/** discrete mpolar FFT */
static int mpolar_dft(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/2)*R*(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];
}
/** 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();
/** NDFT-2D */
nfft_trafo_direct(&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 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);
}
/**
* Compares execution times for the fast and discrete Gauss transform.
*
* \arg ths The pointer to the fgt plan
* \arg dgt If this parameter is set \ref dgt_trafo is called as well
*
* \author Stefan Kunis
*/
double fgt_test_measure_time(fgt_plan *ths, unsigned dgt)
{
int r;
ticks t0, t1;
double t_out;
double tau=0.01;
t_out=0;
r=0;
while(t_out<tau)
{
r++;
t0 = getticks();
if (dgt)
dgt_trafo(ths);
else
fgt_trafo(ths);
t1 = getticks();
t_out += nfft_elapsed_seconds(t1,t0);
}
t_out/=r;
return t_out;
}
int main(int argc, char **argv)
{
int j,k,t; /**< indices */
int d; /**< number of dimensions */
int N; /**< number of source nodes */
int M; /**< number of target nodes */
int n; /**< expansion degree */
int m; /**< cut-off parameter */
int p; /**< degree of smoothness */
char *s; /**< name of kernel */
double _Complex (*kernel)(double , int , const double *); /**< kernel function */
double c; /**< parameter for kernel */
fastsum_plan my_fastsum_plan; /**< plan for fast summation */
double _Complex *direct; /**< array for direct computation */
ticks t0, t1; /**< for time measurement */
double time; /**< for time measurement */
double error=0.0; /**< for error computation */
double eps_I; /**< inner boundary */
double eps_B; /**< outer boundary */
if (argc!=11)
{
printf("\nfastsum_test d N M n m p kernel c eps_I eps_B\n\n");
printf(" d dimension \n");
printf(" N number of source nodes \n");
printf(" M number of target nodes \n");
printf(" n expansion degree \n");
printf(" m cut-off parameter \n");
printf(" p degree of smoothness \n");
printf(" kernel kernel function (e.g., gaussian)\n");
printf(" c kernel parameter \n");
printf(" eps_I inner boundary \n");
printf(" eps_B outer boundary \n\n");
exit(-1);
}
else
{
d=atoi(argv[1]);
N=atoi(argv[2]); c=1.0/pow((double)N,1.0/(double)d);
M=atoi(argv[3]);
n=atoi(argv[4]);
m=atoi(argv[5]);
p=atoi(argv[6]);
s=argv[7];
c=atof(argv[8]);
eps_I=atof(argv[9]);
eps_B=atof(argv[10]);
if (strcmp(s,"gaussian")==0)
kernel = gaussian;
else if (strcmp(s,"multiquadric")==0)
kernel = multiquadric;
else if (strcmp(s,"inverse_multiquadric")==0)
kernel = inverse_multiquadric;
else if (strcmp(s,"logarithm")==0)
kernel = logarithm;
else if (strcmp(s,"thinplate_spline")==0)
kernel = thinplate_spline;
else if (strcmp(s,"one_over_square")==0)
kernel = one_over_square;
else if (strcmp(s,"one_over_modulus")==0)
kernel = one_over_modulus;
else if (strcmp(s,"one_over_x")==0)
kernel = one_over_x;
else if (strcmp(s,"inverse_multiquadric3")==0)
kernel = inverse_multiquadric3;
else if (strcmp(s,"sinc_kernel")==0)
kernel = sinc_kernel;
else if (strcmp(s,"cosc")==0)
kernel = cosc;
else if (strcmp(s,"cot")==0)
kernel = kcot;
else
{
s="multiquadric";
kernel = multiquadric;
}
}
printf("d=%d, N=%d, M=%d, n=%d, m=%d, p=%d, kernel=%s, c=%g, eps_I=%g, eps_B=%g \n",d,N,M,n,m,p,s,c,eps_I,eps_B);
#ifdef NF_KUB
printf("nearfield correction using piecewise cubic Lagrange interpolation\n");
#elif defined(NF_QUADR)
printf("nearfield correction using piecewise quadratic Lagrange interpolation\n");
#elif defined(NF_LIN)
printf("nearfield correction using piecewise linear Lagrange interpolation\n");
#endif
#ifdef _OPENMP
#pragma omp parallel
{
#pragma omp single
{
printf("nthreads=%d\n", omp_get_max_threads());
}
}
fftw_init_threads();
#endif
/** init d-dimensional fastsum plan */
fastsum_init_guru(&my_fastsum_plan, d, N, M, kernel, &c, 0, n, m, p, eps_I, eps_B);
//fastsum_init_guru(&my_fastsum_plan, d, N, M, kernel, &c, NEARFIELD_BOXES, n, m, p, eps_I, eps_B);
if (my_fastsum_plan.flags & NEARFIELD_BOXES)
printf("determination of nearfield candidates based on partitioning into boxes\n");
else
printf("determination of nearfield candidates based on search tree\n");
/** init source knots in a d-ball with radius 0.25-eps_b/2 */
k = 0;
while (k < N)
{
double r_max = 0.25 - my_fastsum_plan.eps_B/2.0;
double r2 = 0.0;
for (j=0; j<d; j++)
my_fastsum_plan.x[k*d+j] = 2.0 * r_max * (double)rand()/(double)RAND_MAX - r_max;
for (j=0; j<d; j++)
r2 += my_fastsum_plan.x[k*d+j] * my_fastsum_plan.x[k*d+j];
if (r2 >= r_max * r_max)
continue;
k++;
}
for (k=0; k<N; k++)
{
/* double r=(0.25-my_fastsum_plan.eps_B/2.0)*pow((double)rand()/(double)RAND_MAX,1.0/d);
my_fastsum_plan.x[k*d+0] = r;
for (j=1; j<d; j++)
{
double phi=2.0*KPI*(double)rand()/(double)RAND_MAX;
my_fastsum_plan.x[k*d+j] = r;
for (t=0; t<j; t++)
{
my_fastsum_plan.x[k*d+t] *= cos(phi);
}
my_fastsum_plan.x[k*d+j] *= sin(phi);
}
*/
my_fastsum_plan.alpha[k] = (double)rand()/(double)RAND_MAX + _Complex_I*(double)rand()/(double)RAND_MAX;
}
/** init target knots in a d-ball with radius 0.25-eps_b/2 */
k = 0;
while (k < M)
{
double r_max = 0.25 - my_fastsum_plan.eps_B/2.0;
double r2 = 0.0;
for (j=0; j<d; j++)
my_fastsum_plan.y[k*d+j] = 2.0 * r_max * (double)rand()/(double)RAND_MAX - r_max;
for (j=0; j<d; j++)
r2 += my_fastsum_plan.y[k*d+j] * my_fastsum_plan.y[k*d+j];
if (r2 >= r_max * r_max)
continue;
k++;
}
/* for (k=0; k<M; k++)
{
double r=(0.25-my_fastsum_plan.eps_B/2.0)*pow((double)rand()/(double)RAND_MAX,1.0/d);
my_fastsum_plan.y[k*d+0] = r;
for (j=1; j<d; j++)
{
double phi=2.0*KPI*(double)rand()/(double)RAND_MAX;
my_fastsum_plan.y[k*d+j] = r;
for (t=0; t<j; t++)
{
my_fastsum_plan.y[k*d+t] *= cos(phi);
}
my_fastsum_plan.y[k*d+j] *= sin(phi);
}
} */
/** direct computation */
printf("direct computation: "); fflush(NULL);
t0 = getticks();
fastsum_exact(&my_fastsum_plan);
t1 = getticks();
time=nfft_elapsed_seconds(t1,t0);
printf("%fsec\n",time);
/** copy result */
direct = (double _Complex *)nfft_malloc(my_fastsum_plan.M_total*(sizeof(double _Complex)));
for (j=0; j<my_fastsum_plan.M_total; j++)
direct[j]=my_fastsum_plan.f[j];
/** precomputation */
printf("pre-computation: "); fflush(NULL);
t0 = getticks();
fastsum_precompute(&my_fastsum_plan);
t1 = getticks();
time=nfft_elapsed_seconds(t1,t0);
printf("%fsec\n",time);
/** fast computation */
printf("fast computation: "); fflush(NULL);
t0 = getticks();
fastsum_trafo(&my_fastsum_plan);
t1 = getticks();
time=nfft_elapsed_seconds(t1,t0);
printf("%fsec\n",time);
/** compute max error */
error=0.0;
for (j=0; j<my_fastsum_plan.M_total; j++)
{
if (cabs(direct[j]-my_fastsum_plan.f[j])/cabs(direct[j])>error)
error=cabs(direct[j]-my_fastsum_plan.f[j])/cabs(direct[j]);
}
printf("max relative error: %e\n",error);
/** finalise the plan */
fastsum_finalize(&my_fastsum_plan);
return 0;
}
void bench_openmp(int trafo_adjoint, int N, int M, double *x, C *f_hat, C *f, int m, int nfsft_flags, int psi_flags)
{
nfsft_plan plan;
int k, n;
// int N, M, trafo_adjoint;
int t, j;
ticks t0, t1;
double tt_total, tt_pre;
// fscanf(infile, "%d %d %d", &trafo_adjoint, &N, &M);
/*#ifdef _OPENMP
fftw_import_wisdom_from_filename("nfsft_benchomp_detail_threads.plan");
#else
fftw_import_wisdom_from_filename("nfsft_benchomp_detail_single.plan");
#endif*/
/* precomputation (for fast polynomial transform) */
// nfsft_precompute(N,1000.0,0U,0U);
/* Initialize transform plan using the guru interface. All input and output
* arrays are allocated by nfsft_init_guru(). Computations are performed with
* respect to L^2-normalized spherical harmonics Y_k^n. The array of spherical
* Fourier coefficients is preserved during transformations. The NFFT uses a
* cut-off parameter m = 6. See the NFFT 3 manual for details.
