938900e-01_R;

            _weights[ 0]=7.6306059065231890951709176867159e-03_R;
            _weights[ 1]=1.7387926076195012545310092581185e-02_R;
            _weights[ 2]=2.6287260083203306468723755830943e-02_R;
            _weights[ 3]=3.3886790344403175515158905218748e-02_R;
            _weights[ 4]=3.9845977571398966444570950002831e-02_R;
            _weights[ 5]=4.3935570635150377464859835729052e-02_R;
            _weights[ 6]=4.6050270723257502074077985626262e-02_R;
            _weights[ 7]=4.6212552611022412660350368837561e-02_R;
            _weights[ 8]=4.4566874686154606866984823191992e-02_R;
            _weights[ 9]=4.1364760396997617354403702904192e-02_R;
            _weights[10]=3.6942012648499385551903205764287e-02_R;
            _weights[11]=3.1689953050127340376763333466278e-02_R;
            _weights[12]=2.6023046795895555117823162899995e-02_R;
            _weights[13]=2.0345549389821508292035088652126e-02_R;
            _weights[14]=1.5019872613192784763520392446339e-02_R;
            _weights[15]=1.0339209757970312663832726410241e-02_R;
            _weights[16]=6.5065974236456053354067512991831e-03_R;
            _weights[17]=3.6220528697449398652362737797211e-03_R;
            _weights[18]=1.6787560215669155362763365937815e-03_R;
            _weights[19]=5.6849852669976417861179123569953e-04_R;
            _weights[20]=9.5861868529721828979599842865244e-05_R;

            return;
          }

        case FORTYSECOND:
        case FORTYTHIRD:
          {
            _points.resize (22);
            _weights.resize(22);

            _points[ 0](0)=2.7314460088842296840089704503200e-03_R;
            _points[ 1](0)=1.4335933483699706185308039285053e-02_R;
            _points[ 2](0)=3.4986328351216449387218814071085e-02_R;
            _points[ 3](0)=6.4302641132158882531275071395686e-02_R;
            _points[ 4](0)=1.0173934345216392401258226593794e-01_R;
            _points[ 5](0)=1.4659920015766541692656584266952e-01_R;
            _points[ 6](0)=1.9804660411818261484660504028001e-01_R;
            _points[ 7](0)=2.5512320697168696957682873507625e-01_R;
            _points[ 8](0)=3.1676578871044727183421117602379e-01_R;
            _points[ 9](0)=3.8182606925675020305095127628112e-01_R;
            _points[10](0)=4.4909210098681733251387195042393e-01_R;
            _points[11](0)=5.1731084595099112005136286684174e-01_R;
            _points[12](0)=5.8521151795129912975524533467408e-01_R;
            _points[13](0)=6.5152925489581447403580682231185e-01_R;
            _points[14](0)=7.1502868047476240261215783933800e-01_R;
            _points[15](0)=7.7452691606482263532020273841099e-01_R;
            _points[16](0)=8.2891561362172651235400549854277e-01_R;
            _points[17](0)=8.7718159746542002099358323827803e-01_R;
            _points[18](0)=9.1842572498984926327926994425432e-01_R;
            _points[19](0)=9.5187959322971991452332541323047e-01_R;
            _points[20](0)=9.7691966323712886717816657113704e-01_R;
            _points[21](0)=9.9307748504434821490300210664154e-01_R;

            _weights[ 0]=6.9842561136978136538216549700282e-03_R;
            _weights[ 1]=1.5944053454778496864565929126309e-02_R;
            _weights[ 2]=2.4184236671890499758870393233781e-02_R;
            _weights[ 3]=3.1327596999375227892408958559682e-02_R;
            _weights[ 4]=3.7077054093202864483217335909271e-02_R;
            _weights[ 5]=4.1222404906411452577079119693783e-02_R;
            _weights[ 6]=4.3651203786303462995293138094828e-02_R;
            _weights[ 7]=4.4353370900419806188626977124445e-02_R;
            _weights[ 8]=4.3418750145417827908334525766667e-02_R;
            _weights[ 9]=4.1027795781940901638265438618895e-02_R;
            _weights[10]=3.7436116466930019239662981188891e-02_R;
            _weights[11]=3.2954058785385534039887856528676e-02_R;
            _weights[12]=2.7922870823442631249079662456458e-02_R;
            _weights[13]=2.2689228598160995380212860776143e-02_R;
            _weights[14]=1.7580017560152292742735027157072e-02_R;
            _weights[15]=1.2879230281365339696348205046681e-02_R;
            _weights[16]=8.8086724401109070881737532508054e-03_R;
            _weights[17]=5.5138751021276410109163746634529e-03_R;
            _weights[18]=3.0562141131504037344643025112362e-03_R;
            _weights[19]=1.4117668531394242829582650189559e-03_R;
            _weights[20]=4.7692790565900675904839748933142e-04_R;
            _weights[21]=8.0298216937450816028842814607537e-05_R;

            return;
          }

        default:
          libmesh_error_msg("Quadrature rule " << _order << " not supported!");
        } // end switch(_order + 2*p)
    } // end if ((_alpha == 1) && (_beta == 0))



  else if ((_alpha == 2) && (_beta == 0))
    {

      switch(get_order())
        {
        case CONSTANT:
        case FIRST:
          {
            _points.resize (1);
            _weights.resize(1);

            _points[0](0)  = 0.25;

            _weights[0]    = 1/Real(3);

            return;
          }
        case SECOND:
        case THIRD:
          {
            _points.resize (2);
            _weights.resize(2);

            _points[ 0](0)=1.2251482265544137786674043037115e-01_R;
            _points[ 1](0)=5.4415184401122528879992623629551e-01_R;

            _weights[ 0]=2.3254745125350790274997694884235e-01_R;
            _weights[ 1]=1.0078588207982543058335638449099e-01_R;

            return;
          }
        case FOURTH:
        case FIFTH:
          {
            _points.resize (3);
            _weights.resize(3);

            _points[ 0](0)=7.2994024073149732155837979012003e-02_R;
            _points[ 1](0)=3.4700376603835188472176354340395e-01_R;
            _points[ 2](0)=7.0500220988849838312239847758405e-01_R;

            _weights[ 0]=1.5713636106488661331834482221327e-01_R;
            _weights[ 1]=1.4624626925986602200351202036424e-01_R;
            _weights[ 2]=2.9950703008580698011476490755827e-02_R;

            return;
          }
        case SIXTH:
        case SEVENTH:
          {
            _points.resize (4);
            _weights.resize(4);

            _points[ 0](0)=4.8500549446997329297067257098986e-02_R;
            _points[ 1](0)=2.3860073755186230505898141272470e-01_R;
            _points[ 2](0)=5.1704729510436750234057336938307e-01_R;
            _points[ 3](0)=7.9585141789677286330337796079324e-01_R;

            _weights[ 0]=1.1088841561127798368323131746895e-01_R;
            _weights[ 1]=1.4345878979921420904832801427594e-01_R;
            _weights[ 2]=6.8633887172923075317376345041811e-02_R;
            _weights[ 3]=1.0352240749918065284397656546639e-02_R;

            return;
          }
        case EIGHTH:
        case NINTH:
          {
            _points.resize (5);
            _weights.resize(5);

            _points[ 0](0)=3.4578939918215091524457428631527e-02_R;
            _points[ 1](0)=1.7348032077169572310459241798618e-01_R;
            _points[ 2](0)=3.8988638706551932824089541038499e-01_R;
            _points[ 3](0)=6.3433347263088677234716388892062e-01_R;
            _points[ 4](0)=8.5105421294701641811622418741001e-01_R;

            _weights[ 0]=8.1764784285770917904880732922352e-02_R;
            _weights[ 1]=1.2619896189991148802883293516467e-01_R;
            _weights[ 2]=8.9200161221590000186254493070384e-02_R;
            _weights[ 3]=3.2055600722961919254748930556633e-02_R;
            _weights[ 4]=4.1138252030990079586162416192983e-03_R;

            return;
          }
        case TENTH:
        case ELEVENTH:
          {
            _points.resize (6);
            _weights.resize(6);

            _points[ 0](0)=2.5904555093667192754643606997235e-02_R;
            _points[ 1](0)=1.3156394165798513398691085074097e-01_R;
            _points[ 2](0)=3.0243691802289123274990557791855e-01_R;
            _points[ 3](0)=5.0903641316475208401103990516772e-01_R;
            _points[ 4](0)=7.1568112731171391876766262459361e-01_R;
            _points[ 5](0)=8.8680561617756186630126600601049e-01_R;

