nnfft.c
/*
* 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"
#define MACRO_nndft_init_result_trafo memset(f,0,ths->M_total*sizeof(double _Complex));
#define MACRO_nndft_init_result_conjugated MACRO_nndft_init_result_trafo
#define MACRO_nndft_init_result_adjoint memset(f_hat,0,ths->N_total*sizeof(double _Complex));
#define MACRO_nndft_init_result_transposed MACRO_nndft_init_result_adjoint
#define MACRO_nndft_sign_trafo (-2.0*KPI)
#define MACRO_nndft_sign_conjugated (+2.0*KPI)
#define MACRO_nndft_sign_adjoint (+2.0*KPI)
#define MACRO_nndft_sign_transposed (-2.0*KPI)
#define MACRO_nndft_compute_trafo (*fj) += (*f_hat_k)*cexp(+ _Complex_I*omega);
#define MACRO_nndft_compute_conjugated MACRO_nndft_compute_trafo
#define MACRO_nndft_compute_adjoint (*f_hat_k) += (*fj)*cexp(+ _Complex_I*omega);
#define MACRO_nndft_compute_transposed MACRO_nndft_compute_adjoint
#define MACRO_nndft(which_one) \
void nnfft_ ## which_one ## _direct (nnfft_plan *ths) \
{ \
int j; \
int t; \
int l; \
double _Complex *f_hat, *f; \
double _Complex *f_hat_k; \
double _Complex *fj; \
double omega; \
\
f_hat=ths->f_hat; f=ths->f; \
\
MACRO_nndft_init_result_ ## which_one \
\
for(j=0, fj=f; j<ths->M_total; j++, fj++) \
{ \
for(l=0, f_hat_k=f_hat; l<ths->N_total; l++, f_hat_k++) \
{ \
omega=0.0; \
for(t = 0; t<ths->d; t++) \
omega+=ths->v[l*ths->d+t] * ths->x[j*ths->d+t] * ths->N[t]; \
\
omega*= MACRO_nndft_sign_ ## which_one; \
\
MACRO_nndft_compute_ ## which_one \
\
} /* for(l) */ \
} /* for(j) */ \
} /* nndft_trafo */ \
MACRO_nndft(trafo)
MACRO_nndft(adjoint)
static void nnfft_uo(nnfft_plan *ths,int j,int *up,int *op,int act_dim)
{
double c;
int u,o;
c = ths->v[j*ths->d+act_dim] * ths->n[act_dim];
u = c; o = c;
if(c < 0)
u = u-1;
else
o = o+1;
u = u - (ths->m); o = o + (ths->m);
up[0]=u; op[0]=o;
}
#define MACRO_nnfft_B_init_result_A memset(f,0,ths->N_total*sizeof(double _Complex));
#define MACRO_nnfft_B_init_result_T memset(g,0,ths->aN1_total*sizeof(double _Complex));
#define MACRO_nnfft_B_PRE_FULL_PSI_compute_A { \
(*fj) += ths->psi[ix] * g[ths->psi_index_g[ix]]; \
}
#define MACRO_nnfft_B_PRE_FULL_PSI_compute_T { \
g[ths->psi_index_g[ix]] += ths->psi[ix] * (*fj); \
}
#define MACRO_nnfft_B_compute_A { \
(*fj) += phi_prod[ths->d] * g[ll_plain[ths->d]]; \
}
#define MACRO_nnfft_B_compute_T { \
g[ll_plain[ths->d]] += phi_prod[ths->d] * (*fj); \
}
#define MACRO_with_PRE_LIN_PSI (ths->psi[(ths->K+1)*t2+y_u[t2]]* \
(y_u[t2]+1-y[t2]) + \
ths->psi[(ths->K+1)*t2+y_u[t2]+1]* \
(y[t2]-y_u[t2]))
