template<typename _MatrixType, unsigned int UpLo>
class Eigen::SelfAdjointView< _MatrixType, UpLo >
Expression of a selfadjoint matrix from a triangular part of a dense matrix.
- 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> |
| internal::conditional< Cond, ConjugateReturnType, ConstSelfAdjointView >::type |
conjugateIf () const |
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| MatrixType::ConstDiagonalReturnType |
diagonal () const |
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|
EigenvaluesReturnType |
eigenvalues () const |
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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 |
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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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|
TransposeReturnType |
transpose () |
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| const ConstTransposeReturnType |
transpose () const |
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| template<unsigned int TriMode> |
| internal::conditional<(TriMode &(Upper|Lower))==(UpLo &(Upper|Lower)), TriangularView< MatrixType, TriMode >, TriangularView< typename MatrixType::AdjointReturnType, TriMode > >::type |
triangularView () const |
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 Public Member Functions inherited from Eigen::TriangularBase< SelfAdjointView< _MatrixType, UpLo > >
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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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Public Member Functions inherited from Eigen::EigenBase< Derived >
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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:
MatrixXd ones = MatrixXd::Ones(3,3);
VectorXd eivals = ones.selfadjointView<Lower>().eigenvalues();
cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;
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:
MatrixXd ones = MatrixXd::Ones(3,3);
cout << "The operator norm of the 3x3 matrix of ones is "
<< ones.selfadjointView<Lower>().operatorNorm() << endl;
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
