taylor_nfft.c
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/*
* Copyright (c) 2002, 2017 Jens Keiner, Stefan Kunis, Daniel Potts
*
* This program is free software; you can redistribute it and/or modify it under
* the terms of the GNU General Public License as published by the Free Software
* Foundation; either version 2 of the License, or (at your option) any later
* version.
*
* This program is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along with
* this program; if not, write to the Free Software Foundation, Inc., 51
* Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include "config.h"
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>
#ifdef HAVE_COMPLEX_H
#include <complex.h>
#endif
#include "nfft3.h"
#include "infft.h"
typedef struct
{
NFFT(plan) p; /* used for fftw and data */
INT *idx0; /* index of next neighbour of x_j on the oversampled regular grid */
R *deltax0; /* distance to the grid point */
} taylor_plan;
static void taylor_init(taylor_plan *ths, int N, int M, int n, int m)
{
/* Note: no nfft precomputation! */
NFFT(init_guru)((NFFT(plan)*) ths, 1, &N, M, &n, m,
MALLOC_X | MALLOC_F_HAT | MALLOC_F | FFTW_INIT | FFT_OUT_OF_PLACE,
FFTW_ESTIMATE | FFTW_PRESERVE_INPUT);
ths->idx0 = (INT*) NFFT(malloc)((size_t)(M) * sizeof(INT));
ths->deltax0 = (R*) NFFT(malloc)((size_t)(M) * sizeof(R));
}
static void taylor_precompute(taylor_plan *ths)
{
INT j;
NFFT(plan)* cths = (NFFT(plan)*) ths;
for (j = 0; j < cths->M_total; j++)
{
ths->idx0[j] = (LRINT(ROUND((cths->x[j] + K(0.5)) * (R)(cths->n[0])))
+ cths->n[0] / 2) % cths->n[0];
ths->deltax0[j] = cths->x[j]
- (ROUND((cths->x[j] + K(0.5)) * (R)(cths->n[0])) / (R)(cths->n[0]) - K(0.5));
}
}
static void taylor_finalize(taylor_plan *ths)
{
NFFT(free)(ths->deltax0);
NFFT(free)(ths->idx0);
NFFT(finalize)((NFFT(plan)*) ths);
}
static void taylor_trafo(taylor_plan *ths)
{
INT j, k, l, ll;
C *f, *f_hat, *g1;
R *deltax;
INT *idx;
NFFT(plan) *cths = (NFFT(plan)*) ths;
for (j = 0, f = cths->f; j < cths->M_total; j++)
*f++ = K(0.0);
for (k = 0; k < cths->n_total; k++)
cths->g1[k] = K(0.0);
for (k = -cths->N_total / 2, g1 = cths->g1 + cths->n_total
- cths->N_total / 2, f_hat = cths->f_hat; k < 0; k++)
(*g1++) = CPOW(-K2PI * II * (R)(k), (R)(cths->m)) * (*f_hat++);
cths->g1[0] = cths->f_hat[cths->N_total / 2];
for (k = 1, g1 = cths->g1 + 1, f_hat = cths->f_hat + cths->N_total / 2 + 1;
k < cths->N_total / 2; k++)
(*g1++) = CPOW(-K2PI * II * (R)(k), (R)(cths->m)) * (*f_hat++);
for (l = cths->m - 1; l >= 0; l--)
{
for (k = -cths->N_total / 2, g1 = cths->g1 + cths->n_total
- cths->N_total / 2; k < 0; k++)
(*g1++) /= (-K2PI * II * (R)(k));
for (k = 1, g1 = cths->g1 + 1; k < cths->N_total / 2; k++)
(*g1++) /= (-K2PI * II * (R)(k));
FFTW(execute)(cths->my_fftw_plan1);
ll = (l == 0 ? 1 : l);
for (j = 0, f = cths->f, deltax = ths->deltax0, idx = ths->idx0;
j < cths->M_total; j++, f++)
(*f) = ((*f) * (*deltax++) + cths->g2[*idx++]) / (R)(ll);
}
}
static void taylor_time_accuracy(int N, int M, int n, int m, int n_taylor,
int m_taylor, unsigned test_accuracy)
{
int r;
R t_ndft, t_nfft, t_taylor, t;
C *swapndft = NULL;
ticks t0, t1;
taylor_plan tp;
NFFT(plan) np;
printf("%d\t%d\t", N, M);
taylor_init(&tp, N, M, n_taylor, m_taylor);
NFFT(init_guru)(&np, 1, &N, M, &n, m,
PRE_PHI_HUT | PRE_FG_PSI | FFTW_INIT | FFT_OUT_OF_PLACE,
FFTW_ESTIMATE | FFTW_DESTROY_INPUT);
/* share nodes, input, and output vectors */
np.x = tp.p.x;
np.f_hat = tp.p.f_hat;
np.f = tp.p.f;
/* output vector ndft */
if (test_accuracy)
swapndft = (C*) NFFT(malloc)((size_t)(M) * sizeof(C));
/* init pseudo random nodes */
NFFT(vrand_shifted_unit_double)(np.x, np.M_total);
/* nfft precomputation */
taylor_precompute(&tp);
/* nfft precomputation */
if (np.flags & PRE_ONE_PSI)
NFFT(precompute_one_psi)(&np);
/* init pseudo random Fourier coefficients */
NFFT(vrand_unit_complex)(np.f_hat, np.N_total);
/* NDFT */
if (test_accuracy)
{
CSWAP(np.f, swapndft);
