Poster of Linux kernelThe best gift for a Linux geek
QJacobi

QJacobi

Section: C Library Functions (3) Updated: Thu Apr 7 2011
Local index Up
 

NAME

QJacobi -  

SYNOPSIS


#include <quadrature_jacobi.h>

Inherits QBase.  

Public Member Functions


QJacobi (const unsigned int _dim, const Order _order=INVALID_ORDER, const unsigned int _alpha=1, const unsigned int _beta=0)

~QJacobi ()

QuadratureType type () const

ElemType get_elem_type () const

unsigned int get_p_level () const

unsigned int n_points () const

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

void init (const ElemType _type=INVALID_ELEM, unsigned int p_level=0)

Order get_order () const

void print_info (std::ostream &os=std::cout) const

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

Static Public Member Functions


static AutoPtr< QBase > build (const std::string &name, const unsigned int _dim, const Order _order=INVALID_ORDER)

static AutoPtr< QBase > build (const QuadratureType _qt, const unsigned int _dim, const Order _order=INVALID_ORDER)

static void print_info ()

static std::string get_info ()

static unsigned int n_objects ()
 

Public Attributes


bool allow_rules_with_negative_weights
 

Protected Types


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

Protected Member Functions


virtual void init_0D (const ElemType _type=INVALID_ELEM, unsigned int p_level=0)

virtual void init_2D (const ElemType, unsigned int=0)

void increment_constructor_count (const std::string &name)

void increment_destructor_count (const std::string &name)
 

Protected Attributes


std::cerr<< 'ERROR: Seems as if this quadrature rule'<< std::endl<< ' is not implemented for 2D.'<< std::endl;libmesh_error();}#endif virtual void init_3D(const ElemType, unsigned int=0)#ifndef DEBUG{}#else{std::cerr<< 'ERROR: Seems as if this quadrature rule'<< std::endl<< ' is not implemented for 3D.'<< std::endl;libmesh_error();}#endif void tensor_product_quad(const QBase &q1D);void tensor_product_hex(const QBase &q1D);void tensor_product_prism(const QBase &q1D, const QBase &q2D);const unsigned int _dim;const Order _order;ElemType _type;unsigned int _p_level;std::vector< Point > _points

std::vector< Real > _weights
 

Static Protected Attributes


static Counts _counts

static Threads::atomic< unsigned int > _n_objects

static Threads::spin_mutex _mutex
 

Private Member Functions


void init_1D (const ElemType _type=INVALID_ELEM, unsigned int p_level=0)
 

Private Attributes


const unsigned int _alpha

const unsigned int _beta
 

Friends


std::ostream & operator<< (std::ostream &os, const QBase &q)
 

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 FIFTH.

Definition at line 51 of file quadrature_jacobi.h.  

Member Typedef Documentation

 

typedef std::map<std::string, std::pair<unsigned int, unsigned int> > ReferenceCounter::Counts [protected, inherited]Data structure to log the information. The log is identified by the class name.

Definition at line 105 of file reference_counter.h.  

Constructor & Destructor Documentation

 

QJacobi::QJacobi (const unsigned int_dim, const Order_order = INVALID_ORDER, const unsigned int_alpha = 1, const unsigned int_beta = 0) [inline]Constructor. Currently, only one-dimensional rules provided. Check QGauss for versions of Jacobi quadrature rule for higher dimensions.

Definition at line 92 of file quadrature_jacobi.h.

References libMeshEnums::EDGE2, and QBase::init().

                                       : QBase(d,o), _alpha(a), _beta(b)
{
  // explicitly call the init function in 1D since the
  // other tensor-product rules require this one.
  // note that EDGE will not be used internally, however
  // if we called the function with INVALID_ELEM it would try to
  // be smart and return, thinking it had already done the work.
  if (_dim == 1)
    init(EDGE2);
}
 

QJacobi::~QJacobi () [inline]Destructor. Empty.

Definition at line 68 of file quadrature_jacobi.h.

{}
 

Member Function Documentation

 

AutoPtr< QBase > QBase::build (const std::string &name, const unsigned int_dim, const Order_order = INVALID_ORDER) [static, inherited]Builds a specific quadrature rule, identified through the name string. An AutoPtr<QBase> is returned to prevent a memory leak. This way the user need not remember to delete the object. Enables run-time decision of the quadrature rule. The input parameter name must be mappable through the Utility::string_to_enum<>() function.

Definition at line 36 of file quadrature_build.C.

References Utility::string_to_enum< QuadratureType >().

Referenced by InfFE< Dim, T_radial, T_map >::attach_quadrature_rule().

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

AutoPtr< QBase > QBase::build (const QuadratureType_qt, const unsigned int_dim, const Order_order = INVALID_ORDER) [static, inherited]Builds a specific quadrature rule, identified through the QuadratureType. An AutoPtr<QBase> is returned to prevent a memory leak. This way the user need not remember to delete the object. Enables run-time decision of the quadrature rule.

Definition at line 47 of file quadrature_build.C.

References libMeshEnums::FIRST, libMeshEnums::FORTYTHIRD, libMeshEnums::QCLOUGH, libMeshEnums::QGAUSS, libMeshEnums::QJACOBI_1_0, libMeshEnums::QJACOBI_2_0, libMeshEnums::QSIMPSON, libMeshEnums::QTRAP, libMeshEnums::THIRD, and libMeshEnums::TWENTYTHIRD.

{
  switch (_qt)
    {
      
    case QCLOUGH:
      {
#ifdef DEBUG
        if (_order > TWENTYTHIRD)
          {
            std::cout << 'WARNING: Clough quadrature implemented' << std::endl
                      << ' up to TWENTYTHIRD order.' << std::endl;
          }
#endif

        AutoPtr<QBase> ap(new QClough(_dim, _order));
        return ap;
      }

    case QGAUSS:
      {

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

        AutoPtr<QBase> ap(new QGauss(_dim, _order));
        return ap;
      }

    case QJACOBI_1_0:
      {

#ifdef DEBUG
        if (_order > TWENTYTHIRD)
          {
            std::cout << 'WARNING: Jacobi(1,0) quadrature implemented' << std::endl
                      << ' up to TWENTYTHIRD order.' << std::endl;
          }

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

        AutoPtr<QBase> ap(new QJacobi(_dim, _order, 1, 0));
        return ap;
      }

    case QJACOBI_2_0:
      {

#ifdef DEBUG
        if (_order > TWENTYTHIRD)
          {
            std::cout << 'WARNING: Jacobi(2,0) quadrature implemented' << std::endl
                      << ' up to TWENTYTHIRD order.' << std::endl;
          }

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

        AutoPtr<QBase> ap(new QJacobi(_dim, _order, 2, 0));
        return ap;
      }

    case QSIMPSON:
      {

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

        AutoPtr<QBase> ap(new QSimpson(_dim));
        return ap;
      }

    case QTRAP:
      {

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

        AutoPtr<QBase> ap(new QTrap(_dim));
        return ap;
      }


    default:
      { 
        std::cerr << 'ERROR: Bad qt=' << _qt << std::endl;
        libmesh_error();
      }
    }


  libmesh_error();
  AutoPtr<QBase> ap(NULL);
  return ap;
}
 

unsigned int QBase::get_dim () const [inline, inherited]Returns:

the dimension of the quadrature rule.

Definition at line 121 of file quadrature.h.

Referenced by InfFE< Dim, T_radial, T_map >::attach_quadrature_rule(), QConical::conical_product_pyramid(), QConical::conical_product_tet(), and QConical::conical_product_tri().

{ return _dim;  }
 

ElemType QBase::get_elem_type () const [inline, inherited]Returns:

the current element type we're set up for

Definition at line 103 of file quadrature.h.

    { return _type; }
 

std::string ReferenceCounter::get_info () [static, inherited]Gets a string containing the reference information.

Definition at line 45 of file reference_counter.C.

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

Referenced by ReferenceCounter::print_info().

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

  std::ostringstream out;
  
  out << '
      << ' ---------------------------------------------------------------------------- 
      << '| Reference count information                                                |
      << ' ---------------------------------------------------------------------------- ;
  
  for (Counts::iterator it = _counts.begin();
       it != _counts.end(); ++it)
    {
      const std::string name(it->first);
      const unsigned int creations    = it->second.first;
      const unsigned int destructions = it->second.second;

      out << '| ' << name << ' reference count information:
          << '|  Creations:    ' << creations    << '
          << '|  Destructions: ' << destructions << ';
    }
  
  out << ' ---------------------------------------------------------------------------- ;

  return out.str();

#else

  return '';
  
#endif
}
 

Order QBase::get_order () const [inline, inherited]Returns:

the order of the quadrature rule.

Definition at line 167 of file quadrature.h.

Referenced by InfFE< Dim, T_radial, T_map >::attach_quadrature_rule().

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

unsigned int QBase::get_p_level () const [inline, inherited]Returns:

the current p refinement level we're initialized with

Definition at line 109 of file quadrature.h.

    { return _p_level; }
 

const std::vector<Point>& QBase::get_points () const [inline, inherited]Returns:

a std::vector containing the quadrature point locations on a reference object.

Definition at line 127 of file quadrature.h.

References QBase::_points.

Referenced by FE< Dim, T >::edge_reinit(), QClough::init_1D(), QMonomial::init_2D(), QGauss::init_2D(), QClough::init_2D(), QMonomial::init_3D(), QGauss::init_3D(), InfFE< Dim, T_radial, T_map >::init_face_shape_functions(), InfFE< Dim, T_radial, T_map >::reinit(), and REINIT_ERROR().

{ return _points;  }
 

std::vector<Point>& QBase::get_points () [inline, inherited]Returns:

a std::vector containing the quadrature point locations on a reference object as a writeable reference.

Definition at line 133 of file quadrature.h.

References QBase::_points.

{ return _points;  }
 

const std::vector<Real>& QBase::get_weights () const [inline, inherited]Returns:

a std::vector containing the quadrature weights.

Definition at line 138 of file quadrature.h.

References QBase::_weights.

Referenced by FE< Dim, T >::edge_reinit(), QClough::init_1D(), QMonomial::init_2D(), QGauss::init_2D(), QClough::init_2D(), QMonomial::init_3D(), QGauss::init_3D(), InfFE< Dim, T_radial, T_map >::init_face_shape_functions(), and REINIT_ERROR().

{ return _weights; }
 

std::vector<Real>& QBase::get_weights () [inline, inherited]Returns:

a std::vector containing the quadrature weights.

Definition at line 143 of file quadrature.h.

References QBase::_weights.

{ return _weights; }
 

void ReferenceCounter::increment_constructor_count (const std::string &name) [inline, protected, inherited]Increments the construction counter. Should be called in the constructor of any derived class that will be reference counted.

Definition at line 149 of file reference_counter.h.

References ReferenceCounter::_counts, Quality::name(), and Threads::spin_mtx.

Referenced by ReferenceCountedObject< Value >::ReferenceCountedObject().

{
  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
  std::pair<unsigned int, unsigned int>& p = _counts[name];

  p.first++;
}
 

void ReferenceCounter::increment_destructor_count (const std::string &name) [inline, protected, inherited]Increments the destruction counter. Should be called in the destructor of any derived class that will be reference counted.

Definition at line 167 of file reference_counter.h.

References ReferenceCounter::_counts, Quality::name(), and Threads::spin_mtx.

Referenced by ReferenceCountedObject< Value >::~ReferenceCountedObject().

{
  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
  std::pair<unsigned int, unsigned int>& p = _counts[name];

  p.second++;
}
 

void QBase::init (const ElemType_type = INVALID_ELEM, unsigned intp_level = 0) [inherited]Initializes the data structures to contain a quadrature rule for an object of type type.

Definition at line 26 of file quadrature.C.

References QBase::init_0D(), QBase::init_1D(), and QBase::init_2D().

Referenced by FE< Dim, T >::edge_reinit(), QClough::init_1D(), QTrap::init_2D(), QSimpson::init_2D(), QMonomial::init_2D(), QGrid::init_2D(), QGauss::init_2D(), QClough::init_2D(), QTrap::init_3D(), QSimpson::init_3D(), QMonomial::init_3D(), QGrid::init_3D(), QGauss::init_3D(), InfFE< Dim, T_radial, T_map >::init_face_shape_functions(), QGauss::QGauss(), QJacobi(), QSimpson::QSimpson(), QTrap::QTrap(), InfFE< Dim, T_radial, T_map >::reinit(), and REINIT_ERROR().

{
  // check to see if we have already
  // done the work for this quadrature rule
  if (t == _type && p == _p_level)
    return;
  else
    {
      _type = t;
      _p_level = p;
    }
    
  
  
  switch(_dim)
    {
    case 0:
      this->init_0D(_type,_p_level);

      return;
      
    case 1:
      this->init_1D(_type,_p_level);

      return;
      
    case 2:
      this->init_2D(_type,_p_level);

      return;

    case 3:
      this->init_3D(_type,_p_level);

      return;

    default:
      libmesh_error();
    }
}
 

void QBase::init_0D (const ElemType_type = INVALID_ELEM, unsigned intp_level = 0) [protected, virtual, inherited]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 70 of file quadrature.C.