            _weights[ 0]=6.2538702726580937878526556468332e-02_R;
            _weights[ 1]=1.0737649973678063260575568234795e-01_R;
            _weights[ 2]=9.4577186748541203568292051720052e-02_R;
            _weights[ 3]=5.1289571129616210220129325076919e-02_R;
            _weights[ 4]=1.5720297184945051327851262130020e-02_R;
            _weights[ 5]=1.8310758068692977327784555900562e-03_R;

            return;
          }
        case TWELFTH:
        case THIRTEENTH:
          {
            _points.resize (7);
            _weights.resize(7);

            _points[ 0](0)=2.0132773773400507230501687117472e-02_R;
            _points[ 1](0)=1.0308902914804901475222678600595e-01_R;
            _points[ 2](0)=2.4055412604805753665369914150100e-01_R;
            _points[ 3](0)=4.1400214459705974641828724885057e-01_R;
            _points[ 4](0)=6.0002151327899293019396877288994e-01_R;
            _points[ 5](0)=7.7351724659143750111199899642603e-01_R;
            _points[ 6](0)=9.1118316656300276363931736720905e-01_R;

            _weights[ 0]=4.9276501776438120823429129084905e-02_R;
            _weights[ 1]=9.0698824612686144536967479972374e-02_R;
            _weights[ 2]=9.1733803279795254111416595896867e-02_R;
            _weights[ 3]=6.3146378708891297709533940481199e-02_R;
            _weights[ 4]=2.9422211289528614840745351985011e-02_R;
            _weights[ 5]=8.1629256323046945072318090687213e-03_R;
            _weights[ 6]=8.9268803368920680400902684425561e-04_R;

            return;
          }
        case FOURTEENTH:
        case FIFTEENTH:
          {
            _points.resize (8);
            _weights.resize(8);

            _points[ 0](0)=1.6097759551921033532013550096618e-02_R;
            _points[ 1](0)=8.2900617485651102700366353380388e-02_R;
            _points[ 2](0)=1.9547516848873991732426660953061e-01_R;
            _points[ 3](0)=3.4165199147720222027296226216240e-01_R;
            _points[ 4](0)=5.0559707818448917194006186500608e-01_R;
            _points[ 5](0)=6.6955227182436145183011451055437e-01_R;
            _points[ 6](0)=8.1577170358328376075475178697587e-01_R;
            _points[ 7](0)=9.2850896495990689720101861784923e-01_R;

            _weights[ 0]=3.9778957806690559830106455926398e-02_R;
            _weights[ 1]=7.6818093267222624804506735068290e-02_R;
            _weights[ 2]=8.5284769171938765209441226265186e-02_R;
            _weights[ 3]=6.8447183421653272247027200610852e-02_R;
            _weights[ 4]=4.0814426388544023186461596152148e-02_R;
            _weights[ 5]=1.7246863780234982804243655774862e-02_R;
            _weights[ 6]=4.4745217130144079957565210032836e-03_R;
            _weights[ 7]=4.6851778403469725578994253231334e-04_R;

            return;
          }
        case SIXTEENTH:
        case SEVENTEENTH:
          {
            _points.resize (9);
            _weights.resize(9);

            _points[ 0](0)=1.3165885597114490545190537817972e-02_R;
            _points[ 1](0)=6.8084529593767587476505856986822e-02_R;
            _points[ 2](0)=1.6175951676407464206981091232919e-01_R;
            _points[ 3](0)=2.8589108833922039772798956691264e-01_R;
            _points[ 4](0)=4.2945364538781279250924800228659e-01_R;
            _points[ 5](0)=5.7969405635116312626577241331199e-01_R;
            _points[ 6](0)=7.2326857174033543181796015820021e-01_R;
            _points[ 7](0)=8.4743684201323732017318042501962e-01_R;
            _points[ 8](0)=9.4124586421327421141434212713498e-01_R;

            _weights[ 0]=3.2760145111039721461819540084274e-02_R;
            _weights[ 1]=6.5489537033396631781939107203912e-02_R;
            _weights[ 2]=7.7673569160555504078595170478444e-02_R;
            _weights[ 3]=6.9284395689804709215727785348892e-02_R;
            _weights[ 4]=4.8540627864506507959528062424865e-02_R;
            _weights[ 5]=2.6343280902549835737974696002673e-02_R;
            _weights[ 6]=1.0406116579352237052426337235938e-02_R;
            _weights[ 7]=2.5743986456087231023317159056037e-03_R;
            _weights[ 8]=2.6126234651946294299091864873302e-04_R;

            return;
          }
        case EIGHTTEENTH:
        case NINETEENTH:
          {
            _points.resize (10);
            _weights.resize(10);

            _points[ 0](0)=1.0968452456174134250281032990432e-02_R;
            _points[ 1](0)=5.6898150533657920711434859379121e-02_R;
            _points[ 2](0)=1.3595023405022895426576342938519e-01_R;
            _points[ 3](0)=2.4228119613252356111139455536509e-01_R;
            _points[ 4](0)=3.6800785044933771760476956625017e-01_R;
            _points[ 5](0)=5.0380712641487390700553064205723e-01_R;
            _points[ 6](0)=6.3960948865470970932853650616696e-01_R;
            _points[ 7](0)=7.6534767954810789620953312724460e-01_R;
            _points[ 8](0)=8.7171007457440848761186134200542e-01_R;
            _points[ 9](0)=9.5087429264052316644634948461033e-01_R;

            _weights[ 0]=2.7434088710097496960451648584485e-02_R;
            _weights[ 1]=5.6272936402808126282415832152709e-02_R;
            _weights[ 2]=7.0069507708666334086372455308183e-02_R;
            _weights[ 3]=6.7452219381437824970525794313691e-02_R;
            _weights[ 4]=5.2883788766964158209884838942421e-02_R;
            _weights[ 5]=3.3854565016814116044101071309373e-02_R;
            _weights[ 6]=1.7197575046553008079137502323978e-02_R;
            _weights[ 7]=6.4698890685585292297306065609276e-03_R;
            _weights[ 8]=1.5455231947365786285853268147186e-03_R;
            _weights[ 9]=1.5324003669716084212825702284675e-04_R;

            return;
          }
        case TWENTIETH:
        case TWENTYFIRST:
          {
            _points.resize (11);
            _weights.resize(11);

            _points[ 0](0)=9.2789738313488342029466103013448e-03_R;
            _points[ 1](0)=4.8249692094286258286483723731132e-02_R;
            _points[ 2](0)=1.1578862662939522596030591825565e-01_R;
            _points[ 3](0)=2.0766834159705988244389542530053e-01_R;
            _points[ 4](0)=3.1811795190623396637744646657914e-01_R;
            _points[ 5](0)=4.4019839985886246708268132217632e-01_R;
            _points[ 6](0)=5.6623983915456831356751247193488e-01_R;
            _points[ 7](0)=6.8832423986295668569553397580809e-01_R;
            _points[ 8](0)=7.9878435859091464197460872800735e-01_R;
            _points[ 9](0)=8.9069109935439218915081289990608e-01_R;
            _points[10](0)=9.5832514378664820192443912466615e-01_R;

            _weights[ 0]=2.3300850051388377415061404350855e-02_R;
            _weights[ 1]=4.8745861030664491864450329028080e-02_R;
            _weights[ 2]=6.2979543000367394338333998811129e-02_R;
            _weights[ 3]=6.4183559349755944992539371306173e-02_R;
            _weights[ 4]=5.4632222321044926070678715192708e-02_R;
            _weights[ 5]=3.9290217798435612246535835921329e-02_R;
            _weights[ 6]=2.3589663538806928649316661943808e-02_R;
            _weights[ 7]=1.1414590918097618249921262806781e-02_R;
            _weights[ 8]=4.1400042632190223547676874553245e-03_R;
            _weights[ 9]=9.6302057554323908320037373956771e-04_R;
            _weights[10]=9.3800486009778068527692777578977e-05_R;

            return;
          }
        case TWENTYSECOND:
        case TWENTYTHIRD:
          {
            _points.resize (12);
            _weights.resize(12);

            _points[ 0](0)=7.9520457026384368762190933400404e-03_R;
            _points[ 1](0)=4.1427810454294590790770165194795e-02_R;
            _points[ 2](0)=9.9757625542614157066081703480300e-02_R;
            _points[ 3](0)=1.7981078905242324954164334430721e-01_R;
            _points[ 4](0)=2.7727345779931511981753891831052e-01_R;
            _points[ 5](0)=3.8689200999768979166563470380544e-01_R;
            _points[ 6](0)=5.0275736044903220327930927843912e-01_R;
            _points[ 7](0)=6.1862386345845604629354886189114e-01_R;
            _points[ 8](0)=7.2824645295307268642888033006114e-01_R;
            _points[ 9](0)=8.2571851421478690176408336295370e-01_R;
            _points[10](0)=9.0579507354454372680179647039974e-01_R;
            _points[11](0)=9.6420653529267155121295530627839e-01_R;

