dune-grid  2.7.1
algebra.hh
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1 // -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2 // vi: set et ts=4 sw=2 sts=2:
3 #ifndef DUNE_ALBERTA_ALGEBRA_HH
4 #define DUNE_ALBERTA_ALGEBRA_HH
5 
6 #include <dune/common/fvector.hh>
7 #include <dune/common/fmatrix.hh>
8 
9 namespace Dune
10 {
11 
12  namespace Alberta
13  {
14 
15  template< class K >
16  inline static FieldVector< K, 3 >
17  vectorProduct ( const FieldVector< K, 3 > &u, const FieldVector< K, 3 > &v )
18  {
19  FieldVector< K, 3 > w;
20  w[ 0 ] = u[ 1 ] * v[ 2 ] - u[ 2 ] * v[ 1 ];
21  w[ 1 ] = u[ 2 ] * v[ 0 ] - u[ 0 ] * v[ 2 ];
22  w[ 2 ] = u[ 0 ] * v[ 1 ] - u[ 1 ] * v[ 0 ];
23  return w;
24  }
25 
26 
27  template< class K, int m >
28  inline static K determinant ( const FieldMatrix< K, 0, m > &matrix )
29  {
30  return K( 1 );
31  }
32 
33  template< class K >
34  inline static K determinant ( const FieldMatrix< K, 1, 1 > &matrix )
35  {
36  return matrix[ 0 ][ 0 ];
37  }
38 
39  template< class K, int m >
40  inline static K determinant ( const FieldMatrix< K, 1, m > &matrix )
41  {
42  K sum = matrix[ 0 ][ 0 ] * matrix[ 0 ][ 0 ];
43  for( int i = 1; i < m; ++i )
44  sum += matrix[ 0 ][ i ] * matrix[ 0 ][ i ];
45  return sqrt( sum );
46  }
47 
48  template< class K >
49  inline static K determinant ( const FieldMatrix< K, 2, 2 > &matrix )
50  {
51  return matrix[ 0 ][ 0 ] * matrix[ 1 ][ 1 ] - matrix[ 0 ][ 1 ] * matrix[ 1 ][ 0 ];
52  }
53 
54  template< class K >
55  inline static K determinant ( const FieldMatrix< K, 2, 3 > &matrix )
56  {
57  return vectorProduct( matrix[ 0 ], matrix[ 1 ] ).two_norm();
58  }
59 
60  template< class K, int m >
61  inline static K determinant ( const FieldMatrix< K, 2, m > &matrix )
62  {
63  const K tmpA = matrix[ 0 ].two_norm2();
64  const K tmpB = matrix[ 1 ].two_norm2();
65  const K tmpC = matrix[ 0 ] * matrix[ 1 ];
66  return sqrt( tmpA * tmpB - tmpC * tmpC );
67  }
68 
69  template< class K >
70  inline static K determinant ( const FieldMatrix< K, 3, 3 > &matrix )
71  {
72  return matrix[ 0 ] * vectorProduct( matrix[ 1 ], matrix[ 2 ] );
73  }
74 
75 
76  template< class K, int m >
77  inline static K invert ( const FieldMatrix< K, 0, m > &matrix,
78  FieldMatrix< K, m, 0 > &inverse )
79  {
80  return K( 1 );
81  }
82 
83  template< class K >
84  inline static K invert ( const FieldMatrix< K, 1, 1 > &matrix,
85  FieldMatrix< K, 1, 1 > &inverse )
86  {
87  inverse[ 0 ][ 0 ] = K( 1 ) / matrix[ 0 ][ 0 ];
88  return matrix[ 0 ][ 0 ];
89  }
90 
91  template< class K, int m >
92  inline static K invert ( const FieldMatrix< K, 1, m > &matrix,
93  FieldMatrix< K, m, 1 > &inverse )
94  {
95  K detSqr = matrix[ 0 ].two_norm2();
96  K invDetSqr = K( 1 ) / detSqr;
97  for( int i = 0; i < m; ++i )
98  inverse[ i ][ 0 ] = invDetSqr * matrix[ 0 ][ i ];
99  return sqrt( detSqr );
100  }
101 
102  template< class K >
103  inline static K invert ( const FieldMatrix< K, 2, 2 > &matrix,
104  FieldMatrix< K, 2, 2 > &inverse )
105  {
106  K det = determinant( matrix );
107  K invDet = K( 1 ) / det;
108  inverse[ 0 ][ 0 ] = invDet * matrix[ 1 ][ 1 ];
109  inverse[ 0 ][ 1 ] = - invDet * matrix[ 0 ][ 1 ];
110  inverse[ 1 ][ 0 ] = - invDet * matrix[ 1 ][ 0 ];
111  inverse[ 1 ][ 1 ] = invDet * matrix[ 0 ][ 0 ];
112  return det;
113  }
114 
115  template< class K, int m >
116  inline static K invert ( const FieldMatrix< K, 2, m > &matrix,
117  FieldMatrix< K, m, 2 > &inverse )
118  {
119  const K tmpA = matrix[ 0 ].two_norm2();
120  const K tmpB = matrix[ 1 ].two_norm2();
121  const K tmpC = matrix[ 0 ] * matrix[ 1 ];
122  const K detSqr = tmpA * tmpB - tmpC * tmpC;
123  const K invDetSqr = K( 1 ) / detSqr;
124  for( int i = 0; i < m; ++i )
125  {
126  inverse[ i ][ 0 ] = invDetSqr * (tmpB * matrix[ 0 ][ i ] - tmpC * matrix[ 1 ][ i ]);
127  inverse[ i ][ 1 ] = invDetSqr * (tmpA * matrix[ 1 ][ i ] - tmpC * matrix[ 0 ][ i ]);
128  }
129  return sqrt( detSqr );
130  }
131 
132  template< class K >
133  inline static K invert ( const FieldMatrix< K, 3, 3 > &matrix,
134  FieldMatrix< K, 3, 3 > &inverse )
135  {
136  return FMatrixHelp::invertMatrix( matrix, inverse );
137  }
138  }
139 
140 }
141 
142 #endif // #ifndef DUNE_ALBERTA_ALGEBRA_HH
Include standard header files.
Definition: agrid.hh:59
static K determinant(const FieldMatrix< K, 0, m > &matrix)
Definition: algebra.hh:28
static K invert(const FieldMatrix< K, 0, m > &matrix, FieldMatrix< K, m, 0 > &inverse)
Definition: algebra.hh:77
static FieldVector< K, 3 > vectorProduct(const FieldVector< K, 3 > &u, const FieldVector< K, 3 > &v)
Definition: algebra.hh:17