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# DSGNHEP

Dense Generalized Non-Hermitian Eigenvalue Problem.

## Notes

The problem is expressed as \(AX = BX\Lambda\), where \((A,B)\) is the input matrix pencil. \(\Lambda\) is a diagonal matrix whose diagonal elements are the arguments of `DSSolve()`. After solve, \((A,B)\) is overwritten with the generalized (real) Schur form \((S,T) = (Z^*AQ,Z^*BQ)\), with the first matrix being upper quasi-triangular and the second one triangular.

## Used DS matrices

- `DS_MAT_A` - first problem matrix

- `DS_MAT_B` - second problem matrix

- `DS_MAT_Q` - first orthogonal/unitary transformation that reduces to generalized (real) Schur form

- `DS_MAT_Z` - second orthogonal/unitary transformation that reduces to generalized (real) Schur form

## Implemented methods

- 0 - QZ iteration (`_gges`)

- 1 - blocked QZ iteration (`_gges3`, if available)

## See Also

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

## Level

beginner

## Location

src/sys/classes/ds/impls/gnhep/dsgnhep.c

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