            _weights[ 0]=2.0031112584748752943807724216722e-02_R;
            _weights[ 1]=4.2556615367405637772968490900760e-02_R;
            _weights[ 2]=5.6584184749474069646478036154467e-02_R;
            _weights[ 3]=6.0250607487604518170935343500906e-02_R;
            _weights[ 4]=5.4573941164231582825558709780290e-02_R;
            _weights[ 5]=4.2764763570188902317265936785879e-02_R;
            _weights[ 6]=2.8908051838727360494403492180206e-02_R;
            _weights[ 7]=1.6547343644609412101387213540038e-02_R;
            _weights[ 8]=7.7163670238864266187877366246530e-03_R;
            _weights[ 9]=2.7208421441038393545415361663513e-03_R;
            _weights[10]=6.1995339854451942336673117135933e-04_R;
            _weights[11]=5.9550359808311663832382311702501e-05_R;

            return;
          }

        case TWENTYFOURTH:
        case TWENTYFIFTH:
          {
            _points.resize (13);
            _weights.resize(13);

            _points[ 0](0)=6.8908313099587313966815341534070e-03_R;
            _points[ 1](0)=3.5953362700170095501132811969521e-02_R;
            _points[ 2](0)=8.6811780157585433284280307690601e-02_R;
            _points[ 3](0)=1.5709997419650927473052206555148e-01_R;
            _points[ 4](0)=2.4353289958712844441903410356775e-01_R;
            _points[ 5](0)=3.4206951264607532347450799656627e-01_R;
            _points[ 6](0)=4.4810263890570985362873430879398e-01_R;
            _points[ 7](0)=5.5667462262945501069694664236208e-01_R;
            _points[ 8](0)=6.6270931356038854232146315212326e-01_R;
            _points[ 9](0)=7.6124976630827697227665952639343e-01_R;
            _points[10](0)=8.4769104394723239091031404895142e-01_R;
            _points[11](0)=9.1799964553720667953362597028835e-01_R;
            _points[12](0)=9.6892889422858896211181181730274e-01_R;

            _weights[ 0]=1.7401228610061845488081141733526e-02_R;
            _weights[ 1]=3.7426708168844039953666298186474e-02_R;
            _weights[ 2]=5.0909830712695019092906847187640e-02_R;
            _weights[ 3]=5.6111537130827396185039872203667e-02_R;
            _weights[ 4]=5.3340021605871745725401666422880e-02_R;
            _weights[ 5]=4.4624600755614954430566337477243e-02_R;
            _weights[ 6]=3.2940451678432790083648445397381e-02_R;
            _weights[ 7]=2.1254996714756613031113108888658e-02_R;
            _weights[ 8]=1.1728259593101880662970381149369e-02_R;
            _weights[ 9]=5.3135693388326384480559144318474e-03_R;
            _weights[10]=1.8323911392393785873485644191745e-03_R;
            _weights[11]=4.1072089179088541678428389490865e-04_R;
            _weights[12]=3.9016993264146227750471940564101e-05_R;

            return;
          }

        case TWENTYSIXTH:
        case TWENTYSEVENTH:
          {
            _points.resize (14);
            _weights.resize(14);

            _points[ 0](0)=6.0288088710666481700887477121600e-03_R;
            _points[ 1](0)=3.1494259818657590707306712766317e-02_R;
            _points[ 2](0)=7.6213622474853867586406786340023e-02_R;
            _points[ 3](0)=1.3836652595947406914513833295825e-01_R;
            _points[ 4](0)=2.1540975706889557490069553208515e-01_R;
            _points[ 5](0)=3.0418952814165630963236635490440e-01_R;
            _points[ 6](0)=4.0107137869715435758118603205199e-01_R;
            _points[ 7](0)=5.0208913974997841006932539804960e-01_R;
            _points[ 8](0)=6.0310739672759678368189556654036e-01_R;
            _points[ 9](0)=6.9999091716990649741073666393849e-01_R;
            _points[10](0)=7.8877423843456071534030488559891e-01_R;
            _points[11](0)=8.6582490073159695367114083518102e-01_R;
            _points[12](0)=9.2799573874675232498377812203940e-01_R;
            _points[13](0)=9.7277712074118323045296336316727e-01_R;

            _weights[ 0]=1.5255206119448295373511341972378e-02_R;
            _weights[ 1]=3.3139595469960559875930225836517e-02_R;
            _weights[ 2]=4.5914772114671178911403799944693e-02_R;
            _weights[ 3]=5.2025865410701701832827358849471e-02_R;
            _weights[ 4]=5.1389924039471503273808065266413e-02_R;
            _weights[ 5]=4.5253432254460881465122373566022e-02_R;
            _weights[ 6]=3.5739010292514612984162525810346e-02_R;
            _weights[ 7]=2.5216183536839055034306220202219e-02_R;
            _weights[ 8]=1.5694332285072957184930434798487e-02_R;
            _weights[ 9]=8.4129767371364622096077152778570e-03_R;
            _weights[10]=3.7248756752828588215538124784652e-03_R;
            _weights[11]=1.2617838951574880413283334197260e-03_R;
            _weights[12]=2.7909934094687847008945560658272e-04_R;
            _weights[13]=2.6276161668899854751670304157309e-05_R;

            return;
          }

        case TWENTYEIGHTH:
        case TWENTYNINTH:
          {
            _points.resize (15);
            _weights.resize(15);

            _points[ 0](0)=5.3190520028437405909978402739774e-03_R;
            _points[ 1](0)=2.7814561918260051571980709238074e-02_R;
            _points[ 2](0)=6.7431865838998613384568577571818e-02_R;
            _points[ 3](0)=1.2274828621549783933958732401303e-01_R;
            _points[ 4](0)=1.9176570627765362550282684505042e-01_R;
            _points[ 5](0)=2.7198996592948620305633800793026e-01_R;
            _points[ 6](0)=3.6052169358705764815778444077840e-01_R;
            _points[ 7](0)=4.5416123575447709916009624996188e-01_R;
            _points[ 8](0)=5.4952435559355131365468962196031e-01_R;
            _points[ 9](0)=6.4316460176878493853949400884187e-01_R;
            _points[10](0)=7.3169797305252320629933948467521e-01_R;
            _points[11](0)=8.1192547727500966668969312120195e-01_R;
            _points[12](0)=8.8094952871531360238808055493652e-01_R;
            _points[13](0)=9.3628182173551874210251937228715e-01_R;
            _points[14](0)=9.7595387433502370956200384127912e-01_R;

            _weights[ 0]=1.3481662725134304090265733542410e-02_R;
            _weights[ 1]=2.9527650756798205089388266870014e-02_R;
            _weights[ 2]=4.1531307651604265373799456795289e-02_R;
            _weights[ 3]=4.8132057668529815888404876719886e-02_R;
            _weights[ 4]=4.9041267894409180565196427508457e-02_R;
            _weights[ 5]=4.4991555820615933365730152800755e-02_R;
            _weights[ 6]=3.7473875792101303095319296790068e-02_R;
            _weights[ 7]=2.8326553174241247644068974123766e-02_R;
            _weights[ 8]=1.9293416585274520485988288429744e-02_R;
            _weights[ 9]=1.1668582484776638563534331197891e-02_R;
            _weights[10]=6.1110501102060490412153142922240e-03_R;
            _weights[11]=2.6556629857743191811282114211333e-03_R;
            _weights[12]=8.8657363523409667398227745346013e-04_R;
            _weights[13]=1.9398726306394554934013378631178e-04_R;
            _weights[14]=1.8128785569508725971591601924058e-05_R;

            return;
          }


        case THIRTIETH:
        case THIRTYFIRST:
          {
            _points.resize (16);
            _weights.resize(16);

            _points[ 0](0)=4.7276871229345922061506104450645e-03_R;
            _points[ 1](0)=2.4742967619434984512603456269536e-02_R;
            _points[ 2](0)=6.0076437716637992275242255328112e-02_R;
            _points[ 3](0)=1.0960060925877060286789758461950e-01_R;
            _points[ 4](0)=1.7172475948300210790307417791270e-01_R;
            _points[ 5](0)=2.4445243174451137730207656160275e-01_R;
            _points[ 6](0)=3.2544621002412961482683685190181e-01_R;
            _points[ 7](0)=4.1210296411685959691728421362251e-01_R;
            _points[ 8](0)=5.0163755615318759370013043235084e-01_R;
            _points[ 9](0)=5.9117238531650308897076051877634e-01_R;
            _points[10](0)=6.7782991741456081130251277264148e-01_R;
            _points[11](0)=7.5882525794914141335427940535114e-01_R;
            _points[12](0)=8.3155588302646195188920635482406e-01_R;
            _points[13](0)=8.9368597454880401881486969876816e-01_R;
            _points[14](0)=9.4322428571224559352545066239296e-01_R;
            _points[15](0)=9.7860643749869701257280091378128e-01_R;

