nfct.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.
*/
/* Nonequispaced fast cosine transform */
/* Author: Steffen Klatt 2004-2006, Jens Keiner 2010 */
/* configure header */
#include "config.h"
/* complex datatype (maybe) */
#ifdef HAVE_COMPLEX_H
#include<complex.h>
#endif
/* NFFT headers */
#include "nfft3.h"
#include "infft.h"
#ifdef _OPENMP
#include <omp.h>
#endif
#ifdef OMP_ASSERT
#include <assert.h>
#endif
#undef X
#define X(name) NFCT(name)
static inline INT intprod(const INT *vec, const INT a, const INT d)
{
INT t, p;
p = 1;
for (t = 0; t < d; t++)
p *= vec[t] - a;
return p;
}
/* handy shortcuts */
#define BASE(x) COS(x)
#define NN(x) (x - 1)
#define OFFSET 0
#define FOURIER_TRAFO FFTW_REDFT00
#define FFTW_DEFAULT_FLAGS FFTW_ESTIMATE | FFTW_DESTROY_INPUT
#define NODE(p,r) (ths->x[(p) * ths->d + (r)])
#define MACRO_with_FG_PSI fg_psi[t][lj[t]]
#define MACRO_with_PRE_PSI ths->psi[(j * ths->d + t) * (2 * ths->m + 2) + lj[t]]
#define MACRO_without_PRE_PSI PHI((2 * NN(ths->n[t])), ((ths->x[(j) * ths->d + t]) \
- ((R)(lj[t] + u[t])) / (K(2.0) * ((R)NN(ths->n[t])))), t)
#define MACRO_compute_PSI PHI((2 * NN(ths->n[t])), (NODE(j,t) - ((R)(lj[t] + u[t])) / (K(2.0) * ((R)NN(ths->n[t])))), t)
void X(trafo_direct)(const X(plan) *ths)
{
R *f_hat = (R*)ths->f_hat, *f = (R*)ths->f;
memset(f, 0, (size_t)(ths->M_total) * sizeof(R));
if (ths->d == 1)
{
/* specialize for univariate case, rationale: faster */
INT j;
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(j)
#endif
for (j = 0; j < ths->M_total; j++)
{
INT k_L;
for (k_L = 0; k_L < ths->N_total; k_L++)
{
R omega = K2PI * ((R)(k_L + OFFSET)) * ths->x[j];
f[j] += f_hat[k_L] * BASE(omega);
}
}
}
else
{
/* multivariate case */
INT j;
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(j)
#endif
for (j = 0; j < ths->M_total; j++)
{
R x[ths->d], omega, Omega[ths->d + 1];
INT t, t2, k_L, k[ths->d];
Omega[0] = K(1.0);
for (t = 0; t < ths->d; t++)
{
k[t] = OFFSET;
x[t] = K2PI * ths->x[j * ths->d + t];
Omega[t+1] = BASE(((R)(k[t])) * x[t]) * Omega[t];
}
omega = Omega[ths->d];
for (k_L = 0; k_L < ths->N_total; k_L++)
{
f[j] += f_hat[k_L] * omega;
{
for (t = ths->d - 1; (t >= 1) && (k[t] == (ths->N[t] - 1)); t--)
k[t] = OFFSET;
k[t]++;
for (t2 = t; t2 < ths->d; t2++)
Omega[t2+1] = BASE(((R)(k[t2])) * x[t2]) * Omega[t2];
omega = Omega[ths->d];
}
}
}
}
}
void X(adjoint_direct)(const X(plan) *ths)
{
R *f_hat = (R*)ths->f_hat, *f = (R*)ths->f;
memset(f_hat, 0, (size_t)(ths->N_total) * sizeof(R));
if (ths->d == 1)
{
/* specialize for univariate case, rationale: faster */
#ifdef _OPENMP
INT k_L;
#pragma omp parallel for default(shared) private(k_L)
for (k_L = 0; k_L < ths->N_total; k_L++)
{
INT j;
for (j = 0; j < ths->M_total; j++)
{
R omega = K2PI * ((R)(k_L + OFFSET)) * ths->x[j];
f_hat[k_L] += f[j] * BASE(omega);
}
}
#else
INT j;
for (j = 0; j < ths->M_total; j++)
{
INT k_L;
for (k_L = 0; k_L < ths->N_total; k_L++)
{
R omega = K2PI * ((R)(k_L + OFFSET)) * ths->x[j];
f_hat[k_L] += f[j] * BASE(omega);
}
}
#endif
}
else
{
/* multivariate case */
INT j, k_L;
#ifdef _OPENMP
