* Lewis and Michael Wester. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2007 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 <iostream>
+#include <vector>
+#include "ginac.h"
+#include "timer.h"
+using namespace std;
+using namespace GiNaC;
-static unsigned test(void)
+static unsigned test(unsigned n)
{
- matrix h80(80,80);
-
- for (unsigned r=0; r<80; ++r)
- for (unsigned c=0; c<80; ++c)
- h80.set(r,c,numeric(1,r+c+1));
- ex det = h80.determinant();
-
- if (abs(det.evalf()-numeric(".10097939769690107E-3789"))>numeric("1.E-3800")) {
- clog << "determinant of 80x80 erroneously returned " << det << endl;
- return 1;
- }
- return 0;
+ 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(void)
+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)
{
- unsigned result = 0;
- unsigned count = 1;
- timer rolex;
- double time = .0;
-
- cout << "timing Lewis-Wester test H (det of 80x80 Hilbert)" << flush;
- clog << "-------Lewis-Wester test H (det of 80x80 Hilbert)" << endl;
-
- rolex.start();
- // correct for very small times:
- do {
- result = test();
- ++count;
- } while ((time=rolex.read())<0.1 && !result);
- cout << '.' << flush;
-
- if (!result) {
- cout << " passed ";
- clog << "(no output)" << endl;
- } else {
- cout << " failed ";
- }
- cout << int(1000*(time/count))*0.001 << 's' << endl;
-
- return result;
+ randomify_symbol_serials();
+ cout << setprecision(2) << showpoint;
+ return time_lw_H();
}