1 | // This file is part of Eigen, a lightweight C++ template library
|
---|
2 | // for linear algebra.
|
---|
3 | //
|
---|
4 | // Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
|
---|
5 | // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
|
---|
6 | //
|
---|
7 | // This Source Code Form is subject to the terms of the Mozilla
|
---|
8 | // Public License v. 2.0. If a copy of the MPL was not distributed
|
---|
9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
---|
10 |
|
---|
11 | #ifndef EIGEN_PARTIALLU_H
|
---|
12 | #define EIGEN_PARTIALLU_H
|
---|
13 |
|
---|
14 | namespace Eigen {
|
---|
15 |
|
---|
16 | /** \ingroup LU_Module
|
---|
17 | *
|
---|
18 | * \class PartialPivLU
|
---|
19 | *
|
---|
20 | * \brief LU decomposition of a matrix with partial pivoting, and related features
|
---|
21 | *
|
---|
22 | * \param MatrixType the type of the matrix of which we are computing the LU decomposition
|
---|
23 | *
|
---|
24 | * This class represents a LU decomposition of a \b square \b invertible matrix, with partial pivoting: the matrix A
|
---|
25 | * is decomposed as A = PLU where L is unit-lower-triangular, U is upper-triangular, and P
|
---|
26 | * is a permutation matrix.
|
---|
27 | *
|
---|
28 | * Typically, partial pivoting LU decomposition is only considered numerically stable for square invertible
|
---|
29 | * matrices. Thus LAPACK's dgesv and dgesvx require the matrix to be square and invertible. The present class
|
---|
30 | * does the same. It will assert that the matrix is square, but it won't (actually it can't) check that the
|
---|
31 | * matrix is invertible: it is your task to check that you only use this decomposition on invertible matrices.
|
---|
32 | *
|
---|
33 | * The guaranteed safe alternative, working for all matrices, is the full pivoting LU decomposition, provided
|
---|
34 | * by class FullPivLU.
|
---|
35 | *
|
---|
36 | * This is \b not a rank-revealing LU decomposition. Many features are intentionally absent from this class,
|
---|
37 | * such as rank computation. If you need these features, use class FullPivLU.
|
---|
38 | *
|
---|
39 | * This LU decomposition is suitable to invert invertible matrices. It is what MatrixBase::inverse() uses
|
---|
40 | * in the general case.
|
---|
41 | * On the other hand, it is \b not suitable to determine whether a given matrix is invertible.
|
---|
42 | *
|
---|
43 | * The data of the LU decomposition can be directly accessed through the methods matrixLU(), permutationP().
|
---|
44 | *
|
---|
45 | * \sa MatrixBase::partialPivLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class FullPivLU
|
---|
46 | */
|
---|
47 | template<typename _MatrixType> class PartialPivLU
|
---|
48 | {
|
---|
49 | public:
|
---|
50 |
|
---|
51 | typedef _MatrixType MatrixType;
|
---|
52 | enum {
|
---|
53 | RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
---|
54 | ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
---|
55 | Options = MatrixType::Options,
|
---|
56 | MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
---|
57 | MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
|
---|
58 | };
|
---|
59 | typedef typename MatrixType::Scalar Scalar;
|
---|
60 | typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
|
---|
61 | typedef typename internal::traits<MatrixType>::StorageKind StorageKind;
|
---|
62 | typedef typename MatrixType::Index Index;
|
---|
63 | typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
|
---|
64 | typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
|
---|
65 |
|
---|
66 |
|
---|
67 | /**
|
---|
68 | * \brief Default Constructor.
|
---|
69 | *
|
---|
70 | * The default constructor is useful in cases in which the user intends to
|
---|
71 | * perform decompositions via PartialPivLU::compute(const MatrixType&).
