source: pacpussensors/trunk/Vislab/lib3dv/eigen/Eigen/src/UmfPackSupport/UmfPackSupport.h@ 136

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1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#ifndef EIGEN_UMFPACKSUPPORT_H
11#define EIGEN_UMFPACKSUPPORT_H
12
13namespace Eigen {
14
15/* TODO extract L, extract U, compute det, etc... */
16
17// generic double/complex<double> wrapper functions:
18
19inline void umfpack_free_numeric(void **Numeric, double)
20{ umfpack_di_free_numeric(Numeric); *Numeric = 0; }
21
22inline void umfpack_free_numeric(void **Numeric, std::complex<double>)
23{ umfpack_zi_free_numeric(Numeric); *Numeric = 0; }
24
25inline void umfpack_free_symbolic(void **Symbolic, double)
26{ umfpack_di_free_symbolic(Symbolic); *Symbolic = 0; }
27
28inline void umfpack_free_symbolic(void **Symbolic, std::complex<double>)
29{ umfpack_zi_free_symbolic(Symbolic); *Symbolic = 0; }
30
31inline int umfpack_symbolic(int n_row,int n_col,
32 const int Ap[], const int Ai[], const double Ax[], void **Symbolic,
33 const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
34{
35 return umfpack_di_symbolic(n_row,n_col,Ap,Ai,Ax,Symbolic,Control,Info);
36}
37
38inline int umfpack_symbolic(int n_row,int n_col,
39 const int Ap[], const int Ai[], const std::complex<double> Ax[], void **Symbolic,
40 const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
41{
42 return umfpack_zi_symbolic(n_row,n_col,Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Control,Info);
43}
44
45inline int umfpack_numeric( const int Ap[], const int Ai[], const double Ax[],
46 void *Symbolic, void **Numeric,
47 const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
48{
49 return umfpack_di_numeric(Ap,Ai,Ax,Symbolic,Numeric,Control,Info);
50}
51
52inline int umfpack_numeric( const int Ap[], const int Ai[], const std::complex<double> Ax[],
53 void *Symbolic, void **Numeric,
54 const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
55{
56 return umfpack_zi_numeric(Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Numeric,Control,Info);
57}
58
59inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const double Ax[],
60 double X[], const double B[], void *Numeric,
61 const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
62{
63 return umfpack_di_solve(sys,Ap,Ai,Ax,X,B,Numeric,Control,Info);
64}
65
66inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const std::complex<double> Ax[],
67 std::complex<double> X[], const std::complex<double> B[], void *Numeric,
68 const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
69{
70 return umfpack_zi_solve(sys,Ap,Ai,&numext::real_ref(Ax[0]),0,&numext::real_ref(X[0]),0,&numext::real_ref(B[0]),0,Numeric,Control,Info);
71}
72
73inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, double)
74{
75 return umfpack_di_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
76}
77
78inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, std::complex<double>)
79{
80 return umfpack_zi_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
81}
82
83inline int umfpack_get_numeric(int Lp[], int Lj[], double Lx[], int Up[], int Ui[], double Ux[],
84 int P[], int Q[], double Dx[], int *do_recip, double Rs[], void *Numeric)
85{
86 return umfpack_di_get_numeric(Lp,Lj,Lx,Up,Ui,Ux,P,Q,Dx,do_recip,Rs,Numeric);
87}
88
89inline int umfpack_get_numeric(int Lp[], int Lj[], std::complex<double> Lx[], int Up[], int Ui[], std::complex<double> Ux[],
90 int P[], int Q[], std::complex<double> Dx[], int *do_recip, double Rs[], void *Numeric)
91{
92 double& lx0_real = numext::real_ref(Lx[0]);
93 double& ux0_real = numext::real_ref(Ux[0]);
94 double& dx0_real = numext::real_ref(Dx[0]);
95 return umfpack_zi_get_numeric(Lp,Lj,Lx?&lx0_real:0,0,Up,Ui,Ux?&ux0_real:0,0,P,Q,
96 Dx?&dx0_real:0,0,do_recip,Rs,Numeric);
97}
98
99inline int umfpack_get_determinant(double *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])
100{
101 return umfpack_di_get_determinant(Mx,Ex,NumericHandle,User_Info);
102}
103
104inline int umfpack_get_determinant(std::complex<double> *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO])
105{
106 double& mx_real = numext::real_ref(*Mx);
107 return umfpack_zi_get_determinant(&mx_real,0,Ex,NumericHandle,User_Info);
108}
109
110namespace internal {
111 template<typename T> struct umfpack_helper_is_sparse_plain : false_type {};
112 template<typename Scalar, int Options, typename StorageIndex>
113 struct umfpack_helper_is_sparse_plain<SparseMatrix<Scalar,Options,StorageIndex> >
114 : true_type {};
115 template<typename Scalar, int Options, typename StorageIndex>
116 struct umfpack_helper_is_sparse_plain<MappedSparseMatrix<Scalar,Options,StorageIndex> >
117 : true_type {};
118}
119
120/** \ingroup UmfPackSupport_Module
121 * \brief A sparse LU factorization and solver based on UmfPack
122 *
123 * This class allows to solve for A.X = B sparse linear problems via a LU factorization
124 * using the UmfPack library. The sparse matrix A must be squared and full rank.
