index 1621a6e117e69d7da938a69dfa4af0cd5bf7f885..c9e30c0080710c3b47074d43e97f7a1bb5fac4a5 100644 (file)
@@ -4,7 +4,7 @@
*  Lewis and Michael Wester. */

/*
- *  GiNaC Copyright (C) 1999-2001 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:

-       // 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;
@@ -54,16 +53,16 @@ static unsigned test(unsigned n)
return 0;
}

-unsigned time_lw_H(void)
+unsigned time_lw_H()
{
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;
-
+       clog << "-------Lewis-Wester test H (det of 80x80 Hilbert):" << endl;
+
rolex.start();
// correct for very small times:
do {
@@ -71,7 +70,7 @@ unsigned time_lw_H(void)
++count;
cout << '.' << flush;
-
+
if (!result) {
cout << " passed ";
clog << "(no output)" << endl;
@@ -79,6 +78,6 @@ unsigned time_lw_H(void)
cout << " failed ";
}
cout << int(1000*(time/count))*0.001 << 's' << endl;
-
+
return result;
}