#define MACRO_with_PRE_PSI ths->psi[(j*ths->d+t2)*(2*ths->m+2)+lj[t2]]
#define MACRO_without_PRE_PSI PHI(ths->n[t2], -ths->v[j*ths->d+t2]+ \
((double)l[t2])/ths->N1[t2], t2)
#define MACRO_init_uo_l_lj_t { \
for(t = ths->d-1; t>=0; t--) \
{ \
nnfft_uo(ths,j,&u[t],&o[t],t); \
l[t] = u[t]; \
lj[t] = 0; \
} /* for(t) */ \
t++; \
}
#define MACRO_update_with_PRE_PSI_LIN { \
for(t2=t; t2<ths->d; t2++) \
{ \
y[t2] = fabs(((-ths->N1[t2]*ths->v[j*ths->d+t2]+(double)l[t2]) \
* ((double)ths->K))/(ths->m+1)); \
y_u[t2] = (int)y[t2]; \
} /* for(t2) */ \
}
#define MACRO_update_phi_prod_ll_plain(which_one) { \
for(t2=t; t2<ths->d; t2++) \
{ \
phi_prod[t2+1]=phi_prod[t2]* MACRO_ ## which_one; \
ll_plain[t2+1]=ll_plain[t2]*ths->aN1[t2] + \
(l[t2]+ths->aN1[t2]*3/2)%ths->aN1[t2]; \
/* 3/2 because of the (not needed) fftshift and to be in [0 aN1[t2]]?!*/\
} /* for(t2) */ \
}
#define MACRO_count_uo_l_lj_t { \
for(t = ths->d-1; (t>0)&&(l[t]==o[t]); t--) \
{ \
l[t] = u[t]; \
lj[t] = 0; \
} /* for(t) */ \
\
l[t]++; \
lj[t]++; \
}
#define MACRO_nnfft_B(which_one) \
static inline void nnfft_B_ ## which_one (nnfft_plan *ths) \
{ \
int lprod; \
int u[ths->d], o[ths->d]; \
int t, t2; \
int j; \
int l_L, ix; \
int l[ths->d]; \
int lj[ths->d]; \
int ll_plain[ths->d+1]; \
double phi_prod[ths->d+1]; \
double _Complex *f, *g; \
double _Complex *fj; \
double y[ths->d]; \
int y_u[ths->d]; \
\
f=ths->f_hat; g=ths->F; \
\
MACRO_nnfft_B_init_result_ ## which_one \
\
if(ths->nnfft_flags & PRE_FULL_PSI) \
{ \
for(ix=0, j=0, fj=f; j<ths->N_total; j++,fj++) \
for(l_L=0; l_L<ths->psi_index_f[j]; l_L++, ix++) \
MACRO_nnfft_B_PRE_FULL_PSI_compute_ ## which_one; \
return; \
} \
\
phi_prod[0]=1; \
ll_plain[0]=0; \
\
for(t=0,lprod = 1; t<ths->d; t++) \
lprod *= (2*ths->m+2); \
\
if(ths->nnfft_flags & PRE_PSI) \
{ \
for(j=0, fj=f; j<ths->N_total; j++, fj++) \
{ \
MACRO_init_uo_l_lj_t; \
\
for(l_L=0; l_L<lprod; l_L++) \
{ \
MACRO_update_phi_prod_ll_plain(with_PRE_PSI); \
\
MACRO_nnfft_B_compute_ ## which_one; \
\
MACRO_count_uo_l_lj_t; \
} /* for(l_L) */ \
} /* for(j) */ \
return; \
} /* if(PRE_PSI) */ \
\
if(ths->nnfft_flags & PRE_LIN_PSI) \
{ \
for(j=0, fj=f; j<ths->N_total; j++, fj++) \
{ \
MACRO_init_uo_l_lj_t; \
\
for(l_L=0; l_L<lprod; l_L++) \
{ \
MACRO_update_with_PRE_PSI_LIN; \
\
MACRO_update_phi_prod_ll_plain(with_PRE_LIN_PSI); \
\
MACRO_nnfft_B_compute_ ## which_one; \
\
MACRO_count_uo_l_lj_t; \
} /* for(l_L) */ \
} /* for(j) */ \
return; \
} /* if(PRE_LIN_PSI) */ \
\
/* no precomputed psi at all */ \
