text: // @HEADER
  // ************************************************************************
  //
  //                           Intrepid Package
  //                 Copyright (2007) Sandia Corporation
  //
  // Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
  // license for use of this work by or on behalf of the U.S. Government.
  //
  // Redistribution and use in source and binary forms, with or without
  // modification, are permitted provided that the following conditions are
  // met:
  //
  // 1. Redistributions of source code must retain the above copyright
  // notice, this list of conditions and the following disclaimer.
  //
  // 2. Redistributions in binary form must reproduce the above copyright
  // notice, this list of conditions and the following disclaimer in the
  // documentation and/or other materials provided with the distribution.
  //
  // 3. Neither the name of the Corporation nor the names of the
  // contributors may be used to endorse or promote products derived from
  // this software without specific prior written permission.
  //
  // THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
  // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  // PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
  // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
  // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
  // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
  // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
  // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  //
  // Questions? Contact Pavel Bochev  (pbboche@sandia.gov)
  //                    Denis Ridzal  (dridzal@sandia.gov), or
  //                    Kara Peterson (kjpeter@sandia.gov)
  //
  // ************************************************************************
  // @HEADER
  
  /** \file   Intrepid_CubatureDirectTriDefaultDef.hpp
      \brief  Definition file for the Intrepid::CubatureDirectTriDefault class.
      \author Created by P. Bochev, D. Ridzal, and D. Day.
  */
  
  namespace Intrepid {
  
  template <class Scalar, class ArrayPoint, class ArrayWeight>
  CubatureDirectTriDefault<Scalar,ArrayPoint,ArrayWeight>::CubatureDirectTriDefault(const int degree) {
    this->degree_    = degree;
    this->dimension_ = 2;
    TEUCHOS_TEST_FOR_EXCEPTION((degree < 0) || (degree > INTREPID_CUBATURE_TRI_DEFAULT_MAX_ENUM),
                       std::out_of_range,
                       ">>> ERROR (CubatureDirectTriDefault): No direct cubature rule implemented for the desired polynomial degree.");
  } // end constructor
  
  
  
  template <class Scalar, class ArrayPoint, class ArrayWeight>
  const CubatureTemplate *  CubatureDirectTriDefault<Scalar,ArrayPoint,ArrayWeight>::exposeCubatureData() const {
    return cubature_data_;
  }
  
  
  
  template <class Scalar, class ArrayPoint, class ArrayWeight>
  int CubatureDirectTriDefault<Scalar,ArrayPoint,ArrayWeight>::getMaxAccuracy() const {
    return INTREPID_CUBATURE_TRI_DEFAULT_MAX_ENUM;
  }
  
  
  
  template <class Scalar, class ArrayPoint, class ArrayWeight>
  const char* CubatureDirectTriDefault<Scalar,ArrayPoint,ArrayWeight>::getName() const {
    return cubature_name_;
  } // end getName
  
  
  
  template <class Scalar, class ArrayPoint, class ArrayWeight>
  const char* CubatureDirectTriDefault<Scalar,ArrayPoint,ArrayWeight>::cubature_name_ = "INTREPID_CUBATURE_TRI_DEFAULT";
  
  
  //-------------------------------------------------------------------------------------//
  //                          Definition of cubature templates                           //
  //-------------------------------------------------------------------------------------//
  
  /*
     Cubature templates for lines are defined the reference Triangle:
  
     Triangle      -> (0,0,0),(1,0,0),(0,1,0)
  */
  
  /*
     This static const member contains templates for default triangle rules.
  */
  