|
---|
72 | */
|
---|
73 | PartialPivLU();
|
---|
74 |
|
---|
75 | /** \brief Default Constructor with memory preallocation
|
---|
76 | *
|
---|
77 | * Like the default constructor but with preallocation of the internal data
|
---|
78 | * according to the specified problem \a size.
|
---|
79 | * \sa PartialPivLU()
|
---|
80 | */
|
---|
81 | PartialPivLU(Index size);
|
---|
82 |
|
---|
83 | /** Constructor.
|
---|
84 | *
|
---|
85 | * \param matrix the matrix of which to compute the LU decomposition.
|
---|
86 | *
|
---|
87 | * \warning The matrix should have full rank (e.g. if it's square, it should be invertible).
|
---|
88 | * If you need to deal with non-full rank, use class FullPivLU instead.
|
---|
89 | */
|
---|
90 | PartialPivLU(const MatrixType& matrix);
|
---|
91 |
|
---|
92 | PartialPivLU& compute(const MatrixType& matrix);
|
---|
93 |
|
---|
94 | /** \returns the LU decomposition matrix: the upper-triangular part is U, the
|
---|
95 | * unit-lower-triangular part is L (at least for square matrices; in the non-square
|
---|
96 | * case, special care is needed, see the documentation of class FullPivLU).
|
---|
97 | *
|
---|
98 | * \sa matrixL(), matrixU()
|
---|
99 | */
|
---|
100 | inline const MatrixType& matrixLU() const
|
---|
101 | {
|
---|
102 | eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
|
---|
103 | return m_lu;
|
---|
104 | }
|
---|
105 |
|
---|
106 | /** \returns the permutation matrix P.
|
---|
107 | */
|
---|
108 | inline const PermutationType& permutationP() const
|
---|
109 | {
|
---|
110 | eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
|
---|
111 | return m_p;
|
---|
112 | }
|
---|
113 |
|
---|
114 | /** This method returns the solution x to the equation Ax=b, where A is the matrix of which
|
---|
115 | * *this is the LU decomposition.
|
---|
116 | *
|
---|
117 | * \param b the right-hand-side of the equation to solve. Can be a vector or a matrix,
|
---|
118 | * the only requirement in order for the equation to make sense is that
|
---|
119 | * b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.
|
---|
120 | *
|
---|
121 | * \returns the solution.
|
---|
122 | *
|
---|
123 | * Example: \include PartialPivLU_solve.cpp
|
---|
124 | * Output: \verbinclude PartialPivLU_solve.out
|
---|
125 | *
|
---|
126 | * Since this PartialPivLU class assumes anyway that the matrix A is invertible, the solution
|
---|
127 | * theoretically exists and is unique regardless of b.
|
---|
128 | *
|
---|
129 | * \sa TriangularView::solve(), inverse(), computeInverse()
|
---|
130 | */
|
---|
131 | template<typename Rhs>
|
---|
132 | inline const internal::solve_retval<PartialPivLU, Rhs>
|
---|
133 | solve(const MatrixBase<Rhs>& b) const
|
---|
134 | {
|
---|
135 | eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
|
---|
136 | return internal::solve_retval<PartialPivLU, Rhs>(*this, b.derived());
|
---|
137 | }
|
---|
138 |
|
---|
139 | /** \returns the inverse of the matrix of which *this is the LU decomposition.
|
---|
140 | *
|
---|
141 | * \warning The matrix being decomposed here is assumed to be invertible. If you need to check for
|
---|
142 | * invertibility, use class FullPivLU instead.
|
---|
143 | *
|
---|
144 | * \sa MatrixBase::inverse(), LU::inverse()
|
---|
145 | */
|
---|
146 | inline const internal::solve_retval<PartialPivLU,typename MatrixType::IdentityReturnType> inverse() const
|
---|
147 | {
|
---|
148 | eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
|
---|
149 | return internal::solve_retval<PartialPivLU,typename MatrixType::IdentityReturnType>
|
---|
150 | (*this, MatrixType::Identity(m_lu.rows(), m_lu.cols()));
|
---|
151 | }
|
---|
152 |
|
---|
153 | /** \returns the determinant of the matrix of which
|
---|
154 | * *this is the LU decomposition. It has only linear complexity
|
---|
155 | * (that is, O(n) where n is the dimension of the square matrix)
|
---|
156 | * as the LU decomposition has already been computed.