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

Referenced by QBase::init().

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

void QJacobi::init_1D (const ElemType_type = INVALID_ELEM, unsigned intp_level = 0) [private, virtual]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 QBase.

Definition at line 27 of file quadrature_jacobi_1D.C.

References _alpha, _beta, QBase::_points, QBase::_weights, libMeshEnums::CONSTANT, libMeshEnums::EIGHTH, libMeshEnums::EIGHTTEENTH, libMeshEnums::ELEVENTH, libMeshEnums::FIFTEENTH, libMeshEnums::FIFTH, libMeshEnums::FIRST, libMeshEnums::FORTIETH, libMeshEnums::FORTYFIRST, libMeshEnums::FORTYSECOND, libMeshEnums::FORTYTHIRD, libMeshEnums::FOURTEENTH, libMeshEnums::FOURTH, libMeshEnums::NINTEENTH, libMeshEnums::NINTH, libMeshEnums::SECOND, libMeshEnums::SEVENTEENTH, libMeshEnums::SEVENTH, libMeshEnums::SIXTEENTH, libMeshEnums::SIXTH, libMeshEnums::TENTH, libMeshEnums::THIRD, libMeshEnums::THIRTEENTH, libMeshEnums::THIRTIETH, libMeshEnums::THIRTYEIGHTH, libMeshEnums::THIRTYFIFTH, libMeshEnums::THIRTYFIRST, libMeshEnums::THIRTYFOURTH, libMeshEnums::THIRTYNINTH, libMeshEnums::THIRTYSECOND, libMeshEnums::THIRTYSEVENTH, libMeshEnums::THIRTYSIXTH, libMeshEnums::THIRTYTHIRD, libMeshEnums::TWELFTH, libMeshEnums::TWENTIETH, libMeshEnums::TWENTYEIGHTH, libMeshEnums::TWENTYFIFTH, libMeshEnums::TWENTYFIRST, libMeshEnums::TWENTYFOURTH, libMeshEnums::TWENTYNINTH, libMeshEnums::TWENTYSECOND, libMeshEnums::TWENTYSEVENTH, libMeshEnums::TWENTYSIXTH, and libMeshEnums::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(_order + 2*p)
        {
        case CONSTANT:
        case FIRST:
          {
            _points.resize (1);
            _weights.resize(1);
        
            _points[0](0)  = 1./3.;
        
            _weights[0]    = 0.5;
        
            return;
          }
        case SECOND:
        case THIRD:
          {
            _points.resize (2);
            _weights.resize(2);
              
            _points[ 0](0)=1.5505102572168219018027159252941e-01L;      _weights[ 0]=3.1804138174397716939436900207516e-01L;
            _points[ 1](0)=6.4494897427831780981972840747059e-01L;      _weights[ 1]=1.8195861825602283060563099792484e-01L;

            return;
          }
        case FOURTH:
        case FIFTH:
          {
            _points.resize (3);
            _weights.resize(3);
              
            _points[ 0](0)=8.8587959512703947395546143769456e-02L;      _weights[ 0]=2.0093191373895963077219813326460e-01L;
            _points[ 1](0)=4.0946686444073471086492625206883e-01L;      _weights[ 1]=2.2924110635958624669392059455632e-01L;
            _points[ 2](0)=7.8765946176084705602524188987600e-01L;      _weights[ 2]=6.9826979901454122533881272179077e-02L;

            return;
          }
        case SIXTH:
        case SEVENTH:
          {
            _points.resize (4);
            _weights.resize(4);
              
            _points[ 0](0)=5.7104196114517682193121192554116e-02L;      _weights[ 0]=1.3550691343148811620826417407794e-01L;
            _points[ 1](0)=2.7684301363812382768004599768563e-01L;      _weights[ 1]=2.0346456801027136079140447593585e-01L;
            _points[ 2](0)=5.8359043236891682005669766866292e-01L;      _weights[ 2]=1.2984754760823244082645620288963e-01L;
            _points[ 3](0)=8.6024013565621944784791291887512e-01L;      _weights[ 3]=3.1180970950008082173875147096575e-02L;

            return;
          }
        case EIGHTH:
        case NINTH:
          {
            _points.resize (5);
            _weights.resize(5);
              
            _points[ 0](0)=3.9809857051468742340806690093333e-02L;      _weights[ 0]=9.6781590226651679274360971636151e-02L;
            _points[ 1](0)=1.9801341787360817253579213679530e-01L;      _weights[ 1]=1.6717463809436956549167562309770e-01L;
            _points[ 2](0)=4.3797481024738614400501252000523e-01L;      _weights[ 2]=1.4638698708466980869803786935596e-01L;
            _points[ 3](0)=6.9546427335363609451461482372117e-01L;      _weights[ 3]=7.3908870072616670350633219341704e-02L;
            _points[ 4](0)=9.0146491420117357387650110211225e-01L;      _weights[ 4]=1.5747914521692276185292316568488e-02L;

            return;
          }
        case TENTH:
        case ELEVENTH:
          {
        
            _points.resize (6);
            _weights.resize(6);
              
            _points[ 0](0)=2.9316427159784891972050276913165e-02L;      _weights[ 0]=7.2310330725508683655454326124832e-02L;
            _points[ 1](0)=1.4807859966848429184997685249598e-01L;      _weights[ 1]=1.3554249723151861684069039663805e-01L;
            _points[ 2](0)=3.3698469028115429909705297208078e-01L;      _weights[ 2]=1.4079255378819892811907683907093e-01L;
            _points[ 3](0)=5.5867151877155013208139334180552e-01L;      _weights[ 3]=9.8661150890655264120584510548360e-02L;
            _points[ 4](0)=7.6923386203005450091688336011565e-01L;      _weights[ 4]=4.3955165550508975508176624305430e-02L;
            _points[ 5](0)=9.2694567131974111485187396581968e-01L;      _weights[ 5]=8.7383018136095317560173033123989e-03L;

            return;
          }
        case TWELFTH:
        case THIRTEENTH:
          {
            _points.resize (7);
            _weights.resize(7);
              
            _points[ 0](0)=2.2479386438712498108825499570845e-02L;      _weights[ 0]=5.5967363423491051151562113429926e-02L;
            _points[ 1](0)=1.1467905316090423190964023706751e-01L;      _weights[ 1]=1.1050925819087460242112073636961e-01L;
            _points[ 2](0)=2.6578982278458946847678939169339e-01L;      _weights[ 2]=1.2739089729958832691873448577496e-01L;
            _points[ 3](0)=4.5284637366944461699855144234765e-01L;      _weights[ 3]=1.0712506569587366999091225299986e-01L;
            _points[ 4](0)=6.4737528288683036262609222982876e-01L;      _weights[ 4]=6.6384696465491469983647988763640e-02L;
            _points[ 5](0)=8.1975930826310763501242005719082e-01L;      _weights[ 5]=2.7408356721873475444331048358226e-02L;
            _points[ 6](0)=9.4373743946307785353434780896769e-01L;      _weights[ 6]=5.2143622028074040896913743037830e-03L;

            return;
          }
        case FOURTEENTH:
        case FIFTEENTH:
          {
            _points.resize (8);
            _weights.resize(8);
              
            _points[ 0](0)=1.7779915147363451813205101037679e-02L;      _weights[ 0]=4.4550804361555931326215619533963e-02L;
            _points[ 1](0)=9.1323607899793956003741458074541e-02L;      _weights[ 1]=9.1119023636373626345722461782880e-02L;
            _points[ 2](0)=2.1430847939563075835754126758167e-01L;      _weights[ 2]=1.1250579947088736617177209860428e-01L;
            _points[ 3](0)=3.7193216458327230243085396048263e-01L;      _weights[ 3]=1.0604735943593001070453109641116e-01L;
            _points[ 4](0)=5.4518668480342664903227222995321e-01L;      _weights[ 4]=7.9199599492319160120408189359892e-02L;
            _points[ 5](0)=7.1317524285556948105131376025091e-01L;      _weights[ 5]=4.5439319504698898083055421095694e-02L;
            _points[ 6](0)=8.5563374295785442851478147977179e-01L;      _weights[ 6]=1.7842902655986208393552797201042e-02L;
            _points[ 7](0)=9.5536604471003014926687897814169e-01L;      _weights[ 7]=3.2951914422487988547423160110891e-03L;

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

            _points[ 0](0)=1.4412409648876548632826740810813e-02L;      _weights[ 0]=3.6278003523279871459649597941160e-02L;
            _points[ 1](0)=7.4387389709196044635918185955999e-02L;      _weights[ 1]=7.6074255109308162580079303753964e-02L;
            _points[ 2](0)=1.7611665616299528186317574607257e-01L;      _weights[ 2]=9.8533742172345705160173020369274e-02L;
            _points[ 3](0)=3.0966757992763781705962046722948e-01L;      _weights[ 3]=1.0030880919336828965415022473259e-01L;
            _points[ 4](0)=4.6197040108101093488314310868056e-01L;      _weights[ 4]=8.4358321844920349394250019958587e-02L;
            _points[ 5](0)=6.1811723469529402463922975160350e-01L;      _weights[ 5]=5.8401195295165110565731522901640e-02L;
            _points[ 6](0)=7.6282301518503961468269330714673e-01L;      _weights[ 6]=3.1804821491054001261690106935870e-02L;
            _points[ 7](0)=8.8192102121000129980771488800526e-01L;      _weights[ 7]=1.2060004284785379051727152286900e-02L;
            _points[ 8](0)=9.6374218711679053905883569923192e-01L;      _weights[ 8]=2.1808470857731308725490511200170e-03L;

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

            _points[ 0](0)=1.1917613432415596909745586958986e-02L;      _weights[ 0]=3.0099508024037023300654755523879e-02L;
            _points[ 1](0)=6.1732071877148125522629367194250e-02L;      _weights[ 1]=6.4287154509082572874826538628865e-02L;
            _points[ 2](0)=1.4711144964307024042759943557982e-01L;      _weights[ 2]=8.6211300289176036428333360711914e-02L;
            _points[ 3](0)=2.6115967600845624026605165805485e-01L;      _weights[ 3]=9.2696893677723415844756991929711e-02L;
            _points[ 4](0)=3.9463984688578684296195210507761e-01L;      _weights[ 4]=8.4557109690827332430645582165501e-02L;
            _points[ 5](0)=5.3673876571566063287309517771189e-01L;      _weights[ 5]=6.6053075563350379166074502504878e-02L;
            _points[ 6](0)=6.7594446167666510735715050893476e-01L;      _weights[ 6]=4.3401906407150625922456117586384e-02L;
            _points[ 7](0)=8.0097892103689884513794630161724e-01L;      _weights[ 7]=2.2774591453263032586487649426060e-02L;
            _points[ 8](0)=9.0171098779014677034879897840977e-01L;      _weights[ 8]=8.4193197829831874175163655187011e-03L;
            _points[ 9](0)=9.6997096783851350295693564236559e-01L;      _weights[ 9]=1.4991406024063940282481360041064e-03L;

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

            _points[ 0](0)=1.0018280461680405843024729867805e-02L;      _weights[ 0]=2.5367340688141426184944658517383e-02L;
            _points[ 1](0)=5.2035451127180552583542695772964e-02L;      _weights[ 1]=5.4938091132871498258746681665651e-02L;
            _points[ 2](0)=1.2461922514444307373529958726391e-01L;      _weights[ 2]=7.5620048057186998321377054841660e-02L;
            _points[ 3](0)=2.2284060704383785550783145345736e-01L;      _weights[ 3]=8.4659422884017621219239388551910e-02L;
            _points[ 4](0)=3.4000815791466518823360523389702e-01L;      _weights[ 4]=8.1879102988063470389586851943461e-02L;
            _points[ 5](0)=4.6813761308958404208311038075775e-01L;      _weights[ 5]=6.9531875158183049799050889633934e-02L;
            _points[ 6](0)=5.9849727976713918322772071367304e-01L;      _weights[ 6]=5.1591360672297580193086641744608e-02L;
            _points[ 7](0)=7.2220328489096792556332130780461e-01L;      _weights[ 7]=3.2641546713833346017953865389764e-02L;
            _points[ 8](0)=8.3082489962281857403056654390566e-01L;      _weights[ 8]=1.6663623451680692415747124573826e-02L;
            _points[ 9](0)=9.1695838655259485329313462701803e-01L;      _weights[ 9]=6.0439209604797757927329621765769e-03L;
            _points[10](0)=9.7472637960247965024666881353837e-01L;      _weights[10]=1.0636672932445414075338809612253e-03L;

