1 | // |
---|
2 | // Copyright (c) 2000-2002 |
---|
3 | // Joerg Walter, Mathias Koch |
---|
4 | // |
---|
5 | // Distributed under the Boost Software License, Version 1.0. (See |
---|
6 | // accompanying file LICENSE_1_0.txt or copy at |
---|
7 | // http://www.boost.org/LICENSE_1_0.txt) |
---|
8 | // |
---|
9 | // The authors gratefully acknowledge the support of |
---|
10 | // GeNeSys mbH & Co. KG in producing this work. |
---|
11 | // |
---|
12 | |
---|
13 | #ifndef _BOOST_UBLAS_LU_ |
---|
14 | #define _BOOST_UBLAS_LU_ |
---|
15 | |
---|
16 | #include <boost/numeric/ublas/operation.hpp> |
---|
17 | #include <boost/numeric/ublas/vector_proxy.hpp> |
---|
18 | #include <boost/numeric/ublas/matrix_proxy.hpp> |
---|
19 | #include <boost/numeric/ublas/vector.hpp> |
---|
20 | #include <boost/numeric/ublas/triangular.hpp> |
---|
21 | |
---|
22 | // LU factorizations in the spirit of LAPACK and Golub & van Loan |
---|
23 | |
---|
24 | namespace boost { namespace numeric { namespace ublas { |
---|
25 | |
---|
26 | /** \brief |
---|
27 | * |
---|
28 | * \tparam T |
---|
29 | * \tparam A |
---|
30 | */ |
---|
31 | template<class T = std::size_t, class A = unbounded_array<T> > |
---|
32 | class permutation_matrix: |
---|
33 | public vector<T, A> { |
---|
34 | public: |
---|
35 | typedef vector<T, A> vector_type; |
---|
36 | typedef typename vector_type::size_type size_type; |
---|
37 | |
---|
38 | // Construction and destruction |
---|
39 | BOOST_UBLAS_INLINE |
---|
40 | explicit |
---|
41 | permutation_matrix (size_type size): |
---|
42 | vector<T, A> (size) { |
---|
43 | for (size_type i = 0; i < size; ++ i) |
---|
44 | (*this) (i) = i; |
---|
45 | } |
---|
46 | BOOST_UBLAS_INLINE |
---|
47 | explicit |
---|
48 | permutation_matrix (const vector_type & init) |
---|
49 | : vector_type(init) |
---|
50 | { } |
---|
51 | BOOST_UBLAS_INLINE |
---|
52 | ~permutation_matrix () {} |
---|
53 | |
---|
54 | // Assignment |
---|
55 | BOOST_UBLAS_INLINE |
---|
56 | permutation_matrix &operator = (const permutation_matrix &m) { |
---|
57 | vector_type::operator = (m); |
---|
58 | return *this; |
---|
59 | } |
---|
60 | }; |
---|
61 | |
---|
62 | template<class PM, class MV> |
---|
63 | BOOST_UBLAS_INLINE |
---|
64 | void swap_rows (const PM &pm, MV &mv, vector_tag) { |
---|
65 | typedef typename PM::size_type size_type; |
---|
66 | typedef typename MV::value_type value_type; |
---|
67 | |
---|
68 | size_type size = pm.size (); |
---|
69 | for (size_type i = 0; i < size; ++ i) { |
---|
70 | if (i != pm (i)) |
---|
71 | std::swap (mv (i), mv (pm (i))); |
---|
72 | } |
---|
73 | } |
---|
74 | template<class PM, class MV> |
---|
75 | BOOST_UBLAS_INLINE |
---|
76 | void swap_rows (const PM &pm, MV &mv, matrix_tag) { |
---|
77 | typedef typename PM::size_type size_type; |
---|
78 | typedef typename MV::value_type value_type; |
---|
79 | |
---|
80 | size_type size = pm.size (); |
---|
81 | for (size_type i = 0; i < size; ++ i) { |
---|
82 | if (i != pm (i)) |
---|
83 | row (mv, i).swap (row (mv, pm (i))); |
---|
84 | } |
---|
85 | } |
---|
86 | // Dispatcher |
