static void construct(char * file, int N, int M, int Z)
{
int j,k,l; /* some variables */
double real;
nfft_plan my_plan; /* plan for the three dimensional nfft */
FILE* fp,*fk;
int my_N[3],my_n[3]; /* to init the nfft */
/* initialise my_plan */
//nfft_init_3d(&my_plan,Z,N,N,M);
my_N[0]=Z; my_n[0]=ceil(Z*1.2);
my_N[1]=N; my_n[1]=ceil(N*1.2);
my_N[2]=N; my_n[2]=ceil(N*1.2);
nfft_init_guru(&my_plan, 3, my_N, M, my_n, 6,
PRE_PHI_HUT| PRE_PSI |MALLOC_X| MALLOC_F_HAT|
MALLOC_F| FFTW_INIT| FFT_OUT_OF_PLACE,
FFTW_MEASURE| FFTW_DESTROY_INPUT);
fp=fopen("knots.dat","r");
for(j=0;j<M;j++)
fscanf(fp,"%le %le %le",&my_plan.x[3*(j)+1],
&my_plan.x[3*(j)+2],&my_plan.x[3*(j)+0]);
fclose(fp);
fp=fopen("input_f.dat","r");
fk=fopen(file,"w");
for(l=0;l<Z;l++) {
for(j=0;j<N;j++)
{
for(k=0;k<N;k++)
{
//fscanf(fp,"%le ",&my_plan.f_hat[(N*N*(Z-l)+N*j+k+N*N*Z/2)%(N*N*Z)][0]);
fscanf(fp,"%le ",&real);
my_plan.f_hat[(N*N*l+N*j+k)] = real;
}
}
}
if(my_plan.nfft_flags & PRE_PSI)
nfft_precompute_psi(&my_plan);
nfft_trafo(&my_plan);
for(j=0;j<my_plan.M_total;j++)
fprintf(fk,"%le %le %le %le %le\n",my_plan.x[3*j+1],
my_plan.x[3*j+2],my_plan.x[3*j+0],creal(my_plan.f[j]),cimag(my_plan.f[j]));
fclose(fk);
fclose(fp);
nfft_finalize(&my_plan);
}
static void simple_test_nfft_1d(void)
{
nfft_plan p;
double t;
int N=14;
int M=19;
ticks t0, t1;
/** init an one dimensional plan */
nfft_init_1d(&p,N,M);
/** init pseudo random nodes */
nfft_vrand_shifted_unit_double(p.x,p.M_total);
/** precompute psi, the entries of the matrix B */
if(p.nfft_flags & PRE_ONE_PSI)
nfft_precompute_one_psi(&p);
/** init pseudo random Fourier coefficients and show them */
nfft_vrand_unit_complex(p.f_hat,p.N_total);
nfft_vpr_complex(p.f_hat,p.N_total,"given Fourier coefficients, vector f_hat");
/** direct trafo and show the result */
t0 = getticks();
nfft_trafo_direct(&p);
t1 = getticks();
t = nfft_elapsed_seconds(t1,t0);
nfft_vpr_complex(p.f,p.M_total,"ndft, vector f");
printf(" took %e seconds.\n",t);
/** approx. trafo and show the result */
nfft_trafo(&p);
nfft_vpr_complex(p.f,p.M_total,"nfft, vector f");
/** approx. adjoint and show the result */
nfft_adjoint_direct(&p);
nfft_vpr_complex(p.f_hat,p.N_total,"adjoint ndft, vector f_hat");
/** approx. adjoint and show the result */
nfft_adjoint(&p);
nfft_vpr_complex(p.f_hat,p.N_total,"adjoint nfft, vector f_hat");
/** finalise the one dimensional plan */
nfft_finalize(&p);
}
/**
* construct makes an 2d-nfft for every slice
*/
static void construct(char * file, int N, int M, int Z, fftw_complex *mem)
{
int j,z; /* some variables */
double tmp; /* a placeholder */
nfft_plan my_plan; /* plan for the two dimensional nfft */
FILE* fp;
/* initialise my_plan */
nfft_init_2d(&my_plan,N,N,M/Z);
fp=fopen("knots.dat","r");
for(j=0;j<my_plan.M_total;j++)
{
fscanf(fp,"%le %le %le",&my_plan.x[2*j+0],&my_plan.x[2*j+1],&tmp);
}
fclose(fp);
fp=fopen(file,"w");
for(z=0;z<Z;z++) {
tmp = (double) z;
for(j=0;j<N*N;j++)
my_plan.f_hat[j] = mem[(z*N*N+N*N*Z/2+j)%(N*N*Z)];
if(my_plan.flags & PRE_PSI)
nfft_precompute_psi(&my_plan);
nfft_trafo(&my_plan);
for(j=0;j<my_plan.M_total;j++)
{
fprintf(fp,"%le %le %le %le %le\n",my_plan.x[2*j+0],my_plan.x[2*j+1],tmp/Z-0.5,
creal(my_plan.f[j]),cimag(my_plan.f[j]));
}
}
fclose(fp);
nfft_finalize(&my_plan);
}
/**
* Executes the fast Gauss transform.
