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Tobias Wood
2023-11-29 11:12:48 +00:00
parent 9ea520fc45
commit f38e16c193
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Eigen/src/Cholesky/LDLT.h
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@@ -19,329 +19,308 @@
namespace Eigen {
namespace internal {
template<typename MatrixType_, int UpLo_> struct traits<LDLT<MatrixType_, UpLo_> >
: traits<MatrixType_>
{
typedef MatrixXpr XprKind;
typedef SolverStorage StorageKind;
typedef int StorageIndex;
enum { Flags = 0 };
};
template <typename MatrixType_, int UpLo_>
struct traits<LDLT<MatrixType_, UpLo_> > : traits<MatrixType_> {
typedef MatrixXpr XprKind;
typedef SolverStorage StorageKind;
typedef int StorageIndex;
enum { Flags = 0 };
};
template<typename MatrixType, int UpLo> struct LDLT_Traits;
template <typename MatrixType, int UpLo>
struct LDLT_Traits;
// PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef
enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
}
// PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef
enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
} // namespace internal
/** \ingroup Cholesky_Module
*
* \class LDLT
*
* \brief Robust Cholesky decomposition of a matrix with pivoting
*
* \tparam MatrixType_ the type of the matrix of which to compute the LDL^T Cholesky decomposition
* \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper.
* The other triangular part won't be read.
*
* Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
* matrix \f$ A \f$ such that \f$ A = P^TLDL^*P \f$, where P is a permutation matrix, L
* is lower triangular with a unit diagonal and D is a diagonal matrix.
*
* The decomposition uses pivoting to ensure stability, so that D will have
* zeros in the bottom right rank(A) - n submatrix. Avoiding the square root
* on D also stabilizes the computation.
*
* Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky
* decomposition to determine whether a system of equations has a solution.
*
* This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
*
* \sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT
*/
template<typename MatrixType_, int UpLo_> class LDLT
: public SolverBase<LDLT<MatrixType_, UpLo_> >
{
public:
typedef MatrixType_ MatrixType;
typedef SolverBase<LDLT> Base;
friend class SolverBase<LDLT>;
*
* \class LDLT
*
* \brief Robust Cholesky decomposition of a matrix with pivoting
*
* \tparam MatrixType_ the type of the matrix of which to compute the LDL^T Cholesky decomposition
* \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper.
* The other triangular part won't be read.
*
* Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
* matrix \f$ A \f$ such that \f$ A = P^TLDL^*P \f$, where P is a permutation matrix, L
* is lower triangular with a unit diagonal and D is a diagonal matrix.
*
* The decomposition uses pivoting to ensure stability, so that D will have
* zeros in the bottom right rank(A) - n submatrix. Avoiding the square root
* on D also stabilizes the computation.
*
* Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky
* decomposition to determine whether a system of equations has a solution.
*
* This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
*
* \sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT
*/
template <typename MatrixType_, int UpLo_>
class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
public:
typedef MatrixType_ MatrixType;
typedef SolverBase<LDLT> Base;
friend class SolverBase<LDLT>;
EIGEN_GENERIC_PUBLIC_INTERFACE(LDLT)
enum {
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
UpLo = UpLo_
};
typedef Matrix<Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1> TmpMatrixType;
EIGEN_GENERIC_PUBLIC_INTERFACE(LDLT)
enum {
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
UpLo = UpLo_
};
typedef Matrix<Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1> TmpMatrixType;
typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
typedef internal::LDLT_Traits<MatrixType,UpLo> Traits;
typedef internal::LDLT_Traits<MatrixType, UpLo> Traits;
/** \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LDLT::compute(const MatrixType&).
*/
LDLT()
: m_matrix(),
m_transpositions(),
m_sign(internal::ZeroSign),
m_isInitialized(false)
{}
/** \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LDLT::compute(const MatrixType&).
*/
LDLT() : m_matrix(), m_transpositions(), m_sign(internal::ZeroSign), m_isInitialized(false) {}
/** \brief Default Constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
* \sa LDLT()
*/
explicit LDLT(Index size)
/** \brief Default Constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
* \sa LDLT()
*/
explicit LDLT(Index size)
: m_matrix(size, size),
m_transpositions(size),
m_temporary(size),
m_sign(internal::ZeroSign),
m_isInitialized(false)
{}
m_isInitialized(false) {}
/** \brief Constructor with decomposition
*
* This calculates the decomposition for the input \a matrix.
*
* \sa LDLT(Index size)
*/
template<typename InputType>
explicit LDLT(const EigenBase<InputType>& matrix)
/** \brief Constructor with decomposition
*
* This calculates the decomposition for the input \a matrix.
*
* \sa LDLT(Index size)
*/
template <typename InputType>
explicit LDLT(const EigenBase<InputType>& matrix)
: m_matrix(matrix.rows(), matrix.cols()),
m_transpositions(matrix.rows()),
m_temporary(matrix.rows()),
m_sign(internal::ZeroSign),
m_isInitialized(false)
{
compute(matrix.derived());
}
m_isInitialized(false) {
compute(matrix.derived());
}
/** \brief Constructs a LDLT factorization from a given matrix
*
* This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref.
*
* \sa LDLT(const EigenBase&)
*/
template<typename InputType>
explicit LDLT(EigenBase<InputType>& matrix)
/** \brief Constructs a LDLT factorization from a given matrix
*
* This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c
* MatrixType is a Eigen::Ref.
*
* \sa LDLT(const EigenBase&)
*/
template <typename InputType>
explicit LDLT(EigenBase<InputType>& matrix)
: m_matrix(matrix.derived()),
m_transpositions(matrix.rows()),
m_temporary(matrix.rows()),
m_sign(internal::ZeroSign),
m_isInitialized(false)
{
compute(matrix.derived());
}
m_isInitialized(false) {
compute(matrix.derived());
}
/** Clear any existing decomposition
* \sa rankUpdate(w,sigma)
*/
void setZero()
{
m_isInitialized = false;
}
/** Clear any existing decomposition
* \sa rankUpdate(w,sigma)
*/
void setZero() { m_isInitialized = false; }
/** \returns a view of the upper triangular matrix U */
inline typename Traits::MatrixU matrixU() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Traits::getU(m_matrix);
}
/** \returns a view of the upper triangular matrix U */
inline typename Traits::MatrixU matrixU() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Traits::getU(m_matrix);
}
/** \returns a view of the lower triangular matrix L */
inline typename Traits::MatrixL matrixL() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Traits::getL(m_matrix);
}
/** \returns a view of the lower triangular matrix L */
inline typename Traits::MatrixL matrixL() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Traits::getL(m_matrix);
}
/** \returns the permutation matrix P as a transposition sequence.
*/
inline const TranspositionType& transpositionsP() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_transpositions;
}
/** \returns the permutation matrix P as a transposition sequence.
*/
inline const TranspositionType& transpositionsP() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_transpositions;
}
/** \returns the coefficients of the diagonal matrix D */
inline Diagonal<const MatrixType> vectorD() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_matrix.diagonal();
}
/** \returns the coefficients of the diagonal matrix D */
inline Diagonal<const MatrixType> vectorD() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_matrix.diagonal();
}
/** \returns true if the matrix is positive (semidefinite) */
inline bool isPositive() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;
}
/** \returns true if the matrix is positive (semidefinite) */
inline bool isPositive() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;
}
/** \returns true if the matrix is negative (semidefinite) */
inline bool isNegative(void) const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;
}
/** \returns true if the matrix is negative (semidefinite) */
inline bool isNegative(void) const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* This function also supports in-place solves using the syntax <tt>x = decompositionObject.solve(x)</tt> .