            _weights[ 0]=1.1999405624691969586506695404143e-02_R;
            _weights[ 1]=2.6460842517339527040437264564557e-02_R;
            _weights[ 2]=3.7685824681918572833315081444311e-02_R;
            _weights[ 3]=4.4496573472543214976151049587710e-02_R;
            _weights[ 4]=4.6506239397362658797012521100333e-02_R;
            _weights[ 5]=4.4112657675899371113911374089320e-02_R;
            _weights[ 6]=3.8348046951185955673582690910292e-02_R;
            _weights[ 7]=3.0612037917837609541948834407964e-02_R;
            _weights[ 8]=2.2357185649529930223334734263644e-02_R;
            _weights[ 9]=1.4803776657751738340239250997704e-02_R;
            _weights[10]=8.7475454956120699745801506391282e-03_R;
            _weights[11]=4.4948488514798588832066397608164e-03_R;
            _weights[12]=1.9235319260667742273824398535627e-03_R;
            _weights[13]=6.3445999956883686801084896849641e-04_R;
            _weights[14]=1.3757810397555175246959527906570e-04_R;
            _weights[15]=1.2778410569693501244162062287056e-05_R;

            return;
          }


        case THIRTYSECOND:
        case THIRTYTHIRD:
          {
            _points.resize (17);
            _weights.resize(17);

            _points[ 0](0)=4.2297654864907678749919877813007e-03_R;
            _points[ 1](0)=2.2152705311830232294209002101573e-02_R;
            _points[ 2](0)=5.3856014827184829566760322013645e-02_R;
            _points[ 3](0)=9.8434936830541362494246924237098e-02_R;
            _points[ 4](0)=1.5460792826588562987838903880788e-01_R;
            _points[ 5](0)=2.2075922519215138391363787768336e-01_R;
            _points[ 6](0)=2.9498586629802348865100598497056e-01_R;
            _points[ 7](0)=3.7515254164081788200834771392226e-01_R;
            _points[ 8](0)=4.5895305335301908085933451474375e-01_R;
            _points[ 9](0)=5.4397667809047570974515217435547e-01_R;
            _points[10](0)=6.2777753854681427256560538094776e-01_R;
            _points[11](0)=7.0794500138508556794362242607309e-01_R;
            _points[12](0)=7.8217310308122112810113854015572e-01_R;
            _points[13](0)=8.4832708570995060757906353137179e-01_R;
            _points[14](0)=9.0450542331432870037906100932836e-01_R;
            _points[15](0)=9.4909701659654457024654762835657e-01_R;
            _points[16](0)=9.8084389384741256367666372092760e-01_R;

            _weights[ 0]=1.0748151030768621662834062204936e-02_R;
            _weights[ 1]=2.3837762018703244620506074665265e-02_R;
            _weights[ 2]=3.4307889795671880028436869439002e-02_R;
            _weights[ 3]=4.1143975847068207121110777965721e-02_R;
            _weights[ 4]=4.3922618772592577808611328095136e-02_R;
            _weights[ 5]=4.2825403927934553301439133345126e-02_R;
            _weights[ 6]=3.8555241947102353628223582107170e-02_R;
            _weights[ 7]=3.2163570112378639217164962127759e-02_R;
            _weights[ 8]=2.4829256111976082802381065145755e-02_R;
            _weights[ 9]=1.7638789331050110518481458865839e-02_R;
            _weights[10]=1.1413642238636687747573403275566e-02_R;
            _weights[11]=6.6164197603617147286557116199452e-03_R;
            _weights[12]=3.3465172918198153715474254116460e-03_R;
            _weights[13]=1.4138837589561322316624033902623e-03_R;
            _weights[14]=4.6167405877711308077043506706165e-04_R;
            _weights[15]=9.9356525335473959962406835119113e-05_R;
            _weights[16]=9.1808042001255039722337720228143e-06_R;

            return;
          }

        case THIRTYFOURTH:
        case THIRTYFIFTH:
          {
            _points.resize (18);
            _weights.resize(18);

            _points[ 0](0)=3.8065822475018763836485343548908e-03_R;
            _points[ 1](0)=1.9948351047343018666301273550578e-02_R;
            _points[ 2](0)=4.8549645304224630965525818224597e-02_R;
            _points[ 3](0)=8.8876259116497388048181392194957e-02_R;
            _points[ 4](0)=1.3988457083516926493003835526765e-01_R;
            _points[ 5](0)=2.0025369592363033820671255853211e-01_R;
            _points[ 6](0)=2.6842018278660208442014712803618e-01_R;
            _points[ 7](0)=3.4261859780200830045140484446480e-01_R;
            _points[ 8](0)=4.2092727587031795580391095608392e-01_R;
            _points[ 9](0)=5.0131810275027358836467598537906e-01_R;
            _points[10](0)=5.8170905267091792822883758529331e-01_R;
            _points[11](0)=6.6001812722531554655212340270381e-01_R;
            _points[12](0)=7.3421730813501325031921736140253e-01_R;
            _points[13](0)=8.0238514983641747020667379058517e-01_R;
            _points[14](0)=8.6275672070005501336081662021610e-01_R;
            _points[15](0)=9.1376986411079293616612318979159e-01_R;
            _points[16](0)=9.5410789551731665881890309384613e-01_R;
            _points[17](0)=9.8274840759428696063307389954630e-01_R;

            _weights[ 0]=9.6823988037660231774964807691529e-03_R;
            _weights[ 1]=2.1578772679193827027157750409882e-02_R;
            _weights[ 2]=3.1333907671729513327950397913143e-02_R;
            _weights[ 3]=3.8075134253447687665457823100366e-02_R;
            _weights[ 4]=4.1377182287519565332651504100178e-02_R;
            _weights[ 5]=4.1283665809957749414286828772884e-02_R;
            _weights[ 6]=3.8262794672349299757849656256339e-02_R;
            _weights[ 7]=3.3095976202072497795672769135623e-02_R;
            _weights[ 8]=2.6723424368960119486097972811646e-02_R;
            _weights[ 9]=2.0078641696369720179443819032712e-02_R;
            _weights[10]=1.3943897653647906425703531920973e-02_R;
            _weights[11]=8.8522782250949774435502470347624e-03_R;
            _weights[12]=5.0502487883546813166841235600508e-03_R;
            _weights[13]=2.5207216384362558022745702364513e-03_R;
            _weights[14]=1.0535502839571923712409403476880e-03_R;
            _weights[15]=3.4109120368765498289598525047321e-04_R;
            _weights[16]=7.2937008664118705328162954331465e-05_R;
            _weights[17]=6.7100861245431215907697266774769e-06_R;

            return;
          }

        case THIRTYSIXTH:
        case THIRTYSEVENTH:
          {
            _points.resize (19);
            _weights.resize(19);

            _points[ 0](0)=3.4438904038624902806940509331722e-03_R;
            _points[ 1](0)=1.8056978337900562863030093954343e-02_R;
            _points[ 2](0)=4.3987395090842734455198832773659e-02_R;
            _points[ 3](0)=8.0633276366661415469721776663016e-02_R;
            _points[ 4](0)=1.2713640986156026953002535083969e-01_R;
            _points[ 5](0)=1.8240698366909185313069695387128e-01_R;
            _points[ 6](0)=2.4514956909516857055249217701821e-01_R;
            _points[ 7](0)=3.1389356741821822415240859865307e-01_R;
            _points[ 8](0)=3.8702770276933220341545290751683e-01_R;
            _points[ 9](0)=4.6283779855202027820220487054694e-01_R;
            _points[10](0)=5.3954696279208808766943066332998e-01_R;
            _points[11](0)=6.1535724480454716546694016358337e-01_R;
            _points[12](0)=6.8849179091409498918986551203802e-01_R;
            _points[13](0)=7.5723651917329793549736932794667e-01_R;
            _points[14](0)=8.1998035706323733537954006841029e-01_R;
            _points[15](0)=8.7525316298382668006594890887609e-01_R;
            _points[16](0)=9.2176068172914004889937421632274e-01_R;
            _points[17](0)=9.5841690242340714510347790926694e-01_R;
            _points[18](0)=9.8438280655170201067612761745569e-01_R;