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

            _points[ 0](0)=8.5390549884274193686644608778398e-03L;      _weights[ 0]=2.1664860886871767324583472077976e-02L;
            _points[ 1](0)=4.4446463155407723025466798785553e-02L;      _weights[ 1]=4.7427851980377470134309182197087e-02L;
            _points[ 2](0)=1.0685449088347665763410677043250e-01L;      _weights[ 2]=6.6606750626673198130834485351975e-02L;
            _points[ 3](0)=1.9215105452985404099105725622861e-01L;      _weights[ 3]=7.6896602680041006281204469112373e-02L;
            _points[ 4](0)=2.9538088426258022162291683437601e-01L;      _weights[ 4]=7.7696316815531026628765631099760e-02L;
            _points[ 5](0)=4.1054508120145768248903435055933e-01L;      _weights[ 5]=7.0109339997630094495921805029671e-02L;
            _points[ 6](0)=5.3095084931281767062893024289682e-01L;      _weights[ 6]=5.6613843713667631943701105156121e-02L;
            _points[ 7](0)=6.4960065027725499276629172334298e-01L;      _weights[ 7]=4.0451653706913616760646424250646e-02L;
            _points[ 8](0)=7.5959888952522705374260257404342e-01L;      _weights[ 8]=2.4876780409265432012508172290016e-02L;
            _points[ 9](0)=8.5455254376493588079021191640562e-01L;      _weights[ 9]=1.2436009166422265607483293056674e-02L;
            _points[10](0)=9.2894210126441101784881015513432e-01L;      _weights[10]=4.4448077956684623227961458658283e-03L;
            _points[11](0)=9.7843793683414963909190691691700e-01L;      _weights[11]=7.7518222093802835724581451187414e-04L;

            return;
          }

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

            _points[ 0](0)=7.3646510260893216506914984138223e-03L;      _weights[ 0]=1.8714731585615175193374408664994e-02L;
            _points[ 1](0)=3.8398138739678350376832524864142e-02L;      _weights[ 1]=4.1320289419839298476611706952624e-02L;
            _points[ 2](0)=9.2595224699002635282891375438616e-02L;      _weights[ 2]=5.8953937956647082536161503261961e-02L;
            _points[ 3](0)=1.6725101139155773149552247875936e-01L;      _weights[ 3]=6.9713468282144398251416629950427e-02L;
            _points[ 4](0)=2.5862354070576251658979073282269e-01L;      _weights[ 4]=7.2849696515818223079384033843973e-02L;
            _points[ 5](0)=3.6213139728223880040868129822732e-01L;      _weights[ 5]=6.8815529487565417217837889436694e-02L;
            _points[ 6](0)=4.7258438600411772517509464267860e-01L;      _weights[ 6]=5.9120481314092327419290155953032e-02L;
            _points[ 7](0)=5.8444396402134045550422084781091e-01L;      _weights[ 7]=4.5995780676052393313259784530213e-02L;
            _points[ 8](0)=6.9210100171960165689704195168767e-01L;      _weights[ 8]=3.1936787162203148842381371158461e-02L;
            _points[ 9](0)=7.9015702827343748555286333249938e-01L;      _weights[ 9]=1.9213957164719820645895497863743e-02L;
            _points[10](0)=8.7369482130668941936771456713174e-01L;      _weights[10]=9.4489244795927503661800865492413e-03L;
            _points[11](0)=9.3852445910073101239763338676530e-01L;      _weights[11]=3.3383592507737718066104206420419e-03L;
            _points[12](0)=9.8138963498901214856028062215971e-01L;      _weights[12]=5.7805670493619285159651119259460e-04L;
            
            return;
          }

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

            _points[ 0](0)=6.4167607928184568108204640945072e-03L;      _weights[ 0]=1.6326754322596839819449429350767e-02L;
            _points[ 1](0)=3.3501404532013140035963928570572e-02L;      _weights[ 1]=3.6296078055443693187652118821852e-02L;
            _points[ 2](0)=8.0985499681955184392451307739982e-02L;      _weights[ 2]=5.2445953501916745591081806162678e-02L;
            _points[ 3](0)=1.4680486768121372992366016526080e-01L;      _weights[ 3]=6.3213025574329203442529115357932e-02L;
            _points[ 4](0)=2.2808427064925799153464409861994e-01L;      _weights[ 4]=6.7831659604182837102347339834146e-02L;
            _points[ 5](0)=3.2127174398893617440234039741304e-01L;      _weights[ 5]=6.6392350626085425132821358651277e-02L;
            _points[ 6](0)=4.2229465730757025784040898751810e-01L;      _weights[ 6]=5.9785559022531584222614059168587e-02L;
            _points[ 7](0)=5.2673786133987303205372694481288e-01L;      _weights[ 7]=4.9519454523203004580936179335753e-02L;
            _points[ 8](0)=6.3003668837040395788448059413143e-01L;      _weights[ 8]=3.7443096458985826655938301826886e-02L;
            _points[ 9](0)=7.2767645288926468543602672799033e-01L;      _weights[ 9]=2.5423465407148762115069898757459e-02L;
            _points[10](0)=8.1538973944347464197307421861206e-01L;      _weights[10]=1.5032303743928643503408714751315e-02L;
            _points[11](0)=8.8934280881951553969087166094649e-01L;      _weights[11]=7.2964841332126214434099222674776e-03L;
            _points[12](0)=9.4630270006027538353340594342472e-01L;      _weights[12]=2.5541013176876539479794996099427e-03L;
            _points[13](0)=9.8377523409860023828122800914100e-01L;      _weights[13]=4.3971370874715925476225610392609e-04L;

            return;
          }

        case TWENTYEIGHTH:
        case TWENTYNINTH:
          {
            _points.resize (15);
            _weights.resize(15);
            
            _points[ 0](0)=5.6406889725117097575064665794442e-03L;      _weights[ 0]=1.4367069621712523019113300206269e-02L;
            _points[ 1](0)=2.9482298647942486631640984718004e-02L;      _weights[ 1]=3.2119044874965915878547666076448e-02L;
            _points[ 2](0)=7.1412953115158840054783901746735e-02L;      _weights[ 2]=4.6891639944059925679345570546797e-02L;
            _points[ 3](0)=1.2983102555359105597125453809429e-01L;      _weights[ 3]=5.7398825506941289374618916116414e-02L;
            _points[ 4](0)=2.0249275505010404756821998832023e-01L;      _weights[ 4]=6.2918106648596909592665349230551e-02L;
            _points[ 5](0)=2.8660608625752705998402604548440e-01L;      _weights[ 5]=6.3343955161511392519350738069297e-02L;
            _points[ 6](0)=3.7893868864697803810652900914277e-01L;      _weights[ 6]=5.9174192059712931565021168664588e-02L;
            _points[ 7](0)=4.7594230846323486057258899201585e-01L;      _weights[ 7]=5.1412362311886468530400169371359e-02L;
            _points[ 8](0)=5.7388916090668588067145385523753e-01L;      _weights[ 8]=4.1400735184422578228813150524935e-02L;
            _points[ 9](0)=6.6901519502995987653869563905314e-01L;      _weights[ 9]=3.0609769586468540804291808789747e-02L;
            _points[10](0)=7.5766473903134271199707427774029e-01L;      _weights[10]=2.0416309272619835691190995270654e-02L;
            _points[11](0)=8.3643096060561012397555908565418e-01L;      _weights[11]=1.1904190355097578843030186960250e-02L;
            _points[12](0)=9.0228670067937802663123850466201e-01L;      _weights[12]=5.7172223947211761716246502974268e-03L;
            _points[13](0)=9.5270040990583331433804420752426e-01L;      _weights[13]=1.9862346931450380410338051145760e-03L;
            _points[14](0)=9.8573054526317422526590063305913e-01L;      _weights[14]=3.4034238413789606095252476068833e-04L;

            return;
          }


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

            _points[ 0](0)=4.9972996637719210426511496015207e-03L;      _weights[ 0]=1.2739310657334184747549845879578e-02L;
            _points[ 1](0)=2.6143513681394051978549323380543e-02L;      _weights[ 1]=2.8612452590143149357558068987418e-02L;
            _points[ 2](0)=6.3430945583836745492528222770701e-02L;      _weights[ 2]=4.2129431157428284757515740541878e-02L;
            _points[ 3](0)=1.1559843757981594017892362824740e-01L;      _weights[ 3]=5.2228594403959147363509678893029e-02L;
            _points[ 4](0)=1.8087055965788366624757339125570e-01L;      _weights[ 4]=5.8254240209855835379301779422393e-02L;
            _points[ 5](0)=2.5702480784517085992294423955927e-01L;      _weights[ 5]=6.0000854888113507055385942002166e-02L;
            _points[ 6](0)=3.4146792754782306862589929793869e-01L;      _weights[ 6]=5.7718879609267823617681995467969e-02L;
            _points[ 7](0)=4.3132434359562537508359226958274e-01L;      _weights[ 7]=5.2064137843806583754973352189273e-02L;
            _points[ 8](0)=5.2353411602516832051747016507566e-01L;      _weights[ 8]=4.3997382189243923173481417304490e-02L;
            _points[ 9](0)=6.1495715187648951748964083381908e-01L;      _weights[ 9]=3.4647816579285799103084877873731e-02L;
            _points[10](0)=7.0248013792504104445480697553762e-01L;      _weights[10]=2.5159233106470040585653957496918e-02L;
            _points[11](0)=7.8312255396486808385218178256205e-01L;      _weights[11]=1.6539584355635793501225242083105e-02L;
            _points[12](0)=8.5413814777521063366511368381932e-01L;      _weights[12]=9.5341678846659366549669638207733e-03L;
            _points[13](0)=9.1310837653714127462958554670327e-01L;      _weights[13]=4.5392323861386350682211111786128e-03L;
            _points[14](0)=9.5802441769047545454495934455429e-01L;      _weights[14]=1.5671884735958197030724006964051e-03L;
            _points[15](0)=9.8735302062604161803115590316790e-01L;      _weights[15]=2.6749366505553617681762616226073e-04L;

            return;
          }


        case THIRTYSECOND:
        case THIRTYTHIRD:
          {
            _points.resize (17);
            _weights.resize(17);
        
            _points[ 0](0)=4.4579935677873917545062291115464e-03L;      _weights[ 0]=1.1372703113196894148880104403419e-02L;
            _points[ 1](0)=2.3340094123774273967021528207683e-02L;      _weights[ 1]=2.5642427920205179185750205247311e-02L;
            _points[ 2](0)=5.6707968769078239532713331556521e-02L;      _weights[ 2]=3.8025728825742400201474917006665e-02L;
            _points[ 3](0)=1.0355543293519706341349122696131e-01L;      _weights[ 3]=4.7641869374618441920575209265709e-02L;
            _points[ 4](0)=1.6246000342813654998162954391410e-01L;      _weights[ 4]=5.3907931667527480191616020246527e-02L;
            _points[ 5](0)=2.3163212577717218294679722573836e-01L;      _weights[ 5]=5.6573611382471512986991034182850e-02L;
            _points[ 6](0)=3.0897011775219590331752426128626e-01L;      _weights[ 6]=5.5734917923560549577129019490753e-02L;
            _points[ 7](0)=3.9212413472209565803361946333190e-01L;      _weights[ 7]=5.1809741929296333255214704762820e-02L;
            _points[ 8](0)=4.7856759685307958878371046285937e-01L;      _weights[ 8]=4.5477790399142277497438924164211e-02L;
            _points[ 9](0)=5.6567396688663433190330697600965e-01L;      _weights[ 9]=3.7592325487112238031431998524319e-02L;
            _points[10](0)=6.5079655845338226473148740732315e-01L;      _weights[10]=2.9074524087705050563187355467924e-02L;
            _points[11](0)=7.3134895273405138213302149556298e-01L;      _weights[11]=2.0803278010295362060012866375773e-02L;
            _points[12](0)=8.0488357852496649199917770139703e-01L;      _weights[12]=1.3513697452300780909638958310491e-02L;
            _points[13](0)=8.6916605956741361920444649801116e-01L;      _weights[13]=7.7164222148059386958884227660543e-03L;
            _points[14](0)=9.2224303459229840848710732823038e-01L;      _weights[14]=3.6472304834214064450344565237838e-03L;
            _points[15](0)=9.6250119782335004125046077538851e-01L;      _weights[15]=1.2526834393912207489106525201067e-03L;
            _points[16](0)=9.8871404063224375141712140225296e-01L;      _weights[16]=2.1311628920693358082515074128342e-04L;
        