|
---|
157 | *
|
---|
158 | * \note For fixed-size matrices of size up to 4, MatrixBase::determinant() offers
|
---|
159 | * optimized paths.
|
---|
160 | *
|
---|
161 | * \warning a determinant can be very big or small, so for matrices
|
---|
162 | * of large enough dimension, there is a risk of overflow/underflow.
|
---|
163 | *
|
---|
164 | * \sa MatrixBase::determinant()
|
---|
165 | */
|
---|
166 | typename internal::traits<MatrixType>::Scalar determinant() const;
|
---|
167 |
|
---|
168 | MatrixType reconstructedMatrix() const;
|
---|
169 |
|
---|
170 | inline Index rows() const { return m_lu.rows(); }
|
---|
171 | inline Index cols() const { return m_lu.cols(); }
|
---|
172 |
|
---|
173 | protected:
|
---|
174 |
|
---|
175 | static void check_template_parameters()
|
---|
176 | {
|
---|
177 | EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
|
---|
178 | }
|
---|
179 |
|
---|
180 | MatrixType m_lu;
|
---|
181 | PermutationType m_p;
|
---|
182 | TranspositionType m_rowsTranspositions;
|
---|
183 | Index m_det_p;
|
---|
184 | bool m_isInitialized;
|
---|
185 | };
|
---|
186 |
|
---|
187 | template<typename MatrixType>
|
---|
188 | PartialPivLU<MatrixType>::PartialPivLU()
|
---|
189 | : m_lu(),
|
---|
190 | m_p(),
|
---|
191 | m_rowsTranspositions(),
|
---|
192 | m_det_p(0),
|
---|
193 | m_isInitialized(false)
|
---|
194 | {
|
---|
195 | }
|
---|
196 |
|
---|
197 | template<typename MatrixType>
|
---|
198 | PartialPivLU<MatrixType>::PartialPivLU(Index size)
|
---|
199 | : m_lu(size, size),
|
---|
200 | m_p(size),
|
---|
201 | m_rowsTranspositions(size),
|
---|
202 | m_det_p(0),
|
---|
203 | m_isInitialized(false)
|
---|
204 | {
|
---|
205 | }
|
---|
206 |
|
---|
207 | template<typename MatrixType>
|
---|
208 | PartialPivLU<MatrixType>::PartialPivLU(const MatrixType& matrix)
|
---|
209 | : m_lu(matrix.rows(), matrix.rows()),
|
---|
210 | m_p(matrix.rows()),
|
---|
211 | m_rowsTranspositions(matrix.rows()),
|
---|
212 | m_det_p(0),
|
---|
213 | m_isInitialized(false)
|
---|
214 | {
|
---|
215 | compute(matrix);
|
---|
216 | }
|
---|
217 |
|
---|
218 | namespace internal {
|
---|
219 |
|
---|
220 | /** \internal This is the blocked version of fullpivlu_unblocked() */
|
---|
221 | template<typename Scalar, int StorageOrder, typename PivIndex>
|
---|
222 | struct partial_lu_impl
|
---|
223 | {
|
---|
224 | // FIXME add a stride to Map, so that the following mapping becomes easier,
|
---|
225 | // another option would be to create an expression being able to automatically
|
---|
226 | // warp any Map, Matrix, and Block expressions as a unique type, but since that's exactly
|
---|
227 | // a Map + stride, why not adding a stride to Map, and convenient ctors from a Matrix,
|
---|
228 | // and Block.