            _weights[ 0]=8.7672970568792323661393261305840e-03_R;
            _weights[ 1]=1.9620856340232434512901283777202e-02_R;
            _weights[ 2]=2.8708149778704086122791006941433e-02_R;
            _weights[ 3]=3.5278117199476000434599584597235e-02_R;
            _weights[ 4]=3.8922386222261737550985848811514e-02_R;
            _weights[ 5]=3.9598248214880677015066061570123e-02_R;
            _weights[ 6]=3.7607500520347543950912173611332e-02_R;
            _weights[ 7]=3.3525068070610283960905700567460e-02_R;
            _weights[ 8]=2.8091607936102907649141378579235e-02_R;
            _weights[ 9]=2.2090563149823990465333672755377e-02_R;
            _weights[10]=1.6231815321996325630177612472423e-02_R;
            _weights[11]=1.1061440629037007897211784796273e-02_R;
            _weights[12]=6.9108110779321981973514541466546e-03_R;
            _weights[13]=3.8897848125530902102984958782958e-03_R;
            _weights[14]=1.9197884726923132048372710905667e-03_R;
            _weights[15]=7.9504432544855937325482850317179e-04_R;
            _weights[16]=2.5553085889097125647555166013802e-04_R;
            _weights[17]=5.4342643132004416773622274012570e-05_R;
            _weights[18]=4.9807023319691181766751703037610e-06_R;

            return;
          }

        case THIRTYEIGHTH:
        case THIRTYNINTH:
          {
            _points.resize (20);
            _weights.resize(20);

            _points[ 0](0)=3.1306837407435895621501417495463e-03_R;
            _points[ 1](0)=1.6422088133987832902541614256258e-02_R;
            _points[ 2](0)=4.0036900461906780996320149828793e-02_R;
            _points[ 3](0)=7.3477191785285283057566545285874e-02_R;
            _points[ 4](0)=1.1603090765548680494669743156748e-01_R;
            _points[ 5](0)=1.6679125348100943001298070145849e-01_R;
            _points[ 6](0)=2.2467641938430503840938196483210e-01_R;
            _points[ 7](0)=2.8845271218127238477194070665240e-01_R;
            _points[ 8](0)=3.5676087010245310564705506663326e-01_R;
            _points[ 9](0)=4.2814504093325668461542503477245e-01_R;
            _points[10](0)=5.0108381548284855137062465413693e-01_R;
            _points[11](0)=5.7402265818282687172751219665371e-01_R;
            _points[12](0)=6.4540704577736756661732083476397e-01_R;
            _points[13](0)=7.1371561101528768074208343535393e-01_R;
            _points[14](0)=7.7749259203548675355112594583658e-01_R;
            _points[15](0)=8.3537891463156172517151839471341e-01_R;
            _points[16](0)=8.8614130291454714368728293036495e-01_R;
            _points[17](0)=9.2869901491875054534509783716727e-01_R;
            _points[18](0)=9.6214871215049818970916080642292e-01_R;
            _points[19](0)=9.8579578884064184668002313135922e-01_R;

            _weights[ 0]=7.9757927362766516852273101574255e-03_R;
            _weights[ 1]=1.7913752325738559101773958866323e-02_R;
            _weights[ 2]=2.6382564429125584794513408474046e-02_R;
            _weights[ 3]=3.2734644317573148047479656498988e-02_R;
            _weights[ 4]=3.6587916553227064986609295576925e-02_R;
            _weights[ 5]=3.7847390376922340715354694449373e-02_R;
            _weights[ 6]=3.6697420472018132713254249570653e-02_R;
            _weights[ 7]=3.3556431453475493479002714822739e-02_R;
            _weights[ 8]=2.9002404745589285169916357261403e-02_R;
            _weights[ 9]=2.3682290414246053980866450266495e-02_R;
            _weights[10]=1.8220503418268691551843315309759e-02_R;
            _weights[11]=1.3140919256661651742108133720781e-02_R;
            _weights[12]=8.8135560782433553289252731679767e-03_R;
            _weights[13]=5.4320908061230274500120111426487e-03_R;
            _weights[14]=3.0224891709073793749184859780611e-03_R;
            _weights[15]=1.4774444419714858062838576456553e-03_R;
            _weights[16]=6.0704570426725825415272373108771e-04_R;
            _weights[17]=1.9388830961751181076983851525948e-04_R;
            _weights[18]=4.1039102087320205549074040898061e-05_R;
            _weights[19]=3.7492209933371347725241368372638e-06_R;

            return;
          }


        case FORTIETH:
        case FORTYFIRST:
          {
            _points.resize (21);
            _weights.resize(21);

            _points[ 0](0)=2.8583506000918943222556277168267e-03_R;
            _points[ 1](0)=1.4999364972075522340357135916023e-02_R;
            _points[ 2](0)=3.6593863281140122626545055282186e-02_R;
            _points[ 3](0)=6.7226441667938638526563947674675e-02_R;
            _points[ 4](0)=1.0630147973769311755044868847393e-01_R;
            _points[ 5](0)=1.5305857495571921224970195300963e-01_R;
            _points[ 6](0)=2.0658770608253356867698033417515e-01_R;
            _points[ 7](0)=2.6584701401081590981089215154372e-01_R;
            _points[ 8](0)=3.2968309899010272373734914205452e-01_R;
            _points[ 9](0)=3.9685347698561900950394342909483e-01_R;
            _points[10](0)=4.6605076663517464847296649003812e-01_R;
            _points[11](0)=5.3592813869303216093268951839176e-01_R;
            _points[12](0)=6.0512553397610192844810985230774e-01_R;
            _points[13](0)=6.7229614098692961628997049948121e-01_R;
            _points[14](0)=7.3613262059728734846410297670221e-01_R;
            _points[15](0)=7.9539257374613146232498650332774e-01_R;
            _points[16](0)=8.4892277353768883984401746895126e-01_R;
            _points[17](0)=8.9568174292546676052820257429765e-01_R;
            _points[18](0)=9.3476043640122994798279429359660e-01_R;
            _points[19](0)=9.6540160736574245809294907904429e-01_R;
            _points[20](0)=9.8702556657875783654690055164718e-01_R;

            _weights[ 0]=7.2866317313744308995629793584932e-03_R;
            _weights[ 1]=1.6417061144242818824757454238052e-02_R;
            _weights[ 2]=2.4316074956305588348553255406534e-02_R;
            _weights[ 3]=3.0423854654878694196479542521305e-02_R;
            _weights[ 4]=3.4388553550627421941340376509459e-02_R;
            _weights[ 5]=3.6085277384893044986268336555960e-02_R;
            _weights[ 6]=3.5615944774693119613624648820995e-02_R;
            _weights[ 7]=3.3281046762833346236473134492600e-02_R;
            _weights[ 8]=2.9528072702082493907799384765866e-02_R;
            _weights[ 9]=2.4885083875255978309567929915161e-02_R;
            _weights[10]=1.9889780066352815019424534213776e-02_R;
            _weights[11]=1.5024528041917190276613254752701e-02_R;
            _weights[12]=1.0666270365508680718786852036243e-02_R;
            _weights[13]=7.0573209743621604363614669672455e-03_R;
            _weights[14]=4.2993100642134152210363702100934e-03_R;
            _weights[15]=2.3686215346115318974092271035074e-03_R;
            _weights[16]=1.1482414207164748272703814817286e-03_R;
            _weights[17]=4.6857361253397420043294612589344e-04_R;
            _weights[18]=1.4884999898655056859287865070751e-04_R;
            _weights[19]=3.1377233396792732027953172274463e-05_R;
            _weights[20]=2.8584835468101709504260347382715e-06_R;

            return;
          }

        case FORTYSECOND:
        case FORTYTHIRD:
          {
            _points.resize (22);
            _weights.resize(22);

            _points[ 0](0)=2.6200747203711594248593674552649e-03_R;
            _points[ 1](0)=1.3753657987385804025756750709059e-02_R;
            _points[ 2](0)=3.3575226848026692714308191640158e-02_R;
            _points[ 3](0)=6.1735561623069601690826574395308e-02_R;
            _points[ 4](0)=9.7732696675368642458479884996723e-02_R;
            _points[ 5](0)=1.4092439775695158519450619775816e-01_R;
            _points[ 6](0)=1.9053995518421662849913969152881e-01_R;
            _points[ 7](0)=2.4569399962450332222446519900435e-01_R;
            _points[ 8](0)=3.0540231844259902315260853518244e-01_R;
            _points[ 9](0)=3.6859942495594128250321664201293e-01_R;
            _points[10](0)=4.3415757484015513750820121247106e-01_R;
            _points[11](0)=5.0090689264793505011775015892772e-01_R;
            _points[12](0)=5.6765625027260978702177266771788e-01_R;
            _points[13](0)=6.3321452557266284279166256182373e-01_R;
            _points[14](0)=6.9641186298595172661126707689713e-01_R;
            _points[15](0)=7.5612055917893487122928793527786e-01_R;
            _points[16](0)=8.1127520683922050787811864631196e-01_R;
            _points[17](0)=8.6089175276286621730656128908876e-01_R;
            _points[18](0)=9.0408517849775272066170136431884e-01_R;
            _points[19](0)=9.4008566921081846961603077466108e-01_R;
            _points[20](0)=9.6825388381656365288164210087944e-01_R;
            _points[21](0)=9.8810245999087788318348935085438e-01_R;

