index d9604b1145463887d9aa3224c650212cf039d1f0..fe64b3ab68e8548cd456e4d6a86517a200f16130 100644 (file)

#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;
@@ -52,7 +69,7 @@ unsigned time_lw_H(void)
rolex.start();
// correct for very small times:
do {
-               result = test();
+               result = test(80);
++count;
} while ((time=rolex.read())<0.1 && !result);
cout << '.' << flush;