*/
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2015 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
*
* 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
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include "times.h"
+#include "ginac.h"
+#include "timer.h"
+using namespace GiNaC;
+
+#include <iostream>
+#include <vector>
+using namespace std;
static unsigned toeplitz_det(unsigned size)
{
- unsigned result = 0;
- symbol a("a"), b("b");
- ex p[8] = {a,
- b,
- a+b,
- pow(a,2) + a*b + pow(b,2),
- pow(a,3) + pow(a,2)*b - a*pow(b,2) + pow(b,3),
- pow(a,4) + pow(a,3)*b + pow(a*b,2) + a*pow(b,3) + pow(b,4),
- pow(a,5) + pow(a,4)*b + pow(a,3)*pow(b,2) - pow(a,2)*pow(b,3) + a*pow(b,4) + pow(b,5),
- pow(a,6) + pow(a,5)*b + pow(a,4)*pow(b,2) + pow(a*b,3) + pow(a,2)*pow(b,4) + a*pow(b,5) + pow(b,6)
- };
-
- // construct Toeplitz matrix:
- 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 result = 0;
+ const symbol a("a"), b("b");
+ ex p[10] = {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}),
+ 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})
+ };
+
+ // 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 time_toeplitz()
+{
+ unsigned result = 0;
+
+ cout << "timing determinant of polyvariate symbolic Toeplitz matrices" << flush;
+
+ vector<unsigned> sizes;
+ vector<double> times;
+ timer longines;
+
+ sizes.push_back(7);
+ sizes.push_back(8);
+ sizes.push_back(9);
+ sizes.push_back(10);
+
+ 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;
+ }
+
+ // 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)
{
- 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(5);
- sizes.push_back(6);
- sizes.push_back(7);
- sizes.push_back(8);
-
- 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;
+ randomify_symbol_serials();
+ cout << setprecision(2) << showpoint;
+ return time_toeplitz();
}
git://www.ginac.de / ginac.git / blobdiff