Properties of the discretizations for the Korteweg-de Vries equation. More...

#include "fnft__akns_discretization_t.h"
#include "fnft__errwarn.h"

Include dependency graph for fnft__akns_discretization.h:

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Functions
FNFT_UINT	fnft__akns_discretization_degree (fnft__akns_discretization_t discretization)
	This routine returns the max degree d of the polynomials in a single scattering matrix or zero if the discretization is unknown. More...

FNFT_REAL	fnft__akns_discretization_boundary_coeff (fnft__akns_discretization_t discretization)
	This routine returns the boundary coefficient based on the discretization. More...

FNFT_INT	fnft__akns_lambda_to_z (const FNFT_UINT n, const FNFT_REAL eps_t, FNFT_COMPLEX *const vals, fnft__akns_discretization_t discretization)
	This routine maps lambda from continuous-time domain to z in the discrete-time domain based on the discretization. More...

FNFT_INT	fnft__akns_z_to_lambda (const FNFT_UINT n, const FNFT_REAL eps_t, FNFT_COMPLEX *const vals, fnft__akns_discretization_t discretization)
	This routine maps z from the discrete-time domain to lambda in the continuous-time domain based on the discretization. More...

Detailed Description

Properties of the discretizations for the Korteweg-de Vries equation.

Function Documentation

◆ fnft__akns_discretization_boundary_coeff()

FNFT_REAL fnft__akns_discretization_boundary_coeff ( fnft__akns_discretization_t discretization )

This routine returns the boundary coefficient based on the discretization.

The boundary coefficient is the fraction of the step size that a discretized potential extends beyond the last sample. This routine returns this value based on the discretization of type fnft__akns_discretization_t.

Parameters

[in] discretization The type of discretization to be used. Should be of type fnft__akns_discretization_t.

Returns: the boundary coefficient, or NAN for discretizations not supported by fnft__akns_fscatter.

◆ fnft__akns_discretization_degree()

FNFT_UINT fnft__akns_discretization_degree ( fnft__akns_discretization_t discretization )

This routine returns the max degree d of the polynomials in a single scattering matrix or zero if the discretization is unknown.

It defines the step size of the frequency grid \(z = \text{e}^{2*j*\xi*\epsilon_t/d}\) based on the discretization type.

Parameters

[in] discretization The type of discretization to be used. Should be of type fnft_kdv_discretization_t.

Returns: polynomial degree, or 0 for discretizations not supported by fnft__akns_fscatter.

◆ fnft__akns_lambda_to_z()

FNFT_INT fnft__akns_lambda_to_z	(	const FNFT_UINT	n,
		const FNFT_REAL	eps_t,
		FNFT_COMPLEX *const	vals,
		fnft__akns_discretization_t	discretization
	)

This routine maps lambda from continuous-time domain to z in the discrete-time domain based on the discretization.

This routine maps continuous-time domain value lambda to discrete-time domain value z = exp(2i*lambda*eps_t/degree1step), where degree1step is based on the discretization of type fnft__akns_discretization_t.

Parameters

[in]	n	Number of values to be mapped.
[in]	eps_t	Real-valued discretization step-size.
[in,out]	vals	Pointer to location of first element of array containing complex-valued continuous-time domain spectral parameter lambda. The values are replaced with discrete-time domain values z.
[in]	discretization	Discretization of type fnft__akns_discretization_t.

Returns: FNFT_SUCCESS or one of the FNFT_EC_... error codes defined in fnft_errwarn.h.

◆ fnft__akns_z_to_lambda()

FNFT_INT fnft__akns_z_to_lambda	(	const FNFT_UINT	n,
		const FNFT_REAL	eps_t,
		FNFT_COMPLEX *const	vals,
		fnft__akns_discretization_t	discretization
	)

This routine maps z from the discrete-time domain to lambda in the continuous-time domain based on the discretization.

This routine maps discrete-time domain value z to continuous-time domain value lambda = degree1step*log(z)/(2i*eps_t), where degree1step is based on the discretization of type fnft__akns_discretization_t.

Parameters

[in]	n	Number of values to be mapped.
[in]	eps_t	Real-valued discretization step-size.
[in,out]	vals	Pointer to location of first element of array containing complex-valued discrete-time domain spectral parameter z. The values are replaced with continuous-time domain values lambda.
[in]	discretization	Discretization of type fnft__akns_discretization_t.

Returns: FNFT_SUCCESS or one of the FNFT_EC_... error codes defined in fnft_errwarn.h.

Functions

Detailed Description

Function Documentation

◆ fnft__akns_discretization_boundary_coeff()

◆ fnft__akns_discretization_degree()

◆ fnft__akns_lambda_to_z()

◆ fnft__akns_z_to_lambda()