#pragma omp parallel for default(shared) private(j, k_L)
for (k_L = 0; k_L < ths->N_total; k_L++)
{
INT k[ths->d], k_temp, t;
k_temp = k_L;
for (t = ths->d - 1; t >= 0; t--)
{
k[t] = k_temp % ths->N[t];
k_temp /= ths->N[t];
}
for (j = 0; j < ths->M_total; j++)
{
R omega = K(1.0);
for (t = 0; t < ths->d; t++)
omega *= BASE(K2PI * (k[t] + OFFSET) * ths->x[j * ths->d + t]);
f_hat[k_L] += f[j] * omega;
}
}
#else
for (j = 0; j < ths->M_total; j++)
{
R x[ths->d], omega, Omega[ths->d+1];
INT t, t2, k[ths->d];
Omega[0] = K(1.0);
for (t = 0; t < ths->d; t++)
{
k[t] = OFFSET;
x[t] = K2PI * ths->x[j * ths->d + t];
Omega[t+1] = BASE(((R)(k[t])) * x[t]) * Omega[t];
}
omega = Omega[ths->d];
for (k_L = 0; k_L < ths->N_total; k_L++)
{
f_hat[k_L] += f[j] * omega;
for (t = ths->d-1; (t >= 1) && (k[t] == ths->N[t] - 1); t--)
k[t] = OFFSET;
k[t]++;
for (t2 = t; t2 < ths->d; t2++)
Omega[t2+1] = BASE(((R)(k[t2])) * x[t2]) * Omega[t2];
omega = Omega[ths->d];
}
}
#endif
}
}
static inline void uo(const X(plan) *ths, const INT j, INT *up, INT *op,
const INT act_dim)
{
const R xj = ths->x[j * ths->d + act_dim];
INT c = LRINT(xj * (2 * NN(ths->n[(act_dim)])));
(*up) = c - (ths->m);
(*op) = c + 1 + (ths->m);
}
#define MACRO_D_compute_A \
{ \
g_hat[kg_plain[ths->d]] = f_hat[k_L] * c_phi_inv_k[ths->d]; \
}
#define MACRO_D_compute_T \
{ \
f_hat[k_L] = g_hat[kg_plain[ths->d]] * c_phi_inv_k[ths->d]; \
}
#define MACRO_D_init_result_A memset(g_hat, 0, (size_t)(ths->n_total) * sizeof(R));
#define MACRO_D_init_result_T memset(f_hat, 0, (size_t)(ths->N_total) * sizeof(R));
#define MACRO_with_PRE_PHI_HUT ths->c_phi_inv[t][kg[t]]
#define MACRO_compute_PHI_HUT_INV (K(1.0) / (PHI_HUT((2 * NN(ths->n[t])), kg[t] + OFFSET, t)))
#define MACRO_init_k_ks \
{ \
for (t = 0; t < ths->d; t++) \
{ \
kg[t] = 0; \
} \
i = 0; \
}
#define MACRO_update_c_phi_inv_k(what_kind, which_phi) \
{ \
for (t = i; t < ths->d; t++) \
{ \
MACRO_update_c_phi_inv_k_ ## what_kind(which_phi); \
kg_plain[t+1] = kg_plain[t] * ths->n[t] + kg[t]; \
} \
}
#define MACRO_update_c_phi_inv_k_A(which_phi) \
{ \
c_phi_inv_k[t+1] = (kg[t] == 0 ? K(1.0) : K(0.5)) * c_phi_inv_k[t] * MACRO_ ## which_phi; \
}
#define MACRO_update_c_phi_inv_k_T(which_phi) \
{ \
c_phi_inv_k[t+1] = c_phi_inv_k[t] * MACRO_ ## which_phi; \
}
#define MACRO_count_k_ks \
{ \
kg[ths->d - 1]++; \
i = ths->d - 1; \
\
while ((kg[i] == ths->N[i]) && (i > 0)) \
{ \
kg[i - 1]++; \
kg[i] = 0; \
i--; \
} \
}
/* sub routines for the fast transforms matrix vector multiplication with D, D^T */
#define MACRO_D(which_one) \
static inline void D_ ## which_one (X(plan) *ths) \
{ \
R *g_hat, *f_hat; /* local copy */ \
R c_phi_inv_k[ths->d+1]; /* postfix product of PHI_HUT */ \
INT t; /* index dimensions */ \
INT i; \
INT k_L; /* plain index */ \
INT kg[ths->d]; /* multi index in g_hat */ \
INT kg_plain[ths->d+1]; /* postfix plain index */ \
\
f_hat = (R*)ths->f_hat; g_hat = (R*)ths->g_hat; \
MACRO_D_init_result_ ## which_one; \
\
c_phi_inv_k[0] = K(1.0); \
kg_plain[0] = 0; \
\
MACRO_init_k_ks; \
\
if (ths->flags & PRE_PHI_HUT) \
{ \
for (k_L = 0; k_L < ths->N_total; k_L++) \