for(j=0, fj=f; j<ths->N_total; j++, fj++) \
{ \
\
MACRO_init_uo_l_lj_t; \
\
for(l_L=0; l_L<lprod; l_L++) \
{ \
MACRO_update_phi_prod_ll_plain(without_PRE_PSI); \
\
MACRO_nnfft_B_compute_ ## which_one; \
\
MACRO_count_uo_l_lj_t; \
} /* for(l_L) */ \
} /* for(j) */ \
} /* nnfft_B */
MACRO_nnfft_B(A)
MACRO_nnfft_B(T)
static inline void nnfft_D (nnfft_plan *ths){
int j,t;
double tmp;
if(ths->nnfft_flags & PRE_PHI_HUT)
{
for(j=0; j<ths->M_total; j++)
ths->f[j] *= ths->c_phi_inv[j];
}
else
{
for(j=0; j<ths->M_total; j++)
{
tmp = 1.0;
/* multiply with N1, because x was modified */
for(t=0; t<ths->d; t++)
tmp*= 1.0 /((PHI_HUT(ths->n[t], ths->x[ths->d*j + t]*((double)ths->N[t]),t)) );
ths->f[j] *= tmp;
}
}
}
void nnfft_trafo(nnfft_plan *ths)
{
int j,t;
nnfft_B_T(ths);
for(j=0;j<ths->M_total;j++) {
for(t=0;t<ths->d;t++) {
ths->x[j*ths->d+t]= ths->x[j*ths->d+t] / ((double)ths->sigma[t]);
}
}
/* allows for external swaps of ths->f */
ths->direct_plan->f = ths->f;
nfft_trafo(ths->direct_plan);
for(j=0;j<ths->M_total;j++) {
for(t=0;t<ths->d;t++) {
ths->x[j*ths->d+t]= ths->x[j*ths->d+t] * ((double)ths->sigma[t]);
}
}
nnfft_D(ths);
} /* nnfft_trafo */
void nnfft_adjoint(nnfft_plan *ths)
{
int j,t;
nnfft_D(ths);
for(j=0;j<ths->M_total;j++) {
for(t=0;t<ths->d;t++) {
ths->x[j*ths->d+t]= ths->x[j*ths->d+t] / ((double)ths->sigma[t]);
}
}
/* allows for external swaps of ths->f */
ths->direct_plan->f=ths->f;
nfft_adjoint(ths->direct_plan);
for(j=0;j<ths->M_total;j++) {
for(t=0;t<ths->d;t++) {
ths->x[j*ths->d+t]= ths->x[j*ths->d+t] * ((double)ths->sigma[t]);
}
}
nnfft_B_A(ths);
} /* nnfft_adjoint */
void nnfft_precompute_phi_hut(nnfft_plan *ths)
{
int j;
int t;
double tmp;
ths->c_phi_inv= (double*)nfft_malloc(ths->M_total*sizeof(double));
for(j=0; j<ths->M_total; j++)
{
tmp = 1.0;
for(t=0; t<ths->d; t++)
tmp*= 1.0 /(PHI_HUT(ths->n[t],ths->x[ths->d*j + t]*((double)ths->N[t]),t));
ths->c_phi_inv[j]=tmp;
}
} /* nnfft_phi_hut */
void nnfft_precompute_lin_psi(nnfft_plan *ths)
{
int t;
int j;
double step;
nfft_precompute_lin_psi(ths->direct_plan);
for (t=0; t<ths->d; t++)
{
step=((double)(ths->m+1))/(ths->K*ths->N1[t]);
for(j=0;j<=ths->K;j++)
{
ths->psi[(ths->K+1)*t + j] = PHI(ths->n[t],j*step,t);
} /* for(j) */
} /* for(t) */
}
void nnfft_precompute_psi(nnfft_plan *ths)
{
int t;
int j;
int l;
int lj;
int u, o;
for (t=0; t<ths->d; t++)
for(j=0;j<ths->N_total;j++)
{
nnfft_uo(ths,j,&u,&o,t);
for(l=u, lj=0; l <= o; l++, lj++)
ths->psi[(j*ths->d+t)*(2*ths->m+2)+lj]=
(PHI(ths->n[t],(-ths->v[j*ths->d+t]+((double)l)/((double)ths->N1[t])),t));