|
---|
229 | typedef Map<Matrix<Scalar, Dynamic, Dynamic, StorageOrder> > MapLU;
|
---|
230 | typedef Block<MapLU, Dynamic, Dynamic> MatrixType;
|
---|
231 | typedef Block<MatrixType,Dynamic,Dynamic> BlockType;
|
---|
232 | typedef typename MatrixType::RealScalar RealScalar;
|
---|
233 | typedef typename MatrixType::Index Index;
|
---|
234 |
|
---|
235 | /** \internal performs the LU decomposition in-place of the matrix \a lu
|
---|
236 | * using an unblocked algorithm.
|
---|
237 | *
|
---|
238 | * In addition, this function returns the row transpositions in the
|
---|
239 | * vector \a row_transpositions which must have a size equal to the number
|
---|
240 | * of columns of the matrix \a lu, and an integer \a nb_transpositions
|
---|
241 | * which returns the actual number of transpositions.
|
---|
242 | *
|
---|
243 | * \returns The index of the first pivot which is exactly zero if any, or a negative number otherwise.
|
---|
244 | */
|
---|
245 | static Index unblocked_lu(MatrixType& lu, PivIndex* row_transpositions, PivIndex& nb_transpositions)
|
---|
246 | {
|
---|
247 | const Index rows = lu.rows();
|
---|
248 | const Index cols = lu.cols();
|
---|
249 | const Index size = (std::min)(rows,cols);
|
---|
250 | nb_transpositions = 0;
|
---|
251 | Index first_zero_pivot = -1;
|
---|
252 | for(Index k = 0; k < size; ++k)
|
---|
253 | {
|
---|
254 | Index rrows = rows-k-1;
|
---|
255 | Index rcols = cols-k-1;
|
---|
256 |
|
---|
257 | Index row_of_biggest_in_col;
|
---|
258 | RealScalar biggest_in_corner
|
---|
259 | = lu.col(k).tail(rows-k).cwiseAbs().maxCoeff(&row_of_biggest_in_col);
|
---|
260 | row_of_biggest_in_col += k;
|
---|
261 |
|
---|
262 | row_transpositions[k] = PivIndex(row_of_biggest_in_col);
|
---|
263 |
|
---|
264 | if(biggest_in_corner != RealScalar(0))
|
---|
265 | {
|
---|
266 | if(k != row_of_biggest_in_col)
|
---|
267 | {
|
---|
268 | lu.row(k).swap(lu.row(row_of_biggest_in_col));
|
---|
269 | ++nb_transpositions;
|
---|
270 | }
|
---|
271 |
|
---|
272 | // FIXME shall we introduce a safe quotient expression in cas 1/lu.coeff(k,k)
|
---|
273 | // overflow but not the actual quotient?
|
---|
274 | lu.col(k).tail(rrows) /= lu.coeff(k,k);
|
---|
275 | }
|
---|
276 | else if(first_zero_pivot==-1)
|
---|
277 | {
|
---|
278 | // the pivot is exactly zero, we record the index of the first pivot which is exactly 0,
|
---|
279 | // and continue the factorization such we still have A = PLU
|
---|
280 | first_zero_pivot = k;
|
---|
281 | }
|
---|
282 |
|
---|
283 | if(k<rows-1)
|
---|
284 | lu.bottomRightCorner(rrows,rcols).noalias() -= lu.col(k).tail(rrows) * lu.row(k).tail(rcols);
|
---|
285 | }
|
---|
286 | return first_zero_pivot;
|
---|
287 | }
|
---|
288 |
|
---|
289 | /** \internal performs the LU decomposition in-place of the matrix represented
|
---|
290 | * by the variables \a rows, \a cols, \a lu_data, and \a lu_stride using a
|
---|
291 | * recursive, blocked algorithm.
|
---|
292 | *
|
---|
293 | * In addition, this function returns the row transpositions in the
|
---|
294 | * vector \a row_transpositions which must have a size equal to the number
|
---|
295 | * of columns of the matrix \a lu, and an integer \a nb_transpositions
|
---|
296 | * which returns the actual number of transpositions.
