19 template<
typename MatrixType,
int UpLo>
struct LDLT_Traits;
22 enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
48 template<
typename _MatrixType,
int _UpLo>
class LDLT
51 typedef _MatrixType MatrixType;
53 RowsAtCompileTime = MatrixType::RowsAtCompileTime,
54 ColsAtCompileTime = MatrixType::ColsAtCompileTime,
56 MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
57 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
60 typedef typename MatrixType::Scalar Scalar;
62 typedef typename MatrixType::Index Index;
68 typedef internal::LDLT_Traits<MatrixType,UpLo> Traits;
78 m_sign(internal::ZeroSign),
79 m_isInitialized(false)
89 : m_matrix(size, size),
90 m_transpositions(size),
92 m_sign(internal::ZeroSign),
93 m_isInitialized(false)
102 : m_matrix(matrix.rows(), matrix.cols()),
103 m_transpositions(matrix.rows()),
104 m_temporary(matrix.rows()),
105 m_sign(internal::ZeroSign),
106 m_isInitialized(false)
116 m_isInitialized =
false;
120 inline typename Traits::MatrixU
matrixU()
const
122 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
123 return Traits::getU(m_matrix);
127 inline typename Traits::MatrixL
matrixL()
const
129 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
130 return Traits::getL(m_matrix);
137 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
138 return m_transpositions;
144 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
145 return m_matrix.diagonal();
151 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
152 return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;
155 #ifdef EIGEN2_SUPPORT
156 inline bool isPositiveDefinite()
const
165 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
166 return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;
184 template<
typename Rhs>
185 inline const internal::solve_retval<LDLT, Rhs>
188 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
189 eigen_assert(m_matrix.rows()==b.rows()
190 &&
"LDLT::solve(): invalid number of rows of the right hand side matrix b");
191 return internal::solve_retval<LDLT, Rhs>(*
this, b.derived());
194 #ifdef EIGEN2_SUPPORT
195 template<
typename OtherDerived,
typename ResultType>
198 *result = this->
solve(b);
203 template<
typename Derived>
204 bool solveInPlace(MatrixBase<Derived> &bAndX)
const;
208 template <
typename Derived>
209 LDLT& rankUpdate(
const MatrixBase<Derived>& w,
const RealScalar& alpha=1);
217 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
223 inline Index rows()
const {
return m_matrix.rows(); }
224 inline Index cols()
const {
return m_matrix.cols(); }
233 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
246 TranspositionType m_transpositions;
247 TmpMatrixType m_temporary;
248 internal::SignMatrix m_sign;
249 bool m_isInitialized;
254 template<
int UpLo>
struct ldlt_inplace;
256 template<>
struct ldlt_inplace<
Lower>
258 template<
typename MatrixType,
typename TranspositionType,
typename Workspace>
259 static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
262 typedef typename MatrixType::Scalar Scalar;
263 typedef typename MatrixType::RealScalar RealScalar;
264 typedef typename MatrixType::Index Index;
265 eigen_assert(mat.rows()==mat.cols());
266 const Index size = mat.rows();
270 transpositions.setIdentity();
271 if (numext::real(mat.coeff(0,0)) > 0) sign = PositiveSemiDef;
272 else if (numext::real(mat.coeff(0,0)) < 0) sign = NegativeSemiDef;
273 else sign = ZeroSign;
277 RealScalar cutoff(0), biggest_in_corner;
279 for (Index k = 0; k < size; ++k)
282 Index index_of_biggest_in_corner;
283 biggest_in_corner = mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
284 index_of_biggest_in_corner += k;
291 cutoff = abs(NumTraits<Scalar>::epsilon() * biggest_in_corner);
295 if(biggest_in_corner < cutoff)
297 for(Index i = k; i < size; i++) transpositions.coeffRef(i) = i;
301 transpositions.coeffRef(k) = index_of_biggest_in_corner;
302 if(k != index_of_biggest_in_corner)
