49 int main(
int argc,
char **argv)
59 C (*kernel)(R, int,
const R *);
71 printf(
"\nfastsum_test d N M n m p kernel c eps_I eps_B\n\n");
72 printf(
" d dimension \n");
73 printf(
" N number of source nodes \n");
74 printf(
" M number of target nodes \n");
75 printf(
" n expansion degree \n");
76 printf(
" m cut-off parameter \n");
77 printf(
" p degree of smoothness \n");
78 printf(
" kernel kernel function (e.g., gaussian)\n");
79 printf(
" c kernel parameter \n");
80 printf(
" eps_I inner boundary \n");
81 printf(
" eps_B outer boundary \n\n");
88 c = K(1.0) / POW((R)(N), K(1.0) / ((R)(d)));
94 c = (R)(atof(argv[8]));
95 eps_I = (R)(atof(argv[9]));
96 eps_B = (R)(atof(argv[10]));
97 if (strcmp(s,
"gaussian") == 0)
99 else if (strcmp(s,
"multiquadric") == 0)
101 else if (strcmp(s,
"inverse_multiquadric") == 0)
103 else if (strcmp(s,
"logarithm") == 0)
105 else if (strcmp(s,
"thinplate_spline") == 0)
107 else if (strcmp(s,
"one_over_square") == 0)
109 else if (strcmp(s,
"one_over_modulus") == 0)
111 else if (strcmp(s,
"one_over_x") == 0)
113 else if (strcmp(s,
"inverse_multiquadric3") == 0)
115 else if (strcmp(s,
"sinc_kernel") == 0)
117 else if (strcmp(s,
"cosc") == 0)
119 else if (strcmp(s,
"cot") == 0)
121 else if (strcmp(s,
"one_over_cube") == 0)
123 else if (strcmp(s,
"log_sin") == 0)
132 "d=%d, N=%d, M=%d, n=%d, m=%d, p=%d, kernel=%s, c=%" __FGS__
", eps_I=%" __FGS__
", eps_B=%" __FGS__
" \n",
133 d, N, M, n, m, p, s, c, eps_I, eps_B);
135 printf(
"nearfield correction using piecewise cubic Lagrange interpolation\n");
136 #elif defined(NF_QUADR)
137 printf(
"nearfield correction using piecewise quadratic Lagrange interpolation\n");
138 #elif defined(NF_LIN)
139 printf(
"nearfield correction using piecewise linear Lagrange interpolation\n");
147 printf(
"nthreads=%d\n", omp_get_max_threads());
151 FFTW(init_threads)();
155 fastsum_init_guru(&my_fastsum_plan, d, N, M, kernel, &c, 0, n, m, p, eps_I,
159 if (my_fastsum_plan.
flags & NEARFIELD_BOXES)
161 "determination of nearfield candidates based on partitioning into boxes\n");
163 printf(
"determination of nearfield candidates based on search tree\n");
169 R r_max = K(0.25) - my_fastsum_plan.
eps_B / K(2.0);
172 for (j = 0; j < d; j++)
173 my_fastsum_plan.
x[k * d + j] = K(2.0) * r_max * NFFT(drand48)() - r_max;
175 for (j = 0; j < d; j++)
176 r2 += my_fastsum_plan.
x[k * d + j] * my_fastsum_plan.
x[k * d + j];
178 if (r2 >= r_max * r_max)
184 for (k = 0; k < N; k++)
199 my_fastsum_plan.
alpha[k] = NFFT(drand48)() + II * NFFT(drand48)();
206 R r_max = K(0.25) - my_fastsum_plan.
eps_B / K(2.0);
209 for (j = 0; j < d; j++)
210 my_fastsum_plan.
y[k * d + j] = K(2.0) * r_max * NFFT(drand48)() - r_max;
212 for (j = 0; j < d; j++)
213 r2 += my_fastsum_plan.
y[k * d + j] * my_fastsum_plan.
y[k * d + j];
215 if (r2 >= r_max * r_max)
237 printf(
"direct computation: ");
242 time = NFFT(elapsed_seconds)(t1, t0);
243 printf(__FI__
"sec\n", time);
246 direct = (C *) NFFT(malloc)((size_t)(my_fastsum_plan.
M_total) * (
sizeof(C)));
247 for (j = 0; j < my_fastsum_plan.
M_total; j++)
248 direct[j] = my_fastsum_plan.
f[j];
251 printf(
"pre-computation: ");
256 time = NFFT(elapsed_seconds)(t1, t0);
257 printf(__FI__
"sec\n", time);
260 printf(
"fast computation: ");
265 time = NFFT(elapsed_seconds)(t1, t0);
266 printf(__FI__
"sec\n", time);
270 for (j = 0; j < my_fastsum_plan.
M_total; j++)
272 if (CABS(direct[j] - my_fastsum_plan.
f[j]) / CABS(direct[j]) > error)
273 error = CABS(direct[j] - my_fastsum_plan.
f[j]) / CABS(direct[j]);
275 printf(
"max relative error: %" __FES__
"\n", error);
int M_total
number of target knots
C inverse_multiquadric3(R x, int der, const R *param)
K(x) = 1/sqrt(x^2+c^2)^3.
C one_over_cube(R x, int der, const R *param)
K(x) = 1/x^3.
C gaussian(R x, int der, const R *param)
K(x)=exp(-x^2/c^2)
Header file with predefined kernels for the fast summation algorithm.
C cosc(R x, int der, const R *param)
K(x) = cos(cx)/x.
C one_over_x(R x, int der, const R *param)
K(x) = 1/x.
C thinplate_spline(R x, int der, const R *param)
K(x) = x^2 log |x|.
C sinc_kernel(R x, int der, const R *param)
K(x) = sin(cx)/x.
plan for fast summation algorithm
Header file for the fast NFFT-based summation algorithm.
C * alpha
source coefficients
unsigned flags
flags precomp.
void fastsum_trafo(fastsum_plan *ths)
fast NFFT-based summation
void fastsum_precompute(fastsum_plan *ths)
precomputation for fastsum
C one_over_square(R x, int der, const R *param)
K(x) = 1/x^2.
C one_over_modulus(R x, int der, const R *param)
K(x) = 1/|x|.
C logarithm(R x, int der, const R *param)
K(x)=log |x|.
void fastsum_init_guru(fastsum_plan *ths, int d, int N_total, int M_total, kernel k, R *param, unsigned flags, int nn, int m, int p, R eps_I, R eps_B)
initialization of fastsum plan
C inverse_multiquadric(R x, int der, const R *param)
K(x)=1/sqrt(x^2+c^2)
R * y
target knots in d-ball with radius 1/4-eps_b/2
C kcot(R x, int der, const R *param)
K(x) = cot(cx)
C multiquadric(R x, int der, const R *param)
K(x)=sqrt(x^2+c^2)
void fastsum_finalize(fastsum_plan *ths)
finalization of fastsum plan
void fastsum_exact(fastsum_plan *ths)
direct computation of sums
C log_sin(R x, int der, const R *param)
K(x) = log(|sin(cx)|)
R * x
source knots in d-ball with radius 1/4-eps_b/2