17 template<
typename _MatrixType,
int _UpLo>
struct traits<LLT<_MatrixType, _UpLo> >
20 typedef MatrixXpr XprKind;
21 typedef SolverStorage StorageKind;
22 typedef int StorageIndex;
26 template<
typename MatrixType,
int UpLo>
struct LLT_Traits;
66 template<
typename _MatrixType,
int _UpLo>
class LLT 70 typedef _MatrixType MatrixType;
74 EIGEN_GENERIC_PUBLIC_INTERFACE(LLT)
76 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
80 PacketSize = internal::packet_traits<Scalar>::size,
81 AlignmentMask = int(PacketSize)-1,
85 typedef internal::LLT_Traits<MatrixType,UpLo> Traits;
93 LLT() : m_matrix(), m_isInitialized(false) {}
102 m_isInitialized(false) {}
104 template<
typename InputType>
106 : m_matrix(matrix.
rows(), matrix.
cols()),
107 m_isInitialized(
false)
119 template<
typename InputType>
121 : m_matrix(matrix.derived()),
122 m_isInitialized(false)
128 inline typename Traits::MatrixU
matrixU()
const 130 eigen_assert(m_isInitialized &&
"LLT is not initialized.");
131 return Traits::getU(m_matrix);
135 inline typename Traits::MatrixL
matrixL()
const 137 eigen_assert(m_isInitialized &&
"LLT is not initialized.");
138 return Traits::getL(m_matrix);
141 #ifdef EIGEN_PARSED_BY_DOXYGEN 152 template<
typename Rhs>
157 template<
typename Derived>
160 template<
typename InputType>
168 eigen_assert(m_isInitialized &&
"LLT is not initialized.");
169 eigen_assert(m_info ==
Success &&
"LLT failed because matrix appears to be negative");
170 return internal::rcond_estimate_helper(m_l1_norm, *
this);
179 eigen_assert(m_isInitialized &&
"LLT is not initialized.");
183 MatrixType reconstructedMatrix()
const;
193 eigen_assert(m_isInitialized &&
"LLT is not initialized.");
202 const LLT&
adjoint() const EIGEN_NOEXCEPT {
return *
this; };
204 inline EIGEN_CONSTEXPR
Index rows()
const EIGEN_NOEXCEPT {
return m_matrix.rows(); }
205 inline EIGEN_CONSTEXPR
Index cols()
const EIGEN_NOEXCEPT {
return m_matrix.cols(); }
207 template<
typename VectorType>
208 LLT & rankUpdate(
const VectorType& vec,
const RealScalar& sigma = 1);
210 #ifndef EIGEN_PARSED_BY_DOXYGEN 211 template<
typename RhsType,
typename DstType>
212 void _solve_impl(
const RhsType &rhs, DstType &dst)
const;
214 template<
bool Conjugate,
typename RhsType,
typename DstType>
215 void _solve_impl_transposed(
const RhsType &rhs, DstType &dst)
const;
220 static void check_template_parameters()
222 EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
230 RealScalar m_l1_norm;
231 bool m_isInitialized;
237 template<
typename Scalar,
int UpLo>
struct llt_inplace;
239 template<
typename MatrixType,
typename VectorType>
240 static Index llt_rank_update_lower(MatrixType& mat,
const VectorType& vec,
const typename MatrixType::RealScalar& sigma)
243 typedef typename MatrixType::Scalar Scalar;
244 typedef typename MatrixType::RealScalar RealScalar;
245 typedef typename MatrixType::ColXpr ColXpr;
246 typedef typename internal::remove_all<ColXpr>::type ColXprCleaned;
247 typedef typename ColXprCleaned::SegmentReturnType ColXprSegment;
249 typedef typename TempVectorType::SegmentReturnType TempVecSegment;
251 Index n = mat.cols();
252 eigen_assert(mat.rows()==n && vec.size()==n);
261 temp =
sqrt(sigma) * vec;
263 for(
Index i=0; i<n; ++i)
271 ColXprSegment x(mat.col(i).tail(rs));