{ \
MACRO_update_c_phi_inv_k(which_one, with_PRE_PHI_HUT); \
MACRO_D_compute_ ## which_one; \
MACRO_count_k_ks; \
} \
} \
else \
{ \
for (k_L = 0; k_L < ths->N_total; k_L++) \
{ \
MACRO_update_c_phi_inv_k(which_one,compute_PHI_HUT_INV); \
MACRO_D_compute_ ## which_one; \
MACRO_count_k_ks; \
} \
} \
}
MACRO_D(A)
MACRO_D(T)
/* sub routines for the fast transforms matrix vector multiplication with B, B^T */
#define MACRO_B_init_result_A memset(f, 0, (size_t)(ths->M_total) * sizeof(R));
#define MACRO_B_init_result_T memset(g, 0, (size_t)(ths->n_total) * sizeof(R));
#define MACRO_B_PRE_FULL_PSI_compute_A \
{ \
(*fj) += ths->psi[ix] * g[ths->psi_index_g[ix]]; \
}
#define MACRO_B_PRE_FULL_PSI_compute_T \
{ \
R factor = K(1.0); \
INT d = ths->psi_index_g[ix]; \
for (t = ths->d - 1; t >= 0; t--) \
{ \
INT m = d % ths->n[t]; \
if (m != 0 && m != ths->n[t] - 1) \
factor *= K(0.5); \
d = d / ths->n[t]; \
} \
g[ths->psi_index_g[ix]] += factor * ths->psi[ix] * (*fj); \
}
#define MACRO_B_compute_A \
{ \
(*fj) += phi_prod[ths->d] * g[ll_plain[ths->d]]; \
}
#define MACRO_B_compute_T \
{ \
g[ll_plain[ths->d]] += phi_prod[ths->d] * (*fj); \
}
#define MACRO_init_uo_l_lj_t \
{ \
for (t2 = 0; t2 < ths->d; t2++) \
{ \
uo(ths, j, &u[t2], &o[t2], t2); \
\
/* determine index in g-array corresponding to u[(t2)] */ \
if (u[(t2)] < 0) \
lg_offset[(t2)] = \
(u[(t2)] % (2 * NN(ths->n[(t2)]))) + (2 * NN(ths->n[(t2)])); \
else \
lg_offset[(t2)] = u[(t2)] % (2 * NN(ths->n[(t2)])); \
if (lg_offset[(t2)] > NN(ths->n[(t2)])) \
lg_offset[(t2)] = -(2 * NN(ths->n[(t2)]) - lg_offset[(t2)]); \
\
if (lg_offset[t2] <= 0) \
{ \
l[t2] = -lg_offset[t2]; \
count_lg[t2] = -1; \
} \
else \
{ \
l[t2] = +lg_offset[t2]; \
count_lg[t2] = +1; \
} \
\
lj[t2] = 0; \
} \
t2 = 0; \
}
#define FOO_A K(1.0)
#define FOO_T ((l[t] == 0 || l[t] == ths->n[t] - 1) ? K(1.0) : K(0.5))
#define MACRO_update_phi_prod_ll_plain(which_one,which_psi) \
{ \
for (t = t2; t < ths->d; t++) \
{ \
phi_prod[t+1] = (FOO_ ## which_one) * phi_prod[t] * (MACRO_ ## which_psi); \
ll_plain[t+1] = ll_plain[t] * ths->n[t] + l[t]; \
} \
}
#define MACRO_count_uo_l_lj_t \
{ \
/* turn around if we hit one of the boundaries */ \
if ((l[(ths->d-1)] == 0) || (l[(ths->d-1)] == NN(ths->n[(ths->d-1)]))) \
count_lg[(ths->d-1)] *= -1; \
\
/* move array index */ \
l[(ths->d-1)] += count_lg[(ths->d-1)]; \
\
lj[ths->d - 1]++; \
t2 = ths->d - 1; \
\
while ((lj[t2] == (2 * ths->m + 2)) && (t2 > 0)) \
{ \
lj[t2 - 1]++; \
lj[t2] = 0; \
/* ansonsten lg[i-1] verschieben */ \
\
/* turn around if we hit one of the boundaries */ \
if ((l[(t2 - 1)] == 0) || (l[(t2 - 1)] == NN(ths->n[(t2 - 1)]))) \
count_lg[(t2 - 1)] *= -1; \
/* move array index */ \
l[(t2 - 1)] += count_lg[(t2 - 1)]; \
\
/* lg[i] = anfangswert */ \
if (lg_offset[t2] <= 0) \
{ \
l[t2] = -lg_offset[t2]; \
count_lg[t2] = -1; \
} \
else \
{ \
l[t2] = +lg_offset[t2]; \
count_lg[t2] = +1; \
} \
\
t2--; \
} \
}
#define MACRO_B(which_one) \
static inline void B_ ## which_one (X(plan) *ths) \
{ \
INT lprod; /* 'regular bandwidth' of matrix B */ \
