NFFT 3.5.3alpha
Macros | Functions
fpt.c File Reference

Implementation file for the FPT module. More...

#include "config.h"
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include "nfft3.h"
#include "infft.h"
#include "fpt.h"
Include dependency graph for fpt.c:

Go to the source code of this file.

Macros

#define K_START_TILDE(x, y)
 If defined, perform critical computations in three-term recurrence always in long double instead of using adaptive version that starts in double and switches to long double if required.
#define K_END_TILDE(x, y)
 Maximum degree at top of a cascade.
#define FIRST_L(x, y)
 Index of first block of four functions at level.
#define LAST_L(x, y)
 Index of last block of four functions at level.
#define N_TILDE(y)
#define IS_SYMMETRIC(x, y, z)
#define FPT_BREAK_EVEN   4
#define ABUVXPWY_SYMMETRIC(NAME, S1, S2)
#define ABUVXPWY_SYMMETRIC_1(NAME, S1)
#define ABUVXPWY_SYMMETRIC_2(NAME, S1)
#define FPT_DO_STEP(NAME, M1_FUNCTION, M2_FUNCTION)
#define FPT_DO_STEP_TRANSPOSED(NAME, M1_FUNCTION, M2_FUNCTION)

Functions

static void abuvxpwy (double a, double b, double _Complex *u, double _Complex *x, double *v, double _Complex *y, double *w, int n)
static void abuvxpwy_symmetric1 (double a, double b, double _Complex *u, double _Complex *x, double *v, double _Complex *y, double *w, int n)
static void abuvxpwy_symmetric2 (double a, double b, double _Complex *u, double _Complex *x, double *v, double _Complex *y, double *w, int n)
static void abuvxpwy_symmetric1_1 (double a, double b, double _Complex *u, double _Complex *x, double *v, double _Complex *y, int n, double *xx)
static void abuvxpwy_symmetric1_2 (double a, double b, double _Complex *u, double _Complex *x, double *v, double _Complex *y, int n, double *xx)
static void abuvxpwy_symmetric2_1 (double a, double b, double _Complex *u, double _Complex *x, double _Complex *y, double *w, int n, double *xx)
static void abuvxpwy_symmetric2_2 (double a, double b, double _Complex *u, double _Complex *x, double _Complex *y, double *w, int n, double *xx)
static void auvxpwy (double a, double _Complex *u, double _Complex *x, double *v, double _Complex *y, double *w, int n)
static void auvxpwy_symmetric (double a, double _Complex *u, double _Complex *x, double *v, double _Complex *y, double *w, int n)
static void auvxpwy_symmetric_1 (double a, double _Complex *u, double _Complex *x, double *v, double _Complex *y, double *w, int n, double *xx)
static void auvxpwy_symmetric_2 (double a, double _Complex *u, double _Complex *x, double *v, double _Complex *y, double *w, int n, double *xx)
static void fpt_do_step (double _Complex *a, double _Complex *b, double *a11, double *a12, double *a21, double *a22, double g, int tau, fpt_set set)
static void fpt_do_step_symmetric (double _Complex *a, double _Complex *b, double *a11, double *a12, double *a21, double *a22, double g, int tau, fpt_set set)
static void fpt_do_step_symmetric_u (double _Complex *a, double _Complex *b, double *a11, double *a12, double *a21, double *a22, double *x, double gam, int tau, fpt_set set)
static void fpt_do_step_symmetric_l (double _Complex *a, double _Complex *b, double *a11, double *a12, double *a21, double *a22, double *x, double gam, int tau, fpt_set set)
static void fpt_do_step_t (double _Complex *a, double _Complex *b, double *a11, double *a12, double *a21, double *a22, double g, int tau, fpt_set set)
static void fpt_do_step_t_symmetric (double _Complex *a, double _Complex *b, double *a11, double *a12, double *a21, double *a22, double g, int tau, fpt_set set)
static void fpt_do_step_t_symmetric_u (double _Complex *a, double _Complex *b, double *a11, double *a12, double *x, double gam, int tau, fpt_set set)
static void fpt_do_step_t_symmetric_l (double _Complex *a, double _Complex *b, double *a21, double *a22, double *x, double gam, int tau, fpt_set set)
static void eval_clenshaw (const double *x, double *y, int size, int k, const double *alpha, const double *beta, const double *gam)
static void eval_clenshaw2 (const double *x, double *z, double *y, int size1, int size, int k, const double *alpha, const double *beta, const double *gam)
static int eval_clenshaw_thresh2 (const double *x, double *z, double *y, int size, int k, const double *alpha, const double *beta, const double *gam, const double threshold)
static void eval_sum_clenshaw_fast (const int N, const int M, const double _Complex *a, const double *x, double _Complex *y, const double *alpha, const double *beta, const double *gam, const double lambda)
static void eval_sum_clenshaw_transposed (int N, int M, double _Complex *a, double *x, double _Complex *y, double _Complex *temp, double *alpha, double *beta, double *gam, double lambda)
 Clenshaw algorithm.
static void eval_sum_clenshaw_transposed_ld (int N, int M, double _Complex *a, double *x, double _Complex *y, double _Complex *temp, double *alpha, double *beta, double *gam, double lambda)
fpt_set fpt_init (const int M, const int t, const unsigned int flags)
void fpt_precompute_1 (fpt_set set, const int m, int k_start)
void fpt_precompute_2 (fpt_set set, const int m, double *alpha, double *beta, double *gam, int k_start, const double threshold)
void fpt_precompute (fpt_set set, const int m, double *alpha, double *beta, double *gam, int k_start, const double threshold)
void fpt_trafo_direct (fpt_set set, const int m, const double _Complex *x, double _Complex *y, const int k_end, const unsigned int flags)
void fpt_trafo (fpt_set set, const int m, const double _Complex *x, double _Complex *y, const int k_end, const unsigned int flags)
void fpt_transposed_direct (fpt_set set, const int m, double _Complex *x, double _Complex *y, const int k_end, const unsigned int flags)
void fpt_transposed (fpt_set set, const int m, double _Complex *x, double _Complex *y, const int k_end, const unsigned int flags)
void fpt_finalize (fpt_set set)