306 Index s = size-index_of_biggest_in_corner-1;
307 mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));
308 mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));
309 std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));
310 for(
int i=k+1;i<index_of_biggest_in_corner;++i)
312 Scalar tmp = mat.coeffRef(i,k);
313 mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));
314 mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);
316 if(NumTraits<Scalar>::IsComplex)
317 mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));
324 Index rs = size - k - 1;
325 Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
326 Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
327 Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
331 temp.head(k) = mat.diagonal().head(k).asDiagonal() * A10.adjoint();
332 mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
334 A21.noalias() -= A20 * temp.head(k);
336 if((rs>0) && (abs(mat.coeffRef(k,k)) > cutoff))
337 A21 /= mat.coeffRef(k,k);
339 RealScalar realAkk = numext::real(mat.coeffRef(k,k));
340 if (sign == PositiveSemiDef) {
341 if (realAkk < 0) sign = Indefinite;
342 }
else if (sign == NegativeSemiDef) {
343 if (realAkk > 0) sign = Indefinite;
344 }
else if (sign == ZeroSign) {
345 if (realAkk > 0) sign = PositiveSemiDef;
346 else if (realAkk < 0) sign = NegativeSemiDef;
360 template<
typename MatrixType,
typename WDerived>
361 static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w,
const typename MatrixType::RealScalar& sigma=1)
363 using numext::isfinite;
364 typedef typename MatrixType::Scalar Scalar;
365 typedef typename MatrixType::RealScalar RealScalar;
366 typedef typename MatrixType::Index Index;
368 const Index size = mat.rows();
369 eigen_assert(mat.cols() == size && w.size()==size);
371 RealScalar alpha = 1;
374 for (Index j = 0; j < size; j++)
377 if (!(isfinite)(alpha))
381 RealScalar dj = numext::real(mat.coeff(j,j));
382 Scalar wj = w.coeff(j);
383 RealScalar swj2 = sigma*numext::abs2(wj);
384 RealScalar gamma = dj*alpha + swj2;
386 mat.coeffRef(j,j) += swj2/alpha;
392 w.tail(rs) -= wj * mat.col(j).tail(rs);
394 mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);
399 template<
typename MatrixType,
typename TranspositionType,
typename Workspace,
typename WType>
400 static bool update(MatrixType& mat,
const TranspositionType& transpositions, Workspace& tmp,
const WType& w,
const typename MatrixType::RealScalar& sigma=1)
403 tmp = transpositions * w;
405 return ldlt_inplace<Lower>::updateInPlace(mat,tmp,sigma);
409 template<>
struct ldlt_inplace<
Upper>
411 template<
typename MatrixType,
typename TranspositionType,
typename Workspace>
412 static EIGEN_STRONG_INLINE
bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
414 Transpose<MatrixType> matt(mat);
415 return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
418 template<
typename MatrixType,
typename TranspositionType,
typename Workspace,
typename WType>
419 static EIGEN_STRONG_INLINE
bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w,
const typename MatrixType::RealScalar& sigma=1)
421 Transpose<MatrixType> matt(mat);
422 return ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);
426 template<
typename MatrixType>
struct LDLT_Traits<MatrixType,
Lower>
428 typedef const TriangularView<const MatrixType, UnitLower> MatrixL;
429 typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;
430 static inline MatrixL getL(
const MatrixType& m) {
return m; }
431 static inline MatrixU getU(
const MatrixType& m) {
return m.adjoint(); }
434 template<
typename MatrixType>
struct LDLT_Traits<MatrixType,
Upper>
436 typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;
437 typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;
438 static inline MatrixL getL(
const MatrixType& m) {
return m.adjoint(); }
439 static inline MatrixU getU(
const MatrixType& m) {
return m; }
446 template<
typename MatrixType,
int _UpLo>