} /* for(j) */
for(j=0;j<ths->M_total;j++) {
for(t=0;t<ths->d;t++) {
ths->x[j*ths->d+t]= ths->x[j*ths->d+t] / ((double)ths->sigma[t]);
}
}
nfft_precompute_psi(ths->direct_plan);
for(j=0;j<ths->M_total;j++) {
for(t=0;t<ths->d;t++) {
ths->x[j*ths->d+t]= ths->x[j*ths->d+t] * ((double)ths->sigma[t]);
}
}
/* for(t) */
} /* nfft_precompute_psi */
void nnfft_precompute_full_psi(nnfft_plan *ths)
{
int t,t2;
int j;
int l_L;
int l[ths->d];
int lj[ths->d];
int ll_plain[ths->d+1];
int lprod;
int u[ths->d], o[ths->d];
double phi_prod[ths->d+1];
int ix,ix_old;
for(j=0;j<ths->M_total;j++) {
for(t=0;t<ths->d;t++) {
ths->x[j*ths->d+t]= ths->x[j*ths->d+t] / ((double)ths->sigma[t]);
}
}
nnfft_precompute_psi(ths);
nfft_precompute_full_psi(ths->direct_plan);
for(j=0;j<ths->M_total;j++) {
for(t=0;t<ths->d;t++) {
ths->x[j*ths->d+t]= ths->x[j*ths->d+t] * ((double)ths->sigma[t]);
}
}
phi_prod[0]=1;
ll_plain[0]=0;
for(t=0,lprod = 1; t<ths->d; t++)
lprod *= 2*ths->m+2;
for(j=0,ix=0,ix_old=0; j<ths->N_total; j++)
{
MACRO_init_uo_l_lj_t;
for(l_L=0; l_L<lprod; l_L++, ix++)
{
MACRO_update_phi_prod_ll_plain(without_PRE_PSI);
ths->psi_index_g[ix]=ll_plain[ths->d];
ths->psi[ix]=phi_prod[ths->d];
MACRO_count_uo_l_lj_t;
} /* for(l_L) */
ths->psi_index_f[j]=ix-ix_old;
ix_old=ix;
} /* for(j) */
}
void nnfft_precompute_one_psi(nnfft_plan *ths)
{
if(ths->nnfft_flags & PRE_PSI)
nnfft_precompute_psi(ths);
if(ths->nnfft_flags & PRE_FULL_PSI)
nnfft_precompute_full_psi(ths);
if(ths->nnfft_flags & PRE_LIN_PSI)
nnfft_precompute_lin_psi(ths);
if(ths->nnfft_flags & PRE_PHI_HUT)
nnfft_precompute_phi_hut(ths);
}
static void nnfft_init_help(nnfft_plan *ths, int m2, unsigned nfft_flags, unsigned fftw_flags)
{
int t;
int lprod;
int N2[ths->d];
ths->aN1 = (int*) nfft_malloc(ths->d*sizeof(int));
ths->a = (double*) nfft_malloc(ths->d*sizeof(double));
ths->sigma = (double*) nfft_malloc(ths->d*sizeof(double));
ths->n = ths->N1;
ths->aN1_total=1;
for(t = 0; t<ths->d; t++) {
ths->a[t] = 1.0 + (2.0*((double)ths->m))/((double)ths->N1[t]);
ths->aN1[t] = ths->a[t] * ((double)ths->N1[t]);
/* aN1 should be even */
if(ths->aN1[t]%2 != 0)
ths->aN1[t] = ths->aN1[t] +1;
ths->aN1_total*=ths->aN1[t];
ths->sigma[t] = ((double) ths->N1[t] )/((double) ths->N[t]);;
/* take the same oversampling factor in the inner NFFT */
N2[t] = ceil(ths->sigma[t]*(ths->aN1[t]));
/* N2 should be even */
if(N2[t]%2 != 0)
N2[t] = N2[t] +1;
}
WINDOW_HELP_INIT
if(ths->nnfft_flags & MALLOC_X)
ths->x = (double*)nfft_malloc(ths->d*ths->M_total*sizeof(double));