INT u[ths->d], o[ths->d]; /* multi band with respect to x_j */ \
INT t, t2; /* index dimensions */ \
INT j; /* index nodes */ \
INT l_L, ix; /* index one row of B */ \
INT l[ths->d]; /* multi index u<=l<=o (real index of g in array) */ \
INT lj[ths->d]; /* multi index 0<=lc<2m+2 */ \
INT ll_plain[ths->d+1]; /* postfix plain index in g */ \
R phi_prod[ths->d+1]; /* postfix product of PHI */ \
R *f, *g; /* local copy */ \
R *fj; /* local copy */ \
R y[ths->d]; \
R fg_psi[ths->d][2*ths->m+2]; \
R fg_exp_l[ths->d][2*ths->m+2]; \
INT l_fg,lj_fg; \
R tmpEXP1, tmpEXP2, tmpEXP2sq, tmp1, tmp2, tmp3; \
R ip_w; \
INT ip_u; \
INT ip_s = ths->K/(ths->m+2); \
INT lg_offset[ths->d]; /* offset in g according to u */ \
INT count_lg[ths->d]; /* count summands (2m+2) */ \
\
f = (R*)ths->f; g = (R*)ths->g; \
\
MACRO_B_init_result_ ## which_one \
\
if (ths->flags & PRE_FULL_PSI) \
{ \
for (ix = 0, j = 0, fj = f; j < ths->M_total; j++, fj++) \
{ \
for (l_L = 0; l_L < ths->psi_index_f[j]; l_L++, ix++) \
{ \
MACRO_B_PRE_FULL_PSI_compute_ ## which_one; \
} \
} \
return; \
} \
\
phi_prod[0] = K(1.0); \
ll_plain[0] = 0; \
\
for (t = 0, lprod = 1; t < ths->d; t++) \
lprod *= (2 * ths->m + 2); \
\
if (ths->flags & PRE_PSI) \
{ \
for (j = 0, fj = f; j < ths->M_total; j++, fj++) \
{ \
MACRO_init_uo_l_lj_t; \
\
for (l_L = 0; l_L < lprod; l_L++) \
{ \
MACRO_update_phi_prod_ll_plain(which_one, with_PRE_PSI); \
\
MACRO_B_compute_ ## which_one; \
\
MACRO_count_uo_l_lj_t; \
} /* for(l_L) */ \
} /* for(j) */ \
return; \
} /* if(PRE_PSI) */ \
\
if (ths->flags & PRE_FG_PSI) \
{ \
for (t = 0; t < ths->d; t++) \
{ \
tmpEXP2 = EXP(K(-1.0) / ths->b[t]); \
tmpEXP2sq = tmpEXP2 * tmpEXP2; \
tmp2 = K(1.0); \
tmp3 = K(1.0); \
fg_exp_l[t][0] = K(1.0); \
\
for (lj_fg = 1; lj_fg <= (2 * ths->m + 2); lj_fg++) \
{ \
tmp3 = tmp2 * tmpEXP2; \
tmp2 *= tmpEXP2sq; \
fg_exp_l[t][lj_fg] = fg_exp_l[t][lj_fg-1] * tmp3; \
} \
} \
\
for (j = 0, fj = f; j < ths->M_total; j++, fj++) \
{ \
MACRO_init_uo_l_lj_t; \
\
for (t = 0; t < ths->d; t++) \
{ \
fg_psi[t][0] = ths->psi[2 * (j * ths->d + t)]; \
tmpEXP1 = ths->psi[2 * (j * ths->d + t) + 1]; \
tmp1 = K(1.0); \
\
for (l_fg = u[t] + 1, lj_fg = 1; l_fg <= o[t]; l_fg++, lj_fg++) \
{ \
tmp1 *= tmpEXP1; \
fg_psi[t][lj_fg] = fg_psi[t][0] * tmp1 * fg_exp_l[t][lj_fg]; \
} \
} \
\
for (l_L= 0; l_L < lprod; l_L++) \
{ \
MACRO_update_phi_prod_ll_plain(which_one, with_FG_PSI); \
\
MACRO_B_compute_ ## which_one; \
\
MACRO_count_uo_l_lj_t; \
} \
} \
return; \
} \
\
if (ths->flags & FG_PSI) \
{ \
for (t = 0; t < ths->d; t++) \
{ \
tmpEXP2 = EXP(K(-1.0) / ths->b[t]); \
tmpEXP2sq = tmpEXP2 * tmpEXP2; \
tmp2 = K(1.0); \
tmp3 = K(1.0); \
fg_exp_l[t][0] = K(1.0); \
for (lj_fg = 1; lj_fg <= (2 * ths->m + 2); lj_fg++) \
{ \
tmp3 = tmp2 * tmpEXP2; \
tmp2 *= tmpEXP2sq; \
fg_exp_l[t][lj_fg] = fg_exp_l[t][lj_fg-1] * tmp3; \
} \
} \
\
for (j = 0, fj = f; j < ths->M_total; j++, fj++) \
{ \
MACRO_init_uo_l_lj_t; \
\
for (t = 0; t < ths->d; t++) \
{ \
fg_psi[t][0] = (PHI((2 * NN(ths->n[t])), (ths->x[j*ths->d+t] - ((R)u[t])/(2 * NN(ths->n[t]))),(t)));\
\