Detailed Description

Implementation file for the FPT module.

Author
Jens Keiner

Definition in file fpt.c.

Macro Definition Documentation

◆ K_START_TILDE

#define K_START_TILDE ( x,
y )
Value:
(MAX(MIN(x,y-2),0))

If defined, perform critical computations in three-term recurrence always in long double instead of using adaptive version that starts in double and switches to long double if required.

Minimum degree at top of a cascade

Definition at line 48 of file fpt.c.

Referenced by fpt_transposed().

◆ K_END_TILDE

#define K_END_TILDE ( x,
y )
Value:
MIN(x,y-1)

Maximum degree at top of a cascade.

Definition at line 51 of file fpt.c.

Referenced by fpt_transposed().

◆ FIRST_L

#define FIRST_L ( x,
y )
Value:
(LRINT(floor((x)/(double)y)))

Index of first block of four functions at level.

Definition at line 54 of file fpt.c.

Referenced by fpt_transposed().

◆ LAST_L

#define LAST_L ( x,
y )
Value:
(LRINT(ceil(((x)+1)/(double)y))-1)

Index of last block of four functions at level.

Definition at line 57 of file fpt.c.

Referenced by fpt_transposed().

◆ N_TILDE

#define N_TILDE ( y)
Value:
(y-1)

Definition at line 59 of file fpt.c.

◆ IS_SYMMETRIC

#define IS_SYMMETRIC ( x,
y,
z )
Value:
(x >= ((y-1.0)/z))

Definition at line 61 of file fpt.c.

◆ FPT_BREAK_EVEN

#define FPT_BREAK_EVEN   4

Definition at line 63 of file fpt.c.

◆ ABUVXPWY_SYMMETRIC

#define ABUVXPWY_SYMMETRIC ( NAME,
S1,
S2 )
Value:
static inline void NAME(double a, double b, double _Complex* u, double _Complex* x, \
double* v, double _Complex* y, double* w, int n) \
{ \
const int n2 = n>>1; \
int l; double _Complex *u_ptr = u, *x_ptr = x, *y_ptr = y; \
double *v_ptr = v, *w_ptr = w; \
for (l = 0; l < n2; l++) \
*u_ptr++ = a * (b * (*v_ptr++) * (*x_ptr++) + (*w_ptr++) * (*y_ptr++)); \
v_ptr--; w_ptr--; \
for (l = 0; l < n2; l++) \
*u_ptr++ = a * (b * S1 * (*v_ptr--) * (*x_ptr++) + S2 * (*w_ptr--) * (*y_ptr++)); \
}

Definition at line 77 of file fpt.c.

