45 template<
typename _MatrixType,
int _UpLo>
class LDLT 50 RowsAtCompileTime = MatrixType::RowsAtCompileTime,
51 ColsAtCompileTime = MatrixType::ColsAtCompileTime,
53 MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
54 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
57 typedef typename MatrixType::Scalar
Scalar;
59 typedef typename MatrixType::Index
Index;
72 LDLT() : m_matrix(), m_transpositions(), m_isInitialized(false) {}
81 : m_matrix(size, size),
82 m_transpositions(size),
84 m_isInitialized(false)
92 LDLT(
const MatrixType& matrix)
93 : m_matrix(matrix.rows(), matrix.cols()),
94 m_transpositions(matrix.rows()),
95 m_temporary(matrix.rows()),
96 m_isInitialized(false)
106 m_isInitialized =
false;
110 inline typename Traits::MatrixU
matrixU()
const 112 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
113 return Traits::getU(m_matrix);
117 inline typename Traits::MatrixL
matrixL()
const 119 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
120 return Traits::getL(m_matrix);
127 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
128 return m_transpositions;
134 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
135 return m_matrix.diagonal();
141 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
145 #ifdef EIGEN2_SUPPORT 146 inline bool isPositiveDefinite()
const 155 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
174 template<
typename Rhs>
178 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
180 &&
"LDLT::solve(): invalid number of rows of the right hand side matrix b");
184 #ifdef EIGEN2_SUPPORT 185 template<
typename OtherDerived,
typename ResultType>
188 *result = this->solve(b);
193 template<
typename Derived>
196 LDLT& compute(
const MatrixType& matrix);
198 template <
typename Derived>
207 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
211 MatrixType reconstructedMatrix()
const;
213 inline Index
rows()
const {
return m_matrix.rows(); }
214 inline Index
cols()
const {
return m_matrix.cols(); }
223 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
248 template<
typename MatrixType,
typename TranspositionType,
typename Workspace>
249 static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp,
int* sign=0)
252 typedef typename MatrixType::Scalar Scalar;
253 typedef typename MatrixType::RealScalar RealScalar;
254 typedef typename MatrixType::Index Index;
256 const Index size = mat.rows();
260 transpositions.setIdentity();
266 RealScalar cutoff(0), biggest_in_corner;
268 for (Index k = 0; k < size; ++k)
271 Index index_of_biggest_in_corner;
272 biggest_in_corner = mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
273 index_of_biggest_in_corner += k;
284 if(biggest_in_corner < cutoff)
286 for(Index i = k; i < size; i++) transpositions.coeffRef(i) = i;
291 transpositions.coeffRef(k) = index_of_biggest_in_corner;
292 if(k != index_of_biggest_in_corner)
296 Index s = size-index_of_biggest_in_corner-1;
297 mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));
298 mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));
299 std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));
300 for(
int i=k+1;i<index_of_biggest_in_corner;++i)
302 Scalar tmp = mat.coeffRef(i,k);
303 mat.coeffRef(i,k) =
numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));
304 mat.coeffRef(index_of_biggest_in_corner,i) =
numext::conj(tmp);
307 mat.coeffRef(index_of_biggest_in_corner,k) =
numext::conj(mat.coeff(index_of_biggest_in_corner,k));
314 Index rs = size - k - 1;
321 temp.head(k) = mat.diagonal().head(k).asDiagonal() * A10.adjoint();
322 mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
324 A21.noalias() -= A20 * temp.head(k);
326 if((rs>0) && (
abs(mat.coeffRef(k,k)) > cutoff))
327 A21 /= mat.coeffRef(k,k);
332 int newSign =
numext::real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0;
335 else if(*sign != newSign)
350 template<
typename MatrixType,
typename WDerived>
354 typedef typename MatrixType::Scalar Scalar;
355 typedef typename MatrixType::RealScalar RealScalar;
356 typedef typename MatrixType::Index Index;
358 const Index size = mat.rows();
361 RealScalar alpha = 1;
364 for (Index j = 0; j < size; j++)
372 Scalar wj = w.coeff(j);
374 RealScalar gamma = dj*alpha + swj2;
376 mat.coeffRef(j,j) += swj2/alpha;
382 w.
tail(rs) -= wj * mat.col(j).tail(rs);
389 template<
typename MatrixType,
typename TranspositionType,
typename Workspace,
typename WType>
390 static bool update(MatrixType& mat,
const TranspositionType& transpositions, Workspace& tmp,
const WType& w,
const typename MatrixType::RealScalar& sigma=1)
393 tmp = transpositions * w;
401 template<
typename MatrixType,
typename TranspositionType,
typename Workspace>
408 template<
typename MatrixType,
typename TranspositionType,
typename Workspace,
typename WType>
409 static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w,
const typename MatrixType::RealScalar& sigma=1)
420 static inline MatrixL
getL(
const MatrixType& m) {
return m; }
421 static inline MatrixU
getU(
const MatrixType& m) {
return m.
adjoint(); }
428 static inline MatrixL
getL(
const MatrixType& m) {
return m.
