/**
* Initialisation of a transform plan, guru.
*
* \arg ths The pointer to a fpt plan
* \arg N The number of source nodes
* \arg M The number of target nodes
* \arg sigma The parameter of the Gaussian
* \arg n The polynomial expansion degree
* \arg p the periodisation length, at least 1
* \arg m The spatial cut-off of the nfft
* \arg flags FGT flags to use
*
* \author Stefan Kunis
*/
void fgt_init_guru(fgt_plan *ths, int N, int M, double _Complex sigma, int n,
double p, int m, unsigned flags)
{
int j,n_fftw;
fftw_plan fplan;
ths->M = M;
ths->N = N;
ths->sigma = sigma;
ths->flags = flags;
ths->x = (double*)nfft_malloc(ths->N*sizeof(double));
ths->y = (double*)nfft_malloc(ths->M*sizeof(double));
ths->alpha = (double _Complex*)nfft_malloc(ths->N*sizeof(double _Complex));
ths->f = (double _Complex*)nfft_malloc(ths->M*sizeof(double _Complex));
ths->n = n;
ths->p = p;
ths->b = (double _Complex*)nfft_malloc(ths->n*sizeof(double _Complex));
ths->nplan1 = (nfft_plan*) nfft_malloc(sizeof(nfft_plan));
ths->nplan2 = (nfft_plan*) nfft_malloc(sizeof(nfft_plan));
n_fftw=X(next_power_of_2)(2*ths->n);
nfft_init_guru(ths->nplan1, 1, &(ths->n), ths->N, &n_fftw, m, PRE_PHI_HUT|
PRE_PSI| MALLOC_X| MALLOC_F_HAT| FFTW_INIT, FFTW_MEASURE);
nfft_init_guru(ths->nplan2, 1, &(ths->n), ths->M, &n_fftw, m, PRE_PHI_HUT|
PRE_PSI| MALLOC_X| FFTW_INIT, FFTW_MEASURE);
ths->nplan1->f = ths->alpha;
ths->nplan2->f_hat = ths->nplan1->f_hat;
ths->nplan2->f = ths->f;
if(ths->flags & FGT_APPROX_B)
{
fplan = fftw_plan_dft_1d(ths->n, ths->b, ths->b, FFTW_FORWARD,
FFTW_MEASURE);
for(j=0; j<ths->n; j++)
ths->b[j] = cexp(-ths->p*ths->p*ths->sigma*(j-ths->n/2)*(j-ths->n/2)/
((double)ths->n*ths->n)) / ths->n;
nfft_fftshift_complex(ths->b, 1, &ths->n);
fftw_execute(fplan);
nfft_fftshift_complex(ths->b, 1, &ths->n);
fftw_destroy_plan(fplan);
}
else
{
for(j=0; j<ths->n; j++)
ths->b[j] = 1.0/ths->p * csqrt(PI/ths->sigma)*
cexp(-PI*PI*(j-ths->n/2)*(j-ths->n/2)/
(ths->p*ths->p*ths->sigma));
}
}
/** precomputation for fastsum */
void fastsum_precompute(fastsum_plan *ths)
{
int j,k,t;
int n_total;
ticks t0, t1;
ths->MEASURE_TIME_t[0] = 0.0;
ths->MEASURE_TIME_t[1] = 0.0;
ths->MEASURE_TIME_t[2] = 0.0;
ths->MEASURE_TIME_t[3] = 0.0;
#ifdef MEASURE_TIME
t0 = getticks();
#endif
if (ths->flags & NEARFIELD_BOXES)
{
BuildBox(ths);
}
else
{
/** sort source knots */
BuildTree(ths->d,0,ths->x,ths->alpha,ths->N_total);
}
#ifdef MEASURE_TIME
t1 = getticks();
ths->MEASURE_TIME_t[3] += nfft_elapsed_seconds(t1,t0);
#endif
#ifdef MEASURE_TIME
t0 = getticks();
#endif
/** precompute spline values for near field*/
if (!(ths->flags & EXACT_NEARFIELD))
{
if (ths->d==1)
#pragma omp parallel for default(shared) private(k)
for (k=-ths->Ad/2-2; k <= ths->Ad/2+2; k++)
ths->Add[k+ths->Ad/2+2] = regkern1(ths->k, ths->eps_I*(double)k/ths->Ad*2, ths->p, ths->kernel_param, ths->eps_I, ths->eps_B);
