17template<
typename _MatrixType,
int _UpLo>
struct traits<
LLT<_MatrixType, _UpLo> >
26template<
typename MatrixType,
int UpLo>
struct LLT_Traits;
66template<
typename _MatrixType,
int _UpLo>
class LLT
104 template<
typename InputType>
119 template<
typename InputType>
128 inline typename Traits::MatrixU
matrixU()
const
135 inline typename Traits::MatrixL
matrixL()
const
141 #ifdef EIGEN_PARSED_BY_DOXYGEN
152 template<
typename Rhs>
157 template<
typename Derived>
160 template<
typename InputType>
207 template<
typename VectorType>
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>
239template<
typename MatrixType,
typename VectorType>
243 typedef typename MatrixType::Scalar Scalar;
244 typedef typename MatrixType::RealScalar RealScalar;
251 Index n = mat.cols();
263 for(
Index i=0; i<n; ++i)
271 ColXprSegment x(mat.col(i).tail(rs));
272 TempVecSegment
y(temp.tail(rs));
281 for(
Index j=0; j<n; ++j)
285 Scalar wj = temp.coeff(j);
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);
312 template<
typename MatrixType>
328 if (k>0) x -= A10.squaredNorm();
331 mat.coeffRef(k,k) = x =
sqrt(x);
332 if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
338 template<
typename MatrixType>
347 blockSize = (blockSize/16)*16;
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>
381 template<
typename MatrixType>
387 template<
typename MatrixType>
393 template<
typename MatrixType,
typename VectorType>
430template<
typename MatrixType,
int _UpLo>
431template<
typename InputType>
434 check_template_parameters();
443 m_l1_norm = RealScalar(0);
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);
467template<
typename _MatrixType,
int _UpLo>
468template<
typename VectorType>
482#ifndef EIGEN_PARSED_BY_DOXYGEN
483template<
typename _MatrixType,
int _UpLo>
484template<
typename RhsType,
typename DstType>
487 _solve_impl_transposed<true>(rhs, dst);
490template<
typename _MatrixType,
int _UpLo>
491template<
bool Conjugate,
typename RhsType,
typename DstType>
496 matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
497 matrixU().template conjugateIf<!Conjugate>().solveInPlace(dst);
514template<
typename MatrixType,
int _UpLo>
515template<
typename Derived>
518 eigen_assert(m_isInitialized &&
"LLT is not initialized.");
520 matrixL().solveInPlace(bAndX);
521 matrixU().solveInPlace(bAndX);
527template<
typename MatrixType,
int _UpLo>
530 eigen_assert(m_isInitialized &&
"LLT is not initialized.");
531 return matrixL() * matrixL().adjoint().toDenseMatrix();
538template<
typename Derived>
549template<
typename MatrixType,
unsigned int UpLo>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ColXpr col(Index i)
This is the const version of col().
Definition: BlockMethods.h:1097
VectorBlock< Derived > SegmentReturnType
Definition: BlockMethods.h:38
Block< Derived, internal::traits< Derived >::RowsAtCompileTime, 1, !IsRowMajor > ColXpr
Definition: BlockMethods.h:14
EIGEN_DEVICE_FUNC RealReturnType real() const
Definition: CommonCwiseUnaryOps.h:100
#define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived)
Just a side note.
Definition: Macros.h:1274
#define EIGEN_NOEXCEPT
Definition: Macros.h:1428
#define EIGEN_CONSTEXPR
Definition: Macros.h:797
#define eigen_assert(x)
Definition: Macros.h:1047
#define EIGEN_STRONG_INLINE
Definition: Macros.h:927
#define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE)
Definition: StaticAssert.h:187
#define EIGEN_STATIC_ASSERT_VECTOR_ONLY(TYPE)
Definition: StaticAssert.h:142
constexpr common_return_t< T1, T2 > beta(const T1 a, const T2 b) noexcept
Compile-time beta function.
Definition: beta.hpp:36
Expression of a fixed-size or dynamic-size block.
Definition: Block.h:105
\jacobi_module
Definition: Jacobi.h:35
EIGEN_DEVICE_FUNC void makeGivens(const Scalar &p, const Scalar &q, Scalar *r=0)
Makes *this as a Givens rotation G such that applying to the left of the vector yields: .
