double BEF(double p, double t)
{
double g;
int n, N=10;
double r[N], sum_accel, err, sum = 0.0;
double np1;
if(t < 1.0)
{
g = gsl_sf_zeta(p);
printf("error!\n");
}
else if(t > 1.0)
{
// exp(mu(t)/t)^n/n^(p)need mu function
gsl_sum_levin_u_workspace * w = gsl_sum_levin_u_alloc(N);
for (n = 0; n < N; n++)
{
np1 = n + 1.0;
r[n] = pow(exp( mu(t)/t ) ,np1) / pow(np1, p);
sum += r[n];
}
gsl_sum_levin_u_accel(r, N, w, &sum_accel, &err);
g = sum_accel;
gsl_sum_levin_u_free(w);
}
return g;
}
static VALUE rb_gsl_sum_levin_u_new(VALUE klass, VALUE nn)
{
gsl_sum_levin_u_workspace *w = NULL;
CHECK_FIXNUM(nn);
w = gsl_sum_levin_u_alloc(FIX2INT(nn));
return Data_Wrap_Struct(klass, 0, gsl_sum_levin_u_free, w);
}
static VALUE rb_gsl_sum_accel(VALUE obj)
{
gsl_sum_levin_u_workspace *w = NULL;
double sum, err, sum_plain, *ptr;
size_t terms_used, n, stride;
ptr = get_vector_ptr(obj, &stride, &n);
w = gsl_sum_levin_u_alloc(n);
gsl_sum_levin_u_accel(ptr, n, w, &sum, &err);
sum_plain = w->sum_plain;
terms_used = w->terms_used;
gsl_sum_levin_u_free(w);
return rb_ary_new3(4, rb_float_new(sum), rb_float_new(err),
rb_float_new(sum_plain), INT2FIX(terms_used));
}
void
check_full (double * t, double expected, const char * desc)
{
double sum_accel, err_est, sd_actual, sd_est;
gsl_sum_levin_u_workspace * w = gsl_sum_levin_u_alloc (N);
gsl_sum_levin_u_accel (t, N, w, &sum_accel, &err_est);
gsl_test_rel (sum_accel, expected, 1e-8, "full result, %s", desc);
sd_est = -log10 (err_est/fabs(sum_accel) + GSL_DBL_EPSILON);
sd_actual = -log10 (DBL_EPSILON + fabs ((sum_accel - expected)/expected));
/* Allow one digit of slop */
gsl_test (sd_est > sd_actual + 1.0, "full significant digits, %s (%g vs %g)", desc, sd_est, sd_actual);
gsl_sum_levin_u_free (w);
}
//高温領域でのmuの温度依存性を調べる関数
double mu(double t)
{
int j, N;
double mu1, mu2, g2=-5.0, g, g_exact;
int N2 = 10;
double r[N2], sum_accel, err, sum = 0.0;
int n;
double np1;
g_exact = gsl_sf_zeta(3.0/2.0)/pow(t, 3.0/2.0);
//partition
N = 1000;
for(j=0; j<=6.5*N; j++)
{
mu1 = 0.0 - 1.0*j/N;
gsl_sum_levin_u_workspace * w = gsl_sum_levin_u_alloc(N2);
for (n = 0; n < N2; n++)
{
np1 = n + 1.0;
r[n] = pow(exp( mu1/t ) ,np1) / pow(np1, 3.0/2.0);
sum += r[n];
}
gsl_sum_levin_u_accel(r, N2, w, &sum_accel, &err);
g = sum_accel;
gsl_sum_levin_u_free(w);
if( fabs( g - g_exact ) < fabs( g2 - g_exact ) )
{
//printf("%f %f %20.16f %20.16f %20.16f\n",t, mu1, g, g2, g_exact);
}else
{
//printf("%f %f %20.16f %20.16f %20.16f\n",t, mu1, g, g2, g_exact);
break;
}
g2 = g;
mu2 = mu1;
}
return mu2;
}
int
main (void)
{
double t[N];
double sum_accel, err;
double sum = 0;
int n;
gsl_sum_levin_u_workspace * w
= gsl_sum_levin_u_alloc (N);
const double zeta_2 = M_PI * M_PI / 6.0;
/* terms for zeta(2) = \sum_{n=1}^{\infty} 1/n^2 */
for (n = 0; n < N; n++)
{
double np1 = n + 1.0;
t[n] = 1.0 / (np1 * np1);
sum += t[n];
}
gsl_sum_levin_u_accel (t, N, w, &sum_accel, &err);
printf ("term-by-term sum = % .16f using %d terms\n",
sum, N);
printf ("term-by-term sum = % .16f using "F_ZU" terms\n",
w->sum_plain, w->terms_used);
printf ("exact value = % .16f\n", zeta_2);
printf ("accelerated sum = % .16f using "F_ZU" terms\n",
sum_accel, w->terms_used);
printf ("estimated error = % .16f\n", err);
printf ("actual error = % .16f\n",
sum_accel - zeta_2);
gsl_sum_levin_u_free (w);
return 0;
}
void Hamaker_sommatoria(double* risultato) {
// da: http://www.gnu.org/software/gsl/manual/html_node/Example-of-accelerating-a-series.html
double epsilon_st, epsilon_me, epsilon_p, epsilon_h;
int xi, xi_n;
xi = (int) (2* M_PI * GSL_CONST_MKSA_BOLTZMANN * (in.T) / GSL_CONST_MKSA_PLANCKS_CONSTANT_HBAR);
int numero_iterazioni = 100;
double t[numero_iterazioni];
double sum_accel, err;
//double sum = 0;
int n;
gsl_sum_levin_u_workspace * w
= gsl_sum_levin_u_alloc (numero_iterazioni);
for (n = 0; n < numero_iterazioni; n++)
{
xi_n = xi * n;
// assumo le parentesi quadre della formula come parti intere
epsilon_st = (74.8/(int)(1+xi_n/6.5E-5)) + (1.464/(int)(1+pow((xi_n/0.021), 2)))+ (0.737/(int)(1+pow((xi_n/0.067),2)))+ (0.153/(int) pow(1+(xi_n/0.092),2))+(0.014/(int)(1+pow((xi_n/0.2),2)))+(0.075/(int)(1+pow((xi_n/0.42),2)))+(0.078/(int)(1+pow((xi_n/12.7),2)))+ 1;
epsilon_p = (1+(in.C1)/(int)(1+(xi_n/10)*(xi_n/10)));
epsilon_h = (1+1/(int)(1+(xi_n/10.4)*(xi_n/10.4)));
epsilon_me = (in.ni_p) * epsilon_p + (1-(in.ni_p)) * epsilon_h;
t[n] = pow((epsilon_st-epsilon_me)/(epsilon_st+epsilon_me), 2);
}
gsl_sum_levin_u_accel (t, numero_iterazioni, w, &sum_accel, &err);
gsl_sum_levin_u_free (w);
*risultato = sum_accel;
}