            return;
          }

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

            _points[ 0](0)=4.0014793838673867970427199102708e-03L;      _weights[ 0]=1.0214339435040633872267566728543e-02L;
            _points[ 1](0)=2.0963648393766477995135600986561e-02L;      _weights[ 1]=2.3106350163377066931289331193145e-02L;
            _points[ 2](0)=5.0994041587890553966774921299853e-02L;      _weights[ 2]=3.4471118921922024965038695158493e-02L;
            _points[ 3](0)=9.3280395928544950777609058826066e-02L;      _weights[ 3]=4.3573907074643088262181650935306e-02L;
            _points[ 4](0)=1.4667010367761795715160882973461e-01L;      _weights[ 4]=4.9902226917702713891102223856106e-02L;
            _points[ 5](0)=2.0970703958884296672188171145203e-01L;      _weights[ 5]=5.3192334631835660026223777017865e-02L;
            _points[ 6](0)=2.8067179006017169910681926203455e-01L;      _weights[ 6]=5.3445287802814027020361560753181e-02L;
            _points[ 7](0)=3.5762864997663462939832714298390e-01L;      _weights[ 7]=5.0916928856374093181562996165432e-02L;
            _points[ 8](0)=4.3847844922413811765185426038741e-01L;      _weights[ 8]=4.6082400990241280762086995392822e-02L;
            _points[ 9](0)=5.2101582087077614731981479158547e-01L;      _weights[ 9]=3.9579162288607878726422969126448e-02L;
            _points[10](0)=6.0298936055983207213748070418747e-01L;      _weights[10]=3.2134806127628549240737903166505e-02L;
            _points[11](0)=6.8216303911365156501882207998153e-01L;      _weights[11]=2.4487590001291716597869859208141e-02L;
            _points[12](0)=7.5637719340615062679816733590978e-01L;      _weights[12]=1.7308300480899289815470186505791e-02L;
            _points[13](0)=8.2360742977486956587394885462062e-01L;      _weights[13]=1.1131870097409362452892993478578e-02L;
            _points[14](0)=8.8201982536207914673124120886230e-01L;      _weights[14]=6.3060388823805337332782426625400e-03L;
            _points[15](0)=9.3002088969969321648195850472769e-01L;      _weights[15]=2.9624430644328375036535062298419e-03L;
            _points[16](0)=9.6630075194563254241150674649068e-01L;      _weights[16]=1.0130251793010471252471709101709e-03L;
            _points[17](0)=9.8986684820259713441676302277596e-01L;      _weights[17]=1.7186908409819589231237151109171e-04L;
        
            return;
          }

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

            _points[ 0](0)=3.6116428185568930344532101262520e-03L;      _weights[ 0]=9.2240377250330766917668248692203e-03L;
            _points[ 1](0)=1.8931837031588217250264524316949e-02L;      _weights[ 1]=2.0924651751979890481445228332988e-02L;
            _points[ 2](0)=4.6097933048431083573924770835459e-02L;      _weights[ 2]=3.1376275285732898854356814457609e-02L;
            _points[ 3](0)=8.4447222784209820599847900451170e-02L;      _weights[ 3]=3.9962370048991741940293076442317e-02L;
            _points[ 4](0)=1.3303618855809877542408742397522e-01L;      _weights[ 4]=4.6234928168578411765380785132191e-02L;
            _points[ 5](0)=1.9066859490476335108747466488719e-01L;      _weights[ 5]=4.9934138240419379553284105838773e-02L;
            _points[ 6](0)=2.5592540348210296025204739729528e-01L;      _weights[ 6]=5.1004186626719396295755229568486e-02L;
            _points[ 7](0)=3.2719980076381171572842996527566e-01L;      _weights[ 7]=4.9591046468706580141316052533532e-02L;
            _points[ 8](0)=4.0273678616507709512304701110488e-01L;      _weights[ 8]=4.6021985716138412908362881060678e-02L;
            _points[ 9](0)=4.8067639357855190263322135248271e-01L;      _weights[ 9]=4.0768870871836685572301729841664e-02L;
            _points[10](0)=5.5909949264903198784692797587908e-01L;      _weights[10]=3.4398957951907391429559705435925e-02L;
            _points[11](0)=6.3607504487927089469109105709816e-01L;      _weights[11]=2.7518058144347978141481142479516e-02L;
            _points[12](0)=7.0970765165390239884374678311164e-01L;      _weights[12]=2.0711672562757804879837159838775e-02L;
            _points[13](0)=7.7818422297676161420929964704208e-01L;      _weights[13]=1.4489847112109724657001233005036e-02L;
            _points[14](0)=8.3981861570871107783863629442929e-01L;      _weights[14]=9.2410919293165977626976877702861e-03L;
            _points[15](0)=8.9309313498184497075098115456491e-01L;      _weights[15]=5.1997813282783796868055465441831e-03L;
            _points[16](0)=9.3669584807436508054390550208195e-01L;      _weights[16]=2.4300917120432807075681660438661e-03L;
            _points[17](0)=9.6955263708022088547192878623227e-01L;      _weights[17]=8.2788076092398219334600301771448e-04L;
            _points[18](0)=9.9085180527095568535309483522012e-01L;      _weights[18]=1.4012759417838633744062778723898e-04L;
        
            return;
          }

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

            _points[ 0](0)=3.2761066690500989752646761128711e-03L;      _weights[ 0]=8.3708441762725569742347797346057e-03L;
            _points[ 1](0)=1.7181218145255713738247704631582e-02L;      _weights[ 1]=1.9034969463701666952317752319364e-02L;
            _points[ 2](0)=4.1871431117765195244234634143709e-02L;      _weights[ 2]=2.8668237379130596303519483134423e-02L;
            _points[ 3](0)=7.6800837089621970481870523019947e-02L;      _weights[ 3]=3.6750239836647855880170014918540e-02L;
            _points[ 4](0)=1.2118986732367606561768615229454e-01L;      _weights[ 4]=4.2890295837978204214146023790200e-02L;
            _points[ 5](0)=1.7404711263554216522415793419966e-01L;      _weights[ 5]=4.6841691862557827847492882468251e-02L;
            _points[ 6](0)=2.3419188631359219089445571283230e-01L;      _weights[ 6]=4.8516105059854090810181874268668e-02L;
            _points[ 7](0)=3.0028067683595016436625841871717e-01L;      _weights[ 7]=4.7985461609943912515256158210751e-02L;
            _points[ 8](0)=3.7083718058439689644532207953771e-01L;      _weights[ 8]=4.5470588941353475125260875269943e-02L;
            _points[ 9](0)=4.4428528696301116212882391783598e-01L;      _weights[ 9]=4.1317706816665737825832945172262e-02L;
            _points[10](0)=5.1898428870357372961841176083024e-01L;      _weights[10]=3.5964919153862747854063187859799e-02L;
            _points[11](0)=5.9326553348350648796739308654437e-01L;      _weights[11]=2.9901741842629013049082489189589e-02L;
            _points[12](0)=6.6546969890551364795372958813385e-01L;      _weights[12]=2.3625296173548892813066360441583e-02L;
            _points[13](0)=7.3398385823565944973202719329584e-01L;      _weights[13]=1.7597066879206016267686128655074e-02L;
            _points[14](0)=7.9727750833659468770218885137527e-01L;      _weights[14]=1.2204046126680104278798703245791e-02L;
            _points[15](0)=8.5393675303589045708900439161802e-01L;      _weights[15]=7.7276679300514628735780671415898e-03L;
            _points[16](0)=9.0269587179345369227634694169967e-01L;      _weights[16]=4.3232191126901531337390520742896e-03L;
            _points[17](0)=9.4246554236318633869089187742766e-01L;      _weights[17]=2.0114576139640780069071394684122e-03L;
            _points[18](0)=9.7235694664743691118470187166465e-01L;      _weights[18]=6.8306227608592198451771987553801e-04L;
            _points[19](0)=9.9169995579293273076654365969470e-01L;      _weights[19]=1.1538190717568529014836276132844e-04L;
        
            return;
          }

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

            _points[ 0](0)=2.9852372832130627418887840757498e-03L;      _weights[ 0]=7.6306059065231890951709176867159e-03L;
            _points[ 1](0)=1.5662280557573547332895610655678e-02L;      _weights[ 1]=1.7387926076195012545310092581185e-02L;
            _points[ 2](0)=3.8198288245073553344832819395658e-02L;      _weights[ 2]=2.6287260083203306468723755830943e-02L;
            _points[ 3](0)=7.0139619062325798139842656763758e-02L;      _weights[ 3]=3.3886790344403175515158905218748e-02L;
            _points[ 4](0)=1.1083667332036350223762530758616e-01L;      _weights[ 4]=3.9845977571398966444570950002831e-02L;
            _points[ 5](0)=1.5946112944406525026381380836555e-01L;      _weights[ 5]=4.3935570635150377464859835729052e-02L;
            _points[ 6](0)=2.1502318535802028508091216764592e-01L;      _weights[ 6]=4.6050270723257502074077985626262e-02L;
            _points[ 7](0)=2.7639177909378317240968620976306e-01L;      _weights[ 7]=4.6212552611022412660350368837561e-02L;
            _points[ 8](0)=3.4231763295873079372348132371246e-01L;      _weights[ 8]=4.4566874686154606866984823191992e-02L;
            _points[ 9](0)=4.1145869156190519892697533612651e-01L;      _weights[ 9]=4.1364760396997617354403702904192e-02L;
            _points[10](0)=4.8240744461243888053531852185958e-01L;      _weights[10]=3.6942012648499385551903205764287e-02L;
            _points[11](0)=5.5371958072829359140036561243486e-01L;      _weights[11]=3.1689953050127340376763333466278e-02L;
            _points[12](0)=6.2394338972128194749630581474409e-01L;      _weights[12]=2.6023046795895555117823162899995e-02L;
            _points[13](0)=6.9164931501296225721944667896925e-01L;      _weights[13]=2.0345549389821508292035088652126e-02L;
            _points[14](0)=7.5545905444968698626584997281486e-01L;      _weights[14]=1.5019872613192784763520392446339e-02L;
            _points[15](0)=8.1407361651269741678894410957934e-01L;      _weights[15]=1.0339209757970312663832726410241e-02L;
            _points[16](0)=8.6629975897095659707636330435792e-01L;      _weights[16]=6.5065974236456053354067512991831e-03L;
            _points[17](0)=9.1107426580261577477966643276619e-01L;      _weights[17]=3.6220528697449398652362737797211e-03L;
            _points[18](0)=9.4748554440639734668609897166113e-01L;      _weights[18]=1.6787560215669155362763365937815e-03L;
            _points[19](0)=9.7479197566036565307915209128675e-01L;      _weights[19]=5.6849852669976417861179123569953e-04L;
            _points[20](0)=9.9243549072562147749379027938900e-01L;      _weights[20]=9.5861868529721828979599842865244e-05L;
        
            return;
          }

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

            _points[ 0](0)=2.7314460088842296840089704503200e-03L;      _weights[ 0]=6.9842561136978136538216549700282e-03L;
            _points[ 1](0)=1.4335933483699706185308039285053e-02L;      _weights[ 1]=1.5944053454778496864565929126309e-02L;
            _points[ 2](0)=3.4986328351216449387218814071085e-02L;      _weights[ 2]=2.4184236671890499758870393233781e-02L;
            _points[ 3](0)=6.4302641132158882531275071395686e-02L;      _weights[ 3]=3.1327596999375227892408958559682e-02L;
            _points[ 4](0)=1.0173934345216392401258226593794e-01L;      _weights[ 4]=3.7077054093202864483217335909271e-02L;
            _points[ 5](0)=1.4659920015766541692656584266952e-01L;      _weights[ 5]=4.1222404906411452577079119693783e-02L;
            _points[ 6](0)=1.9804660411818261484660504028001e-01L;      _weights[ 6]=4.3651203786303462995293138094828e-02L;
            _points[ 7](0)=2.5512320697168696957682873507625e-01L;      _weights[ 7]=4.4353370900419806188626977124445e-02L;
            _points[ 8](0)=3.1676578871044727183421117602379e-01L;      _weights[ 8]=4.3418750145417827908334525766667e-02L;
            _points[ 9](0)=3.8182606925675020305095127628112e-01L;      _weights[ 9]=4.1027795781940901638265438618895e-02L;
            _points[10](0)=4.4909210098681733251387195042393e-01L;      _weights[10]=3.7436116466930019239662981188891e-02L;
            _points[11](0)=5.1731084595099112005136286684174e-01L;      _weights[11]=3.2954058785385534039887856528676e-02L;
            _points[12](0)=5.8521151795129912975524533467408e-01L;      _weights[12]=2.7922870823442631249079662456458e-02L;
            _points[13](0)=6.5152925489581447403580682231185e-01L;      _weights[13]=2.2689228598160995380212860776143e-02L;
            _points[14](0)=7.1502868047476240261215783933800e-01L;      _weights[14]=1.7580017560152292742735027157072e-02L;
            _points[15](0)=7.7452691606482263532020273841099e-01L;      _weights[15]=1.2879230281365339696348205046681e-02L;
            _points[16](0)=8.2891561362172651235400549854277e-01L;      _weights[16]=8.8086724401109070881737532508054e-03L;
            _points[17](0)=8.7718159746542002099358323827803e-01L;      _weights[17]=5.5138751021276410109163746634529e-03L;
            _points[18](0)=9.1842572498984926327926994425432e-01L;      _weights[18]=3.0562141131504037344643025112362e-03L;
            _points[19](0)=9.5187959322971991452332541323047e-01L;      _weights[19]=1.4117668531394242829582650189559e-03L;
            _points[20](0)=9.7691966323712886717816657113704e-01L;      _weights[20]=4.7692790565900675904839748933142e-04L;
            _points[21](0)=9.9307748504434821490300210664154e-01L;      _weights[21]=8.0298216937450816028842814607537e-05L;
        
            return;
          }
      
        default:
          {
            std::cerr << 'Quadrature rule ' << _order
                      << ' not supported!' << std::endl;
              
            libmesh_error();
          }
        } // end switch(_order + 2*p)

      libmesh_error();
    } // end if ((_alpha == 1) && (_beta == 0))


  
  else if ((_alpha == 2) && (_beta == 0))
    {
      
      switch(_order + 2*p)
        {
        case CONSTANT:
        case FIRST:
          {
            _points.resize (1);
            _weights.resize(1);
        