125 * The vectors or matrices X and B can be either dense or sparse.
126 *
127 * \warning The input matrix A should be in a \b compressed and \b column-major form.
128 * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
129 * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
130 *
131 * \sa \ref TutorialSparseDirectSolvers
132 */
133template<typename _MatrixType>
134class UmfPackLU : internal::noncopyable
135{
136 public:
137 typedef _MatrixType MatrixType;
138 typedef typename MatrixType::Scalar Scalar;
139 typedef typename MatrixType::RealScalar RealScalar;
140 typedef typename MatrixType::Index Index;
141 typedef Matrix<Scalar,Dynamic,1> Vector;
142 typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
143 typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
144 typedef SparseMatrix<Scalar> LUMatrixType;
145 typedef SparseMatrix<Scalar,ColMajor,int> UmfpackMatrixType;
146
147 public:
148
149 UmfPackLU() { init(); }
150
151 UmfPackLU(const MatrixType& matrix)
152 {
153 init();
154 compute(matrix);
155 }
156
157 ~UmfPackLU()
158 {
159 if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());
160 if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar());
161 }
162
163 inline Index rows() const { return m_copyMatrix.rows(); }
164 inline Index cols() const { return m_copyMatrix.cols(); }
165
166 /** \brief Reports whether previous computation was successful.
167 *
168 * \returns \c Success if computation was succesful,
169 * \c NumericalIssue if the matrix.appears to be negative.
170 */
171 ComputationInfo info() const
172 {
173 eigen_assert(m_isInitialized && "Decomposition is not initialized.");
174 return m_info;
175 }
176
177 inline const LUMatrixType& matrixL() const
178 {
179 if (m_extractedDataAreDirty) extractData();
180 return m_l;
181 }
182
183 inline const LUMatrixType& matrixU() const
184 {
185 if (m_extractedDataAreDirty) extractData();
186 return m_u;
187 }
188
189 inline const IntColVectorType& permutationP() const
190 {
191 if (m_extractedDataAreDirty) extractData();
192 return m_p;
193 }
194
195 inline const IntRowVectorType& permutationQ() const
196 {
197 if (m_extractedDataAreDirty) extractData();
198 return m_q;
199 }
200
201 /** Computes the sparse Cholesky decomposition of \a matrix
202 * Note that the matrix should be column-major, and in compressed format for best performance.
203 * \sa SparseMatrix::makeCompressed().
204 */
205 template<typename InputMatrixType>
206 void compute(const InputMatrixType& matrix)
207 {
208 if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());
209 if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar());
210 grapInput(matrix.derived());
211 analyzePattern_impl();
212 factorize_impl();
213 }
214
215 /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
216 *
217 * \sa compute()
218 */
219 template<typename Rhs>
220 inline const internal::solve_retval<UmfPackLU, Rhs> solve(const MatrixBase<Rhs>& b) const
221 {
222 eigen_assert(m_isInitialized && "UmfPackLU is not initialized.");
223 eigen_assert(rows()==b.rows()
224 && "UmfPackLU::solve(): invalid number of rows of the right hand side matrix b");
225 return internal::solve_retval<UmfPackLU, Rhs>(*this, b.derived());
226 }
227
228 /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
229 *
230 * \sa compute()
231 */
232 template<typename Rhs>
233 inline const internal::sparse_solve_retval<UmfPackLU, Rhs> solve(const SparseMatrixBase<Rhs>& b) const
234 {
235 eigen_assert(m_isInitialized && "UmfPackLU is not initialized.");
236 eigen_assert(rows()==b.rows()
237 && "UmfPackLU::solve(): invalid number of rows of the right hand side matrix b");
238 return internal::sparse_solve_retval<UmfPackLU, Rhs>(*this, b.derived());
239 }
240
241 /** Performs a symbolic decomposition on the sparcity of \a matrix.
