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# DSNEP

Dense Nonlinear Eigenvalue Problem.

## Notes

The problem is expressed as \(T(\lambda)x = 0\), where \(T(\lambda)\) is a parameter-dependent matrix written as \(T(\lambda) = \sum_i E_i f_i(\lambda)\). The eigenvalues \(\lambda\) are the arguments returned by `DSSolve()`.

The coefficient matrices \(E_i\) are the extra matrices of the `DS`, and the scalar functions \(f_i\) are passed via `DSNEPSetFN()`. Optionally, a callback function to fill the \(E_i\) matrices can be set with `DSNEPSetComputeMatrixFunction()`.

## Used DS matrices

- `DS_MAT_E0` to `DS_MAT_E9` - coefficient matrices of the split form of \(T(\lambda)\)

- `DS_MAT_X` - eigenvectors

- `DS_MAT_A` - (workspace) \(T(\lambda)\) evaluated at a given \(\lambda\) (SLP only)

- `DS_MAT_B` - (workspace) \(T'(\lambda)\) evaluated at a given \(\lambda\) (SLP only)

- `DS_MAT_Q` - (workspace) left Hankel matrix (contour only)

- `DS_MAT_Z` - (workspace) right Hankel matrix (contour only)

- `DS_MAT_U` - (workspace) left singular vectors (contour only)

- `DS_MAT_V` - (workspace) right singular vectors (contour only)

- `DS_MAT_W` - (workspace) auxiliary matrix of size \(n\times n\)

## Implemented methods

- 0 - Successive Linear Problems (SLP), computes just one eigenpair

- 1 - Contour integral, computes all eigenvalues inside a region

## See Also

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

## Level

beginner

## Location

src/sys/classes/ds/impls/nep/dsnep.c

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