Properties of the discretization for the Manakov equation. More...

#include "fnft_manakov_discretization_t.h"
#include "fnft__errwarn.h"
#include "fnft__misc.h"

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Functions
FNFT_UINT	fnft__manakov_discretization_degree (fnft_manakov_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.

FNFT_UINT	fnft__manakov_discretization_upsampling_factor (fnft_manakov_discretization_t discretization)
	This routine returns the scaling for effective number of samples based on the discretization. Returns 0 for unknown discretization.

FNFT_UINT	fnft__manakov_discretization_method_order (fnft_manakov_discretization_t discretization)
	Returns the order of the chosen discretization method. 0 for unknown discretizations.

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

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

FNFT_INT	fnft__manakov_discretization_phase_factor_rho (const FNFT_REAL eps_t, const FNFT_REAL T1, FNFT_REAL *const phase_factor_rho, fnft_manakov_discretization_t discretization)
	This routine returns the phase factor for reflection coefficient (rho). It is required for applying boundary conditions to the transfer matrix values based on the discretization.

FNFT_INT	fnft__manakov_discretization_phase_factor_a (const FNFT_REAL eps_t, const FNFT_UINT D, FNFT_REAL const const T, FNFT_REAL const phase_factor_a, fnft_manakov_discretization_t discretization)
	This routine returns the phase factor for the NFT coefficient a. It is required for applying boundary conditions to the transfer matrix values based on the discretization.

FNFT_INT	fnft__manakov_discretization_phase_factor_b (const FNFT_REAL eps_t, const FNFT_UINT D, FNFT_REAL const const T, FNFT_REAL const phase_factor_b, fnft_manakov_discretization_t discretization)
	This routine returns the phase factor for the NFT coefficient b1, b2. It is required for applying boundary conditions to the transfer matrix values based on the discretization.

FNFT_INT	fnft__manakov_discretization_preprocess_signal (const FNFT_UINT D, FNFT_COMPLEX const const q1, FNFT_COMPLEX const const q2, FNFT_REAL const eps_t, FNFT_UINT const Dsub_ptr, FNFT_COMPLEX q1_preprocessed_ptr, FNFT_COMPLEX q2_preprocessed_ptr, FNFT_UINT const first_last_index, manakov_discretization_t discretization)
	This routine computes the downsampled and interpolated version of the samples if required.

FNFT_REAL	fnft__manakov_discretization_boundary_coeff (fnft_manakov_discretization_t discretization)
	This routine returns the boundary coefficient based on the discretization.

Detailed Description

Properties of the discretization for the Manakov equation.

Function Documentation

◆ fnft__manakov_discretization_boundary_coeff()

FNFT_REAL fnft__manakov_discretization_boundary_coeff ( fnft_manakov_discretization_t discretization )

This routine returns the boundary coefficient based on the discretization.

Parameters

[in] discretization discretization Should be of type fnft_manakov_discretization_t

Returns: the boundary coefficient

◆ fnft__manakov_discretization_degree()

FNFT_UINT fnft__manakov_discretization_degree ( fnft_manakov_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.

Parameters

[in] discretization discretization Should be of type fnft_manakov_discretization_t

Returns: polynomial degree, or 0 for unknown discretizations

◆ fnft__manakov_discretization_lambda_to_z()

FNFT_INT fnft__manakov_discretization_lambda_to_z	(	const FNFT_UINT	n,
		const FNFT_REAL	eps_t,
		FNFT_COMPLEX *const	vals,
		fnft_manakov_discretization_t	discretization
	)

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

Parameters

[in]	n	Length of array vals (number of \(\lambda\) 's)
[in]	eps_t	timestep size
[in,out]	vals	Pointer to first element of array of size n. Upon entry, this array contains the continuous-time values \(\lambda\). Upon exit, the array contains the corresponding discrete-time values \(z\).
[in]	discretization	discretization Should be of type fnft_manakov_discretization_t

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

◆ fnft__manakov_discretization_method_order()

FNFT_UINT fnft__manakov_discretization_method_order ( fnft_manakov_discretization_t discretization )

Returns the order of the chosen discretization method. 0 for unknown discretizations.

Parameters

[in] discretization discretization Should be of type fnft_manakov_discretization_t

Returns: order of the chosen discretization method

◆ fnft__manakov_discretization_phase_factor_a()

FNFT_INT fnft__manakov_discretization_phase_factor_a	(	const FNFT_REAL	eps_t,
		const FNFT_UINT	D,
		FNFT_REAL const *const	T,
		FNFT_REAL *const	phase_factor_a,
		fnft_manakov_discretization_t	discretization
	)

This routine returns the phase factor for the NFT coefficient a. It is required for applying boundary conditions to the transfer matrix values based on the discretization.

Parameters

[in]	eps_t	timestep size
[in]	D	effective number of samples
[in]	T	real array containing the time t of the first and last sample T=[T[0] T[1]]
[in,out]	phase_factor_a	pointer to real-valued variable where the computed phase factor is will be stored
[in]	discretization	discretization Should be of type fnft_manakov_discretization_t

Returns: FNFT_SUCCESS or the FNFT__E_INVALID_ARGUMENT(discretization) code

◆ fnft__manakov_discretization_phase_factor_b()

FNFT_INT fnft__manakov_discretization_phase_factor_b	(	const FNFT_REAL	eps_t,
		const FNFT_UINT	D,
		FNFT_REAL const *const	T,
		FNFT_REAL *const	phase_factor_b,
		fnft_manakov_discretization_t	discretization
	)

This routine returns the phase factor for the NFT coefficient b1, b2. It is required for applying boundary conditions to the transfer matrix values based on the discretization.

