/**
* Simple example that computes fast and discrete Gauss transforms.
*
* \arg ths The pointer to the fgt plan
* \arg sigma The parameter of the Gaussian
* \arg eps The target accuracy
*
* \author Stefan Kunis
*/
void fgt_test_simple(int N, int M, double _Complex sigma, double eps)
{
fgt_plan my_plan;
double _Complex *swap_dgt;
fgt_init(&my_plan, N, M, sigma, eps);
swap_dgt = (double _Complex*)nfft_malloc(my_plan.M*sizeof(double _Complex));
fgt_test_init_rand(&my_plan);
fgt_init_node_dependent(&my_plan);
NFFT_SWAP_complex(swap_dgt,my_plan.f);
dgt_trafo(&my_plan);
nfft_vpr_complex(my_plan.f,my_plan.M,"discrete gauss transform");
NFFT_SWAP_complex(swap_dgt,my_plan.f);
fgt_trafo(&my_plan);
nfft_vpr_complex(my_plan.f,my_plan.M,"fast gauss transform");
printf("\n relative error: %1.3e\n", X(error_l_infty_1_complex)(swap_dgt,
my_plan.f, my_plan.M, my_plan.alpha, my_plan.N));
nfft_free(swap_dgt);
fgt_finalize(&my_plan);
}
static void simple_test_nsfft(int d, int J, int M)
{
int K=12;
nsfft_plan p;
nsfft_init(&p, d, J, M, 6, NSDFT);
nsfft_init_random_nodes_coeffs(&p);
nfft_vpr_complex(p.f_hat, K, "frequencies, vector f_hat (first few entries)");
/** direct trafo and show the result */
nsfft_trafo_direct(&p);
nfft_vpr_complex(p.f, K, "nsdft, vector f (first few entries)");
/** approx. trafo and show the result */
nsfft_trafo(&p);
nfft_vpr_complex(p.f, K, "nsfft, vector f (first few entries)");
/** direct adjoint and show the result */
nsfft_adjoint_direct(&p);
nfft_vpr_complex(p.f_hat, K, "adjoint nsdft, vector f_hat, (first few entries)");
/** approx. adjoint and show the result */
nsfft_adjoint(&p);
nfft_vpr_complex(p.f_hat, K, "adjoint nsfft, vector f_hat, (first few entries)");
/** finalise the one dimensional plan */
nsfft_finalize(&p);
}
static void simple_test_nnfft_2d(void)
{
int j,k; /**< index for nodes and freqencies */
nnfft_plan my_plan; /**< plan for the nfft */
int N[2];
N[0]=12;
N[1]=14;
/** init an one dimensional plan */
nnfft_init(&my_plan, 2,12*14,19, N);
/** init pseudo random nodes */
for(j=0;j<my_plan.M_total;j++)
{
my_plan.x[2*j]=((double)rand())/((double)RAND_MAX)-0.5;
my_plan.x[2*j+1]=((double)rand())/((double)RAND_MAX)-0.5;
}
/** init pseudo random nodes */
for(j=0;j<my_plan.N_total;j++)
{
my_plan.v[2*j]=((double)rand())/((double)RAND_MAX)-0.5;
my_plan.v[2*j+1]=((double)rand())/((double)RAND_MAX)-0.5;
}
/** precompute psi, the entries of the matrix B */
if(my_plan.nnfft_flags & PRE_PSI)
nnfft_precompute_psi(&my_plan);
if(my_plan.nnfft_flags & PRE_FULL_PSI)
nnfft_precompute_full_psi(&my_plan);
if(my_plan.nnfft_flags & PRE_LIN_PSI)
nnfft_precompute_lin_psi(&my_plan);
/** precompute phi_hut, the entries of the matrix D */
if(my_plan.nnfft_flags & PRE_PHI_HUT)
nnfft_precompute_phi_hut(&my_plan);
/** init pseudo random Fourier coefficients and show them */
for(k=0;k<my_plan.N_total;k++)
my_plan.f_hat[k] = ((double)rand())/((double)RAND_MAX) + _Complex_I*((double)rand())/((double)RAND_MAX);
nfft_vpr_complex(my_plan.f_hat,12,
"given Fourier coefficients, vector f_hat (first 12 entries)");
/** direct trafo and show the result */
nnfft_trafo_direct(&my_plan);
nfft_vpr_complex(my_plan.f,my_plan.M_total,"ndft, vector f");
/** approx. trafo and show the result */
nnfft_trafo(&my_plan);
nfft_vpr_complex(my_plan.f,my_plan.M_total,"nfft, vector f");
/** finalise the one dimensional plan */
nnfft_finalize(&my_plan);
}
static void simple_test_adjoint_nnfft_1d(void)
