/**
* 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;
}
/**
* 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;
}