t_ndft = K(0.0);
r = 0;
while (t_ndft < K(0.01))
{
r++;
t0 = getticks();
NFFT(trafo_direct)(&np);
t1 = getticks();
t = NFFT(elapsed_seconds)(t1, t0);
t_ndft += t;
}
t_ndft /= (R)(r);
CSWAP(np.f, swapndft);
printf("%.2" __FES__ "\t", t_ndft);
}
else
printf("NaN\t");
/* NFFT */
t_nfft = K(0.0);
r = 0;
while (t_nfft < K(0.01))
{
r++;
t0 = getticks();
NFFT(trafo)(&np);
t1 = getticks();
t = NFFT(elapsed_seconds)(t1, t0);
t_nfft += t;
}
t_nfft /= (R)(r);
printf("%.2" __FES__ "\t%d\t%.2" __FES__ "\t", ((R)(n)) / ((R)(N)), m, t_nfft);
if (test_accuracy)
printf("%.2" __FES__ "\t", NFFT(error_l_infty_complex)(swapndft, np.f, np.M_total));
else
printf("NaN\t");
t_taylor = K(0.0);
r = 0;
while (t_taylor < K(0.01))
{
r++;
t0 = getticks();
taylor_trafo(&tp);
t1 = getticks();
t = NFFT(elapsed_seconds)(t1, t0);
t_taylor += t;
}
t_taylor /= (R)(r);
printf("%.2" __FES__ "\t%d\t%.2" __FES__ "\t", ((R)(n_taylor)) / ((R)(N)), m_taylor, t_taylor);
if (test_accuracy)
printf("%.2" __FES__ "\n", NFFT(error_l_infty_complex)(swapndft, np.f, np.M_total));
else
printf("NaN\n");
fflush(stdout);
/* finalise */
if (test_accuracy)
NFFT(free)(swapndft);
NFFT(finalize)(&np);
taylor_finalize(&tp);
}
int main(int argc, char **argv)
{
int l, m, trial;
if (argc <= 2)
{
fprintf(stderr,
"taylor_nfft type first last trials sigma_nfft sigma_taylor.\n");
return EXIT_FAILURE;
}
fprintf(stderr, "Testing the Nfft & a Taylor expansion based version.\n\n");
fprintf(stderr, "Columns: N, M, t_ndft, sigma_nfft, m_nfft, t_nfft, e_nfft");
fprintf(stderr, ", sigma_taylor, m_taylor, t_taylor, e_taylor\n");
/* time vs. N = M */
if (atoi(argv[1]) == 0)
{
fprintf(stderr, "Fixed target accuracy, timings.\n\n");
int arg2 = atoi(argv[2]);
int arg3 = atoi(argv[3]);
int arg4 = atoi(argv[4]);
for (l = arg2; l <= arg3; l++)
{
int N = (int)(1U << l);
int M = (int)(1U << l);
int arg5 = (int)(atof(argv[5]) * N);
int arg6 = (int)(atof(argv[6]) * N);
for (trial = 0; trial < arg4; trial++)
{
taylor_time_accuracy(N, M, arg5, 6, arg6, 6, l <= 10 ? 1 : 0);
}
}
}
/* error vs. m */
if (atoi(argv[1]) == 1)
{
int arg2 = atoi(argv[2]);
int arg3 = atoi(argv[3]);
int arg4 = atoi(argv[4]);
int N = atoi(argv[7]);
int arg5 = (int) (atof(argv[5]) * N);
int arg6 = (int) (atof(argv[6]) * N);
fprintf(stderr, "Fixed N=M=%d, error vs. m.\n\n", N);
for (m = arg2; m <= arg3; m++)
{
for (trial = 0; trial < arg4; trial++)
{
taylor_time_accuracy(N, N, arg5, m, arg6, m, 1);
}
}
}
return EXIT_SUCCESS;
}
MALLOC_F_HAT
#define MALLOC_F_HAT
Definition nfft3.h:188
MALLOC_X
#define MALLOC_X
Definition nfft3.h:187
PRE_ONE_PSI
#define PRE_ONE_PSI
Definition nfft3.h:194
FFT_OUT_OF_PLACE
#define FFT_OUT_OF_PLACE
Definition nfft3.h:190
PRE_FG_PSI
#define PRE_FG_PSI
Definition nfft3.h:184
MALLOC_F
#define MALLOC_F
Definition nfft3.h:189
FFTW_INIT
#define FFTW_INIT
Definition nfft3.h:191
PRE_PHI_HUT
#define PRE_PHI_HUT
Definition nfft3.h:181
CSWAP
#define CSWAP(x, y)
Swap two vectors.
Definition infft.h:139
infft.h
Internal header file for auxiliary definitions and functions.
nfft3.h
Header file for the nfft3 library.
taylor_plan
Definition taylor_nfft.c:42
taylor_finalize
static void taylor_finalize(taylor_plan *ths)
Destroys a transform plan.
Definition taylor_nfft.c:99
taylor_precompute
static void taylor_precompute(taylor_plan *ths)
Precomputation of weights and indices in Taylor expansion.
Definition taylor_nfft.c:77
taylor_time_accuracy
static void taylor_time_accuracy(int N, int M, int n, int m, int n_taylor, int m_taylor, unsigned test_accuracy)
Compares NDFT, NFFT, and Taylor-NFFT.
Definition taylor_nfft.c:174
taylor_init
static void taylor_init(taylor_plan *ths, int N, int M, int n, int m)
Initialisation of a transform plan.
Definition taylor_nfft.c:59
taylor_trafo
static void taylor_trafo(taylor_plan *ths)
Executes a Taylor-NFFT, see equation (1.1) in [Guide], computes fast and approximate by means of a Ta...
Definition taylor_nfft.c:117