*
* \note_about_checking_solutions
*
* More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$
* by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$,
* \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then
* \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the
* least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function
* computes the least-square solution of \f$ A x = b \f$ if \f$ A \f$ is singular.
*
* \sa MatrixBase::ldlt(), SelfAdjointView::ldlt()
*/
template<typename Rhs>
inline const Solve<LDLT, Rhs>
solve(const MatrixBase<Rhs>& b) const;
#endif
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* This function also supports in-place solves using the syntax <tt>x = decompositionObject.solve(x)</tt> .
*
* \note_about_checking_solutions
*
* More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$
* by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$,
* \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then
* \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the
* least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function
* computes the least-square solution of \f$ A x = b \f$ if \f$ A \f$ is singular.
*
* \sa MatrixBase::ldlt(), SelfAdjointView::ldlt()
*/
template <typename Rhs>
inline const Solve<LDLT, Rhs> solve(const MatrixBase<Rhs>& b) const;
#endif
template<typename Derived>
bool solveInPlace(MatrixBase<Derived> &bAndX) const;
template <typename Derived>
bool solveInPlace(MatrixBase<Derived>& bAndX) const;
template<typename InputType>
LDLT& compute(const EigenBase<InputType>& matrix);
template <typename InputType>
LDLT& compute(const EigenBase<InputType>& matrix);
/** \returns an estimate of the reciprocal condition number of the matrix of
* which \c *this is the LDLT decomposition.
*/
RealScalar rcond() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return internal::rcond_estimate_helper(m_l1_norm, *this);
}
/** \returns an estimate of the reciprocal condition number of the matrix of
* which \c *this is the LDLT decomposition.
*/
RealScalar rcond() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return internal::rcond_estimate_helper(m_l1_norm, *this);
}
template <typename Derived>
LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha=1);
template <typename Derived>
LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha = 1);
/** \returns the internal LDLT decomposition matrix
*
* TODO: document the storage layout
*/
inline const MatrixType& matrixLDLT() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_matrix;
}
/** \returns the internal LDLT decomposition matrix
*
* TODO: document the storage layout
*/
inline const MatrixType& matrixLDLT() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_matrix;
}
MatrixType reconstructedMatrix() const;
MatrixType reconstructedMatrix() const;
/** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.
*
* This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
* \code x = decomposition.adjoint().solve(b) \endcode
*/
const LDLT& adjoint() const { return *this; }
/** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix
* is self-adjoint.
*
* This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
* \code x = decomposition.adjoint().solve(b) \endcode
*/
const LDLT& adjoint() const { return *this; }
EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful,
* \c NumericalIssue if the factorization failed because of a zero pivot.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_info;
}
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful,
* \c NumericalIssue if the factorization failed because of a zero pivot.
*/
ComputationInfo info() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return m_info;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename RhsType, typename DstType>
void _solve_impl(const RhsType &rhs, DstType &dst) const;
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename RhsType, typename DstType>
void _solve_impl(const RhsType& rhs, DstType& dst) const;
template<bool Conjugate, typename RhsType, typename DstType>
void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
#endif
template <bool Conjugate, typename RhsType, typename DstType>
void _solve_impl_transposed(const RhsType& rhs, DstType& dst) const;
#endif
protected:
protected:
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
/** \internal
* Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
* The strict upper part is used during the decomposition, the strict lower
* part correspond to the coefficients of L (its diagonal is equal to 1 and
* is not stored), and the diagonal entries correspond to D.
*/
MatrixType m_matrix;
RealScalar m_l1_norm;
TranspositionType m_transpositions;
TmpMatrixType m_temporary;
internal::SignMatrix m_sign;
bool m_isInitialized;
ComputationInfo m_info;
/** \internal
* Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
* The strict upper part is used during the decomposition, the strict lower
* part correspond to the coefficients of L (its diagonal is equal to 1 and
* is not stored), and the diagonal entries correspond to D.
*/
MatrixType m_matrix;
RealScalar m_l1_norm;
TranspositionType m_transpositions;
TmpMatrixType m_temporary;
internal::SignMatrix m_sign;
bool m_isInitialized;
ComputationInfo m_info;
};
namespace internal {
template<int UpLo> struct ldlt_inplace;
template <int UpLo>
struct ldlt_inplace;
template<> struct ldlt_inplace<Lower>
{
template<typename MatrixType, typename TranspositionType, typename Workspace>
static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
{
template <>
struct ldlt_inplace<Lower> {
template <typename MatrixType, typename TranspositionType, typename Workspace>
static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign) {
using std::abs;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename TranspositionType::StorageIndex IndexType;
eigen_assert(mat.rows()==mat.cols());
eigen_assert(mat.rows() == mat.cols());
const Index size = mat.rows();
bool found_zero_pivot = false;
bool ret = true;
if (size <= 1)
{
if (size <= 1) {
transpositions.setIdentity();
if(size==0) sign = ZeroSign;
else if (numext::real(mat.coeff(0,0)) > static_cast<RealScalar>(0) ) sign = PositiveSemiDef;
else if (numext::real(mat.coeff(0,0)) < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
else sign = ZeroSign;
if (size == 0)
sign = ZeroSign;
else if (numext::real(mat.coeff(0, 0)) > static_cast<RealScalar>(0))
sign = PositiveSemiDef;
else if (numext::real(mat.coeff(0, 0)) < static_cast<RealScalar>(0))
sign = NegativeSemiDef;
else
sign = ZeroSign;
return true;
}
for (Index k = 0; k < size; ++k)
{
for (Index k = 0; k < size; ++k) {
// Find largest diagonal element
Index index_of_biggest_in_corner;
mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
mat.diagonal().tail(size - k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
index_of_biggest_in_corner += k;
transpositions.coeffRef(k) = IndexType(index_of_biggest_in_corner);
if(k != index_of_biggest_in_corner)
{
if (k != index_of_biggest_in_corner) {
// apply the transposition while taking care to consider only
// the lower triangular part
Index s = size-index_of_biggest_in_corner-1; // trailing size after the biggest element
Index s = size - index_of_biggest_in_corner - 1; // trailing size after the biggest element
mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));
mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));
std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));
for(Index i=k+1;i<index_of_biggest_in_corner;++i)
{
Scalar tmp = mat.coeffRef(i,k);
mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));
mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);
std::swap(mat.coeffRef(k, k), mat.coeffRef(index_of_biggest_in_corner, index_of_biggest_in_corner));
for (Index i = k + 1; i < index_of_biggest_in_corner; ++i) {
Scalar tmp = mat.coeffRef(i, k);
mat.coeffRef(i, k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner, i));
mat.coeffRef(index_of_biggest_in_corner, i) = numext::conj(tmp);
}
if(NumTraits<Scalar>::IsComplex)
mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));
if (NumTraits<Scalar>::IsComplex)
mat.coeffRef(index_of_biggest_in_corner, k) = numext::conj(mat.coeff(index_of_biggest_in_corner, k));
}
// partition the matrix:
@@ -349,53 +328,53 @@ template<> struct ldlt_inplace<Lower>
// lu = A10 | A11 | -
// A20 | A21 | A22
Index rs = size - k - 1;
Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
Block<MatrixType, Dynamic, 1> A21(mat, k + 1, k, rs, 1);
Block<MatrixType, 1, Dynamic> A10(mat, k, 0, 1, k);
Block<MatrixType, Dynamic, Dynamic> A20(mat, k + 1, 0, rs, k);
if(k>0)
{
if (k > 0) {
temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();
mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
if(rs>0)
A21.noalias() -= A20 * temp.head(k);
mat.coeffRef(k, k) -= (A10 * temp.head(k)).value();
if (rs > 0) A21.noalias() -= A20 * temp.head(k);
}
// In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
// was smaller than the cutoff value. However, since LDLT is not rank-revealing
// we should only make sure that we do not introduce INF or NaN values.
