/** @file time_gammaseries.cpp
*
* Some timings on series expansion of the Gamma function around a pole. */
/*
* GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include "times.h"
unsigned Gammaseries(unsigned order)
{
unsigned result = 0;
symbol x;
ex myseries = series(Gamma(x),x==0,order);
// compute the last coefficient numerically:
ex last_coeff = myseries.coeff(x,order-1).evalf();
// compute a bound for that coefficient using a variation of the leading
// term in Stirling's formula:
ex bound = evalf(exp(ex(-.57721566490153286*(order-1)))/(order-1));
if (evalf(abs((last_coeff-pow(-1,order))/bound)) > numeric(1)) {
clog << "The " << order-1
<< "th order coefficient in the power series expansion of Gamma(0) was erroneously found to be "
<< last_coeff << ", violating a simple estimate." << endl;
++result;
}
return result;
}
unsigned time_gammaseries(void)
{
unsigned result = 0;
cout << "timing Laurent series expansion of Gamma function" << flush;
clog << "-------Laurent series expansion of Gamma function:" << endl;
vector sizes;
vector times;
timer omega;
sizes.push_back(10);
sizes.push_back(15);
sizes.push_back(20);
sizes.push_back(25);
for (vector::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
omega.start();
result += Gammaseries(*i);
times.push_back(omega.read());
cout << '.' << flush;
}
if (!result) {
cout << " passed ";
clog << "(no output)" << endl;
} else {
cout << " failed ";
}
// print the report:
cout << endl << " order: ";
for (vector::iterator i=sizes.begin(); i!=sizes.end(); ++i)
cout << '\t' << (*i);
cout << endl << " time/s:";
for (vector::iterator i=times.begin(); i!=times.end(); ++i)
cout << '\t' << int(1000*(*i))*0.001;
cout << endl;
return result;
}