else
#pragma omp parallel for default(shared) private(k)
for (k=0; k <= ths->Ad+2; k++)
ths->Add[k] = regkern3(ths->k, ths->eps_I*(double)k/ths->Ad, ths->p, ths->kernel_param, ths->eps_I, ths->eps_B);
}
#ifdef MEASURE_TIME
t1 = getticks();
ths->MEASURE_TIME_t[0] += nfft_elapsed_seconds(t1,t0);
#endif
#ifdef MEASURE_TIME
t0 = getticks();
#endif
/** init NFFT plan for transposed transform in first step*/
for (k=0; k<ths->mv1.M_total; k++)
for (t=0; t<ths->mv1.d; t++)
ths->mv1.x[ths->mv1.d*k+t] = - ths->x[ths->mv1.d*k+t]; /* note the factor -1 for transposed transform instead of adjoint*/
/** precompute psi, the entries of the matrix B */
if(ths->mv1.nfft_flags & PRE_LIN_PSI)
nfft_precompute_lin_psi(&(ths->mv1));
if(ths->mv1.nfft_flags & PRE_PSI)
nfft_precompute_psi(&(ths->mv1));
if(ths->mv1.nfft_flags & PRE_FULL_PSI)
nfft_precompute_full_psi(&(ths->mv1));
#ifdef MEASURE_TIME
t1 = getticks();
ths->MEASURE_TIME_t[1] += nfft_elapsed_seconds(t1,t0);
#endif
/** init Fourier coefficients */
for(k=0; k<ths->mv1.M_total;k++)
ths->mv1.f[k] = ths->alpha[k];
#ifdef MEASURE_TIME
t0 = getticks();
#endif
/** init NFFT plan for transform in third step*/
for (j=0; j<ths->mv2.M_total; j++)
for (t=0; t<ths->mv2.d; t++)
ths->mv2.x[ths->mv2.d*j+t] = - ths->y[ths->mv2.d*j+t]; /* note the factor -1 for conjugated transform instead of standard*/
/** precompute psi, the entries of the matrix B */
if(ths->mv2.nfft_flags & PRE_LIN_PSI)
nfft_precompute_lin_psi(&(ths->mv2));
if(ths->mv2.nfft_flags & PRE_PSI)
nfft_precompute_psi(&(ths->mv2));
if(ths->mv2.nfft_flags & PRE_FULL_PSI)
nfft_precompute_full_psi(&(ths->mv2));
#ifdef MEASURE_TIME
t1 = getticks();
ths->MEASURE_TIME_t[2] += nfft_elapsed_seconds(t1,t0);
#endif
#ifdef MEASURE_TIME
t0 = getticks();
#endif
/** precompute Fourier coefficients of regularised kernel*/
n_total = 1;
for (t=0; t<ths->d; t++)
n_total *= ths->n;
#pragma omp parallel for default(shared) private(j,k,t)
for (j=0; j<n_total; j++)
{
if (ths->d==1)
ths->b[j] = regkern1(ths->k, (double)j / (ths->n) - 0.5, ths->p, ths->kernel_param, ths->eps_I, ths->eps_B)/n_total;
else
{
k=j;
ths->b[j]=0.0;
for (t=0; t<ths->d; t++)
{
ths->b[j] += ((double)(k % (ths->n)) / (ths->n) - 0.5) * ((double)(k % (ths->n)) / (ths->n) - 0.5);
k = k / (ths->n);
}
ths->b[j] = regkern3(ths->k, sqrt(ths->b[j]), ths->p, ths->kernel_param, ths->eps_I, ths->eps_B)/n_total;
}
}
nfft_fftshift_complex(ths->b, ths->mv1.d, ths->mv1.N);
fftw_execute(ths->fft_plan);
nfft_fftshift_complex(ths->b, ths->mv1.d, ths->mv1.N);
#ifdef MEASURE_TIME
t1 = getticks();
ths->MEASURE_TIME_t[0] += nfft_elapsed_seconds(t1,t0);
#endif
}
/** computes the inverse discrete Radon transform of Rf
* on the grid given by gridfcn() with T angles and R offsets
* by a NFFT-based CG-type algorithm