            _weights[ 0]=6.6829315239216368796332393406135e-03_R;
            _weights[ 1]=1.5098062421623821319493004238262e-02_R;
            _weights[ 2]=2.2473713734526648003280648297671e-02_R;
            _weights[ 3]=2.8324458025288763364233486167273e-02_R;
            _weights[ 4]=3.2329473952869436965326587507885e-02_R;
            _weights[ 5]=3.4348599664417779736425965942178e-02_R;
            _weights[ 6]=3.4426309828130701949676126316990e-02_R;
            _weights[ 7]=3.2774586900497126738748991342107e-02_R;
            _weights[ 8]=2.9737336628427308246400548097974e-02_R;
            _weights[ 9]=2.5741821234796918381507016798653e-02_R;
            _weights[10]=2.1244167813524304464862872202199e-02_R;
            _weights[11]=1.6676482379699419616981906191727e-02_R;
            _weights[12]=1.2402453510959574984251948178874e-02_R;
            _weights[13]=8.6866984738749141556196547655377e-03_R;
            _weights[14]=5.6807683849250404394970034550940e-03_R;
            _weights[15]=3.4260685209698087638377353482425e-03_R;
            _weights[16]=1.8713879532585689543042377871244e-03_R;
            _weights[17]=9.0066625279251987400261357834378e-04_R;
            _weights[18]=3.6536328467284676654467859219800e-04_R;
            _weights[19]=1.1551470917602499323205530447797e-04_R;
            _weights[20]=2.4263177919766775694554800111547e-05_R;
            _weights[21]=2.2049570604019597784590797971169e-06_R;

            return;
          }


        default:
          libmesh_error_msg("Quadrature rule " << _order << " not supported!");
        } // end switch(_order + 2*p)
    } // end else if ((_alpha == 2) && (_beta == 0))

  else
    {
      libMesh::err << "Unsupported combination of (alpha,beta) = ("
                   << _alpha
                   << ","
                   << _beta
                   << ") requested in Jacobi-Gauss quadrature rule."
                   << std::endl;
    }
}

init_2D()

void libMesh::QBase::init_2D ( )

protectedvirtualinherited

Initializes the 2D quadrature rule by filling the points and weights vectors with the appropriate values.

The order of the rule will be defined by the implementing class. Should not be pure virtual since a derived quadrature rule may only be defined in 1D. If not overridden, throws an error.

Reimplemented in libMesh::QGrundmann_Moller, libMesh::QMonomial, libMesh::QNodal, libMesh::QConical, libMesh::QGrid, libMesh::QGauss, libMesh::QSimpson, libMesh::QTrap, libMesh::QClough, and libMesh::QGaussLobatto.

Definition at line 208 of file quadrature.C.

Referenced by libMesh::QBase::init().

{
  libmesh_not_implemented();
}

init_3D()

void libMesh::QBase::init_3D ( )

protectedvirtualinherited

Initializes the 3D quadrature rule by filling the points and weights vectors with the appropriate values.

The order of the rule will be defined by the implementing class. Should not be pure virtual since a derived quadrature rule may only be defined in 1D. If not overridden, throws an error.

Reimplemented in libMesh::QGrundmann_Moller, libMesh::QMonomial, libMesh::QNodal, libMesh::QConical, libMesh::QGrid, libMesh::QGauss, libMesh::QSimpson, libMesh::QTrap, libMesh::QClough, and libMesh::QGaussLobatto.

Definition at line 215 of file quadrature.C.

Referenced by libMesh::QBase::init().

{
  libmesh_not_implemented();
}

n_objects()

static unsigned int libMesh::ReferenceCounter::n_objects ( )

inlinestaticinherited

Prints the number of outstanding (created, but not yet destroyed) objects.

Definition at line 85 of file reference_counter.h.

References libMesh::ReferenceCounter::_n_objects.

Referenced by libMesh::LibMeshInit::~LibMeshInit().

  { return _n_objects; }

n_points()

unsigned int libMesh::QBase::n_points ( ) const

inlineinherited

Returns

The number of points associated with the quadrature rule.

Definition at line 131 of file quadrature.h.

References libMesh::QBase::_points, and libMesh::libmesh_assert().

Referenced by libMesh::ExactSolution::_compute_error(), assemble(), assemble_1D(), assemble_ellipticdg(), assemble_helmholtz(), assemble_poisson(), assemble_shell(), assemble_wave(), assembly_with_dg_fem_context(), AssemblyA0::boundary_assembly(), AssemblyA1::boundary_assembly(), AssemblyF0::boundary_assembly(), AssemblyF1::boundary_assembly(), AssemblyA2::boundary_assembly(), AssemblyF2::boundary_assembly(), A2::boundary_assembly(), A3::boundary_assembly(), F0::boundary_assembly(), Output0::boundary_assembly(), compute_enriched_soln(), libMesh::FirstOrderUnsteadySolver::compute_second_order_eqns(), libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::HDGProblem::create_identity_jacobian(), libMesh::HDGProblem::create_identity_residual(), SecondOrderScalarSystemSecondOrderTimeSolverBase::damping_residual(), SecondOrderScalarSystemFirstOrderTimeSolverBase::damping_residual(), NavierSystem::element_constraint(), CoupledSystem::element_constraint(), PoissonSystem::element_postprocess(), LaplaceSystem::element_postprocess(), LaplaceQoI::element_qoi(), HeatSystem::element_qoi(), LaplaceQoI::element_qoi_derivative(), LaplaceSystem::element_qoi_derivative(), HeatSystem::element_qoi_derivative(), NavierSystem::element_time_derivative(), SolidSystem::element_time_derivative(), PoissonSystem::element_time_derivative(), LaplaceSystem::element_time_derivative(), CurlCurlSystem::element_time_derivative(), ElasticitySystem::element_time_derivative(), CoupledSystem::element_time_derivative(), HilbertSystem::element_time_derivative(), HeatSystem::element_time_derivative(), FirstOrderScalarSystemBase::element_time_derivative(), SecondOrderScalarSystemFirstOrderTimeSolverBase::element_time_derivative(), fe_assembly(), A0::interior_assembly(), B::interior_assembly(), M0::interior_assembly(), A1::interior_assembly(), AssemblyA0::interior_assembly(), AcousticsInnerProduct::interior_assembly(), AssemblyA1::interior_assembly(), A2::interior_assembly(), AssemblyA2::interior_assembly(), F0::interior_assembly(), OutputAssembly::interior_assembly(), EIM_IP_assembly::interior_assembly(), EIM_F::interior_assembly(), AssemblyEIM::interior_assembly(), InnerProductAssembly::interior_assembly(), AssemblyF0::interior_assembly(), AssemblyF1::interior_assembly(), Ex6InnerProduct::interior_assembly(), LaplaceYoung::jacobian(), NavierSystem::mass_residual(), ElasticitySystem::mass_residual(), libMesh::FEMPhysics::mass_residual(), FirstOrderScalarSystemBase::mass_residual(), SecondOrderScalarSystemSecondOrderTimeSolverBase::mass_residual(), SecondOrderScalarSystemFirstOrderTimeSolverBase::mass_residual(), libMesh::FEAbstract::n_quadrature_points(), libMesh::QBase::print_info(), LaplaceYoung::residual(), LaplaceSystem::side_constraint(), LaplaceSystem::side_postprocess(), CoupledSystemQoI::side_qoi(), CoupledSystemQoI::side_qoi_derivative(), LaplaceSystem::side_qoi_derivative(), SolidSystem::side_time_derivative(), CurlCurlSystem::side_time_derivative(), ElasticitySystem::side_time_derivative(), libMesh::QBase::size(), libMesh::QBase::tensor_product_hex(), libMesh::QBase::tensor_product_prism(), libMesh::QBase::tensor_product_quad(), and QuadratureTest::testPolynomial().