Definition: Jacobi.h:162
Standard Cholesky decomposition (LL^T) of a matrix and associated features.
Definition: LLT.h:68
SolverBase< LLT > Base
Definition: LLT.h:71
LLT(const EigenBase< InputType > &matrix)
Definition: LLT.h:105
LLT()
Default Constructor.
Definition: LLT.h:93
LLT(EigenBase< InputType > &matrix)
Constructs a LLT factorization from a given matrix.
Definition: LLT.h:120
Traits::MatrixU matrixU() const
Definition: LLT.h:128
RealScalar m_l1_norm
Definition: LLT.h:230
void _solve_impl(const RhsType &rhs, DstType &dst) const
Definition: LLT.h:485
EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT
Definition: LLT.h:205
ComputationInfo m_info
Definition: LLT.h:232
@ MaxColsAtCompileTime
Definition: LLT.h:76
_MatrixType MatrixType
Definition: LLT.h:70
void solveInPlace(const MatrixBase< Derived > &bAndX) const
Definition: LLT.h:516
RealScalar rcond() const
Definition: LLT.h:166
LLT & rankUpdate(const VectorType &vec, const RealScalar &sigma=1)
internal::LLT_Traits< MatrixType, UpLo > Traits
Definition: LLT.h:85
const MatrixType & matrixLLT() const
Definition: LLT.h:177
static void check_template_parameters()
Definition: LLT.h:220
Traits::MatrixL matrixL() const
Definition: LLT.h:135
const LLT & adjoint() const EIGEN_NOEXCEPT
Definition: LLT.h:202
EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT
Definition: LLT.h:204
MatrixType reconstructedMatrix() const
Definition: LLT.h:528
bool m_isInitialized
Definition: LLT.h:231
LLT & compute(const EigenBase< InputType > &matrix)
LLT(Index size)
Default Constructor with memory preallocation.
Definition: LLT.h:101
MatrixType m_matrix
Definition: LLT.h:229
@ PacketSize
Definition: LLT.h:80
@ UpLo
Definition: LLT.h:82
@ AlignmentMask
Definition: LLT.h:81
ComputationInfo info() const
Reports whether previous computation was successful.
Definition: LLT.h:191
void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const
Definition: LLT.h:492
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
const LLT< PlainObject > llt() const
\cholesky_module
Definition: LLT.h:540
const LLT< PlainObject, UpLo > llt() const
\cholesky_module
Definition: LLT.h:551
Pseudo expression representing a solving operation.
Definition: Solve.h:63
A base class for matrix decomposition and solvers.
Definition: SolverBase.h:69
internal::traits< LLT< _MatrixType, _UpLo > >::Scalar Scalar
Definition: SolverBase.h:73
const Solve< LLT< _MatrixType, _UpLo >, Rhs > solve(const MatrixBase< Rhs > &b) const
Definition: SolverBase.h:106
EIGEN_DEVICE_FUNC LLT< _MatrixType, _UpLo > & derived()
Definition: EigenBase.h:46
Expression of the transpose of a matrix.
Definition: Transpose.h:54
Expression of a triangular part in a matrix.
Definition: TriangularMatrix.h:189
auto sqrt(const UnitType &value) noexcept -> unit_t< square_root< typename units::traits::unit_t_traits< UnitType >::unit_type >, typename units::traits::unit_t_traits< UnitType >::underlying_type, linear_scale >
computes the square root of value
Definition: math.h:483
ComputationInfo
Enum for reporting the status of a computation.
Definition: Constants.h:440
@ Lower
View matrix as a lower triangular matrix.
Definition: Constants.h:209
@ Upper
View matrix as an upper triangular matrix.
Definition: Constants.h:211
@ NumericalIssue
The provided data did not satisfy the prerequisites.
Definition: Constants.h:444
@ Success
Computation was successful.
Definition: Constants.h:442
constexpr common_t< T1, T2 > max(const T1 x, const T2 y) noexcept
Compile-time pairwise maximum function.
Definition: max.hpp:35
constexpr common_t< T1, T2 > min(const T1 x, const T2 y) noexcept
Compile-time pairwise minimum function.
