3.0 API Reference

FPT - Fast polynomial transform

This module implements fast polynomial transforms. More...


Defines
#define	FPT_NO_FAST_ALGORITHM (1U << 2)
	If set, TODO complete comment.
#define	FPT_NO_DIRECT_ALGORITHM (1U << 3)
	If set, TODO complete comment.
#define	FPT_NO_STABILIZATION (1U << 0)
	If set, no stabilization will be used.
#define	FPT_PERSISTENT_DATA (1U << 4)
	If set, TODO complete comment.
#define	FPT_FUNCTION_VALUES (1U << 5)
	If set, the output are function values at Chebyshev nodes rather than Chebyshev coefficients.
#define	FPT_AL_SYMMETRY (1U << 6)
	TODO Don't use this flag!
Typedefs
typedef fpt_set_s_ *	fpt_set
	A set of precomputed data for a set of DPT transforms of equal maximum length.
Functions
fpt_set	fpt_init (const int M, const int t, const unsigned int flags)
	Initializes a set of precomputed data for DPT transforms of equal length.
void	fpt_precompute (fpt_set set, const int m, const double alpha, const double beta, const double *gamma, int k_start, const double threshold)
	Computes the data required for a single DPT transform.
void	dpt_trafo (fpt_set set, const int m, const double complex x, double complex y, const int k_end, const unsigned int flags)
	Computes a single DPT transform.
void	fpt_trafo (fpt_set set, const int m, const double complex x, double complex y, const int k_end, const unsigned int flags)
	Computes a single DPT transform.
void	dpt_transposed (fpt_set set, const int m, double complex x, double complex y, const int k_end, const unsigned int flags)
	Computes a single DPT transform.
void	fpt_transposed (fpt_set set, const int m, double complex x, const double complex y, const int k_end, const unsigned int flags)
	Computes a single DPT transform.
void	fpt_finalize (fpt_set set)

Detailed Description

This module implements fast polynomial transforms.

In the following, we abbreviate the term "fast polynomial transforms" by FPT.

Function Documentation

fpt_set fpt_init ( const int M,

const int t,

const unsigned int flags

)

Initializes a set of precomputed data for DPT transforms of equal length.
Polynomial length
Cascade level
Index m
Allocate memory for auxilliary arrays.
Allocate memory for auxilliary arrays.
Initialize FFTW plans.
Definition at line 586 of file fpt.c.
References fpt_set_s_::dpt, fpt_set_s_::flags, FPT_NO_DIRECT_ALGORITHM, FPT_NO_FAST_ALGORITHM, fpt_set_s_::kinds, fpt_set_s_::kindsr, fpt_set_s_::lengths, fpt_set_s_::M, fpt_set_s_::N, PI, fpt_set_s_::plans_dct2, fpt_set_s_::plans_dct3, fpt_set_s_::result, fpt_data_::steps, fpt_set_s_::t, fpt_set_s_::temp, fpt_set_s_::vec3, fpt_set_s_::vec4, fpt_set_s_::work, fpt_set_s_::xc_slow, fpt_set_s_::xcvecs, and fpt_set_s_::z.
Referenced by nfsft_precompute().

void fpt_precompute ( fpt_set set,

const int m,

const double * alpha,

const double * beta,

const double * gamma,

int k_start,

const double threshold

)

Computes the data required for a single DPT transform.
< Cascade level
< Level index
< Length of polynomials for the next level in the cascade
< Degree of polynomials for the current level in the cascade
< First index l for current cascade level
< Last index l for current cascade level and current
< Length of polynomials for the next level in the cascade for stabilization
< Degree of polynomials for the current level in the cascade for stabilization
< Array containing function values of the (1,1)-component of U_k^n.
< Array containing function values of the (1,2)-component of U_k^n.
< Array containing function values of the (2,1)-component of U_k^n.
< Array containing function values of the (2,2)-component of U_k^n.
< Used to indicate that stabilization is neccessary.
Increase polynomial degree to next power of two.
Definition at line 698 of file fpt.c.
References fpt_step_::a11, fpt_step_::a12, fpt_step_::a21, fpt_step_::a22, fpt_data_::alpha, fpt_data_::alpha_0, fpt_data_::alphaN, fpt_data_::beta, fpt_data_::beta_0, fpt_data_::betaN, fpt_set_s_::dpt, eval_clenshaw(), eval_clenshaw_thresh(), FIRST_L, fpt_set_s_::flags, FPT_AL_SYMMETRY, FPT_NO_DIRECT_ALGORITHM, FPT_NO_FAST_ALGORITHM, FPT_NO_STABILIZATION, FPT_PERSISTENT_DATA, fpt_step_::gamma, fpt_data_::gamma, fpt_data_::gamma_m1, fpt_data_::gammaN, IS_SYMMETRIC, fpt_data_::k_start, K_START_TILDE, LAST_L, fpt_set_s_::N, fpt_step_::N_stab, N_TILDE, nfft_next_power_of_2(), nfft_next_power_of_2_exp(), fpt_step_::stable, fpt_data_::steps, fpt_set_s_::t, fpt_step_::t_stab, and fpt_set_s_::xcvecs.
Referenced by nfsft_precompute().