◆ ABUVXPWY_SYMMETRIC_1

#define ABUVXPWY_SYMMETRIC_1 ( NAME,
S1 )
Value:
static inline void NAME(double a, double b, double _Complex* u, double _Complex* x, \
double* v, double _Complex* y, int n, double *xx) \
{ \
const int n2 = n>>1; \
int l; double _Complex *u_ptr = u, *x_ptr = x, *y_ptr = y; \
double *v_ptr = v, *xx_ptr = xx; \
for (l = 0; l < n2; l++, v_ptr++) \
*u_ptr++ = a * (b * (*v_ptr) * (*x_ptr++) + ((*v_ptr)*(1.0+*xx_ptr++)) * (*y_ptr++)); \
v_ptr--; \
for (l = 0; l < n2; l++, v_ptr--) \
*u_ptr++ = a * (b * S1 * (*v_ptr) * (*x_ptr++) + (S1 * (*v_ptr) * (1.0+*xx_ptr++)) * (*y_ptr++)); \
}

Definition at line 94 of file fpt.c.

◆ ABUVXPWY_SYMMETRIC_2

#define ABUVXPWY_SYMMETRIC_2 ( NAME,
S1 )
Value:
static inline void NAME(double a, double b, double _Complex* u, double _Complex* x, \
double _Complex* y, double* w, int n, double *xx) \
{ \
const int n2 = n>>1; \
int l; double _Complex *u_ptr = u, *x_ptr = x, *y_ptr = y; \
double *w_ptr = w, *xx_ptr = xx; \
for (l = 0; l < n2; l++, w_ptr++) \
*u_ptr++ = a * (b * (*w_ptr/(1.0+*xx_ptr++)) * (*x_ptr++) + (*w_ptr) * (*y_ptr++)); \
w_ptr--; \
for (l = 0; l < n2; l++, w_ptr--) \
*u_ptr++ = a * (b * (S1 * (*w_ptr)/(1.0+*xx_ptr++) ) * (*x_ptr++) + S1 * (*w_ptr) * (*y_ptr++)); \
}

Definition at line 111 of file fpt.c.

◆ FPT_DO_STEP

#define FPT_DO_STEP ( NAME,
M1_FUNCTION,
M2_FUNCTION )

Definition at line 180 of file fpt.c.

◆ FPT_DO_STEP_TRANSPOSED

#define FPT_DO_STEP_TRANSPOSED ( NAME,
M1_FUNCTION,
M2_FUNCTION )
Value:
static inline void NAME(double _Complex *a, double _Complex *b, double *a11, \
double *a12, double *a21, double *a22, double g, int tau, fpt_set set) \
{ \ \
int length = 1<<(tau+1); \ \
double norm = 1.0/(length<<1); \
\
/* Compute function values from Chebyshev-coefficients using a DCT-III. */ \
fftw_execute_r2r(set->plans_dct3[tau-1],(double*)a,(double*)a); \
fftw_execute_r2r(set->plans_dct3[tau-1],(double*)b,(double*)b); \
\
/* Perform matrix multiplication. */ \
M1_FUNCTION(norm,g,set->z,a,a11,b,a21,length); \
M2_FUNCTION(norm,g,b,a,a12,b,a22,length); \
memcpy(a,set->z,length*sizeof(double _Complex)); \
\
/* Compute Chebyshev-coefficients using a DCT-II. */ \
fftw_execute_r2r(set->plans_dct2[tau-1],(double*)a,(double*)a); \
fftw_execute_r2r(set->plans_dct2[tau-1],(double*)b,(double*)b); \
}
fpt_set
struct fpt_set_s_ * fpt_set
A set of precomputed data for a set of DPT transforms of equal maximum length.
Definition nfft3.h:633

Definition at line 335 of file fpt.c.

Function Documentation

◆ abuvxpwy()

void abuvxpwy ( double a,
double b,
double _Complex * u,
double _Complex * x,
double * v,
double _Complex * y,
double * w,
int n )
inlinestatic

Definition at line 68 of file fpt.c.