tmpEXP1 = EXP(K(2.0) * ((2 * NN(ths->n[t])) * ths->x[j * ths->d + t] - u[t]) / ths->b[t]); \
tmp1 = K(1.0); \
for (l_fg = u[t] + 1, lj_fg = 1; l_fg <= o[t]; l_fg++, lj_fg++) \
{ \
tmp1 *= tmpEXP1; \
fg_psi[t][lj_fg] = fg_psi[t][0] * tmp1 * fg_exp_l[t][lj_fg]; \
} \
} \
\
for (l_L = 0; l_L < lprod; l_L++) \
{ \
MACRO_update_phi_prod_ll_plain(which_one, with_FG_PSI); \
\
MACRO_B_compute_ ## which_one; \
\
MACRO_count_uo_l_lj_t; \
} \
} \
return; \
} \
\
if (ths->flags & PRE_LIN_PSI) \
{ \
for (j = 0, fj = f; j < ths->M_total; j++, fj++) \
{ \
MACRO_init_uo_l_lj_t; \
\
for (t = 0; t < ths->d; t++) \
{ \
y[t] = (((2 * NN(ths->n[t])) * ths->x[j * ths->d + t] - (R)u[t]) \
* ((R)ths->K))/(ths->m + 2); \
ip_u = LRINT(FLOOR(y[t])); \
ip_w = y[t]-ip_u; \
for (l_fg = u[t], lj_fg = 0; l_fg <= o[t]; l_fg++, lj_fg++) \
{ \
fg_psi[t][lj_fg] = ths->psi[(ths->K+1)*t + ABS(ip_u-lj_fg*ip_s)] \
* (1-ip_w) + ths->psi[(ths->K+1)*t + ABS(ip_u-lj_fg*ip_s+1)] \
* (ip_w); \
} \
} \
\
for (l_L = 0; l_L < lprod; l_L++) \
{ \
MACRO_update_phi_prod_ll_plain(which_one, with_FG_PSI); \
\
MACRO_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[0]; j < ths->M_total; j++, fj += 1) \
{ \
MACRO_init_uo_l_lj_t; \
\
for (l_L = 0; l_L < lprod; l_L++) \
{ \
MACRO_update_phi_prod_ll_plain(which_one, without_PRE_PSI); \
\
MACRO_B_compute_ ## which_one; \
\
MACRO_count_uo_l_lj_t; \
} /* for (l_L) */ \
} /* for (j) */ \
} /* B */
MACRO_B(A)
MACRO_B(T)
void X(trafo)(X(plan) *ths)
{
switch(ths->d)
{
default:
{
/* use ths->my_fftw_r2r_plan */
ths->g_hat = ths->g1;
ths->g = ths->g2;
/* form \f$ \hat g_k = \frac{\hat f_k}{c_k\left(\phi\right)} \text{ for }
* k \in I_N \f$ */
TIC(0)
D_A(ths);
TOC(0)
/* Compute by d-variate discrete Fourier transform
* \f$ g_l = \sum_{k \in I_N} \hat g_k {\rm e}^{-2\pi {\rm i} \frac{kl}{n}}
* \text{ for } l \in I_n \f$ */
TIC_FFTW(1)
FFTW(execute)(ths->my_fftw_r2r_plan);
TOC_FFTW(1)
/*if (ths->flags & PRE_FULL_PSI)
full_psi__A(ths);*/
/* Set \f$ f_j = \sum_{l \in I_n,m(x_j)} g_l \psi\left(x_j-\frac{l}{n}\right)
* \text{ for } j=0,\dots,M-1 \f$ */
TIC(2)
B_A(ths);
TOC(2)
/*if (ths->flags & PRE_FULL_PSI)
{
Y(free)(ths->psi_index_g);
Y(free)(ths->psi_index_f);
}*/
}
}
} /* trafo */
void X(adjoint)(X(plan) *ths)
{
switch(ths->d)
{
default:
{
/* use ths->my_fftw_plan */
ths->g_hat = ths->g2;
ths->g = ths->g1;
/*if (ths->flags & PRE_FULL_PSI)
full_psi__T(ths);*/
/* Set \f$ g_l = \sum_{j=0}^{M-1} f_j \psi\left(x_j-\frac{l}{n}\right)
* \text{ for } l \in I_n,m(x_j) \f$ */
TIC(2)
B_T(ths);
TOC(2)
/* Compute by d-variate discrete cosine transform
* \f$ \hat g_k = \sum_{l \in I_n} g_l {\rm e}^{-2\pi {\rm i} \frac{kl}{n}}
* \text{ for } k \in I_N\f$ */
TIC_FFTW(1)
FFTW(execute)(ths->my_fftw_r2r_plan);
TOC_FFTW(1)
/* Form \f$ \hat f_k = \frac{\hat g_k}{c_k\left(\phi\right)} \text{ for }
* k \in I_N \f$ */
TIC(0)
D_T(ths);
TOC(0)
}
}
} /* adjoint */
static inline void precompute_phi_hut(X(plan) *ths)
{
INT ks[ths->d]; /* index over all frequencies */
INT t; /* index over all dimensions */
ths->c_phi_inv = (R**) Y(malloc)((size_t)(ths->d) * sizeof(R*));
for (t = 0; t < ths->d; t++)
{
