static unsigned vandermonde_det(unsigned size)
{
unsigned result = 0;
- symbol a("a");
-
+ const symbol a("a");
+
// construct Vandermonde matrix:
matrix M(size,size);
for (unsigned ro=0; ro<size; ++ro) {
for (unsigned co=0; co<size; ++co) {
if (ro%2)
- M.set(ro,co,pow(-pow(a,1+ro/2),co));
+ M(ro,co) = pow(-pow(a,1+ro/2),co);
else
- M.set(ro,co,pow(pow(a,1+ro/2),co));
+ M(ro,co) = pow(pow(a,1+ro/2),co);
}
}
-
+
// compute determinant:
- ex vdet = M.determinant();
-
- // dirty consistency check of result:
- if (!vdet.subs(a==1).is_zero()) {
+ ex det = M.determinant();
+
+ // check the result:
+ ex vanddet = 1;
+ for (unsigned i=0; i<size; ++i)
+ for (unsigned j=0; j<i; ++j)
+ vanddet *= M(i,1) - M(j,1);
+
+ if (expand(det - vanddet) != 0) {
clog << "Determaint of Vandermonde matrix " << endl
<< "M==" << M << endl
- << "was miscalculated: det(M)==" << vdet << endl;
+ << "was miscalculated: det(M)==" << det << endl;
++result;
}
-
+
return result;
}
vector<double> times;
timer swatch;
- sizes.push_back(4);
sizes.push_back(6);
sizes.push_back(8);
sizes.push_back(10);
+ sizes.push_back(12);
for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
int count = 1;