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 */
const char *s; /**< name of kernel */
C (*kernel)(R, int, const R *); /**< kernel function */
R c; /**< parameter for kernel */
fastsum_plan my_fastsum_plan; /**< plan for fast summation */
C *direct; /**< array for direct computation */
ticks t0, t1; /**< for time measurement */
R time; /**< for time measurement */
R error = K(0.0); /**< for error computation */
R eps_I; /**< inner boundary */
R eps_B; /**< outer boundary */
FILE *fid1, *fid2;
R temp;
if (argc != 11)
{
printf("\nfastsum_test d N M n m p kernel c\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 = K(1.0) / POW((R)(N), K(1.0) / ((R)(d)));
M = atoi(argv[3]);
n = atoi(argv[4]);
m = atoi(argv[5]);
p = atoi(argv[6]);
s = argv[7];
c = (R)(atof(argv[8]));
eps_I = (R)(atof(argv[9]));
eps_B = (R)(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=%" __FGS__ ", eps_I=%" __FGS__ ", eps_B=%" __FGS__ " \n",
d, N, M, n, m, p, s, c, eps_I, eps_B);
/** init two 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, EXACT_NEARFIELD, n, m, p);*/
/** load source knots and coefficients */
fid1 = fopen("x.dat", "r");
fid2 = fopen("alpha.dat", "r");
for (k = 0; k < N; k++)
{
for (t = 0; t < d; t++)
{
fscanf(fid1, __FR__, &my_fastsum_plan.x[k * d + t]);
}
fscanf(fid2, __FR__, &temp);
my_fastsum_plan.alpha[k] = temp;
fscanf(fid2, __FR__, &temp);
my_fastsum_plan.alpha[k] += temp * II;
}
fclose(fid1);
fclose(fid2);
/** load target knots */
fid1 = fopen("y.dat", "r");
for (j = 0; j < M; j++)
{
for (t = 0; t < d; t++)
{
fscanf(fid1, __FR__, &my_fastsum_plan.y[j * d + t]);
}
}
fclose(fid1);
/** direct computation */
printf("direct computation: ");
fflush(NULL);
t0 = getticks();
fastsum_exact(&my_fastsum_plan);
t1 = getticks();
time = NFFT(elapsed_seconds)(t1, t0);
printf(__FI__ "sec\n", time);
/** copy result */
direct = (C *) NFFT(malloc)((size_t)(my_fastsum_plan.M_total) * (sizeof(C)));
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(__FI__ "sec\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(__FI__ "sec\n", time);
/** compute max error */
error = K(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: " __FE__ "\n", error);
/** write result to file */
fid1 = fopen("f.dat", "w+");
fid2 = fopen("f_direct.dat", "w+");
if (fid1 == NULL)
{
printf("Fehler!\n");
exit(EXIT_FAILURE);
}
for (j = 0; j < M; j++)
{
temp = CREAL(my_fastsum_plan.f[j]);
fprintf(fid1, " % .16" __FES__ "", temp);
temp = CIMAG(my_fastsum_plan.f[j]);
fprintf(fid1, " % .16" __FES__ "\n", temp);
temp = CREAL(direct[j]);
fprintf(fid2, " % .16" __FES__ "", temp);
temp = CIMAG(direct[j]);
fprintf(fid2, " % .16" __FES__ "\n", temp);
}
fclose(fid1);
fclose(fid2);
/** finalise the plan */
fastsum_finalize(&my_fastsum_plan);
return EXIT_SUCCESS;
}
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;
}
int bench_openmp(FILE *infile, int n, int m, int p,
C (*kernel)(R, int, const R *), R c, R eps_I, R eps_B)
{
fastsum_plan my_fastsum_plan;
int d, L, M;
