mql5-skills/skills/mql5/references/docs/06-matrix/0417-matrix-openblas-eigen-values.md

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
EigenSolver	Compute eigenvalues and eigenvectors of a regular square matrix using the classical algorithm (LAPACK function GEEV ).
EigenSolverX	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 ).
EigenSolverSchur	Compute eigenvalues, upper triangular matrix in Schur form, and matrix of Schur vectors (LAPACK function GEES ). See also Schur decomposition .
EigenSolver2	Compute generalized eigenvalues and eigenvectors for a pair of ordinary square matrices (LAPACK function GGEV ).
EigenSolver2X	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.
EigenSolver2Schur	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 ).
EigenSolver2Blocked	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 .
EigenSolver2SchurBlocked	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 ).
EigenHessenbergSchurQ	Computes the eigenvalues of a Hessenberg matrix H and the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors. LAPACK function HSEQR . See also Schur decomposition .
EigenSymmetricDC	Compute eigenvalues and eigenvectors of a symmetric or Hermitian (complex conjugate) matrix using the divide-and-conquer algorithm (LAPACK functions SYEVD , HEEVD ).
EigenSymmetricQR	Compute eigenvalues and eigenvectors of a symmetric or Hermitian (complex conjugate) matrix using the QR algorithm (LAPACK functions SYEV , HEEV ).
EigenSymmetricRobust	Compute eigenvalues and eigenvectors of a symmetric or Hermitian (complex conjugate) matrix using the Multiple Relatively Robust Representations, MRRR algorithm (LAPACK functions SYEVR , HEEVR ).
EigenSymmetricBisect	Compute eigenvalues and eigenvectors of a symmetric or Hermitian (complex conjugate) matrix using the bisection algorithm (LAPACK functions SYEVX , HEEVX ).
EigenSymmetricDC2s	Compute all eigenvalues and, optionally, eigenvectors of a real symmetric or Hermitian (complex conjugated) matrix using the 2stage technique for the reduction to tridiagonal. If eigenvectors are desired, it uses a divide and conquer algorithm (LAPACK functions SYEVD_2STAGE, HEEVD_2STAGE).
EigenSymmetricQR2s	Compute all eigenvalues and, optionally, eigenvectors of a real symmetric or Hermitian (complex conjugated) matrix using the 2stage technique for the reduction to tridiagonal (LAPACK functions SYEV_2STAGE , HEEV_2STAGE).
EigenSymmetricRobust2s	Compute eigenvalues and eigenvectors of a symmetric or Hermitian (complex conjugated) matrix using the 2stage technique for the reduction to tridiagonal then using the Multiple Relatively Robust Representations, MRRR algorithm (LAPACK functions SYEVR_2STAGE , HEEVR_2STAGE).
EigenSymmetricBisect2s	Compute eigenvalues and eigenvectors of a symmetric or Hermitian (complex conjugated) matrix using the 2stage technique for the reduction to tridiagonal then using the bisection algorithm (LAPACK functions SYEVX_2STAGE , HEEVX_2STAGE).
EigenSymmetric2DC	Compute all the eigenvalues, and optionally, the eigenvectors of a generalized symmetric-definite eigenproblem, of the form  Ax=(lambda)Bx,  ABx=(lambda)x,  or BA*x=(lambda)*x. LAPACK functions SYGVD , HEGVD .
EigenSymmetric2QR	Compute all the eigenvalues, and optionally, the eigenvectors of a generalized symmetric-definite eigenproblem, of the form Ax=(lambda)Bx,  ABx=(lambda)x,  or BA*x=(lambda)*x. LAPACK functions SYGV , HEGV .
EigenSymmetric2Bisect	Compute all the eigenvalues, and optionally, the eigenvectors of a generalized symmetric-definite eigenproblem, of the form Ax=(lambda)Bx,  ABx=(lambda)x,  or BA*x=(lambda)*x. LAPACK functions SYGVX , HEGVX .
EigenTridiagonalDC	Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide-and-conquer algorithm (LAPACK function STEVD ).
EigenTridiagonalQR	Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the QR algorithm (LAPACK function STEV ).
EigenTridiagonalRobust	Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the Multiple Relatively Robust Representations, MRRR algorithm (LAPACK function STEVR ).
EigenTridiagonalBisect	Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the bisection algorithm (LAPACK function STEVX ).
EigenTridiagonalQL	Compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm (LAPACK function STERF ).
EigenTridiagonalDCQ	Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide-and-conquer algorithm (LAPACK function STEDC ).
EigenTridiagonalQRQ	Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the QR algorithm (LAPACK function STEQR ).
EigenTridiagonalPosDefQ	Compute eigenvalues and eigenvectors of a symmetric positive definite (положительно определённая) tridiagonal matrix using the QR algorithm (LAPACK function PTEQR ).