Basis_HGRAD_LINE_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_LINE_Cn_FEM( const int n ,
									const EPointType &pointType ):
    latticePts_( n+1 , 1 ),
    Phis_( n ),
    V_(n+1,n+1),
    Vinv_(n+1,n+1)
  {
    const int N = n+1;
    this -> basisCardinality_  = N;
    this -> basisDegree_       = n;
    this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() );
    this -> basisType_         = BASIS_FEM_FIAT;
    this -> basisCoordinates_  = COORDINATES_CARTESIAN;
    this -> basisTagsAreSet_   = false;

    switch(pointType) {
    case POINTTYPE_EQUISPACED:
      PointTools::getLattice<Scalar,ArrayScalar >( latticePts_ ,  this->basisCellTopology_ , n , 0 , POINTTYPE_EQUISPACED );
      break;
    case POINTTYPE_SPECTRAL: 
    case POINTTYPE_WARPBLEND:
      PointTools::getLattice<Scalar,ArrayScalar >( latticePts_ ,  this->basisCellTopology_ , n , 0 , POINTTYPE_WARPBLEND );
      break;
    case POINTTYPE_SPECTRAL_OPEN: 
      PointTools::getGaussPoints<Scalar,ArrayScalar >( latticePts_ , n );
      break;
    default:
      TEUCHOS_TEST_FOR_EXCEPTION( true , std::invalid_argument , "Basis_HGRAD_LINE_Cn_FEM:: invalid point type" );
      break;
    }

    // form Vandermonde matrix.  Actually, this is the transpose of the VDM,
    // so we transpose on copy below.
  
    Phis_.getValues( V_ , latticePts_ , OPERATOR_VALUE );

    // now I need to copy V into a Teuchos array to do the inversion
    Teuchos::SerialDenseMatrix<int,Scalar> Vsdm(N,N);
    for (int i=0;i<N;i++) {
      for (int j=0;j<N;j++) {
        Vsdm(i,j) = V_(i,j);
      }
    }

    // invert the matrix
    Teuchos::SerialDenseSolver<int,Scalar> solver;
    solver.setMatrix( rcp( &Vsdm , false ) );
    solver.invert( );

    // now I need to copy the inverse into Vinv
    for (int i=0;i<N;i++) {
      for (int j=0;j<N;j++) {
        Vinv_(i,j) = Vsdm(j,i);
      }
    }

    initializeTags();
    this->basisTagsAreSet_ = true;
  }  
  Basis_HGRAD_TRI_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_TRI_Cn_FEM( const int n ,
                                                                      const EPointType pointType ):
    Phis( n ),
    V((n+1)*(n+2)/2,(n+1)*(n+2)/2),
    Vinv((n+1)*(n+2)/2,(n+1)*(n+2)/2),
    latticePts( (n+1)*(n+2)/2 , 2 )
  {
    TEUCHOS_TEST_FOR_EXCEPTION( n <= 0, std::invalid_argument, "polynomial order must be >= 1");

    const int N = (n+1)*(n+2)/2;
    this -> basisCardinality_  = N;
    this -> basisDegree_       = n;
    this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
    this -> basisType_         = BASIS_FEM_FIAT;
    this -> basisCoordinates_  = COORDINATES_CARTESIAN;
    this -> basisTagsAreSet_   = false;

    // construct lattice

    shards::CellTopology myTri_3( shards::getCellTopologyData< shards::Triangle<3> >() );  

    PointTools::getLattice<Scalar,FieldContainer<Scalar> >( latticePts ,
                                                            myTri_3 ,
                                                            n ,
                                                            0 ,
                                                            pointType );

    
    // form Vandermonde matrix.  Actually, this is the transpose of the VDM,
    // so we transpose on copy below.
  
