mql5-skills/skills/mql5/references/docs/06-matrix/0442-matrix-openblas-eigen-values-tridiagonalmatrices.md

Tridiagonal Matrices

Functions for computing eigenvalues and eigenvectors of symmetric tridiagonal matrices using various algorithms. Each function implements a specific solution method and supports matrix types double and float.

Common Parameters:

• jobv — Determines whether to compute eigenvectors (EIGVALUES_V) or only eigenvalues (EIGVALUES_N).
• range — Specifies the range of computed eigenvalues (BLASRANGE_A, BLASRANGE_V, BLASRANGE_I).
• lower and upper — Lower and upper bounds for computing a subset of the spectrum.
• abstol — Absolute error tolerance.

All functions operate on symmetric tridiagonal matrices and allow selecting the most suitable algorithm depending on performance and accuracy requirements.

Function	Action
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 ).