+ unsigned result = 0;
+ symbol a("a"), b("b"), c("c");
+
+ for (unsigned size=3; size<8; ++size) {
+ matrix A(size,size);
+ for (unsigned co=0; co<size-1; ++co) {
+ // populate one or two elements in each row:
+ for (unsigned ec=0; ec<2; ++ec) {
+ ex numer = sparse_tree(a, b, c, 1+rand()%3, true, true, false);
+ ex denom;
+ do {
+ denom = sparse_tree(a, b, c, rand()%2, false, true, false);
+ } while (denom.is_zero());
+ A.set(unsigned(rand()%size),co,numer/denom);
+ }
+ }
+ // set the last column to a linear combination of two other columns
+ // to guarantee that the determinant is zero:
+ for (unsigned ro=0; ro<size; ++ro)
+ A.set(ro,size-1,A(ro,0)-A(ro,size-2));
+ if (!A.determinant().is_zero()) {
+ clog << "Determinant of " << size << "x" << size << " matrix "
+ << endl << A << endl
+ << "was not found to vanish!" << endl;
+ ++result;
+ }
+ }
+
+ return result;
+}
+
+/* compare results from different determinant algorithms.*/
+static unsigned compare_matrix_determinants()
+{
+ unsigned result = 0;
+ symbol a("a");
+
+ for (unsigned size=2; size<8; ++size) {
+ matrix A(size,size);
+ for (unsigned co=0; co<size; ++co) {
+ for (unsigned ro=0; ro<size; ++ro) {
+ // populate some elements
+ ex elem = 0;
+ if (rand()%(size/2) == 0)
+ elem = sparse_tree(a, a, a, rand()%3, false, true, false);
+ A.set(ro,co,elem);
+ }
+ }
+ ex det_gauss = A.determinant(determinant_algo::gauss);
+ ex det_laplace = A.determinant(determinant_algo::laplace);
+ ex det_divfree = A.determinant(determinant_algo::divfree);
+ ex det_bareiss = A.determinant(determinant_algo::bareiss);
+ if ((det_gauss-det_laplace).normal() != 0 ||
+ (det_bareiss-det_laplace).normal() != 0 ||
+ (det_divfree-det_laplace).normal() != 0) {
+ clog << "Determinant of " << size << "x" << size << " matrix "
+ << endl << A << endl
+ << "is inconsistent between different algorithms:" << endl
+ << "Gauss elimination: " << det_gauss << endl
+ << "Minor elimination: " << det_laplace << endl
+ << "Division-free elim.: " << det_divfree << endl
+ << "Fraction-free elim.: " << det_bareiss << endl;
+ ++result;
+ }
+ }
+
+ return result;
+}
+
+static unsigned symbolic_matrix_inverse()
+{
+ unsigned result = 0;
+ symbol a("a"), b("b"), c("c");
+
+ for (unsigned size=2; size<6; ++size) {
+ matrix A(size,size);
+ do {
+ for (unsigned co=0; co<size; ++co) {
+ for (unsigned ro=0; ro<size; ++ro) {
+ // populate some elements
+ ex elem = 0;
+ if (rand()%(size/2) == 0)
+ elem = sparse_tree(a, b, c, rand()%2, false, true, false);
+ A.set(ro,co,elem);
+ }
+ }
+ } while (A.determinant() == 0);
+ matrix B = A.inverse();
+ matrix C = A.mul(B);
+ bool ok = true;
+ for (unsigned ro=0; ro<size; ++ro)
+ for (unsigned co=0; co<size; ++co)
+ if (C(ro,co).normal() != (ro==co?1:0))
+ ok = false;
+ if (!ok) {
+ clog << "Inverse of " << size << "x" << size << " matrix "
+ << endl << A << endl
+ << "erroneously returned: "
+ << endl << B << endl;
+ ++result;
+ }
+ }
+
+ return result;
+}
+
+unsigned check_matrices()
+{
+ unsigned result = 0;
+
+ cout << "checking symbolic matrix manipulations" << flush;
+ clog << "---------symbolic matrix manipulations:" << endl;
+
+ result += integdom_matrix_determinants(); cout << '.' << flush;
+ result += rational_matrix_determinants(); cout << '.' << flush;
+ result += funny_matrix_determinants(); cout << '.' << flush;
+ result += compare_matrix_determinants(); cout << '.' << flush;
+ result += symbolic_matrix_inverse(); cout << '.' << flush;
+
+ if (!result) {
+ cout << " passed " << endl;
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed " << endl;
+ }
+
+ return result;