---|
87 | template<class PM, class MV> |
---|
88 | BOOST_UBLAS_INLINE |
---|
89 | void swap_rows (const PM &pm, MV &mv) { |
---|
90 | swap_rows (pm, mv, typename MV::type_category ()); |
---|
91 | } |
---|
92 | |
---|
93 | // LU factorization without pivoting |
---|
94 | template<class M> |
---|
95 | typename M::size_type lu_factorize (M &m) { |
---|
96 | typedef M matrix_type; |
---|
97 | typedef typename M::size_type size_type; |
---|
98 | typedef typename M::value_type value_type; |
---|
99 | |
---|
100 | #if BOOST_UBLAS_TYPE_CHECK |
---|
101 | matrix_type cm (m); |
---|
102 | #endif |
---|
103 | size_type singular = 0; |
---|
104 | size_type size1 = m.size1 (); |
---|
105 | size_type size2 = m.size2 (); |
---|
106 | size_type size = (std::min) (size1, size2); |
---|
107 | for (size_type i = 0; i < size; ++ i) { |
---|
108 | matrix_column<M> mci (column (m, i)); |
---|
109 | matrix_row<M> mri (row (m, i)); |
---|
110 | if (m (i, i) != value_type/*zero*/()) { |
---|
111 | value_type m_inv = value_type (1) / m (i, i); |
---|
112 | project (mci, range (i + 1, size1)) *= m_inv; |
---|
113 | } else if (singular == 0) { |
---|
114 | singular = i + 1; |
---|
115 | } |
---|
116 | project (m, range (i + 1, size1), range (i + 1, size2)).minus_assign ( |
---|
117 | outer_prod (project (mci, range (i + 1, size1)), |
---|
118 | project (mri, range (i + 1, size2)))); |
---|
119 | } |
---|
120 | #if BOOST_UBLAS_TYPE_CHECK |
---|
121 | BOOST_UBLAS_CHECK (singular != 0 || |
---|
122 | detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m), |
---|
123 | triangular_adaptor<matrix_type, upper> (m)), |
---|
124 | cm), internal_logic ()); |
---|
125 | #endif |
---|
126 | return singular; |
---|
127 | } |
---|
128 | |
---|
129 | // LU factorization with partial pivoting |
---|
130 | template<class M, class PM> |
---|
131 | typename M::size_type lu_factorize (M &m, PM &pm) { |
---|
132 | typedef M matrix_type; |
---|
133 | typedef typename M::size_type size_type; |
---|
134 | typedef typename M::value_type value_type; |
---|
135 | |
---|
136 | #if BOOST_UBLAS_TYPE_CHECK |
---|
137 | matrix_type cm (m); |
---|
138 | #endif |
---|
139 | size_type singular = 0; |
---|
140 | size_type size1 = m.size1 (); |
---|
141 | size_type size2 = m.size2 (); |
---|
142 | size_type size = (std::min) (size1, size2); |
---|
143 | for (size_type i = 0; i < size; ++ i) { |
---|
144 | matrix_column<M> mci (column (m, i)); |
---|
145 | matrix_row<M> mri (row (m, i)); |
---|
146 | size_type i_norm_inf = i + index_norm_inf (project (mci, range (i, size1))); |
---|
147 | BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ()); |
---|
148 | if (m (i_norm_inf, i) != value_type/*zero*/()) { |
---|
149 | if (i_norm_inf != i) { |
---|
150 | pm (i) = i_norm_inf; |
---|
151 | row (m, i_norm_inf).swap (mri); |
---|
152 | } else { |
---|
153 | BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ()); |
---|
154 | } |
---|
155 | value_type m_inv = value_type (1) / m (i, i); |
---|
156 | project (mci, range (i + 1, size1)) *= m_inv; |
---|
157 | } else if (singular == 0) { |