    Phis.getValues( V , latticePts , OPERATOR_VALUE );

    // now I need to copy V into a Teuchos array to do the inversion
    Teuchos::SerialDenseMatrix<int,Scalar> Vsdm(N,N);
    for (int i=0;i<N;i++) {
      for (int j=0;j<N;j++) {
        Vsdm(i,j) = V(i,j);
      }
    }

    // invert the matrix
    Teuchos::SerialDenseSolver<int,Scalar> solver;
    solver.setMatrix( rcp( &Vsdm , false ) );
    solver.invert( );

    // now I need to copy the inverse into Vinv
    for (int i=0;i<N;i++) {
      for (int j=0;j<N;j++) {
        Vinv(i,j) = Vsdm(j,i);
      }
    }

  }  
  Basis_HGRAD_TET_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_TET_Cn_FEM( const int n ,
                                                                      const EPointType pointType ):
    Phis( n ),
    V((n+1)*(n+2)*(n+3)/6,(n+1)*(n+2)*(n+3)/6),
    Vinv((n+1)*(n+2)*(n+3)/6,(n+1)*(n+2)*(n+3)/6),
    latticePts( (n+1)*(n+2)*(n+3)/6 , 3 )
  {
    const int N = (n+1)*(n+2)*(n+3)/6;
    this -> basisCardinality_  = N;
    this -> basisDegree_       = n;
    this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Tetrahedron<4> >() );
    this -> basisType_         = BASIS_FEM_FIAT;
    this -> basisCoordinates_  = COORDINATES_CARTESIAN;
    this -> basisTagsAreSet_   = false;

    // construct lattice

    PointTools::getLattice<Scalar,ArrayScalar >( latticePts ,
                                                            this->getBaseCellTopology() ,
                                                            n ,
                                                            0 ,
                                                            pointType );

    
    // form Vandermonde matrix.  Actually, this is the transpose of the VDM,
    // so we transpose on copy below.
  
    Phis.getValues( V , latticePts , OPERATOR_VALUE );

    // now I need to copy V into a Teuchos array to do the inversion
    Teuchos::SerialDenseMatrix<int,Scalar> Vsdm(N,N);
    for (int i=0;i<N;i++) {
      for (int j=0;j<N;j++) {
        Vsdm(i,j) = V(i,j);
      }
    }

    // invert the matrix
    Teuchos::SerialDenseSolver<int,Scalar> solver;
    solver.setMatrix( rcp( &Vsdm , false ) );
    solver.invert( );

    // now I need to copy the inverse into Vinv
    for (int i=0;i<N;i++) {
      for (int j=0;j<N;j++) {
        Vinv(i,j) = Vsdm(j,i);
      }
    }

    initializeTags();
    this->basisTagsAreSet_ = true;
  }  
  Basis_HGRAD_LINE_Cn_FEM<Scalar,ArrayScalar>::Basis_HGRAD_LINE_Cn_FEM( const int n ,
									const ArrayScalar &pts ):
    latticePts_( n+1 , 1 ),
    Phis_( n ),
    V_(n+1,n+1),
    Vinv_(n+1,n+1)
  {
    const int N = n+1;
    this -> basisCardinality_  = N;
    this -> basisDegree_       = n;
    this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() );
    this -> basisType_         = BASIS_FEM_FIAT;
    this -> basisCoordinates_  = COORDINATES_CARTESIAN;
    this -> basisTagsAreSet_   = false;


    // check validity of points
    for (int i=0;i<n;i++) {
      TEUCHOS_TEST_FOR_EXCEPTION( pts(i,0) >= pts(i+1,0) ,
			  std::runtime_error ,
			  "Intrepid2::Basis_HGRAD_LINE_Cn_FEM Illegal points given to constructor" );
    }

    // copy points int latticePts, correcting endpoints if needed
    if (std::abs(pts(0,0)+1.0) < INTREPID_TOL) {
      latticePts_(0,0) = -1.0;
    }
    else {
      latticePts_(0,0) = pts(0,0);
    }
    for (int i=1;i<n;i++) {
      latticePts_(i,0) = pts(i,0);
    }
    if (std::abs(pts(n,0)-1.0) < INTREPID_TOL) {
      latticePts_(n,0) = 1.0;
    }
    else {
      latticePts_(n,0) = pts(n,0);
    }
    
    // form Vandermonde matrix.  Actually, this is the transpose of the VDM,
    // so we transpose on copy below.
  
