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Eigen
3.2.91
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Expression of a selfadjoint matrix from a triangular part of a dense matrix.
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.
Public Types | |
typedef Matrix< RealScalar, internal::traits< MatrixType >::ColsAtCompileTime, 1 > | EigenvaluesReturnType |
typedef Eigen::Index | Index |
The interface type of indices. More... | |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef internal::traits< SelfAdjointView >::Scalar | Scalar |
The type of coefficients in this matrix. | |
Public Member Functions | |
Scalar | coeff (Index row, Index col) const |
Scalar & | coeffRef (Index row, Index col) |
void | copyCoeff (Index row, Index col, Other &other) |
Derived & | derived () |
const Derived & | derived () const |
EigenvaluesReturnType | eigenvalues () const |
Computes the eigenvalues of a matrix. More... | |
const LDLT< PlainObject, UpLo > | ldlt () const |
const LLT< PlainObject, UpLo > | llt () const |
template<typename OtherDerived > | |
const Product< SelfAdjointView, OtherDerived > | operator* (const MatrixBase< OtherDerived > &rhs) const |
RealScalar | operatorNorm () const |
Computes the L2 operator norm. More... | |
template<typename DerivedU , typename DerivedV > | |
SelfAdjointView & | rankUpdate (const MatrixBase< DerivedU > &u, const MatrixBase< DerivedV > &v, const Scalar &alpha=Scalar(1)) |
template<typename DerivedU > | |
SelfAdjointView & | rankUpdate (const MatrixBase< DerivedU > &u, const Scalar &alpha=Scalar(1)) |
Index | size () const |
Friends | |
template<typename OtherDerived > | |
const Product< OtherDerived, SelfAdjointView > | operator* (const MatrixBase< OtherDerived > &lhs, const SelfAdjointView &rhs) |
typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> Eigen::SelfAdjointView< _MatrixType, UpLo >::EigenvaluesReturnType |
Return type of eigenvalues()
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inherited |
The interface type of indices.
To change this, #define
the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE
.
typedef NumTraits<Scalar>::Real Eigen::SelfAdjointView< _MatrixType, UpLo >::RealScalar |
Real part of Scalar
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inlineinherited |
References Eigen::EigenBase< Derived >::derived().
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inlineinherited |
Referenced by Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::analyzePattern(), Eigen::MatrixBase< Derived >::applyOnTheLeft(), Eigen::MatrixBase< Derived >::applyOnTheRight(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::applyTranspositionOnTheLeft(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::applyTranspositionOnTheRight(), Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::bottomRightCorner(), Eigen::EigenBase< BandMatrixWrapper< _CoefficientsType, _Rows, _Cols, _Supers, _Subs, _Options > >::cols(), Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::cols(), Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::compute(), Eigen::TriangularBase< SelfAdjointView< _MatrixType, UpLo > >::copyCoeff(), Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::eval(), Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::factorize(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::indices(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::inverse(), Eigen::RotationBase< Derived, 3 >::operator*(), Eigen::SparseSelfAdjointView< MatrixType, _Mode >::operator*(), Eigen::Translation< _Scalar, _Dim >::operator*(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::operator*(), Eigen::SparseMatrixBase< Derived >::operator*(), Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::operator*(), Eigen::MatrixBase< Derived >::operator*=(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::operator=(), Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::operator=(), Eigen::DenseBase< Derived >::operator=(), Eigen::PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::operator=(), Eigen::PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::PlainObjectBase(), Eigen::PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::resizeLike(), Eigen::EigenBase< BandMatrixWrapper< _CoefficientsType, _Rows, _Cols, _Supers, _Subs, _Options > >::rows(), Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::rows(), Eigen::SparseSolverBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >::solve(), Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::SparseMatrix(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::toDenseMatrix(), Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::topLeftCorner(), Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::Transform(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::transpose(), and Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::twistedBy().
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Computes the eigenvalues of a matrix.
This is defined in the Eigenvalues module.
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:
Output:
The eigenvalues of the 3x3 matrix of ones are: -3.09e-16 0 3
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inherited |
Assigns a triangular or selfadjoint matrix to a dense matrix. If the matrix is triangular, the opposite part is set to zero.
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inherited |
Assigns a triangular or selfadjoint matrix to a dense matrix. If the matrix is triangular, the opposite part is set to zero.
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inline |
This is defined in the Cholesky module.
*this
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inline |
This is defined in the Cholesky module.
*this
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inline |
Efficient triangular matrix times vector/matrix product
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inline |
Computes the L2 operator norm.
This is defined in the Eigenvalues module.
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:
Output:
The operator norm of the 3x3 matrix of ones is 3
SelfAdjointView& Eigen::SelfAdjointView< _MatrixType, UpLo >::rankUpdate | ( | const MatrixBase< DerivedU > & | u, |
const MatrixBase< DerivedV > & | v, | ||
const Scalar & | alpha = Scalar(1) |
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Perform a symmetric rank 2 update of the selfadjoint matrix *this
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*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.
SelfAdjointView& Eigen::SelfAdjointView< _MatrixType, UpLo >::rankUpdate | ( | const MatrixBase< DerivedU > & | u, |
const Scalar & | alpha = Scalar(1) |
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Perform a symmetric rank K update of the selfadjoint matrix *this
: where u is a vector or matrix.
*this
Note that to perform you can simply call this function with u.adjoint().
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inlineinherited |
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Efficient vector/matrix times triangular matrix product