- unsigned result = 0;
- 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));
- else
- M.set(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()) {
- clog << "Determaint of Vandermonde matrix " << endl
- << "M==" << M << endl
- << "was miscalculated: det(M)==" << vdet << endl;
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+ 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(ro,co) = pow(-pow(a,1+ro/2),co);
+ else
+ M(ro,co) = pow(pow(a,1+ro/2),co);
+ }
+ }
+
+ // compute determinant:
+ 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)==" << det << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+unsigned time_vandermonde()
+{
+ unsigned result = 0;
+
+ cout << "timing determinant of univariate symbolic Vandermonde matrices" << flush;
+
+ vector<unsigned> sizes;
+ vector<double> times;
+ timer swatch;
+
+ sizes.push_back(8);
+ sizes.push_back(10);
+ sizes.push_back(12);
+ sizes.push_back(14);
+
+ for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i) {
+ int count = 1;
+ swatch.start();
+ result += vandermonde_det(*i);
+ // correct for very small times:
+ while (swatch.read()<0.02) {
+ vandermonde_det(*i);
+ ++count;
+ }
+ times.push_back(swatch.read()/count);
+ cout << '.' << flush;
+ }
+
+ // print the report:
+ cout << endl << " dim: ";
+ for (vector<unsigned>::iterator i=sizes.begin(); i!=sizes.end(); ++i)
+ cout << '\t' << *i << 'x' << *i;
+ cout << endl << " time/s:";
+ for (vector<double>::iterator i=times.begin(); i!=times.end(); ++i)
+ cout << '\t' << *i;
+ cout << endl;
+
+ return result;