    Phis_.getValues( V_ , latticePts_ , OPERATOR_VALUE );

    // now I need to copy V into a Teuchos array to do the inversion
    Teuchos::SerialDenseMatrix<int,Scalar> Vsdm(N,N);
    for (int i=0;i<N;i++) {
      for (int j=0;j<N;j++) {
        Vsdm(i,j) = V_(i,j);
      }
    }

    // invert the matrix
    Teuchos::SerialDenseSolver<int,Scalar> solver;
    solver.setMatrix( rcp( &Vsdm , false ) );
    solver.invert( );

    // now I need to copy the inverse into Vinv
    for (int i=0;i<N;i++) {
      for (int j=0;j<N;j++) {
        Vinv_(i,j) = Vsdm(j,i);
      }
    }

  }  
  Basis_HDIV_TRI_In_FEM<Scalar,ArrayScalar>::Basis_HDIV_TRI_In_FEM( const int n ,
                                                                    const EPointType pointType ):
    Phis( n ),
    coeffs( (n+1)*(n+2) , n*(n+2) )
  {
    const int N = n*(n+2);
    this -> basisCardinality_  = N;
    this -> basisDegree_       = n;
    this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
    this -> basisType_         = BASIS_FEM_FIAT;
    this -> basisCoordinates_  = COORDINATES_CARTESIAN;
    this -> basisTagsAreSet_   = false;


    const int littleN = n*(n+1);   // dim of (P_{n-1})^2 -- smaller space
    const int bigN = (n+1)*(n+2);  // dim of (P_{n})^2 -- larger space
    const int scalarSmallestN = (n-1)*n / 2;
    const int scalarLittleN = littleN/2;
    const int scalarBigN = bigN/2;

    // first, need to project the basis for RT space onto the
    // orthogonal basis of degree n
    // get coefficients of PkHx

    Teuchos::SerialDenseMatrix<int,Scalar> V1(bigN, N);

    // basis for the space is 
    // { (phi_i,0) }_{i=0}^{scalarLittleN-1} ,
    // { (0,phi_i) }_{i=0}^{scalarLittleN-1} ,
    // { (x,y) . phi_i}_{i=scalarLittleN}^{scalarBigN-1}
    // columns of V1 are expansion of this basis in terms of the basis
    // for P_{n}^2

    // these two loops get the first two sets of basis functions
    for (int i=0;i<scalarLittleN;i++) {
      V1(i,i) = 1.0;
      V1(scalarBigN+i,scalarLittleN+i) = 1.0;
    }

    // now I need to integrate { (x,y) phi } against the big basis
    // first, get a cubature rule.
    CubatureDirectTriDefault<Scalar,ArrayScalar > myCub( 2 * n );
    ArrayScalar cubPoints( myCub.getNumPoints() , 2 );
    ArrayScalar cubWeights( myCub.getNumPoints() );
    myCub.getCubature( cubPoints , cubWeights );

    // tabulate the scalar orthonormal basis at cubature points
    ArrayScalar phisAtCubPoints( scalarBigN , myCub.getNumPoints() );
    Phis.getValues( phisAtCubPoints , cubPoints , OPERATOR_VALUE );

    // now do the integration
    for (int i=0;i<n;i++) {
      for (int j=0;j<scalarBigN;j++) { // int (x,y) phi_i \cdot (phi_j,0)
        V1(j,littleN+i) = 0.0;
        for (int k=0;k<myCub.getNumPoints();k++) {
          V1(j,littleN+i) += 
            cubWeights(k) * cubPoints(k,0) 
            * phisAtCubPoints(scalarSmallestN+i,k) 
            * phisAtCubPoints(j,k);
        }
      }
      for (int j=0;j<scalarBigN;j++) {  // int (x,y) phi_i \cdot (0,phi_j)
        V1(j+scalarBigN,littleN+i) = 0.0;
        for (int k=0;k<myCub.getNumPoints();k++) {
          V1(j+scalarBigN,littleN+i) += 
            cubWeights(k) * cubPoints(k,1) 
            * phisAtCubPoints(scalarSmallestN+i,k) 
            * phisAtCubPoints(j,k);
        }
      }
    }

