GetFEM  5.4.2
gmm_dense_sylvester.h
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30 ===========================================================================*/
31 
32 /** @file gmm_dense_sylvester.h
33  @author Yves Renard <[email protected]>
34  @date June 5, 2003.
35  @brief Sylvester equation solver.
36 */
37 #ifndef GMM_DENSE_SYLVESTER_H
38 #define GMM_DENSE_SYLVESTER_H
39 
40 #include "gmm_kernel.h"
41 
42 namespace gmm {
43 
44  /* ********************************************************************* */
45  /* Kronecker system matrix. */
46  /* ********************************************************************* */
47  template <typename MAT1, typename MAT2, typename MAT3>
48  void kron(const MAT1 &m1, const MAT2 &m2, const MAT3 &m3_,
49  bool init = true) {
50  MAT3 &m3 = const_cast<MAT3 &>(m3_);
51  size_type m = mat_nrows(m1), n = mat_ncols(m1);
52  size_type l = mat_nrows(m2), k = mat_ncols(m2);
53 
54  GMM_ASSERT2(mat_nrows(m3) == m*l && mat_ncols(m3) == n*k,
55  "dimensions mismatch");
56 
57  for (size_type i = 0; i < m; ++i)
58  for (size_type j = 0; j < m; ++j)
59  if (init)
60  gmm::copy(gmm::scaled(m2, m1(i,j)),
61  gmm::sub_matrix(m3, sub_interval(l*i, l),
62  sub_interval(k*j, k)));
63  else
64  gmm::add(gmm::scaled(m2, m1(i,j)),
65  gmm::sub_matrix(m3, sub_interval(l*i, l),
66  sub_interval(k*j, k)));
67  }
68 
69 
70  /* ********************************************************************* */
71  /* Copy a matrix into a vector. */
72  /* ********************************************************************* */
73 
74  template <typename MAT, typename VECT>
75  colmatrix_to_vector(const MAT &A, VECT &v, col_major) {
76  size_type m = mat_nrows(A), n = mat_ncols(A);
77  GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
78  for (size_type i = 0; i < n; ++i)
79  gmm::copy(mat_col(A, i), sub_vector(v, sub_interval(i*m, m)));
80  }
81 
82  template <typename MAT, typename VECT>
83  colmatrix_to_vector(const MAT &A, VECT &v, row_and_col)
84  { colmatrix_to_vector(A, v, col_major()); }
85 
86  template <typename MAT, typename VECT>
87  colmatrix_to_vector(const MAT &A, VECT &v, col_and_row)
88  { colmatrix_to_vector(A, v, col_major()); }
89 
90  template <typename MAT, typename VECT>
91  colmatrix_to_vector(const MAT &A, VECT &v, row_major) {
92  size_type m = mat_nrows(mat), n = mat_ncols(A);
93  GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
94  for (size_type i = 0; i < m; ++i)
95  gmm::copy(mat_row(A, i), sub_vector(v, sub_slice(i, n, m)));
96  }
97 
98  template <typename MAT, typename VECT> inline
99  colmatrix_to_vector(const MAT &A, const VECT &v_) {
100  VECT &v = const_cast<VECT &>(v_);
101  colmatrix_to_vector(A, v, typename linalg_traits<MAT>::sub_orientation());
102  }
103 
104 
105  /* ********************************************************************* */
106  /* Copy a vector into a matrix. */
107  /* ********************************************************************* */
108 
109  template <typename MAT, typename VECT>
110  vector_to_colmatrix(const VECT &v, MAT &A, col_major) {
111  size_type m = mat_nrows(A), n = mat_ncols(A);
112  GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
113  for (size_type i = 0; i < n; ++i)
114  gmm::copy(sub_vector(v, sub_interval(i*m, m)), mat_col(A, i));
115  }
116 
117  template <typename MAT, typename VECT>
118  vector_to_colmatrix(const VECT &v, MAT &A, row_and_col)
119  { vector_to_colmatrix(v, A, col_major()); }
120 
121  template <typename MAT, typename VECT>
122  vector_to_colmatrix(const VECT &v, MAT &A, col_and_row)
123  { vector_to_colmatrix(v, A, col_major()); }
124 
125  template <typename MAT, typename VECT>
126  vector_to_colmatrix(const VECT &v, MAT &A, row_major) {
127  size_type m = mat_nrows(mat), n = mat_ncols(A);
128  GMM_ASSERT2(m*n == vect_size(v), "dimensions mismatch");
129  for (size_type i = 0; i < m; ++i)
130  gmm::copy(sub_vector(v, sub_slice(i, n, m)), mat_row(A, i));
131  }
132 
133  template <typename MAT, typename VECT> inline
134  vector_to_colmatrix(const VECT &v, const MAT &A_) {
135  MAT &A = const_cast<MAT &>(A_);
136  vector_to_colmatrix(v, A, typename linalg_traits<MAT>::sub_orientation());
137  }
138 
139  /* ********************************************************************* */
140  /* Solve sylvester equation. */
141  /* ********************************************************************* */
142 
143  // very prohibitive solver, to be replaced ...
144  template <typename MAT1, typename MAT2, typename MAT3, typename MAT4 >
145  void sylvester(const MAT1 &m1, const MAT2 &m2, const MAT3 &m3,
146  const MAT4 &m4_) {
147  typedef typename linalg_traits<Mat>::value_type T;
148 
149  MAT3 &m4 = const_cast<MAT4 &>(m4_);
150  size_type m = mat_nrows(m1), n = mat_ncols(m1);
151  size_type l = mat_nrows(m2), k = mat_ncols(m2);
152 
153  GMM_ASSERT2(m == n && l == k && m == mat_nrows(m3) &&
154  l == mat_ncols(m3) && m == mat_nrows(m4) && l == mat_ncols(m4),
155  "dimensions mismatch");
156 
157  gmm::dense_matrix<T> akronb(m*l, m*l);
158  gmm::dense_matrix<T> idm(m, m), idl(l,l);
159  gmm::copy(identity_matrix(), idm);
160  gmm::copy(identity_matrix(), idl);
161  std::vector<T> x(m*l), c(m*l);
162 
163  kron(idl, m1, akronb);
164  kron(gmm::transposed(m2), idm, akronb, false);
165 
166  colmatrix_to_vector(m3, c);
167  lu_solve(akronb, c, x);
168  vector_to_colmatrix(x, m4);
169 
170  }
171 }
172 
173 #endif
174 
bgeot::size_type
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:49
gmm::lu_solve
void lu_solve(const DenseMatrix &LU, const Pvector &pvector, VectorX &x, const VectorB &b)
LU Solve : Solve equation Ax=b, given an LU factored matrix.
Definition: gmm_dense_lu.h:163
gmm_kernel.h
Include the base gmm files.