Eigen Values
The section features functions for computing eigenvalues and eigenvectors. It describes methods for solving standard linear algebra problems using the LAPACK library algorithms. These functions are efficient for matrix analysis, diagonalization, system stabilization, and other tasks.
- EigenSolver: The function is designed to compute the eigenvalues and eigenvectors of an arbitrary square matrix using the classical algorithm represented by the GEEV lapack function. This method is applied to a wide range of matrices, allowing the decomposition of matrices into their eigenvalues and eigenvectors.
- EigenSymmetricDC: The function for computing eigenvalues and eigenvectors of symmetric or Hermitian matrices using the divide-and-conquer algorithm. The lapack functions SYEVD and HEEVD enable the efficient handling of symmetric or Hermitian matrices, providing faster and more accurate processing of such matrices.
Function |
Action |
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Compute eigenvalues and eigenvectors of a regular square matrix using the classical algorithm (lapack function GEEV). |
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Compute eigenvalues and eigenvectors of a regular square matrix in Expert mode, i.e. with the ability to influence the computation algorithm and the ability to obtain accompanying computation data (lapack function GEEVX). |
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Compute eigenvalues, upper triangular matrix in Schur form, and matrix of Schur vectors (lapack function GEES). See also Schur decomposition. |
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Compute generalized eigenvalues and eigenvectors for a pair of ordinary square matrices (lapack function GGEV). |
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Compute generalized eigenvalues and eigenvectors for a pair of regular square matrices in Expert mode, i.e. with the ability to influence the computation algorithm and the ability to obtain accompanying computation data (lapack function GGEVX). Both matrices must be the same size. |
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Compute a pair of ordinary square matrices of generalized eigenvalues, generalized eigenvectors, generalized Schur forms, as well as left and right Schur vectors (lapack function GGES). |
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Compute generalized eigenvalues and eigenvectors for a pair of regular square matrices using a block algorithm (lapack function GGEV3). Both matrices must be the same size. The method parameters are exactly the same as EigenSolver2. |
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Compute a pair of regular square matrices of generalized eigenvalues, generalized eigenvectors, generalized Schur forms, as well as left and right Schur vectors (lapack function GGES3). |
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Compute eigenvalues and eigenvectors of a symmetric or Hermitian (complex conjugate) matrix using the divide-and-conquer algorithm (lapack functions SYEVD, HEEVD). |
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Compute eigenvalues and eigenvectors of a symmetric or Hermitian (complex conjugate) matrix using the QR algorithm (lapack functions SYEV, HEEV). |
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Compute eigenvalues and eigenvectors of a symmetric or Hermitian (complex conjugate) matrix using the Multiple Relatively Robust Representations, MRRR algorithm (lapack functions SYEVR, HEEVR). |
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Compute eigenvalues and eigenvectors of a symmetric or Hermitian (complex conjugate) matrix using the bisection algorithm (lapack functions SYEVX, HEEVX). |