*
* \arg ths The pointer to a fgt plan
*
* \author Stefan Kunis
*/
void fgt_trafo(fgt_plan *ths)
{
int l;
if(ths->flags & FGT_NDFT)
{
nfft_adjoint_direct(ths->nplan1);
for(l=0; l<ths->n; l++)
ths->nplan1->f_hat[l] *= ths->b[l];
nfft_trafo_direct(ths->nplan2);
}
else
{
nfft_adjoint(ths->nplan1);
for(l=0; l<ths->n; l++)
ths->nplan1->f_hat[l] *= ths->b[l];
nfft_trafo(ths->nplan2);
}
}
void // frequency to space
mad_cmat_infft (const cnum_t x[], const num_t r_node[], cnum_t r[], ssz_t m, ssz_t n, ssz_t nx)
{
assert( x && r );
int precomp = 0;
if (m != p_n1 || n != p_n2 || nx != p_m) {
nfft_finalize(&p);
nfft_init_2d (&p, m, n, nx);
p_n1 = m, p_n2 = n, p_m = nx, precomp = 1;
}
if (r_node || precomp) {
for (ssz_t i=0; i < m*n; i++) // forward transform needs -r_node
p.x[i] = r_node[i] == -0.5 ? 0.4999999999999999 : -r_node[i];
if(p.flags & PRE_ONE_PSI) nfft_precompute_one_psi(&p);
}
// mad_cvec_copy(x, p.f_hat, nx);
mad_cvec_copy(x+nx/2, p.f_hat, nx/2); // for compatibility with FFTW ?? (TBC)
mad_cvec_copy(x, p.f_hat+nx/2, nx/2);
const char *error_str = nfft_check(&p);
if (error_str) error("%s", error_str);
nfft_trafo(&p); // nfft_trafo_direct(&p);
mad_cvec_copy(p.f, r, m*n);
mad_cvec_muln(r, 1.0/(m*n), r, m*n);
}
/** Reconstruction routine with cross validation */
static void glacier_cv(int N,int M,int M_cv,unsigned solver_flags)
{
int j,k,k0,k1,l,my_N[2],my_n[2];
double tmp_y,r;
nfft_plan p,cp;
solver_plan_complex ip;
double _Complex* cp_y;
FILE* fp;
int M_re=M-M_cv;
/* initialise p for reconstruction */
my_N[0]=N; my_n[0]=X(next_power_of_2)(N);
my_N[1]=N; my_n[1]=X(next_power_of_2)(N);
nfft_init_guru(&p, 2, my_N, M_re, my_n, 6,
PRE_PHI_HUT| PRE_FULL_PSI|
MALLOC_X| MALLOC_F_HAT| MALLOC_F|
FFTW_INIT| FFT_OUT_OF_PLACE,
FFTW_MEASURE| FFTW_DESTROY_INPUT);
/* initialise ip, specific */
solver_init_advanced_complex(&ip,(nfft_mv_plan_complex*)(&p), solver_flags);
/* initialise cp for validation */
cp_y = (double _Complex*) nfft_malloc(M*sizeof(double _Complex));
nfft_init_guru(&cp, 2, my_N, M, my_n, 6,
PRE_PHI_HUT| PRE_FULL_PSI|
MALLOC_X| MALLOC_F|
FFTW_INIT| FFT_OUT_OF_PLACE,
FFTW_MEASURE| FFTW_DESTROY_INPUT);
cp.f_hat=ip.f_hat_iter;
/* set up data in cp and cp_y */
fp=fopen("input_data.dat","r");
for(j=0;j<cp.M_total;j++)
{
fscanf(fp,"%le %le %le",&cp.x[2*j+0],&cp.x[2*j+1],&tmp_y);
cp_y[j]=tmp_y;
}
fclose(fp);
/* copy part of the data to p and ip */
for(j=0;j<p.M_total;j++)
{
p.x[2*j+0]=cp.x[2*j+0];
p.x[2*j+1]=cp.x[2*j+1];
ip.y[j]=tmp_y;
}
/* precompute psi */
if(p.nfft_flags & PRE_ONE_PSI)
nfft_precompute_one_psi(&p);
/* precompute psi */
if(cp.nfft_flags & PRE_ONE_PSI)
nfft_precompute_one_psi(&cp);
/* initialise damping factors */