  template <class Scalar, class ArrayPoint, class ArrayWeight>
  const CubatureTemplate CubatureDirectTriDefault<Scalar,ArrayPoint,ArrayWeight>::cubature_data_[INTREPID_CUBATURE_TRI_DEFAULT_MAX_ENUM+1] =
  {
    // Cubature templates for the reference triangle {(0,0), (1,0), (0,1)}
    //
    {
      1,
      {{1./3., 1./3., 0.0}},
      {1./2.}
    },
    {
      1,
      {{1./3., 1./3., 0.0}},
      {1./2.}
    },
    {
      3,
      {{1./6., 1./6., 0.0},
       {1./6., 2./3., 0.0},
       {2./3., 1./6., 0.0}},
      {1./6.,
       1./6.,
       1./6.}
    },
    {
      4,
      {{1./3., 1./3., 0.0},
       {1./5., 1./5., 0.0},
       {1./5., 3./5., 0.0},
       {3./5., 1./5., 0.0}},
      {-9./32.,
       25./96.,
       25./96.,
       25./96.}
    },
    {
      6,
      {{4.4594849091596487577332043252695176084800e-1,  4.4594849091596487577332043252695176084800e-1, 0.0},
       {4.4594849091596487577332043252695176084800e-1,  1.0810301816807024845335913494609647830400e-1, 0.0},
       {1.0810301816807024845335913494609647830400e-1,  4.4594849091596487577332043252695176084800e-1, 0.0},
       {9.1576213509770745141706146463816673424873e-2,  9.1576213509770745141706146463816673424873e-2, 0.0},
       {9.1576213509770745141706146463816673424873e-2,  8.1684757298045850971658770707236665315025e-1, 0.0},
       {8.1684757298045850971658770707236665315025e-1,  9.1576213509770745141706146463816673424873e-2, 0.0}},
      {1.1169079483900573053953942803038657817028e-1,
       1.1169079483900573053953942803038657817028e-1,
       1.1169079483900573053953942803038657817028e-1,
       5.4975871827660936395761590801109078322738e-2,
       5.4975871827660936395761590801109078322738e-2,
       5.4975871827660936395761590801109078322738e-2}
    },
    {
      7,
      {{3.3333333333333333333333333333333333333333e-1,  3.3333333333333333333333333333333333333333e-1, 0.0},
       {1.0128650732345633880098736191512382805558e-1,  1.0128650732345633880098736191512382805558e-1, 0.0},
       {7.9742698535308732239802527616975234388885e-1,  1.0128650732345633880098736191512382805558e-1, 0.0},
       {1.0128650732345633880098736191512382805558e-1,  7.9742698535308732239802527616975234388885e-1, 0.0},
       {4.7014206410511508977044120951344760051585e-1,  4.7014206410511508977044120951344760051585e-1, 0.0},
       {5.9715871789769820459117580973104798968293e-2,  4.7014206410511508977044120951344760051585e-1, 0.0},
       {4.7014206410511508977044120951344760051585e-1,  5.9715871789769820459117580973104798968293e-2, 0.0}},
      {1.1250000000000000000000000000000000000000e-1,
       6.2969590272413576297841972750090666828820e-2,
       6.2969590272413576297841972750090666828820e-2,
       6.2969590272413576297841972750090666828820e-2,
       6.6197076394253090368824693916575999837847e-2,
       6.6197076394253090368824693916575999837847e-2,
       6.6197076394253090368824693916575999837847e-2}
    },
    {
      12,
      {{6.3089014491502228340331602870819157341003e-2,  6.3089014491502228340331602870819157341003e-2, 0.0},
       {6.3089014491502228340331602870819157341003e-2,  8.7382197101699554331933679425836168531799e-1, 0.0},
       {8.7382197101699554331933679425836168531799e-1,  6.3089014491502228340331602870819157341003e-2, 0.0},
       {2.4928674517091042129163855310701907608796e-1,  2.4928674517091042129163855310701907608796e-1, 0.0},
