for (int size=3; size<20; ++size) {
matrix A(size,size);
- for (int r=0; r<size-1; ++r) {
- // populate one element in each row:
+ // populate one element in each row:
+ for (int r=0; r<size-1; ++r)
A.set(r,unsigned(rand()%size),dense_univariate_poly(a,5));
- }
- for (int c=0; c<size; ++c) {
- // set the last line to a linear combination of two other lines
- // to guarantee that the determinant is zero:
+ // set the last row to a linear combination of two other lines
+ // to guarantee that the determinant is zero:
+ for (int c=0; c<size; ++c)
A.set(size-1,c,A(0,c)-A(size-2,c));
- }
if (!A.determinant().is_zero()) {
clog << "Determinant of " << size << "x" << size << " matrix "
<< endl << A << endl
return result;
}
-/* determinants of some sparse symbolic matrices with multivariate rational
- * function coefficients. */
+/* determinants of some symbolic matrices with multivariate rational function
+ * coefficients. */
static unsigned rational_matrix_determinants(void)
{
unsigned result = 0;
symbol a("a"), b("b"), c("c");
-
+
for (int size=3; size<8; ++size) {
matrix A(size,size);
for (int r=0; r<size-1; ++r) {
- // populate one element in each row:
- ex numer = sparse_tree(a, b, c, 4, false, false, false);
- ex denom;
- do {
- denom = sparse_tree(a, b, c, 1, false, false, false);
- } while (denom.is_zero());
- A.set(r,unsigned(rand()%size),numer/denom);
- }
- for (int c=0; c<size; ++c) {
- // set the last line to a linear combination of two other lines
- // to guarantee that the determinant is zero:
- A.set(size-1,c,A(0,c)-A(size-2,c));
+ // populate one or two elements in each row:
+ for (int ec=0; ec<2; ++ec) {
+ ex numer = sparse_tree(a, b, c, 1+rand()%4, false, false, false);
+ ex denom;
+ do {
+ denom = sparse_tree(a, b, c, rand()%2, false, false, false);
+ } while (denom.is_zero());
+ A.set(r,unsigned(rand()%size),numer/denom);
+ }
}
+ // set the last row to a linear combination of two other lines
+ // to guarantee that the determinant is zero:
+ for (int co=0; co<size; ++co)
+ A.set(size-1,co,A(0,co)-A(size-2,co));
if (!A.determinant().is_zero()) {
clog << "Determinant of " << size << "x" << size << " matrix "
<< endl << A << endl
return result;
}
-/* Some quite wild determinants with functions and stuff like that. */
-static unsigned wild_matrix_determinants(void)
+/* Some quite funny determinants with functions and stuff like that inside. */
+static unsigned funny_matrix_determinants(void)
{
unsigned result = 0;
symbol a("a"), b("b"), c("c");
- for (int size=3; size<6; ++size) {
+ for (int size=3; size<7; ++size) {
matrix A(size,size);
- for (int r=0; r<size-1; ++r) {
- // populate one element in each row:
- ex numer = sparse_tree(a, b, c, 3, true, true, false);
- ex denom;
- do {
- denom = sparse_tree(a, b, c, 1, false, true, false);
- } while (denom.is_zero());
- A.set(r,unsigned(rand()%size),numer/denom);
- }
- for (int c=0; c<size; ++c) {
- // set the last line to a linear combination of two other lines
- // to guarantee that the determinant is zero:
- A.set(size-1,c,A(0,c)-A(size-2,c));
+ for (int co=0; co<size-1; ++co) {
+ // populate one or two elements in each row:
+ for (int 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 lines
+ // to guarantee that the determinant is zero:
+ for (int 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
return result;
}
+/* compare results from different determinant algorithms.*/
+static unsigned compare_matrix_determinants(void)
+{
+ unsigned result = 0;
+ symbol a("a");
+
+ for (int size=2; size<6; ++size) {
+ matrix A(size,size);
+ for (int co=0; co<size; ++co) {
+ for (int ro=0; ro<size; ++ro) {
+ // populate some elements
+ ex elem = 0;
+ if (rand()%(size-1) == 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_bareiss = A.determinant(determinant_algo::bareiss);
+ if ((det_gauss-det_laplace).normal() != 0 ||
+ (det_bareiss-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
+ << "Fraction-free elim.: " << det_bareiss << endl;
+ ++result;
+ }
+ }
+
+ return result;
+}
+
unsigned check_matrices(void)
{
unsigned result = 0;
result += integdom_matrix_determinants(); cout << '.' << flush;
result += rational_matrix_determinants(); cout << '.' << flush;
- result += wild_matrix_determinants(); cout << '.' << flush;
+ result += funny_matrix_determinants(); cout << '.' << flush;
+ result += compare_matrix_determinants(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;
git://www.ginac.de / ginac.git / blobdiff