◆ abuvxpwy_symmetric1()

void abuvxpwy_symmetric1 ( double a,
double b,
double _Complex * u,
double _Complex * x,
double * v,
double _Complex * y,
double * w,
int n )
inlinestatic

Definition at line 91 of file fpt.c.

◆ abuvxpwy_symmetric2()

void abuvxpwy_symmetric2 ( double a,
double b,
double _Complex * u,
double _Complex * x,
double * v,
double _Complex * y,
double * w,
int n )
inlinestatic

Definition at line 92 of file fpt.c.

◆ abuvxpwy_symmetric1_1()

void abuvxpwy_symmetric1_1 ( double a,
double b,
double _Complex * u,
double _Complex * x,
double * v,
double _Complex * y,
int n,
double * xx )
inlinestatic

Definition at line 108 of file fpt.c.

◆ abuvxpwy_symmetric1_2()

void abuvxpwy_symmetric1_2 ( double a,
double b,
double _Complex * u,
double _Complex * x,
double * v,
double _Complex * y,
int n,
double * xx )
inlinestatic

Definition at line 109 of file fpt.c.

◆ abuvxpwy_symmetric2_1()

void abuvxpwy_symmetric2_1 ( double a,
double b,
double _Complex * u,
double _Complex * x,
double _Complex * y,
double * w,
int n,
double * xx )
inlinestatic

Definition at line 125 of file fpt.c.

◆ abuvxpwy_symmetric2_2()

void abuvxpwy_symmetric2_2 ( double a,
double b,
double _Complex * u,
double _Complex * x,
double _Complex * y,
double * w,
int n,
double * xx )
inlinestatic

Definition at line 126 of file fpt.c.

◆ auvxpwy()

void auvxpwy ( double a,
double _Complex * u,
double _Complex * x,
double * v,
double _Complex * y,
double * w,
int n )
inlinestatic

Definition at line 128 of file fpt.c.

◆ auvxpwy_symmetric()

void auvxpwy_symmetric ( double a,
double _Complex * u,
double _Complex * x,
double * v,
double _Complex * y,
double * w,
int n )
inlinestatic

Definition at line 138 of file fpt.c.

◆ auvxpwy_symmetric_1()

void auvxpwy_symmetric_1 ( double a,
double _Complex * u,
double _Complex * x,
double * v,
double _Complex * y,
double * w,
int n,
double * xx )
inlinestatic

Definition at line 152 of file fpt.c.

◆ auvxpwy_symmetric_2()

void auvxpwy_symmetric_2 ( double a,
double _Complex * u,
double _Complex * x,
double * v,
double _Complex * y,
double * w,
int n,
double * xx )
inlinestatic

Definition at line 166 of file fpt.c.

◆ fpt_do_step()

void fpt_do_step ( double _Complex * a,
double _Complex * b,
double * a11,
double * a12,
double * a21,
double * a22,
double g,
int tau,
fpt_set set )
inlinestatic

Definition at line 229 of file fpt.c.

◆ fpt_do_step_symmetric()

void fpt_do_step_symmetric ( double _Complex * a,
double _Complex * b,
double * a11,
double * a12,
double * a21,
double * a22,
double g,
int tau,
fpt_set set )
inlinestatic

Definition at line 230 of file fpt.c.

◆ fpt_do_step_symmetric_u()

void fpt_do_step_symmetric_u ( double _Complex * a,
double _Complex * b,
double * a11,
double * a12,
double * a21,
double * a22,
double * x,
double gam,
int tau,
fpt_set set )
inlinestatic

Definition at line 234 of file fpt.c.

◆ fpt_do_step_symmetric_l()

void fpt_do_step_symmetric_l ( double _Complex * a,
double _Complex * b,
double * a11,
double * a12,
double * a21,
double * a22,
double * x,
double gam,
int tau,
fpt_set set )
inlinestatic

Definition at line 285 of file fpt.c.

◆ fpt_do_step_t()

void fpt_do_step_t ( double _Complex * a,
double _Complex * b,
double * a11,
double * a12,
double * a21,
double * a22,
double g,
int tau,
fpt_set set )
inlinestatic

Definition at line 358 of file fpt.c.