*/
nfsft_init_guru(&plan, N, M, nfsft_flags | NFSFT_MALLOC_X | NFSFT_MALLOC_F |
NFSFT_MALLOC_F_HAT | NFSFT_NORMALIZED | NFSFT_PRESERVE_F_HAT,
PRE_PHI_HUT | psi_flags | FFTW_INIT | FFT_OUT_OF_PLACE, m);
/*#ifdef _OPENMP
fftw_export_wisdom_to_filename("nfsft_benchomp_detail_threads.plan");
#else
fftw_export_wisdom_to_filename("nfsft_benchomp_detail_single.plan");
#endif*/
for (j=0; j < plan.M_total; j++)
{
for (t=0; t < 2; t++)
// fscanf(infile, "%lg", plan.x+2*j+t);
plan.x[2*j+t] = x[2*j+t];
}
if (trafo_adjoint==0)
{
memset(plan.f_hat,0U,plan.N_total*sizeof(double _Complex));
for (k = 0; k <= plan.N; k++)
for (n = -k; n <= k; n++)
{
// fscanf(infile, "%lg %lg", &re, &im);
// plan.f_hat[NFSFT_INDEX(k,n,&plan)] = re + _Complex_I * im;
plan.f_hat[NFSFT_INDEX(k,n,&plan)] = f_hat[NFSFT_INDEX(k,n,&plan)];
}
}
else
{
for (j=0; j < plan.M_total; j++)
{
// fscanf(infile, "%lg %lg", &re, &im);
// plan.f[j] = re + _Complex_I * im;
plan.f[j] = f[j];
}
memset(plan.f_hat,0U,plan.N_total*sizeof(double _Complex));
}
t0 = getticks();
/* precomputation (for NFFT, node-dependent) */
nfsft_precompute_x(&plan);
t1 = getticks();
tt_pre = nfft_elapsed_seconds(t1,t0);
if (trafo_adjoint==0)
nfsft_trafo(&plan);
else
nfsft_adjoint(&plan);
t1 = getticks();
tt_total = nfft_elapsed_seconds(t1,t0);
#ifndef MEASURE_TIME
plan.MEASURE_TIME_t[0] = 0.0;
plan.MEASURE_TIME_t[2] = 0.0;
#endif
#ifndef MEASURE_TIME_FFTW
plan.MEASURE_TIME_t[1] = 0.0;
#endif
printf("%.6e %.6e %6e %.6e %.6e %.6e\n", tt_pre, plan.MEASURE_TIME_t[0], plan.MEASURE_TIME_t[1], plan.MEASURE_TIME_t[2], tt_total-tt_pre-plan.MEASURE_TIME_t[0]-plan.MEASURE_TIME_t[1]-plan.MEASURE_TIME_t[2], tt_total);
/** finalise the one dimensional plan */
nfsft_finalize(&plan);
}
/**
* The main program.
*
* \param argc The number of arguments
* \param argv An array containing the arguments as C-strings
*
* \return Exit code
*/
int main (int argc, char **argv)
{
int tc; /**< The index variable for testcases */
int tc_max; /**< The number of testcases */
int *NQ; /**< The array containing the cut-off degrees *
\f$N\f$ */
int NQ_max; /**< The maximum cut-off degree \f$N\f$ for the*
current testcase */
int *SQ; /**< The array containing the grid size
parameters */
int SQ_max; /**< The maximum grid size parameter */
int *RQ; /**< The array containing the grid size
parameters */
int iNQ; /**< Index variable for cut-off degrees */
int iNQ_max; /**< The maximum number of cut-off degrees */
int testfunction; /**< The testfunction */
int N; /**< The test function's bandwidth */
int use_nfsft; /**< Whether to use the NFSFT algorithm or not */
int use_nfft; /**< Whether to use the NFFT algorithm or not */
int use_fpt; /**< Whether to use the FPT algorithm or not */
int cutoff; /**< The current NFFT cut-off parameter */
double threshold; /**< The current NFSFT threshold parameter */
int gridtype; /**< The type of quadrature grid to be used */
int repetitions; /**< The number of repetitions to be performed */
int mode; /**< The number of repetitions to be performed */
double *w; /**< The quadrature weights */
double *x_grid; /**< The quadrature nodes */
double *x_compare; /**< The quadrature nodes */
double _Complex *f_grid; /**< The reference function values */
double _Complex *f_compare; /**< The function values */
double _Complex *f; /**< The function values */
double _Complex *f_hat_gen; /**< The reference spherical Fourier *
coefficients */
double _Complex *f_hat; /**< The spherical Fourier coefficients */
nfsft_plan plan_adjoint; /**< The NFSFT plan */
nfsft_plan plan; /**< The NFSFT plan */
nfsft_plan plan_gen; /**< The NFSFT plan */
double t_avg; /**< The average computation time needed */
double err_infty_avg; /**< The average error \f$E_\infty\f$ */
double err_2_avg; /**< The average error \f$E_2\f$ */
int i; /**< A loop variable */
int k; /**< A loop variable */
int n; /**< A loop variable */
int d; /**< A loop variable */
int m_theta; /**< The current number of different *
colatitudinal angles (for grids) */
int m_phi; /**< The current number of different *
longitudinal angles (for grids). */
int m_total; /**< The total number nodes. */
double *theta; /**< An array for saving the angles theta of a *
grid */
double *phi; /**< An array for saving the angles phi of a *
grid */
fftw_plan fplan; /**< An FFTW plan for computing Clenshaw-Curtis
quadrature weights */
//int nside; /**< The size parameter for the HEALPix grid */
int d2;
int M;
double theta_s;
double x1,x2,x3,temp;
int m_compare;
nfsft_plan *plan_adjoint_ptr;
nfsft_plan *plan_ptr;
double *w_temp;
int testmode;
ticks t0, t1;
/* Read the number of testcases. */
fscanf(stdin,"testcases=%d\n",&tc_max);
fprintf(stdout,"%d\n",tc_max);
/* Process each testcase. */
for (tc = 0; tc < tc_max; tc++)
{
/* Check if the fast transform shall be used. */
fscanf(stdin,"nfsft=%d\n",&use_nfsft);
fprintf(stdout,"%d\n",use_nfsft);
if (use_nfsft != NO)
{
/* Check if the NFFT shall be used. */
fscanf(stdin,"nfft=%d\n",&use_nfft);
fprintf(stdout,"%d\n",use_nfsft);
if (use_nfft != NO)
{
/* Read the cut-off parameter. */
fscanf(stdin,"cutoff=%d\n",&cutoff);
fprintf(stdout,"%d\n",cutoff);
}
else
{
/* TODO remove this */
/* Initialize unused variable with dummy value. */
cutoff = 1;
}
/* Check if the fast polynomial transform shall be used. */
fscanf(stdin,"fpt=%d\n",&use_fpt);
fprintf(stdout,"%d\n",use_fpt);
if (use_fpt != NO)
{
/* Read the NFSFT threshold parameter. */
fscanf(stdin,"threshold=%lf\n",&threshold);
fprintf(stdout,"%lf\n",threshold);
}
else
{
/* TODO remove this */
/* Initialize unused variable with dummy value. */
threshold = 1000.0;
}
}
else
{
/* TODO remove this */
/* Set dummy values. */
use_nfft = NO;
use_fpt = NO;
cutoff = 3;
threshold = 1000.0;
}
/* Read the testmode type. */
fscanf(stdin,"testmode=%d\n",&testmode);
fprintf(stdout,"%d\n",testmode);
if (testmode == ERROR)
{
/* Read the quadrature grid type. */
fscanf(stdin,"gridtype=%d\n",&gridtype);
fprintf(stdout,"%d\n",gridtype);
/* Read the test function. */
fscanf(stdin,"testfunction=%d\n",&testfunction);
fprintf(stdout,"%d\n",testfunction);
/* Check if random bandlimited function has been chosen. */
if (testfunction == FUNCTION_RANDOM_BANDLIMITED)
{
/* Read the bandwidht. */
fscanf(stdin,"bandlimit=%d\n",&N);
fprintf(stdout,"%d\n",N);
}
else
{
N = 1;
}
/* Read the number of repetitions. */
fscanf(stdin,"repetitions=%d\n",&repetitions);
fprintf(stdout,"%d\n",repetitions);
fscanf(stdin,"mode=%d\n",&mode);
fprintf(stdout,"%d\n",mode);
if (mode == RANDOM)
{
/* Read the bandwidht. */
fscanf(stdin,"points=%d\n",&m_compare);
fprintf(stdout,"%d\n",m_compare);
x_compare = (double*) nfft_malloc(2*m_compare*sizeof(double));
d = 0;
while (d < m_compare)
{
x1 = 2.0*(((double)rand())/RAND_MAX) - 1.0;
x2 = 2.0*(((double)rand())/RAND_MAX) - 1.0;
x3 = 2.0*(((double)rand())/RAND_MAX) - 1.0;
temp = sqrt(x1*x1+x2*x2+x3*x3);
if (temp <= 1)
{
x_compare[2*d+1] = acos(x3);
if (x_compare[2*d+1] == 0 || x_compare[2*d+1] == KPI)
{
x_compare[2*d] = 0.0;
}
else
{
x_compare[2*d] = atan2(x2/sin(x_compare[2*d+1]),x1/sin(x_compare[2*d+1]));
}
x_compare[2*d] *= 1.0/(2.0*KPI);
x_compare[2*d+1] *= 1.0/(2.0*KPI);
d++;
}
}
f_compare = (double _Complex*) nfft_malloc(m_compare*sizeof(double _Complex));
f = (double _Complex*) nfft_malloc(m_compare*sizeof(double _Complex));
}
}
/* Initialize maximum cut-off degree and grid size parameter. */