Definition: min.hpp:35
static Index llt_rank_update_lower(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma)
Definition: LLT.h:240
const Scalar & y
Definition: MathFunctions.h:821
EIGEN_DEVICE_FUNC bool is_same_dense(const T1 &mat1, const T2 &mat2, typename enable_if< possibly_same_dense< T1, T2 >::value >::type *=0)
Definition: XprHelper.h:695
EIGEN_CONSTEXPR Index size(const T &x)
Definition: Meta.h:479
EIGEN_DEVICE_FUNC void apply_rotation_in_the_plane(DenseBase< VectorX > &xpr_x, DenseBase< VectorY > &xpr_y, const JacobiRotation< OtherScalar > &j)
\jacobi_module Applies the clock wise 2D rotation j to the set of 2D vectors of coordinates x and y:
Definition: Jacobi.h:453
Decomposition::RealScalar rcond_estimate_helper(typename Decomposition::RealScalar matrix_norm, const Decomposition &dec)
Reciprocal condition number estimator.
Definition: ConditionEstimator.h:159
EIGEN_DEVICE_FUNC bool abs2(bool x)
Definition: MathFunctions.h:1292
Namespace containing all symbols from the Eigen library.
Definition: MatrixExponential.h:16
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
Definition: Eigen_Colamd.h:50
static constexpr const unit_t< compound_unit< power::watts, inverse< area::square_meters >, inverse< squared< squared< temperature::kelvin > > > > > sigma((2 *math::cpow< 5 >(pi) *math::cpow< 4 >(R))/(15 *math::cpow< 3 >(h) *math::cpow< 2 >(c) *math::cpow< 4 >(N_A)))
Stefan-Boltzmann constant.
Common base class for all classes T such that MatrixBase has an operator=(T) and a constructor Matrix...
Definition: EigenBase.h:30
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT
Definition: EigenBase.h:63
Eigen::Index Index
The interface type of indices.
Definition: EigenBase.h:39
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT
Definition: EigenBase.h:67
EIGEN_DEVICE_FUNC Derived & derived()
Definition: EigenBase.h:46
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT
Definition: EigenBase.h:60
The type used to identify a matrix expression.
Definition: Constants.h:522
Holds information about the various numeric (i.e.
Definition: NumTraits.h:233
The type used to identify a general solver (factored) storage.
Definition: Constants.h:513
static bool inplace_decomposition(MatrixType &m)
Definition: LLT.h:407
const TriangularView< const typename MatrixType::AdjointReturnType, Upper > MatrixU
Definition: LLT.h:404
const TriangularView< const MatrixType, Lower > MatrixL
Definition: LLT.h:403
static MatrixL getL(const MatrixType &m)
Definition: LLT.h:405
static MatrixU getU(const MatrixType &m)
Definition: LLT.h:406
const TriangularView< const MatrixType, Upper > MatrixU
Definition: LLT.h:414
static MatrixU getU(const MatrixType &m)
Definition: LLT.h:416
static MatrixL getL(const MatrixType &m)
Definition: LLT.h:415
const TriangularView< const typename MatrixType::AdjointReturnType, Lower > MatrixL
Definition: LLT.h:413
static bool inplace_decomposition(MatrixType &m)
Definition: LLT.h:417
NumTraits< Scalar >::Real RealScalar
Definition: LLT.h:311
static Index blocked(MatrixType &m)
Definition: LLT.h:339
static Index unblocked(MatrixType &mat)
Definition: LLT.h:313
static Index rankUpdate(MatrixType &mat, const VectorType &vec, const RealScalar &sigma)
Definition: LLT.h:371
static EIGEN_STRONG_INLINE Index unblocked(MatrixType &mat)
Definition: LLT.h:382
NumTraits< Scalar >::Real RealScalar
Definition: LLT.h:379
static EIGEN_STRONG_INLINE Index blocked(MatrixType &mat)
Definition: LLT.h:388
static Index rankUpdate(MatrixType &mat, const VectorType &vec, const RealScalar &sigma)
Definition: LLT.h:394
Definition: GenericPacketMath.h:107
T type
Definition: Meta.h:126
MatrixXpr XprKind
Definition: LLT.h:20
SolverStorage StorageKind
Definition: LLT.h:21
int StorageIndex
Definition: LLT.h:22
Definition: ForwardDeclarations.h:17