272 TempVecSegment y(temp.tail(rs));
273 apply_rotation_in_the_plane(x, y, g);
281 for(
Index j=0; j<n; ++j)
283 RealScalar Ljj = numext::real(mat.coeff(j,j));
284 RealScalar dj = numext::abs2(Ljj);
285 Scalar wj = temp.coeff(j);
286 RealScalar swj2 = sigma*numext::abs2(wj);
287 RealScalar gamma = dj*beta + swj2;
289 RealScalar x = dj + swj2/beta;
290 if (x<=RealScalar(0))
292 RealScalar nLjj =
sqrt(x);
293 mat.coeffRef(j,j) = nLjj;
300 temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);
302 mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs);
309 template<
typename Scalar>
struct llt_inplace<Scalar, Lower>
312 template<
typename MatrixType>
313 static Index unblocked(MatrixType& mat)
317 eigen_assert(mat.rows()==mat.cols());
318 const Index size = mat.rows();
319 for(
Index k = 0; k < size; ++k)
327 RealScalar x = numext::real(mat.coeff(k,k));
328 if (k>0) x -= A10.squaredNorm();
329 if (x<=RealScalar(0))
331 mat.coeffRef(k,k) = x =
sqrt(x);
332 if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
338 template<
typename MatrixType>
339 static Index blocked(MatrixType& m)
341 eigen_assert(m.rows()==m.cols());
342 Index size = m.rows();
346 Index blockSize = size/8;
347 blockSize = (blockSize/16)*16;
348 blockSize = (std::min)((std::max)(blockSize,
Index(8)),
Index(128));
350 for (
Index k=0; k<size; k+=blockSize)
356 Index bs = (std::min)(blockSize, size-k);
357 Index rs = size - k - bs;
363 if((ret=unblocked(A11))>=0)
return k+ret;
364 if(rs>0) A11.adjoint().template triangularView<Upper>().
template solveInPlace<OnTheRight>(A21);
370 template<
typename MatrixType,
typename VectorType>
371 static Index rankUpdate(MatrixType& mat,
const VectorType& vec,
const RealScalar& sigma)
373 return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
377 template<
typename Scalar>
struct llt_inplace<Scalar, Upper>
381 template<
typename MatrixType>
382 static EIGEN_STRONG_INLINE
Index unblocked(MatrixType& mat)
385 return llt_inplace<Scalar, Lower>::unblocked(matt);
387 template<
typename MatrixType>
388 static EIGEN_STRONG_INLINE
Index blocked(MatrixType& mat)
391 return llt_inplace<Scalar, Lower>::blocked(matt);
393 template<
typename MatrixType,
typename VectorType>
394 static Index rankUpdate(MatrixType& mat,
const VectorType& vec,
const RealScalar& sigma)
397 return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma);
401 template<
typename MatrixType>
struct LLT_Traits<MatrixType,Lower>
405 static inline MatrixL getL(
const MatrixType& m) {
return MatrixL(m); }
406 static inline MatrixU getU(
const MatrixType& m) {
return MatrixU(m.adjoint()); }
407 static bool inplace_decomposition(MatrixType& m)
408 {
return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m)==-1; }
411 template<
typename MatrixType>
struct LLT_Traits<MatrixType,Upper>
415 static inline MatrixL getL(
const MatrixType& m) {
return MatrixL(m.adjoint()); }
416 static inline MatrixU getU(
const MatrixType& m) {
return MatrixU(m); }
417 static bool inplace_decomposition(MatrixType& m)
418 {
return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m)==-1; }
430 template<
typename MatrixType,
int _UpLo>
431 template<
typename InputType>
434 check_template_parameters();
438 m_matrix.resize(size, size);
439 if (!internal::is_same_dense(m_matrix, a.