449 eigen_assert(a.rows()==a.cols());
450 const Index size = a.rows();
454 m_transpositions.resize(size);
455 m_isInitialized =
false;
456 m_temporary.resize(size);
458 internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign);
460 m_isInitialized =
true;
469 template<
typename MatrixType,
int _UpLo>
470 template<
typename Derived>
473 const Index size = w.rows();
476 eigen_assert(m_matrix.rows()==size);
480 m_matrix.resize(size,size);
482 m_transpositions.resize(size);
483 for (Index i = 0; i < size; i++)
484 m_transpositions.coeffRef(i) = i;
485 m_temporary.resize(size);
486 m_sign = sigma>=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;
487 m_isInitialized =
true;
490 internal::ldlt_inplace<UpLo>::update(m_matrix, m_transpositions, m_temporary, w, sigma);
496 template<
typename _MatrixType,
int _UpLo,
typename Rhs>
497 struct solve_retval<
LDLT<_MatrixType,_UpLo>, Rhs>
498 : solve_retval_base<LDLT<_MatrixType,_UpLo>, Rhs>
501 EIGEN_MAKE_SOLVE_HELPERS(LDLTType,Rhs)
503 template<typename Dest>
void evalTo(Dest& dst)
const
505 eigen_assert(rhs().rows() == dec().matrixLDLT().rows());
507 dst = dec().transpositionsP() * rhs();
510 dec().matrixL().solveInPlace(dst);
516 typedef typename LDLTType::MatrixType MatrixType;
517 typedef typename LDLTType::Scalar Scalar;
518 typedef typename LDLTType::RealScalar RealScalar;
522 for (Index i = 0; i < vectorD.size(); ++i) {
523 if(abs(vectorD(i)) > tolerance)
524 dst.row(i) /= vectorD(i);
526 dst.row(i).setZero();
530 dec().matrixU().solveInPlace(dst);
533 dst = dec().transpositionsP().transpose() * dst;
551 template<
typename MatrixType,
int _UpLo>
552 template<
typename Derived>
553 bool LDLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX)
const
555 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
556 eigen_assert(m_matrix.rows() == bAndX.rows());
558 bAndX = this->solve(bAndX);
566 template<
typename MatrixType,
int _UpLo>
569 eigen_assert(m_isInitialized &&
"LDLT is not initialized.");
570 const Index size = m_matrix.rows();
571 MatrixType res(size,size);
575 res = transpositionsP() * res;
577 res = matrixU() * res;
579 res = vectorD().asDiagonal() * res;
581 res = matrixL() * res;
583 res = transpositionsP().transpose() * res;
591 template<
typename MatrixType,
unsigned int UpLo>
601 template<
typename Derived>
610 #endif // EIGEN_LDLT_H
Robust Cholesky decomposition of a matrix with pivoting.
Definition: LDLT.h:48
ComputationInfo info() const
Reports whether previous computation was successful.
Definition: LDLT.h:231
LDLT(const MatrixType &matrix)
Constructor with decomposition.
Definition: LDLT.h:101
MatrixType reconstructedMatrix() const
Definition: LDLT.h:567
const TranspositionType & transpositionsP() const
Definition: LDLT.h:135
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:88
Traits::MatrixL matrixL() const
Definition: LDLT.h:127
const internal::solve_retval< LDLT, Rhs > solve(const MatrixBase< Rhs > &b) const
Definition: LDLT.h:186
bool isPositive() const
Definition: LDLT.h:149
const LDLT< PlainObject, UpLo > ldlt() const
Definition: LDLT.h:593
Definition: Constants.h:169
Definition: Constants.h:167
LDLT & compute(const MatrixType &matrix)
Definition: LDLT.h:447
LDLT(Index size)
Default Constructor with memory preallocation.
Definition: LDLT.h:88
void setZero()
Definition: LDLT.h:114
Diagonal< const MatrixType > vectorD() const
Definition: LDLT.h:142
LDLT()
Default Constructor.
Definition: LDLT.h:75
Definition: Constants.h:376
bool isNegative(void) const
Definition: LDLT.h:163
const unsigned int RowMajorBit
Definition: Constants.h:53
Expression of a diagonal/subdiagonal/superdiagonal in a matrix.
Definition: Diagonal.h:64
ComputationInfo
Definition: Constants.h:374
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
const LDLT< PlainObject > ldlt() const
Definition: LDLT.h:603
Traits::MatrixU matrixU() const
Definition: LDLT.h:120
const MatrixType & matrixLDLT() const
Definition: LDLT.h:215