|
---|
297 | *
|
---|
298 | * \returns The index of the first pivot which is exactly zero if any, or a negative number otherwise.
|
---|
299 | *
|
---|
300 | * \note This very low level interface using pointers, etc. is to:
|
---|
301 | * 1 - reduce the number of instanciations to the strict minimum
|
---|
302 | * 2 - avoid infinite recursion of the instanciations with Block<Block<Block<...> > >
|
---|
303 | */
|
---|
304 | static Index blocked_lu(Index rows, Index cols, Scalar* lu_data, Index luStride, PivIndex* row_transpositions, PivIndex& nb_transpositions, Index maxBlockSize=256)
|
---|
305 | {
|
---|
306 | MapLU lu1(lu_data,StorageOrder==RowMajor?rows:luStride,StorageOrder==RowMajor?luStride:cols);
|
---|
307 | MatrixType lu(lu1,0,0,rows,cols);
|
---|
308 |
|
---|
309 | const Index size = (std::min)(rows,cols);
|
---|
310 |
|
---|
311 | // if the matrix is too small, no blocking:
|
---|
312 | if(size<=16)
|
---|
313 | {
|
---|
314 | return unblocked_lu(lu, row_transpositions, nb_transpositions);
|
---|
315 | }
|
---|
316 |
|
---|
317 | // automatically adjust the number of subdivisions to the size
|
---|
318 | // of the matrix so that there is enough sub blocks:
|
---|
319 | Index blockSize;
|
---|
320 | {
|
---|
321 | blockSize = size/8;
|
---|
322 | blockSize = (blockSize/16)*16;
|
---|
323 | blockSize = (std::min)((std::max)(blockSize,Index(8)), maxBlockSize);
|
---|
324 | }
|
---|
325 |
|
---|
326 | nb_transpositions = 0;
|
---|
327 | Index first_zero_pivot = -1;
|
---|
328 | for(Index k = 0; k < size; k+=blockSize)
|
---|
329 | {
|
---|
330 | Index bs = (std::min)(size-k,blockSize); // actual size of the block
|
---|
331 | Index trows = rows - k - bs; // trailing rows
|
---|
332 | Index tsize = size - k - bs; // trailing size
|
---|
333 |
|
---|
334 | // partition the matrix:
|
---|
335 | // A00 | A01 | A02
|
---|
336 | // lu = A_0 | A_1 | A_2 = A10 | A11 | A12
|
---|
337 | // A20 | A21 | A22
|
---|
338 | BlockType A_0(lu,0,0,rows,k);
|
---|
339 | BlockType A_2(lu,0,k+bs,rows,tsize);
|
---|
340 | BlockType A11(lu,k,k,bs,bs);
|
---|
341 | BlockType A12(lu,k,k+bs,bs,tsize);
|
---|
342 | BlockType A21(lu,k+bs,k,trows,bs);
|
---|
343 | BlockType A22(lu,k+bs,k+bs,trows,tsize);
|
---|
344 |
|
---|
345 | PivIndex nb_transpositions_in_panel;
|
---|
346 | // recursively call the blocked LU algorithm on [A11^T A21^T]^T
|
---|
347 | // with a very small blocking size:
|
---|
348 | Index ret = blocked_lu(trows+bs, bs, &lu.coeffRef(k,k), luStride,
|
---|
349 | row_transpositions+k, nb_transpositions_in_panel, 16);
|
---|
350 | if(ret>=0 && first_zero_pivot==-1)
|
---|
351 | first_zero_pivot = k+ret;
|
---|
352 |
|
---|
353 | nb_transpositions += nb_transpositions_in_panel;
|
---|
354 | // update permutations and apply them to A_0
|
---|
355 | for(Index i=k; i<k+bs; ++i)
|
---|
356 | {
|
---|
357 | Index piv = (row_transpositions[i] += k);
|
---|
358 | A_0.row(i).swap(A_0.row(piv));
|
---|
359 | }
|
---|
360 |
|
---|
361 | if(trows)
|
---|
362 | {
|
---|
363 | // apply permutations to A_2
|
---|
364 | for(Index i=k;i<k+bs; ++i)
|
---|
365 | A_2.row(i).swap(A_2.row(row_transpositions[i]));
|
---|
366 |
|
---|
367 | // A12 = A11^-1 A12
|
---|
368 | A11.template triangularView<UnitLower>().solveInPlace(A12);
|
---|
369 |
|
---|
370 | A22.noalias() -= A21 * A12;
|
---|
371 | }
|
---|
372 | }
|
---|
373 | return first_zero_pivot;
|
---|
374 | }
|
---|
375 | };
|
---|
376 |
|
---|
377 | /** \internal performs the LU decomposition with partial pivoting in-place.