ths->c_phi_inv[t] = (R*)Y(malloc)((size_t)(ths->N[t] - OFFSET) * sizeof(R));
for (ks[t] = 0; ks[t] < ths->N[t] - OFFSET; ks[t]++)
{
ths->c_phi_inv[t][ks[t]] = (K(1.0) / (PHI_HUT((2 * NN(ths->n[t])), ks[t] + OFFSET, t)));
}
}
} /* phi_hut */
void X(precompute_lin_psi)(X(plan) *ths)
{
INT t;
INT j;
R step;
for (t = 0; t < ths->d; t++)
{
step = ((R)(ths->m+2)) / (((R)ths->K) * (2 * NN(ths->n[t])));
for (j = 0; j <= ths->K; j++)
{
ths->psi[(ths->K + 1) * t + j] = PHI((2 * NN(ths->n[t])), (j * step), t);
} /* for(j) */
} /* for(t) */
}
void X(precompute_fg_psi)(X(plan) *ths)
{
INT t; /* index over all dimensions */
INT u, o; /* depends on x_j */
// sort(ths);
for (t = 0; t < ths->d; t++)
{
INT j;
// #pragma omp parallel for default(shared) private(j,u,o)
for (j = 0; j < ths->M_total; j++)
{
uo(ths, j, &u, &o, t);
ths->psi[2 * (j*ths->d + t)] = (PHI((2 * NN(ths->n[t])),(ths->x[j * ths->d + t] - ((R)u) / (2 * NN(ths->n[t]))),(t)));
ths->psi[2 * (j*ths->d + t) + 1] = EXP(K(2.0) * ( (2 * NN(ths->n[t])) * ths->x[j * ths->d + t] - u) / ths->b[t]);
} /* for(j) */
}
/* for(t) */
} /* nfft_precompute_fg_psi */
void X(precompute_psi)(X(plan) *ths)
{
INT t; /* index over all dimensions */
INT lj; /* index 0<=lj<u+o+1 */
INT u, o; /* depends on x_j */
//sort(ths);
for (t = 0; t < ths->d; t++)
{
INT j;
for (j = 0; j < ths->M_total; j++)
{
uo(ths, j, &u, &o, t);
for(lj = 0; lj < (2 * ths->m + 2); lj++)
ths->psi[(j * ths->d + t) * (2 * ths->m + 2) + lj] =
(PHI((2 * NN(ths->n[t])), ((ths->x[(j) * ths->d + (t)]) - ((R)(lj + u)) / (K(2.0) * ((R)NN(ths->n[t])))), t));
} /* for (j) */
} /* for (t) */
} /* precompute_psi */
void X(precompute_full_psi)(X(plan) *ths)
{
//#ifdef _OPENMP
// sort(ths);
//
// nfft_precompute_full_psi_omp(ths);
//#else
INT t, t2; /* index over all dimensions */
INT j; /* index over all nodes */
INT l_L; /* plain index 0 <= l_L < lprod */
INT l[ths->d]; /* multi index u<=l<=o */
INT lj[ths->d]; /* multi index 0<=lj<u+o+1 */
INT ll_plain[ths->d+1]; /* postfix plain index */
INT lprod; /* 'bandwidth' of matrix B */
INT u[ths->d], o[ths->d]; /* depends on x_j */
INT count_lg[ths->d];
INT lg_offset[ths->d];
R phi_prod[ths->d+1];
INT ix, ix_old;
//sort(ths);
phi_prod[0] = K(1.0);
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->M_total; j++)
{
MACRO_init_uo_l_lj_t;
for (l_L = 0; l_L < lprod; l_L++, ix++)
{
MACRO_update_phi_prod_ll_plain(A, 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) */
//#endif
}
void X(precompute_one_psi)(X(plan) *ths)
{
if(ths->flags & PRE_PSI)
X(precompute_psi)(ths);
if(ths->flags & PRE_FULL_PSI)
X(precompute_full_psi)(ths);
if(ths->flags & PRE_FG_PSI)
X(precompute_fg_psi)(ths);
if(ths->flags & PRE_LIN_PSI)
X(precompute_lin_psi)(ths);
}
static inline void init_help(X(plan) *ths)
{
INT t; /* index over all dimensions */
INT lprod; /* 'bandwidth' of matrix B */
if (ths->flags & NFFT_OMP_BLOCKWISE_ADJOINT)
ths->flags |= NFFT_SORT_NODES;
ths->N_total = intprod(ths->N, OFFSET, ths->d);
ths->n_total = intprod(ths->n, 0, ths->d);
ths->sigma = (R*)Y(malloc)((size_t)(ths->d) * sizeof(R));
