This module implements fast polynomial transforms. More...

Macros
#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)
	If set, TODO complete comment.

Functions
fpt_set	fpt_init (const int M, const int t, const unsigned int flags)

void	fpt_precompute (fpt_set set, const int m, double alpha, double beta, double *gam, int k_start, const double threshold)

void	fpt_transposed (fpt_set set, const int m, double _Complex x, double _Complex y, const int k_end, const unsigned int flags)

Detailed Description

This module implements fast polynomial transforms.

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

Function Documentation

Initializes a set of precomputed data for DPT transforms of equal length.

M The maximum DPT transform index $M \in \mathbb{N}_0$ . The individual transforms are addressed by and index number $m \in \mathbb{N}_0$ with range $m = 0,\ldots,M$ . The total number of transforms is therefore .
t The exponent $t \in \mathbb{N}, t \ge 2$ of the transform length $N = 2^t \in \mathbb{N}, N \ge 4$
flags A bitwise combination of the flags FPT_NO_STABILIZATION,

Definition at line 755 of file fpt.c.

Computes the data required for a single DPT transform.

set The set of DPT transform data where the computed data will be stored.
m The transform index $m \in \mathbb{N}, 0 \le m \le M$ .
alpha The three-term recurrence coefficients $\alpha_k \in \mathbb{R}$ for $k=0,\ldots,N$ such that alpha[k] $=\alpha_k$ .
beta The three-term recurrence coefficients $\beta_k \in \mathbb{R}$ for $k=0,\ldots,N$ such that beta[k] $=\beta_k$ .
gamma The three-term recurrence coefficients $\gamma_k \in \mathbb{R}$ for $k=0,\ldots,N$ such that gamma[k] $=\gamma_k$ .
k_start The index $k_{\text{start}} \in \mathbb{N}_0, 0 \le k_{\text{start}} \le N$
threshold The treshold $\kappa \in \mathbb{R}, \kappa > 0$ .