adjoint(); }
429 static inline MatrixU
getU(
const MatrixType& m) {
return m; }
436 template<
typename MatrixType,
int _UpLo>
440 const Index size = a.rows();
444 m_transpositions.resize(size);
445 m_isInitialized =
false;
446 m_temporary.resize(size);
450 m_isInitialized =
true;
459 template<
typename MatrixType,
int _UpLo>
460 template<
typename Derived>
463 const Index size = w.rows();
470 m_matrix.resize(size,size);
472 m_transpositions.resize(size);
473 for (
Index i = 0; i < size; i++)
474 m_transpositions.coeffRef(i) = i;
475 m_temporary.resize(size);
476 m_sign = sigma>=0 ? 1 : -1;
477 m_isInitialized =
true;
486 template<
typename _MatrixType,
int _UpLo,
typename Rhs>
493 template<typename Dest>
void evalTo(Dest& dst)
const 497 dst = dec().transpositionsP() *
rhs();
500 dec().matrixL().solveInPlace(dst);
512 for (
Index i = 0; i < vectorD.size(); ++i) {
513 if(
abs(vectorD(i)) > tolerance)
514 dst.row(i) /= vectorD(i);
516 dst.row(i).setZero();
520 dec().matrixU().solveInPlace(dst);
523 dst = dec().transpositionsP().transpose() * dst;
541 template<
typename MatrixType,
int _UpLo>
542 template<
typename Derived>
545 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
548 bAndX = this->solve(bAndX);
556 template<
typename MatrixType,
int _UpLo>
559 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
560 const Index size = m_matrix.rows();
565 res = transpositionsP() * res;
567 res = matrixU() * res;
569 res = vectorD().asDiagonal() * res;
571 res = matrixL() * res;
573 res = transpositionsP().transpose() * res;
581 template<
typename MatrixType,
unsigned int UpLo>
591 template<
typename Derived>
600 #endif // EIGEN_LDLT_H Robust Cholesky decomposition of a matrix with pivoting.
const AutoDiffScalar< DerType > & conj(const AutoDiffScalar< DerType > &x)
TranspositionType m_transpositions
const LDLT< PlainObject > ldlt() const
NumTraits< typename MatrixType::Scalar >::Real RealScalar
static bool update(MatrixType &mat, const TranspositionType &transpositions, Workspace &tmp, const WType &w, const typename MatrixType::RealScalar &sigma=1)
#define EIGEN_STRONG_INLINE
const TriangularView< const typename MatrixType::AdjointReturnType, TransposeMode > adjoint() const
SegmentReturnType tail(Index vecSize)
Expression of the transpose of a matrix.
LDLT(Index size)
Default Constructor with memory preallocation.
iterative scaling algorithm to equilibrate rows and column norms in matrices
LDLT & rankUpdate(const MatrixBase< Derived > &w, const RealScalar &alpha=1)
static bool unblocked(MatrixType &mat, TranspositionType &transpositions, Workspace &temp, int *sign=0)
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
static bool updateInPlace(MatrixType &mat, MatrixBase< WDerived > &w, const typename MatrixType::RealScalar &sigma=1)
const unsigned int RowMajorBit
Matrix< Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1 > TmpMatrixType
EIGEN_STRONG_INLINE const CwiseUnaryOp< internal::scalar_abs2_op< Scalar >, const Derived > abs2() const
const MatrixType & matrixLDLT() const
EIGEN_STRONG_INLINE const CwiseUnaryOp< internal::scalar_abs_op< Scalar >, const Derived > abs() const
RealReturnType real() const
static EIGEN_STRONG_INLINE bool update(MatrixType &mat, TranspositionType &transpositions, Workspace &tmp, WType &w, const typename MatrixType::RealScalar &sigma=1)
LDLT()
Default Constructor.
bool solveInPlace(MatrixBase< Derived > &bAndX) const
bool isNegative(void) const
const TriangularView< const typename MatrixType::AdjointReturnType, UnitLower > MatrixL
Provides a generic way to set and pass user-specified options.
const TriangularView< const MatrixType, UnitLower > MatrixL
Transpositions< RowsAtCompileTime, MaxRowsAtCompileTime > TranspositionType
MatrixType reconstructedMatrix() const
static MatrixL getL(const MatrixType &m)
internal::LDLT_Traits< MatrixType, UpLo > Traits
const TranspositionType & transpositionsP() const
static MatrixU getU(const MatrixType &m)
Traits::MatrixU matrixU() const
void rhs(const real_t *x, real_t *f)
TmpMatrixType m_temporary
LDLT< _MatrixType, _UpLo > LDLTType
static MatrixU getU(const MatrixType &m)
ComputationInfo info() const
Reports whether previous computation was successful.
Expression of a fixed-size or dynamic-size block.
MatrixType::Scalar Scalar
Diagonal< const MatrixType > vectorD() const
Traits::MatrixL matrixL() const
Base class for triangular part in a matrix.
static EIGEN_STRONG_INLINE bool unblocked(MatrixType &mat, TranspositionType &transpositions, Workspace &temp, int *sign=0)
#define EIGEN_MAKE_SOLVE_HELPERS(DecompositionType, Rhs)
const TriangularView< const MatrixType, UnitUpper > MatrixU
const TriangularView< const typename MatrixType::AdjointReturnType, UnitUpper > MatrixU
Expression of a diagonal/subdiagonal/superdiagonal in a matrix.
const internal::solve_retval< LDLT, Rhs > solve(const MatrixBase< Rhs > &b) const
Base class for all dense matrices, vectors, and expressions.
PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime > PermutationType
bool() isfinite(const T &x)
LDLT & compute(const MatrixType &matrix)
LDLT(const MatrixType &matrix)
Constructor with decomposition.
const LDLT< PlainObject, UpLo > ldlt() const
static MatrixL getL(const MatrixType &m)