    //std::cout << V1 << "\n";

    
    // next, apply the RT nodes (rows) to the basis for (P_n)^2 (columns)
    Teuchos::SerialDenseMatrix<int,Scalar> V2(N , bigN);

    // first 3 * degree nodes are normals at each edge
    // get the points on the line
    ArrayScalar linePts( n , 1 );
    if (pointType == POINTTYPE_WARPBLEND) {
      CubatureDirectLineGauss<Scalar> edgeRule( n );
      ArrayScalar edgeCubWts( n );
      edgeRule.getCubature( linePts , edgeCubWts );
    }
    else if (pointType == POINTTYPE_EQUISPACED ) {
      shards::CellTopology linetop(shards::getCellTopologyData<shards::Line<2> >() );

      PointTools::getLattice<Scalar,ArrayScalar >( linePts , 
                                                              linetop ,
                                                              n+1 , 1 ,
                                                              POINTTYPE_EQUISPACED );
    }
    // holds the image of the line points 
    ArrayScalar edgePts( n , 2 );
    ArrayScalar phisAtEdgePoints( scalarBigN , n );

    // these are scaled by the appropriate edge lengths.
    const Scalar nx[] = {0.0,1.0,-1.0};
    const Scalar ny[] = {-1.0,1.0,0.0};
    
    for (int i=0;i<3;i++) {  // loop over edges
      CellTools<Scalar>::mapToReferenceSubcell( edgePts ,
                                                linePts ,
                                                1 ,
                                                i ,
                                                this->basisCellTopology_ );

      Phis.getValues( phisAtEdgePoints , edgePts , OPERATOR_VALUE );

      // loop over points (rows of V2)
      for (int j=0;j<n;j++) {
        // loop over orthonormal basis functions (columns of V2)
        for (int k=0;k<scalarBigN;k++) {
          V2(n*i+j,k) = nx[i] * phisAtEdgePoints(k,j);
          V2(n*i+j,k+scalarBigN) = ny[i] * phisAtEdgePoints(k,j);
        }
      }
    }

    // next map the points to each edge


    // remaining nodes are divided into two pieces:  point value of x
    // components and point values of y components.  These are
    // evaluated at the interior of a lattice of degree + 1, For then
    // the degree == 1 space corresponds classicaly to RT0 and so gets
    // no internal nodes, and degree == 2 corresponds to RT1 and needs
    // one internal node per vector component.
    const int numInternalPoints = PointTools::getLatticeSize( this->getBaseCellTopology() ,
                                                              n + 1 ,
                                                              1 );

    if (numInternalPoints > 0) {
      ArrayScalar internalPoints( numInternalPoints , 2 );
      PointTools::getLattice<Scalar,ArrayScalar >( internalPoints ,
                                                              this->getBaseCellTopology() , 
                                                              n + 1 ,
                                                              1 ,
                                                              pointType );
      
      ArrayScalar phisAtInternalPoints( scalarBigN , numInternalPoints );
      Phis.getValues( phisAtInternalPoints , internalPoints , OPERATOR_VALUE );
      
      // copy values into right positions of V2
      for (int i=0;i<numInternalPoints;i++) {
        for (int j=0;j<scalarBigN;j++) {
          // x component
          V2(3*n+i,j) = phisAtInternalPoints(j,i);
          // y component
          V2(3*n+numInternalPoints+i,scalarBigN+j) = phisAtInternalPoints(j,i);
        }
      }
    }
//     std::cout << "Nodes on big basis\n";
//     std::cout << V2 << "\n";
//     std::cout << "End nodes\n";

    Teuchos::SerialDenseMatrix<int,Scalar> Vsdm( N , N );

    // multiply V2 * V1 --> V
    Vsdm.multiply( Teuchos::NO_TRANS , Teuchos::NO_TRANS , 1.0 , V2 , V1 , 0.0 );

//     std::cout << "Vandermonde:\n";
//     std::cout << Vsdm << "\n";
//     std::cout << "End Vandermonde\n";
    
    Teuchos::SerialDenseSolver<int,Scalar> solver;
    solver.setMatrix( rcp( &Vsdm , false ) );
    solver.invert( );