// Remark that LAPACK also uses 0 as the cutoff value.
RealScalar realAkk = numext::real(mat.coeffRef(k,k));
RealScalar realAkk = numext::real(mat.coeffRef(k, k));
bool pivot_is_valid = (abs(realAkk) > RealScalar(0));
if(k==0 && !pivot_is_valid)
{
if (k == 0 && !pivot_is_valid) {
// The entire diagonal is zero, there is nothing more to do
// except filling the transpositions, and checking whether the matrix is zero.
sign = ZeroSign;
for(Index j = 0; j<size; ++j)
{
for (Index j = 0; j < size; ++j) {
transpositions.coeffRef(j) = IndexType(j);
ret = ret && (mat.col(j).tail(size-j-1).array()==Scalar(0)).all();
ret = ret && (mat.col(j).tail(size - j - 1).array() == Scalar(0)).all();
}
return ret;
}
if((rs>0) && pivot_is_valid)
if ((rs > 0) && pivot_is_valid)
A21 /= realAkk;
else if(rs>0)
ret = ret && (A21.array()==Scalar(0)).all();
else if (rs > 0)
ret = ret && (A21.array() == Scalar(0)).all();
if(found_zero_pivot && pivot_is_valid) ret = false; // factorization failed
else if(!pivot_is_valid) found_zero_pivot = true;
if (found_zero_pivot && pivot_is_valid)
ret = false; // factorization failed
else if (!pivot_is_valid)
found_zero_pivot = true;
if (sign == PositiveSemiDef) {
if (realAkk < static_cast<RealScalar>(0)) sign = Indefinite;
} else if (sign == NegativeSemiDef) {
if (realAkk > static_cast<RealScalar>(0)) sign = Indefinite;
} else if (sign == ZeroSign) {
if (realAkk > static_cast<RealScalar>(0)) sign = PositiveSemiDef;
else if (realAkk < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
if (realAkk > static_cast<RealScalar>(0))
sign = PositiveSemiDef;
else if (realAkk < static_cast<RealScalar>(0))
sign = NegativeSemiDef;
}
}
@@ -409,96 +388,91 @@ template<> struct ldlt_inplace<Lower>
// original matrix is not of full rank.
// Here only rank-1 updates are implemented, to reduce the
// requirement for intermediate storage and improve accuracy
template<typename MatrixType, typename WDerived>
static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, const typename MatrixType::RealScalar& sigma=1)
{
template <typename MatrixType, typename WDerived>
static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w,
const typename MatrixType::RealScalar& sigma = 1) {
using numext::isfinite;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
const Index size = mat.rows();
eigen_assert(mat.cols() == size && w.size()==size);
eigen_assert(mat.cols() == size && w.size() == size);
RealScalar alpha = 1;
// Apply the update
for (Index j = 0; j < size; j++)
{
for (Index j = 0; j < size; j++) {
// Check for termination due to an original decomposition of low-rank
if (!(isfinite)(alpha))
break;
if (!(isfinite)(alpha)) break;
// Update the diagonal terms
RealScalar dj = numext::real(mat.coeff(j,j));
RealScalar dj = numext::real(mat.coeff(j, j));
Scalar wj = w.coeff(j);
RealScalar swj2 = sigma*numext::abs2(wj);
RealScalar gamma = dj*alpha + swj2;
mat.coeffRef(j,j) += swj2/alpha;
alpha += swj2/dj;
RealScalar swj2 = sigma * numext::abs2(wj);
RealScalar gamma = dj * alpha + swj2;
mat.coeffRef(j, j) += swj2 / alpha;
alpha += swj2 / dj;
// Update the terms of L
Index rs = size-j-1;
Index rs = size - j - 1;
w.tail(rs) -= wj * mat.col(j).tail(rs);
if(!numext::is_exactly_zero(gamma))
mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);
if (!numext::is_exactly_zero(gamma)) mat.col(j).tail(rs) += (sigma * numext::conj(wj) / gamma) * w.tail(rs);
}
return true;
}
template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w, const typename MatrixType::RealScalar& sigma=1)
{
template <typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w,
const typename MatrixType::RealScalar& sigma = 1) {
// Apply the permutation to the input w
tmp = transpositions * w;
return ldlt_inplace<Lower>::updateInPlace(mat,tmp,sigma);
return ldlt_inplace<Lower>::updateInPlace(mat, tmp, sigma);
}
};
template<> struct ldlt_inplace<Upper>
{
template<typename MatrixType, typename TranspositionType, typename Workspace>
static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
{
template <>
struct ldlt_inplace<Upper> {
template <typename MatrixType, typename TranspositionType, typename Workspace>
static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp,
SignMatrix& sign) {
Transpose<MatrixType> matt(mat);
return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
}
template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w, const typename MatrixType::RealScalar& sigma=1)
{
template <typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w,
const typename MatrixType::RealScalar& sigma = 1) {
Transpose<MatrixType> matt(mat);
return ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);
}
};
template<typename MatrixType> struct LDLT_Traits<MatrixType,Lower>
{
template <typename MatrixType>
struct LDLT_Traits<MatrixType, Lower> {
typedef const TriangularView<const MatrixType, UnitLower> MatrixL;
typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
};
template<typename MatrixType> struct LDLT_Traits<MatrixType,Upper>
{
template <typename MatrixType>
struct LDLT_Traits<MatrixType, Upper> {
typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;
typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
};
} // end namespace internal
} // end namespace internal
/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
*/
template<typename MatrixType, int UpLo_>
template<typename InputType>
LDLT<MatrixType,UpLo_>& LDLT<MatrixType,UpLo_>::compute(const EigenBase<InputType>& a)
{
eigen_assert(a.rows()==a.cols());
*/
template <typename MatrixType, int UpLo_>
template <typename InputType>
LDLT<MatrixType, UpLo_>& LDLT<MatrixType, UpLo_>::compute(const EigenBase<InputType>& a) {
eigen_assert(a.rows() == a.cols());
const Index size = a.rows();
m_matrix = a.derived();
@@ -509,11 +483,12 @@ LDLT<MatrixType,UpLo_>& LDLT<MatrixType,UpLo_>::compute(const EigenBase<InputTyp
for (Index col = 0; col < size; ++col) {
RealScalar abs_col_sum;
if (UpLo_ == Lower)
abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
abs_col_sum =
m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
else
abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
if (abs_col_sum > m_l1_norm)
m_l1_norm = abs_col_sum;
abs_col_sum =
m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
if (abs_col_sum > m_l1_norm) m_l1_norm = abs_col_sum;
}
m_transpositions.resize(size);
@@ -521,7 +496,8 @@ LDLT<MatrixType,UpLo_>& LDLT<MatrixType,UpLo_>::compute(const EigenBase<InputTyp
m_temporary.resize(size);
m_sign = internal::ZeroSign;
m_info = internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? Success : NumericalIssue;
m_info = internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? Success
: NumericalIssue;
m_isInitialized = true;
return *this;
@@ -529,28 +505,24 @@ LDLT<MatrixType,UpLo_>& LDLT<MatrixType,UpLo_>::compute(const EigenBase<InputTyp
/** Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.
* \param w a vector to be incorporated into the decomposition.
* \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1.
