Make symmetrixMatrix isometric

- We have to add the factor 1./sqrt(2) in read access for off-diagonal entries
- The random write access is removed
- As replacement a setEntry method is provided that ensures isometry

dune/fufem/symmetricmatrix.hh

@@ -50,32 +50,34 @@ public:
     return *this;
   }
 
-  /** \brief Matrix style random read/write access to components
+  /** \brief Random write access to components
    *  \param i line index
    *  \param j column index
-   * \note You need to know what you are doing:  You can only access the lower
-   * left triangular submatrix using this methods.  It requires i>=j.
+   *  The off-diagonal entries are scaled by sqrt(2) to ensure isometry
    */
-  T& operator() (int i, int j)
+  void setEntry(int i, int j, const T& entry)
   {
-    if( i >= j )
-      return data_[i*(i+1)/2+j];
-    else
-      return data_[j*(j+1)/2+i];
+    if( i > j )
+      data_[i*(i+1)/2+j] = std::sqrt(2.) * entry;
+    else if ( i < j )
+      data_[j*(j+1)/2+i] = std::sqrt(2.) * entry;
+    else // ( i == j )
+      data_[i*(i+1)/2+i] = entry;
   }
 
   /** \brief Matrix style random read access to components
    *  \param i line index
    *  \param j column index
-   * \note You need to know what you are doing:  You can only access the lower
-   * left triangular submatrix using this methods.  It requires i>=j.
+   *  The off-diagonal entries are scaled by 1/sqrt(2) to ensure isometry
    */
-  const T& operator() (int i, int j) const
+  const T operator() (int i, int j) const
   {
-    if( i >= j )
-      return data_[i*(i+1)/2+j];
-    else
-      return data_[j*(j+1)/2+i];
+    if( i > j )
+      return 1./std::sqrt(2.) * data_[i*(i+1)/2+j];
+    else if ( i < j )
+      return 1./std::sqrt(2.) * data_[j*(j+1)/2+i];
+    else // ( i == j )
+      return data_[i*(i+1)/2+i];
   }
 
   T energyScalarProduct (const FieldVector<T,N>& v1, const FieldVector<T,N>& v2) const
@@ -92,14 +94,11 @@ public:
     data_.axpy(a,other.data_);
   }
 
-  /** \brief Compute the Frobenius norm of the matrix */
+  /** \brief Compute the Frobenius norm of the matrix
+  *   Make use the isometry */
   T frobenius_norm2() const
   {
-    T result = 0;
-    for (size_t i=0; i<N; ++i)
-      for (size_t j=0; j<N; ++j)
-        result += operator()(i,j)*operator()(i,j);
-    return result;
+    data_.two_norm2();
   }
 
   /** \brief Compute the Frobenius norm of the matrix */