       {2.4928674517091042129163855310701907608796e-1,  5.0142650965817915741672289378596184782407e-1, 0.0},
       {5.0142650965817915741672289378596184782407e-1,  2.4928674517091042129163855310701907608796e-1, 0.0},
       {3.1035245103378441286759566723265117140082e-1,  5.3145049844816939902261738355299128796183e-2, 0.0},
       {6.3650249912139865667831578657006182134850e-1,  3.1035245103378439596843454179854003165774e-1, 0.0},
       {5.3145049844816930454088546197287007250682e-2,  6.3650249912139866412930371984616083954608e-1, 0.0},
       {5.3145049844816939902261738355299128796183e-2,  3.1035245103378441286759566723265117140082e-1, 0.0},
       {6.3650249912139866412930371984616083954608e-1,  5.3145049844816930454088546197287007250682e-2, 0.0},
       {3.1035245103378439596843454179854003165774e-1,  6.3650249912139865667831578657006182134850e-1, 0.0}},
      {2.5422453185103408460468404553434492023395e-2,
       2.5422453185103408460468404553434492023395e-2,
       2.5422453185103408460468404553434492023395e-2,
       5.8393137863189683012644805692789720663043e-2,
       5.8393137863189683012644805692789720663043e-2,
       5.8393137863189683012644805692789720663043e-2,
       4.1425537809186787596776728210221226990114e-2,
       4.1425537809186787596776728210221226990114e-2,
       4.1425537809186787596776728210221226990114e-2,
       4.1425537809186787596776728210221226990114e-2,
       4.1425537809186787596776728210221226990114e-2,
       4.1425537809186787596776728210221226990114e-2}
    },
    {
      13,
      {{3.33333333333333e-01, 3.33333333333333e-01, 0.0},
       {2.60345966079040e-01, 2.60345966079040e-01, 0.0},
       {2.60345966079040e-01, 4.79308067841920e-01, 0.0},
       {4.79308067841920e-01, 2.60345966079040e-01, 0.0},
       {6.51301029022160e-02, 6.51301029022160e-02, 0.0},
       {6.51301029022160e-02, 8.69739794195568e-01, 0.0},
       {8.69739794195568e-01, 6.51301029022160e-02, 0.0},
       {3.12865496004874e-01, 6.38444188569810e-01, 0.0},
       {6.38444188569810e-01, 4.86903154253160e-02, 0.0},
       {4.86903154253160e-02, 3.12865496004874e-01, 0.0},
       {3.12865496004874e-01, 4.86903154253160e-02, 0.0},
       {6.38444188569810e-01, 3.12865496004874e-01, 0.0},
       {4.86903154253160e-02, 6.38444188569810e-01, 0.0}},
      {-7.47850222338410e-02,
       8.78076287166040e-02,
       8.78076287166040e-02,
       8.78076287166040e-02,
       2.66736178044190e-02,
       2.66736178044190e-02,
       2.66736178044190e-02,
       3.85568804451285e-02,
       3.85568804451285e-02,
       3.85568804451285e-02,
       3.85568804451285e-02,
       3.85568804451285e-02,
       3.85568804451285e-02}
    },
    {
      16,
      {{3.33333333333333e-01, 3.33333333333333e-01, 0.0},
       {4.59292588292723e-01, 4.59292588292723e-01, 0.0},
       {4.59292588292723e-01, 8.14148234145540e-02, 0.0},
       {8.14148234145540e-02, 4.59292588292723e-01, 0.0},
       {1.70569307751760e-01, 1.70569307751760e-01, 0.0},
       {1.70569307751760e-01, 6.58861384496480e-01, 0.0},
       {6.58861384496480e-01, 1.70569307751760e-01, 0.0},
       {5.05472283170310e-02, 5.05472283170310e-02, 0.0},
       {5.05472283170310e-02, 8.98905543365938e-01, 0.0},
       {8.98905543365938e-01, 5.05472283170310e-02, 0.0},
       {2.63112829634638e-01, 7.28492392955404e-01, 0.0},
       {7.28492392955404e-01, 8.39477740995798e-03, 0.0},
       {8.39477740995798e-03, 2.63112829634638e-01, 0.0},