            _points[0](0)  = 0.25;
        
            _weights[0]    = 1./3.;
        
            return;
          }
        case SECOND:
        case THIRD:
          {
            _points.resize (2);
            _weights.resize(2);
            
            _points[ 0](0)=1.2251482265544137786674043037115e-01L;      _weights[ 0]=2.3254745125350790274997694884235e-01L;
            _points[ 1](0)=5.4415184401122528879992623629551e-01L;      _weights[ 1]=1.0078588207982543058335638449099e-01L;

            return;
          }
        case FOURTH:
        case FIFTH:
          {
            _points.resize (3);
            _weights.resize(3);
              
            _points[ 0](0)=7.2994024073149732155837979012003e-02L;      _weights[ 0]=1.5713636106488661331834482221327e-01L;
            _points[ 1](0)=3.4700376603835188472176354340395e-01L;      _weights[ 1]=1.4624626925986602200351202036424e-01L;
            _points[ 2](0)=7.0500220988849838312239847758405e-01L;      _weights[ 2]=2.9950703008580698011476490755827e-02L;

            return;
          }
        case SIXTH:
        case SEVENTH:
          {
            _points.resize (4);
            _weights.resize(4);
              
            _points[ 0](0)=4.8500549446997329297067257098986e-02L;      _weights[ 0]=1.1088841561127798368323131746895e-01L;
            _points[ 1](0)=2.3860073755186230505898141272470e-01L;      _weights[ 1]=1.4345878979921420904832801427594e-01L;
            _points[ 2](0)=5.1704729510436750234057336938307e-01L;      _weights[ 2]=6.8633887172923075317376345041811e-02L;
            _points[ 3](0)=7.9585141789677286330337796079324e-01L;      _weights[ 3]=1.0352240749918065284397656546639e-02L;

            return;
          }
        case EIGHTH:
        case NINTH:
          {
            _points.resize (5);
            _weights.resize(5);
              
            _points[ 0](0)=3.4578939918215091524457428631527e-02L;      _weights[ 0]=8.1764784285770917904880732922352e-02L;
            _points[ 1](0)=1.7348032077169572310459241798618e-01L;      _weights[ 1]=1.2619896189991148802883293516467e-01L;
            _points[ 2](0)=3.8988638706551932824089541038499e-01L;      _weights[ 2]=8.9200161221590000186254493070384e-02L;
            _points[ 3](0)=6.3433347263088677234716388892062e-01L;      _weights[ 3]=3.2055600722961919254748930556633e-02L;
            _points[ 4](0)=8.5105421294701641811622418741001e-01L;      _weights[ 4]=4.1138252030990079586162416192983e-03L;

            return;
          }
        case TENTH:
        case ELEVENTH:
          {
        
            _points.resize (6);
            _weights.resize(6);
              
            _points[ 0](0)=2.5904555093667192754643606997235e-02L;      _weights[ 0]=6.2538702726580937878526556468332e-02L;
            _points[ 1](0)=1.3156394165798513398691085074097e-01L;      _weights[ 1]=1.0737649973678063260575568234795e-01L;
            _points[ 2](0)=3.0243691802289123274990557791855e-01L;      _weights[ 2]=9.4577186748541203568292051720052e-02L;
            _points[ 3](0)=5.0903641316475208401103990516772e-01L;      _weights[ 3]=5.1289571129616210220129325076919e-02L;
            _points[ 4](0)=7.1568112731171391876766262459361e-01L;      _weights[ 4]=1.5720297184945051327851262130020e-02L;
            _points[ 5](0)=8.8680561617756186630126600601049e-01L;      _weights[ 5]=1.8310758068692977327784555900562e-03L;

            return;
          }
        case TWELFTH:
        case THIRTEENTH:
          {
            _points.resize (7);
            _weights.resize(7);
              
            _points[ 0](0)=2.0132773773400507230501687117472e-02L;      _weights[ 0]=4.9276501776438120823429129084905e-02L;
            _points[ 1](0)=1.0308902914804901475222678600595e-01L;      _weights[ 1]=9.0698824612686144536967479972374e-02L;
            _points[ 2](0)=2.4055412604805753665369914150100e-01L;      _weights[ 2]=9.1733803279795254111416595896867e-02L;
            _points[ 3](0)=4.1400214459705974641828724885057e-01L;      _weights[ 3]=6.3146378708891297709533940481199e-02L;
            _points[ 4](0)=6.0002151327899293019396877288994e-01L;      _weights[ 4]=2.9422211289528614840745351985011e-02L;
            _points[ 5](0)=7.7351724659143750111199899642603e-01L;      _weights[ 5]=8.1629256323046945072318090687213e-03L;
            _points[ 6](0)=9.1118316656300276363931736720905e-01L;      _weights[ 6]=8.9268803368920680400902684425561e-04L;

            return;
          }
        case FOURTEENTH:
        case FIFTEENTH:
          {
            _points.resize (8);
            _weights.resize(8);
              
            _points[ 0](0)=1.6097759551921033532013550096618e-02L;      _weights[ 0]=3.9778957806690559830106455926398e-02L;
            _points[ 1](0)=8.2900617485651102700366353380388e-02L;      _weights[ 1]=7.6818093267222624804506735068290e-02L;
            _points[ 2](0)=1.9547516848873991732426660953061e-01L;      _weights[ 2]=8.5284769171938765209441226265186e-02L;
            _points[ 3](0)=3.4165199147720222027296226216240e-01L;      _weights[ 3]=6.8447183421653272247027200610852e-02L;
            _points[ 4](0)=5.0559707818448917194006186500608e-01L;      _weights[ 4]=4.0814426388544023186461596152148e-02L;
            _points[ 5](0)=6.6955227182436145183011451055437e-01L;      _weights[ 5]=1.7246863780234982804243655774862e-02L;
            _points[ 6](0)=8.1577170358328376075475178697587e-01L;      _weights[ 6]=4.4745217130144079957565210032836e-03L;
            _points[ 7](0)=9.2850896495990689720101861784923e-01L;      _weights[ 7]=4.6851778403469725578994253231334e-04L;

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

            _points[ 0](0)=1.3165885597114490545190537817972e-02L;      _weights[ 0]=3.2760145111039721461819540084274e-02L;
            _points[ 1](0)=6.8084529593767587476505856986822e-02L;      _weights[ 1]=6.5489537033396631781939107203912e-02L;
            _points[ 2](0)=1.6175951676407464206981091232919e-01L;      _weights[ 2]=7.7673569160555504078595170478444e-02L;
            _points[ 3](0)=2.8589108833922039772798956691264e-01L;      _weights[ 3]=6.9284395689804709215727785348892e-02L;
            _points[ 4](0)=4.2945364538781279250924800228659e-01L;      _weights[ 4]=4.8540627864506507959528062424865e-02L;
            _points[ 5](0)=5.7969405635116312626577241331199e-01L;      _weights[ 5]=2.6343280902549835737974696002673e-02L;
            _points[ 6](0)=7.2326857174033543181796015820021e-01L;      _weights[ 6]=1.0406116579352237052426337235938e-02L;
            _points[ 7](0)=8.4743684201323732017318042501962e-01L;      _weights[ 7]=2.5743986456087231023317159056037e-03L;
            _points[ 8](0)=9.4124586421327421141434212713498e-01L;      _weights[ 8]=2.6126234651946294299091864873302e-04L;

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

            _points[ 0](0)=1.0968452456174134250281032990432e-02L;      _weights[ 0]=2.7434088710097496960451648584485e-02L;
            _points[ 1](0)=5.6898150533657920711434859379121e-02L;      _weights[ 1]=5.6272936402808126282415832152709e-02L;
            _points[ 2](0)=1.3595023405022895426576342938519e-01L;      _weights[ 2]=7.0069507708666334086372455308183e-02L;
            _points[ 3](0)=2.4228119613252356111139455536509e-01L;      _weights[ 3]=6.7452219381437824970525794313691e-02L;
            _points[ 4](0)=3.6800785044933771760476956625017e-01L;      _weights[ 4]=5.2883788766964158209884838942421e-02L;
            _points[ 5](0)=5.0380712641487390700553064205723e-01L;      _weights[ 5]=3.3854565016814116044101071309373e-02L;
            _points[ 6](0)=6.3960948865470970932853650616696e-01L;      _weights[ 6]=1.7197575046553008079137502323978e-02L;
            _points[ 7](0)=7.6534767954810789620953312724460e-01L;      _weights[ 7]=6.4698890685585292297306065609276e-03L;
            _points[ 8](0)=8.7171007457440848761186134200542e-01L;      _weights[ 8]=1.5455231947365786285853268147186e-03L;
            _points[ 9](0)=9.5087429264052316644634948461033e-01L;      _weights[ 9]=1.5324003669716084212825702284675e-04L;

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

            _points[ 0](0)=9.2789738313488342029466103013448e-03L;      _weights[ 0]=2.3300850051388377415061404350855e-02L;
            _points[ 1](0)=4.8249692094286258286483723731132e-02L;      _weights[ 1]=4.8745861030664491864450329028080e-02L;
            _points[ 2](0)=1.1578862662939522596030591825565e-01L;      _weights[ 2]=6.2979543000367394338333998811129e-02L;
            _points[ 3](0)=2.0766834159705988244389542530053e-01L;      _weights[ 3]=6.4183559349755944992539371306173e-02L;
            _points[ 4](0)=3.1811795190623396637744646657914e-01L;      _weights[ 4]=5.4632222321044926070678715192708e-02L;
            _points[ 5](0)=4.4019839985886246708268132217632e-01L;      _weights[ 5]=3.9290217798435612246535835921329e-02L;
            _points[ 6](0)=5.6623983915456831356751247193488e-01L;      _weights[ 6]=2.3589663538806928649316661943808e-02L;
            _points[ 7](0)=6.8832423986295668569553397580809e-01L;      _weights[ 7]=1.1414590918097618249921262806781e-02L;
            _points[ 8](0)=7.9878435859091464197460872800735e-01L;      _weights[ 8]=4.1400042632190223547676874553245e-03L;
            _points[ 9](0)=8.9069109935439218915081289990608e-01L;      _weights[ 9]=9.6302057554323908320037373956771e-04L;
            _points[10](0)=9.5832514378664820192443912466615e-01L;      _weights[10]=9.3800486009778068527692777578977e-05L;