NQ_max = 0;
SQ_max = 0;
/* Read the number of cut-off degrees. */
fscanf(stdin,"bandwidths=%d\n",&iNQ_max);
fprintf(stdout,"%d\n",iNQ_max);
/* Allocate memory for the cut-off degrees and grid size parameters. */
NQ = (int*) nfft_malloc(iNQ_max*sizeof(int));
SQ = (int*) nfft_malloc(iNQ_max*sizeof(int));
if (testmode == TIMING)
{
RQ = (int*) nfft_malloc(iNQ_max*sizeof(int));
}
/* Read the cut-off degrees and grid size parameters. */
for (iNQ = 0; iNQ < iNQ_max; iNQ++)
{
if (testmode == TIMING)
{
/* Read cut-off degree and grid size parameter. */
fscanf(stdin,"%d %d %d\n",&NQ[iNQ],&SQ[iNQ],&RQ[iNQ]);
fprintf(stdout,"%d %d %d\n",NQ[iNQ],SQ[iNQ],RQ[iNQ]);
NQ_max = MAX(NQ_max,NQ[iNQ]);
SQ_max = MAX(SQ_max,SQ[iNQ]);
}
else
{
/* Read cut-off degree and grid size parameter. */
fscanf(stdin,"%d %d\n",&NQ[iNQ],&SQ[iNQ]);
fprintf(stdout,"%d %d\n",NQ[iNQ],SQ[iNQ]);
NQ_max = MAX(NQ_max,NQ[iNQ]);
SQ_max = MAX(SQ_max,SQ[iNQ]);
}
}
/* Do precomputation. */
//fprintf(stderr,"NFSFT Precomputation\n");
//fflush(stderr);
nfsft_precompute(NQ_max, threshold,
((use_nfsft==NO)?(NFSFT_NO_FAST_ALGORITHM):(0U)), 0U);
if (testmode == TIMING)
{
/* Allocate data structures. */
f_hat = (double _Complex*) nfft_malloc(NFSFT_F_HAT_SIZE(NQ_max)*sizeof(double _Complex));
f = (double _Complex*) nfft_malloc(SQ_max*sizeof(double _Complex));
x_grid = (double*) nfft_malloc(2*SQ_max*sizeof(double));
for (d = 0; d < SQ_max; d++)
{
f[d] = (((double)rand())/RAND_MAX)-0.5 + _Complex_I*((((double)rand())/RAND_MAX)-0.5);
x_grid[2*d] = (((double)rand())/RAND_MAX) - 0.5;
x_grid[2*d+1] = (((double)rand())/RAND_MAX) * 0.5;
}
}
//fprintf(stderr,"Entering loop\n");
//fflush(stderr);
/* Process all cut-off bandwidths. */
for (iNQ = 0; iNQ < iNQ_max; iNQ++)
{
if (testmode == TIMING)
{
nfsft_init_guru(&plan,NQ[iNQ],SQ[iNQ], NFSFT_NORMALIZED |
((use_nfft!=NO)?(0U):(NFSFT_USE_NDFT)) |
((use_fpt!=NO)?(0U):(NFSFT_USE_DPT)),
PRE_PHI_HUT | PRE_PSI | FFTW_INIT | FFTW_MEASURE | FFT_OUT_OF_PLACE,
cutoff);
plan.f_hat = f_hat;
plan.x = x_grid;
plan.f = f;
nfsft_precompute_x(&plan);
t_avg = 0.0;
for (i = 0; i < RQ[iNQ]; i++)
{
t0 = getticks();
if (use_nfsft != NO)
{
/* Execute the adjoint NFSFT transformation. */
nfsft_adjoint(&plan);
}
else
{
/* Execute the adjoint direct NDSFT transformation. */
nfsft_adjoint_direct(&plan);
}
t1 = getticks();
t_avg += nfft_elapsed_seconds(t1,t0);
}
t_avg = t_avg/((double)RQ[iNQ]);
nfsft_finalize(&plan);
fprintf(stdout,"%+le\n", t_avg);
fprintf(stderr,"%d: %4d %4d %+le\n", tc, NQ[iNQ], SQ[iNQ], t_avg);
}
else
{
/* Determine the maximum number of nodes. */
switch (gridtype)
{
case GRID_GAUSS_LEGENDRE:
/* Calculate grid dimensions. */
m_theta = SQ[iNQ] + 1;
m_phi = 2*SQ[iNQ] + 2;
m_total = m_theta*m_phi;
break;
case GRID_CLENSHAW_CURTIS:
/* Calculate grid dimensions. */
m_theta = 2*SQ[iNQ] + 1;
m_phi = 2*SQ[iNQ] + 2;
m_total = m_theta*m_phi;
break;
case GRID_HEALPIX:
m_theta = 1;
m_phi = 12*SQ[iNQ]*SQ[iNQ];
m_total = m_theta * m_phi;
//fprintf("HEALPix: SQ = %d, m_theta = %d, m_phi= %d, m");
break;
case GRID_EQUIDISTRIBUTION:
case GRID_EQUIDISTRIBUTION_UNIFORM:
m_theta = 2;
//fprintf(stderr,"ed: m_theta = %d\n",m_theta);
for (k = 1; k < SQ[iNQ]; k++)
{
m_theta += (int)floor((2*KPI)/acos((cos(KPI/(double)SQ[iNQ])-
cos(k*KPI/(double)SQ[iNQ])*cos(k*KPI/(double)SQ[iNQ]))/
(sin(k*KPI/(double)SQ[iNQ])*sin(k*KPI/(double)SQ[iNQ]))));
//fprintf(stderr,"ed: m_theta = %d\n",m_theta);
}
//fprintf(stderr,"ed: m_theta final = %d\n",m_theta);
m_phi = 1;
m_total = m_theta * m_phi;
break;
}
/* Allocate memory for data structures. */
w = (double*) nfft_malloc(m_theta*sizeof(double));
x_grid = (double*) nfft_malloc(2*m_total*sizeof(double));
//fprintf(stderr,"NQ = %d\n",NQ[iNQ]);
//fflush(stderr);
switch (gridtype)
{
case GRID_GAUSS_LEGENDRE:
//fprintf(stderr,"Generating grid for NQ = %d, SQ = %d\n",NQ[iNQ],SQ[iNQ]);
//fflush(stderr);
/* Read quadrature weights. */
for (k = 0; k < m_theta; k++)
{
fscanf(stdin,"%le\n",&w[k]);
w[k] *= (2.0*KPI)/((double)m_phi);
}
//fprintf(stderr,"Allocating theta and phi\n");
//fflush(stderr);
/* Allocate memory to store the grid's angles. */
theta = (double*) nfft_malloc(m_theta*sizeof(double));
phi = (double*) nfft_malloc(m_phi*sizeof(double));
//if (theta == NULL || phi == NULL)
//{
//fprintf(stderr,"Couldn't allocate theta and phi\n");
//fflush(stderr);
//}
/* Read angles theta. */
for (k = 0; k < m_theta; k++)
{
fscanf(stdin,"%le\n",&theta[k]);
}
/* Generate the grid angles phi. */
for (n = 0; n < m_phi; n++)
{
phi[n] = n/((double)m_phi);
phi[n] -= ((phi[n]>=0.5)?(1.0):(0.0));
}
//fprintf(stderr,"Generating grid nodes\n");
//fflush(stderr);
/* Generate the grid's nodes. */
d = 0;
for (k = 0; k < m_theta; k++)
{
for (n = 0; n < m_phi; n++)
{
x_grid[2*d] = phi[n];
x_grid[2*d+1] = theta[k];
d++;
}
}
//fprintf(stderr,"Freeing theta and phi\n");
//fflush(stderr);
/* Free the arrays for the grid's angles. */
nfft_free(theta);
nfft_free(phi);
break;
case GRID_CLENSHAW_CURTIS:
/* Allocate memory to store the grid's angles. */
theta = (double*) nfft_malloc(m_theta*sizeof(double));
phi = (double*) nfft_malloc(m_phi*sizeof(double));
/* Generate the grid angles theta. */
for (k = 0; k < m_theta; k++)
{
theta[k] = k/((double)2*(m_theta-1));
}
/* Generate the grid angles phi. */
for (n = 0; n < m_phi; n++)
{
phi[n] = n/((double)m_phi);
phi[n] -= ((phi[n]>=0.5)?(1.0):(0.0));
}
/* Generate quadrature weights. */
fplan = fftw_plan_r2r_1d(SQ[iNQ]+1, w, w, FFTW_REDFT00, 0U);
for (k = 0; k < SQ[iNQ]+1; k++)
{
w[k] = -2.0/(4*k*k-1);
}
fftw_execute(fplan);
w[0] *= 0.5;
for (k = 0; k < SQ[iNQ]+1; k++)
{
w[k] *= (2.0*KPI)/((double)(m_theta-1)*m_phi);
w[m_theta-1-k] = w[k];
}
fftw_destroy_plan(fplan);
/* Generate the grid's nodes. */
d = 0;
for (k = 0; k < m_theta; k++)
{
for (n = 0; n < m_phi; n++)
{
x_grid[2*d] = phi[n];
x_grid[2*d+1] = theta[k];
d++;
}
}
/* Free the arrays for the grid's angles. */
nfft_free(theta);
nfft_free(phi);
break;
case GRID_HEALPIX:
d = 0;
for (k = 1; k <= SQ[iNQ]-1; k++)
{
for (n = 0; n <= 4*k-1; n++)
{
x_grid[2*d+1] = 1 - (k*k)/((double)(3.0*SQ[iNQ]*SQ[iNQ]));
x_grid[2*d] = ((n+0.5)/(4*k));
x_grid[2*d] -= (x_grid[2*d]>=0.5)?(1.0):(0.0);
d++;
}
}
d2 = d-1;
for (k = SQ[iNQ]; k <= 3*SQ[iNQ]; k++)
{
for (n = 0; n <= 4*SQ[iNQ]-1; n++)
{
x_grid[2*d+1] = 2.0/(3*SQ[iNQ])*(2*SQ[iNQ]-k);
x_grid[2*d] = (n+((k%2==0)?(0.5):(0.0)))/(4*SQ[iNQ]);
x_grid[2*d] -= (x_grid[2*d]>=0.5)?(1.0):(0.0);
d++;
}
}
for (k = 1; k <= SQ[iNQ]-1; k++)
{
for (n = 0; n <= 4*k-1; n++)
{
x_grid[2*d+1] = -x_grid[2*d2+1];
x_grid[2*d] = x_grid[2*d2];
d++;
d2--;
}
}
for (d = 0; d < m_total; d++)
{
x_grid[2*d+1] = acos(x_grid[2*d+1])/(2.0*KPI);
}
w[0] = (4.0*KPI)/(m_total);
break;
case GRID_EQUIDISTRIBUTION:
case GRID_EQUIDISTRIBUTION_UNIFORM:
/* TODO Compute the weights. */
if (gridtype == GRID_EQUIDISTRIBUTION)
{
w_temp = (double*) nfft_malloc((SQ[iNQ]+1)*sizeof(double));
fplan = fftw_plan_r2r_1d(SQ[iNQ]/2+1, w_temp, w_temp, FFTW_REDFT00, 0U);
for (k = 0; k < SQ[iNQ]/2+1; k++)
{
w_temp[k] = -2.0/(4*k*k-1);
}
fftw_execute(fplan);
w_temp[0] *= 0.5;
for (k = 0; k < SQ[iNQ]/2+1; k++)
{
w_temp[k] *= (2.0*KPI)/((double)(SQ[iNQ]));
w_temp[SQ[iNQ]-k] = w_temp[k];
}
fftw_destroy_plan(fplan);
}
d = 0;
x_grid[2*d] = -0.5;
x_grid[2*d+1] = 0.0;
if (gridtype == GRID_EQUIDISTRIBUTION)
{
w[d] = w_temp[0];
}
else
{
w[d] = (4.0*KPI)/(m_total);
}
d = 1;
x_grid[2*d] = -0.5;
