template<typename MatrixType_, unsigned int UpLo>
class Eigen::SelfAdjointView< MatrixType_, UpLo >
Expression of a selfadjoint matrix from a triangular part of a dense matrix.
- Template Parameters
-
MatrixType | the type of the dense matrix storing the coefficients |
TriangularPart | can be either Lower or Upper |
This class is an expression of a sefladjoint matrix from a triangular part of a matrix with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView() and most of the time this is the only way that it is used.
- See also
- class TriangularBase, MatrixBase::selfadjointView()
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const AdjointReturnType | adjoint () const |
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Scalar | coeff (Index row, Index col) const |
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Scalar & | coeffRef (Index row, Index col) |
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const ConjugateReturnType | conjugate () const |
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template<bool Cond> |
std::conditional_t< Cond, ConjugateReturnType, ConstSelfAdjointView > | conjugateIf () const |
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MatrixType::ConstDiagonalReturnType | diagonal () const |
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EigenvaluesReturnType | eigenvalues () const |
| Computes the eigenvalues of a matrix. More...
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const LDLT< PlainObject, UpLo > | ldlt () const |
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const LLT< PlainObject, UpLo > | llt () const |
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template<typename OtherDerived > |
const Product< SelfAdjointView, OtherDerived > | operator* (const MatrixBase< OtherDerived > &rhs) const |
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RealScalar | operatorNorm () const |
| Computes the L2 operator norm. More...
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template<typename DerivedU , typename DerivedV > |
SelfAdjointView & | rankUpdate (const MatrixBase< DerivedU > &u, const MatrixBase< DerivedV > &v, const Scalar &alpha=Scalar(1)) |
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template<typename DerivedU > |
SelfAdjointView & | rankUpdate (const MatrixBase< DerivedU > &u, const Scalar &alpha=Scalar(1)) |
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const ConstTransposeReturnType | transpose () const |
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template<class Dummy = int> |
TransposeReturnType | transpose (std::enable_if_t< Eigen::internal::is_lvalue< MatrixType >::value, Dummy * >=nullptr) |
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template<unsigned int TriMode> |
std::conditional_t<(TriMode &(Upper|Lower))==(UpLo &(Upper|Lower)), TriangularView< MatrixType, TriMode >, TriangularView< typename MatrixType::AdjointReturnType, TriMode > > | triangularView () const |
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void | copyCoeff (Index row, Index col, Other &other) |
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void | evalTo (MatrixBase< DenseDerived > &other) const |
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void | evalToLazy (MatrixBase< DenseDerived > &other) const |
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EIGEN_CONSTEXPR Index | cols () const EIGEN_NOEXCEPT |
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Derived & | derived () |
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const Derived & | derived () const |
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EIGEN_CONSTEXPR Index | rows () const EIGEN_NOEXCEPT |
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EIGEN_CONSTEXPR Index | size () const EIGEN_NOEXCEPT |
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template<typename MatrixType , unsigned int UpLo>
Computes the eigenvalues of a matrix.
- Returns
- Column vector containing the eigenvalues.
This is defined in the Eigenvalues module.
#include <Eigen/Eigenvalues>
This function computes the eigenvalues with the help of the SelfAdjointEigenSolver class. The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.
Example:
cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;
static const ConstantReturnType Ones()
Definition: CwiseNullaryOp.h:672
EigenvaluesReturnType eigenvalues() const
Computes the eigenvalues of a matrix.
Definition: MatrixBaseEigenvalues.h:90
@ Lower
Definition: Constants.h:211
Matrix< double, Dynamic, 1 > VectorXd
DynamicĂ—1 vector of type double.
Definition: Matrix.h:501
Matrix< double, Dynamic, Dynamic > MatrixXd
DynamicĂ—Dynamic matrix of type double.
Definition: Matrix.h:501
Output:
The eigenvalues of the 3x3 matrix of ones are:
-3.09e-16
0
3
- See also
- SelfAdjointEigenSolver::eigenvalues(), MatrixBase::eigenvalues()
template<typename MatrixType , unsigned int UpLo>
Computes the L2 operator norm.
- Returns
- Operator norm of the matrix.
This is defined in the Eigenvalues module.
#include <Eigen/Eigenvalues>
This function computes the L2 operator norm of a self-adjoint matrix. For a self-adjoint matrix, the operator norm is the largest eigenvalue.
The current implementation uses the eigenvalues of the matrix, as computed by eigenvalues(), to compute the operator norm of the matrix.
Example:
cout << "The operator norm of the 3x3 matrix of ones is "
RealScalar operatorNorm() const
Computes the L2 operator norm.
Definition: MatrixBaseEigenvalues.h:153
Output:
The operator norm of the 3x3 matrix of ones is 3
- See also
- eigenvalues(), MatrixBase::operatorNorm()
template<typename MatrixType_ , unsigned int UpLo>
template<typename DerivedU , typename DerivedV >
Perform a symmetric rank 2 update of the selfadjoint matrix *this
: \( this = this + \alpha u v^* + conj(\alpha) v u^* \)
- Returns
- a reference to
*this
The vectors u and v
must be column vectors, however they can be a adjoint expression without any overhead. Only the meaningful triangular part of the matrix is updated, the rest is left unchanged.
- See also
- rankUpdate(const MatrixBase<DerivedU>&, Scalar)
template<typename MatrixType_ , unsigned int UpLo>
template<unsigned int TriMode>
- Returns
- an expression of a triangular view extracted from the current selfadjoint view of a given triangular part
The parameter TriMode can have the following values: Upper
, StrictlyUpper
, UnitUpper
, Lower
, StrictlyLower
, UnitLower
.
If TriMode
references the same triangular part than *this
, then this method simply return a TriangularView
of the nested expression, otherwise, the nested expression is first transposed, thus returning a TriangularView<Transpose<MatrixType>>
object.
- See also
- MatrixBase::triangularView(), class TriangularView