static void simple_test_nfct_1d(void)
{
NFCT(plan) p;
const char *error_str;
int N = 14;
int M = 19;
/** init an one dimensional plan */
NFCT(init_1d)(&p,N,M);
/** init pseudo random nodes */
NFFT(vrand_real)(p.x, p.M_total, NFFT_K(0.0), NFFT_K(0.5));
/** precompute psi, the entries of the matrix B */
if( p.flags & PRE_ONE_PSI)
NFCT(precompute_one_psi)(&p);
/** init pseudo random Fourier coefficients and show them */
NFFT(vrand_real)(p.f_hat, p.N_total, NFFT_K(0.0), NFFT_K(1.0));
NFFT(vpr_double)(p.f_hat,p.N_total,"given Fourier coefficients, vector f_hat");
/** check for valid parameters before calling any trafo/adjoint method */
error_str = NFCT(check)(&p);
if (error_str != 0)
{
printf("Error in nfct module: %s\n", error_str);
return;
}
/** direct trafo and show the result */
NFCT(trafo_direct)(&p);
NFFT(vpr_double)(p.f,p.M_total,"ndct, vector f");
/** approx. trafo and show the result */
NFCT(trafo)(&p);
NFFT(vpr_double)(p.f,p.M_total,"nfct, vector f");
/** approx. adjoint and show the result */
NFCT(adjoint_direct)(&p);
NFFT(vpr_double)(p.f_hat,p.N_total,"adjoint ndct, vector f_hat");
/** approx. adjoint and show the result */
NFCT(adjoint)(&p);
NFFT(vpr_double)(p.f_hat,p.N_total,"adjoint nfct, vector f_hat");
/** finalise the one dimensional plan */
NFCT(finalize)(&p);
}
/** generates the points x with weights w
* for the linogram grid with T slopes and R offsets
*/
static int linogram_grid(int T, int S, NFFT_R *x, NFFT_R *w)
{
int t, r;
NFFT_R W = (NFFT_R) T * (((NFFT_R) S / NFFT_K(2.0)) * ((NFFT_R) S / NFFT_K(2.0)) + NFFT_K(1.0) / NFFT_K(4.0));
for (t = -T / 2; t < T / 2; t++)
{
for (r = -S / 2; r < S / 2; r++)
{
if (t < 0)
{
x[2 * ((t + T / 2) * S + (r + S / 2)) + 0] = (NFFT_R) r / (NFFT_R)(S);
x[2 * ((t + T / 2) * S + (r + S / 2)) + 1] = NFFT_K(4.0) * ((NFFT_R)(t) + (NFFT_R)(T) / NFFT_K(4.0)) / (NFFT_R)(T) * (NFFT_R)(r)
/ (NFFT_R)(S);
}
else
{
x[2 * ((t + T / 2) * S + (r + S / 2)) + 0] = -NFFT_K(4.0) * ((NFFT_R)(t) - (NFFT_R)(T) / NFFT_K(4.0)) / (NFFT_R)(T)
* (NFFT_R)(r) / (NFFT_R)(S);
x[2 * ((t + T / 2) * S + (r + S / 2)) + 1] = (NFFT_R) r / (NFFT_R)(S);
}
if (r == 0)
w[(t + T / 2) * S + (r + S / 2)] = NFFT_K(1.0) / NFFT_K(4.0) / W;
else
w[(t + T / 2) * S + (r + S / 2)] = NFFT_M(fabs)((NFFT_R) r) / W;
}
}
return 0;
}
/** generates the points x with weights w
* for the polar grid with T angles and R offsets
*/
static int polar_grid(int T, int S, NFFT_R *x, NFFT_R *w)
{
int t, r;
NFFT_R W = (NFFT_R) T * (((NFFT_R) S / NFFT_K(2.0)) * ((NFFT_R) S / NFFT_K(2.0)) + NFFT_K(1.0) / NFFT_K(4.0));
for (t = -T / 2; t < T / 2; t++)
{
for (r = -S / 2; r < S / 2; r++)
{
x[2 * ((t + T / 2) * S + (r + S / 2)) + 0] = (NFFT_R) r / (NFFT_R)(S) * NFFT_M(cos)(NFFT_KPI * (NFFT_R)(t) / (NFFT_R)(T));
x[2 * ((t + T / 2) * S + (r + S / 2)) + 1] = (NFFT_R) r / (NFFT_R)(S) * NFFT_M(sin)(NFFT_KPI * (NFFT_R)(t) / (NFFT_R)(T));
if (r == 0)
w[(t + T / 2) * S + (r + S / 2)] = NFFT_K(1.0) / NFFT_K(4.0) / W;
else
w[(t + T / 2) * S + (r + S / 2)] = NFFT_M(fabs)((NFFT_R) r) / W;
}
}
return 0;
}
/** Simple test routine for the inverse nfft */
static void simple_test_solver_nfft_1d(int N, int M, int iter)
{
int k, l; /**< index for nodes, freqencies,iter*/