---|
158 | singular = i + 1; |
---|
159 | } |
---|
160 | project (m, range (i + 1, size1), range (i + 1, size2)).minus_assign ( |
---|
161 | outer_prod (project (mci, range (i + 1, size1)), |
---|
162 | project (mri, range (i + 1, size2)))); |
---|
163 | } |
---|
164 | #if BOOST_UBLAS_TYPE_CHECK |
---|
165 | swap_rows (pm, cm); |
---|
166 | BOOST_UBLAS_CHECK (singular != 0 || |
---|
167 | detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m), |
---|
168 | triangular_adaptor<matrix_type, upper> (m)), cm), internal_logic ()); |
---|
169 | #endif |
---|
170 | return singular; |
---|
171 | } |
---|
172 | |
---|
173 | template<class M, class PM> |
---|
174 | typename M::size_type axpy_lu_factorize (M &m, PM &pm) { |
---|
175 | typedef M matrix_type; |
---|
176 | typedef typename M::size_type size_type; |
---|
177 | typedef typename M::value_type value_type; |
---|
178 | typedef vector<value_type> vector_type; |
---|
179 | |
---|
180 | #if BOOST_UBLAS_TYPE_CHECK |
---|
181 | matrix_type cm (m); |
---|
182 | #endif |
---|
183 | size_type singular = 0; |
---|
184 | size_type size1 = m.size1 (); |
---|
185 | size_type size2 = m.size2 (); |
---|
186 | size_type size = (std::min) (size1, size2); |
---|
187 | #ifndef BOOST_UBLAS_LU_WITH_INPLACE_SOLVE |
---|
188 | matrix_type mr (m); |
---|
189 | mr.assign (zero_matrix<value_type> (size1, size2)); |
---|
190 | vector_type v (size1); |
---|
191 | for (size_type i = 0; i < size; ++ i) { |
---|
192 | matrix_range<matrix_type> lrr (project (mr, range (0, i), range (0, i))); |
---|
193 | vector_range<matrix_column<matrix_type> > urr (project (column (mr, i), range (0, i))); |
---|
194 | urr.assign (solve (lrr, project (column (m, i), range (0, i)), unit_lower_tag ())); |
---|
195 | project (v, range (i, size1)).assign ( |
---|
196 | project (column (m, i), range (i, size1)) - |
---|
197 | axpy_prod<vector_type> (project (mr, range (i, size1), range (0, i)), urr)); |
---|
198 | size_type i_norm_inf = i + index_norm_inf (project (v, range (i, size1))); |
---|
199 | BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ()); |
---|
200 | if (v (i_norm_inf) != value_type/*zero*/()) { |
---|
201 | if (i_norm_inf != i) { |
---|
202 | pm (i) = i_norm_inf; |
---|
203 | std::swap (v (i_norm_inf), v (i)); |
---|
204 | project (row (m, i_norm_inf), range (i + 1, size2)).swap (project (row (m, i), range (i + 1, size2))); |
---|
205 | } else { |
---|
206 | BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ()); |
---|
207 | } |
---|
208 | project (column (mr, i), range (i + 1, size1)).assign ( |
---|
209 | project (v, range (i + 1, size1)) / v (i)); |
---|
210 | if (i_norm_inf != i) { |
---|
211 | project (row (mr, i_norm_inf), range (0, i)).swap (project (row (mr, i), range (0, i))); |
---|
212 | } |
---|
213 | } else if (singular == 0) { |
---|
214 | singular = i + 1; |
---|
215 | } |
---|
216 | mr (i, i) = v (i); |
---|
217 | } |
---|
218 | m.assign (mr); |
---|
219 | #else |
---|
220 | matrix_type lr (m); |
---|
221 | matrix_type ur (m); |
---|
222 | lr.assign (identity_matrix<value_type> (size1, size2)); |