x_grid[2*d+1] = 0.5;
if (gridtype == GRID_EQUIDISTRIBUTION)
{
w[d] = w_temp[SQ[iNQ]];
}
else
{
w[d] = (4.0*KPI)/(m_total);
}
d = 2;
for (k = 1; k < SQ[iNQ]; k++)
{
theta_s = (double)k*KPI/(double)SQ[iNQ];
M = (int)floor((2.0*KPI)/acos((cos(KPI/(double)SQ[iNQ])-
cos(theta_s)*cos(theta_s))/(sin(theta_s)*sin(theta_s))));
for (n = 0; n < M; n++)
{
x_grid[2*d] = (n + 0.5)/M;
x_grid[2*d] -= (x_grid[2*d]>=0.5)?(1.0):(0.0);
x_grid[2*d+1] = theta_s/(2.0*KPI);
if (gridtype == GRID_EQUIDISTRIBUTION)
{
w[d] = w_temp[k]/((double)(M));
}
else
{
w[d] = (4.0*KPI)/(m_total);
}
d++;
}
}
if (gridtype == GRID_EQUIDISTRIBUTION)
{
nfft_free(w_temp);
}
break;
default:
break;
}
/* Allocate memory for grid values. */
f_grid = (double _Complex*) nfft_malloc(m_total*sizeof(double _Complex));
if (mode == RANDOM)
{
}
else
{
m_compare = m_total;
f_compare = (double _Complex*) nfft_malloc(m_compare*sizeof(double _Complex));
x_compare = x_grid;
f = f_grid;
}
//fprintf(stderr,"Generating test function\n");
//fflush(stderr);
switch (testfunction)
{
case FUNCTION_RANDOM_BANDLIMITED:
f_hat_gen = (double _Complex*) nfft_malloc(NFSFT_F_HAT_SIZE(N)*sizeof(double _Complex));
//fprintf(stderr,"Generating random test function\n");
//fflush(stderr);
/* Generate random function samples by sampling a bandlimited
* function. */
nfsft_init_guru(&plan_gen,N,m_total, NFSFT_NORMALIZED |
((use_nfft!=NO)?(0U):(NFSFT_USE_NDFT)) |
((use_fpt!=NO)?(0U):(NFSFT_USE_DPT)),
((N>512)?(0U):(PRE_PHI_HUT | PRE_PSI)) | FFTW_INIT |
FFT_OUT_OF_PLACE, cutoff);
plan_gen.f_hat = f_hat_gen;
plan_gen.x = x_grid;
plan_gen.f = f_grid;
nfsft_precompute_x(&plan_gen);
for (k = 0; k < plan_gen.N_total; k++)
{
f_hat_gen[k] = 0.0;
}
for (k = 0; k <= N; k++)
{
for (n = -k; n <= k; n++)
{
f_hat_gen[NFSFT_INDEX(k,n,&plan_gen)] =
(((double)rand())/RAND_MAX)-0.5 + _Complex_I*((((double)rand())/RAND_MAX)-0.5);
}
}
if (use_nfsft != NO)
{
/* Execute the NFSFT transformation. */
nfsft_trafo(&plan_gen);
}
else
{
/* Execute the direct NDSFT transformation. */
nfsft_trafo_direct(&plan_gen);
}
nfsft_finalize(&plan_gen);
if (mode == RANDOM)
{
nfsft_init_guru(&plan_gen,N,m_compare, NFSFT_NORMALIZED |
((use_nfft!=NO)?(0U):(NFSFT_USE_NDFT)) |
((use_fpt!=NO)?(0U):(NFSFT_USE_DPT)),
((N>512)?(0U):(PRE_PHI_HUT | PRE_PSI)) | FFTW_INIT |
FFT_OUT_OF_PLACE, cutoff);
plan_gen.f_hat = f_hat_gen;
plan_gen.x = x_compare;
plan_gen.f = f_compare;
nfsft_precompute_x(&plan_gen);
if (use_nfsft != NO)
{
/* Execute the NFSFT transformation. */
nfsft_trafo(&plan_gen);
}
else
{
/* Execute the direct NDSFT transformation. */
nfsft_trafo_direct(&plan_gen);
}
nfsft_finalize(&plan_gen);
}
else
{
memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
}
nfft_free(f_hat_gen);
break;
case FUNCTION_F1:
for (d = 0; d < m_total; d++)
{
x1 = sin(x_grid[2*d+1]*2.0*KPI)*cos(x_grid[2*d]*2.0*KPI);
x2 = sin(x_grid[2*d+1]*2.0*KPI)*sin(x_grid[2*d]*2.0*KPI);
x3 = cos(x_grid[2*d+1]*2.0*KPI);
f_grid[d] = x1*x2*x3;
}
if (mode == RANDOM)
{
for (d = 0; d < m_compare; d++)
{
x1 = sin(x_compare[2*d+1]*2.0*KPI)*cos(x_compare[2*d]*2.0*KPI);
x2 = sin(x_compare[2*d+1]*2.0*KPI)*sin(x_compare[2*d]*2.0*KPI);
x3 = cos(x_compare[2*d+1]*2.0*KPI);
f_compare[d] = x1*x2*x3;
}
}
else
{
memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
}
break;
case FUNCTION_F2:
for (d = 0; d < m_total; d++)
{
x1 = sin(x_grid[2*d+1]*2.0*KPI)*cos(x_grid[2*d]*2.0*KPI);
x2 = sin(x_grid[2*d+1]*2.0*KPI)*sin(x_grid[2*d]*2.0*KPI);
x3 = cos(x_grid[2*d+1]*2.0*KPI);
f_grid[d] = 0.1*exp(x1+x2+x3);
}
if (mode == RANDOM)
{
for (d = 0; d < m_compare; d++)
{
x1 = sin(x_compare[2*d+1]*2.0*KPI)*cos(x_compare[2*d]*2.0*KPI);
x2 = sin(x_compare[2*d+1]*2.0*KPI)*sin(x_compare[2*d]*2.0*KPI);
x3 = cos(x_compare[2*d+1]*2.0*KPI);
f_compare[d] = 0.1*exp(x1+x2+x3);
}
}
else
{
memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
}
break;
case FUNCTION_F3:
for (d = 0; d < m_total; d++)
{
x1 = sin(x_grid[2*d+1]*2.0*KPI)*cos(x_grid[2*d]*2.0*KPI);
x2 = sin(x_grid[2*d+1]*2.0*KPI)*sin(x_grid[2*d]*2.0*KPI);
x3 = cos(x_grid[2*d+1]*2.0*KPI);
temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
f_grid[d] = 0.1*temp;
}
if (mode == RANDOM)
{
for (d = 0; d < m_compare; d++)
{
x1 = sin(x_compare[2*d+1]*2.0*KPI)*cos(x_compare[2*d]*2.0*KPI);
x2 = sin(x_compare[2*d+1]*2.0*KPI)*sin(x_compare[2*d]*2.0*KPI);
x3 = cos(x_compare[2*d+1]*2.0*KPI);
temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
f_compare[d] = 0.1*temp;
}
}
else
{
memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
}
break;
case FUNCTION_F4:
for (d = 0; d < m_total; d++)
{
x1 = sin(x_grid[2*d+1]*2.0*KPI)*cos(x_grid[2*d]*2.0*KPI);
x2 = sin(x_grid[2*d+1]*2.0*KPI)*sin(x_grid[2*d]*2.0*KPI);
x3 = cos(x_grid[2*d+1]*2.0*KPI);
temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
f_grid[d] = 1.0/(temp);
}
if (mode == RANDOM)
{
for (d = 0; d < m_compare; d++)
{
x1 = sin(x_compare[2*d+1]*2.0*KPI)*cos(x_compare[2*d]*2.0*KPI);
x2 = sin(x_compare[2*d+1]*2.0*KPI)*sin(x_compare[2*d]*2.0*KPI);
x3 = cos(x_compare[2*d+1]*2.0*KPI);
temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
f_compare[d] = 1.0/(temp);
}
}
else
{
memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
}
break;
case FUNCTION_F5:
for (d = 0; d < m_total; d++)
{
x1 = sin(x_grid[2*d+1]*2.0*KPI)*cos(x_grid[2*d]*2.0*KPI);
x2 = sin(x_grid[2*d+1]*2.0*KPI)*sin(x_grid[2*d]*2.0*KPI);
x3 = cos(x_grid[2*d+1]*2.0*KPI);
temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
f_grid[d] = 0.1*sin(1+temp)*sin(1+temp);
}
if (mode == RANDOM)
{
for (d = 0; d < m_compare; d++)
{
x1 = sin(x_compare[2*d+1]*2.0*KPI)*cos(x_compare[2*d]*2.0*KPI);
x2 = sin(x_compare[2*d+1]*2.0*KPI)*sin(x_compare[2*d]*2.0*KPI);
x3 = cos(x_compare[2*d+1]*2.0*KPI);
temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
f_compare[d] = 0.1*sin(1+temp)*sin(1+temp);
}
}
else
{
memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
}
break;
case FUNCTION_F6:
for (d = 0; d < m_total; d++)
{
if (x_grid[2*d+1] <= 0.25)
{
f_grid[d] = 1.0;
}
else
{
f_grid[d] = 1.0/(sqrt(1+3*cos(2.0*KPI*x_grid[2*d+1])*cos(2.0*KPI*x_grid[2*d+1])));
}
}
if (mode == RANDOM)
{
for (d = 0; d < m_compare; d++)
{
if (x_compare[2*d+1] <= 0.25)
{
f_compare[d] = 1.0;
}
else
{
f_compare[d] = 1.0/(sqrt(1+3*cos(2.0*KPI*x_compare[2*d+1])*cos(2.0*KPI*x_compare[2*d+1])));
}
}
}
else
{
memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
}
break;
default:
//fprintf(stderr,"Generating one function\n");
//fflush(stderr);
for (d = 0; d < m_total; d++)
{
f_grid[d] = 1.0;
}
if (mode == RANDOM)
{
for (d = 0; d < m_compare; d++)
{
f_compare[d] = 1.0;
}
}
else
{
memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
}
break;
}
//fprintf(stderr,"Initializing trafo\n");
//fflush(stderr);
/* Init transform plan. */
nfsft_init_guru(&plan_adjoint,NQ[iNQ],m_total, NFSFT_NORMALIZED |
((use_nfft!=NO)?(0U):(NFSFT_USE_NDFT)) |
((use_fpt!=NO)?(0U):(NFSFT_USE_DPT)),
((NQ[iNQ]>512)?(0U):(PRE_PHI_HUT | PRE_PSI)) | FFTW_INIT |
FFT_OUT_OF_PLACE, cutoff);
plan_adjoint_ptr = &plan_adjoint;
if (mode == RANDOM)
{
nfsft_init_guru(&plan,NQ[iNQ],m_compare, NFSFT_NORMALIZED |
((use_nfft!=NO)?(0U):(NFSFT_USE_NDFT)) |
((use_fpt!=NO)?(0U):(NFSFT_USE_DPT)),
((NQ[iNQ]>512)?(0U):(PRE_PHI_HUT | PRE_PSI)) | FFTW_INIT |
FFT_OUT_OF_PLACE, cutoff);
plan_ptr = &plan;
}
else
{
plan_ptr = &plan_adjoint;
}
f_hat = (double _Complex*) nfft_malloc(NFSFT_F_HAT_SIZE(NQ[iNQ])*sizeof(double _Complex));
plan_adjoint_ptr->f_hat = f_hat;