242 *
243 * This function is particularly useful when solving for several problems having the same structure.
244 *
245 * \sa factorize(), compute()
246 */
247 template<typename InputMatrixType>
248 void analyzePattern(const InputMatrixType& matrix)
249 {
250 if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar());
251 if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar());
252
253 grapInput(matrix.derived());
254
255 analyzePattern_impl();
256 }
257
258 /** Performs a numeric decomposition of \a matrix
259 *
260 * The given matrix must has the same sparcity than the matrix on which the pattern anylysis has been performed.
261 *
262 * \sa analyzePattern(), compute()
263 */
264 template<typename InputMatrixType>
265 void factorize(const InputMatrixType& matrix)
266 {
267 eigen_assert(m_analysisIsOk && "UmfPackLU: you must first call analyzePattern()");
268 if(m_numeric)
269 umfpack_free_numeric(&m_numeric,Scalar());
270
271 grapInput(matrix.derived());
272
273 factorize_impl();
274 }
275
276 #ifndef EIGEN_PARSED_BY_DOXYGEN
277 /** \internal */
278 template<typename BDerived,typename XDerived>
279 bool _solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const;
280 #endif
281
282 Scalar determinant() const;
283
284 void extractData() const;
285
286 protected:
287
288 void init()
289 {
290 m_info = InvalidInput;
291 m_isInitialized = false;
292 m_numeric = 0;
293 m_symbolic = 0;
294 m_outerIndexPtr = 0;
295 m_innerIndexPtr = 0;
296 m_valuePtr = 0;
297 m_extractedDataAreDirty = true;
298 }
299
300 template<typename InputMatrixType>
301 void grapInput_impl(const InputMatrixType& mat, internal::true_type)
302 {
303 m_copyMatrix.resize(mat.rows(), mat.cols());
304 if( ((MatrixType::Flags&RowMajorBit)==RowMajorBit) || sizeof(typename MatrixType::Index)!=sizeof(int) || !mat.isCompressed() )
305 {
306 // non supported input -> copy
307 m_copyMatrix = mat;
308 m_outerIndexPtr = m_copyMatrix.outerIndexPtr();
309 m_innerIndexPtr = m_copyMatrix.innerIndexPtr();
310 m_valuePtr = m_copyMatrix.valuePtr();
311 }
312 else
313 {
314 m_outerIndexPtr = mat.outerIndexPtr();
315 m_innerIndexPtr = mat.innerIndexPtr();
316 m_valuePtr = mat.valuePtr();
317 }
318 }
319
320 template<typename InputMatrixType>
321 void grapInput_impl(const InputMatrixType& mat, internal::false_type)
322 {
323 m_copyMatrix = mat;
324 m_outerIndexPtr = m_copyMatrix.outerIndexPtr();
325 m_innerIndexPtr = m_copyMatrix.innerIndexPtr();
326 m_valuePtr = m_copyMatrix.valuePtr();
327 }
328
329 template<typename InputMatrixType>
330 void grapInput(const InputMatrixType& mat)
331 {
332 grapInput_impl(mat, internal::umfpack_helper_is_sparse_plain<InputMatrixType>());
333 }
334
335 void analyzePattern_impl()
336 {
337 int errorCode = 0;
338 errorCode = umfpack_symbolic(m_copyMatrix.rows(), m_copyMatrix.cols(), m_outerIndexPtr, m_innerIndexPtr, m_valuePtr,
339 &m_symbolic, 0, 0);
340
341 m_isInitialized = true;
342 m_info = errorCode ? InvalidInput : Success;
343 m_analysisIsOk = true;
344 m_factorizationIsOk = false;
345 m_extractedDataAreDirty = true;
346 }
347
348 void factorize_impl()
349 {
350 int errorCode;
351 errorCode = umfpack_numeric(m_outerIndexPtr, m_innerIndexPtr, m_valuePtr,
352 m_symbolic, &m_numeric, 0, 0);
353
354 m_info = errorCode ? NumericalIssue : Success;
355 m_factorizationIsOk = true;
356 m_extractedDataAreDirty = true;
357 }
358
359 // cached data to reduce reallocation, etc.
