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NFFT
3.5.3
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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) |
Variables | |
*We expand this macro for each supported precision * | X |
This module implements fast polynomial transforms.
In the following, we abbreviate the term "fast polynomial transforms" by FPT.
Let be given recursion coefficients of the polynomials
defined by
,
and
for . The Chebyshev polnyomials of the first kind are defined by
Let be a polynomial of degree
. The FPT transforms the polynomial coefficients
from
into Chebyshev coefficients from
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.
Definition at line 795 of file fpt.c.
References fpt_set_s_::flags, fpt_set_s_::M, fpt_set_s_::N, fpt_set_s_::t, and X.
Referenced by nfsft_precompute().
void fpt_precompute | ( | fpt_set | set, |
const int | m, | ||
double * | alpha, | ||
double * | beta, | ||
double * | gam, | ||
int | k_start, | ||
const double | threshold | ||
) |
Computes the data required for a single DPT transform.
alpha[k]
beta[k]
gamma[k]
void fpt_transposed | ( | fpt_set | set, |
const int | m, | ||
double _Complex * | x, | ||
double _Complex * | y, | ||
const int | k_end, | ||
const unsigned int | flags | ||
) |
void X |
Computes a single DPT transform.
Initialisation of a transform plan, guru.
Definition at line 94 of file nfft3.h.
Referenced by fpt_init(), nfsft_precompute(), nfsoft_adjoint(), and nfsoft_trafo().