*/
int Inverse_Radon_trafo(int (*gridfcn)(), int T, int S, double *Rf, int NN, double *f, int max_i)
{
int j,k; /**< index for nodes and freqencies */
nfft_plan my_nfft_plan; /**< plan for the nfft-2D */
solver_plan_complex my_infft_plan; /**< plan for the inverse nfft */
fftw_complex *fft; /**< variable for the fftw-1Ds */
fftw_plan my_fftw_plan; /**< plan for the fftw-1Ds */
int t,r; /**< index for directions and offsets */
double *x, *w; /**< knots and associated weights */
int l; /**< index for iterations */
int N[2],n[2];
int M=T*S;
N[0]=NN; n[0]=2*N[0];
N[1]=NN; n[1]=2*N[1];
fft = (fftw_complex *)nfft_malloc(S*sizeof(fftw_complex));
my_fftw_plan = fftw_plan_dft_1d(S,fft,fft,FFTW_FORWARD,FFTW_MEASURE);
x = (double *)nfft_malloc(2*T*S*(sizeof(double)));
if (x==NULL)
return -1;
w = (double *)nfft_malloc(T*S*(sizeof(double)));
if (w==NULL)
return -1;
/** init two dimensional NFFT plan */
nfft_init_guru(&my_nfft_plan, 2, N, M, n, 4,
PRE_PHI_HUT| PRE_PSI| MALLOC_X | MALLOC_F_HAT| MALLOC_F| FFTW_INIT | FFT_OUT_OF_PLACE,
FFTW_MEASURE| FFTW_DESTROY_INPUT);
/** init two dimensional infft plan */
solver_init_advanced_complex(&my_infft_plan,(nfft_mv_plan_complex*)(&my_nfft_plan), CGNR | PRECOMPUTE_WEIGHT);
/** init nodes and weights of grid*/
gridfcn(T,S,x,w);
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];
if (j%S)
my_infft_plan.w[j] = w[j];
else
my_infft_plan.w[j] = 0.0;
}
/** 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);
/** compute 1D-ffts and init given samples and weights */
for(t=0; t<T; t++)
{
/* for(r=0; r<R/2; r++)
fft[r] = cexp(I*KPI*r)*Rf[t*R+(r+R/2)];
for(r=0; r<R/2; r++)
fft[r+R/2] = cexp(I*KPI*r)*Rf[t*R+r];
*/
for(r=0; r<S; r++)
fft[r] = Rf[t*S+r] + _Complex_I*0.0;
nfft_fftshift_complex(fft, 1, &S);
fftw_execute(my_fftw_plan);
nfft_fftshift_complex(fft, 1, &S);
my_infft_plan.y[t*S] = 0.0;
for(r=-S/2+1; r<S/2; r++)
my_infft_plan.y[t*S+(r+S/2)] = fft[r+S/2]/KERNEL(r);
}
/** initialise some guess f_hat_0 */
for(k=0;k<my_nfft_plan.N_total;k++)
my_infft_plan.f_hat_iter[k] = 0.0 + _Complex_I*0.0;
/** solve the system */
solver_before_loop_complex(&my_infft_plan);
if (max_i<1)
{
l=1;
for(k=0;k<my_nfft_plan.N_total;k++)
my_infft_plan.f_hat_iter[k] = my_infft_plan.p_hat_iter[k];
}
else
{
for(l=1;l<=max_i;l++)
{
solver_loop_one_step_complex(&my_infft_plan);
/*if (sqrt(my_infft_plan.dot_r_iter)<=1e-12) break;*/
}
}
/*printf("after %d iteration(s): weighted 2-norm of original residual vector = %g\n",l-1,sqrt(my_infft_plan.dot_r_iter));*/
/** copy result */
for(k=0;k<my_nfft_plan.N_total;k++)
f[k] = creal(my_infft_plan.f_hat_iter[k]);
/** finalise the plans and free the variables */
fftw_destroy_plan(my_fftw_plan);
nfft_free(fft);
solver_finalize_complex(&my_infft_plan);
nfft_finalize(&my_nfft_plan);
nfft_free(x);
nfft_free(w);
return 0;
}
