From dc0554655ebbd05ac7e033fea5acd36cc883f26d Mon Sep 17 00:00:00 2001
From: Oliver Sander <oliver.sander@tu-dresden.de>
Date: Mon, 15 Jan 2018 13:53:08 +0100
Subject: [PATCH] Add stubs to allow building projected FE with
OrthogonalMatrix
---
dune/gfe/orthogonalmatrix.hh | 112 ++++++++++++++++++++++++++++++++++-
1 file changed, 109 insertions(+), 3 deletions(-)
diff --git a/dune/gfe/orthogonalmatrix.hh b/dune/gfe/orthogonalmatrix.hh
index 2e00270a..36d7c10b 100644
--- a/dune/gfe/orthogonalmatrix.hh
+++ b/dune/gfe/orthogonalmatrix.hh
@@ -3,6 +3,8 @@
#include <dune/common/fmatrix.hh>
+#include <dune/gfe/skewmatrix.hh>
+
/** \brief An orthogonal \f$ n \times n \f$ matrix
* \tparam T Type of the matrix entries
* \tparam N Space dimension
@@ -11,7 +13,24 @@ template <class T, int N>
class OrthogonalMatrix
{
public:
-
+ /** \brief The type used for coordinates */
+ typedef T ctype;
+
+ /** \brief Dimension of the manifold formed by the orthogonal matrices */
+ static const int dim = N*(N-1)/2;
+
+ /** \brief Coordinates are embedded into a Euclidean space of N x N - matrices */
+ static const int embeddedDim = N*N;
+
+ /** \brief The type used for global coordinates */
+ typedef Dune::FieldVector<T,embeddedDim> CoordinateType;
+
+ /** \brief Member of the corresponding Lie algebra. This really is a skew-symmetric matrix */
+ typedef Dune::FieldVector<T,dim> TangentVector;
+
+ /** \brief A tangent vector as a vector in the surrounding coordinate space */
+ typedef Dune::FieldVector<T,embeddedDim> EmbeddedTangentVector;
+
/** \brief Default constructor -- leaves the matrix uninitialized */
OrthogonalMatrix()
{}
@@ -24,6 +43,15 @@ public:
: data_(matrix)
{}
+ /** \brief Copy constructor
+ *
+ * It is not checked whether the matrix is really orthogonal
+ */
+ explicit OrthogonalMatrix(const CoordinateType& other)
+ {
+ DUNE_THROW(Dune::NotImplemented, "constructor");
+ }
+
/** \brief Const access to the matrix entries */
const Dune::FieldMatrix<T,N,N>& data() const
{
@@ -63,7 +91,85 @@ public:
return result;
}
-
+
+ /** \brief Rebind the OrthogonalMatrix to another coordinate type */
+ template<class U>
+ struct rebind
+ {
+ typedef OrthogonalMatrix<U,N> other;
+ };
+
+ OrthogonalMatrix& operator= (const CoordinateType& other)
+ {
+ std::size_t idx = 0;
+ for (int i=0; i<N; i++)
+ for (int j=0; j<N; j++)
+ data_[i][j] = other[idx++];
+ return *this;
+ }
+
+ /** \brief The exponential map from a given point $p \in SO(n)$.
+
+ \param v A tangent vector.
+ */
+ static OrthogonalMatrix<T,3> exp(const OrthogonalMatrix<T,N>& p, const TangentVector& v)
+ {
+ DUNE_THROW(Dune::NotImplemented, "exp");
+ }
+
+ /** \brief Return the actual matrix */
+ void matrix(Dune::FieldMatrix<T,N,N>& m) const
+ {
+ m = data_;
+ }
+
+ /** \brief Project tangent vector of R^n onto the normal space space */
+ EmbeddedTangentVector projectOntoNormalSpace(const EmbeddedTangentVector& v) const
+ {
+ DUNE_THROW(Dune::NotImplemented, "projectOntoNormalSpace");
+ }
+
+ /** \brief The Weingarten map */
+ EmbeddedTangentVector weingarten(const EmbeddedTangentVector& z, const EmbeddedTangentVector& v) const
+ {
+ EmbeddedTangentVector result;
+ DUNE_THROW(Dune::NotImplemented, "weingarten");
+ return result;
+ }
+
+ static OrthogonalMatrix<T,N> projectOnto(const CoordinateType& p)
+ {
+ DUNE_THROW(Dune::NotImplemented, "projectOnto");
+ }
+
+ // TODO return type is wrong
+ static Dune::FieldMatrix<T,1,1> derivativeOfProjection(const CoordinateType& p)
+ {
+ Dune::FieldMatrix<T,1,1> result;
+ return result;
+ }
+
+ /** \brief The global coordinates, if you really want them */
+ CoordinateType globalCoordinates() const
+ {
+ CoordinateType result;
+ std::size_t idx = 0;
+
+ for (int i=0; i<N; i++)
+ for (int j=0; j<N; j++)
+ result[idx++] = data_[i][j];
+
+ return result;
+ }
+
+ /** \brief Compute an orthonormal basis of the tangent space of SO(n). */
+ Dune::FieldMatrix<T,dim,embeddedDim> orthonormalFrame() const
+ {
+ Dune::FieldMatrix<T,dim,embeddedDim> result;
+ DUNE_THROW(Dune::NotImplemented, "orthonormalFrame");
+ return result;
+ }
+
private:
/** \brief The actual data */
@@ -71,4 +177,4 @@ private:
};
-#endif // ORTHOGONAL_MATRIX_HH
\ No newline at end of file
+#endif // ORTHOGONAL_MATRIX_HH
--
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