    Teuchos::SerialDenseMatrix<int,Scalar> Csdm( bigN , N );
    Csdm.multiply( Teuchos::NO_TRANS , Teuchos::NO_TRANS , 1.0 , V1 , Vsdm , 0.0 );

    //    std::cout << Csdm << "\n";

    for (int i=0;i<bigN;i++) {
      for (int j=0;j<N;j++) {
        coeffs(i,j) = Csdm(i,j);
      }
    }
  }  
示例#6
0
void DislocationDensity<EvalT, Traits>::
evaluateFields(typename Traits::EvalData workset)
{

  Teuchos::SerialDenseMatrix<int, double> A;
  Teuchos::SerialDenseMatrix<int, double> X;
  Teuchos::SerialDenseMatrix<int, double> B;
  Teuchos::SerialDenseSolver<int, double> solver;

  A.shape(numNodes,numNodes);
  X.shape(numNodes,numNodes);
  B.shape(numNodes,numNodes);
  
  // construct Identity for RHS
  for (int i = 0; i < numNodes; ++i)
    B(i,i) = 1.0;

  for (int i=0; i < G.size() ; i++) G[i] = 0.0;

  // construct the node --> point operator
  for (std::size_t cell=0; cell < workset.numCells; ++cell)
  {
    for (std::size_t node=0; node < numNodes; ++node) 
      for (std::size_t qp=0; qp < numQPs; ++qp) 
	A(qp,node) = BF(cell,node,qp);
    
    X = 0.0;

    solver.setMatrix( Teuchos::rcp( &A, false) );
    solver.setVectors( Teuchos::rcp( &X, false ), Teuchos::rcp( &B, false ) );

    // Solve the system A X = B to find A_inverse
    int status = 0;
    status = solver.factor();
    status = solver.solve();

    // compute nodal Fp
    nodalFp.initialize(0.0);
    for (std::size_t node=0; node < numNodes; ++node) 
      for (std::size_t qp=0; qp < numQPs; ++qp) 
	for (std::size_t i=0; i < numDims; ++i) 
	  for (std::size_t j=0; j < numDims; ++j) 
	    nodalFp(node,i,j) += X(node,qp) * Fp(cell,qp,i,j);

    // compute the curl using nodalFp
    curlFp.initialize(0.0);
    for (std::size_t node=0; node < numNodes; ++node) 
    {
      for (std::size_t qp=0; qp < numQPs; ++qp) 
      {
	curlFp(qp,0,0) += nodalFp(node,0,2) * GradBF(cell,node,qp,1) - nodalFp(node,0,1) * GradBF(cell,node,qp,2);
	curlFp(qp,0,1) += nodalFp(node,1,2) * GradBF(cell,node,qp,1) - nodalFp(node,1,1) * GradBF(cell,node,qp,2);
	curlFp(qp,0,2) += nodalFp(node,2,2) * GradBF(cell,node,qp,1) - nodalFp(node,2,1) * GradBF(cell,node,qp,2);

	curlFp(qp,1,0) += nodalFp(node,0,0) * GradBF(cell,node,qp,2) - nodalFp(node,0,2) * GradBF(cell,node,qp,0);
	curlFp(qp,1,1) += nodalFp(node,1,0) * GradBF(cell,node,qp,2) - nodalFp(node,1,2) * GradBF(cell,node,qp,0);
	curlFp(qp,1,2) += nodalFp(node,2,0) * GradBF(cell,node,qp,2) - nodalFp(node,2,2) * GradBF(cell,node,qp,0);

	curlFp(qp,2,0) += nodalFp(node,0,1) * GradBF(cell,node,qp,0) - nodalFp(node,0,0) * GradBF(cell,node,qp,1);
	curlFp(qp,2,1) += nodalFp(node,1,1) * GradBF(cell,node,qp,0) - nodalFp(node,1,0) * GradBF(cell,node,qp,1);
	curlFp(qp,2,2) += nodalFp(node,2,1) * GradBF(cell,node,qp,0) - nodalFp(node,2,0) * GradBF(cell,node,qp,1);
      }
    }