|
---|
378 | */
|
---|
379 | template<typename MatrixType, typename TranspositionType>
|
---|
380 | void partial_lu_inplace(MatrixType& lu, TranspositionType& row_transpositions, typename TranspositionType::Index& nb_transpositions)
|
---|
381 | {
|
---|
382 | eigen_assert(lu.cols() == row_transpositions.size());
|
---|
383 | eigen_assert((&row_transpositions.coeffRef(1)-&row_transpositions.coeffRef(0)) == 1);
|
---|
384 |
|
---|
385 | partial_lu_impl
|
---|
386 | <typename MatrixType::Scalar, MatrixType::Flags&RowMajorBit?RowMajor:ColMajor, typename TranspositionType::Index>
|
---|
387 | ::blocked_lu(lu.rows(), lu.cols(), &lu.coeffRef(0,0), lu.outerStride(), &row_transpositions.coeffRef(0), nb_transpositions);
|
---|
388 | }
|
---|
389 |
|
---|
390 | } // end namespace internal
|
---|
391 |
|
---|
392 | template<typename MatrixType>
|
---|
393 | PartialPivLU<MatrixType>& PartialPivLU<MatrixType>::compute(const MatrixType& matrix)
|
---|
394 | {
|
---|
395 | check_template_parameters();
|
---|
396 |
|
---|
397 | // the row permutation is stored as int indices, so just to be sure:
|
---|
398 | eigen_assert(matrix.rows()<NumTraits<int>::highest());
|
---|
399 |
|
---|
400 | m_lu = matrix;
|
---|
401 |
|
---|
402 | eigen_assert(matrix.rows() == matrix.cols() && "PartialPivLU is only for square (and moreover invertible) matrices");
|
---|
403 | const Index size = matrix.rows();
|
---|
404 |
|
---|
405 | m_rowsTranspositions.resize(size);
|
---|
406 |
|
---|
407 | typename TranspositionType::Index nb_transpositions;
|
---|
408 | internal::partial_lu_inplace(m_lu, m_rowsTranspositions, nb_transpositions);
|
---|
409 | m_det_p = (nb_transpositions%2) ? -1 : 1;
|
---|
410 |
|
---|
411 | m_p = m_rowsTranspositions;
|
---|
412 |
|
---|
413 | m_isInitialized = true;
|
---|
414 | return *this;
|
---|
415 | }
|
---|
416 |
|
---|
417 | template<typename MatrixType>
|
---|
418 | typename internal::traits<MatrixType>::Scalar PartialPivLU<MatrixType>::determinant() const
|
---|
419 | {
|
---|
420 | eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
|
---|
421 | return Scalar(m_det_p) * m_lu.diagonal().prod();
|
---|
422 | }
|
---|
423 |
|
---|
424 | /** \returns the matrix represented by the decomposition,
|
---|
425 | * i.e., it returns the product: P^{-1} L U.