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

            _points[ 0](0)=7.9520457026384368762190933400404e-03L;      _weights[ 0]=2.0031112584748752943807724216722e-02L;
            _points[ 1](0)=4.1427810454294590790770165194795e-02L;      _weights[ 1]=4.2556615367405637772968490900760e-02L;
            _points[ 2](0)=9.9757625542614157066081703480300e-02L;      _weights[ 2]=5.6584184749474069646478036154467e-02L;
            _points[ 3](0)=1.7981078905242324954164334430721e-01L;      _weights[ 3]=6.0250607487604518170935343500906e-02L;
            _points[ 4](0)=2.7727345779931511981753891831052e-01L;      _weights[ 4]=5.4573941164231582825558709780290e-02L;
            _points[ 5](0)=3.8689200999768979166563470380544e-01L;      _weights[ 5]=4.2764763570188902317265936785879e-02L;
            _points[ 6](0)=5.0275736044903220327930927843912e-01L;      _weights[ 6]=2.8908051838727360494403492180206e-02L;
            _points[ 7](0)=6.1862386345845604629354886189114e-01L;      _weights[ 7]=1.6547343644609412101387213540038e-02L;
            _points[ 8](0)=7.2824645295307268642888033006114e-01L;      _weights[ 8]=7.7163670238864266187877366246530e-03L;
            _points[ 9](0)=8.2571851421478690176408336295370e-01L;      _weights[ 9]=2.7208421441038393545415361663513e-03L;
            _points[10](0)=9.0579507354454372680179647039974e-01L;      _weights[10]=6.1995339854451942336673117135933e-04L;
            _points[11](0)=9.6420653529267155121295530627839e-01L;      _weights[11]=5.9550359808311663832382311702501e-05L;

            return;
          }

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

            _points[ 0](0)=6.8908313099587313966815341534070e-03L;      _weights[ 0]=1.7401228610061845488081141733526e-02L;
            _points[ 1](0)=3.5953362700170095501132811969521e-02L;      _weights[ 1]=3.7426708168844039953666298186474e-02L;
            _points[ 2](0)=8.6811780157585433284280307690601e-02L;      _weights[ 2]=5.0909830712695019092906847187640e-02L;
            _points[ 3](0)=1.5709997419650927473052206555148e-01L;      _weights[ 3]=5.6111537130827396185039872203667e-02L;
            _points[ 4](0)=2.4353289958712844441903410356775e-01L;      _weights[ 4]=5.3340021605871745725401666422880e-02L;
            _points[ 5](0)=3.4206951264607532347450799656627e-01L;      _weights[ 5]=4.4624600755614954430566337477243e-02L;
            _points[ 6](0)=4.4810263890570985362873430879398e-01L;      _weights[ 6]=3.2940451678432790083648445397381e-02L;
            _points[ 7](0)=5.5667462262945501069694664236208e-01L;      _weights[ 7]=2.1254996714756613031113108888658e-02L;
            _points[ 8](0)=6.6270931356038854232146315212326e-01L;      _weights[ 8]=1.1728259593101880662970381149369e-02L;
            _points[ 9](0)=7.6124976630827697227665952639343e-01L;      _weights[ 9]=5.3135693388326384480559144318474e-03L;
            _points[10](0)=8.4769104394723239091031404895142e-01L;      _weights[10]=1.8323911392393785873485644191745e-03L;
            _points[11](0)=9.1799964553720667953362597028835e-01L;      _weights[11]=4.1072089179088541678428389490865e-04L;
            _points[12](0)=9.6892889422858896211181181730274e-01L;      _weights[12]=3.9016993264146227750471940564101e-05L;
        
            return;
          }

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

            _points[ 0](0)=6.0288088710666481700887477121600e-03L;      _weights[ 0]=1.5255206119448295373511341972378e-02L;
            _points[ 1](0)=3.1494259818657590707306712766317e-02L;      _weights[ 1]=3.3139595469960559875930225836517e-02L;
            _points[ 2](0)=7.6213622474853867586406786340023e-02L;      _weights[ 2]=4.5914772114671178911403799944693e-02L;
            _points[ 3](0)=1.3836652595947406914513833295825e-01L;      _weights[ 3]=5.2025865410701701832827358849471e-02L;
            _points[ 4](0)=2.1540975706889557490069553208515e-01L;      _weights[ 4]=5.1389924039471503273808065266413e-02L;
            _points[ 5](0)=3.0418952814165630963236635490440e-01L;      _weights[ 5]=4.5253432254460881465122373566022e-02L;
            _points[ 6](0)=4.0107137869715435758118603205199e-01L;      _weights[ 6]=3.5739010292514612984162525810346e-02L;
            _points[ 7](0)=5.0208913974997841006932539804960e-01L;      _weights[ 7]=2.5216183536839055034306220202219e-02L;
            _points[ 8](0)=6.0310739672759678368189556654036e-01L;      _weights[ 8]=1.5694332285072957184930434798487e-02L;
            _points[ 9](0)=6.9999091716990649741073666393849e-01L;      _weights[ 9]=8.4129767371364622096077152778570e-03L;
            _points[10](0)=7.8877423843456071534030488559891e-01L;      _weights[10]=3.7248756752828588215538124784652e-03L;
            _points[11](0)=8.6582490073159695367114083518102e-01L;      _weights[11]=1.2617838951574880413283334197260e-03L;
            _points[12](0)=9.2799573874675232498377812203940e-01L;      _weights[12]=2.7909934094687847008945560658272e-04L;
            _points[13](0)=9.7277712074118323045296336316727e-01L;      _weights[13]=2.6276161668899854751670304157309e-05L;
        
            return;
          }

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

            _points[ 0](0)=5.3190520028437405909978402739774e-03L;      _weights[ 0]=1.3481662725134304090265733542410e-02L;
            _points[ 1](0)=2.7814561918260051571980709238074e-02L;      _weights[ 1]=2.9527650756798205089388266870014e-02L;
            _points[ 2](0)=6.7431865838998613384568577571818e-02L;      _weights[ 2]=4.1531307651604265373799456795289e-02L;
            _points[ 3](0)=1.2274828621549783933958732401303e-01L;      _weights[ 3]=4.8132057668529815888404876719886e-02L;
            _points[ 4](0)=1.9176570627765362550282684505042e-01L;      _weights[ 4]=4.9041267894409180565196427508457e-02L;
            _points[ 5](0)=2.7198996592948620305633800793026e-01L;      _weights[ 5]=4.4991555820615933365730152800755e-02L;
            _points[ 6](0)=3.6052169358705764815778444077840e-01L;      _weights[ 6]=3.7473875792101303095319296790068e-02L;
            _points[ 7](0)=4.5416123575447709916009624996188e-01L;      _weights[ 7]=2.8326553174241247644068974123766e-02L;
            _points[ 8](0)=5.4952435559355131365468962196031e-01L;      _weights[ 8]=1.9293416585274520485988288429744e-02L;
            _points[ 9](0)=6.4316460176878493853949400884187e-01L;      _weights[ 9]=1.1668582484776638563534331197891e-02L;
            _points[10](0)=7.3169797305252320629933948467521e-01L;      _weights[10]=6.1110501102060490412153142922240e-03L;
            _points[11](0)=8.1192547727500966668969312120195e-01L;      _weights[11]=2.6556629857743191811282114211333e-03L;
            _points[12](0)=8.8094952871531360238808055493652e-01L;      _weights[12]=8.8657363523409667398227745346013e-04L;
            _points[13](0)=9.3628182173551874210251937228715e-01L;      _weights[13]=1.9398726306394554934013378631178e-04L;
            _points[14](0)=9.7595387433502370956200384127912e-01L;      _weights[14]=1.8128785569508725971591601924058e-05L;
        
            return;
          }


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

            _points[ 0](0)=4.7276871229345922061506104450645e-03L;      _weights[ 0]=1.1999405624691969586506695404143e-02L;
            _points[ 1](0)=2.4742967619434984512603456269536e-02L;      _weights[ 1]=2.6460842517339527040437264564557e-02L;
            _points[ 2](0)=6.0076437716637992275242255328112e-02L;      _weights[ 2]=3.7685824681918572833315081444311e-02L;
            _points[ 3](0)=1.0960060925877060286789758461950e-01L;      _weights[ 3]=4.4496573472543214976151049587710e-02L;
            _points[ 4](0)=1.7172475948300210790307417791270e-01L;      _weights[ 4]=4.6506239397362658797012521100333e-02L;
            _points[ 5](0)=2.4445243174451137730207656160275e-01L;      _weights[ 5]=4.4112657675899371113911374089320e-02L;
            _points[ 6](0)=3.2544621002412961482683685190181e-01L;      _weights[ 6]=3.8348046951185955673582690910292e-02L;
            _points[ 7](0)=4.1210296411685959691728421362251e-01L;      _weights[ 7]=3.0612037917837609541948834407964e-02L;
            _points[ 8](0)=5.0163755615318759370013043235084e-01L;      _weights[ 8]=2.2357185649529930223334734263644e-02L;
            _points[ 9](0)=5.9117238531650308897076051877634e-01L;      _weights[ 9]=1.4803776657751738340239250997704e-02L;
            _points[10](0)=6.7782991741456081130251277264148e-01L;      _weights[10]=8.7475454956120699745801506391282e-03L;
            _points[11](0)=7.5882525794914141335427940535114e-01L;      _weights[11]=4.4948488514798588832066397608164e-03L;
            _points[12](0)=8.3155588302646195188920635482406e-01L;      _weights[12]=1.9235319260667742273824398535627e-03L;
            _points[13](0)=8.9368597454880401881486969876816e-01L;      _weights[13]=6.3445999956883686801084896849641e-04L;
            _points[14](0)=9.4322428571224559352545066239296e-01L;      _weights[14]=1.3757810397555175246959527906570e-04L;
            _points[15](0)=9.7860643749869701257280091378128e-01L;      _weights[15]=1.2778410569693501244162062287056e-05L;
        
            return;
          }


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

            _points[ 0](0)=4.2297654864907678749919877813007e-03L;      _weights[ 0]=1.0748151030768621662834062204936e-02L;
            _points[ 1](0)=2.2152705311830232294209002101573e-02L;      _weights[ 1]=2.3837762018703244620506074665265e-02L;
            _points[ 2](0)=5.3856014827184829566760322013645e-02L;      _weights[ 2]=3.4307889795671880028436869439002e-02L;
            _points[ 3](0)=9.8434936830541362494246924237098e-02L;      _weights[ 3]=4.1143975847068207121110777965721e-02L;
            _points[ 4](0)=1.5460792826588562987838903880788e-01L;      _weights[ 4]=4.3922618772592577808611328095136e-02L;
            _points[ 5](0)=2.2075922519215138391363787768336e-01L;      _weights[ 5]=4.2825403927934553301439133345126e-02L;
            _points[ 6](0)=2.9498586629802348865100598497056e-01L;      _weights[ 6]=3.8555241947102353628223582107170e-02L;
            _points[ 7](0)=3.7515254164081788200834771392226e-01L;      _weights[ 7]=3.2163570112378639217164962127759e-02L;
            _points[ 8](0)=4.5895305335301908085933451474375e-01L;      _weights[ 8]=2.4829256111976082802381065145755e-02L;
            _points[ 9](0)=5.4397667809047570974515217435547e-01L;      _weights[ 9]=1.7638789331050110518481458865839e-02L;
            _points[10](0)=6.2777753854681427256560538094776e-01L;      _weights[10]=1.1413642238636687747573403275566e-02L;
            _points[11](0)=7.0794500138508556794362242607309e-01L;      _weights[11]=6.6164197603617147286557116199452e-03L;
            _points[12](0)=7.8217310308122112810113854015572e-01L;      _weights[12]=3.3465172918198153715474254116460e-03L;
            _points[13](0)=8.4832708570995060757906353137179e-01L;      _weights[13]=1.4138837589561322316624033902623e-03L;
            _points[14](0)=9.0450542331432870037906100932836e-01L;      _weights[14]=4.6167405877711308077043506706165e-04L;
            _points[15](0)=9.4909701659654457024654762835657e-01L;      _weights[15]=9.9356525335473959962406835119113e-05L;
            _points[16](0)=9.8084389384741256367666372092760e-01L;      _weights[16]=9.1808042001255039722337720228143e-06L;
        
            return;
          }

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

            _points[ 0](0)=3.8065822475018763836485343548908e-03L;      _weights[ 0]=9.6823988037660231774964807691529e-03L;
            _points[ 1](0)=1.9948351047343018666301273550578e-02L;      _weights[ 1]=2.1578772679193827027157750409882e-02L;
            _points[ 2](0)=4.8549645304224630965525818224597e-02L;      _weights[ 2]=3.1333907671729513327950397913143e-02L;
            _points[ 3](0)=8.8876259116497388048181392194957e-02L;      _weights[ 3]=3.8075134253447687665457823100366e-02L;
            _points[ 4](0)=1.3988457083516926493003835526765e-01L;      _weights[ 4]=4.1377182287519565332651504100178e-02L;
            _points[ 5](0)=2.0025369592363033820671255853211e-01L;      _weights[ 5]=4.1283665809957749414286828772884e-02L;
            _points[ 6](0)=2.6842018278660208442014712803618e-01L;      _weights[ 6]=3.8262794672349299757849656256339e-02L;
            _points[ 7](0)=3.4261859780200830045140484446480e-01L;      _weights[ 7]=3.3095976202072497795672769135623e-02L;
            _points[ 8](0)=4.2092727587031795580391095608392e-01L;      _weights[ 8]=2.6723424368960119486097972811646e-02L;
            _points[ 9](0)=5.0131810275027358836467598537906e-01L;      _weights[ 9]=2.0078641696369720179443819032712e-02L;
            _points[10](0)=5.8170905267091792822883758529331e-01L;      _weights[10]=1.3943897653647906425703531920973e-02L;
            _points[11](0)=6.6001812722531554655212340270381e-01L;      _weights[11]=8.8522782250949774435502470347624e-03L;
            _points[12](0)=7.3421730813501325031921736140253e-01L;      _weights[12]=5.0502487883546813166841235600508e-03L;
            _points[13](0)=8.0238514983641747020667379058517e-01L;      _weights[13]=2.5207216384362558022745702364513e-03L;
            _points[14](0)=8.6275672070005501336081662021610e-01L;      _weights[14]=1.0535502839571923712409403476880e-03L;
            _points[15](0)=9.1376986411079293616612318979159e-01L;      _weights[15]=3.4109120368765498289598525047321e-04L;
            _points[16](0)=9.5410789551731665881890309384613e-01L;      _weights[16]=7.2937008664118705328162954331465e-05L;
            _points[17](0)=9.8274840759428696063307389954630e-01L;      _weights[17]=6.7100861245431215907697266774769e-06L;
        