for (t = 0; t < ths->d; t++)
ths->sigma[t] = ((R)NN(ths->n[t])) / ths->N[t];
/* Assign r2r transform kinds for each dimension */
ths->r2r_kind = (FFTW(r2r_kind)*)Y(malloc)((size_t)(ths->d) * sizeof (FFTW(r2r_kind)));
for (t = 0; t < ths->d; t++)
ths->r2r_kind[t] = FOURIER_TRAFO;
WINDOW_HELP_INIT;
if (ths->flags & MALLOC_X)
ths->x = (R*)Y(malloc)((size_t)(ths->d * ths->M_total) * sizeof(R));
if (ths->flags & MALLOC_F_HAT)
ths->f_hat = (R*)Y(malloc)((size_t)(ths->N_total) * sizeof(R));
if (ths->flags & MALLOC_F)
ths->f = (R*)Y(malloc)((size_t)(ths->M_total) * sizeof(R));
if (ths->flags & PRE_PHI_HUT)
precompute_phi_hut(ths);
if(ths->flags & PRE_LIN_PSI)
{
ths->K = (1U<< 10) * (ths->m+2);
ths->psi = (R*) Y(malloc)((size_t)((ths->K + 1) * ths->d) * sizeof(R));
}
if(ths->flags & PRE_FG_PSI)
ths->psi = (R*) Y(malloc)((size_t)(ths->M_total * ths->d * 2) * sizeof(R));
if (ths->flags & PRE_PSI)
ths->psi = (R*) Y(malloc)((size_t)(ths->M_total * ths->d * (2 * ths->m + 2 )) * sizeof(R));
if(ths->flags & PRE_FULL_PSI)
{
for (t = 0, lprod = 1; t < ths->d; t++)
lprod *= 2 * ths->m + 2;
ths->psi = (R*) Y(malloc)((size_t)(ths->M_total * lprod) * sizeof(R));
ths->psi_index_f = (INT*) Y(malloc)((size_t)(ths->M_total) * sizeof(INT));
ths->psi_index_g = (INT*) Y(malloc)((size_t)(ths->M_total * lprod) * sizeof(INT));
}
if (ths->flags & FFTW_INIT)
{
ths->g1 = (R*)Y(malloc)((size_t)(ths->n_total) * sizeof(R));
if (ths->flags & FFT_OUT_OF_PLACE)
ths->g2 = (R*) Y(malloc)((size_t)(ths->n_total) * sizeof(R));
else
ths->g2 = ths->g1;
{
int *_n = Y(malloc)((size_t)(ths->d) * sizeof(int));
for (t = 0; t < ths->d; t++)
_n[t] = (int)(ths->n[t]);
ths->my_fftw_r2r_plan = FFTW(plan_r2r)((int)ths->d, _n, ths->g1, ths->g2, ths->r2r_kind, ths->fftw_flags);
Y(free)(_n);
}
}
// if(ths->flags & NFFT_SORT_NODES)
// ths->index_x = (INT*) Y(malloc)(sizeof(INT)*2*ths->M_total);
// else
// ths->index_x = NULL;
ths->mv_trafo = (void (*) (void* ))X(trafo);
ths->mv_adjoint = (void (*) (void* ))X(adjoint);
}
void X(init)(X(plan) *ths, int d, int *N, int M_total)
{
int t; /* index over all dimensions */
ths->d = (INT)d;
ths->N = (INT*) Y(malloc)((size_t)(d) * sizeof(INT));
for (t = 0; t < d; t++)
ths->N[t] = (INT)N[t];
ths->M_total = (INT)M_total;
ths->n = (INT*) Y(malloc)((size_t)(d) * sizeof(INT));
for (t = 0; t < d; t++)
ths->n[t] = 2 * (Y(next_power_of_2)(ths->N[t]) - 1) + OFFSET;
ths->m = WINDOW_HELP_ESTIMATE_m;
if (d > 1)
{
//#ifdef _OPENMP
// ths->flags = PRE_PHI_HUT | PRE_PSI | MALLOC_X| MALLOC_F_HAT | MALLOC_F |
// FFTW_INIT | FFT_OUT_OF_PLACE | NFFT_SORT_NODES |
// NFFT_OMP_BLOCKWISE_ADJOINT;
//#else
ths->flags = PRE_PHI_HUT | PRE_PSI | MALLOC_X| MALLOC_F_HAT | MALLOC_F |
FFTW_INIT | FFT_OUT_OF_PLACE | NFFT_SORT_NODES;
//#endif
}
else
ths->flags = PRE_PHI_HUT | PRE_PSI | MALLOC_X| MALLOC_F_HAT | MALLOC_F |
FFTW_INIT | FFT_OUT_OF_PLACE;
ths->fftw_flags = FFTW_ESTIMATE | FFTW_DESTROY_INPUT;
init_help(ths);
}
void X(init_guru)(X(plan) *ths, int d, int *N, int M_total, int *n, int m,
unsigned flags, unsigned fftw_flags)
{
INT t; /* index over all dimensions */
ths->d = (INT)d;