* \sa setZero()
*/
template<typename MatrixType, int UpLo_>
template<typename Derived>
LDLT<MatrixType,UpLo_>& LDLT<MatrixType,UpLo_>::rankUpdate(const MatrixBase<Derived>& w, const typename LDLT<MatrixType,UpLo_>::RealScalar& sigma)
{
* \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column
* vectors. Optional; default value is +1. \sa setZero()
*/
template <typename MatrixType, int UpLo_>
template <typename Derived>
LDLT<MatrixType, UpLo_>& LDLT<MatrixType, UpLo_>::rankUpdate(
const MatrixBase<Derived>& w, const typename LDLT<MatrixType, UpLo_>::RealScalar& sigma) {
typedef typename TranspositionType::StorageIndex IndexType;
const Index size = w.rows();
if (m_isInitialized)
{
eigen_assert(m_matrix.rows()==size);
}
else
{
m_matrix.resize(size,size);
if (m_isInitialized) {
eigen_assert(m_matrix.rows() == size);
} else {
m_matrix.resize(size, size);
m_matrix.setZero();
m_transpositions.resize(size);
for (Index i = 0; i < size; i++)
m_transpositions.coeffRef(i) = IndexType(i);
for (Index i = 0; i < size; i++) m_transpositions.coeffRef(i) = IndexType(i);
m_temporary.resize(size);
m_sign = sigma>=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;
m_sign = sigma >= 0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;
m_isInitialized = true;
}
@@ -560,17 +532,15 @@ LDLT<MatrixType,UpLo_>& LDLT<MatrixType,UpLo_>::rankUpdate(const MatrixBase<Deri
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename MatrixType_, int UpLo_>
template<typename RhsType, typename DstType>
void LDLT<MatrixType_,UpLo_>::_solve_impl(const RhsType &rhs, DstType &dst) const
{
template <typename MatrixType_, int UpLo_>
template <typename RhsType, typename DstType>
void LDLT<MatrixType_, UpLo_>::_solve_impl(const RhsType& rhs, DstType& dst) const {
_solve_impl_transposed<true>(rhs, dst);
}
template<typename MatrixType_,int UpLo_>
template<bool Conjugate, typename RhsType, typename DstType>
void LDLT<MatrixType_,UpLo_>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
{
template <typename MatrixType_, int UpLo_>
template <bool Conjugate, typename RhsType, typename DstType>
void LDLT<MatrixType_, UpLo_>::_solve_impl_transposed(const RhsType& rhs, DstType& dst) const {
// dst = P b
dst = m_transpositions * rhs;
@@ -585,15 +555,13 @@ void LDLT<MatrixType_,UpLo_>::_solve_impl_transposed(const RhsType &rhs, DstType
const typename Diagonal<const MatrixType>::RealReturnType vecD(vectorD());
// In some previous versions, tolerance was set to the max of 1/highest (or rather numeric_limits::min())
// and the maximal diagonal entry * epsilon as motivated by LAPACK's xGELSS:
// RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest());
// However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest
// diagonal element is not well justified and leads to numerical issues in some cases.
// Moreover, Lapack's xSYTRS routines use 0 for the tolerance.
// Using numeric_limits::min() gives us more robustness to denormals.
// RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits<RealScalar>::epsilon(),RealScalar(1)
// / NumTraits<RealScalar>::highest()); However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the
// highest diagonal element is not well justified and leads to numerical issues in some cases. Moreover, Lapack's
// xSYTRS routines use 0 for the tolerance. Using numeric_limits::min() gives us more robustness to denormals.
RealScalar tolerance = (std::numeric_limits<RealScalar>::min)();
for (Index i = 0; i < vecD.size(); ++i)
{
if(abs(vecD(i)) > tolerance)
for (Index i = 0; i < vecD.size(); ++i) {
if (abs(vecD(i)) > tolerance)
dst.row(i) /= vecD(i);
else
dst.row(i).setZero();
@@ -610,22 +578,21 @@ void LDLT<MatrixType_,UpLo_>::_solve_impl_transposed(const RhsType &rhs, DstType
#endif
/** \internal use x = ldlt_object.solve(x);
*
* This is the \em in-place version of solve().
*
* \param bAndX represents both the right-hand side matrix b and result x.
*
* \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
*
* This version avoids a copy when the right hand side matrix b is not
* needed anymore.
*
* \sa LDLT::solve(), MatrixBase::ldlt()
*/
template<typename MatrixType,int UpLo_>
template<typename Derived>
bool LDLT<MatrixType,UpLo_>::solveInPlace(MatrixBase<Derived> &bAndX) const
{
*
* This is the \em in-place version of solve().
*
* \param bAndX represents both the right-hand side matrix b and result x.
*
* \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
*
* This version avoids a copy when the right hand side matrix b is not
* needed anymore.
*
* \sa LDLT::solve(), MatrixBase::ldlt()
*/
template <typename MatrixType, int UpLo_>
template <typename Derived>
bool LDLT<MatrixType, UpLo_>::solveInPlace(MatrixBase<Derived>& bAndX) const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
eigen_assert(m_matrix.rows() == bAndX.rows());
@@ -637,12 +604,11 @@ bool LDLT<MatrixType,UpLo_>::solveInPlace(MatrixBase<Derived> &bAndX) const
/** \returns the matrix represented by the decomposition,
* i.e., it returns the product: P^T L D L^* P.
* This function is provided for debug purpose. */
template<typename MatrixType, int UpLo_>
MatrixType LDLT<MatrixType,UpLo_>::reconstructedMatrix() const
{
template <typename MatrixType, int UpLo_>
MatrixType LDLT<MatrixType, UpLo_>::reconstructedMatrix() const {
eigen_assert(m_isInitialized && "LDLT is not initialized.");
const Index size = m_matrix.rows();
MatrixType res(size,size);
MatrixType res(size, size);
// P
res.setIdentity();
@@ -660,27 +626,24 @@ MatrixType LDLT<MatrixType,UpLo_>::reconstructedMatrix() const
}
/** \cholesky_module
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
* \sa MatrixBase::ldlt()
*/
template<typename MatrixType, unsigned int UpLo>
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
* \sa MatrixBase::ldlt()
*/
template <typename MatrixType, unsigned int UpLo>
inline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
SelfAdjointView<MatrixType, UpLo>::ldlt() const
{
return LDLT<PlainObject,UpLo>(m_matrix);
SelfAdjointView<MatrixType, UpLo>::ldlt() const {
return LDLT<PlainObject, UpLo>(m_matrix);
}
/** \cholesky_module
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
* \sa SelfAdjointView::ldlt()
*/
template<typename Derived>
inline const LDLT<typename MatrixBase<Derived>::PlainObject>
MatrixBase<Derived>::ldlt() const
{
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
* \sa SelfAdjointView::ldlt()
*/
template <typename Derived>
inline const LDLT<typename MatrixBase<Derived>::PlainObject> MatrixBase<Derived>::ldlt() const {
return LDLT<PlainObject>(derived());
}
} // end namespace Eigen
} // end namespace Eigen
#endif // EIGEN_LDLT_H
#endif // EIGEN_LDLT_H

660
Eigen/src/Cholesky/LLT.h
View File

@@ -15,427 +15,392 @@
namespace Eigen {
namespace internal{
namespace internal {
template<typename MatrixType_, int UpLo_> struct traits<LLT<MatrixType_, UpLo_> >
: traits<MatrixType_>
{
template <typename MatrixType_, int UpLo_>
struct traits<LLT<MatrixType_, UpLo_> > : traits<MatrixType_> {
typedef MatrixXpr XprKind;
typedef SolverStorage StorageKind;
typedef int StorageIndex;
enum { Flags = 0 };
};
template<typename MatrixType, int UpLo> struct LLT_Traits;
}
template <typename MatrixType, int UpLo>
struct LLT_Traits;
} // namespace internal
/** \ingroup Cholesky_Module
*
* \class LLT
*
* \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
*
* \tparam MatrixType_ the type of the matrix of which we are computing the LL^T Cholesky decomposition
* \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper.