|
---|
426 | * This function is provided for debug purpose. */
|
---|
427 | template<typename MatrixType>
|
---|
428 | MatrixType PartialPivLU<MatrixType>::reconstructedMatrix() const
|
---|
429 | {
|
---|
430 | eigen_assert(m_isInitialized && "LU is not initialized.");
|
---|
431 | // LU
|
---|
432 | MatrixType res = m_lu.template triangularView<UnitLower>().toDenseMatrix()
|
---|
433 | * m_lu.template triangularView<Upper>();
|
---|
434 |
|
---|
435 | // P^{-1}(LU)
|
---|
436 | res = m_p.inverse() * res;
|
---|
437 |
|
---|
438 | return res;
|
---|
439 | }
|
---|
440 |
|
---|
441 | /***** Implementation of solve() *****************************************************/
|
---|
442 |
|
---|
443 | namespace internal {
|
---|
444 |
|
---|
445 | template<typename _MatrixType, typename Rhs>
|
---|
446 | struct solve_retval<PartialPivLU<_MatrixType>, Rhs>
|
---|
447 | : solve_retval_base<PartialPivLU<_MatrixType>, Rhs>
|
---|
448 | {
|
---|
449 | EIGEN_MAKE_SOLVE_HELPERS(PartialPivLU<_MatrixType>,Rhs)
|
---|
450 |
|
---|
451 | template<typename Dest> void evalTo(Dest& dst) const
|
---|
452 | {
|
---|
453 | /* The decomposition PA = LU can be rewritten as A = P^{-1} L U.
|
---|
454 | * So we proceed as follows:
|
---|
455 | * Step 1: compute c = Pb.
|
---|
456 | * Step 2: replace c by the solution x to Lx = c.
|
---|
457 | * Step 3: replace c by the solution x to Ux = c.
|
---|
458 | */
|
---|
459 |
|
---|
460 | eigen_assert(rhs().rows() == dec().matrixLU().rows());
|
---|
461 |
|
---|
462 | // Step 1
|
---|
463 | dst = dec().permutationP() * rhs();
|
---|
464 |
|
---|
465 | // Step 2
|
---|
466 | dec().matrixLU().template triangularView<UnitLower>().solveInPlace(dst);
|
---|
467 |
|
---|
468 | // Step 3
|
---|
469 | dec().matrixLU().template triangularView<Upper>().solveInPlace(dst);
|
---|
470 | }
|
---|
471 | };
|
---|
472 |
|
---|
473 | } // end namespace internal
|
---|
474 |
|
---|
475 | /******** MatrixBase methods *******/
|
---|
476 |
|
---|
477 | /** \lu_module
|
---|
478 | *
|
---|
479 | * \return the partial-pivoting LU decomposition of \c *this.
|
---|
480 | *
|
---|
481 | * \sa class PartialPivLU
|
---|
482 | */
|
---|
483 | template<typename Derived>
|
---|
484 | inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject>
|
---|
485 | MatrixBase<Derived>::partialPivLu() const
|
---|
486 | {
|
---|
487 | return PartialPivLU<PlainObject>(eval());
|
---|
488 | }
|
---|
489 |
|
---|
490 | #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
|
---|
491 | /** \lu_module
|
---|
492 | *
|
---|
493 | * Synonym of partialPivLu().
|
---|
494 | *
|
---|
495 | * \return the partial-pivoting LU decomposition of \c *this.
|
---|
496 | *
|
---|
497 | * \sa class PartialPivLU
|
---|
498 | */
|
---|
499 | template<typename Derived>
|
---|
500 | inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject>
|
---|
501 | MatrixBase<Derived>::lu() const
|
---|
502 | {
|
---|
503 | return PartialPivLU<PlainObject>(eval());
|
---|
504 | }
|
---|
505 | #endif
|
---|
506 |
|
---|
507 | } // end namespace Eigen
|
---|
508 |
|
---|
509 | #endif // EIGEN_PARTIALLU_H
|
---|