       {2.63112829634638e-01, 8.39477740995798e-03, 0.0},
       {7.28492392955404e-01, 2.63112829634638e-01, 0.0},
       {8.39477740995798e-03, 7.28492392955404e-01, 0.0}},
      {7.21578038388935e-02,
       4.75458171336425e-02,
       4.75458171336425e-02,
       4.75458171336425e-02,
       5.16086852673590e-02,
       5.16086852673590e-02,
       5.16086852673590e-02,
       1.62292488115990e-02,
       1.62292488115988e-02,
       1.62292488115990e-02,
       1.36151570872175e-02,
       1.36151570872175e-02,
       1.36151570872175e-02,
       1.36151570872175e-02,
       1.36151570872175e-02,
       1.36151570872175e-02}
    },
    {
      19,
      {{3.33333333333333e-01, 3.33333333333333e-01, 0.0},
       {4.89682519198738e-01, 4.89682519198738e-01, 0.0},
       {4.89682519198738e-01, 2.06349616025250e-02, 0.0},
       {2.06349616025250e-02, 4.89682519198738e-01, 0.0},
       {4.37089591492937e-01, 4.37089591492937e-01, 0.0},
       {4.37089591492937e-01, 1.25820817014127e-01, 0.0},
       {1.25820817014127e-01, 4.37089591492937e-01, 0.0},
       {1.88203535619033e-01, 1.88203535619033e-01, 0.0},
       {1.88203535619033e-01, 6.23592928761935e-01, 0.0},
       {6.23592928761935e-01, 1.88203535619033e-01, 0.0},
       {4.47295133944530e-02, 4.47295133944530e-02, 0.0},
       {4.47295133944530e-02, 9.10540973211095e-01, 0.0},
       {9.10540973211095e-01, 4.47295133944530e-02, 0.0},
       {2.21962989160766e-01, 7.41198598784498e-01, 0.0},
       {7.41198598784498e-01, 3.68384120547360e-02, 0.0},
       {3.68384120547360e-02, 2.21962989160766e-01, 0.0},
       {2.21962989160766e-01, 3.68384120547360e-02, 0.0},
       {7.41198598784498e-01, 2.21962989160766e-01, 0.0},
       {3.68384120547360e-02, 7.41198598784498e-01, 0.0}},
      {4.85678981413995e-02,
       1.56673501135695e-02,
       1.56673501135695e-02,
       1.56673501135695e-02,
       3.89137705023870e-02,
       3.89137705023870e-02,
       3.89137705023870e-02,
       3.98238694636050e-02,
       3.98238694636050e-02,
       3.98238694636050e-02,
       1.27888378293490e-02,
       1.27888378293490e-02,
       1.27888378293490e-02,
       2.16417696886445e-02,
       2.16417696886445e-02,
       2.16417696886445e-02,
       2.16417696886445e-02,
       2.16417696886445e-02,
       2.16417696886445e-02}
    },
    {
      24,
      {{3.8102570854643002e-03, 8.6854386943076545e-01, 0.0},
       {8.3865349500109043e-01, 1.6134650499890960e-01, 0.0},
       {0.0                   , 3.9366774470722010e-01, 0.0},
       {7.7757518429429107e-01, 0.0                   , 0.0},
       {4.7768381772022403e-02, 9.2899486985787905e-01, 0.0},
       {1.0939142057119900e-02, 1.7690730625559031e-01, 0.0},
       {4.6374383867430541e-01, 0.0                   , 0.0},
       {9.3049846900263089e-01, 2.9553592846822900e-02, 0.0},
       {3.9099745550423302e-02, 3.5319656252586103e-02, 0.0},
       {4.8798437805397499e-01, 5.0365825075943971e-01, 0.0},
       {1.9305903224251941e-01, 3.0573404093099301e-02, 0.0},
       {2.2376358774275851e-01, 7.4726591728868819e-01, 0.0},
       {3.6036266787907702e-02, 6.3491832379200652e-01, 0.0},
       {7.6777680170023954e-01, 1.0614642990290001e-01, 0.0},
       {1.0954959855585469e-01, 7.5329402776254240e-01, 0.0},
       {6.4203365318662664e-01, 2.9530445535851102e-01, 0.0},
       {1.0999439055630450e-01, 1.6929927488966459e-01, 0.0},