  {
    libmesh_assert (!_points.empty());
    return cast_int<unsigned int>(_points.size());
  }

operator=() [1/2]

QJacobi& libMesh::QJacobi::operator= ( const QJacobi &  )

default

operator=() [2/2]

QJacobi& libMesh::QJacobi::operator= ( QJacobi &&  )

default

print_info() [1/2]

void libMesh::ReferenceCounter::print_info ( std::ostream &  out_stream = libMesh::out )

staticinherited

Prints the reference information, by default to libMesh::out.

Definition at line 81 of file reference_counter.C.

References libMesh::ReferenceCounter::_enable_print_counter, and libMesh::ReferenceCounter::get_info().

Referenced by libMesh::LibMeshInit::~LibMeshInit().

{
  if (_enable_print_counter)
    out_stream << ReferenceCounter::get_info();
}

print_info() [2/2]

void libMesh::QBase::print_info ( std::ostream &  os = libMesh::out ) const

inherited

Prints information relevant to the quadrature rule, by default to libMesh::out.

Definition at line 43 of file quadrature.C.

References libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::index_range(), libMesh::libmesh_assert(), libMesh::QBase::n_points(), and libMesh::Real.

Referenced by libMesh::operator<<().

{
  libmesh_assert(!_points.empty());
  libmesh_assert(!_weights.empty());

  Real summed_weights=0;
  os << "N_Q_Points=" << this->n_points() << std::endl << std::endl;
  for (auto qpoint: index_range(_points))
    {
      os << " Point " << qpoint << ":\n"
         << "  "
         << _points[qpoint]
         << "\n Weight:\n "
         << "  w=" << _weights[qpoint] << "\n" << std::endl;

      summed_weights += _weights[qpoint];
    }
  os << "Summed Weights: " << summed_weights << std::endl;
}

qp()

Point libMesh::QBase::qp ( const unsigned int  i ) const

inlineinherited

Returns

The \( i^{th} \) quadrature point in reference element space.

Definition at line 179 of file quadrature.h.

References libMesh::QBase::_points.

Referenced by libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::QBase::tensor_product_hex(), libMesh::QBase::tensor_product_prism(), libMesh::QBase::tensor_product_quad(), and QuadratureTest::testPolynomial().

  {
    libmesh_assert_less (i, _points.size());
    return _points[i];
  }

scale()

void libMesh::QBase::scale ( std::pair< Real, Real >  old_range, std::pair< Real, Real >  new_range  )

inherited

Maps the points of a 1D quadrature rule defined by "old_range" to another 1D interval defined by "new_range" and scales the weights accordingly.

Definition at line 222 of file quadrature.C.

References libMesh::QBase::_dim, libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::index_range(), and libMesh::Real.

Referenced by libMesh::QConical::conical_product_tet(), and libMesh::QConical::conical_product_tri().

{
  // Make sure we are in 1D
  libmesh_assert_equal_to (_dim, 1);

  Real
    h_new = new_range.second - new_range.first,
    h_old = old_range.second - old_range.first;

  // Make sure that we have sane ranges
  libmesh_assert_greater (h_new, 0.);
  libmesh_assert_greater (h_old, 0.);

  // Make sure there are some points
  libmesh_assert_greater (_points.size(), 0);

  // Compute the scale factor
  Real scfact = h_new/h_old;

  // We're mapping from old_range -> new_range
  for (auto i : index_range(_points))
    {
      _points[i](0) = new_range.first +
        (_points[i](0) - old_range.first) * scfact;

      // Scale the weights
      _weights[i] *= scfact;
    }
}

shapes_need_reinit()

virtual bool libMesh::QBase::shapes_need_reinit ( )

inlinevirtualinherited

Returns

true if the shape functions need to be recalculated, false otherwise.

This may be required if the number of quadrature points or their position changes.

Definition at line 286 of file quadrature.h.

{ return false; }

size()

unsigned int libMesh::QBase::size ( ) const

inlineinherited

Alias for n_points() to enable use in index_range.

Returns

The number of points associated with the quadrature rule.

Definition at line 142 of file quadrature.h.

References libMesh::QBase::n_points().

Referenced by libMesh::Elem::true_centroid().

  {
    return n_points();
  }

tensor_product_hex()

void libMesh::QBase::tensor_product_hex ( const QBase &  q1D )

protectedinherited

Computes the tensor product quadrature rule [q1D x q1D x q1D] from the 1D rule q1D.

Used in the init_3D routines for hexahedral element types.

Definition at line 283 of file quadrature.C.

References libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::QBase::n_points(), libMesh::QBase::qp(), and libMesh::QBase::w().

Referenced by libMesh::QGaussLobatto::init_3D(), libMesh::QTrap::init_3D(), libMesh::QGauss::init_3D(), libMesh::QSimpson::init_3D(), and libMesh::QGrid::init_3D().

{
  const unsigned int np = q1D.n_points();

  _points.resize(np * np * np);

  _weights.resize(np * np * np);

  unsigned int q=0;

  for (unsigned int k=0; k<np; k++)
    for (unsigned int j=0; j<np; j++)
      for (unsigned int i=0; i<np; i++)
        {
          _points[q](0) = q1D.qp(i)(0);
          _points[q](1) = q1D.qp(j)(0);
          _points[q](2) = q1D.qp(k)(0);

          _weights[q] = q1D.w(i) * q1D.w(j) * q1D.w(k);

          q++;
        }
}

tensor_product_prism()

void libMesh::QBase::tensor_product_prism ( const QBase &  q1D, const QBase &  q2D  )

protectedinherited

Computes the tensor product of a 1D quadrature rule and a 2D quadrature rule.

Used in the init_3D routines for prismatic element types.

Definition at line 310 of file quadrature.C.

References libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::QBase::n_points(), libMesh::QBase::qp(), and libMesh::QBase::w().

Referenced by libMesh::QGauss::init_3D(), libMesh::QTrap::init_3D(), libMesh::QSimpson::init_3D(), and libMesh::QGrid::init_3D().

{
  const unsigned int n_points1D = q1D.n_points();
  const unsigned int n_points2D = q2D.n_points();

  _points.resize  (n_points1D * n_points2D);
  _weights.resize (n_points1D * n_points2D);

  unsigned int q=0;

  for (unsigned int j=0; j<n_points1D; j++)
    for (unsigned int i=0; i<n_points2D; i++)
      {
        _points[q](0) = q2D.qp(i)(0);
        _points[q](1) = q2D.qp(i)(1);
        _points[q](2) = q1D.qp(j)(0);

        _weights[q] = q2D.w(i) * q1D.w(j);

        q++;
      }

}

tensor_product_quad()

void libMesh::QBase::tensor_product_quad ( const QBase &  q1D )

protectedinherited

Constructs a 2D rule from the tensor product of q1D with itself.

Used in the init_2D() routines for quadrilateral element types.

Definition at line 256 of file quadrature.C.

References libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::QBase::n_points(), libMesh::QBase::qp(), and libMesh::QBase::w().

Referenced by libMesh::QGaussLobatto::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGauss::init_2D(), libMesh::QSimpson::init_2D(), and libMesh::QGrid::init_2D().

{

  const unsigned int np = q1D.n_points();

  _points.resize(np * np);

  _weights.resize(np * np);

  unsigned int q=0;

  for (unsigned int j=0; j<np; j++)
    for (unsigned int i=0; i<np; i++)
      {
        _points[q](0) = q1D.qp(i)(0);
        _points[q](1) = q1D.qp(j)(0);

        _weights[q] = q1D.w(i)*q1D.w(j);

        q++;
      }
}

type()

QuadratureType libMesh::QJacobi::type ( ) const

overridevirtual

Returns

The QuadratureType, either QJACOBI_1_0 or QJACOBI_2_0.

Implements libMesh::QBase.

Definition at line 30 of file quadrature_jacobi.C.

References _alpha, _beta, libMesh::QJACOBI_1_0, and libMesh::QJACOBI_2_0.

{
  if ((_alpha == 1) && (_beta == 0))
    return QJACOBI_1_0;

  else if ((_alpha == 2) && (_beta == 0))
    return QJACOBI_2_0;

  else
    libmesh_error_msg("Invalid Jacobi quadrature rule: alpha = " << _alpha << ", beta = " << _beta);
}

w()

Real libMesh::QBase::w ( const unsigned int  i ) const

inlineinherited

Returns

The \( i^{th} \) quadrature weight.

Definition at line 188 of file quadrature.h.

References libMesh::QBase::_weights.

Referenced by libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::QBase::tensor_product_hex(), libMesh::QBase::tensor_product_prism(), libMesh::QBase::tensor_product_quad(), and QuadratureTest::testPolynomial().