if(ip.flags & PRECOMPUTE_DAMP)
for(k0=0;k0<p.N[0];k0++)
for(k1=0;k1<p.N[1];k1++)
ip.w_hat[k0*p.N[1]+k1]=
my_weight(((double)(k0-p.N[0]/2))/p.N[0],0.5,3,0.001)*
my_weight(((double)(k1-p.N[1]/2))/p.N[1],0.5,3,0.001);
/* init some guess */
for(k=0;k<p.N_total;k++)
ip.f_hat_iter[k]=0;
/* inverse trafo */
solver_before_loop_complex(&ip);
// fprintf(stderr,"iteration starts,\t");
for(l=0;l<40;l++)
solver_loop_one_step_complex(&ip);
//fprintf(stderr,"r=%1.2e, ",sqrt(ip.dot_r_iter)/M_re);
NFFT_SWAP_complex(p.f_hat,ip.f_hat_iter);
nfft_trafo(&p);
NFFT_SWAP_complex(p.f_hat,ip.f_hat_iter);
nfft_upd_axpy_complex(p.f,-1,ip.y,M_re);
r=sqrt(nfft_dot_complex(p.f,M_re)/nfft_dot_complex(cp_y,M));
fprintf(stderr,"r=%1.2e, ",r);
printf("$%1.1e$ & ",r);
nfft_trafo(&cp);
nfft_upd_axpy_complex(&cp.f[M_re],-1,&cp_y[M_re],M_cv);
r=sqrt(nfft_dot_complex(&cp.f[M_re],M_cv)/nfft_dot_complex(cp_y,M));
fprintf(stderr,"r_1=%1.2e\t",r);
printf("$%1.1e$ & ",r);
nfft_finalize(&cp);
solver_finalize_complex(&ip);
nfft_finalize(&p);
}
/** fast NFFT-based summation */
void fastsum_trafo(fastsum_plan *ths)
{
int j,k,t;
ticks t0, t1;
ths->MEASURE_TIME_t[4] = 0.0;
ths->MEASURE_TIME_t[5] = 0.0;
ths->MEASURE_TIME_t[6] = 0.0;
ths->MEASURE_TIME_t[7] = 0.0;
#ifdef MEASURE_TIME
t0 = getticks();
#endif
/** first step of algorithm */
nfft_adjoint(&(ths->mv1));
#ifdef MEASURE_TIME
t1 = getticks();
ths->MEASURE_TIME_t[4] += nfft_elapsed_seconds(t1,t0);
#endif
#ifdef MEASURE_TIME
t0 = getticks();
#endif
/** second step of algorithm */
#pragma omp parallel for default(shared) private(k)
for (k=0; k<ths->mv2.N_total; k++)
ths->mv2.f_hat[k] = ths->b[k] * ths->mv1.f_hat[k];
#ifdef MEASURE_TIME
t1 = getticks();
ths->MEASURE_TIME_t[5] += nfft_elapsed_seconds(t1,t0);
#endif
#ifdef MEASURE_TIME
t0 = getticks();
#endif
/** third step of algorithm */
nfft_trafo(&(ths->mv2));
#ifdef MEASURE_TIME
t1 = getticks();
ths->MEASURE_TIME_t[6] += nfft_elapsed_seconds(t1,t0);
#endif
#ifdef MEASURE_TIME
t0 = getticks();
#endif
/** add near field */
#pragma omp parallel for default(shared) private(j,k,t)
for (j=0; j<ths->M_total; j++)
{
double ymin[ths->d], ymax[ths->d]; /** limits for d-dimensional near field box */
if (ths->flags & NEARFIELD_BOXES)
{
ths->f[j] = ths->mv2.f[j] + SearchBox(ths->y + ths->d*j, ths);
}
else
{
for (t=0; t<ths->d; t++)
{
ymin[t] = ths->y[ths->d*j+t] - ths->eps_I;
ymax[t] = ths->y[ths->d*j+t] + ths->eps_I;
}
ths->f[j] = ths->mv2.f[j] + SearchTree(ths->d,0, ths->x, ths->alpha, ymin, ymax, ths->N_total, ths->k, ths->kernel_param, ths->Ad, ths->Add, ths->p, ths->flags);
}
/* ths->f[j] = ths->mv2.f[j]; */