int t, j;
R re, im;
R r_max = K(0.25) - my_fastsum_plan.eps_B / K(2.0);
ticks t0, t1;
R tt_total;
fscanf(infile, "%d %d %d", &d, &L, &M);
#ifdef _OPENMP
FFTW(import_wisdom_from_filename)("fastsum_benchomp_detail_threads.plan");
#else
FFTW(import_wisdom_from_filename)("fastsum_benchomp_detail_single.plan");
#endif
fastsum_init_guru(&my_fastsum_plan, d, L, M, kernel, &c, NEARFIELD_BOXES, n,
m, p, eps_I, eps_B);
#ifdef _OPENMP
FFTW(export_wisdom_to_filename)("fastsum_benchomp_detail_threads.plan");
#else
FFTW(export_wisdom_to_filename)("fastsum_benchomp_detail_single.plan");
#endif
for (j = 0; j < L; j++)
{
for (t = 0; t < d; t++)
{
R v;
fscanf(infile, __FR__, &v);
my_fastsum_plan.x[d * j + t] = v * r_max;
}
}
for (j = 0; j < L; j++)
{
fscanf(infile, __FR__ " " __FR__, &re, &im);
my_fastsum_plan.alpha[j] = re + II * im;
}
for (j = 0; j < M; j++)
{
for (t = 0; t < d; t++)
{
R v;
fscanf(infile, __FR__, &v);
my_fastsum_plan.y[d * j + t] = v * r_max;
}
}
/** precomputation */
t0 = getticks();
fastsum_precompute(&my_fastsum_plan);
/** fast computation */
fastsum_trafo(&my_fastsum_plan);
t1 = getticks();
tt_total = NFFT(elapsed_seconds)(t1, t0);
#ifndef MEASURE_TIME
my_fastsum_plan.MEASURE_TIME_t[0] = K(0.0);
my_fastsum_plan.MEASURE_TIME_t[1] = K(0.0);
my_fastsum_plan.MEASURE_TIME_t[2] = K(0.0);
my_fastsum_plan.MEASURE_TIME_t[3] = K(0.0);
my_fastsum_plan.MEASURE_TIME_t[4] = K(0.0);
my_fastsum_plan.MEASURE_TIME_t[5] = K(0.0);
my_fastsum_plan.MEASURE_TIME_t[6] = K(0.0);
my_fastsum_plan.MEASURE_TIME_t[7] = K(0.0);
my_fastsum_plan.mv1.MEASURE_TIME_t[0] = K(0.0);
my_fastsum_plan.mv1.MEASURE_TIME_t[2] = K(0.0);
my_fastsum_plan.mv2.MEASURE_TIME_t[0] = K(0.0);
my_fastsum_plan.mv2.MEASURE_TIME_t[2] = K(0.0);
#endif
#ifndef MEASURE_TIME_FFTW
my_fastsum_plan.mv1.MEASURE_TIME_t[1] = K(0.0);
my_fastsum_plan.mv2.MEASURE_TIME_t[1] = K(0.0);
#endif
printf(
"%.6" __FES__ " %.6" __FES__ " %.6" __FES__ " %6" __FES__ " %.6" __FES__ " %.6" __FES__ " %.6" __FES__ " %.6" __FES__ " %.6" __FES__ " %6" __FES__ " %.6" __FES__ " %.6" __FES__ " %6" __FES__ " %.6" __FES__ " %.6" __FES__ " %6" __FES__ "\n",
my_fastsum_plan.MEASURE_TIME_t[0], my_fastsum_plan.MEASURE_TIME_t[1],
my_fastsum_plan.MEASURE_TIME_t[2], my_fastsum_plan.MEASURE_TIME_t[3],
my_fastsum_plan.MEASURE_TIME_t[4], my_fastsum_plan.MEASURE_TIME_t[5],
my_fastsum_plan.MEASURE_TIME_t[6], my_fastsum_plan.MEASURE_TIME_t[7],
tt_total - my_fastsum_plan.MEASURE_TIME_t[0]
- my_fastsum_plan.MEASURE_TIME_t[1]
- my_fastsum_plan.MEASURE_TIME_t[2]
- my_fastsum_plan.MEASURE_TIME_t[3]
- my_fastsum_plan.MEASURE_TIME_t[4]
- my_fastsum_plan.MEASURE_TIME_t[5]
- my_fastsum_plan.MEASURE_TIME_t[6]
- my_fastsum_plan.MEASURE_TIME_t[7], tt_total,
my_fastsum_plan.mv1.MEASURE_TIME_t[0],
my_fastsum_plan.mv1.MEASURE_TIME_t[1],
my_fastsum_plan.mv1.MEASURE_TIME_t[2],
my_fastsum_plan.mv2.MEASURE_TIME_t[0],
my_fastsum_plan.mv2.MEASURE_TIME_t[1],
my_fastsum_plan.mv2.MEASURE_TIME_t[2]);
fastsum_finalize(&my_fastsum_plan);
return 0;
}
