11 #ifndef EIGEN_TRIDIAGONALIZATION_H
12 #define EIGEN_TRIDIAGONALIZATION_H
18 template<
typename MatrixType>
struct TridiagonalizationMatrixTReturnType;
19 template<
typename MatrixType>
20 struct traits<TridiagonalizationMatrixTReturnType<MatrixType> >
21 :
public traits<typename MatrixType::PlainObject>
23 typedef typename MatrixType::PlainObject ReturnType;
27 template<
typename MatrixType,
typename CoeffVectorType>
28 void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs);
70 typedef typename MatrixType::Scalar Scalar;
75 Size = MatrixType::RowsAtCompileTime,
76 SizeMinusOne = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1),
77 Options = MatrixType::Options,
78 MaxSize = MatrixType::MaxRowsAtCompileTime,
79 MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1)
83 typedef typename internal::plain_col_type<MatrixType, RealScalar>::type DiagonalType;
85 typedef typename internal::remove_all<typename MatrixType::RealReturnType>::type MatrixTypeRealView;
86 typedef internal::TridiagonalizationMatrixTReturnType<MatrixTypeRealView> MatrixTReturnType;
88 typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
89 typename internal::add_const_on_value_type<typename Diagonal<const MatrixType>::RealReturnType>::type,
91 >::type DiagonalReturnType;
93 typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
94 typename internal::add_const_on_value_type<
typename Diagonal<
const MatrixType, -1>::RealReturnType>::type,
96 >::type SubDiagonalReturnType;
114 : m_matrix(size,size),
115 m_hCoeffs(size > 1 ? size-1 : 1),
116 m_isInitialized(false)
131 m_hCoeffs(matrix.cols() > 1 ? matrix.cols()-1 : 1),
132 m_isInitialized(false)
134 internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);
135 m_isInitialized =
true;
158 m_hCoeffs.
resize(matrix.rows()-1, 1);
159 internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);
160 m_isInitialized =
true;
182 eigen_assert(m_isInitialized &&
"Tridiagonalization is not initialized.");
219 eigen_assert(m_isInitialized &&
"Tridiagonalization is not initialized.");
240 eigen_assert(m_isInitialized &&
"Tridiagonalization is not initialized.");
242 .setLength(m_matrix.rows() - 1)
265 eigen_assert(m_isInitialized &&
"Tridiagonalization is not initialized.");
266 return MatrixTReturnType(m_matrix.real());
282 DiagonalReturnType
diagonal()
const;
299 CoeffVectorType m_hCoeffs;
300 bool m_isInitialized;
303 template<
typename MatrixType>
304 typename Tridiagonalization<MatrixType>::DiagonalReturnType
307 eigen_assert(m_isInitialized &&
"Tridiagonalization is not initialized.");
308 return m_matrix.diagonal().real();
311 template<
typename MatrixType>
312 typename Tridiagonalization<MatrixType>::SubDiagonalReturnType
315 eigen_assert(m_isInitialized &&
"Tridiagonalization is not initialized.");
316 return m_matrix.template diagonal<-1>().real();
344 template<
typename MatrixType,
typename CoeffVectorType>
345 void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
348 typedef typename MatrixType::Scalar Scalar;
349 typedef typename MatrixType::RealScalar RealScalar;
350 Index n = matA.rows();
351 eigen_assert(n==matA.cols());
352 eigen_assert(n==hCoeffs.size()+1 || n==1);
354 for (Index i = 0; i<n-1; ++i)
356 Index remainingSize = n-i-1;
359 matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);
363 matA.col(i).coeffRef(i+1) = 1;
365 hCoeffs.tail(n-i-1).noalias() = (matA.bottomRightCorner(remainingSize,remainingSize).template selfadjointView<Lower>()
366 * (conj(h) * matA.col(i).tail(remainingSize)));
368 hCoeffs.tail(n-i-1) += (conj(h)*Scalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);
370 matA.bottomRightCorner(remainingSize, remainingSize).template selfadjointView<Lower>()
371 .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), -1);
373 matA.col(i).coeffRef(i+1) = beta;
374 hCoeffs.coeffRef(i) = h;
379 template<
typename MatrixType,
380 int Size=MatrixType::ColsAtCompileTime,
381 bool IsComplex=NumTraits<typename MatrixType::Scalar>::IsComplex>
382 struct tridiagonalization_inplace_selector;
424 template<
typename MatrixType,
typename DiagonalType,
typename SubDiagonalType>
425 void tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag,
bool extractQ)
427 eigen_assert(mat.cols()==mat.rows() && diag.size()==mat.rows() && subdiag.size()==mat.rows()-1);
428 tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, extractQ);
434 template<
typename MatrixType,
int Size,
bool IsComplex>
435 struct tridiagonalization_inplace_selector
437 typedef typename Tridiagonalization<MatrixType>::CoeffVectorType CoeffVectorType;