NFFT(plan) p; /**< plan for the nfft */
SOLVER(plan_complex) ip; /**< plan for the inverse nfft */
const char *error_str;
/** initialise 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.flags & PRE_ONE_PSI)
NFFT(precompute_one_psi)(&p);
/** initialise inverse plan */
SOLVER(init_complex)(&ip, (NFFT(mv_plan_complex)*) (&p));
/** init pseudo random samples and show them */
NFFT(vrand_unit_complex)(ip.y, p.M_total);
NFFT(vpr_complex)(ip.y, p.M_total, "Given data, vector y");
/** initialise some guess f_hat_0 and solve */
for (k = 0; k < p.N_total; k++)
ip.f_hat_iter[k] = NFFT_K(0.0);
NFFT(vpr_complex)(ip.f_hat_iter, p.N_total,
"Initial guess, vector f_hat_iter");
/** check for valid parameters before calling any trafo/adjoint method */
error_str = NFFT(check)(&p);
if (error_str != 0)
{
printf("Error in nfft module: %s\n", error_str);
return;
}
NFFT_CSWAP(ip.f_hat_iter, p.f_hat);
NFFT(trafo)(&p);
NFFT(vpr_complex)(p.f, p.M_total, "Data fit, vector f");
NFFT_CSWAP(ip.f_hat_iter, p.f_hat);
SOLVER(before_loop_complex)(&ip);
printf("\n Residual r=%" NFFT__FES__ "\n", ip.dot_r_iter);
for (l = 0; l < iter; l++)
{
printf("\n********** Iteration l=%d **********\n", l);
SOLVER(loop_one_step_complex)(&ip);
NFFT(vpr_complex)(ip.f_hat_iter, p.N_total,
"Approximate solution, vector f_hat_iter");
NFFT_CSWAP(ip.f_hat_iter, p.f_hat);
NFFT(trafo)(&p);
NFFT(vpr_complex)(p.f, p.M_total, "Data fit, vector f");
NFFT_CSWAP(ip.f_hat_iter, p.f_hat);
printf("\n Residual r=%" NFFT__FES__ "\n", ip.dot_r_iter);
}
SOLVER(finalize_complex)(&ip);
NFFT(finalize)(&p);
}
/** 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
*/
static int inverse_radon_trafo(int (*gridfcn)(), int T, int S, NFFT_R *Rf, int NN, NFFT_R *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 */
NFFT_C *fft; /**< variable for the fftw-1Ds */
FFTW(plan) my_fftw_plan; /**< plan for the fftw-1Ds */
int t, r; /**< index for directions and offsets */
NFFT_R *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 = (NFFT_C *) NFFT(malloc)((size_t)(S) * sizeof(NFFT_C));
my_fftw_plan = FFTW(plan_dft_1d)(S, fft, fft, FFTW_FORWARD, FFTW_MEASURE);
x = (NFFT_R *) NFFT(malloc)((size_t)(2 * T * S) * (sizeof(NFFT_R)));
if (x == NULL)
return EXIT_FAILURE;
w = (NFFT_R *) NFFT(malloc)((size_t)(T * S) * (sizeof(NFFT_R)));
if (w == NULL)
return EXIT_FAILURE;
/** 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] = NFFT_K(0.0);
}
/** precompute psi, the entries of the matrix B */
if (my_nfft_plan.flags & PRE_LIN_PSI)
NFFT(precompute_lin_psi)(&my_nfft_plan);
if (my_nfft_plan.flags & PRE_PSI)
NFFT(precompute_psi)(&my_nfft_plan);
if (my_nfft_plan.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*NFFT_KPI*r)*Rf[t*R+(r+R/2)];
for(r=0; r<R/2; r++)
fft[r+R/2] = cexp(I*NFFT_KPI*r)*Rf[t*R+r];
*/
for (r = 0; r < S; r++)
fft[r] = Rf[t * S + r] + _Complex_I * NFFT_K(0.0);
NFFT(fftshift_complex_int)(fft, 1, &S);
FFTW(execute)(my_fftw_plan);
NFFT(fftshift_complex_int)(fft, 1, &S);
my_infft_plan.y[t * S] = NFFT_K(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] = NFFT_K(0.0) + _Complex_I * NFFT_K(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] = NFFT_M(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;
}