plan_adjoint_ptr->x = x_grid;
plan_adjoint_ptr->f = f_grid;
plan_ptr->f_hat = f_hat;
plan_ptr->x = x_compare;
plan_ptr->f = f;
//fprintf(stderr,"Precomputing for x\n");
//fflush(stderr);
nfsft_precompute_x(plan_adjoint_ptr);
if (plan_adjoint_ptr != plan_ptr)
{
nfsft_precompute_x(plan_ptr);
}
/* Initialize cumulative time variable. */
t_avg = 0.0;
err_infty_avg = 0.0;
err_2_avg = 0.0;
/* Cycle through all runs. */
for (i = 0; i < 1/*repetitions*/; i++)
{
//fprintf(stderr,"Copying original values\n");
//fflush(stderr);
/* Copy exact funtion values to working array. */
//memcpy(f,f_grid,m_total*sizeof(double _Complex));
/* Initialize time measurement. */
t0 = getticks();
//fprintf(stderr,"Multiplying with quadrature weights\n");
//fflush(stderr);
/* Multiplication with the quadrature weights. */
/*fprintf(stderr,"\n");*/
d = 0;
for (k = 0; k < m_theta; k++)
{
for (n = 0; n < m_phi; n++)
{
/*fprintf(stderr,"f_ref[%d] = %le + I*%le,\t f[%d] = %le + I*%le, \t w[%d] = %le\n",
d,creal(f_ref[d]),cimag(f_ref[d]),d,creal(f[d]),cimag(f[d]),k,
w[k]);*/
f_grid[d] *= w[k];
d++;
}
}
t1 = getticks();
t_avg += nfft_elapsed_seconds(t1,t0);
nfft_free(w);
t0 = getticks();
/*fprintf(stderr,"\n");
d = 0;
for (d = 0; d < grid_total; d++)
{
fprintf(stderr,"f[%d] = %le + I*%le, theta[%d] = %le, phi[%d] = %le\n",
d,creal(f[d]),cimag(f[d]),d,x[2*d+1],d,x[2*d]);
}*/
//fprintf(stderr,"Executing adjoint\n");
//fflush(stderr);
/* Check if the fast NFSFT algorithm shall be tested. */
if (use_nfsft != NO)
{
/* Execute the adjoint NFSFT transformation. */
nfsft_adjoint(plan_adjoint_ptr);
}
else
{
/* Execute the adjoint direct NDSFT transformation. */
nfsft_adjoint_direct(plan_adjoint_ptr);
}
/* Multiplication with the Fourier-Legendre coefficients. */
/*for (k = 0; k <= m[im]; k++)
{
for (n = -k; n <= k; n++)
{
fprintf(stderr,"f_hat[%d,%d] = %le\t + I*%le\n",k,n,
creal(f_hat[NFSFT_INDEX(k,n,&plan_adjoint)]),
cimag(f_hat[NFSFT_INDEX(k,n,&plan_adjoint)]));
}
}*/
//fprintf(stderr,"Executing trafo\n");
//fflush(stderr);
if (use_nfsft != NO)
{
/* Execute the NFSFT transformation. */
nfsft_trafo(plan_ptr);
}
else
{
/* Execute the direct NDSFT transformation. */
nfsft_trafo_direct(plan_ptr);
}
t1 = getticks();
t_avg += nfft_elapsed_seconds(t1,t0);
//fprintf(stderr,"Finalizing\n");
//fflush(stderr);
/* Finalize the NFSFT plans */
nfsft_finalize(plan_adjoint_ptr);
if (plan_ptr != plan_adjoint_ptr)
{
nfsft_finalize(plan_ptr);
}
/* Free data arrays. */
nfft_free(f_hat);
nfft_free(x_grid);
err_infty_avg += X(error_l_infty_complex)(f, f_compare, m_compare);
err_2_avg += X(error_l_2_complex)(f, f_compare, m_compare);
nfft_free(f_grid);
if (mode == RANDOM)
{
}
else
{
nfft_free(f_compare);
}
/*for (d = 0; d < m_total; d++)
{
fprintf(stderr,"f_ref[%d] = %le + I*%le,\t f[%d] = %le + I*%le\n",
d,creal(f_ref[d]),cimag(f_ref[d]),d,creal(f[d]),cimag(f[d]));
}*/
}
//fprintf(stderr,"Calculating the error\n");
//fflush(stderr);
/* Calculate average time needed. */
t_avg = t_avg/((double)repetitions);
/* Calculate the average error. */
err_infty_avg = err_infty_avg/((double)repetitions);
/* Calculate the average error. */
err_2_avg = err_2_avg/((double)repetitions);
/* Print out the error measurements. */
fprintf(stdout,"%+le %+le %+le\n", t_avg, err_infty_avg, err_2_avg);
fprintf(stderr,"%d: %4d %4d %+le %+le %+le\n", tc, NQ[iNQ], SQ[iNQ],
t_avg, err_infty_avg, err_2_avg);
}
} /* for (im = 0; im < im_max; im++) - Process all cut-off
* bandwidths.*/
fprintf(stderr,"\n");
/* Delete precomputed data. */
nfsft_forget();
/* Free memory for cut-off bandwidths and grid size parameters. */
nfft_free(NQ);
nfft_free(SQ);
if (testmode == TIMING)
{
nfft_free(RQ);
}
if (mode == RANDOM)
{
nfft_free(x_compare);
nfft_free(f_compare);
nfft_free(f);
}
if (testmode == TIMING)
{
/* Allocate data structures. */
nfft_free(f_hat);
nfft_free(f);
nfft_free(x_grid);
}
} /* for (tc = 0; tc < tc_max; tc++) - Process each testcase. */
/* Return exit code for successful run. */
return EXIT_SUCCESS;
}
/** 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
}
/** 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
}
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 reconstruct(char* filename,int N,int M,int iteration , int weight)
{
int j,k,l;
double time,min_time,max_time,min_inh,max_inh;
ticks t0, t1;
double t,real,imag;
double w,epsilon=0.0000003; /* epsilon is a the break criterium for
the iteration */;
mri_inh_2d1d_plan my_plan;
solver_plan_complex my_iplan;
FILE* fp,*fw,*fout_real,*fout_imag,*finh,*ftime;
int my_N[3],my_n[3];
int flags = PRE_PHI_HUT| PRE_PSI |MALLOC_X| MALLOC_F_HAT|
MALLOC_F| FFTW_INIT| FFT_OUT_OF_PLACE;
unsigned infft_flags = CGNR | PRECOMPUTE_DAMP;
double Ts;
double W,T;
int N3;
int m=2;
double sigma = 1.25;
ftime=fopen("readout_time.dat","r");
finh=fopen("inh.dat","r");
min_time=INT_MAX; max_time=INT_MIN;
for(j=0;j<M;j++)
{
fscanf(ftime,"%le ",&time);
if(time<min_time)
min_time = time;
if(time>max_time)
max_time = time;
}
fclose(ftime);
Ts=(min_time+max_time)/2.0;
min_inh=INT_MAX; max_inh=INT_MIN;
for(j=0;j<N*N;j++)
{
fscanf(finh,"%le ",&w);
if(w<min_inh)
min_inh = w;
if(w>max_inh)
max_inh = w;
}
fclose(finh);
N3=ceil((MAX(fabs(min_inh),fabs(max_inh))*(max_time-min_time)/2.0+(m)/(2*sigma))*4*sigma);
/* N3 has to be even */
if(N3%2!=0)
N3++;
T=((max_time-min_time)/2.0)/(0.5-((double) (m))/N3);
W=N3/T;
my_N[0]=N; my_n[0]=ceil(N*sigma);
my_N[1]=N; my_n[1]=ceil(N*sigma);
my_N[2]=N3; my_n[2]=N3;
/* initialise nfft */
mri_inh_2d1d_init_guru(&my_plan, my_N, M, my_n, m, sigma, flags,
FFTW_MEASURE| FFTW_DESTROY_INPUT);
/* precompute lin psi if set */
if(my_plan.plan.nfft_flags & PRE_LIN_PSI)
nfft_precompute_lin_psi(&my_plan.plan);
if (weight)
infft_flags = infft_flags | PRECOMPUTE_WEIGHT;
/* initialise my_iplan, advanced */
solver_init_advanced_complex(&my_iplan,(nfft_mv_plan_complex*)(&my_plan), infft_flags );
/* get the weights */
if(my_iplan.flags & PRECOMPUTE_WEIGHT)
{
fw=fopen("weights.dat","r");
for(j=0;j<my_plan.M_total;j++)
{
fscanf(fw,"%le ",&my_iplan.w[j]);
}
fclose(fw);
}
/* get the damping factors */
if(my_iplan.flags & PRECOMPUTE_DAMP)
{
for(j=0;j<N;j++){
for(k=0;k<N;k++) {
int j2= j-N/2;
int k2= k-N/2;
double r=sqrt(j2*j2+k2*k2);
if(r>(double) N/2)
my_iplan.w_hat[j*N+k]=0.0;
else
my_iplan.w_hat[j*N+k]=1.0;
}
}
}
fp=fopen(filename,"r");
ftime=fopen("readout_time.dat","r");
for(j=0;j<my_plan.M_total;j++)
{
fscanf(fp,"%le %le %le %le",&my_plan.plan.x[2*j+0],&my_plan.plan.x[2*j+1],&real,&imag);
my_iplan.y[j]=real+ _Complex_I*imag;
fscanf(ftime,"%le ",&my_plan.t[j]);
my_plan.t[j] = (my_plan.t[j]-Ts)/T;
}
fclose(fp);
fclose(ftime);
finh=fopen("inh.dat","r");
for(j=0;j<N*N;j++)
{
fscanf(finh,"%le ",&my_plan.w[j]);
my_plan.w[j]/=W;
}
fclose(finh);
if(my_plan.plan.nfft_flags & PRE_PSI) {
nfft_precompute_psi(&my_plan.plan);
}
if(my_plan.plan.nfft_flags & PRE_FULL_PSI) {
nfft_precompute_full_psi(&my_plan.plan);
}
/* init some guess */
for(j=0;j<my_plan.N_total;j++)
{
my_iplan.f_hat_iter[j]=0.0;
}
t0 = getticks();
/* inverse trafo */
solver_before_loop_complex(&my_iplan);
for(l=0;l<iteration;l++)
{
/* break if dot_r_iter is smaller than epsilon*/
if(my_iplan.dot_r_iter<epsilon)
break;
fprintf(stderr,"%e, %i of %i\n",sqrt(my_iplan.dot_r_iter),
l+1,iteration);
solver_loop_one_step_complex(&my_iplan);
}
t1 = getticks();
t = nfft_elapsed_seconds(t1,t0);