438 typedef typename Tridiagonalization<MatrixType>::HouseholderSequenceType HouseholderSequenceType;
439 template<
typename DiagonalType,
typename SubDiagonalType>
440 static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag,
bool extractQ)
442 CoeffVectorType hCoeffs(mat.cols()-1);
443 tridiagonalization_inplace(mat,hCoeffs);
444 diag = mat.diagonal().real();
445 subdiag = mat.template diagonal<-1>().real();
447 mat = HouseholderSequenceType(mat, hCoeffs.conjugate())
448 .setLength(mat.rows() - 1)
457 template<
typename MatrixType>
458 struct tridiagonalization_inplace_selector<MatrixType,3,false>
460 typedef typename MatrixType::Scalar Scalar;
461 typedef typename MatrixType::RealScalar RealScalar;
463 template<
typename DiagonalType,
typename SubDiagonalType>
464 static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag,
bool extractQ)
467 const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
469 RealScalar v1norm2 = numext::abs2(mat(2,0));
474 subdiag[0] = mat(1,0);
475 subdiag[1] = mat(2,1);
481 RealScalar beta = sqrt(numext::abs2(mat(1,0)) + v1norm2);
482 RealScalar invBeta = RealScalar(1)/beta;
483 Scalar m01 = mat(1,0) * invBeta;
484 Scalar m02 = mat(2,0) * invBeta;
485 Scalar q = RealScalar(2)*m01*mat(2,1) + m02*(mat(2,2) - mat(1,1));
486 diag[1] = mat(1,1) + m02*q;
487 diag[2] = mat(2,2) - m02*q;
489 subdiag[1] = mat(2,1) - m01 * q;
503 template<
typename MatrixType,
bool IsComplex>
504 struct tridiagonalization_inplace_selector<MatrixType,1,IsComplex>
506 typedef typename MatrixType::Scalar Scalar;
508 template<
typename DiagonalType,
typename SubDiagonalType>
509 static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&,
bool extractQ)
511 diag(0,0) = numext::real(mat(0,0));
513 mat(0,0) = Scalar(1);
524 template<
typename MatrixType>
struct TridiagonalizationMatrixTReturnType
525 :
public ReturnByValue<TridiagonalizationMatrixTReturnType<MatrixType> >
532 TridiagonalizationMatrixTReturnType(
const MatrixType& mat) : m_matrix(mat) { }
534 template <
typename ResultType>
535 inline void evalTo(ResultType& result)
const
538 result.template diagonal<1>() = m_matrix.template diagonal<-1>().conjugate();
539 result.diagonal() = m_matrix.diagonal();
540 result.template diagonal<-1>() = m_matrix.template diagonal<-1>();
543 Index rows()
const {
return m_matrix.rows(); }
544 Index cols()
const {
return m_matrix.cols(); }
547 typename MatrixType::Nested m_matrix;
554 #endif // EIGEN_TRIDIAGONALIZATION_H
HouseholderSequence< MatrixType, typename internal::remove_all< typename CoeffVectorType::ConjugateReturnType >::type > HouseholderSequenceType
Return type of matrixQ()
Definition: Tridiagonalization.h:99
HouseholderSequenceType matrixQ() const
Returns the unitary matrix Q in the decomposition.
Definition: Tridiagonalization.h:238
Eigen::Index Index
Definition: Tridiagonalization.h:72
MatrixTReturnType matrixT() const
Returns an expression of the tridiagonal matrix T in the decomposition.
Definition: Tridiagonalization.h:263
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:107
Tridiagonal decomposition of a selfadjoint matrix.
Definition: Tridiagonalization.h:63
void resize(Index rows, Index cols)
Definition: PlainObjectBase.h:252
Tridiagonalization(const MatrixType &matrix)
Constructor; computes tridiagonal decomposition of given matrix.
Definition: Tridiagonalization.h:129
Sequence of Householder reflections acting on subspaces with decreasing size.
Definition: ForwardDeclarations.h:258
const MatrixType & packedMatrix() const
Returns the internal representation of the decomposition.
Definition: Tridiagonalization.h:217
Tridiagonalization & compute(const MatrixType &matrix)
Computes tridiagonal decomposition of given matrix.
Definition: Tridiagonalization.h:155
DiagonalReturnType diagonal() const
Returns the diagonal of the tridiagonal matrix T in the decomposition.
Definition: Tridiagonalization.h:305
SubDiagonalReturnType subDiagonal() const
Returns the subdiagonal of the tridiagonal matrix T in the decomposition.
Definition: Tridiagonalization.h:313
Definition: Eigen_Colamd.h:54
CoeffVectorType householderCoefficients() const
Returns the Householder coefficients.
Definition: Tridiagonalization.h:180
Tridiagonalization(Index size=Size==Dynamic?2:Size)
Default constructor.
Definition: Tridiagonalization.h:113
Expression of a diagonal/subdiagonal/superdiagonal in a matrix.
Definition: Diagonal.h:63
_MatrixType MatrixType
Synonym for the template parameter _MatrixType.
Definition: Tridiagonalization.h:68