beyn.h File Reference

Beyn's algorithm for nonlinear eigenvalue problems. More...

#include <stddef.h>
#include <complex.h>

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Data Structures
struct	beyn_contour_t
	Complex plane integration contour structure. More...
struct	beyn_result_t
	Beyn algorithm result structure (pure C array version). More...

Typedefs
typedef int(*	beyn_function_M_t) (complex double *target_M, size_t m, complex double z, void *params)
	User-supplied function that provides the (row-major) m × m matrix M(z) whose "roots" are to be found. More...
typedef int(*	beyn_function_M_inv_Vhat_t) (complex double *target_M_inv_Vhat, size_t m, size_t l, const complex double *Vhat, complex double z, void *params)
	(optional) User-supplied function that, given \( \hat V \), calculates \( M(z)^{-1} \hat V \). More...
typedef struct beyn_contour_t	beyn_contour_t
	Complex plane integration contour structure.
typedef struct beyn_result_t	beyn_result_t
	Beyn algorithm result structure (pure C array version).

Enumerations
enum	beyn_contour_halfellipse_orientation { BEYN_CONTOUR_HALFELLIPSE_RE_PLUS = 3 , BEYN_CONTOUR_HALFELLIPSE_RE_MINUS = 1 , BEYN_CONTOUR_HALFELLIPSE_IM_PLUS = 0 , BEYN_CONTOUR_HALFELLIPSE_IM_MINUS = 2 }

Functions
beyn_contour_t *	beyn_contour_ellipse (complex double centre, double halfax_re, double halfax_im, size_t npoints)
	Complex plane elliptic integration contour with axes parallel to the real, imaginary axes. More...
beyn_contour_t *	beyn_contour_halfellipse (complex double centre, double halfax_re, double halfax_im, size_t npoints, beyn_contour_halfellipse_orientation or)
	Complex plane "half-elliptic" integration contour with axes parallel to the real, imaginary axes. More...
beyn_contour_t *	beyn_contour_kidney (complex double centre, double halfax_re, double halfax_im, double rounding, size_t n, beyn_contour_halfellipse_orientation or)
	Similar to halfellipse but with rounded corners. More...
void	beyn_result_free (beyn_result_t *result)
beyn_result_t *	beyn_solve (size_t m, size_t l, beyn_function_M_t M, beyn_function_M_inv_Vhat_t M_inv_Vhat, void *params, const beyn_contour_t *contour, double rank_tol, size_t rank_min_sel, double res_tol)
	Solve a non-linear eigenproblem using Beyn's algorithm. More...

Detailed Description

Beyn's algorithm for nonlinear eigenvalue problems.

Typedef Documentation

beyn_function_M_inv_Vhat_t

typedef int(* beyn_function_M_inv_Vhat_t) (complex double *target_M_inv_Vhat, size_t m, size_t l, const complex double *Vhat, complex double z, void *params)

(optional) User-supplied function that, given \( \hat V \), calculates \( M(z)^{-1} \hat V \).

Pure C array version

beyn_function_M_t

typedef int(* beyn_function_M_t) (complex double *target_M, size_t m, complex double z, void *params)

User-supplied function that provides the (row-major) m × m matrix M(z) whose "roots" are to be found.

Pure C array version

Function Documentation

beyn_contour_ellipse()

beyn_contour_t* beyn_contour_ellipse	(	complex double	centre,
		double	halfax_re,
		double	halfax_im,
		size_t	npoints
	)

Complex plane elliptic integration contour with axes parallel to the real, imaginary axes.

Free using free().

beyn_contour_halfellipse()

beyn_contour_t* beyn_contour_halfellipse	(	complex double	centre,
		double	halfax_re,
		double	halfax_im,
		size_t	npoints,
		beyn_contour_halfellipse_orientation	or
	)

Complex plane "half-elliptic" integration contour with axes parallel to the real, imaginary axes.

Free using free().

beyn_contour_kidney()

beyn_contour_t* beyn_contour_kidney	(	complex double	centre,
		double	halfax_re,
		double	halfax_im,
		double	rounding,
		size_t	n,
		beyn_contour_halfellipse_orientation	or
	)

Similar to halfellipse but with rounded corners.

Parameters

rounding

Must be in interval [0, 0.5)

beyn_solve()

beyn_result_t* beyn_solve	(	size_t	m,
		size_t	l,
		beyn_function_M_t	M,
		beyn_function_M_inv_Vhat_t	M_inv_Vhat,
		void *	params,
		const beyn_contour_t *	contour,
		double	rank_tol,
		size_t	rank_min_sel,
		double	res_tol
	)

Solve a non-linear eigenproblem using Beyn's algorithm.

Parameters

m	Dimension of the matrix M.
l	Number of columns of the random matrix \( \hat V \) (larger than the expected number of solutions).
M	Function providing the matrix \( M(z) \).
M_inv_Vhat	Fuction providing the matrix \( M^{-1}(z) \hat V \) (optional).
params	Parameter pointer passed to M() and M_inv_Vhat().
contour	Integration contour.
rank_tol	(default: `1e-4`) TODO DOC.
rank_min_sel	Minimum number of eigenvalue candidates, even if they don't pass rank_tol.
res_tol	(default: `0.0`) TODO DOC.