       {3.3947290311800549e-01, 9.5379208487721703e-02, 0.0},
       {8.4198522115543697e-02, 3.8729657913960353e-01, 0.0},
       {5.7966325105486349e-01, 8.0491894656105595e-02, 0.0},
       {3.6419744430339263e-01, 5.2433682558924433e-01, 0.0},
       {2.7586334089315973e-01, 2.6481531651496770e-01, 0.0},
       {2.0776116575484829e-01, 5.0550507373529086e-01, 0.0},
       {4.8123289062464247e-01, 2.7542385024412980e-01, 0.0}},
      {5.3333456379563004e-03,
       5.5334733911235499e-03,
       5.9501524071177998e-03,
       6.6995403929284002e-03,
       7.3041646115608498e-03,
       7.4233118233402503e-03,
       7.5781309587828498e-03,
       7.6015470130063496e-03,
       8.8279222964811003e-03,
       9.7797061087609508e-03,
       1.5707351180334426e-02,
       1.6151301011728625e-02,
       2.1481164696039650e-02,
       2.6268329551205824e-02,
       2.6365190704419499e-02,
       2.7457802196927176e-02,
       2.8987070299349601e-02,
       3.0871122933097676e-02,
       3.1343962650456775e-02,
       3.3093067237629975e-02,
       3.7039823668389947e-02,
       4.2207221279855073e-02,
       4.3362019313832399e-02,
       4.7633278635674972e-02}
    },
    {
      27,
      {{3.7802163891336921e-01, 6.1948431533135195e-01, 0.0},
       {3.2899822292186298e-02, 9.3614893514675623e-01, 0.0},
       {9.3551434285897095e-01, 3.3268560622678398e-02, 0.0},
       {3.4222771841359197e-02, 3.2916403878999703e-02, 0.0},
       {1.4354532010930900e-02, 3.9659731669586501e-01, 0.0},
       {2.2120535196161799e-02, 1.6892970982290231e-01, 0.0},
       {8.1562969693268217e-01, 2.6807150626772601e-02, 0.0},
       {2.7719522918618601e-02, 8.1626233715968810e-01, 0.0},
       {1.7400571673032261e-01, 2.5252704638304500e-02, 0.0},
       {3.8913981113319362e-01, 2.2592651051306600e-02, 0.0},
       {8.0364834053903877e-01, 1.6655614492060569e-01, 0.0},
       {1.6429286715713459e-01, 8.0454974747615537e-01, 0.0},
       {6.1758873171277151e-01, 2.5660186833052399e-02, 0.0},
       {2.6297199713764201e-02, 6.1924873232110123e-01, 0.0},
       {5.9895439629934211e-01, 3.7272769861629101e-01, 0.0},
       {8.1721404855381805e-02, 3.2719878157552901e-01, 0.0},
       {1.3035453031942690e-01, 1.3667083534390509e-01, 0.0},
       {7.1027868107761583e-01, 1.3828000204292321e-01, 0.0},
       {1.4118119730952799e-01, 7.0099267949645228e-01, 0.0},
       {5.3141960154079959e-01, 1.2417148586801489e-01, 0.0},
       {3.4992914334288650e-01, 5.6938486195327997e-01, 0.0},
       {3.1909737814681871e-01, 1.1698976413323441e-01, 0.0},
       {1.2454405910544100e-01, 5.1353143433447235e-01, 0.0},
       {4.1132499178904658e-01, 2.6677168071577739e-01, 0.0},
       {5.3634228112084714e-01, 3.2081957909482989e-01, 0.0},
       {2.2789955884347499e-01, 2.8790310224819649e-01, 0.0},
       {2.9133859436942361e-01, 4.6494564773693992e-01, 0.0}},
      {5.6375356078552001e-03,
       6.5529674260441251e-03,
       6.6871546432313500e-03,
       7.2740543402810501e-03,
       9.1794421950682249e-03,
       1.0688904048956826e-02,
       1.1556190176810576e-02,
       1.1821029782882325e-02,
       1.2035150250304100e-02,
       1.3361393587366349e-02,
       1.3378318081626600e-02,
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    {
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       1.5930165141800151e-02}
    } // end Triangle
  
  };
      
  } // end namespace Intrepid
  