1 /** @file time_toeplitz.cpp
3 * Calculates determinants of dense symbolic Toeplitz materices.
4 * For 4x4 our matrix would look like this:
5 * [[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]]
9 * GiNaC Copyright (C) 1999-2024 Johannes Gutenberg University Mainz, Germany
11 * This program is free software; you can redistribute it and/or modify
12 * it under the terms of the GNU General Public License as published by
13 * the Free Software Foundation; either version 2 of the License, or
14 * (at your option) any later version.
16 * This program is distributed in the hope that it will be useful,
17 * but WITHOUT ANY WARRANTY; without even the implied warranty of
18 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 * GNU General Public License for more details.
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23 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
28 using namespace GiNaC;
34 static unsigned toeplitz_det(unsigned size)
37 const symbol a("a"), b("b");
38 ex p[10] = {ex("a",lst{a,b}),
41 ex("a^2+a*b+b^2",lst{a,b}),
42 ex("a^3+a^2*b-a*b^2+b^3",lst{a,b}),
43 ex("a^4+a^3*b+a^2*b^2+a*b^3+b^4",lst{a,b}),
44 ex("a^5+a^4*b+a^3*b^2-a^2*b^3+a*b^4+b^5",lst{a,b}),
45 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}),
46 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}),
47 ex("a^8+a^7*b+a^6*b^2+a^5*b^3+a^4*b^4+a^3*b^5+a^2*b^6+a*b^7+b^8",lst{a,b})
50 // construct Toeplitz matrix (diagonal structure: [[x,y,z],[y,x,y],[z,y,x]]):
52 for (unsigned ro=0; ro<size; ++ro) {
53 for (unsigned nd=ro; nd<size; ++nd) {
54 M.set(nd-ro,nd,p[ro]);
55 M.set(nd,nd-ro,p[ro]);
59 // compute determinant:
60 ex tdet = M.determinant();
62 // dirty consistency check of result:
63 if (!tdet.subs(a==0).subs(b==0).is_zero()) {
64 clog << "Determinant of Toeplitz matrix " << endl
66 << "was miscalculated: det(M)==" << tdet << endl;
73 unsigned time_toeplitz()
77 cout << "timing determinant of polyvariate symbolic Toeplitz matrices" << flush;
79 vector<unsigned> sizes = {7, 8, 9, 10};
83 for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
86 result += toeplitz_det(*i);
87 // correct for very small times:
88 while (longines.read()<0.1) {
92 times.push_back(longines.read()/count);
97 cout << endl << " dim: ";
98 for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i)
99 cout << '\t' << *i << 'x' << *i;
100 cout << endl << " time/s:";
101 for (vector<double>::iterator i=times.begin(); i!=times.end(); ++i)
108 extern void randomify_symbol_serials();
110 int main(int argc, char** argv)
112 randomify_symbol_serials();
113 cout << setprecision(2) << showpoint;
114 return time_toeplitz();