  {
    libmesh_assert_less (i, _weights.size());
    return _weights[i];
  }

Member Data Documentation

_alpha

unsigned int libMesh::QJacobi::_alpha

private

Definition at line 87 of file quadrature_jacobi.h.

Referenced by init_1D(), and type().

_beta

unsigned int libMesh::QJacobi::_beta

private

Definition at line 88 of file quadrature_jacobi.h.

Referenced by init_1D(), and type().

_counts

ReferenceCounter::Counts libMesh::ReferenceCounter::_counts

staticprotectedinherited

Actually holds the data.

Definition at line 124 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::get_info().

_dim

unsigned int libMesh::QBase::_dim

protectedinherited

The spatial dimension of the quadrature rule.

Definition at line 379 of file quadrature.h.

Referenced by libMesh::QBase::build(), libMesh::QBase::get_dim(), libMesh::QBase::init(), libMesh::QGaussLobatto::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGaussLobatto::QGaussLobatto(), QJacobi(), and libMesh::QBase::scale().

_elem

const Elem* libMesh::QBase::_elem

protectedinherited

The element for which the current values were computed, or nullptr if values were computed without a specific element.

Definition at line 397 of file quadrature.h.

Referenced by libMesh::QBase::init(), libMesh::QGauss::init_2D(), libMesh::QNodal::init_2D(), libMesh::QGauss::init_3D(), and libMesh::QNodal::init_3D().

_enable_print_counter

bool libMesh::ReferenceCounter::_enable_print_counter = true

staticprotectedinherited

Flag to control whether reference count information is printed when print_info is called.

Definition at line 143 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::disable_print_counter_info(), libMesh::ReferenceCounter::enable_print_counter_info(), and libMesh::ReferenceCounter::print_info().

_mutex

Threads::spin_mutex libMesh::ReferenceCounter::_mutex

staticprotectedinherited

Mutual exclusion object to enable thread-safe reference counting.

Definition at line 137 of file reference_counter.h.

_n_objects

Threads::atomic< unsigned int > libMesh::ReferenceCounter::_n_objects

staticprotectedinherited

The number of objects.

Print the reference count information when the number returns to 0.

Definition at line 132 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::n_objects(), libMesh::ReferenceCounter::ReferenceCounter(), and libMesh::ReferenceCounter::~ReferenceCounter().

_order

Order libMesh::QBase::_order

protectedinherited

The polynomial order which the quadrature rule is capable of integrating exactly.

Definition at line 385 of file quadrature.h.

Referenced by libMesh::QBase::build(), libMesh::QBase::get_base_order(), libMesh::QBase::get_order(), libMesh::QGaussLobatto::init_1D(), libMesh::QClough::init_1D(), libMesh::QGauss::init_1D(), libMesh::QGrid::init_1D(), libMesh::QNodal::init_1D(), init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGaussLobatto::init_2D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), libMesh::QGrid::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGauss::init_3D(), libMesh::QGrid::init_3D(), libMesh::QNodal::init_3D(), and libMesh::QMonomial::init_3D().

_p_level

unsigned int libMesh::QBase::_p_level

protectedinherited

The p-level of the element for which the current values have been computed.

Definition at line 403 of file quadrature.h.

Referenced by libMesh::QBase::get_order(), libMesh::QBase::get_p_level(), libMesh::QBase::init(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), libMesh::QGauss::init_3D(), libMesh::QSimpson::init_3D(), and libMesh::QTrap::init_3D().

_points

std::vector<Point> libMesh::QBase::_points

protectedinherited

The locations of the quadrature points in reference element space.

Definition at line 409 of file quadrature.h.

Referenced by libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::QGauss::dunavant_rule(), libMesh::QGauss::dunavant_rule2(), libMesh::QBase::get_points(), libMesh::QGrundmann_Moller::gm_rule(), libMesh::QBase::init_0D(), libMesh::QGaussLobatto::init_1D(), libMesh::QClough::init_1D(), libMesh::QGauss::init_1D(), libMesh::QSimpson::init_1D(), libMesh::QTrap::init_1D(), libMesh::QGrid::init_1D(), libMesh::QConical::init_1D(), libMesh::QNodal::init_1D(), init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGrundmann_Moller::init_1D(), libMesh::QGaussLobatto::init_2D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), libMesh::QSimpson::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGrid::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QTrap::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QGauss::init_3D(), libMesh::QGrid::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), libMesh::QGrundmann_Moller::init_3D(), libMesh::QGauss::keast_rule(), libMesh::QMonomial::kim_rule(), libMesh::QBase::n_points(), libMesh::QBase::print_info(), libMesh::QBase::qp(), libMesh::QBase::scale(), libMesh::QMonomial::stroud_rule(), libMesh::QBase::tensor_product_hex(), libMesh::QBase::tensor_product_prism(), libMesh::QBase::tensor_product_quad(), and libMesh::QMonomial::wissmann_rule().

_type

ElemType libMesh::QBase::_type

protectedinherited

The type of element for which the current values have been computed.

Definition at line 391 of file quadrature.h.

Referenced by libMesh::QBase::get_elem_type(), libMesh::QBase::init(), libMesh::QNodal::init_1D(), libMesh::QGaussLobatto::init_2D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), libMesh::QSimpson::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGrid::init_2D(), libMesh::QConical::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGrundmann_Moller::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QClough::init_3D(), libMesh::QGauss::init_3D(), libMesh::QTrap::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QGrid::init_3D(), libMesh::QConical::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), and libMesh::QGrundmann_Moller::init_3D().

_weights

std::vector<Real> libMesh::QBase::_weights

protectedinherited

The quadrature weights.

The order of the weights matches the ordering of the _points vector.

Definition at line 415 of file quadrature.h.

Referenced by libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::QGauss::dunavant_rule(), libMesh::QGauss::dunavant_rule2(), libMesh::QBase::get_weights(), libMesh::QGrundmann_Moller::gm_rule(), libMesh::QBase::init_0D(), libMesh::QGaussLobatto::init_1D(), libMesh::QClough::init_1D(), libMesh::QGauss::init_1D(), libMesh::QSimpson::init_1D(), libMesh::QTrap::init_1D(), libMesh::QGrid::init_1D(), libMesh::QConical::init_1D(), libMesh::QNodal::init_1D(), init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGrundmann_Moller::init_1D(), libMesh::QGaussLobatto::init_2D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), libMesh::QTrap::init_2D(), libMesh::QSimpson::init_2D(), libMesh::QGrid::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QTrap::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QGauss::init_3D(), libMesh::QGrid::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), libMesh::QGrundmann_Moller::init_3D(), libMesh::QGauss::keast_rule(), libMesh::QMonomial::kim_rule(), libMesh::QBase::print_info(), libMesh::QBase::scale(), libMesh::QMonomial::stroud_rule(), libMesh::QBase::tensor_product_hex(), libMesh::QBase::tensor_product_prism(), libMesh::QBase::tensor_product_quad(), libMesh::QBase::w(), and libMesh::QMonomial::wissmann_rule().

allow_nodal_pyramid_quadrature

bool libMesh::QBase::allow_nodal_pyramid_quadrature

inherited

The flag's value defaults to false so that one does not accidentally use a nodal quadrature rule on Pyramid elements, since evaluating the inverse element Jacobian (e.g.

dphi) is not well-defined at the Pyramid apex because the element Jacobian is zero there.

We do not want to completely prevent someone from using a nodal quadrature rule on Pyramids, however, since there are legitimate use cases (lumped mass matrix) so the flag can be set to true to override this behavior.

Definition at line 314 of file quadrature.h.

Referenced by libMesh::QSimpson::init_3D(), libMesh::QTrap::init_3D(), and libMesh::QNodal::init_3D().

allow_rules_with_negative_weights

bool libMesh::QBase::allow_rules_with_negative_weights

inherited

Flag (default true) controlling the use of quadrature rules with negative weights.

Set this to false to require rules with all positive weights.

Rules with negative weights can be unsuitable for some problems. For example, it is possible for a rule with negative weights to obtain a negative result when integrating a positive function.

A particular example: if rules with negative weights are not allowed, a request for TET,THIRD (5 points) will return the TET,FIFTH (14 points) rule instead, nearly tripling the computational effort required!

Definition at line 301 of file quadrature.h.

Referenced by libMesh::QGrundmann_Moller::init_2D(), libMesh::QGauss::init_3D(), libMesh::QMonomial::init_3D(), and libMesh::QGrundmann_Moller::init_3D().

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

• include/quadrature/quadrature_jacobi.h
• src/quadrature/quadrature_jacobi.C
• src/quadrature/quadrature_jacobi_1D.C