{
int j; /**< index for nodes and freqencies */
nnfft_plan my_plan; /**< plan for the nfft */
int N[1];
N[0]=12;
/** init an one dimensional plan */
nnfft_init(&my_plan, 1, 20, 33, N);
/** init pseudo random nodes */
for(j=0;j<my_plan.M_total;j++)
{
my_plan.x[j]=((double)rand())/((double)RAND_MAX)-0.5;
}
/** init pseudo random nodes */
for(j=0;j<my_plan.N_total;j++)
{
my_plan.v[j]=((double)rand())/((double)RAND_MAX)-0.5;
}
/** precompute psi, the entries of the matrix B */
if(my_plan.nnfft_flags & PRE_PSI)
nnfft_precompute_psi(&my_plan);
if(my_plan.nnfft_flags & PRE_FULL_PSI)
nnfft_precompute_full_psi(&my_plan);
if(my_plan.nnfft_flags & PRE_LIN_PSI)
nnfft_precompute_lin_psi(&my_plan);
/** precompute phi_hut, the entries of the matrix D */
if(my_plan.nnfft_flags & PRE_PHI_HUT)
nnfft_precompute_phi_hut(&my_plan);
/** init pseudo random Fourier coefficients and show them */
for(j=0;j<my_plan.M_total;j++)
my_plan.f[j] = ((double)rand())/((double)RAND_MAX) + _Complex_I*((double)rand())/((double)RAND_MAX);
nfft_vpr_complex(my_plan.f,my_plan.M_total,"given Samples, vector f");
/** direct trafo and show the result */
nnfft_adjoint_direct(&my_plan);
nfft_vpr_complex(my_plan.f_hat,my_plan.N_total,"adjoint nndft, vector f_hat");
/** approx. trafo and show the result */
nnfft_adjoint(&my_plan);
nfft_vpr_complex(my_plan.f_hat,my_plan.N_total,"adjoint nnfft, vector f_hat");
/** finalise the one dimensional plan */
nnfft_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);
}
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);
}
static void simple_test_innfft_1d(void)
{
int j,k,l,N=8; /**< index for nodes, freqencies, iter*/
nnfft_plan my_plan; /**< plan for the nnfft */
solver_plan_complex my_iplan; /**< plan for the inverse nnfft */
/** initialise an one dimensional plan */
nnfft_init(&my_plan,1 ,8 ,8 ,&N);
/** initialise my_iplan */
solver_init_advanced_complex(&my_iplan,(nfft_mv_plan_complex*)(&my_plan),CGNR);
/** init pseudo random nodes */
for(j=0;j<my_plan.M_total;j++)
my_plan.x[j]=((double)rand())/((double)RAND_MAX)-0.5;
/** init pseudo random nodes */
for(k=0;k<my_plan.N_total;k++)
my_plan.v[k]=((double)rand())/((double)RAND_MAX)-0.5;
/** precompute psi, the entries of the matrix B */
if(my_plan.nnfft_flags & PRE_PSI)
nnfft_precompute_psi(&my_plan);
if(my_plan.nnfft_flags & PRE_FULL_PSI)
nnfft_precompute_full_psi(&my_plan);
/** precompute phi_hut, the entries of the matrix D */
if(my_plan.nnfft_flags & PRE_PHI_HUT)
nnfft_precompute_phi_hut(&my_plan);
/** init pseudo random samples (real) and show them */
for(j=0;j<my_plan.M_total;j++)
my_iplan.y[j] = ((double)rand())/((double)RAND_MAX);
nfft_vpr_complex(my_iplan.y,my_plan.M_total,"given data, vector given_f");
/** initialise some guess f_hat_0 */
for(k=0;k<my_plan.N_total;k++)
my_iplan.f_hat_iter[k] = 0.0;
nfft_vpr_complex(my_iplan.f_hat_iter,my_plan.N_total,
"approximate solution, vector f_hat_iter");
/** solve the system */
solver_before_loop_complex(&my_iplan);
for(l=0;l<8;l++)
{
printf("iteration l=%d\n",l);
solver_loop_one_step_complex(&my_iplan);
nfft_vpr_complex(my_iplan.f_hat_iter,my_plan.N_total,
"approximate solution, vector f_hat_iter");
CSWAP(my_iplan.f_hat_iter,my_plan.f_hat);
nnfft_trafo(&my_plan);
nfft_vpr_complex(my_plan.f,my_plan.M_total,"fitting the data, vector f");
CSWAP(my_iplan.f_hat_iter,my_plan.f_hat);
}
solver_finalize_complex(&my_iplan);
nnfft_finalize(&my_plan);
}