    for (std::size_t qp=0; qp < numQPs; ++qp) 
      for (std::size_t i=0; i < numDims; ++i) 
	for (std::size_t j=0; j < numDims; ++j) 
	  for (std::size_t k=0; k < numDims; ++k) 
	    G(cell,qp,i,j) += Fp(cell,qp,i,k) * curlFp(qp,k,j);
  }
}
  Basis_HCURL_TRI_In_FEM<Scalar,ArrayScalar>::Basis_HCURL_TRI_In_FEM( const int n ,
                                                                      const EPointType pointType ):
    Phis_( n ),
    coeffs_( (n+1)*(n+2) , n*(n+2) )
  {
    const int N = n*(n+2);
    this -> basisCardinality_  = N;
    this -> basisDegree_       = n;
    this -> basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
    this -> basisType_         = BASIS_FEM_FIAT;
    this -> basisCoordinates_  = COORDINATES_CARTESIAN;
    this -> basisTagsAreSet_   = false;

    const int littleN = n*(n+1);   // dim of (P_{n-1})^2 -- smaller space
    const int bigN = (n+1)*(n+2);  // dim of (P_{n})^2 -- larger space
    const int scalarSmallestN = (n-1)*n / 2;
    const int scalarLittleN = littleN/2;
    const int scalarBigN = bigN/2;

    // first, need to project the basis for Nedelec space onto the
    // orthogonal basis of degree n
    // get coefficients of PkHx

    Teuchos::SerialDenseMatrix<int,Scalar> V1(bigN, N);

    // basis for the space is 
    // { (phi_i,0) }_{i=0}^{scalarLittleN-1} ,
    // { (0,phi_i) }_{i=0}^{scalarLittleN-1} ,
    // { (x,y) \times phi_i}_{i=scalarLittleN}^{scalarBigN-1}
    // { (x,y) \times phi = (y phi , -x \phi)
    // columns of V1 are expansion of this basis in terms of the basis
    // for P_{n}^2

    // these two loops get the first two sets of basis functions
    for (int i=0;i<scalarLittleN;i++) {
      V1(i,i) = 1.0;
      V1(scalarBigN+i,scalarLittleN+i) = 1.0;
    }

    // now I need to integrate { (x,y) \times phi } against the big basis
    // first, get a cubature rule.
    CubatureDirectTriDefault<Scalar,ArrayScalar > myCub( 2 * n );
    ArrayScalar cubPoints( myCub.getNumPoints() , 2 );
    ArrayScalar cubWeights( myCub.getNumPoints() );
    myCub.getCubature( cubPoints , cubWeights );

    // tabulate the scalar orthonormal basis at cubature points
    ArrayScalar phisAtCubPoints( scalarBigN , myCub.getNumPoints() );
    Phis_.getValues( phisAtCubPoints , cubPoints , OPERATOR_VALUE );

    // now do the integration
    for (int i=0;i<n;i++) {
      for (int j=0;j<scalarBigN;j++) { // int (x,y) phi_i \cdot (phi_j,0)
        V1(j,littleN+i) = 0.0;
        for (int k=0;k<myCub.getNumPoints();k++) {
          V1(j,littleN+i) -= 
            cubWeights(k) * cubPoints(k,1) 
            * phisAtCubPoints(scalarSmallestN+i,k) 
            * phisAtCubPoints(j,k);
        }
      }
      for (int j=0;j<scalarBigN;j++) {  // int (x,y) phi_i \cdot (0,phi_j)
        V1(j+scalarBigN,littleN+i) = 0.0;
        for (int k=0;k<myCub.getNumPoints();k++) {
          V1(j+scalarBigN,littleN+i) += 
            cubWeights(k) * cubPoints(k,0) 
            * phisAtCubPoints(scalarSmallestN+i,k) 
            * phisAtCubPoints(j,k);
        }
      }
    }

    //std::cout << V1 << "\n";

    
    // next, apply the RT nodes (rows) to the basis for (P_n)^2 (columns)
    Teuchos::SerialDenseMatrix<int,Scalar> V2(N , bigN);