fout_real=fopen("output_real.dat","w");
fout_imag=fopen("output_imag.dat","w");
for (j=0;j<N*N;j++) {
/* Verschiebung wieder herausrechnen */
my_iplan.f_hat_iter[j]*=cexp(-2.0*_Complex_I*KPI*Ts*my_plan.w[j]*W);
fprintf(fout_real,"%le ",creal(my_iplan.f_hat_iter[j]));
fprintf(fout_imag,"%le ",cimag(my_iplan.f_hat_iter[j]));
}
fclose(fout_real);
fclose(fout_imag);
solver_finalize_complex(&my_iplan);
mri_inh_2d1d_finalize(&my_plan);
}
/** Comparison of the FFTW, mpolar FFT, and inverse mpolar FFT */
static int comparison_fft(FILE *fp, int N, int T, int R)
{
ticks t0, t1;
fftw_plan my_fftw_plan;
fftw_complex *f_hat,*f;
int m,k;
double t_fft, t_dft_mpolar;
f_hat = (fftw_complex *)nfft_malloc(sizeof(fftw_complex)*N*N);
f = (fftw_complex *)nfft_malloc(sizeof(fftw_complex)*(T*R/4)*5);
my_fftw_plan = fftw_plan_dft_2d(N,N,f_hat,f,FFTW_BACKWARD,FFTW_MEASURE);
for(k=0; k<N*N; k++)
f_hat[k] = (((double)rand())/RAND_MAX) + _Complex_I* (((double)rand())/RAND_MAX);
t0 = getticks();
for(m=0;m<65536/N;m++)
{
fftw_execute(my_fftw_plan);
/* touch */
f_hat[2]=2*f_hat[0];
}
t1 = getticks();
GLOBAL_elapsed_time = nfft_elapsed_seconds(t1,t0);
t_fft=N*GLOBAL_elapsed_time/65536;
if(N<256)
{
mpolar_dft(f_hat,N,f,T,R,1);
t_dft_mpolar=GLOBAL_elapsed_time;
}
for (m=3; m<=9; m+=3)
{
if((m==3)&&(N<256))
fprintf(fp,"%d\t&\t&\t%1.1e&\t%1.1e&\t%d\t",N,t_fft,t_dft_mpolar,m);
else
if(m==3)
fprintf(fp,"%d\t&\t&\t%1.1e&\t &\t%d\t",N,t_fft,m);
else
fprintf(fp," \t&\t&\t &\t &\t%d\t",m);
printf("N=%d\tt_fft=%1.1e\tt_dft_mpolar=%1.1e\tm=%d\t",N,t_fft,t_dft_mpolar,m);
mpolar_fft(f_hat,N,f,T,R,m);
fprintf(fp,"%1.1e&\t",GLOBAL_elapsed_time);
printf("t_mpolar=%1.1e\t",GLOBAL_elapsed_time);
inverse_mpolar_fft(f,T,R,f_hat,N,2*m,m);
if(m==9)
fprintf(fp,"%1.1e\\\\\\hline\n",GLOBAL_elapsed_time);
else
fprintf(fp,"%1.1e\\\\\n",GLOBAL_elapsed_time);
printf("t_impolar=%1.1e\n",GLOBAL_elapsed_time);
}
fflush(fp);
nfft_free(f);
nfft_free(f_hat);
return EXIT_SUCCESS;
}
/** inverse NFFT-based mpolar FFT */
static int inverse_mpolar_fft(fftw_complex *f, int T, int R, fftw_complex *f_hat, int NN, int max_i, int m)
{
ticks t0, t1;
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 */
double *x, *w; /**< knots and associated weights */
int l; /**< index for iterations */
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 two dimensional infft plan */
solver_init_advanced_complex(&my_infft_plan,(nfft_mv_plan_complex*)(&my_nfft_plan), CGNR | PRECOMPUTE_WEIGHT );
/** init nodes, given samples and weights */
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];
my_infft_plan.y[j] = f[j];
my_infft_plan.w[j] = w[j];
}
/** 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);
/** initialise damping factors */
if(my_infft_plan.flags & PRECOMPUTE_DAMP)
for(j=0;j<my_nfft_plan.N[0];j++)
for(k=0;k<my_nfft_plan.N[1];k++)
{
my_infft_plan.w_hat[j*my_nfft_plan.N[1]+k]=
(sqrt(pow(j-my_nfft_plan.N[0]/2,2)+pow(k-my_nfft_plan.N[1]/2,2))>(my_nfft_plan.N[0]/2)?0:1);
}
/** 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;
t0 = getticks();
/** 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);
}
}
t1 = getticks();
GLOBAL_elapsed_time = nfft_elapsed_seconds(t1,t0);
/** copy result */
for(k=0;k<my_nfft_plan.N_total;k++)
f_hat[k] = my_infft_plan.f_hat_iter[k];
/** finalise the plans and free the variables */
solver_finalize_complex(&my_infft_plan);
nfft_finalize(&my_nfft_plan);
nfft_free(x);
nfft_free(w);
return EXIT_SUCCESS;
}
/**
* The main program.
*
* \param argc The number of arguments
* \param argv An array containing the arguments as C-strings
*
* \return Exit code
*
* \author Jens Keiner
*/
int main (int argc, char **argv)
{
double **p; /* The array containing the parameter sets *
* for the kernel functions */
int *m; /* The array containing the cut-off degrees M */
int **ld; /* The array containing the numbers of source *
* and target nodes, L and D */
int ip; /* Index variable for p */
int im; /* Index variable for m */
int ild; /* Index variable for l */
int ipp; /* Index for kernel parameters */
int ip_max; /* The maximum index for p */
int im_max; /* The maximum index for m */
int ild_max; /* The maximum index for l */
int ipp_max; /* The maximum index for ip */
int tc_max; /* The number of testcases */
int m_max; /* The maximum cut-off degree M for the *
* current dataset */
int l_max; /* The maximum number of source nodes L for *
* the current dataset */
int d_max; /* The maximum number of target nodes D for *
* the current dataset */
long ld_max_prec; /* The maximum number of source and target *
* nodes for precomputation multiplied */
long l_max_prec; /* The maximum number of source nodes for *
* precomputation */
int tc; /* Index variable for testcases */
int kt; /* The kernel function */
int cutoff; /* The current NFFT cut-off parameter */
double threshold; /* The current NFSFT threshold parameter */
double t_d; /* Time for direct algorithm in seconds */
double t_dp; /* Time for direct algorithm with *
precomputation in seconds */
double t_fd; /* Time for fast direct algorithm in seconds */
double t_f; /* Time for fast algorithm in seconds */
double temp; /* */
double err_f; /* Error E_infty for fast algorithm */
double err_fd; /* Error E_\infty for fast direct algorithm */
ticks t0, t1; /* */
int precompute = NO; /* */
fftw_complex *ptr; /* */
double* steed; /* */
fftw_complex *b; /* The weights (b_l)_{l=0}^{L-1} */
fftw_complex *f_hat; /* The spherical Fourier coefficients */
fftw_complex *a; /* The Fourier-Legendre coefficients */
double *xi; /* Target nodes */
double *eta; /* Source nodes */
fftw_complex *f_m; /* Approximate function values */
fftw_complex *f; /* Exact function values */
fftw_complex *prec = NULL; /* */
nfsft_plan plan; /* NFSFT plan */
nfsft_plan plan_adjoint; /* adjoint NFSFT plan */
int i; /* */
int k; /* */
int n; /* */
int d; /* */
int l; /* */
int use_nfsft; /* */
int use_nfft; /* */
int use_fpt; /* */
int rinc; /* */
double constant; /* */
/* Read the number of testcases. */
fscanf(stdin,"testcases=%d\n",&tc_max);
fprintf(stdout,"%d\n",tc_max);
/* Process each testcase. */
for (tc = 0; tc < tc_max; tc++)
{
/* Check if the fast transform shall be used. */
fscanf(stdin,"nfsft=%d\n",&use_nfsft);
fprintf(stdout,"%d\n",use_nfsft);
if (use_nfsft != NO)
{
/* Check if the NFFT shall be used. */
fscanf(stdin,"nfft=%d\n",&use_nfft);
fprintf(stdout,"%d\n",use_nfft);
if (use_nfft != NO)
{
/* Read the cut-off parameter. */
fscanf(stdin,"cutoff=%d\n",&cutoff);
fprintf(stdout,"%d\n",cutoff);
}
else
{
/* TODO remove this */
/* Initialize unused variable with dummy value. */
cutoff = 1;
}
/* Check if the fast polynomial transform shall be used. */
fscanf(stdin,"fpt=%d\n",&use_fpt);
fprintf(stdout,"%d\n",use_fpt);
/* Read the NFSFT threshold parameter. */
fscanf(stdin,"threshold=%lf\n",&threshold);
fprintf(stdout,"%lf\n",threshold);
}
else
{
/* TODO remove this */
/* Set dummy values. */
cutoff = 3;
threshold = 1000000000000.0;
}
/* Initialize bandwidth bound. */
m_max = 0;
/* Initialize source nodes bound. */
l_max = 0;
/* Initialize target nodes bound. */
d_max = 0;
/* Initialize source nodes bound for precomputation. */
l_max_prec = 0;
/* Initialize source and target nodes bound for precomputation. */
ld_max_prec = 0;
/* Read the kernel type. This is one of KT_ABEL_POISSON, KT_SINGULARITY,
* KT_LOC_SUPP and KT_GAUSSIAN. */
fscanf(stdin,"kernel=%d\n",&kt);
