Classes | |
struct | traits< TridiagonalizationMatrixTReturnType< MatrixType > > |
struct | tridiagonalization_inplace_selector |
struct | tridiagonalization_inplace_selector< MatrixType, 3, false > |
struct | tridiagonalization_inplace_selector< MatrixType, 1, IsComplex > |
struct | TridiagonalizationMatrixTReturnType |
struct | traits< HessenbergDecompositionMatrixHReturnType< MatrixType > > |
struct | HessenbergDecompositionMatrixHReturnType |
More... | |
struct | complex_schur_reduce_to_hessenberg |
struct | complex_schur_reduce_to_hessenberg< MatrixType, false > |
struct | eigenvalues_selector |
struct | eigenvalues_selector< Derived, false > |
struct | traits< solve_retval_base< DecompositionType, Rhs > > |
class | solve_retval_base |
struct | llt_inplace< Lower > |
struct | llt_inplace< Upper > |
struct | LLT_Traits< MatrixType, Lower > |
struct | LLT_Traits< MatrixType, Upper > |
struct | solve_retval< LLT< _MatrixType, UpLo >, Rhs > |
struct | ldlt_inplace< Lower > |
struct | ldlt_inplace< Upper > |
struct | LDLT_Traits< MatrixType, Lower > |
struct | LDLT_Traits< MatrixType, Upper > |
struct | solve_retval< LDLT< _MatrixType, _UpLo >, Rhs > |
struct | solve_retval< HouseholderQR< _MatrixType >, Rhs > |
struct | solve_retval< FullPivHouseholderQR< _MatrixType >, Rhs > |
struct | solve_retval< ColPivHouseholderQR< _MatrixType >, Rhs > |
Functions | |
template<typename MatrixType , typename CoeffVectorType > | |
void | tridiagonalization_inplace (MatrixType &matA, CoeffVectorType &hCoeffs) |
template<typename MatrixType , typename DiagonalType , typename SubDiagonalType > | |
void | tridiagonalization_inplace (MatrixType &mat, DiagonalType &diag, SubDiagonalType &subdiag, bool extractQ) |
Performs a full tridiagonalization in place. | |
template<int StorageOrder, typename RealScalar , typename Scalar , typename Index > | |
static void | tridiagonal_qr_step (RealScalar *diag, RealScalar *subdiag, Index start, Index end, Scalar *matrixQ, Index n) |
template<typename RealScalar > | |
std::complex< RealScalar > | sqrt (const std::complex< RealScalar > &z) |
Computes the principal value of the square root of the complex z. | |
template<typename MatrixQR , typename HCoeffs > | |
void | householder_qr_inplace_unblocked (MatrixQR &mat, HCoeffs &hCoeffs, typename MatrixQR::Scalar *tempData=0) |
template<typename MatrixQR , typename HCoeffs > | |
void | householder_qr_inplace_blocked (MatrixQR &mat, HCoeffs &hCoeffs, typename MatrixQR::Index maxBlockSize=32, typename MatrixQR::Scalar *tempData=0) |
void Eigen::internal::householder_qr_inplace_blocked | ( | MatrixQR & | mat, |
HCoeffs & | hCoeffs, | ||
typename MatrixQR::Index | maxBlockSize = 32 , |
||
typename MatrixQR::Scalar * | tempData = 0 |
||
) |
void Eigen::internal::householder_qr_inplace_unblocked | ( | MatrixQR & | mat, |
HCoeffs & | hCoeffs, | ||
typename MatrixQR::Scalar * | tempData = 0 |
||
) |
std::complex< RealScalar > Eigen::internal::sqrt | ( | const std::complex< RealScalar > & | z | ) |
Computes the principal value of the square root of the complex z.
Definition at line 234 of file Eigenvalues.
static void Eigen::internal::tridiagonal_qr_step | ( | RealScalar * | diag, |
RealScalar * | subdiag, | ||
Index | start, | ||
Index | end, | ||
Scalar * | matrixQ, | ||
Index | n | ||
) | [static] |
Definition at line 434 of file Eigenvalues.
void Eigen::internal::tridiagonalization_inplace | ( | MatrixType & | matA, |
CoeffVectorType & | hCoeffs | ||
) |
Definition at line 360 of file Eigenvalues.
void Eigen::internal::tridiagonalization_inplace | ( | MatrixType & | mat, |
DiagonalType & | diag, | ||
SubDiagonalType & | subdiag, | ||
bool | extractQ | ||
) |
Performs a full tridiagonalization in place.
[in,out] | mat | On input, the selfadjoint matrix whose tridiagonal decomposition is to be computed. Only the lower triangular part referenced. The rest is left unchanged. On output, the orthogonal matrix Q in the decomposition if extractQ is true. |
[out] | diag | The diagonal of the tridiagonal matrix T in the decomposition. |
[out] | subdiag | The subdiagonal of the tridiagonal matrix T in the decomposition. |
[in] | extractQ | If true, the orthogonal matrix Q in the decomposition is computed and stored in mat . |
Computes the tridiagonal decomposition of the selfadjoint matrix mat
in place such that where
is unitary and
a real symmetric tridiagonal matrix.
The tridiagonal matrix T is passed to the output parameters diag
and subdiag
. If extractQ
is true, then the orthogonal matrix Q is passed to mat
. Otherwise the lower part of the matrix mat
is destroyed.
The vectors diag
and subdiag
are not resized. The function assumes that they are already of the correct size. The length of the vector diag
should equal the number of rows in mat
, and the length of the vector subdiag
should be one left.
This implementation contains an optimized path for 3-by-3 matrices which is especially useful for plane fitting.
Example (this uses the same matrix as the example in Tridiagonalization::Tridiagonalization(const MatrixType&)):
Output:
Definition at line 440 of file Eigenvalues.
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