static VALUE rb_gsl_utrunc_accel(VALUE obj)
{
gsl_sum_levin_utrunc_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_utrunc_alloc(n);
gsl_sum_levin_utrunc_accel(ptr, n, w, &sum, &err);
sum_plain = w->sum_plain;
terms_used = w->terms_used;
gsl_sum_levin_utrunc_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_trunc (double * t, double expected, const char * desc)
{
double sum_accel, prec;
gsl_sum_levin_utrunc_workspace * w = gsl_sum_levin_utrunc_alloc (N);
gsl_sum_levin_utrunc_accel (t, N, w, &sum_accel, &prec);
gsl_test_rel (sum_accel, expected, 1e-8, "trunc result, %s", desc);
/* No need to check precision for truncated result since this is not
a meaningful number */
gsl_sum_levin_utrunc_free (w);
}
Real
funcSum_all_accel(boost::function<Real(unsigned int i)> f,
std::size_t max_i, Real tolerance)
{
const Real p_0(f(0));
if (p_0 == 0.0)
{
return 0.0;
}
std::vector<Real> pTable(max_i);
pTable[0] = p_0;
for(std::size_t i=1; i < max_i; ++i)
{
pTable[i] = f(i);
}
Real sum;
Real error;
gsl_sum_levin_utrunc_workspace* workspace(gsl_sum_levin_utrunc_alloc(max_i));
gsl_sum_levin_utrunc_accel(
pTable.data(), pTable.size(), workspace, &sum, &error);
#ifdef ECELL_GREENS_FUNCTIONS_DEBUG_OUTPUT
if (std::abs(error) >= std::abs(sum * tolerance))
{
std::cerr << (boost::format("series acceleration error: %.16g"
" (rel error: %.16g), terms_used = %d (%d given)") %
std::abs(error) % std::abs(error / sum) %
workspace->terms_used % pTable.size()
).str() << std::endl;
}
#endif // ECELL_GREENS_FUNCTIONS_DEBUG_OUTPUT
gsl_sum_levin_utrunc_free(workspace);
return sum;
}
Real
funcSum(boost::function<Real(unsigned int i)> f, std::size_t max_i, Real tolerance)
// funcSum
// ==
// Will simply calculate the sum over a certain function f, until it converges
// (i.e. the sum > tolerance*current_term for a CONVERGENCE_CHECK number of
// terms), or a maximum number of terms is summed (usually 2000).
//
// Input:
// - f: A function object
// - max_i: maximum number of terms it will evaluate
// - tolerance: convergence condition, default value 1-e8 (see .hpp)
{
// DEFAULT = 4
const unsigned int CONVERGENCE_CHECK(4);
const Real p_0(f(0));
if (p_0 == 0.0)
{
return 0.0;
}
Real sum(p_0);
std::vector<Real> pTable;
pTable.reserve(max_i);
pTable.push_back(p_0);
unsigned int convergenceCounter(0);
for(std::size_t i=1; i < max_i; ++i)
{
const Real p_i(f(i));
pTable.push_back(p_i);
sum += p_i;
if (std::abs(sum) * tolerance >= std::abs(p_i)) // '=' is important
{
++convergenceCounter;
}
// this screws it up; why?
else
{
convergenceCounter = 0;
}
if (convergenceCounter >= CONVERGENCE_CHECK)
{
return sum; // converged! series acceleration is not needed! yay!
}
}
Real error;
gsl_sum_levin_utrunc_workspace*
workspace(gsl_sum_levin_utrunc_alloc(max_i));
gsl_sum_levin_utrunc_accel(
pTable.data(), pTable.size(), workspace, &sum, &error);
#ifdef ECELL_GREENS_FUNCTIONS_DEBUG_OUTPUT
if (std::abs(error) >= std::abs(sum * tolerance * 10))
{
std::cerr << (boost::format("series acceleration error: %.16g"
" (rel error: %.16g), terms_used = %d (%d given)") %
std::abs(error) % std::abs(error / sum) %
workspace->terms_used % pTable.size()
).str() << std::endl;
}
#endif // ECELL_GREENS_FUNCTIONS_DEBUG_OUTPUT
gsl_sum_levin_utrunc_free(workspace);
return sum;
}