if(ths->nnfft_flags & MALLOC_F){
ths->f=(double _Complex*)nfft_malloc(ths->M_total*sizeof(double _Complex));
}
if(ths->nnfft_flags & MALLOC_V)
ths->v = (double*)nfft_malloc(ths->d*ths->N_total*sizeof(double));
if(ths->nnfft_flags & MALLOC_F_HAT)
ths->f_hat = (double _Complex*)nfft_malloc(ths->N_total*sizeof(double _Complex));
//BUGFIX SUSE 2
// if(ths->nnfft_flags & PRE_PHI_HUT)
// nnfft_precompute_phi_hut(ths);
if(ths->nnfft_flags & PRE_LIN_PSI)
{
ths->K=(1U<< 10)*(ths->m+1);
ths->psi = (double*) nfft_malloc((ths->K+1)*ths->d*sizeof(double));
}
if(ths->nnfft_flags & PRE_PSI){
ths->psi = (double*)nfft_malloc(ths->N_total*ths->d*(2*ths->m+2)*sizeof(double));
}
if(ths->nnfft_flags & PRE_FULL_PSI)
{
for(t=0,lprod = 1; t<ths->d; t++)
lprod *= 2*ths->m+2;
ths->psi = (double*)nfft_malloc(ths->N_total*lprod*sizeof(double));
ths->psi_index_f = (int*) nfft_malloc(ths->N_total*sizeof(int));
ths->psi_index_g = (int*) nfft_malloc(ths->N_total*lprod*sizeof(int));
}
ths->direct_plan = (nfft_plan*)nfft_malloc(sizeof(nfft_plan));
nfft_init_guru(ths->direct_plan, ths->d, ths->aN1, ths->M_total, N2, m2,
nfft_flags, fftw_flags);
ths->direct_plan->x = ths->x;
ths->direct_plan->f = ths->f;
ths->F = ths->direct_plan->f_hat;
ths->mv_trafo = (void (*) (void* ))nnfft_trafo;
ths->mv_adjoint = (void (*) (void* ))nnfft_adjoint;
}
void nnfft_init_guru(nnfft_plan *ths, int d, int N_total, int M_total, int *N, int *N1,
int m, unsigned nnfft_flags)
{
int t;
unsigned nfft_flags;
unsigned fftw_flags;
ths->d= d;
ths->M_total= M_total;
ths->N_total= N_total;
ths->m= m;
ths->nnfft_flags= nnfft_flags;
fftw_flags= FFTW_ESTIMATE| FFTW_DESTROY_INPUT;
nfft_flags= PRE_PHI_HUT| MALLOC_F_HAT| FFTW_INIT|
((d == 1) ? FFT_OUT_OF_PLACE : 0U) | NFFT_OMP_BLOCKWISE_ADJOINT;
if(ths->nnfft_flags & PRE_PSI)
nfft_flags = nfft_flags | PRE_PSI;
if(ths->nnfft_flags & PRE_FULL_PSI)
nfft_flags = nfft_flags | PRE_FULL_PSI;
if(ths->nnfft_flags & PRE_LIN_PSI)
nfft_flags = nfft_flags | PRE_LIN_PSI;
ths->N = (int*) nfft_malloc(ths->d*sizeof(int));
ths->N1 = (int*) nfft_malloc(ths->d*sizeof(int));
for(t=0; t<d; t++) {
ths->N[t] = N[t];
ths->N1[t] = N1[t];
}
nnfft_init_help(ths,m,nfft_flags,fftw_flags);
}
void nnfft_init(nnfft_plan *ths, int d, int N_total, int M_total, int *N)
{
int t;
unsigned nfft_flags;
unsigned fftw_flags;
ths->d = d;
ths->M_total = M_total;
ths->N_total = N_total;
/* m should be greater to get the same accuracy as the nfft */
/* Was soll dieser Ausdruck machen? Es handelt sich um eine Ganzzahl!
