#include <quadrature_jacobi.h>
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 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 ()
bool allow_rules_with_negative_weights
typedef std::map< std::string, std::pair< unsigned int, unsigned int > > Counts
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)
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 Counts _counts
static Threads::atomic< unsigned int > _n_objects
static Threads::spin_mutex _mutex
void init_1D (const ElemType _type=INVALID_ELEM, unsigned int p_level=0)
const unsigned int _alpha
const unsigned int _beta
std::ostream & operator<< (std::ostream &os, const QBase &q)
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.
Definition at line 105 of file reference_counter.h.
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);
}
Definition at line 68 of file quadrature_jacobi.h.
{}
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);
}
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;
}
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; }
Definition at line 103 of file quadrature.h.
{ return _type; }
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
}
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); }
Definition at line 109 of file quadrature.h.
{ return _p_level; }
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; }
Definition at line 133 of file quadrature.h.
References QBase::_points.
{ return _points; }
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; }
Definition at line 143 of file quadrature.h.
References QBase::_weights.
{ return _weights; }
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++;
}
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++;
}
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();
}
}
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;
}
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;
}
Reimplemented in QClough, QConical, QGauss, QGrid, QMonomial, QSimpson, and QTrap.
Definition at line 234 of file quadrature.h.
Referenced by QBase::init().
{}
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; }
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(); }
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;
}
}
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
}
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]; }
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;
}
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;
}
}
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]; }
Definition at line 196 of file quadrature.C.
{
q.print_info(os);
return os;
}
Definition at line 78 of file quadrature_jacobi.h.
Referenced by init_1D(), and type().
Definition at line 79 of file quadrature_jacobi.h.
Referenced by init_1D(), and type().
Definition at line 110 of file reference_counter.h.
Referenced by ReferenceCounter::get_info(), ReferenceCounter::increment_constructor_count(), and ReferenceCounter::increment_destructor_count().
Definition at line 123 of file reference_counter.h.
Definition at line 118 of file reference_counter.h.
Referenced by ReferenceCounter::n_objects(), ReferenceCounter::ReferenceCounter(), and ReferenceCounter::~ReferenceCounter().
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().
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().
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().
Generated automatically by Doxygen for libMesh from the source code.