    // first 3 * degree nodes are normals at each edge
    // get the points on the line
    ArrayScalar linePts( n , 1 );
    if (pointType == POINTTYPE_WARPBLEND) {
      CubatureDirectLineGauss<Scalar> edgeRule( 2*n - 1 );
      ArrayScalar edgeCubWts( n );
      edgeRule.getCubature( linePts , edgeCubWts );
    }
    else if (pointType == POINTTYPE_EQUISPACED ) {
      shards::CellTopology linetop(shards::getCellTopologyData<shards::Line<2> >() );

      PointTools::getLattice<Scalar,ArrayScalar >( linePts , 
                                                              linetop ,
                                                              n+1 , 1 ,
                                                              POINTTYPE_EQUISPACED );
    }


    ArrayScalar edgePts( n , 2 );
    ArrayScalar phisAtEdgePoints( scalarBigN , n );
    ArrayScalar edgeTan(2);
    
    for (int i=0;i<3;i++) {  // loop over edges
      CellTools<Scalar>::getReferenceEdgeTangent( edgeTan , 
                                                  i , 
                                                  this->basisCellTopology_ );
      /* multiply by 2.0 to account for a Jacobian in Pavel's definition */
      for (int j=0;j<2;j++) {
        edgeTan(j) *= 2.0;
      }

      CellTools<Scalar>::mapToReferenceSubcell( edgePts ,
                                                linePts ,
                                                1 ,
                                                i ,
                                                this->basisCellTopology_ );

      Phis_.getValues( phisAtEdgePoints , edgePts , OPERATOR_VALUE );

      // loop over points (rows of V2)
      for (int j=0;j<n;j++) {
        // loop over orthonormal basis functions (columns of V2)
        for (int k=0;k<scalarBigN;k++) {
          V2(n*i+j,k) = edgeTan(0) * phisAtEdgePoints(k,j);
          V2(n*i+j,k+scalarBigN) = edgeTan(1) * phisAtEdgePoints(k,j);
        }
      }
    }

    // remaining nodes are x- and y- components at internal points, if n > 1
    // this code is exactly the same as it is for HDIV

    const int numInternalPoints = PointTools::getLatticeSize( this->getBaseCellTopology() ,
                                                              n + 1 ,
                                                              1 );

    if (numInternalPoints > 0) {
      ArrayScalar internalPoints( numInternalPoints , 2 );
      PointTools::getLattice<Scalar,ArrayScalar >( internalPoints ,
                                                              this->getBaseCellTopology() , 
                                                              n + 1 ,
                                                              1 ,
                                                              pointType );
      
      ArrayScalar phisAtInternalPoints( scalarBigN , numInternalPoints );
      Phis_.getValues( phisAtInternalPoints , internalPoints , OPERATOR_VALUE );

      // copy values into right positions of V2
      for (int i=0;i<numInternalPoints;i++) {
        for (int j=0;j<scalarBigN;j++) {
          // x component
          V2(3*n+i,j) = phisAtInternalPoints(j,i);
          // y component
          V2(3*n+numInternalPoints+i,scalarBigN+j) = phisAtInternalPoints(j,i);
        }
      }
    }
//     std::cout << "Nodes on big basis\n";
//     std::cout << V2 << "\n";
//     std::cout << "End nodes\n";

    Teuchos::SerialDenseMatrix<int,Scalar> Vsdm( N , N );

    // multiply V2 * V1 --> V
    Vsdm.multiply( Teuchos::NO_TRANS , Teuchos::NO_TRANS , 1.0 , V2 , V1 , 0.0 );

//     std::cout << "Vandermonde:\n";
//     std::cout << Vsdm << "\n";
//     std::cout << "End Vandermonde\n";
    
    Teuchos::SerialDenseSolver<int,Scalar> solver;
    solver.setMatrix( rcp( &Vsdm , false ) );
    solver.invert( );

    Teuchos::SerialDenseMatrix<int,Scalar> Csdm( bigN , N );
    Csdm.multiply( Teuchos::NO_TRANS , Teuchos::NO_TRANS , 1.0 , V1 , Vsdm , 0.0 );