* The other triangular part won't be read.
*
* This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
* matrix A such that A = LL^* = U^*U, where L is lower triangular.
*
* While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b,
* for that purpose, we recommend the Cholesky decomposition without square root which is more stable
* and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other
* situations like generalised eigen problems with hermitian matrices.
*
* Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices,
* use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations
* has a solution.
*
* Example: \include LLT_example.cpp
* Output: \verbinclude LLT_example.out
*
* \b Performance: for best performance, it is recommended to use a column-major storage format
* with the Lower triangular part (the default), or, equivalently, a row-major storage format
* with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization
* step, and rank-updates can be up to 3 times slower.
*
* This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
*
* Note that during the decomposition, only the lower (or upper, as defined by UpLo_) triangular part of A is considered.
* Therefore, the strict lower part does not have to store correct values.
*
* \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT
*/
template<typename MatrixType_, int UpLo_> class LLT
: public SolverBase<LLT<MatrixType_, UpLo_> >
{
public:
typedef MatrixType_ MatrixType;
typedef SolverBase<LLT> Base;
friend class SolverBase<LLT>;
*
* \class LLT
*
* \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
*
* \tparam MatrixType_ the type of the matrix of which we are computing the LL^T Cholesky decomposition
* \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper.
* The other triangular part won't be read.
*
* This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
* matrix A such that A = LL^* = U^*U, where L is lower triangular.
*
* While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b,
* for that purpose, we recommend the Cholesky decomposition without square root which is more stable
* and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other
* situations like generalised eigen problems with hermitian matrices.
*
* Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive
* definite matrices, use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine
* whether a system of equations has a solution.
*
* Example: \include LLT_example.cpp
* Output: \verbinclude LLT_example.out
*
* \b Performance: for best performance, it is recommended to use a column-major storage format
* with the Lower triangular part (the default), or, equivalently, a row-major storage format
* with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization
* step, and rank-updates can be up to 3 times slower.
*
* This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
*
* Note that during the decomposition, only the lower (or upper, as defined by UpLo_) triangular part of A is
* considered. Therefore, the strict lower part does not have to store correct values.
*
* \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT
*/
template <typename MatrixType_, int UpLo_>
class LLT : public SolverBase<LLT<MatrixType_, UpLo_> > {
public:
typedef MatrixType_ MatrixType;
typedef SolverBase<LLT> Base;
friend class SolverBase<LLT>;
EIGEN_GENERIC_PUBLIC_INTERFACE(LLT)
enum {
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
};
EIGEN_GENERIC_PUBLIC_INTERFACE(LLT)
enum { MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime };
enum {
PacketSize = internal::packet_traits<Scalar>::size,
AlignmentMask = int(PacketSize)-1,
UpLo = UpLo_
};
enum { PacketSize = internal::packet_traits<Scalar>::size, AlignmentMask = int(PacketSize) - 1, UpLo = UpLo_ };
typedef internal::LLT_Traits<MatrixType,UpLo> Traits;
typedef internal::LLT_Traits<MatrixType, UpLo> Traits;
/**
* \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LLT::compute(const MatrixType&).
*/
LLT() : m_matrix(), m_isInitialized(false) {}
/**
* \brief Default Constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LLT::compute(const MatrixType&).
*/
LLT() : m_matrix(), m_isInitialized(false) {}
/** \brief Default Constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
* \sa LLT()
*/
explicit LLT(Index size) : m_matrix(size, size),
m_isInitialized(false) {}
/** \brief Default Constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
* \sa LLT()
*/
explicit LLT(Index size) : m_matrix(size, size), m_isInitialized(false) {}
template<typename InputType>
explicit LLT(const EigenBase<InputType>& matrix)
: m_matrix(matrix.rows(), matrix.cols()),
m_isInitialized(false)
{
compute(matrix.derived());
}
template <typename InputType>
explicit LLT(const EigenBase<InputType>& matrix) : m_matrix(matrix.rows(), matrix.cols()), m_isInitialized(false) {
compute(matrix.derived());
}
/** \brief Constructs a LLT factorization from a given matrix
*
* This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when
* \c MatrixType is a Eigen::Ref.
*
* \sa LLT(const EigenBase&)
*/
template<typename InputType>
explicit LLT(EigenBase<InputType>& matrix)
: m_matrix(matrix.derived()),
m_isInitialized(false)
{
compute(matrix.derived());
}
/** \brief Constructs a LLT factorization from a given matrix
*
* This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when
* \c MatrixType is a Eigen::Ref.
*
* \sa LLT(const EigenBase&)
*/
template <typename InputType>
explicit LLT(EigenBase<InputType>& matrix) : m_matrix(matrix.derived()), m_isInitialized(false) {
compute(matrix.derived());
}
/** \returns a view of the upper triangular matrix U */
inline typename Traits::MatrixU matrixU() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return Traits::getU(m_matrix);
}
/** \returns a view of the upper triangular matrix U */
inline typename Traits::MatrixU matrixU() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
return Traits::getU(m_matrix);
}
/** \returns a view of the lower triangular matrix L */
inline typename Traits::MatrixL matrixL() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return Traits::getL(m_matrix);
}
/** \returns a view of the lower triangular matrix L */
inline typename Traits::MatrixL matrixL() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
return Traits::getL(m_matrix);
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* Since this LLT class assumes anyway that the matrix A is invertible, the solution
* theoretically exists and is unique regardless of b.
*
* Example: \include LLT_solve.cpp
* Output: \verbinclude LLT_solve.out
*
* \sa solveInPlace(), MatrixBase::llt(), SelfAdjointView::llt()
*/
template<typename Rhs>
inline const Solve<LLT, Rhs>
solve(const MatrixBase<Rhs>& b) const;
#endif
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* Since this LLT class assumes anyway that the matrix A is invertible, the solution
* theoretically exists and is unique regardless of b.
*
* Example: \include LLT_solve.cpp
* Output: \verbinclude LLT_solve.out
*
* \sa solveInPlace(), MatrixBase::llt(), SelfAdjointView::llt()
*/
template <typename Rhs>
inline const Solve<LLT, Rhs> solve(const MatrixBase<Rhs>& b) const;
#endif
template<typename Derived>
void solveInPlace(const MatrixBase<Derived> &bAndX) const;
template <typename Derived>
void solveInPlace(const MatrixBase<Derived>& bAndX) const;
template<typename InputType>
LLT& compute(const EigenBase<InputType>& matrix);
template <typename InputType>
LLT& compute(const EigenBase<InputType>& matrix);
/** \returns an estimate of the reciprocal condition number of the matrix of
* which \c *this is the Cholesky decomposition.
*/
RealScalar rcond() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative");
return internal::rcond_estimate_helper(m_l1_norm, *this);
}
/** \returns an estimate of the reciprocal condition number of the matrix of
* which \c *this is the Cholesky decomposition.
*/
RealScalar rcond() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative");
return internal::rcond_estimate_helper(m_l1_norm, *this);
}
/** \returns the LLT decomposition matrix
*
* TODO: document the storage layout
*/
inline const MatrixType& matrixLLT() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return m_matrix;
}
/** \returns the LLT decomposition matrix
*
* TODO: document the storage layout
*/
inline const MatrixType& matrixLLT() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
return m_matrix;
}
MatrixType reconstructedMatrix() const;
MatrixType reconstructedMatrix() const;
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful,
* \c NumericalIssue if the matrix.appears not to be positive definite.