void dpt_trafo ( fpt_set set,

const int m,

const double complex * x,

double complex * y,

const int k_end,

const unsigned int flags

)

Computes a single DPT transform.

set

m

x

y

k_end

flags

Definition at line 988 of file fpt.c.
References fpt_data_::alpha, fpt_data_::beta, fpt_set_s_::dpt, eval_sum_clenshaw(), fpt_set_s_::flags, FPT_FUNCTION_VALUES, FPT_NO_DIRECT_ALGORITHM, fpt_data_::gamma, fpt_data_::gamma_m1, fpt_data_::k_start, nfft_next_power_of_2_exp(), PI, fpt_set_s_::plans_dct2, fpt_set_s_::result, fpt_set_s_::temp, fpt_set_s_::work, fpt_set_s_::xc_slow, and fpt_set_s_::xcvecs.
Referenced by nfsft_trafo().

void fpt_trafo ( fpt_set set,

const int m,

const double complex * x,

double complex * y,

const int k_end,

const unsigned int flags

)

Computes a single DPT transform.
Level index $tau$
Index of first block at current level
Index of last block at current level
Block index $l$
Length of polynomial coefficient arrays at next level
Polynomial array length for stabilization
Current matrix $U_{n,tau,l}$
Loop counter
Definition at line 1042 of file fpt.c.
References fpt_step_::a11, fpt_step_::a12, fpt_step_::a21, fpt_step_::a22, fpt_data_::alpha_0, fpt_data_::alphaN, fpt_data_::beta_0, fpt_data_::betaN, fpt_set_s_::dpt, FIRST_L, fpt_set_s_::flags, FPT_AL_SYMMETRY, fpt_do_step(), fpt_do_step_symmetric(), fpt_do_step_symmetric_l(), fpt_do_step_symmetric_u(), FPT_FUNCTION_VALUES, FPT_NO_FAST_ALGORITHM, fpt_step_::gamma, fpt_data_::gamma_m1, fpt_data_::gammaN, IS_SYMMETRIC, K_END_TILDE, fpt_data_::k_start, K_START_TILDE, LAST_L, fpt_step_::N_stab, nfft_next_power_of_2_exp(), fpt_set_s_::result, fpt_step_::stable, fpt_data_::steps, fpt_step_::t_stab, fpt_set_s_::vec3, fpt_set_s_::vec4, and fpt_set_s_::work.
Referenced by nfsft_trafo().

void dpt_transposed ( fpt_set set,

const int m,

double complex * x,

double complex * y,

const int k_end,

const unsigned int flags

)

Computes a single DPT transform.

set

m

x

y

k_end

flags

Definition at line 1297 of file fpt.c.
References fpt_data_::alpha, fpt_data_::beta, fpt_set_s_::dpt, eval_sum_clenshaw_transposed(), fpt_set_s_::flags, FPT_FUNCTION_VALUES, FPT_NO_DIRECT_ALGORITHM, fpt_data_::gamma, fpt_data_::gamma_m1, fpt_data_::k_start, nfft_next_power_of_2_exp(), PI, fpt_set_s_::plans_dct3, fpt_set_s_::result, fpt_set_s_::temp, fpt_set_s_::work, fpt_set_s_::xc_slow, and fpt_set_s_::xcvecs.
Referenced by nfsft_adjoint().

void fpt_transposed ( fpt_set set,

const int m,

double complex * x,

const double complex * y,

const int k_end,

const unsigned int flags

)

Computes a single DPT transform.
Level index $tau$
Index of first block at current level
Index of last block at current level
Block index $l$
Length of polynomial coefficient arrays at next level
Polynomial array length for stabilization
Current matrix $U_{n,tau,l}$
Loop counter
Save copy of inpute data for stabilization steps.
Definition at line 1349 of file fpt.c.
References fpt_step_::a11, fpt_step_::a12, fpt_step_::a21, fpt_step_::a22, fpt_data_::alpha_0, fpt_data_::alphaN, fpt_data_::beta_0, fpt_data_::betaN, fpt_set_s_::dpt, FIRST_L, fpt_set_s_::flags, FPT_AL_SYMMETRY, fpt_do_step_transposed(), fpt_do_step_transposed_symmetric(), fpt_do_step_transposed_symmetric_l(), fpt_do_step_transposed_symmetric_u(), FPT_FUNCTION_VALUES, FPT_NO_FAST_ALGORITHM, fpt_step_::gamma, fpt_data_::gamma_m1, fpt_data_::gammaN, IS_SYMMETRIC, K_END_TILDE, fpt_data_::k_start, K_START_TILDE, LAST_L, fpt_step_::N_stab, nfft_next_power_of_2_exp(), fpt_set_s_::result, fpt_step_::stable, fpt_data_::steps, fpt_step_::t_stab, fpt_set_s_::vec3, fpt_set_s_::vec4, and fpt_set_s_::work.
Referenced by nfsft_adjoint().

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FPT - Fast polynomial transform

Defines

Typedefs

Functions

Detailed Description

Function Documentation