Parameters

[in]	eps_t	timestep size
[in]	D	effective number of samples
[in]	T	real array containing the time t of the first and last sample T=[T[0] T[1]]
[in,out]	phase_factor_b	pointer to real-valued variable where the computed phase factor is will be stored
[in]	discretization	discretization Should be of type fnft_manakov_discretization_t

Returns: FNFT_SUCCESS or the FNFT__E_INVALID_ARGUMENT(discretization) code

◆ fnft__manakov_discretization_phase_factor_rho()

FNFT_INT fnft__manakov_discretization_phase_factor_rho	(	const FNFT_REAL	eps_t,
		const FNFT_REAL	T1,
		FNFT_REAL *const	phase_factor_rho,
		fnft_manakov_discretization_t	discretization
	)

This routine returns the phase factor for reflection coefficient (rho). It is required for applying boundary conditions to the transfer matrix values based on the discretization.

Parameters

[in]	eps_t	timestep size
[in]	T1	time at the last timestep
[in,out]	phase_factor_rho	pointer to real-valued variable where the computed phase factor is will be stored
[in]	discretization	discretization Should be of type fnft_manakov_discretization_t

Returns: FNFT_SUCCESS or the FNFT__E_INVALID_ARGUMENT(discretization) code

◆ fnft__manakov_discretization_preprocess_signal()

FNFT_INT fnft__manakov_discretization_preprocess_signal	(	const FNFT_UINT	D,
		FNFT_COMPLEX const *const	q1,
		FNFT_COMPLEX const *const	q2,
		FNFT_REAL const	eps_t,
		FNFT_UINT *const	Dsub_ptr,
		FNFT_COMPLEX **	q1_preprocessed_ptr,
		FNFT_COMPLEX **	q2_preprocessed_ptr,
		FNFT_UINT *const	first_last_index,
		manakov_discretization_t	discretization
	)

This routine computes the downsampled and interpolated version of the samples if required.

For richardson extrapolation downsampling is needed. This simply means only using a certain number from the original samples. Not all choices for the number od samples are valid as at this stage the samples should still be equidistant and no interpolation is carried out. If the chosen number of samples for downsampling is not valid, the routine chooses a number as close as possible to the desired amount of samples. Certain discretization types from fnft_manakov_discretization_t require non-equidistant samples. In that case, band-limited Fourier interpolation is used after the optional downsampling to get the required samples. Both the downsampling and interpolation step are combined in this function, resulting in a preprocessed array of samples to be used by the other functions in fnft_manakovv

Parameters

[in]	D	the original number of samples
[in]	q1	Pointer to complex array of size D containg the samples of the first element of the potential q1
[in]	q2	Pointer to complex array of size D containg the samples of the second element of the potential q2
[in]	eps_t	timestep size
[in,out]	Dsub_ptr	Pointer to the desired number of samples after subsampling. Upon exit, this contains the actual number of samples after subsampling which ensures that the samples stay equidistant
[out]	q1_preprocessed_ptr	Pointer to a complex array of size Dsub*upsampling_factor containing the optionally downsampled and interpolated (if the discretization required interpolation) samples of q1
[out]	q2_preprocessed_ptr	Pointer to a complex array of size Dsub*upsampling_factor containing the optionally downsampled and interpolated (if the discretization required interpolation) samples of q2
[out]	first_last_index	Pointer to an integer array containing the index of the first and last index from the original samples used in the preprocessed arrays
[in]	discretization	discretization Should be of type fnft_manakov_discretization_t

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

◆ fnft__manakov_discretization_upsampling_factor()

FNFT_UINT fnft__manakov_discretization_upsampling_factor ( fnft_manakov_discretization_t discretization )

This routine returns the scaling for effective number of samples based on the discretization. Returns 0 for unknown discretization.

Parameters

[in] discretization discretization Should be of type fnft_manakov_discretization_t

Returns: upsampling factor. Factor with which to multiply the number of samples to get the effective number of samples for the method

◆ fnft__manakov_discretization_z_to_lambda()

FNFT_INT fnft__manakov_discretization_z_to_lambda	(	const FNFT_UINT	n,
		const FNFT_REAL	eps_t,
		FNFT_COMPLEX *const	vals,
		fnft_manakov_discretization_t	discretization
	)

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

Parameters

[in]	n	Length of array vals (number of z)
[in]	eps_t	timestep size
[in,out]	vals	Pointer to first element of array of size n. Upon entry, this array contains the discrete-time values z. Upon exit, the array contains the corresponding continuous-time values \(\lambda\).
[in]	discretization	discretization Should be of type fnft_manakov_discretization_t

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

Functions

Detailed Description

Function Documentation

◆ fnft__manakov_discretization_boundary_coeff()

◆ fnft__manakov_discretization_degree()

◆ fnft__manakov_discretization_lambda_to_z()

◆ fnft__manakov_discretization_method_order()

◆ fnft__manakov_discretization_phase_factor_a()

◆ fnft__manakov_discretization_phase_factor_b()

◆ fnft__manakov_discretization_phase_factor_rho()

◆ fnft__manakov_discretization_preprocess_signal()

◆ fnft__manakov_discretization_upsampling_factor()

◆ fnft__manakov_discretization_z_to_lambda()