* Lewis and Michael Wester. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * 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
#include "times.h"
-static unsigned test(void)
+static unsigned test(unsigned n)
{
- matrix h80(80,80);
+ matrix hilbert(n,n);
- 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();
+ 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();
- if (abs(det.evalf()-numeric(".10097939769690107E-3789"))>numeric("1.E-3800")) {
- clog << "determinant of 80x80 erroneously returned " << det << endl;
+ /*
+ The closed form of the determinant of n x n Hilbert matrices is:
+
+ n-1 / n-1 \
+ ----- | ----- |
+ | | | pow(factorial(r),2) | | hilbert(r,c) |
+ | | | | | |
+ r = 0 \ c = 0 /
+ */
+
+ ex hilbdet = 1;
+ for (unsigned r=0; r<n; ++r) {
+ hilbdet *= pow(factorial(numeric(r)),2);
+ for (unsigned c=0; c<n; ++c)
+ hilbdet *= hilbert(r,c);
+ }
+
+ if (det != hilbdet) {
+ clog << "determinant of " << n << "x" << n << " erroneously returned " << det << endl;
return 1;
}
return 0;
double time = .0;
cout << "timing Lewis-Wester test H (det of 80x80 Hilbert)" << flush;
- clog << "-------Lewis-Wester test H (det of 80x80 Hilbert)" << endl;
+ clog << "-------Lewis-Wester test H (det of 80x80 Hilbert):" << endl;
rolex.start();
// correct for very small times:
do {
- result = test();
+ result = test(80);
++count;
} while ((time=rolex.read())<0.1 && !result);
cout << '.' << flush;