            return;
          }

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

            _points[ 0](0)=3.4438904038624902806940509331722e-03L;      _weights[ 0]=8.7672970568792323661393261305840e-03L;
            _points[ 1](0)=1.8056978337900562863030093954343e-02L;      _weights[ 1]=1.9620856340232434512901283777202e-02L;
            _points[ 2](0)=4.3987395090842734455198832773659e-02L;      _weights[ 2]=2.8708149778704086122791006941433e-02L;
            _points[ 3](0)=8.0633276366661415469721776663016e-02L;      _weights[ 3]=3.5278117199476000434599584597235e-02L;
            _points[ 4](0)=1.2713640986156026953002535083969e-01L;      _weights[ 4]=3.8922386222261737550985848811514e-02L;
            _points[ 5](0)=1.8240698366909185313069695387128e-01L;      _weights[ 5]=3.9598248214880677015066061570123e-02L;
            _points[ 6](0)=2.4514956909516857055249217701821e-01L;      _weights[ 6]=3.7607500520347543950912173611332e-02L;
            _points[ 7](0)=3.1389356741821822415240859865307e-01L;      _weights[ 7]=3.3525068070610283960905700567460e-02L;
            _points[ 8](0)=3.8702770276933220341545290751683e-01L;      _weights[ 8]=2.8091607936102907649141378579235e-02L;
            _points[ 9](0)=4.6283779855202027820220487054694e-01L;      _weights[ 9]=2.2090563149823990465333672755377e-02L;
            _points[10](0)=5.3954696279208808766943066332998e-01L;      _weights[10]=1.6231815321996325630177612472423e-02L;
            _points[11](0)=6.1535724480454716546694016358337e-01L;      _weights[11]=1.1061440629037007897211784796273e-02L;
            _points[12](0)=6.8849179091409498918986551203802e-01L;      _weights[12]=6.9108110779321981973514541466546e-03L;
            _points[13](0)=7.5723651917329793549736932794667e-01L;      _weights[13]=3.8897848125530902102984958782958e-03L;
            _points[14](0)=8.1998035706323733537954006841029e-01L;      _weights[14]=1.9197884726923132048372710905667e-03L;
            _points[15](0)=8.7525316298382668006594890887609e-01L;      _weights[15]=7.9504432544855937325482850317179e-04L;
            _points[16](0)=9.2176068172914004889937421632274e-01L;      _weights[16]=2.5553085889097125647555166013802e-04L;
            _points[17](0)=9.5841690242340714510347790926694e-01L;      _weights[17]=5.4342643132004416773622274012570e-05L;
            _points[18](0)=9.8438280655170201067612761745569e-01L;      _weights[18]=4.9807023319691181766751703037610e-06L;
        
            return;
          }

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

            _points[ 0](0)=3.1306837407435895621501417495463e-03L;      _weights[ 0]=7.9757927362766516852273101574255e-03L;
            _points[ 1](0)=1.6422088133987832902541614256258e-02L;      _weights[ 1]=1.7913752325738559101773958866323e-02L;
            _points[ 2](0)=4.0036900461906780996320149828793e-02L;      _weights[ 2]=2.6382564429125584794513408474046e-02L;
            _points[ 3](0)=7.3477191785285283057566545285874e-02L;      _weights[ 3]=3.2734644317573148047479656498988e-02L;
            _points[ 4](0)=1.1603090765548680494669743156748e-01L;      _weights[ 4]=3.6587916553227064986609295576925e-02L;
            _points[ 5](0)=1.6679125348100943001298070145849e-01L;      _weights[ 5]=3.7847390376922340715354694449373e-02L;
            _points[ 6](0)=2.2467641938430503840938196483210e-01L;      _weights[ 6]=3.6697420472018132713254249570653e-02L;
            _points[ 7](0)=2.8845271218127238477194070665240e-01L;      _weights[ 7]=3.3556431453475493479002714822739e-02L;
            _points[ 8](0)=3.5676087010245310564705506663326e-01L;      _weights[ 8]=2.9002404745589285169916357261403e-02L;
            _points[ 9](0)=4.2814504093325668461542503477245e-01L;      _weights[ 9]=2.3682290414246053980866450266495e-02L;
            _points[10](0)=5.0108381548284855137062465413693e-01L;      _weights[10]=1.8220503418268691551843315309759e-02L;
            _points[11](0)=5.7402265818282687172751219665371e-01L;      _weights[11]=1.3140919256661651742108133720781e-02L;
            _points[12](0)=6.4540704577736756661732083476397e-01L;      _weights[12]=8.8135560782433553289252731679767e-03L;
            _points[13](0)=7.1371561101528768074208343535393e-01L;      _weights[13]=5.4320908061230274500120111426487e-03L;
            _points[14](0)=7.7749259203548675355112594583658e-01L;      _weights[14]=3.0224891709073793749184859780611e-03L;
            _points[15](0)=8.3537891463156172517151839471341e-01L;      _weights[15]=1.4774444419714858062838576456553e-03L;
            _points[16](0)=8.8614130291454714368728293036495e-01L;      _weights[16]=6.0704570426725825415272373108771e-04L;
            _points[17](0)=9.2869901491875054534509783716727e-01L;      _weights[17]=1.9388830961751181076983851525948e-04L;
            _points[18](0)=9.6214871215049818970916080642292e-01L;      _weights[18]=4.1039102087320205549074040898061e-05L;
            _points[19](0)=9.8579578884064184668002313135922e-01L;      _weights[19]=3.7492209933371347725241368372638e-06L;
        
            return;
          }


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

            _points[ 0](0)=2.8583506000918943222556277168267e-03L;      _weights[ 0]=7.2866317313744308995629793584932e-03L;
            _points[ 1](0)=1.4999364972075522340357135916023e-02L;      _weights[ 1]=1.6417061144242818824757454238052e-02L;
            _points[ 2](0)=3.6593863281140122626545055282186e-02L;      _weights[ 2]=2.4316074956305588348553255406534e-02L;
            _points[ 3](0)=6.7226441667938638526563947674675e-02L;      _weights[ 3]=3.0423854654878694196479542521305e-02L;
            _points[ 4](0)=1.0630147973769311755044868847393e-01L;      _weights[ 4]=3.4388553550627421941340376509459e-02L;
            _points[ 5](0)=1.5305857495571921224970195300963e-01L;      _weights[ 5]=3.6085277384893044986268336555960e-02L;
            _points[ 6](0)=2.0658770608253356867698033417515e-01L;      _weights[ 6]=3.5615944774693119613624648820995e-02L;
            _points[ 7](0)=2.6584701401081590981089215154372e-01L;      _weights[ 7]=3.3281046762833346236473134492600e-02L;
            _points[ 8](0)=3.2968309899010272373734914205452e-01L;      _weights[ 8]=2.9528072702082493907799384765866e-02L;
            _points[ 9](0)=3.9685347698561900950394342909483e-01L;      _weights[ 9]=2.4885083875255978309567929915161e-02L;
            _points[10](0)=4.6605076663517464847296649003812e-01L;      _weights[10]=1.9889780066352815019424534213776e-02L;
            _points[11](0)=5.3592813869303216093268951839176e-01L;      _weights[11]=1.5024528041917190276613254752701e-02L;
            _points[12](0)=6.0512553397610192844810985230774e-01L;      _weights[12]=1.0666270365508680718786852036243e-02L;
            _points[13](0)=6.7229614098692961628997049948121e-01L;      _weights[13]=7.0573209743621604363614669672455e-03L;
            _points[14](0)=7.3613262059728734846410297670221e-01L;      _weights[14]=4.2993100642134152210363702100934e-03L;
            _points[15](0)=7.9539257374613146232498650332774e-01L;      _weights[15]=2.3686215346115318974092271035074e-03L;
            _points[16](0)=8.4892277353768883984401746895126e-01L;      _weights[16]=1.1482414207164748272703814817286e-03L;
            _points[17](0)=8.9568174292546676052820257429765e-01L;      _weights[17]=4.6857361253397420043294612589344e-04L;
            _points[18](0)=9.3476043640122994798279429359660e-01L;      _weights[18]=1.4884999898655056859287865070751e-04L;
            _points[19](0)=9.6540160736574245809294907904429e-01L;      _weights[19]=3.1377233396792732027953172274463e-05L;
            _points[20](0)=9.8702556657875783654690055164718e-01L;      _weights[20]=2.8584835468101709504260347382715e-06L;
        
            return;
          }

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

            _points[ 0](0)=2.6200747203711594248593674552649e-03L;      _weights[ 0]=6.6829315239216368796332393406135e-03L;
            _points[ 1](0)=1.3753657987385804025756750709059e-02L;      _weights[ 1]=1.5098062421623821319493004238262e-02L;
            _points[ 2](0)=3.3575226848026692714308191640158e-02L;      _weights[ 2]=2.2473713734526648003280648297671e-02L;
            _points[ 3](0)=6.1735561623069601690826574395308e-02L;      _weights[ 3]=2.8324458025288763364233486167273e-02L;
            _points[ 4](0)=9.7732696675368642458479884996723e-02L;      _weights[ 4]=3.2329473952869436965326587507885e-02L;
            _points[ 5](0)=1.4092439775695158519450619775816e-01L;      _weights[ 5]=3.4348599664417779736425965942178e-02L;
            _points[ 6](0)=1.9053995518421662849913969152881e-01L;      _weights[ 6]=3.4426309828130701949676126316990e-02L;
            _points[ 7](0)=2.4569399962450332222446519900435e-01L;      _weights[ 7]=3.2774586900497126738748991342107e-02L;
            _points[ 8](0)=3.0540231844259902315260853518244e-01L;      _weights[ 8]=2.9737336628427308246400548097974e-02L;
            _points[ 9](0)=3.6859942495594128250321664201293e-01L;      _weights[ 9]=2.5741821234796918381507016798653e-02L;
            _points[10](0)=4.3415757484015513750820121247106e-01L;      _weights[10]=2.1244167813524304464862872202199e-02L;
            _points[11](0)=5.0090689264793505011775015892772e-01L;      _weights[11]=1.6676482379699419616981906191727e-02L;
            _points[12](0)=5.6765625027260978702177266771788e-01L;      _weights[12]=1.2402453510959574984251948178874e-02L;
            _points[13](0)=6.3321452557266284279166256182373e-01L;      _weights[13]=8.6866984738749141556196547655377e-03L;
            _points[14](0)=6.9641186298595172661126707689713e-01L;      _weights[14]=5.6807683849250404394970034550940e-03L;
            _points[15](0)=7.5612055917893487122928793527786e-01L;      _weights[15]=3.4260685209698087638377353482425e-03L;
            _points[16](0)=8.1127520683922050787811864631196e-01L;      _weights[16]=1.8713879532585689543042377871244e-03L;
            _points[17](0)=8.6089175276286621730656128908876e-01L;      _weights[17]=9.0066625279251987400261357834378e-04L;
            _points[18](0)=9.0408517849775272066170136431884e-01L;      _weights[18]=3.6536328467284676654467859219800e-04L;
            _points[19](0)=9.4008566921081846961603077466108e-01L;      _weights[19]=1.1551470917602499323205530447797e-04L;
            _points[20](0)=9.6825388381656365288164210087944e-01L;      _weights[20]=2.4263177919766775694554800111547e-05L;
            _points[21](0)=9.8810245999087788318348935085438e-01L;      _weights[21]=2.2049570604019597784590797971169e-06L;
        
            return;
          }

      
        default:
          {
            std::cerr << 'Quadrature rule ' << _order
                      << ' not supported!' << std::endl;
              
            libmesh_error();
          }
        } // end switch(_order + 2*p)

      libmesh_error();
    } // end else if ((_alpha == 2) && (_beta == 0))

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

  
  return;
}
 

virtual void QBase::init_2D (const ElemType, unsigned int = 0) [inline, protected, virtual, inherited]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 redefined, gives an error (when DEBUG defined) when called.

Reimplemented in QClough, QConical, QGauss, QGrid, QMonomial, QSimpson, and QTrap.

Definition at line 234 of file quadrature.h.

Referenced by QBase::init().

