- Just because it's fun: make the test more general using a formula for
[ginac.git] / check / time_lw_H.cpp
index a7c5c852ddbe149e04a0f49978f3eb7dbfa48d05..1621a6e117e69d7da938a69dfa4af0cd5bf7f885 100644 (file)
@@ -4,7 +4,7 @@
  *  Lewis and Michael Wester. */
 
 /*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2001 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);
-    
-    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   /                      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;
 }
 
 unsigned time_lw_H(void)
 {
-    unsigned result = 0;
-    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 {
-        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;
+       unsigned result = 0;
+       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 {
+               result = test(80);
+               ++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;
 }