MatrixEigenSym Class Reference
Last update: 16.07.2025Eigen decomposition of symmetric matrices. More...
Public Types | |
| typedef Eigen::Matrix< TScalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor > | Base |
| the Eigen matrix type we refer to | |
| typedef Eigen::Matrix< TScalar, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor > | Base2 |
| the Eigen matrix type which is used by the Eigen solvers | |
| typedef int | TIndex |
| index type of Eigen matrices | |
| typedef number | TScalar |
| the scalar tyta type of matrix elements | |
| typedef Eigen::SelfAdjointEigenSolver< Base2 > | TSolver |
| the solver type for standard eigenvalue problem | |
| typedef Eigen::GeneralizedSelfAdjointEigenSolver< Base2 > | TSolverGeneralized |
| the solver type for generalized eigenvalue problem | |
Public Member Functions | |
| Matrix | __pow__ (TScalar exponent) const |
| operator ^(scalar) in scripting languages by SWIG More... | |
| Matrix | Eigenvalues () const |
| Matrix | Eigenvectors () const |
| bool | EigenvectorsAvailable () const |
| Matrix | Exp () |
| bool | IsGeneralEigenproblem () const |
| Matrix | Log () |
| MatrixEigenSym (Matrix _object, bool computevectors=true) | |
| destructor More... | |
| MatrixEigenSym (Matrix _object, Matrix mass, bool computevectors=true) | |
| constructor of a generalized eigenvalue problem More... | |
| Matrix | OperatorInverseSqrt () const |
| Matrix | OperatorSqrt () const |
| Matrix | Pow (TScalar exponent) |
Detailed Description
Eigen decomposition of symmetric matrices.
This class provides an Eigen decomposition of symmetric matrices. At construction, it factorizes the given matrix and stores eigenvalues and (if asked for) eigenvectors. The constructor accepts either the standard eigenvalues problem (of a single symmetric matrix) or the generalized eigenvalue problem (of 2 symmetric matrices).
The class is equipped with methods and arithmetic operators which provide the
- matrix exponential
- matrix power
- matrix logarithm
- matrix square root using the full decomposition.
Constructor & Destructor Documentation
◆ MatrixEigenSym() [1/2]
| MatrixEigenSym | ( | Matrix | _object, |
| bool | computevectors = true |
||
| ) |
destructor
constructor of a standard eigenvalue problem
- Parameters
-
_object the matrix to be decomposed computevectors if true, then also the eigenvectors are computed. else only eigenvalues
◆ MatrixEigenSym() [2/2]
| MatrixEigenSym | ( | Matrix | _object, |
| Matrix | mass, | ||
| bool | computevectors = true |
||
| ) |
constructor of a generalized eigenvalue problem
- Parameters
-
_object the matrix to be decomposed, eg. the stiffness matrix mass the second matrix, eg. the mass matrix computevectors if true, then also the eigenvectors are computed. else only eigenvalues
Member Function Documentation
◆ __pow__()
operator ^(scalar) in scripting languages by SWIG
- Returns
- the power of the matrix, i.e. $ A^n$ $
- Parameters
-
exponent the exponent $ n $
◆ Eigenvalues()
| Matrix Eigenvalues | ( | ) | const |
- Returns
- the eigenvalues as vector
◆ Eigenvectors()
| Matrix Eigenvectors | ( | ) | const |
- Returns
- the normalized complex eigenvectors as a matrix of column vectors.
◆ EigenvectorsAvailable()
| bool EigenvectorsAvailable | ( | ) | const |
- Returns
- m_eigenvectorsAvailable
◆ Exp()
| Matrix Exp | ( | ) |
- Returns
- the exponential of the matrix
◆ IsGeneralEigenproblem()
| bool IsGeneralEigenproblem | ( | ) | const |
- Returns
- m_isGeneralEigenproblem
◆ Log()
| Matrix Log | ( | ) |
- Returns
- the logarithm of the matrix
◆ OperatorInverseSqrt()
| Matrix OperatorInverseSqrt | ( | ) | const |
- Returns
- the positive inverse square root of the matrix (if positive definite)
◆ OperatorSqrt()
| Matrix OperatorSqrt | ( | ) | const |
- Returns
- the positive square root of the matrix (if positive definite)