*/
ComputationInfo info() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
return m_info;
}
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was successful,
* \c NumericalIssue if the matrix.appears not to be positive definite.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
return m_info;
}
/** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix
* is self-adjoint.
*
* This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
* \code x = decomposition.adjoint().solve(b) \endcode
*/
const LLT& adjoint() const EIGEN_NOEXCEPT { return *this; }
/** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.
*
* This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
* \code x = decomposition.adjoint().solve(b) \endcode
*/
const LLT& adjoint() const EIGEN_NOEXCEPT { return *this; }
inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
template <typename VectorType>
LLT& rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
template<typename VectorType>
LLT & rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
#ifndef EIGEN_PARSED_BY_DOXYGEN
template <typename RhsType, typename DstType>
void _solve_impl(const RhsType& rhs, DstType& dst) const;
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename RhsType, typename DstType>
void _solve_impl(const RhsType &rhs, DstType &dst) const;
template <bool Conjugate, typename RhsType, typename DstType>
void _solve_impl_transposed(const RhsType& rhs, DstType& dst) const;
#endif
template<bool Conjugate, typename RhsType, typename DstType>
void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
#endif
protected:
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
protected:
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
/** \internal
* Used to compute and store L
* The strict upper part is not used and even not initialized.
*/
MatrixType m_matrix;
RealScalar m_l1_norm;
bool m_isInitialized;
ComputationInfo m_info;
/** \internal
* Used to compute and store L
* The strict upper part is not used and even not initialized.
*/
MatrixType m_matrix;
RealScalar m_l1_norm;
bool m_isInitialized;
ComputationInfo m_info;
};
namespace internal {
template<typename Scalar, int UpLo> struct llt_inplace;
template <typename Scalar, int UpLo>
struct llt_inplace;
template<typename MatrixType, typename VectorType>
static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
{
template <typename MatrixType, typename VectorType>
static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec,
const typename MatrixType::RealScalar& sigma) {
using std::sqrt;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::ColXpr ColXpr;
typedef internal::remove_all_t<ColXpr> ColXprCleaned;
typedef typename ColXprCleaned::SegmentReturnType ColXprSegment;
typedef Matrix<Scalar,Dynamic,1> TempVectorType;
typedef Matrix<Scalar, Dynamic, 1> TempVectorType;
typedef typename TempVectorType::SegmentReturnType TempVecSegment;
Index n = mat.cols();
eigen_assert(mat.rows()==n && vec.size()==n);
eigen_assert(mat.rows() == n && vec.size() == n);
TempVectorType temp;
if(sigma>0)
{
if (sigma > 0) {
// This version is based on Givens rotations.
// It is faster than the other one below, but only works for updates,
// i.e., for sigma > 0
temp = sqrt(sigma) * vec;
for(Index i=0; i<n; ++i)
{
for (Index i = 0; i < n; ++i) {
JacobiRotation<Scalar> g;
g.makeGivens(mat(i,i), -temp(i), &mat(i,i));
g.makeGivens(mat(i, i), -temp(i), &mat(i, i));
Index rs = n-i-1;
if(rs>0)
{
Index rs = n - i - 1;
if (rs > 0) {
ColXprSegment x(mat.col(i).tail(rs));
TempVecSegment y(temp.tail(rs));
apply_rotation_in_the_plane(x, y, g);
}
}
}
else
{
} else {
temp = vec;
RealScalar beta = 1;
for(Index j=0; j<n; ++j)
{
RealScalar Ljj = numext::real(mat.coeff(j,j));
for (Index j = 0; j < n; ++j) {
RealScalar Ljj = numext::real(mat.coeff(j, j));
RealScalar dj = numext::abs2(Ljj);
Scalar wj = temp.coeff(j);
RealScalar swj2 = sigma*numext::abs2(wj);
RealScalar gamma = dj*beta + swj2;
RealScalar swj2 = sigma * numext::abs2(wj);
RealScalar gamma = dj * beta + swj2;
RealScalar x = dj + swj2/beta;
if (x<=RealScalar(0))
return j;
RealScalar x = dj + swj2 / beta;
if (x <= RealScalar(0)) return j;
RealScalar nLjj = sqrt(x);
mat.coeffRef(j,j) = nLjj;
beta += swj2/dj;
mat.coeffRef(j, j) = nLjj;
beta += swj2 / dj;
// Update the terms of L
Index rs = n-j-1;
if(rs)
{
temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);
if(!numext::is_exactly_zero(gamma))
mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs);
Index rs = n - j - 1;
if (rs) {
temp.tail(rs) -= (wj / Ljj) * mat.col(j).tail(rs);
if (!numext::is_exactly_zero(gamma))
mat.col(j).tail(rs) =
(nLjj / Ljj) * mat.col(j).tail(rs) + (nLjj * sigma * numext::conj(wj) / gamma) * temp.tail(rs);
}
}
}
return -1;
}
template<typename Scalar> struct llt_inplace<Scalar, Lower>
{
template <typename Scalar>
struct llt_inplace<Scalar, Lower> {
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename MatrixType>
static Index unblocked(MatrixType& mat)
{
template <typename MatrixType>
static Index unblocked(MatrixType& mat) {
using std::sqrt;
eigen_assert(mat.rows()==mat.cols());
eigen_assert(mat.rows() == mat.cols());
const Index size = mat.rows();
for(Index k = 0; k < size; ++k)
{
Index rs = size-k-1; // remaining size
for (Index k = 0; k < size; ++k) {
Index rs = size - k - 1; // remaining size
Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
Block<MatrixType, Dynamic, 1> A21(mat, k + 1, k, rs, 1);
Block<MatrixType, 1, Dynamic> A10(mat, k, 0, 1, k);
Block<MatrixType, Dynamic, Dynamic> A20(mat, k + 1, 0, rs, k);
RealScalar x = numext::real(mat.coeff(k,k));
if (k>0) x -= A10.squaredNorm();
if (x<=RealScalar(0))
return k;
mat.coeffRef(k,k) = x = sqrt(x);
if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
if (rs>0) A21 /= x;
RealScalar x = numext::real(mat.coeff(k, k));
if (k > 0) x -= A10.squaredNorm();
if (x <= RealScalar(0)) return k;
mat.coeffRef(k, k) = x = sqrt(x);
if (k > 0 && rs > 0) A21.noalias() -= A20 * A10.adjoint();
if (rs > 0) A21 /= x;
}
return -1;
}
template<typename MatrixType>
static Index blocked(MatrixType& m)
{
eigen_assert(m.rows()==m.cols());
template <typename MatrixType>
static Index blocked(MatrixType& m) {
eigen_assert(m.rows() == m.cols());
Index size = m.rows();
if(size<32)
return unblocked(m);
if (size < 32) return unblocked(m);
Index blockSize = size/8;
blockSize = (blockSize/16)*16;
blockSize = (std::min)((std::max)(blockSize,Index(8)), Index(128));
Index blockSize = size / 8;
blockSize = (blockSize / 16) * 16;
blockSize = (std::min)((std::max)(blockSize, Index(8)), Index(128));
for (Index k=0; k<size; k+=blockSize)
{
for (Index k = 0; k < size; k += blockSize) {
// partition the matrix:
// A00 | - | -
// lu = A10 | A11 | -
// A20 | A21 | A22
Index bs = (std::min)(blockSize, size-k);
Index bs = (std::min)(blockSize, size - k);
Index rs = size - k - bs;
Block<MatrixType,Dynamic,Dynamic> A11(m,k, k, bs,bs);
Block<MatrixType,Dynamic,Dynamic> A21(m,k+bs,k, rs,bs);
Block<MatrixType,Dynamic,Dynamic> A22(m,k+bs,k+bs,rs,rs);
Block<MatrixType, Dynamic, Dynamic> A11(m, k, k, bs, bs);
Block<MatrixType, Dynamic, Dynamic> A21(m, k + bs, k, rs, bs);
Block<MatrixType, Dynamic, Dynamic> A22(m, k + bs, k + bs, rs, rs);
Index ret;
if((ret=unblocked(A11))>=0) return k+ret;
if(rs>0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21);
