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/** @file time_vandermonde.cpp
*
* Calculates determinants of dense symbolic Vandermonde materices with
* monomials in one single variable as entries.
* For 4x4 our matrix would look like this:
* [[1,a,a^2,a^3], [1,-a,a^2,-a^3], [1,a^2,a^4,a^6], [1,-a^2,a^4,-a^6]]
*/
/*
* GiNaC Copyright (C) 1999-2025 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 vandermonde_det(unsigned size)
{
unsigned result = 0;
const symbol a("a");
// construct Vandermonde matrix:
matrix M(size,size);
for (unsigned ro=0; ro<size; ++ro) {
for (unsigned co=0; co<size; ++co) {
if (ro%2)
M(ro,co) = pow(-pow(a,1+ro/2),co);
else
M(ro,co) = pow(pow(a,1+ro/2),co);
}
}
// compute determinant:
ex det = M.determinant();
// check the result:
ex vanddet = 1;
for (unsigned i=0; i<size; ++i)
for (unsigned j=0; j<i; ++j)
vanddet *= M(i,1) - M(j,1);
if (expand(det - vanddet) != 0) {
clog << "Determinant of Vandermonde matrix " << endl
<< "M==" << M << endl
<< "was miscalculated: det(M)==" << det << endl;
++result;
}
return result;
}
unsigned time_vandermonde()
{
unsigned result = 0;
cout << "timing determinant of univariate symbolic Vandermonde matrices" << flush;
vector<unsigned> sizes = {8, 10, 12, 14};
vector<double> times;
timer swatch;
for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
int count = 1;
swatch.start();
result += vandermonde_det(*i);
// correct for very small times:
while (swatch.read()<0.02) {
vandermonde_det(*i);
++count;
}
times.push_back(swatch.read()/count);
cout << '.' << flush;
}
// print the report:
cout << endl << " dim: ";
for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i)
cout << '\t' << *i << 'x' << *i;
cout << endl << " time/s:";
for (vector<double>::iterator i=times.begin(); i!=times.end(); ++i)
cout << '\t' << *i;
cout << endl;
return result;
}
extern void randomify_symbol_serials();
int main(int argc, char** argv)
{
randomify_symbol_serials();
cout << setprecision(2) << showpoint;
return time_vandermonde();
}
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