derived()))
443 m_l1_norm = RealScalar(0);
445 for (
Index col = 0; col < size; ++col) {
446 RealScalar abs_col_sum;
448 abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
450 abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
451 if (abs_col_sum > m_l1_norm)
452 m_l1_norm = abs_col_sum;
455 m_isInitialized =
true;
456 bool ok = Traits::inplace_decomposition(m_matrix);
467 template<
typename _MatrixType,
int _UpLo>
468 template<
typename VectorType>
471 EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);
472 eigen_assert(v.size()==m_matrix.cols());
473 eigen_assert(m_isInitialized);
474 if(internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix,v,sigma)>=0)
482 #ifndef EIGEN_PARSED_BY_DOXYGEN 483 template<
typename _MatrixType,
int _UpLo>
484 template<
typename RhsType,
typename DstType>
487 _solve_impl_transposed<true>(rhs, dst);
490 template<
typename _MatrixType,
int _UpLo>
491 template<
bool Conjugate,
typename RhsType,
typename DstType>
496 matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
497 matrixU().template conjugateIf<!Conjugate>().solveInPlace(dst);
514 template<
typename MatrixType,
int _UpLo>
515 template<
typename Derived>
518 eigen_assert(m_isInitialized &&
"LLT is not initialized.");
519 eigen_assert(m_matrix.rows()==bAndX.
rows());
520 matrixL().solveInPlace(bAndX);
521 matrixU().solveInPlace(bAndX);
527 template<
typename MatrixType,
int _UpLo>
530 eigen_assert(m_isInitialized &&
"LLT is not initialized.");
531 return matrixL() * matrixL().adjoint().toDenseMatrix();
538 template<
typename Derived>
549 template<
typename MatrixType,
unsigned int UpLo>
558 #endif // EIGEN_LLT_H MatrixType reconstructedMatrix() const
Definition: LLT.h:528
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
Expression of the transpose of a matrix.
Definition: Transpose.h:52
const LLT & adjoint() const EIGEN_NOEXCEPT
Definition: LLT.h:202
LLT(Index size)
Default Constructor with memory preallocation.
Definition: LLT.h:101
Namespace containing all symbols from the Eigen library.
Definition: Core:141
Rotation given by a cosine-sine pair.
Definition: Jacobi.h:34
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:232
Derived & derived()
Definition: EigenBase.h:46
Eigen::Index Index
The interface type of indices.
Definition: EigenBase.h:39
LLT(EigenBase< InputType > &matrix)
Constructs a LLT factorization from a given matrix.
Definition: LLT.h:120
Definition: EigenBase.h:29
Definition: Constants.h:209
RealScalar rcond() const
Definition: LLT.h:166
Standard Cholesky decomposition (LL^T) of a matrix and associated features.
Definition: LLT.h:66
Definition: Constants.h:444
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT
Definition: EigenBase.h:63
ComputationInfo info() const
Reports whether previous computation was successful.
Definition: LLT.h:191
Definition: Constants.h:442
Traits::MatrixL matrixL() const
Definition: LLT.h:135
Definition: Eigen_Colamd.h:50
Expression of a fixed-size or dynamic-size block.
Definition: Block.h:103
Traits::MatrixU matrixU() const
Definition: LLT.h:128
Expression of a triangular part in a matrix.
Definition: TriangularMatrix.h:187
const LLT< PlainObject > llt() const
Definition: LLT.h:540
EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT
Definition: EigenBase.h:60
const MatrixType & matrixLLT() const
Definition: LLT.h:177
Pseudo expression representing a solving operation.
Definition: Solve.h:62
LLT()
Default Constructor.
Definition: LLT.h:93
ComputationInfo
Definition: Constants.h:440
A base class for matrix decomposition and solvers.
Definition: SolverBase.h:68
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
const LLT< PlainObject, UpLo > llt() const
Definition: LLT.h:551
void makeGivens(const Scalar &p, const Scalar &q, Scalar *r=0)
Definition: Jacobi.h:162