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Eigen  3.4.99 (git rev 69adf26aa3e853418002562f623c42a9c7008271)
SuiteSparseQRSupport.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
5 // Copyright (C) 2014 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_SUITESPARSEQRSUPPORT_H
12 #define EIGEN_SUITESPARSEQRSUPPORT_H
13 
14 namespace Eigen {
15 
16  template<typename MatrixType> class SPQR;
17  template<typename SPQRType> struct SPQRMatrixQReturnType;
18  template<typename SPQRType> struct SPQRMatrixQTransposeReturnType;
19  template <typename SPQRType, typename Derived> struct SPQR_QProduct;
20  namespace internal {
21  template <typename SPQRType> struct traits<SPQRMatrixQReturnType<SPQRType> >
22  {
23  typedef typename SPQRType::MatrixType ReturnType;
24  };
25  template <typename SPQRType> struct traits<SPQRMatrixQTransposeReturnType<SPQRType> >
26  {
27  typedef typename SPQRType::MatrixType ReturnType;
28  };
29  template <typename SPQRType, typename Derived> struct traits<SPQR_QProduct<SPQRType, Derived> >
30  {
31  typedef typename Derived::PlainObject ReturnType;
32  };
33  } // End namespace internal
34 
59 template<typename _MatrixType>
60 class SPQR : public SparseSolverBase<SPQR<_MatrixType> >
61 {
62  protected:
64  using Base::m_isInitialized;
65  public:
66  typedef typename _MatrixType::Scalar Scalar;
67  typedef typename _MatrixType::RealScalar RealScalar;
68  typedef SuiteSparse_long StorageIndex ;
71  enum {
72  ColsAtCompileTime = Dynamic,
73  MaxColsAtCompileTime = Dynamic
74  };
75  public:
76  SPQR()
77  : m_analysisIsOk(false),
78  m_factorizationIsOk(false),
79  m_isRUpToDate(false),
80  m_ordering(SPQR_ORDERING_DEFAULT),
81  m_allow_tol(SPQR_DEFAULT_TOL),
82  m_tolerance (NumTraits<Scalar>::epsilon()),
83  m_cR(0),
84  m_E(0),
85  m_H(0),
86  m_HPinv(0),
87  m_HTau(0),
88  m_useDefaultThreshold(true)
89  {
90  cholmod_l_start(&m_cc);
91  }
92 
93  explicit SPQR(const _MatrixType& matrix)
94  : m_analysisIsOk(false),
95  m_factorizationIsOk(false),
96  m_isRUpToDate(false),
97  m_ordering(SPQR_ORDERING_DEFAULT),
98  m_allow_tol(SPQR_DEFAULT_TOL),
99  m_tolerance (NumTraits<Scalar>::epsilon()),
100  m_cR(0),
101  m_E(0),
102  m_H(0),
103  m_HPinv(0),
104  m_HTau(0),
105  m_useDefaultThreshold(true)
106  {
107  cholmod_l_start(&m_cc);
108  compute(matrix);
109  }
110 
111  ~SPQR()
112  {
113  SPQR_free();
114  cholmod_l_finish(&m_cc);
115  }
116  void SPQR_free()
117  {
118  cholmod_l_free_sparse(&m_H, &m_cc);
119  cholmod_l_free_sparse(&m_cR, &m_cc);
120  cholmod_l_free_dense(&m_HTau, &m_cc);
121  std::free(m_E);
122  std::free(m_HPinv);
123  }
124 
125  void compute(const _MatrixType& matrix)
126  {
127  if(m_isInitialized) SPQR_free();
128 
129  MatrixType mat(matrix);
130 
131  /* Compute the default threshold as in MatLab, see:
132  * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing
133  * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3
134  */
135  RealScalar pivotThreshold = m_tolerance;
136  if(m_useDefaultThreshold)
137  {
138  RealScalar max2Norm = 0.0;
139  for (int j = 0; j < mat.cols(); j++) max2Norm = numext::maxi(max2Norm, mat.col(j).norm());
140  if(max2Norm==RealScalar(0))
141  max2Norm = RealScalar(1);
142  pivotThreshold = 20 * (mat.rows() + mat.cols()) * max2Norm * NumTraits<RealScalar>::epsilon();
143  }
144  cholmod_sparse A;
145  A = viewAsCholmod(mat);
146  m_rows = matrix.rows();
147  Index col = matrix.cols();
148  m_rank = SuiteSparseQR<Scalar>(m_ordering, pivotThreshold, col, &A,
149  &m_cR, &m_E, &m_H, &m_HPinv, &m_HTau, &m_cc);
150 
151  if (!m_cR)
152  {
153  m_info = NumericalIssue;
154  m_isInitialized = false;
155  return;
156  }
157  m_info = Success;
158  m_isInitialized = true;
159  m_isRUpToDate = false;
160  }
164  inline Index rows() const {return m_rows; }
165 
169  inline Index cols() const { return m_cR->ncol; }
170 
