unsigned result = 0;
symbol a("a");
- for (int size=3; size<20; ++size) {
+ for (unsigned size=3; size<20; ++size) {
matrix A(size,size);
// populate one element in each row:
- for (int r=0; r<size-1; ++r)
+ for (unsigned r=0; r<size-1; ++r)
A.set(r,unsigned(rand()%size),dense_univariate_poly(a,5));
// 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)
+ for (unsigned 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 "
unsigned result = 0;
symbol a("a"), b("b"), c("c");
- for (int size=3; size<8; ++size) {
+ for (unsigned size=3; size<8; ++size) {
matrix A(size,size);
- for (int r=0; r<size-1; ++r) {
+ for (unsigned r=0; r<size-1; ++r) {
// populate one or two elements in each row:
- for (int ec=0; ec<2; ++ec) {
+ for (unsigned ec=0; ec<2; ++ec) {
ex numer = sparse_tree(a, b, c, 1+rand()%4, false, false, false);
ex denom;
do {
}
// 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)
+ for (unsigned 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 "
unsigned result = 0;
symbol a("a"), b("b"), c("c");
- for (int size=3; size<7; ++size) {
+ for (unsigned size=3; size<7; ++size) {
matrix A(size,size);
- for (int co=0; co<size-1; ++co) {
+ for (unsigned co=0; co<size-1; ++co) {
// populate one or two elements in each row:
- for (int ec=0; ec<2; ++ec) {
+ for (unsigned ec=0; ec<2; ++ec) {
ex numer = sparse_tree(a, b, c, 1+rand()%3, true, true, false);
ex denom;
do {
A.set(unsigned(rand()%size),co,numer/denom);
}
}
- // set the last column to a linear combination of two other lines
+ // set the last column to a linear combination of two other columns
// to guarantee that the determinant is zero:
- for (int ro=0; ro<size; ++ro)
+ 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 "
unsigned result = 0;
symbol a("a");
- for (int size=2; size<6; ++size) {
+ for (unsigned size=2; size<7; ++size) {
matrix A(size,size);
- for (int co=0; co<size; ++co) {
- for (int ro=0; ro<size; ++ro) {
+ for (unsigned co=0; co<size; ++co) {
+ for (unsigned ro=0; ro<size; ++ro) {
// populate some elements
ex elem = 0;
- if (rand()%(size-1) == 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_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(void)
+{
+ unsigned result = 0;
+ symbol a("a"), b("b"), c("c");
+
+ for (unsigned size=2; size<5; ++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(void)
{
unsigned result = 0;
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;