DSHEP#

Dense Hermitian Eigenvalue Problem.

Notes#

The problem is expressed as \(AX = X\Lambda\), where \(A\) is real symmetric (or complex Hermitian). \(\Lambda\) is a diagonal matrix whose diagonal elements are the arguments of DSSolve(). After solve, \(A\) is overwritten with \(\Lambda\).

In the intermediate state \(A\) is reduced to tridiagonal form. In compact storage format, the symmetric tridiagonal matrix is stored in \(T\).

Used DS matrices#

  • DS_MAT_A - problem matrix (used only if compact=PETSC_FALSE)

  • DS_MAT_T - symmetric tridiagonal matrix

  • DS_MAT_Q - orthogonal/unitary transformation that reduces to tridiagonal form (intermediate step) or matrix of orthogonal eigenvectors, which is equal to \(X\)

Implemented methods#

  • 0 - Implicit QR (_steqr)

  • 1 - Multiple Relatively Robust Representations (_stevr)

  • 2 - Divide and Conquer (_stedc)

  • 3 - Block Divide and Conquer (real scalars only)

See Also#

DS: Direct Solver (or Dense System), DSCreate(), DSSetType(), DSType, DSSetCompact()

Level#

beginner

Location#

src/sys/classes/ds/impls/hep/dshep.c

Index of all DS routines Table of Contents for all manual pages Index of all manual pages