    //    std::cout << Csdm << "\n";

    for (int i=0;i<bigN;i++) {
      for (int j=0;j<N;j++) {
        coeffs_(i,j) = Csdm(i,j);
      }
    }

    initializeTags();
    this->basisTagsAreSet_ = true;
  }  
void SaddleOperator<ScalarType, MV, OP>::Apply(const SaddleContainer<ScalarType,MV>& X, SaddleContainer<ScalarType,MV>& Y) const
{
    RCP<SerialDenseMatrix> Xlower = X.getLower();
    RCP<SerialDenseMatrix> Ylower = Y.getLower();

    if(pt_ == NO_PREC)
    {
        // trans does literally nothing, because the operator is symmetric
        // Y.bottom = B'X.top
        MVT::MvTransMv(1., *B_, *(X.upper_), *Ylower);

        // Y.top = A*X.top+B*X.bottom
        A_->Apply(*(X.upper_), *(Y.upper_));
        MVT::MvTimesMatAddMv(1., *B_, *Xlower, 1., *(Y.upper_));
    }
    else if(pt_ == NONSYM)
    {
        // Y.bottom = -B'X.top
        MVT::MvTransMv(-1., *B_, *(X.upper_), *Ylower);

        // Y.top = A*X.top+B*X.bottom
        A_->Apply(*(X.upper_), *(Y.upper_));
        MVT::MvTimesMatAddMv(1., *B_, *Xlower, 1., *(Y.upper_));
    }
    else if(pt_ == BD_PREC)
    {
        Teuchos::SerialDenseSolver<int,ScalarType> MySolver;

        // Solve A Y.X = X.X
        A_->Apply(*(X.upper_),*(Y.upper_));

        // So, let me tell you a funny story about how the SerialDenseSolver destroys the original matrix...
        Teuchos::RCP<SerialDenseMatrix> localSchur = Teuchos::rcp(new SerialDenseMatrix(*Schur_));

        // Solve the small system
        MySolver.setMatrix(localSchur);
        MySolver.setVectors(Ylower, Xlower);
        MySolver.solve();
    }
    // Hermitian-Skew Hermitian splitting has some extra requirements
    // We need B'B = I, which is true for standard eigenvalue problems, but not generalized
    // We also need to use gmres, because our operator is no longer symmetric
    else if(pt_ == HSS_PREC)
    {
//    std::cout << "applying preconditioner to";
//    X.MvPrint(std::cout);

        // Solve (H + alpha I) Y1 = X
        // 1.  Apply preconditioner
        A_->Apply(*(X.upper_),*(Y.upper_));
        // 2. Scale by 1/alpha
        *Ylower = *Xlower;
        Ylower->scale(1./alpha_);

//    std::cout << "H preconditioning produced";
//	Y.setLower(Ylower);
//    Y.MvPrint(std::cout);

        // Solve (S + alpha I) Y = Y1
        // 1.  Y_lower = (B' Y1_upper + alpha Y1_lower) / (1 + alpha^2)
        Teuchos::RCP<SerialDenseMatrix> Y1_lower = Teuchos::rcp(new SerialDenseMatrix(*Ylower));
        MVT::MvTransMv(1,*B_,*(Y.upper_),*Ylower);
//	std::cout << "Y'b1 " << *Ylower;
        Y1_lower->scale(alpha_);
//	std::cout << "alpha b2 " << *Y1_lower;
        *Ylower += *Y1_lower;
//	std::cout << "alpha b2 + Y'b1 " << *Ylower;
        Ylower->scale(1/(1+alpha_*alpha_));
        // 2.  Y_upper = (Y1_upper - B Y_lower) / alpha
        MVT::MvTimesMatAddMv(-1/alpha_,*B_,*Ylower,1/alpha_,*(Y.upper_));

//    std::cout << "preconditioning produced";
//	Y.setLower(Ylower);
//    Y.MvPrint(std::cout);
    }
    else
    {
        std::cout << "Not a valid preconditioner type\n";
    }

    Y.setLower(Ylower);

//  std::cout << "result of applying operator";
//  Y.MvPrint(std::cout);
}