---|
223 | ur.assign (zero_matrix<value_type> (size1, size2)); |
---|
224 | vector_type v (size1); |
---|
225 | for (size_type i = 0; i < size; ++ i) { |
---|
226 | matrix_range<matrix_type> lrr (project (lr, range (0, i), range (0, i))); |
---|
227 | vector_range<matrix_column<matrix_type> > urr (project (column (ur, i), range (0, i))); |
---|
228 | urr.assign (project (column (m, i), range (0, i))); |
---|
229 | inplace_solve (lrr, urr, unit_lower_tag ()); |
---|
230 | project (v, range (i, size1)).assign ( |
---|
231 | project (column (m, i), range (i, size1)) - |
---|
232 | axpy_prod<vector_type> (project (lr, range (i, size1), range (0, i)), urr)); |
---|
233 | size_type i_norm_inf = i + index_norm_inf (project (v, range (i, size1))); |
---|
234 | BOOST_UBLAS_CHECK (i_norm_inf < size1, external_logic ()); |
---|
235 | if (v (i_norm_inf) != value_type/*zero*/()) { |
---|
236 | if (i_norm_inf != i) { |
---|
237 | pm (i) = i_norm_inf; |
---|
238 | std::swap (v (i_norm_inf), v (i)); |
---|
239 | project (row (m, i_norm_inf), range (i + 1, size2)).swap (project (row (m, i), range (i + 1, size2))); |
---|
240 | } else { |
---|
241 | BOOST_UBLAS_CHECK (pm (i) == i_norm_inf, external_logic ()); |
---|
242 | } |
---|
243 | project (column (lr, i), range (i + 1, size1)).assign ( |
---|
244 | project (v, range (i + 1, size1)) / v (i)); |
---|
245 | if (i_norm_inf != i) { |
---|
246 | project (row (lr, i_norm_inf), range (0, i)).swap (project (row (lr, i), range (0, i))); |
---|
247 | } |
---|
248 | } else if (singular == 0) { |
---|
249 | singular = i + 1; |
---|
250 | } |
---|
251 | ur (i, i) = v (i); |
---|
252 | } |
---|
253 | m.assign (triangular_adaptor<matrix_type, strict_lower> (lr) + |
---|
254 | triangular_adaptor<matrix_type, upper> (ur)); |
---|
255 | #endif |
---|
256 | #if BOOST_UBLAS_TYPE_CHECK |
---|
257 | swap_rows (pm, cm); |
---|
258 | BOOST_UBLAS_CHECK (singular != 0 || |
---|
259 | detail::expression_type_check (prod (triangular_adaptor<matrix_type, unit_lower> (m), |
---|
260 | triangular_adaptor<matrix_type, upper> (m)), cm), internal_logic ()); |
---|
261 | #endif |
---|
262 | return singular; |
---|
263 | } |
---|
264 | |
---|
265 | // LU substitution |
---|
266 | template<class M, class E> |
---|
267 | void lu_substitute (const M &m, vector_expression<E> &e) { |
---|
268 | typedef const M const_matrix_type; |
---|
269 | typedef vector<typename E::value_type> vector_type; |
---|
270 | |
---|
271 | #if BOOST_UBLAS_TYPE_CHECK |
---|
272 | vector_type cv1 (e); |
---|
273 | #endif |
---|
274 | inplace_solve (m, e, unit_lower_tag ()); |
---|
275 | #if BOOST_UBLAS_TYPE_CHECK |
---|
276 | BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, unit_lower> (m), e), cv1), internal_logic ()); |
---|
277 | vector_type cv2 (e); |
---|
278 | #endif |
---|
279 | inplace_solve (m, e, upper_tag ()); |
---|
280 | #if BOOST_UBLAS_TYPE_CHECK |
---|
281 | BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, upper> (m), e), cv2), internal_logic ()); |
---|
282 | #endif |
---|
283 | } |
---|