/* ths->f[j] = SearchTree(ths->d,0, ths->x, ths->alpha, ymin, ymax, ths->N_total, ths->k, ths->kernel_param, ths->Ad, ths->Add, ths->p, ths->flags); */
}
#ifdef MEASURE_TIME
t1 = getticks();
ths->MEASURE_TIME_t[7] += nfft_elapsed_seconds(t1,t0);
#endif
}
void FC_FUNC(oct_nfft_trafo,OCT_NFFT_TRAFO)
(nfft_plan *ths)
{
nfft_trafo (ths);
}
static void simple_test_nfft_2d(void)
{
int K,N[2],n[2],M;
double t;
ticks t0, t1;
nfft_plan p;
N[0]=32; n[0]=64;
N[1]=14; n[1]=32;
M=N[0]*N[1];
K=16;
t0 = getticks();
/** init a two dimensional plan */
nfft_init_guru(&p, 2, N, M, n, 7,
PRE_PHI_HUT| PRE_FULL_PSI| MALLOC_F_HAT| MALLOC_X| MALLOC_F |
FFTW_INIT| FFT_OUT_OF_PLACE,
FFTW_ESTIMATE| FFTW_DESTROY_INPUT);
/** init pseudo random nodes */
nfft_vrand_shifted_unit_double(p.x,p.d*p.M_total);
/** precompute psi, the entries of the matrix B */
if(p.nfft_flags & PRE_ONE_PSI)
nfft_precompute_one_psi(&p);
/** init pseudo random Fourier coefficients and show them */
nfft_vrand_unit_complex(p.f_hat,p.N_total);
t1 = getticks();
t = nfft_elapsed_seconds(t1,t0);
nfft_vpr_complex(p.f_hat,K,
"given Fourier coefficients, vector f_hat (first few entries)");
printf(" ... initialisation took %e seconds.\n",t);
/** direct trafo and show the result */
t0 = getticks();
nfft_trafo_direct(&p);
t1 = getticks();
t = nfft_elapsed_seconds(t1,t0);
nfft_vpr_complex(p.f,K,"ndft, vector f (first few entries)");
printf(" took %e seconds.\n",t);
/** approx. trafo and show the result */
t0 = getticks();
nfft_trafo(&p);
t1 = getticks();
t = nfft_elapsed_seconds(t1,t0);
nfft_vpr_complex(p.f,K,"nfft, vector f (first few entries)");
printf(" took %e seconds.\n",t);
/** direct adjoint and show the result */
t0 = getticks();
nfft_adjoint_direct(&p);
t1 = getticks();
t = nfft_elapsed_seconds(t1,t0);
nfft_vpr_complex(p.f_hat,K,"adjoint ndft, vector f_hat (first few entries)");
printf(" took %e seconds.\n",t);
/** approx. adjoint and show the result */
t0 = getticks();
nfft_adjoint(&p);
t1 = getticks();
t = nfft_elapsed_seconds(t1,t0);
nfft_vpr_complex(p.f_hat,K,"adjoint nfft, vector f_hat (first few entries)");
printf(" took %e seconds.\n",t);
/** finalise the two dimensional plan */
nfft_finalize(&p);
}
/** NFFT-based mpolar FFT */
static int mpolar_fft(fftw_complex *f_hat, int NN, fftw_complex *f, int T, int R, int m)
{
ticks t0, t1;
int j,k; /**< index for nodes and freqencies */
nfft_plan my_nfft_plan; /**< plan for the nfft-2D */
double *x, *w; /**< knots and associated weights */
int N[2],n[2];
int M; /**< number of knots */
N[0]=NN; n[0]=2*N[0]; /**< oversampling factor sigma=2 */
N[1]=NN; n[1]=2*N[1]; /**< oversampling factor sigma=2 */
x = (double *)nfft_malloc(5*T*R/2*(sizeof(double)));
if (x==NULL)
return -1;