fprintf(stdout,"%d\n",kt);
/* Read the number of parameter sets. */
fscanf(stdin,"parameter_sets=%d\n",&ip_max);
fprintf(stdout,"%d\n",ip_max);
/* Allocate memory for pointers to parameter sets. */
p = (double**) nfft_malloc(ip_max*sizeof(double*));
/* We now read in the parameter sets. */
/* Read number of parameters. */
fscanf(stdin,"parameters=%d\n",&ipp_max);
fprintf(stdout,"%d\n",ipp_max);
for (ip = 0; ip < ip_max; ip++)
{
/* Allocate memory for the parameters. */
p[ip] = (double*) nfft_malloc(ipp_max*sizeof(double));
/* Read the parameters. */
for (ipp = 0; ipp < ipp_max; ipp++)
{
/* Read the next parameter. */
fscanf(stdin,"%lf\n",&p[ip][ipp]);
fprintf(stdout,"%lf\n",p[ip][ipp]);
}
}
/* Read the number of cut-off degrees. */
fscanf(stdin,"bandwidths=%d\n",&im_max);
fprintf(stdout,"%d\n",im_max);
m = (int*) nfft_malloc(im_max*sizeof(int));
/* Read the cut-off degrees. */
for (im = 0; im < im_max; im++)
{
/* Read cut-off degree. */
fscanf(stdin,"%d\n",&m[im]);
fprintf(stdout,"%d\n",m[im]);
m_max = MAX(m_max,m[im]);
}
/* Read number of node specifications. */
fscanf(stdin,"node_sets=%d\n",&ild_max);
fprintf(stdout,"%d\n",ild_max);
ld = (int**) nfft_malloc(ild_max*sizeof(int*));
/* Read the run specification. */
for (ild = 0; ild < ild_max; ild++)
{
/* Allocate memory for the run parameters. */
ld[ild] = (int*) nfft_malloc(5*sizeof(int));
/* Read number of source nodes. */
fscanf(stdin,"L=%d ",&ld[ild][0]);
fprintf(stdout,"%d\n",ld[ild][0]);
l_max = MAX(l_max,ld[ild][0]);
/* Read number of target nodes. */
fscanf(stdin,"D=%d ",&ld[ild][1]);
fprintf(stdout,"%d\n",ld[ild][1]);
d_max = MAX(d_max,ld[ild][1]);
/* Determine whether direct and fast algorithm shall be compared. */
fscanf(stdin,"compare=%d ",&ld[ild][2]);
fprintf(stdout,"%d\n",ld[ild][2]);
/* Check if precomputation for the direct algorithm is used. */
if (ld[ild][2] == YES)
{
/* Read whether the precomputed version shall also be used. */
fscanf(stdin,"precomputed=%d\n",&ld[ild][3]);
fprintf(stdout,"%d\n",ld[ild][3]);
/* Read the number of repetitions over which measurements are
* averaged. */
fscanf(stdin,"repetitions=%d\n",&ld[ild][4]);
fprintf(stdout,"%d\n",ld[ild][4]);
/* Update ld_max_prec and l_max_prec. */
if (ld[ild][3] == YES)
{
/* Update ld_max_prec. */
ld_max_prec = MAX(ld_max_prec,ld[ild][0]*ld[ild][1]);
/* Update l_max_prec. */
l_max_prec = MAX(l_max_prec,ld[ild][0]);
/* Turn on the precomputation for the direct algorithm. */
precompute = YES;
}
}
else
{
/* Set default value for the number of repetitions. */
ld[ild][4] = 1;
}
}
/* Allocate memory for data structures. */
b = (fftw_complex*) nfft_malloc(l_max*sizeof(fftw_complex));
eta = (double*) nfft_malloc(2*l_max*sizeof(double));
f_hat = (fftw_complex*) nfft_malloc(NFSFT_F_HAT_SIZE(m_max)*sizeof(fftw_complex));
a = (fftw_complex*) nfft_malloc((m_max+1)*sizeof(fftw_complex));
xi = (double*) nfft_malloc(2*d_max*sizeof(double));
f_m = (fftw_complex*) nfft_malloc(d_max*sizeof(fftw_complex));
f = (fftw_complex*) nfft_malloc(d_max*sizeof(fftw_complex));
/* Allocate memory for precomputed data. */
if (precompute == YES)
{
prec = (fftw_complex*) nfft_malloc(ld_max_prec*sizeof(fftw_complex));
}
/* Generate random source nodes and weights. */
for (l = 0; l < l_max; l++)
{
b[l] = (((double)rand())/RAND_MAX) - 0.5;
eta[2*l] = (((double)rand())/RAND_MAX) - 0.5;
eta[2*l+1] = acos(2.0*(((double)rand())/RAND_MAX) - 1.0)/(K2PI);
}
/* Generate random target nodes. */
for (d = 0; d < d_max; d++)
{
xi[2*d] = (((double)rand())/RAND_MAX) - 0.5;
xi[2*d+1] = acos(2.0*(((double)rand())/RAND_MAX) - 1.0)/(K2PI);
}
/* Do precomputation. */
nfsft_precompute(m_max,threshold,
((use_nfsft==NO)?(NFSFT_NO_FAST_ALGORITHM):(0U/*NFSFT_NO_DIRECT_ALGORITHM*/)), 0U);
/* Process all parameter sets. */
for (ip = 0; ip < ip_max; ip++)
{
/* Compute kernel coeffcients up to the maximum cut-off degree m_max. */
switch (kt)
{
case KT_ABEL_POISSON:
/* Compute Fourier-Legendre coefficients for the Poisson kernel. */
for (k = 0; k <= m_max; k++)
a[k] = SYMBOL_ABEL_POISSON(k,p[ip][0]);
break;
case KT_SINGULARITY:
/* Compute Fourier-Legendre coefficients for the singularity
* kernel. */
for (k = 0; k <= m_max; k++)
a[k] = SYMBOL_SINGULARITY(k,p[ip][0]);
break;
case KT_LOC_SUPP:
/* Compute Fourier-Legendre coefficients for the locally supported
* kernel. */
a[0] = 1.0;
if (1 <= m_max)
a[1] = ((p[ip][1]+1+p[ip][0])/(p[ip][1]+2.0))*a[0];
for (k = 2; k <= m_max; k++)
a[k] = (1.0/(k+p[ip][1]+1))*((2*k-1)*p[ip][0]*a[k-1] -
(k-p[ip][1]-2)*a[k-2]);
break;
case KT_GAUSSIAN:
/* Fourier-Legendre coefficients */
steed = (double*) nfft_malloc((m_max+1)*sizeof(double));
smbi(2.0*p[ip][0],0.5,m_max+1,2,steed);
for (k = 0; k <= m_max; k++)
a[k] = K2PI*(sqrt(KPI/p[ip][0]))*steed[k];
nfft_free(steed);
break;
}
/* Normalize Fourier-Legendre coefficients. */
for (k = 0; k <= m_max; k++)
a[k] *= (2*k+1)/(K4PI);
/* Process all node sets. */
for (ild = 0; ild < ild_max; ild++)
{
/* Check if the fast algorithm shall be used. */
if (ld[ild][2] != NO)
{
/* Check if the direct algorithm with precomputation should be
* tested. */
if (ld[ild][3] != NO)
{
/* Get pointer to start of data. */
ptr = prec;
/* Calculate increment from one row to the next. */
rinc = l_max_prec-ld[ild][0];
/* Process al target nodes. */
for (d = 0; d < ld[ild][1]; d++)
{
/* Process all source nodes. */
for (l = 0; l < ld[ild][0]; l++)
{
/* Compute inner product between current source and target
* node. */
temp = innerProduct(eta[2*l],eta[2*l+1],xi[2*d],xi[2*d+1]);
/* Switch by the kernel type. */
switch (kt)
{
case KT_ABEL_POISSON:
/* Evaluate the Poisson kernel for the current value. */
*ptr++ = poissonKernel(temp,p[ip][0]);
break;
case KT_SINGULARITY:
/* Evaluate the singularity kernel for the current
* value. */
*ptr++ = singularityKernel(temp,p[ip][0]);
break;
case KT_LOC_SUPP:
/* Evaluate the localized kernel for the current
* value. */
*ptr++ = locallySupportedKernel(temp,p[ip][0],p[ip][1]);
break;
case KT_GAUSSIAN:
/* Evaluate the spherical Gaussian kernel for the current
* value. */
*ptr++ = gaussianKernel(temp,p[ip][0]);
break;
}
}
/* Increment pointer for next row. */
ptr += rinc;
}
/* Initialize cumulative time variable. */
t_dp = 0.0;
/* Initialize time measurement. */
t0 = getticks();
/* Cycle through all runs. */
for (i = 0; i < ld[ild][4]; i++)
{
/* Reset pointer to start of precomputed data. */
ptr = prec;
/* Calculate increment from one row to the next. */
rinc = l_max_prec-ld[ild][0];
/* Check if the localized kernel is used. */
if (kt == KT_LOC_SUPP)
{
/* Perform final summation */
/* Calculate the multiplicative constant. */
constant = ((p[ip][1]+1)/(K2PI*pow(1-p[ip][0],p[ip][1]+1)));
/* Process all target nodes. */
for (d = 0; d < ld[ild][1]; d++)
{
/* Initialize function value. */
f[d] = 0.0;
/* Process all source nodes. */
for (l = 0; l < ld[ild][0]; l++)
f[d] += b[l]*(*ptr++);
/* Multiply with the constant. */
f[d] *= constant;
/* Proceed to next row. */
ptr += rinc;
}
}
else
{
/* Process all target nodes. */
for (d = 0; d < ld[ild][1]; d++)
{
/* Initialize function value. */
f[d] = 0.0;
/* Process all source nodes. */
for (l = 0; l < ld[ild][0]; l++)
f[d] += b[l]*(*ptr++);
/* Proceed to next row. */
ptr += rinc;
}
}
}
/* Calculate the time needed. */
t1 = getticks();
t_dp = nfft_elapsed_seconds(t1,t0);
/* Calculate average time needed. */
t_dp = t_dp/((double)ld[ild][4]);