284 | template<class M, class E> |
---|
285 | void lu_substitute (const M &m, matrix_expression<E> &e) { |
---|
286 | typedef const M const_matrix_type; |
---|
287 | typedef matrix<typename E::value_type> matrix_type; |
---|
288 | |
---|
289 | #if BOOST_UBLAS_TYPE_CHECK |
---|
290 | matrix_type cm1 (e); |
---|
291 | #endif |
---|
292 | inplace_solve (m, e, unit_lower_tag ()); |
---|
293 | #if BOOST_UBLAS_TYPE_CHECK |
---|
294 | BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, unit_lower> (m), e), cm1), internal_logic ()); |
---|
295 | matrix_type cm2 (e); |
---|
296 | #endif |
---|
297 | inplace_solve (m, e, upper_tag ()); |
---|
298 | #if BOOST_UBLAS_TYPE_CHECK |
---|
299 | BOOST_UBLAS_CHECK (detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, upper> (m), e), cm2), internal_logic ()); |
---|
300 | #endif |
---|
301 | } |
---|
302 | template<class M, class PMT, class PMA, class MV> |
---|
303 | void lu_substitute (const M &m, const permutation_matrix<PMT, PMA> &pm, MV &mv) { |
---|
304 | swap_rows (pm, mv); |
---|
305 | lu_substitute (m, mv); |
---|
306 | } |
---|
307 | template<class E, class M> |
---|
308 | void lu_substitute (vector_expression<E> &e, const M &m) { |
---|
309 | typedef const M const_matrix_type; |
---|
310 | typedef vector<typename E::value_type> vector_type; |
---|
311 | |
---|
312 | #if BOOST_UBLAS_TYPE_CHECK |
---|
313 | vector_type cv1 (e); |
---|
314 | #endif |
---|
315 | inplace_solve (e, m, upper_tag ()); |
---|
316 | #if BOOST_UBLAS_TYPE_CHECK |
---|
317 | BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, upper> (m)), cv1), internal_logic ()); |
---|
318 | vector_type cv2 (e); |
---|
319 | #endif |
---|
320 | inplace_solve (e, m, unit_lower_tag ()); |
---|
321 | #if BOOST_UBLAS_TYPE_CHECK |
---|
322 | BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, unit_lower> (m)), cv2), internal_logic ()); |
---|
323 | #endif |
---|
324 | } |
---|
325 | template<class E, class M> |
---|
326 | void lu_substitute (matrix_expression<E> &e, const M &m) { |
---|
327 | typedef const M const_matrix_type; |
---|
328 | typedef matrix<typename E::value_type> matrix_type; |
---|
329 | |
---|
330 | #if BOOST_UBLAS_TYPE_CHECK |
---|
331 | matrix_type cm1 (e); |
---|
332 | #endif |
---|
333 | inplace_solve (e, m, upper_tag ()); |
---|
334 | #if BOOST_UBLAS_TYPE_CHECK |
---|
335 | BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, upper> (m)), cm1), internal_logic ()); |
---|
336 | matrix_type cm2 (e); |
---|
337 | #endif |
---|
338 | inplace_solve (e, m, unit_lower_tag ()); |
---|
339 | #if BOOST_UBLAS_TYPE_CHECK |
---|
340 | BOOST_UBLAS_CHECK (detail::expression_type_check (prod (e, triangular_adaptor<const_matrix_type, unit_lower> (m)), cm2), internal_logic ()); |
---|
341 | #endif |
---|
342 | } |
---|
343 | template<class MV, class M, class PMT, class PMA> |
---|
344 | void lu_substitute (MV &mv, const M &m, const permutation_matrix<PMT, PMA> &pm) { |
---|
345 | swap_rows (pm, mv); |
---|
346 | lu_substitute (mv, m); |
---|
347 | } |
---|
348 | |
---|
349 | }}} |
---|
350 | |
---|
351 | #endif |
---|