DSHEP#

Dense Hermitian Eigenvalue Problem.

Notes#

The problem is expressed as AX = XLambda, 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=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#

DSCreate(), DSSetType(), DSType

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