◆ fpt_do_step_t_symmetric()

void fpt_do_step_t_symmetric ( double _Complex * a,
double _Complex * b,
double * a11,
double * a12,
double * a21,
double * a22,
double g,
int tau,
fpt_set set )
inlinestatic

Definition at line 359 of file fpt.c.

◆ fpt_do_step_t_symmetric_u()

void fpt_do_step_t_symmetric_u ( double _Complex * a,
double _Complex * b,
double * a11,
double * a12,
double * x,
double gam,
int tau,
fpt_set set )
inlinestatic

Definition at line 364 of file fpt.c.

◆ fpt_do_step_t_symmetric_l()

void fpt_do_step_t_symmetric_l ( double _Complex * a,
double _Complex * b,
double * a21,
double * a22,
double * x,
double gam,
int tau,
fpt_set set )
inlinestatic

Definition at line 387 of file fpt.c.

◆ eval_clenshaw()

void eval_clenshaw ( const double * x,
double * y,
int size,
int k,
const double * alpha,
const double * beta,
const double * gam )
static

Definition at line 411 of file fpt.c.

◆ eval_clenshaw2()

void eval_clenshaw2 ( const double * x,
double * z,
double * y,
int size1,
int size,
int k,
const double * alpha,
const double * beta,
const double * gam )
static

Definition at line 490 of file fpt.c.

◆ eval_clenshaw_thresh2()

int eval_clenshaw_thresh2 ( const double * x,
double * z,
double * y,
int size,
int k,
const double * alpha,
const double * beta,
const double * gam,
const double threshold )
static

Definition at line 546 of file fpt.c.

◆ eval_sum_clenshaw_fast()

void eval_sum_clenshaw_fast ( const int N,
const int M,
const double _Complex * a,
const double * x,
double _Complex * y,
const double * alpha,
const double * beta,
const double * gam,
const double lambda )
inlinestatic

Definition at line 637 of file fpt.c.

◆ eval_sum_clenshaw_transposed()

void eval_sum_clenshaw_transposed ( int N,
int M,
double _Complex * a,
double * x,
double _Complex * y,
double _Complex * temp,
double * alpha,
double * beta,
double * gam,
double lambda )
static

Clenshaw algorithm.

Evaluates a sum of real-valued functions $P_k : \mathbb{R} \rightarrow \mathbb{R}$

\‍[ f(x) = \sum_{k=0}^N a_k P_k(x) \quad (N \in \mathbb{N}_0) \‍]

obeying a three-term recurrence relation

\‍[ P_{k+1}(x) = (alpha_k * x + beta_k)*P_{k}(x) + gamma_k P_{k-1}(x) \quad (alpha_k, beta_k, gamma_k \in \mathbb{R},\; k \ge 0) \‍]

with initial conditions $P_{-1}(x) := 0$, $P_0(x) := \lambda$ for given double _Complex coefficients $\left(a_k\right)_{k=0}^N \in \mathbb{C}^{N+1}$ at given nodes $\left(x_j\right)_{j=0}^M \in \mathbb{R}^{M+1}$, $M \in \mathbb{N}_0$.

Definition at line 717 of file fpt.c.

◆ eval_sum_clenshaw_transposed_ld()

void eval_sum_clenshaw_transposed_ld ( int N,
int M,
double _Complex * a,
double * x,
double _Complex * y,
double _Complex * temp,
double * alpha,
double * beta,
double * gam,
double lambda )
static

Definition at line 759 of file fpt.c.

◆ fpt_precompute_1()

void fpt_precompute_1 ( fpt_set set,
const int m,
int k_start )

Definition at line 942 of file fpt.c.

◆ fpt_precompute_2()

void fpt_precompute_2 ( fpt_set set,
const int m,
double * alpha,
double * beta,
double * gam,
int k_start,
const double threshold )

Definition at line 1028 of file fpt.c.

◆ fpt_trafo_direct()

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

Definition at line 1314 of file fpt.c.

◆ fpt_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 )

Definition at line 1375 of file fpt.c.

◆ fpt_transposed_direct()

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

Definition at line 1683 of file fpt.c.

◆ fpt_finalize()

void fpt_finalize ( fpt_set set)

Definition at line 1979 of file fpt.c.

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