360 mutable LUMatrixType m_l;
361 mutable LUMatrixType m_u;
362 mutable IntColVectorType m_p;
363 mutable IntRowVectorType m_q;
364
365 UmfpackMatrixType m_copyMatrix;
366 const Scalar* m_valuePtr;
367 const int* m_outerIndexPtr;
368 const int* m_innerIndexPtr;
369 void* m_numeric;
370 void* m_symbolic;
371
372 mutable ComputationInfo m_info;
373 bool m_isInitialized;
374 int m_factorizationIsOk;
375 int m_analysisIsOk;
376 mutable bool m_extractedDataAreDirty;
377
378 private:
379 UmfPackLU(UmfPackLU& ) { }
380};
381
382
383template<typename MatrixType>
384void UmfPackLU<MatrixType>::extractData() const
385{
386 if (m_extractedDataAreDirty)
387 {
388 // get size of the data
389 int lnz, unz, rows, cols, nz_udiag;
390 umfpack_get_lunz(&lnz, &unz, &rows, &cols, &nz_udiag, m_numeric, Scalar());
391
392 // allocate data
393 m_l.resize(rows,(std::min)(rows,cols));
394 m_l.resizeNonZeros(lnz);
395
396 m_u.resize((std::min)(rows,cols),cols);
397 m_u.resizeNonZeros(unz);
398
399 m_p.resize(rows);
400 m_q.resize(cols);
401
402 // extract
403 umfpack_get_numeric(m_l.outerIndexPtr(), m_l.innerIndexPtr(), m_l.valuePtr(),
404 m_u.outerIndexPtr(), m_u.innerIndexPtr(), m_u.valuePtr(),
405 m_p.data(), m_q.data(), 0, 0, 0, m_numeric);
406
407 m_extractedDataAreDirty = false;
408 }
409}
410
411template<typename MatrixType>
412typename UmfPackLU<MatrixType>::Scalar UmfPackLU<MatrixType>::determinant() const
413{
414 Scalar det;
415 umfpack_get_determinant(&det, 0, m_numeric, 0);
416 return det;
417}
418
419template<typename MatrixType>
420template<typename BDerived,typename XDerived>
421bool UmfPackLU<MatrixType>::_solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const
422{
423 const int rhsCols = b.cols();
424 eigen_assert((BDerived::Flags&RowMajorBit)==0 && "UmfPackLU backend does not support non col-major rhs yet");
425 eigen_assert((XDerived::Flags&RowMajorBit)==0 && "UmfPackLU backend does not support non col-major result yet");
426 eigen_assert(b.derived().data() != x.derived().data() && " Umfpack does not support inplace solve");
427
428 int errorCode;
429 for (int j=0; j<rhsCols; ++j)
430 {
431 errorCode = umfpack_solve(UMFPACK_A,
432 m_outerIndexPtr, m_innerIndexPtr, m_valuePtr,
433 &x.col(j).coeffRef(0), &b.const_cast_derived().col(j).coeffRef(0), m_numeric, 0, 0);
434 if (errorCode!=0)
435 return false;
436 }
437
438 return true;
439}
440
441
442namespace internal {
443
444template<typename _MatrixType, typename Rhs>
445struct solve_retval<UmfPackLU<_MatrixType>, Rhs>
446 : solve_retval_base<UmfPackLU<_MatrixType>, Rhs>
447{
448 typedef UmfPackLU<_MatrixType> Dec;
449 EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
450
451 template<typename Dest> void evalTo(Dest& dst) const
452 {
453 dec()._solve(rhs(),dst);
454 }
455};
456
457template<typename _MatrixType, typename Rhs>
458struct sparse_solve_retval<UmfPackLU<_MatrixType>, Rhs>
459 : sparse_solve_retval_base<UmfPackLU<_MatrixType>, Rhs>
460{
461 typedef UmfPackLU<_MatrixType> Dec;
462 EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
463
464 template<typename Dest> void evalTo(Dest& dst) const
465 {
466 this->defaultEvalTo(dst);
467 }
468};
469
470} // end namespace internal
471
472} // end namespace Eigen
473
474#endif // EIGEN_UMFPACKSUPPORT_H
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