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/** @file time_toeplitz.cpp
*
* Calculates determinants of dense symbolic Toeplitz materices.
* For 4x4 our matrix would look like this:
* [[a,b,a+b,a^2+a*b+b^2], [b,a,b,a+b], [a+b,b,a,b], [a^2+a*b+b^2,a+b,b,a]]
*/
/*
* GiNaC Copyright (C) 1999-2002 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"
static unsigned toeplitz_det(unsigned size)
{
unsigned result = 0;
const symbol a("a"), b("b");
ex p[9] = {ex("a",lst(a,b)),
ex("b",lst(a,b)),
ex("a+b",lst(a,b)),
ex("a^2+a*b+b^2",lst(a,b)),
ex("a^3+a^2*b-a*b^2+b^3",lst(a,b)),
ex("a^4+a^3*b+a^2*b^2+a*b^3+b^4",lst(a,b)),
ex("a^5+a^4*b+a^3*b^2-a^2*b^3+a*b^4+b^5",lst(a,b)),
ex("a^6+a^5*b+a^4*b^2+a^3*b^3+a^2*b^4+a*b^5+b^6",lst(a,b)),
ex("a^7+a^6*b+a^5*b^2+a^4*b^3-a^3*b^4+a^2*b^5+a*b^6+b^7",lst(a,b))
};
// construct Toeplitz matrix (diagonal structure: [[x,y,z],[y,x,y],[z,y,x]]):
matrix M(size,size);
for (unsigned ro=0; ro<size; ++ro) {
for (unsigned nd=ro; nd<size; ++nd) {
M.set(nd-ro,nd,p[ro]);
M.set(nd,nd-ro,p[ro]);
}
}
// compute determinant:
ex tdet = M.determinant();
// dirty consistency check of result:
if (!tdet.subs(a==0).subs(b==0).is_zero()) {
clog << "Determaint of Toeplitz matrix " << endl
<< "M==" << M << endl
<< "was miscalculated: det(M)==" << tdet << endl;
++result;
}
return result;
}
unsigned time_toeplitz(void)
{
unsigned result = 0;
cout << "timing determinant of polyvariate symbolic Toeplitz matrices" << flush;
clog << "-------determinant of polyvariate symbolic Toeplitz matrices:" << endl;
vector<unsigned> sizes;
vector<double> times;
timer longines;
sizes.push_back(6);
sizes.push_back(7);
sizes.push_back(8);
sizes.push_back(9);
for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
int count = 1;
longines.start();
result += toeplitz_det(*i);
// correct for very small times:
while (longines.read()<0.1) {
toeplitz_det(*i);
++count;
}
times.push_back(longines.read()/count);
cout << '.' << flush;
}
if (!result) {
cout << " passed ";
clog << "(no output)" << endl;
} else {
cout << " failed ";
}
// 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' << int(1000*(*i))*0.001;
cout << endl;
return result;
}
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