* time_lw_H.cpp (test): Simplification of Hilbert determinant formula.
[ginac.git] / check / time_lw_H.cpp
index e988e46b652d90a3f3a14f076a4176489776e9fe..83fdf80975c5d123824cef11173e3963480c85c8 100644 (file)
 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;
@@ -62,10 +59,10 @@ unsigned time_lw_H()
        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 {
@@ -73,7 +70,7 @@ unsigned time_lw_H()
                ++count;
        } while ((time=rolex.read())<0.1 && !result);
        cout << '.' << flush;
-       
+
        if (!result) {
                cout << " passed ";
                clog << "(no output)" << endl;
@@ -81,6 +78,6 @@ unsigned time_lw_H()
                cout << " failed ";
        }
        cout << int(1000*(time/count))*0.001 << 's' << endl;
-       
+
        return result;
 }