ths->M_total = (INT)M_total;
ths->N = (INT*)Y(malloc)((size_t)(ths->d) * sizeof(INT));
for (t = 0; t < d; t++)
ths->N[t] = (INT)N[t];
ths->n = (INT*)Y(malloc)((size_t)(ths->d) * sizeof(INT));
for (t = 0; t < d; t++)
ths->n[t] = (INT)n[t];
ths->m = (INT)m;
ths->flags = flags;
ths->fftw_flags = fftw_flags;
init_help(ths);
}
void X(init_1d)(X(plan) *ths, int N1, int M_total)
{
int N[1];
N[0] = N1;
X(init)(ths, 1, N, M_total);
}
void X(init_2d)(X(plan) *ths, int N1, int N2, int M_total)
{
int N[2];
N[0] = N1;
N[1] = N2;
X(init)(ths, 2, N, M_total);
}
void X(init_3d)(X(plan) *ths, int N1, int N2, int N3, int M_total)
{
int N[3];
N[0] = N1;
N[1] = N2;
N[2] = N3;
X(init)(ths, 3, N, M_total);
}
const char* X(check)(X(plan) *ths)
{
INT j;
if (!ths->f)
return "Member f not initialized.";
if (!ths->x)
return "Member x not initialized.";
if (!ths->f_hat)
return "Member f_hat not initialized.";
for (j = 0; j < ths->M_total * ths->d; j++)
{
if ((ths->x[j] < K(0.0)) || (ths->x[j] >= K(0.5)))
{
return "ths->x out of range [0.0,0.5)";
}
}
for (j = 0; j < ths->d; j++)
{
if (ths->sigma[j] <= 1)
return "Oversampling factor too small";
if(ths->N[j] - 1 <= ths->m)
return "Polynomial degree N is smaller than cut-off m";
if(ths->N[j]%2 == 1)
return "polynomial degree N has to be even";
}
return 0;
}
void X(finalize)(X(plan) *ths)
{
INT t; /* index over dimensions */
// if(ths->flags & NFFT_SORT_NODES)
// Y(free)(ths->index_x);
if (ths->flags & FFTW_INIT)
{
#ifdef _OPENMP
#pragma omp critical (nfft_omp_critical_fftw_plan)
#endif
FFTW(destroy_plan)(ths->my_fftw_r2r_plan);
if (ths->flags & FFT_OUT_OF_PLACE)
Y(free)(ths->g2);
Y(free)(ths->g1);
}
if(ths->flags & PRE_FULL_PSI)
{
Y(free)(ths->psi_index_g);
Y(free)(ths->psi_index_f);
Y(free)(ths->psi);
}
if (ths->flags & PRE_PSI)
Y(free)(ths->psi);
if(ths->flags & PRE_FG_PSI)
Y(free)(ths->psi);
if(ths->flags & PRE_LIN_PSI)
Y(free)(ths->psi);
if (ths->flags & PRE_PHI_HUT)
{
for (t = 0; t < ths->d; t++)
Y(free)(ths->c_phi_inv[t]);
Y(free)(ths->c_phi_inv);
}
if (ths->flags & MALLOC_F)
Y(free)(ths->f);
if(ths->flags & MALLOC_F_HAT)
Y(free)(ths->f_hat);
if (ths->flags & MALLOC_X)
Y(free)(ths->x);
WINDOW_HELP_FINALIZE;
Y(free)(ths->N);
Y(free)(ths->n);
Y(free)(ths->sigma);
Y(free)(ths->r2r_kind);
} /* finalize */
TIC
#define TIC(a)
Timing, method works since the inaccurate timer is updated mostly in the measured function...
Definition: infft.h:1397
PRE_FG_PSI
#define PRE_FG_PSI
Definition: nfft3.h:196
MALLOC_X
#define MALLOC_X
Definition: nfft3.h:199
MALLOC_F_HAT
#define MALLOC_F_HAT
Definition: nfft3.h:200
FFTW_INIT
#define FFTW_INIT
Definition: nfft3.h:203
MALLOC_F
#define MALLOC_F
Definition: nfft3.h:201
X
#define X(name)
Include header for C99 complex datatype.
Definition: fastsum.h:57
FFT_OUT_OF_PLACE
#define FFT_OUT_OF_PLACE
Definition: nfft3.h:202
PRE_LIN_PSI
#define PRE_LIN_PSI
Definition: nfft3.h:195
PRE_PSI
#define PRE_PSI
Definition: nfft3.h:197
PRE_FULL_PSI
#define PRE_FULL_PSI
Definition: nfft3.h:198
nfft3.h
Header file for the nfft3 library.
PRE_PHI_HUT
#define PRE_PHI_HUT
Definition: nfft3.h:193