* Lewis and Michael Wester. */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2004 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
static unsigned test(unsigned n)
{
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 / n-1 \
- ----- | ----- |
- | | | pow(factorial(r),2) | | hilbert(r,c) |
- | | | | | |
- r = 0 \ c = 0 /
+ n-1 / \
+ ----- | pow(factorial(r),3) |
+ | | | ------------------- |
+ | | | factorial(r+n) |
+ r = 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);
- }
-
+ 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;
unsigned count = 0;
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 {
++count;
} while ((time=rolex.read())<0.1 && !result);
cout << '.' << flush;
-
+
if (!result) {
cout << " passed ";
clog << "(no output)" << endl;
cout << " failed ";
}
cout << int(1000*(time/count))*0.001 << 's' << endl;
-
+
return result;
}