  {}
 

static unsigned int ReferenceCounter::n_objects () [inline, static, inherited]Prints the number of outstanding (created, but not yet destroyed) objects.

Definition at line 76 of file reference_counter.h.

References ReferenceCounter::_n_objects.

Referenced by System::read_serialized_blocked_dof_objects(), and System::write_serialized_blocked_dof_objects().

  { return _n_objects; }
 

unsigned int QBase::n_points () const [inline, inherited]Returns:

the number of points associated with the quadrature rule.

Definition at line 115 of file quadrature.h.

References QBase::_points.

Referenced by FEBase::coarsened_dof_values(), QConical::conical_product_pyramid(), QConical::conical_product_tet(), QConical::conical_product_tri(), FEMSystem::eulerian_residual(), InfFE< Dim, T_radial, T_map >::init_face_shape_functions(), FEMSystem::mass_residual(), and QBase::print_info().

    { libmesh_assert (!_points.empty()); return _points.size(); }
 

void QBase::print_info (std::ostream &os = std::cout) const [inline, inherited]Prints information relevant to the quadrature rule.

Definition at line 350 of file quadrature.h.

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

Referenced by operator<<().

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

  os << 'N_Q_Points=' << this->n_points() << std::endl << std::endl;
  for (unsigned int qp=0; qp<this->n_points(); qp++)
    {
      os << ' Point ' << qp << ':
         << '  '
         << _points[qp]
         << ' Weight:'
         << '  w=' << _weights[qp] << ' << std::endl;
    }
}
 

void ReferenceCounter::print_info () [static, inherited]Prints the reference information to std::cout.

Definition at line 83 of file reference_counter.C.

References ReferenceCounter::get_info().

{
#if defined(LIBMESH_ENABLE_REFERENCE_COUNTING) && defined(DEBUG)
  
  std::cout << ReferenceCounter::get_info();
  
#endif
}
 

Point QBase::qp (const unsigned inti) const [inline, inherited]Returns:

the $ i^{th} $ quadrature point on the reference object.

Definition at line 148 of file quadrature.h.

References QBase::_points.

Referenced by QConical::conical_product_pyramid(), QConical::conical_product_tet(), QConical::conical_product_tri(), and QBase::print_info().

    { libmesh_assert (i < _points.size()); return _points[i]; }
 

void QBase::scale (std::pair< Real, Real >old_range, std::pair< Real, Real >new_range) [inherited]Maps the points of a 1D interval quadrature rule (typically [-1,1]) to any other 1D interval (typically [0,1]) and scales the weights accordingly. The quadrature rule will be mapped from the entries of old_range to the entries of new_range.

Definition at line 81 of file quadrature.C.

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

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

{
  // Make sure we are in 1D
  libmesh_assert(_dim == 1);
  
  // Make sure that we have sane ranges 
  libmesh_assert(new_range.second > new_range.first);
  libmesh_assert(old_range.second > old_range.first);

  // Make sure there are some points
  libmesh_assert(_points.size() > 0);

  // We're mapping from old_range -> new_range 
  for (unsigned int i=0; i<_points.size(); i++)
    {
      _points[i](0) =
        (_points[i](0) - old_range.first) *
        (new_range.second - new_range.first) /
        (old_range.second - old_range.first) +
        new_range.first;
    }

  // Compute the scale factor and scale the weights
  const Real scfact = (new_range.second - new_range.first) /
                      (old_range.second - old_range.first);

  for (unsigned int i=0; i<_points.size(); i++)
    _weights[i] *= scfact;
}
 

QuadratureType QJacobi::type () const [inline, virtual]Returns:

the QuadratureType, either QJACOBI_1_0 or QJACOBI_2_0.

Implements QBase.

Definition at line 109 of file quadrature_jacobi.h.

References _alpha, _beta, libMeshEnums::INVALID_Q_RULE, libMeshEnums::QJACOBI_1_0, and libMeshEnums::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();
      return INVALID_Q_RULE;
    }
}
 

Real QBase::w (const unsigned inti) const [inline, inherited]Returns:

the $ i^{th} $ quadrature weight.

Definition at line 154 of file quadrature.h.

References QBase::_weights.

Referenced by QConical::conical_product_pyramid(), QConical::conical_product_tet(), QConical::conical_product_tri(), QGauss::init_3D(), QGauss::keast_rule(), QMonomial::kim_rule(), and QMonomial::stroud_rule().

    { libmesh_assert (i < _weights.size()); return _weights[i]; }
 

Friends And Related Function Documentation

 

std::ostream& operator<< (std::ostream &os, const QBase &q) [friend, inherited]Same as above, but allows you to use the stream syntax.

Definition at line 196 of file quadrature.C.

{
  q.print_info(os);
  return os;
}
 

Member Data Documentation

 

const unsigned int QJacobi::_alpha [private]

Definition at line 78 of file quadrature_jacobi.h.

Referenced by init_1D(), and type().  

const unsigned int QJacobi::_beta [private]

Definition at line 79 of file quadrature_jacobi.h.

Referenced by init_1D(), and type().  

ReferenceCounter::Counts ReferenceCounter::_counts [static, protected, inherited]Actually holds the data.

Definition at line 110 of file reference_counter.h.

Referenced by ReferenceCounter::get_info(), ReferenceCounter::increment_constructor_count(), and ReferenceCounter::increment_destructor_count().  

Threads::spin_mutex ReferenceCounter::_mutex [static, protected, inherited]Mutual exclusion object to enable thread-safe reference counting.

Definition at line 123 of file reference_counter.h.  

Threads::atomic< unsigned int > ReferenceCounter::_n_objects [static, protected, inherited]The number of objects. Print the reference count information when the number returns to 0.

Definition at line 118 of file reference_counter.h.

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

std::cerr<< 'ERROR: Seems as if this quadrature rule' << std::endl << ' is not implemented for 2D.' << std::endl; libmesh_error(); }#endif virtual void init_3D (const ElemType, unsigned int =0)#ifndef DEBUG {}#else { std::cerr << 'ERROR: Seems as if this quadrature rule' << std::endl << ' is not implemented for 3D.' << std::endl; libmesh_error(); }#endif void tensor_product_quad (const QBase& q1D); void tensor_product_hex (const QBase& q1D); void tensor_product_prism (const QBase& q1D, const QBase& q2D); const unsigned int _dim; const Order _order; ElemType _type; unsigned int _p_level; std::vector<Point> QBase::_points [protected, inherited]

Definition at line 320 of file quadrature.h.

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

std::vector<Real> QBase::_weights [protected, inherited]The value of the quadrature weights.

Definition at line 325 of file quadrature.h.

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

bool QBase::allow_rules_with_negative_weights [inherited]Flag (default true) controlling the use of quadrature rules with negative weights. Set this to false to ONLY use (potentially) safer but more expensive rules with all positive weights.

Negative weights typically appear in Gaussian quadrature rules over three-dimensional elements. 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 203 of file quadrature.h.

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

 

Author

Generated automatically by Doxygen for libMesh from the source code.


 

Index

NAME
SYNOPSIS
Public Member Functions
Static Public Member Functions
Public Attributes
Protected Types
Protected Member Functions
Protected Attributes
Static Protected Attributes
Private Member Functions
Private Attributes
Friends
Detailed Description
Member Typedef Documentation
typedef std::map<std::string, std::pair<unsigned int, unsigned int> > ReferenceCounter::Counts [protected, inherited]Data structure to log the information. The log is identified by the class name.
Constructor & Destructor Documentation
QJacobi::QJacobi (const unsigned int_dim, const Order_order = INVALID_ORDER, const unsigned int_alpha = 1, const unsigned int_beta = 0) [inline]Constructor. Currently, only one-dimensional rules provided. Check QGauss for versions of Jacobi quadrature rule for higher dimensions.
QJacobi::~QJacobi () [inline]Destructor. Empty.
Member Function Documentation
AutoPtr< QBase > QBase::build (const std::string &name, const unsigned int_dim, const Order_order = INVALID_ORDER) [static, inherited]Builds a specific quadrature rule, identified through the name string. An AutoPtr<QBase> is returned to prevent a memory leak. This way the user need not remember to delete the object. Enables run-time decision of the quadrature rule. The input parameter name must be mappable through the Utility::string_to_enum<>() function.
AutoPtr< QBase > QBase::build (const QuadratureType_qt, const unsigned int_dim, const Order_order = INVALID_ORDER) [static, inherited]Builds a specific quadrature rule, identified through the QuadratureType. An AutoPtr<QBase> is returned to prevent a memory leak. This way the user need not remember to delete the object. Enables run-time decision of the quadrature rule.
unsigned int QBase::get_dim () const [inline, inherited]Returns:
ElemType QBase::get_elem_type () const [inline, inherited]Returns:
std::string ReferenceCounter::get_info () [static, inherited]Gets a string containing the reference information.
Order QBase::get_order () const [inline, inherited]Returns:
unsigned int QBase::get_p_level () const [inline, inherited]Returns:
const std::vector<Point>& QBase::get_points () const [inline, inherited]Returns:
std::vector<Point>& QBase::get_points () [inline, inherited]Returns:
const std::vector<Real>& QBase::get_weights () const [inline, inherited]Returns:
std::vector<Real>& QBase::get_weights () [inline, inherited]Returns:
void ReferenceCounter::increment_constructor_count (const std::string &name) [inline, protected, inherited]Increments the construction counter. Should be called in the constructor of any derived class that will be reference counted.
void ReferenceCounter::increment_destructor_count (const std::string &name) [inline, protected, inherited]Increments the destruction counter. Should be called in the destructor of any derived class that will be reference counted.
void QBase::init (const ElemType_type = INVALID_ELEM, unsigned intp_level = 0) [inherited]Initializes the data structures to contain a quadrature rule for an object of type type.
void QBase::init_0D (const ElemType_type = INVALID_ELEM, unsigned intp_level = 0) [protected, virtual, inherited]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.
void QJacobi::init_1D (const ElemType_type = INVALID_ELEM, unsigned intp_level = 0) [private, virtual]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.
virtual void QBase::init_2D (const ElemType, unsigned int = 0) [inline, protected, virtual, inherited]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 redefined, gives an error (when DEBUG defined) when called.
static unsigned int ReferenceCounter::n_objects () [inline, static, inherited]Prints the number of outstanding (created, but not yet destroyed) objects.
unsigned int QBase::n_points () const [inline, inherited]Returns:
void QBase::print_info (std::ostream &os = std::cout) const [inline, inherited]Prints information relevant to the quadrature rule.
void ReferenceCounter::print_info () [static, inherited]Prints the reference information to std::cout.
Point QBase::qp (const unsigned inti) const [inline, inherited]Returns:
void QBase::scale (std::pair< Real, Real >old_range, std::pair< Real, Real >new_range) [inherited]Maps the points of a 1D interval quadrature rule (typically [-1,1]) to any other 1D interval (typically [0,1]) and scales the weights accordingly. The quadrature rule will be mapped from the entries of old_range to the entries of new_range.
QuadratureType QJacobi::type () const [inline, virtual]Returns:
Real QBase::w (const unsigned inti) const [inline, inherited]Returns:
Friends And Related Function Documentation
std::ostream& operator<< (std::ostream &os, const QBase &q) [friend, inherited]Same as above, but allows you to use the stream syntax.
Member Data Documentation
const unsigned int QJacobi::_alpha [private]
const unsigned int QJacobi::_beta [private]
ReferenceCounter::Counts ReferenceCounter::_counts [static, protected, inherited]Actually holds the data.
Threads::spin_mutex ReferenceCounter::_mutex [static, protected, inherited]Mutual exclusion object to enable thread-safe reference counting.
Threads::atomic< unsigned int > ReferenceCounter::_n_objects [static, protected, inherited]The number of objects. Print the reference count information when the number returns to 0.
std::cerr<< 'ERROR: Seems as if this quadrature rule' << std::endl << ' is not implemented for 2D.' << std::endl; libmesh_error(); }#endif virtual void init_3D (const ElemType, unsigned int =0)#ifndef DEBUG {}#else { std::cerr << 'ERROR: Seems as if this quadrature rule' << std::endl << ' is not implemented for 3D.' << std::endl; libmesh_error(); }#endif void tensor_product_quad (const QBase& q1D); void tensor_product_hex (const QBase& q1D); void tensor_product_prism (const QBase& q1D, const QBase& q2D); const unsigned int _dim; const Order _order; ElemType _type; unsigned int _p_level; std::vector<Point> QBase::_points [protected, inherited]
std::vector<Real> QBase::_weights [protected, inherited]The value of the quadrature weights.
bool QBase::allow_rules_with_negative_weights [inherited]Flag (default true) controlling the use of quadrature rules with negative weights. Set this to false to ONLY use (potentially) safer but more expensive rules with all positive weights.
Author

This document was created by man2html, using the manual pages.
Time: 21:53:36 GMT, April 16, 2011