if(rs>0) A22.template selfadjointView<Lower>().rankUpdate(A21,typename NumTraits<RealScalar>::Literal(-1)); // bottleneck
if ((ret = unblocked(A11)) >= 0) return k + ret;
if (rs > 0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21);
if (rs > 0)
A22.template selfadjointView<Lower>().rankUpdate(A21,
typename NumTraits<RealScalar>::Literal(-1)); // bottleneck
}
return -1;
}
template<typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
{
template <typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma) {
return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
}
};
template<typename Scalar> struct llt_inplace<Scalar, Upper>
{
template <typename Scalar>
struct llt_inplace<Scalar, Upper> {
typedef typename NumTraits<Scalar>::Real RealScalar;
template<typename MatrixType>
static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat)
{
template <typename MatrixType>
static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat) {
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::unblocked(matt);
}
template<typename MatrixType>
static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat)
{
template <typename MatrixType>
static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat) {
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::blocked(matt);
}
template<typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
{
template <typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma) {
Transpose<MatrixType> matt(mat);
return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma);
}
};
template<typename MatrixType> struct LLT_Traits<MatrixType,Lower>
{
template <typename MatrixType>
struct LLT_Traits<MatrixType, Lower> {
typedef const TriangularView<const MatrixType, Lower> MatrixL;
typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
static bool inplace_decomposition(MatrixType& m)
{ return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m)==-1; }
static bool inplace_decomposition(MatrixType& m) {
return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m) == -1;
}
};
template<typename MatrixType> struct LLT_Traits<MatrixType,Upper>
{
template <typename MatrixType>
struct LLT_Traits<MatrixType, Upper> {
typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL;
typedef const TriangularView<const MatrixType, Upper> MatrixU;
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
static bool inplace_decomposition(MatrixType& m)
{ return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m)==-1; }
static bool inplace_decomposition(MatrixType& m) {
return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m) == -1;
}
};
} // end namespace internal
} // end namespace internal
/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix
*
* \returns a reference to *this
*
* Example: \include TutorialLinAlgComputeTwice.cpp
* Output: \verbinclude TutorialLinAlgComputeTwice.out
*/
template<typename MatrixType, int UpLo_>
template<typename InputType>
LLT<MatrixType,UpLo_>& LLT<MatrixType,UpLo_>::compute(const EigenBase<InputType>& a)
{
eigen_assert(a.rows()==a.cols());
*
* \returns a reference to *this
*
* Example: \include TutorialLinAlgComputeTwice.cpp
* Output: \verbinclude TutorialLinAlgComputeTwice.out
*/
template <typename MatrixType, int UpLo_>
template <typename InputType>
LLT<MatrixType, UpLo_>& LLT<MatrixType, UpLo_>::compute(const EigenBase<InputType>& a) {
eigen_assert(a.rows() == a.cols());
const Index size = a.rows();
m_matrix.resize(size, size);
if (!internal::is_same_dense(m_matrix, a.derived()))
m_matrix = a.derived();
if (!internal::is_same_dense(m_matrix, a.derived())) m_matrix = a.derived();
// Compute matrix L1 norm = max abs column sum.
m_l1_norm = RealScalar(0);
@@ -443,11 +408,12 @@ LLT<MatrixType,UpLo_>& LLT<MatrixType,UpLo_>::compute(const EigenBase<InputType>
for (Index col = 0; col < size; ++col) {
RealScalar abs_col_sum;
if (UpLo_ == Lower)
abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
abs_col_sum =
m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
else
abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
if (abs_col_sum > m_l1_norm)
m_l1_norm = abs_col_sum;
abs_col_sum =
m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
if (abs_col_sum > m_l1_norm) m_l1_norm = abs_col_sum;
}
m_isInitialized = true;
@@ -458,18 +424,17 @@ LLT<MatrixType,UpLo_>& LLT<MatrixType,UpLo_>::compute(const EigenBase<InputType>
}
/** Performs a rank one update (or dowdate) of the current decomposition.
* If A = LL^* before the rank one update,
* then after it we have LL^* = A + sigma * v v^* where \a v must be a vector
* of same dimension.
*/
template<typename MatrixType_, int UpLo_>
template<typename VectorType>
LLT<MatrixType_,UpLo_> & LLT<MatrixType_,UpLo_>::rankUpdate(const VectorType& v, const RealScalar& sigma)
{
* If A = LL^* before the rank one update,
* then after it we have LL^* = A + sigma * v v^* where \a v must be a vector
* of same dimension.
*/
template <typename MatrixType_, int UpLo_>
template <typename VectorType>
LLT<MatrixType_, UpLo_>& LLT<MatrixType_, UpLo_>::rankUpdate(const VectorType& v, const RealScalar& sigma) {
EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);
eigen_assert(v.size()==m_matrix.cols());
eigen_assert(v.size() == m_matrix.cols());
eigen_assert(m_isInitialized);
if(internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix,v,sigma)>=0)
if (internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix, v, sigma) >= 0)
m_info = NumericalIssue;
else
m_info = Success;
@@ -478,43 +443,40 @@ LLT<MatrixType_,UpLo_> & LLT<MatrixType_,UpLo_>::rankUpdate(const VectorType& v,
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename MatrixType_,int UpLo_>
template<typename RhsType, typename DstType>
void LLT<MatrixType_,UpLo_>::_solve_impl(const RhsType &rhs, DstType &dst) const
{
template <typename MatrixType_, int UpLo_>
template <typename RhsType, typename DstType>
void LLT<MatrixType_, UpLo_>::_solve_impl(const RhsType& rhs, DstType& dst) const {
_solve_impl_transposed<true>(rhs, dst);
}
template<typename MatrixType_,int UpLo_>
template<bool Conjugate, typename RhsType, typename DstType>
void LLT<MatrixType_,UpLo_>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
{
dst = rhs;
template <typename MatrixType_, int UpLo_>
template <bool Conjugate, typename RhsType, typename DstType>
void LLT<MatrixType_, UpLo_>::_solve_impl_transposed(const RhsType& rhs, DstType& dst) const {
dst = rhs;
matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
matrixU().template conjugateIf<!Conjugate>().solveInPlace(dst);
matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
matrixU().template conjugateIf<!Conjugate>().solveInPlace(dst);
}
#endif
/** \internal use x = llt_object.solve(x);
*
* This is the \em in-place version of solve().
*
* \param bAndX represents both the right-hand side matrix b and result x.
*
* This version avoids a copy when the right hand side matrix b is not needed anymore.
*
* \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
* This function will const_cast it, so constness isn't honored here.
*
* \sa LLT::solve(), MatrixBase::llt()
*/
template<typename MatrixType, int UpLo_>
template<typename Derived>
void LLT<MatrixType,UpLo_>::solveInPlace(const MatrixBase<Derived> &bAndX) const
{
*
* This is the \em in-place version of solve().
*
* \param bAndX represents both the right-hand side matrix b and result x.
