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NFFT
3.5.2
|
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) |
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.
. The individual transforms are addressed by and index number
with range
. The total number of transforms is therefore
.
of the transform length
Definition at line 795 of file fpt.c.
References nfft_malloc(), 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.
.
for
such that alpha[k]
.
for
such that beta[k]
.
for
such that gamma[k]
.
.
1.8.13