Skip to main content
`Ctrl`+`K`

# DSGHEP

Dense Generalized Hermitian Eigenvalue Problem.

## Notes

The problem is expressed as \(AX = BX\Lambda\), where both \(A\) and \(B\) are real symmetric (or complex Hermitian) and \(B\) is positive-definite. \(\Lambda\) is a diagonal matrix whose diagonal elements are the arguments of `DSSolve()`. After solve, \(A\) is overwritten with \(\Lambda\), and \(B\) is overwritten with \(I\).

No intermediate state is implemented, nor compact storage.

## Used DS matrices

- `DS_MAT_A` - first problem matrix

- `DS_MAT_B` - second problem matrix

- `DS_MAT_Q` - matrix of \(B\)-orthogonal eigenvectors, which is equal to \(X\)

## Implemented methods

- 0 - Divide and Conquer (`_sygvd`)

## See Also

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

## Level

beginner

## Location

src/sys/classes/ds/impls/ghep/dsghep.c

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