*
* This version avoids a copy when the right hand side matrix b is not needed anymore.
*
* \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
* This function will const_cast it, so constness isn't honored here.
*
* \sa LLT::solve(), MatrixBase::llt()
*/
template <typename MatrixType, int UpLo_>
template <typename Derived>
void LLT<MatrixType, UpLo_>::solveInPlace(const MatrixBase<Derived>& bAndX) const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(m_matrix.rows()==bAndX.rows());
eigen_assert(m_matrix.rows() == bAndX.rows());
matrixL().solveInPlace(bAndX);
matrixU().solveInPlace(bAndX);
}
@@ -522,35 +484,31 @@ void LLT<MatrixType,UpLo_>::solveInPlace(const MatrixBase<Derived> &bAndX) const
/** \returns the matrix represented by the decomposition,
* i.e., it returns the product: L L^*.
* This function is provided for debug purpose. */
template<typename MatrixType, int UpLo_>
MatrixType LLT<MatrixType,UpLo_>::reconstructedMatrix() const
{
template <typename MatrixType, int UpLo_>
MatrixType LLT<MatrixType, UpLo_>::reconstructedMatrix() const {
eigen_assert(m_isInitialized && "LLT is not initialized.");
return matrixL() * matrixL().adjoint().toDenseMatrix();
}
/** \cholesky_module
* \returns the LLT decomposition of \c *this
* \sa SelfAdjointView::llt()
*/
template<typename Derived>
inline const LLT<typename MatrixBase<Derived>::PlainObject>
MatrixBase<Derived>::llt() const
{
* \returns the LLT decomposition of \c *this
* \sa SelfAdjointView::llt()
*/
template <typename Derived>
inline const LLT<typename MatrixBase<Derived>::PlainObject> MatrixBase<Derived>::llt() const {
return LLT<PlainObject>(derived());
}
/** \cholesky_module
* \returns the LLT decomposition of \c *this
* \sa SelfAdjointView::llt()
*/
template<typename MatrixType, unsigned int UpLo>
inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
SelfAdjointView<MatrixType, UpLo>::llt() const
{
return LLT<PlainObject,UpLo>(m_matrix);
* \returns the LLT decomposition of \c *this
* \sa SelfAdjointView::llt()
*/
template <typename MatrixType, unsigned int UpLo>
inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo> SelfAdjointView<MatrixType, UpLo>::llt()
const {
return LLT<PlainObject, UpLo>(m_matrix);
}
} // end namespace Eigen
} // end namespace Eigen
#endif // EIGEN_LLT_H
#endif // EIGEN_LLT_H

112
Eigen/src/Cholesky/LLT_LAPACKE.h
View File

@@ -41,63 +41,61 @@ namespace Eigen {
namespace internal {
namespace lapacke_helpers {
// -------------------------------------------------------------------------------------------------------------------
// Dispatch for rank update handling upper and lower parts
// -------------------------------------------------------------------------------------------------------------------
// -------------------------------------------------------------------------------------------------------------------
// Dispatch for rank update handling upper and lower parts
// -------------------------------------------------------------------------------------------------------------------
template<UpLoType Mode>
struct rank_update {};
template <UpLoType Mode>
struct rank_update {};
template<>
struct rank_update<Lower> {
template<typename MatrixType, typename VectorType>
static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
}
};
template <>
struct rank_update<Lower> {
template <typename MatrixType, typename VectorType>
static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
}
};
template<>
struct rank_update<Upper> {
template<typename MatrixType, typename VectorType>
static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
Transpose<MatrixType> matt(mat);
return Eigen::internal::llt_rank_update_lower(matt, vec.conjugate(), sigma);
}
};
template <>
struct rank_update<Upper> {
template <typename MatrixType, typename VectorType>
static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
Transpose<MatrixType> matt(mat);
return Eigen::internal::llt_rank_update_lower(matt, vec.conjugate(), sigma);
}
};
// -------------------------------------------------------------------------------------------------------------------
// Generic lapacke llt implementation that hands of to the dispatches
// -------------------------------------------------------------------------------------------------------------------
// -------------------------------------------------------------------------------------------------------------------
// Generic lapacke llt implementation that hands of to the dispatches
// -------------------------------------------------------------------------------------------------------------------
template<typename Scalar, UpLoType Mode>
struct lapacke_llt {
EIGEN_STATIC_ASSERT(((Mode == Lower) || (Mode == Upper)),MODE_MUST_BE_UPPER_OR_LOWER)
template<typename MatrixType>
static Index blocked(MatrixType& m)
{
eigen_assert(m.rows() == m.cols());
if(m.rows() == 0) {
return -1;
}
/* Set up parameters for ?potrf */
lapack_int size = to_lapack(m.rows());
lapack_int matrix_order = lapack_storage_of(m);
constexpr char uplo = Mode == Upper ? 'U' : 'L';
Scalar* a = &(m.coeffRef(0,0));
lapack_int lda = to_lapack(m.outerStride());
lapack_int info = potrf(matrix_order, uplo, size, to_lapack(a), lda );
info = (info==0) ? -1 : info>0 ? info-1 : size;
return info;
template <typename Scalar, UpLoType Mode>
struct lapacke_llt {
EIGEN_STATIC_ASSERT(((Mode == Lower) || (Mode == Upper)), MODE_MUST_BE_UPPER_OR_LOWER)
template <typename MatrixType>
static Index blocked(MatrixType &m) {
eigen_assert(m.rows() == m.cols());
if (m.rows() == 0) {
return -1;
}
/* Set up parameters for ?potrf */
lapack_int size = to_lapack(m.rows());
lapack_int matrix_order = lapack_storage_of(m);
constexpr char uplo = Mode == Upper ? 'U' : 'L';
Scalar *a = &(m.coeffRef(0, 0));
lapack_int lda = to_lapack(m.outerStride());
template<typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
{
return rank_update<Mode>::run(mat, vec, sigma);
}
};
}
lapack_int info = potrf(matrix_order, uplo, size, to_lapack(a), lda);
info = (info == 0) ? -1 : info > 0 ? info - 1 : size;
return info;
}
template <typename MatrixType, typename VectorType>
static Index rankUpdate(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
return rank_update<Mode>::run(mat, vec, sigma);
}
};
} // namespace lapacke_helpers
// end namespace lapacke_helpers
/*
@@ -106,9 +104,11 @@ namespace lapacke_helpers {
* in LLT.h for double, float and complex double, complex float types.
*/
#define EIGEN_LAPACKE_LLT(EIGTYPE) \
template<> struct llt_inplace<EIGTYPE, Lower> : public lapacke_helpers::lapacke_llt<EIGTYPE, Lower> {}; \
template<> struct llt_inplace<EIGTYPE, Upper> : public lapacke_helpers::lapacke_llt<EIGTYPE, Upper> {};
#define EIGEN_LAPACKE_LLT(EIGTYPE) \
template <> \
struct llt_inplace<EIGTYPE, Lower> : public lapacke_helpers::lapacke_llt<EIGTYPE, Lower> {}; \
template <> \
struct llt_inplace<EIGTYPE, Upper> : public lapacke_helpers::lapacke_llt<EIGTYPE, Upper> {};
EIGEN_LAPACKE_LLT(double)
EIGEN_LAPACKE_LLT(float)
@@ -117,8 +117,8 @@ EIGEN_LAPACKE_LLT(std::complex<float>)
#undef EIGEN_LAPACKE_LLT
} // end namespace internal
} // end namespace internal
} // end namespace Eigen
} // end namespace Eigen
#endif // EIGEN_LLT_LAPACKE_H
#endif // EIGEN_LLT_LAPACKE_H