WINDOW_HELP_ESTIMATE_m;
*/
//BUGFIX SUSE 1
ths->m=WINDOW_HELP_ESTIMATE_m;
ths->N = (int*) nfft_malloc(ths->d*sizeof(int));
ths->N1 = (int*) nfft_malloc(ths->d*sizeof(int));
for(t=0; t<d; t++) {
ths->N[t] = N[t];
/* the standard oversampling factor in the nnfft is 1.5 */
ths->N1[t] = ceil(1.5*ths->N[t]);
/* N1 should be even */
if(ths->N1[t]%2 != 0)
ths->N1[t] = ths->N1[t] +1;
}
ths->nnfft_flags=PRE_PSI| PRE_PHI_HUT| MALLOC_X| MALLOC_V| MALLOC_F_HAT| MALLOC_F;
nfft_flags= PRE_PSI| PRE_PHI_HUT| MALLOC_F_HAT| FFTW_INIT|
((d == 1) ? FFT_OUT_OF_PLACE : 0U)| NFFT_OMP_BLOCKWISE_ADJOINT;
fftw_flags= FFTW_ESTIMATE| FFTW_DESTROY_INPUT;
nnfft_init_help(ths,ths->m,nfft_flags,fftw_flags);
}
void nnfft_init_1d(nnfft_plan *ths,int N1, int M_total)
{
nnfft_init(ths,1,N1,M_total,&N1);
}
void nnfft_finalize(nnfft_plan *ths)
{
nfft_finalize(ths->direct_plan);
nfft_free(ths->direct_plan);
nfft_free(ths->aN1);
nfft_free(ths->N);
nfft_free(ths->N1);
if(ths->nnfft_flags & PRE_FULL_PSI)
{
nfft_free(ths->psi_index_g);
nfft_free(ths->psi_index_f);
nfft_free(ths->psi);
}
if(ths->nnfft_flags & PRE_PSI)
nfft_free(ths->psi);
if(ths->nnfft_flags & PRE_LIN_PSI)
nfft_free(ths->psi);
if(ths->nnfft_flags & PRE_PHI_HUT)
nfft_free(ths->c_phi_inv);
if(ths->nnfft_flags & MALLOC_F)
nfft_free(ths->f);
if(ths->nnfft_flags & MALLOC_F_HAT)
nfft_free(ths->f_hat);
if(ths->nnfft_flags & MALLOC_X)
nfft_free(ths->x);
if(ths->nnfft_flags & MALLOC_V)
nfft_free(ths->v);
}
MALLOC_F_HAT
#define MALLOC_F_HAT
Definition nfft3.h:188
MALLOC_X
#define MALLOC_X
Definition nfft3.h:187
nfft_precompute_lin_psi
void nfft_precompute_lin_psi(nfft_plan *ths)
nfft_adjoint
void nfft_adjoint(nfft_plan *ths)
nfft_finalize
void nfft_finalize(nfft_plan *ths)
PRE_FULL_PSI
#define PRE_FULL_PSI
Definition nfft3.h:186
FFT_OUT_OF_PLACE
#define FFT_OUT_OF_PLACE
Definition nfft3.h:190
PRE_PSI
#define PRE_PSI
Definition nfft3.h:185
nfft_trafo
void nfft_trafo(nfft_plan *ths)
MALLOC_F
#define MALLOC_F
Definition nfft3.h:189
PRE_LIN_PSI
#define PRE_LIN_PSI
Definition nfft3.h:183
FFTW_INIT
#define FFTW_INIT
Definition nfft3.h:191
PRE_PHI_HUT
#define PRE_PHI_HUT
Definition nfft3.h:181
nfft_precompute_psi
void nfft_precompute_psi(nfft_plan *ths)
nfft_precompute_full_psi
void nfft_precompute_full_psi(nfft_plan *ths)
nnfft_init
void nnfft_init(nnfft_plan *ths, int d, int N_total, int M_total, int *N)
Definition nnfft.c:613
nnfft_precompute_lin_psi
void nnfft_precompute_lin_psi(nnfft_plan *ths)
create a lookup table
Definition nnfft.c:367
nnfft_init_guru
void nnfft_init_guru(nnfft_plan *ths, int d, int N_total, int M_total, int *N, int *N1, int m, unsigned nnfft_flags)
Definition nnfft.c:577
nnfft_precompute_full_psi
void nnfft_precompute_full_psi(nnfft_plan *ths)