171  template<typename Rhs, typename Dest>
172  void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
173  {
174  eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
175  eigen_assert(b.cols()==1 && "This method is for vectors only");
176 
177  //Compute Q^T * b
178  typename Dest::PlainObject y, y2;
179  y = matrixQ().transpose() * b;
180 
181  // Solves with the triangular matrix R
182  Index rk = this->rank();
183  y2 = y;
184  y.resize((std::max)(cols(),Index(y.rows())),y.cols());
185  y.topRows(rk) = this->matrixR().topLeftCorner(rk, rk).template triangularView<Upper>().solve(y2.topRows(rk));
186 
187  // Apply the column permutation
188  // colsPermutation() performs a copy of the permutation,
189  // so let's apply it manually:
190  for(Index i = 0; i < rk; ++i) dest.row(m_E[i]) = y.row(i);
191  for(Index i = rk; i < cols(); ++i) dest.row(m_E[i]).setZero();
192 
193 // y.bottomRows(y.rows()-rk).setZero();
194 // dest = colsPermutation() * y.topRows(cols());
195 
196  m_info = Success;
197  }
198 
201  const MatrixType matrixR() const
202  {
203  eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
204  if(!m_isRUpToDate) {
205  m_R = viewAsEigen<Scalar,ColMajor, typename MatrixType::StorageIndex>(*m_cR);
206  m_isRUpToDate = true;
207  }
208  return m_R;
209  }
211  SPQRMatrixQReturnType<SPQR> matrixQ() const
212  {
213  return SPQRMatrixQReturnType<SPQR>(*this);
214  }
217  {
218  eigen_assert(m_isInitialized && "Decomposition is not initialized.");
219  return PermutationType(m_E, m_cR->ncol);
220  }
225  Index rank() const
226  {
227  eigen_assert(m_isInitialized && "Decomposition is not initialized.");
228  return m_cc.SPQR_istat[4];
229  }
231  void setSPQROrdering(int ord) { m_ordering = ord;}
233  void setPivotThreshold(const RealScalar& tol)
234  {
235  m_useDefaultThreshold = false;
236  m_tolerance = tol;
237  }
238 
240  cholmod_common *cholmodCommon() const { return &m_cc; }
241 
242 
249  {
250  eigen_assert(m_isInitialized && "Decomposition is not initialized.");
251  return m_info;
252  }
253  protected:
254  bool m_analysisIsOk;
255  bool m_factorizationIsOk;
256  mutable bool m_isRUpToDate;
257  mutable ComputationInfo m_info;
258  int m_ordering; // Ordering method to use, see SPQR's manual
259  int m_allow_tol; // Allow to use some tolerance during numerical factorization.
260  RealScalar m_tolerance; // treat columns with 2-norm below this tolerance as zero
261  mutable cholmod_sparse *m_cR; // The sparse R factor in cholmod format
262  mutable MatrixType m_R; // The sparse matrix R in Eigen format
263  mutable StorageIndex *m_E; // The permutation applied to columns
264  mutable cholmod_sparse *m_H; //The householder vectors
265  mutable StorageIndex *m_HPinv; // The row permutation of H
266  mutable cholmod_dense *m_HTau; // The Householder coefficients
267  mutable Index m_rank; // The rank of the matrix
268  mutable cholmod_common m_cc; // Workspace and parameters
269  bool m_useDefaultThreshold; // Use default threshold
270  Index m_rows;
271  template<typename ,typename > friend struct SPQR_QProduct;
272 };
273 
274 template <typename SPQRType, typename Derived>
275 struct SPQR_QProduct : ReturnByValue<SPQR_QProduct<SPQRType,Derived> >
276 {
277  typedef typename SPQRType::Scalar Scalar;
278  typedef typename SPQRType::StorageIndex StorageIndex;
279  //Define the constructor to get reference to argument types
280  SPQR_QProduct(const SPQRType& spqr, const Derived& other, bool transpose) : m_spqr(spqr),m_other(other),m_transpose(transpose) {}
281 
282  inline Index rows() const { return m_transpose ? m_spqr.rows() : m_spqr.cols(); }
283  inline Index cols() const { return m_other.cols(); }
284  // Assign to a vector
285  template<typename ResType>
286  void evalTo(ResType& res) const
287  {
288  cholmod_dense y_cd;
289  cholmod_dense *x_cd;
290  int method = m_transpose ? SPQR_QTX : SPQR_QX;
