- Just because it's fun: make the test more general using a formula for
authorRichard Kreckel <Richard.Kreckel@uni-mainz.de>
Tue, 12 Jun 2001 22:52:22 +0000 (22:52 +0000)
committerRichard Kreckel <Richard.Kreckel@uni-mainz.de>
Tue, 12 Jun 2001 22:52:22 +0000 (22:52 +0000)
  the closed form of the result suggested by David B.

check/time_lw_H.cpp

index d9604b1145463887d9aa3224c650212cf039d1f0..1621a6e117e69d7da938a69dfa4af0cd5bf7f885 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 +67,7 @@ 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;