}
else
{
/* Initialize cumulative time variable with dummy value. */
t_dp = -1.0;
}
/* Initialize cumulative time variable. */
t_d = 0.0;
/* Initialize time measurement. */
t0 = getticks();
/* Cycle through all runs. */
for (i = 0; i < ld[ild][4]; i++)
{
/* Switch by the kernel type. */
switch (kt)
{
case KT_ABEL_POISSON:
/* Process all target nodes. */
for (d = 0; d < ld[ild][1]; d++)
{
/* Initialize function value. */
f[d] = 0.0;
/* Process all source nodes. */
for (l = 0; l < ld[ild][0]; l++)
{
/* Compute the inner product for the current source and
* target nodes. */
temp = innerProduct(eta[2*l],eta[2*l+1],xi[2*d],xi[2*d+1]);
/* Evaluate the Poisson kernel for the current value and add
* to the result. */
f[d] += b[l]*poissonKernel(temp,p[ip][0]);
}
}
break;
case KT_SINGULARITY:
/* Process all target nodes. */
for (d = 0; d < ld[ild][1]; d++)
{
/* Initialize function value. */
f[d] = 0.0;
/* Process all source nodes. */
for (l = 0; l < ld[ild][0]; l++)
{
/* Compute the inner product for the current source and
* target nodes. */
temp = innerProduct(eta[2*l],eta[2*l+1],xi[2*d],xi[2*d+1]);
/* Evaluate the Poisson kernel for the current value and add
* to the result. */
f[d] += b[l]*singularityKernel(temp,p[ip][0]);
}
}
break;
case KT_LOC_SUPP:
/* Calculate the multiplicative constant. */
constant = ((p[ip][1]+1)/(K2PI*pow(1-p[ip][0],p[ip][1]+1)));
/* Process all target nodes. */
for (d = 0; d < ld[ild][1]; d++)
{
/* Initialize function value. */
f[d] = 0.0;
/* Process all source nodes. */
for (l = 0; l < ld[ild][0]; l++)
{
/* Compute the inner product for the current source and
* target nodes. */
temp = innerProduct(eta[2*l],eta[2*l+1],xi[2*d],xi[2*d+1]);
/* Evaluate the Poisson kernel for the current value and add
* to the result. */
f[d] += b[l]*locallySupportedKernel(temp,p[ip][0],p[ip][1]);
}
/* Multiply result with constant. */
f[d] *= constant;
}
break;
case KT_GAUSSIAN:
/* Process all target nodes. */
for (d = 0; d < ld[ild][1]; d++)
{
/* Initialize function value. */
f[d] = 0.0;
/* Process all source nodes. */
for (l = 0; l < ld[ild][0]; l++)
{
/* Compute the inner product for the current source and
* target nodes. */
temp = innerProduct(eta[2*l],eta[2*l+1],xi[2*d],xi[2*d+1]);
/* Evaluate the Poisson kernel for the current value and add
* to the result. */
f[d] += b[l]*gaussianKernel(temp,p[ip][0]);
}
}
break;
}
}
/* Calculate and add the time needed. */
t1 = getticks();
t_d = nfft_elapsed_seconds(t1,t0);
/* Calculate average time needed. */
t_d = t_d/((double)ld[ild][4]);
}
else
{
/* Initialize cumulative time variable with dummy value. */
t_d = -1.0;
t_dp = -1.0;
}
/* Initialize error and cumulative time variables for the fast
* algorithm. */
err_fd = -1.0;
err_f = -1.0;
t_fd = -1.0;
t_f = -1.0;
/* Process all cut-off bandwidths. */
for (im = 0; im < im_max; im++)
{
/* Init transform plans. */
nfsft_init_guru(&plan_adjoint, m[im],ld[ild][0],
((use_nfft!=0)?(0U):(NFSFT_USE_NDFT)) |
((use_fpt!=0)?(0U):(NFSFT_USE_DPT)),
PRE_PHI_HUT | PRE_PSI | FFTW_INIT |
FFT_OUT_OF_PLACE, cutoff);
nfsft_init_guru(&plan,m[im],ld[ild][1],
((use_nfft!=0)?(0U):(NFSFT_USE_NDFT)) |
((use_fpt!=0)?(0U):(NFSFT_USE_DPT)),
PRE_PHI_HUT | PRE_PSI | FFTW_INIT |
FFT_OUT_OF_PLACE,
cutoff);
plan_adjoint.f_hat = f_hat;
plan_adjoint.x = eta;
plan_adjoint.f = b;
plan.f_hat = f_hat;
plan.x = xi;
plan.f = f_m;
nfsft_precompute_x(&plan_adjoint);
nfsft_precompute_x(&plan);
/* Check if direct algorithm shall also be tested. */
if (use_nfsft == BOTH)
{
/* Initialize cumulative time variable. */
t_fd = 0.0;
/* Initialize time measurement. */
t0 = getticks();
/* Cycle through all runs. */
for (i = 0; i < ld[ild][4]; i++)
{
/* Execute adjoint direct NDSFT transformation. */
nfsft_adjoint_direct(&plan_adjoint);
/* Multiplication with the Fourier-Legendre coefficients. */
for (k = 0; k <= m[im]; k++)
for (n = -k; n <= k; n++)
f_hat[NFSFT_INDEX(k,n,&plan_adjoint)] *= a[k];
/* Execute direct NDSFT transformation. */
nfsft_trafo_direct(&plan);
}
/* Calculate and add the time needed. */
t1 = getticks();
t_fd = nfft_elapsed_seconds(t1,t0);
/* Calculate average time needed. */
t_fd = t_fd/((double)ld[ild][4]);
/* Check if error E_infty should be computed. */
if (ld[ild][2] != NO)
{
/* Compute the error E_infinity. */
err_fd = X(error_l_infty_1_complex)(f, f_m, ld[ild][1], b,
ld[ild][0]);
}
}
/* Check if the fast NFSFT algorithm shall also be tested. */
if (use_nfsft != NO)
{
/* Initialize cumulative time variable for the NFSFT algorithm. */
t_f = 0.0;
}
else
{
/* Initialize cumulative time variable for the direct NDSFT
* algorithm. */
t_fd = 0.0;
}
/* Initialize time measurement. */
t0 = getticks();
/* Cycle through all runs. */
for (i = 0; i < ld[ild][4]; i++)
{
/* Check if the fast NFSFT algorithm shall also be tested. */
if (use_nfsft != NO)
{
/* Execute the adjoint NFSFT transformation. */
nfsft_adjoint(&plan_adjoint);
}
else
{
/* Execute the adjoint direct NDSFT transformation. */
nfsft_adjoint_direct(&plan_adjoint);
}
/* Multiplication with the Fourier-Legendre coefficients. */
for (k = 0; k <= m[im]; k++)
for (n = -k; n <= k; n++)
f_hat[NFSFT_INDEX(k,n,&plan_adjoint)] *= a[k];
/* Check if the fast NFSFT algorithm shall also be tested. */
if (use_nfsft != NO)
{
/* Execute the NFSFT transformation. */
nfsft_trafo(&plan);
}
else
{
/* Execute the NDSFT transformation. */
nfsft_trafo_direct(&plan);
}
}
/* Check if the fast NFSFT algorithm has been used. */
t1 = getticks();
if (use_nfsft != NO)
t_f = nfft_elapsed_seconds(t1,t0);
else
t_fd = nfft_elapsed_seconds(t1,t0);
/* Check if the fast NFSFT algorithm has been used. */
if (use_nfsft != NO)
{
/* Calculate average time needed. */
t_f = t_f/((double)ld[ild][4]);
}
else
{
/* Calculate average time needed. */
t_fd = t_fd/((double)ld[ild][4]);
}
/* Check if error E_infty should be computed. */
if (ld[ild][2] != NO)
{
/* Check if the fast NFSFT algorithm has been used. */
if (use_nfsft != NO)
{
/* Compute the error E_infinity. */
err_f = X(error_l_infty_1_complex)(f, f_m, ld[ild][1], b,
ld[ild][0]);
}
else
{
/* Compute the error E_infinity. */
err_fd = X(error_l_infty_1_complex)(f, f_m, ld[ild][1], b,
ld[ild][0]);
}
}
/* Print out the error measurements. */
fprintf(stdout,"%e\n%e\n%e\n%e\n%e\n%e\n\n",t_d,t_dp,t_fd,t_f,err_fd,
err_f);
/* Finalize the NFSFT plans */
nfsft_finalize(&plan_adjoint);
nfsft_finalize(&plan);
} /* for (im = 0; im < im_max; im++) - Process all cut-off
* bandwidths.*/
} /* for (ild = 0; ild < ild_max; ild++) - Process all node sets. */
} /* for (ip = 0; ip < ip_max; ip++) - Process all parameter sets. */
/* Delete precomputed data. */
nfsft_forget();
/* Check if memory for precomputed data of the matrix K has been
* allocated. */
if (precompute == YES)
{
/* Free memory for precomputed matrix K. */
nfft_free(prec);
}
/* Free data arrays. */
nfft_free(f);
nfft_free(f_m);
nfft_free(xi);
nfft_free(eta);
nfft_free(a);
nfft_free(f_hat);
nfft_free(b);
/* Free memory for node sets. */
for (ild = 0; ild < ild_max; ild++)
nfft_free(ld[ild]);
nfft_free(ld);
/* Free memory for cut-off bandwidths. */
nfft_free(m);
/* Free memory for parameter sets. */
for (ip = 0; ip < ip_max; ip++)
nfft_free(p[ip]);
nfft_free(p);
} /* for (tc = 0; tc < tc_max; tc++) - Process each testcase. */
/* Return exit code for successful run. */
return EXIT_SUCCESS;
}
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);
}