291  cholmod_common *cc = m_spqr.cholmodCommon();
292  y_cd = viewAsCholmod(m_other.const_cast_derived());
293  x_cd = SuiteSparseQR_qmult<Scalar>(method, m_spqr.m_H, m_spqr.m_HTau, m_spqr.m_HPinv, &y_cd, cc);
294  res = Matrix<Scalar,ResType::RowsAtCompileTime,ResType::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x), x_cd->nrow, x_cd->ncol);
295  cholmod_l_free_dense(&x_cd, cc);
296  }
297  const SPQRType& m_spqr;
298  const Derived& m_other;
299  bool m_transpose;
300 
301 };
302 template<typename SPQRType>
303 struct SPQRMatrixQReturnType{
304 
305  SPQRMatrixQReturnType(const SPQRType& spqr) : m_spqr(spqr) {}
306  template<typename Derived>
307  SPQR_QProduct<SPQRType, Derived> operator*(const MatrixBase<Derived>& other)
308  {
309  return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(),false);
310  }
311  SPQRMatrixQTransposeReturnType<SPQRType> adjoint() const
312  {
313  return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr);
314  }
315  // To use for operations with the transpose of Q
316  SPQRMatrixQTransposeReturnType<SPQRType> transpose() const
317  {
318  return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr);
319  }
320  const SPQRType& m_spqr;
321 };
322 
323 template<typename SPQRType>
324 struct SPQRMatrixQTransposeReturnType{
325  SPQRMatrixQTransposeReturnType(const SPQRType& spqr) : m_spqr(spqr) {}
326  template<typename Derived>
327  SPQR_QProduct<SPQRType,Derived> operator*(const MatrixBase<Derived>& other)
328  {
329  return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(), true);
330  }
331  const SPQRType& m_spqr;
332 };
333 
334 }// End namespace Eigen
335 #endif
Derived & setZero()
Definition: CwiseNullaryOp.h:546
EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT
Definition: EigenBase.h:63
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:96
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
static ConstMapType Map(const Scalar *data)
Definition: PlainObjectBase.h:644
Sparse QR factorization based on SuiteSparseQR library.
Definition: SuiteSparseQRSupport.h:61
ComputationInfo info() const
Reports whether previous computation was successful.
Definition: SuiteSparseQRSupport.h:248
Index rank() const
Definition: SuiteSparseQRSupport.h:225
Index rows() const
Definition: SuiteSparseQRSupport.h:164
cholmod_common * cholmodCommon() const
Definition: SuiteSparseQRSupport.h:240
SPQRMatrixQReturnType< SPQR > matrixQ() const
Get an expression of the matrix Q.
Definition: SuiteSparseQRSupport.h:211
Index cols() const
Definition: SuiteSparseQRSupport.h:169
PermutationType colsPermutation() const
Get the permutation that was applied to columns of A.
Definition: SuiteSparseQRSupport.h:216
void setPivotThreshold(const RealScalar &tol)
Set the tolerance tol to treat columns with 2-norm < =tol as zero.
Definition: SuiteSparseQRSupport.h:233
const MatrixType matrixR() const
Definition: SuiteSparseQRSupport.h:201
void setSPQROrdering(int ord)
Set the fill-reducing ordering method to be used.
Definition: SuiteSparseQRSupport.h:231
Index rows() const
Definition: SparseMatrix.h:138
Index cols() const
Definition: SparseMatrix.h:140
A base class for sparse solvers.
Definition: SparseSolverBase.h:68
ComputationInfo
Definition: Constants.h:440
@ NumericalIssue
Definition: Constants.h:444
@ Success
Definition: Constants.h:442
Namespace containing all symbols from the Eigen library.
Definition: Core:141
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
const Product< MatrixDerived, PermutationDerived, AliasFreeProduct > operator*(const MatrixBase< MatrixDerived > &matrix, const PermutationBase< PermutationDerived > &permutation)
Definition: PermutationMatrix.h:515
cholmod_sparse viewAsCholmod(Ref< SparseMatrix< _Scalar, _Options, _StorageIndex > > mat)
Definition: CholmodSupport.h:58
const int Dynamic
Definition: Constants.h:22
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:233