w = (double *)nfft_malloc(5*T*R/4*(sizeof(double)));
if (w==NULL)
return -1;
/** init two dimensional NFFT plan */
M=mpolar_grid(T,R,x,w);
nfft_init_guru(&my_nfft_plan, 2, N, M, n, m,
PRE_PHI_HUT| PRE_PSI| MALLOC_X | MALLOC_F_HAT| MALLOC_F| FFTW_INIT | FFT_OUT_OF_PLACE,
FFTW_MEASURE| FFTW_DESTROY_INPUT);
/** init nodes from mpolar grid*/
for(j=0;j<my_nfft_plan.M_total;j++)
{
my_nfft_plan.x[2*j+0] = x[2*j+0];
my_nfft_plan.x[2*j+1] = x[2*j+1];
}
/** precompute psi, the entries of the matrix B */
if(my_nfft_plan.nfft_flags & PRE_LIN_PSI)
nfft_precompute_lin_psi(&my_nfft_plan);
if(my_nfft_plan.nfft_flags & PRE_PSI)
nfft_precompute_psi(&my_nfft_plan);
if(my_nfft_plan.nfft_flags & PRE_FULL_PSI)
nfft_precompute_full_psi(&my_nfft_plan);
/** init Fourier coefficients from given image */
for(k=0;k<my_nfft_plan.N_total;k++)
my_nfft_plan.f_hat[k] = f_hat[k];
t0 = getticks();
/** NFFT-2D */
nfft_trafo(&my_nfft_plan);
t1 = getticks();
GLOBAL_elapsed_time = nfft_elapsed_seconds(t1,t0);
/** copy result */
for(j=0;j<my_nfft_plan.M_total;j++)
f[j] = my_nfft_plan.f[j];
/** finalise the plans and free the variables */
nfft_finalize(&my_nfft_plan);
nfft_free(x);
nfft_free(w);
return EXIT_SUCCESS;
}
static PyObject *nfft(PyObject *self, PyObject *args, PyObject *kwargs)
{
PyObject *in_obj, *coord_obj;
static char *kwlist[] = {"real_space", "coordinates", NULL};
if (!PyArg_ParseTupleAndKeywords(args, kwargs, "OO", kwlist, &in_obj, &coord_obj)) {
return NULL;
}
PyObject *coord_array = PyArray_FROM_OTF(coord_obj, NPY_DOUBLE, NPY_IN_ARRAY);
PyObject *in_array = PyArray_FROM_OTF(in_obj, NPY_COMPLEX128, NPY_IN_ARRAY);
if (coord_array == NULL || in_array == NULL) {
Py_XDECREF(coord_array);
Py_XDECREF(in_array);
return NULL;
}
int ndim = PyArray_NDIM(in_array);
if (ndim <= 0) {
PyErr_SetString(PyExc_ValueError, "Input array can't be 0 dimensional\n");
return NULL;
}
if ((PyArray_NDIM(coord_array) != 2 || PyArray_DIM(coord_array, 1) != ndim) && (ndim != 1 || PyArray_NDIM(coord_array) != 1)) {
PyErr_SetString(PyExc_ValueError, "Coordinates must be given as array of dimensions [NUMBER_OF_POINTS, NUMBER_OF_DIMENSIONS] of [NUMBER_OF_POINTS for 1D transforms.\n");
Py_XDECREF(coord_array);
Py_XDECREF(in_array);
return NULL;
}
int number_of_points = (int) PyArray_DIM(coord_array, 0);
nfft_plan my_plan;
int total_number_of_pixels = 1;
int dims[ndim];
int dim;
for (dim = 0; dim < ndim; ++dim) {
dims[dim] = (int)PyArray_DIM(in_array, dim);
total_number_of_pixels *= dims[dim];
}
#if defined(ENABLE_THREADS)
printf("OMP_NUM_THREADS=%s\n",getenv("OMP_NUM_THREADS"));
printf("nthreads = %d\n", nfft_get_num_threads());
fftw_init_threads();
#endif
nfft_init(&my_plan, ndim, dims, number_of_points);
