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/** @file time_lw_H.cpp
*
* Test H from the paper "Comparison of Polynomial-Oriented CAS" by Robert H.
* Lewis and Michael Wester. */
/*
* GiNaC Copyright (C) 1999-2010 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include "ginac.h"
#include "timer.h"
using namespace GiNaC;
#include <iostream>
#include <vector>
using namespace std;
static unsigned test(unsigned n)
{
matrix hilbert(n,n);
for (unsigned r=0; r<n; ++r)
for (unsigned c=0; c<n; ++c)
hilbert.set(r,c,numeric(1,r+c+1));
ex det = hilbert.determinant();
/*
The closed form of the determinant of n x n Hilbert matrices is:
n-1 / \
----- | pow(factorial(r),3) |
| | | ------------------- |
| | | factorial(r+n) |
r = 0 \ /
*/
ex hilbdet = 1;
for (unsigned r=0; r<n; ++r)
hilbdet *= pow(factorial(r),3)/(factorial(r+n));
if (det != hilbdet) {
clog << "determinant of " << n << "x" << n << " erroneously returned " << det << endl;
return 1;
}
return 0;
}
unsigned time_lw_H()
{
unsigned result = 0;
unsigned count = 0;
timer rolex;
double time = .0;
cout << "timing Lewis-Wester test H (det of 80x80 Hilbert)" << flush;
rolex.start();
// correct for very small times:
do {
result = test(80);
++count;
} while ((time=rolex.read())<0.1 && !result);
cout << '.' << flush;
cout << time/count << 's' << endl;
return result;
}
extern void randomify_symbol_serials();
int main(int argc, char** argv)
{
randomify_symbol_serials();
cout << setprecision(2) << showpoint;
return time_lw_H();
}
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