computes all entries of B explicitly
Definition nnfft.c:424
nnfft_precompute_psi
void nnfft_precompute_psi(nnfft_plan *ths)
Definition nnfft.c:385
nnfft_trafo
void nnfft_trafo(nnfft_plan *ths)
user routines
Definition nnfft.c:291
nnfft_finalize
void nnfft_finalize(nnfft_plan *ths)
Definition nnfft.c:657
nnfft_precompute_phi_hut
void nnfft_precompute_phi_hut(nnfft_plan *ths)
initialisation of direct transform
Definition nnfft.c:347
MALLOC_V
#define MALLOC_V
Definition nfft3.h:423
nnfft_adjoint
void nnfft_adjoint(nnfft_plan *ths)
Definition nnfft.c:319
infft.h
Internal header file for auxiliary definitions and functions.
nfft3.h
Header file for the nfft3 library.
nfft_malloc
void * nfft_malloc(size_t n)
nfft_free
void nfft_free(void *p)
nfft_plan
nnfft_plan
data structure for an NNFFT (nonequispaced in time and frequency fast Fourier transform) plan with do...
Definition nfft3.h:419
nnfft_plan::v
double * v
nodes (in fourier domain)
Definition nfft3.h:419
nnfft_plan::a
double * a
1 + 2*m/N1
Definition nfft3.h:419
nnfft_plan::m
int m
cut-off parameter in time-domain
Definition nfft3.h:419
nnfft_plan::psi_index_f
int * psi_index_f
only for thin B
Definition nfft3.h:419
nnfft_plan::M_total
NFFT_INT M_total
Total number of samples.
Definition nfft3.h:419
nnfft_plan::N
int * N
cut-off-frequencies
Definition nfft3.h:419
nnfft_plan::direct_plan
nfft_plan * direct_plan
plan for the nfft
Definition nfft3.h:419
nnfft_plan::K
int K
number of precomp.
Definition nfft3.h:419
nnfft_plan::nnfft_flags
unsigned nnfft_flags
flags for precomputation, malloc
Definition nfft3.h:419
nnfft_plan::sigma
double * sigma
oversampling-factor
Definition nfft3.h:419
nnfft_plan::n
int * n
n=N1, for the window function
Definition nfft3.h:419
nnfft_plan::N_total
NFFT_INT N_total
Total number of Fourier coefficients.
Definition nfft3.h:419
nnfft_plan::N1
int * N1
sigma*N
Definition nfft3.h:419
nnfft_plan::f
fftw_complex * f
Samples.
Definition nfft3.h:419
nnfft_plan::mv_trafo
void(* mv_trafo)(void *)
Transform.
Definition nfft3.h:419
nnfft_plan::c_phi_inv
double * c_phi_inv
precomputed data, matrix D
Definition nfft3.h:419
nnfft_plan::d
int d
dimension, rank
Definition nfft3.h:419
nnfft_plan::psi_index_g
int * psi_index_g
only for thin B
Definition nfft3.h:419
nnfft_plan::f_hat
fftw_complex * f_hat
Fourier coefficients.
Definition nfft3.h:419
nnfft_plan::x
double * x
nodes (in time/spatial domain)
Definition nfft3.h:419
nnfft_plan::aN1_total
int aN1_total
aN1_total=aN1[0]* ... *aN1[d-1]
Definition nfft3.h:419
nnfft_plan::psi
double * psi
precomputed data, matrix B
Definition nfft3.h:419
nnfft_plan::mv_adjoint
void(* mv_adjoint)(void *)
Adjoint transform.
Definition nfft3.h:419
nnfft_plan::aN1
int * aN1
sigma*a*N
Definition nfft3.h:419