memcpy(my_plan.f_hat, PyArray_DATA(in_array), total_number_of_pixels*sizeof(fftw_complex));
memcpy(my_plan.x, PyArray_DATA(coord_array), ndim*number_of_points*sizeof(double));
if (my_plan.nfft_flags &PRE_PSI) {
nfft_precompute_one_psi(&my_plan);
}
nfft_trafo(&my_plan);
int out_dim[] = {number_of_points};
PyObject *out_array = (PyObject *)PyArray_FromDims(1, out_dim, NPY_COMPLEX128);
memcpy(PyArray_DATA(out_array), my_plan.f, number_of_points*sizeof(fftw_complex));
// Clean up memory
nfft_finalize(&my_plan);
#if defined(ENABLE_THREADS)
fftw_cleanup_threads();
#endif
Py_XDECREF(coord_array);
Py_XDECREF(in_array);
return out_array;
}
void bench_openmp(FILE *infile, int m, int psi_flag)
{
nfft_plan p;
int *N;
int *n;
int M, d, trafo_adjoint;
int t, j;
double re,im;
ticks t0, t1;
double tt_total, tt_preonepsi;
fscanf(infile, "%d %d", &d, &trafo_adjoint);
N = malloc(d*sizeof(int));
n = malloc(d*sizeof(int));
for (t=0; t<d; t++)
fscanf(infile, "%d", N+t);
for (t=0; t<d; t++)
fscanf(infile, "%d", n+t);
fscanf(infile, "%d", &M);
#ifdef _OPENMP
fftw_import_wisdom_from_filename("nfft_benchomp_detail_threads.plan");
#else
fftw_import_wisdom_from_filename("nfft_benchomp_detail_single.plan");
#endif
/** init an d-dimensional plan */
nfft_init_guru(&p, d, N, M, n, m,
PRE_PHI_HUT| psi_flag | MALLOC_X | MALLOC_F_HAT| MALLOC_F| FFTW_INIT | FFT_OUT_OF_PLACE,
FFTW_MEASURE| FFTW_DESTROY_INPUT);
#ifdef _OPENMP
fftw_export_wisdom_to_filename("nfft_benchomp_detail_threads.plan");
#else
fftw_export_wisdom_to_filename("nfft_benchomp_detail_single.plan");
#endif
for (j=0; j < p.M_total; j++)
{
for (t=0; t < p.d; t++)
fscanf(infile, "%lg", p.x+p.d*j+t);
}
if (trafo_adjoint==0)
{
for (j=0; j < p.N_total; j++)
{
fscanf(infile, "%lg %lg", &re, &im);
p.f_hat[j] = re + _Complex_I * im;
}
}
else
{
for (j=0; j < p.M_total; j++)
{
fscanf(infile, "%lg %lg", &re, &im);
p.f[j] = re + _Complex_I * im;
}
}
t0 = getticks();
/** precompute psi, the entries of the matrix B */
if(p.nfft_flags & PRE_ONE_PSI)
nfft_precompute_one_psi(&p);
t1 = getticks();
tt_preonepsi = nfft_elapsed_seconds(t1,t0);
if (trafo_adjoint==0)
nfft_trafo(&p);
else
nfft_adjoint(&p);
t1 = getticks();
tt_total = nfft_elapsed_seconds(t1,t0);
#ifndef MEASURE_TIME
p.MEASURE_TIME_t[0] = 0.0;
p.MEASURE_TIME_t[2] = 0.0;
#endif
#ifndef MEASURE_TIME_FFTW
p.MEASURE_TIME_t[1] = 0.0;
#endif
printf("%.6e %.6e %6e %.6e %.6e %.6e\n", tt_preonepsi, p.MEASURE_TIME_t[0], p.MEASURE_TIME_t[1], p.MEASURE_TIME_t[2], tt_total-tt_preonepsi-p.MEASURE_TIME_t[0]-p.MEASURE_TIME_t[1]-p.MEASURE_TIME_t[2], tt_total);
// printf("%.6e\n", tt);
free(N);
free(n);
/** finalise the one dimensional plan */
nfft_finalize(&p);
}
