* an integral domain. */
static unsigned integdom_matrix_determinants(void)
{
- unsigned result = 0;
- symbol a("a");
-
- for (unsigned size=3; size<20; ++size) {
- matrix A(size,size);
- // populate one element in each row:
- 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 (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 "
- << endl << A << endl
- << "was not found to vanish!" << endl;
- ++result;
- }
- }
-
- return result;
+ unsigned result = 0;
+ symbol a("a");
+
+ for (unsigned size=3; size<20; ++size) {
+ matrix A(size,size);
+ // populate one element in each row:
+ 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 (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 "
+ << endl << A << endl
+ << "was not found to vanish!" << endl;
+ ++result;
+ }
+ }
+
+ return result;
}
/* 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 (unsigned size=3; size<8; ++size) {
- matrix A(size,size);
- for (unsigned r=0; r<size-1; ++r) {
- // populate one or two elements in each row:
- for (unsigned 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 (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 "
- << endl << A << endl
- << "was not found to vanish!" << endl;
- ++result;
- }
- }
-
- return result;
+ unsigned result = 0;
+ symbol a("a"), b("b"), c("c");
+
+ for (unsigned size=3; size<8; ++size) {
+ matrix A(size,size);
+ for (unsigned r=0; r<size-1; ++r) {
+ // populate one or two elements in each row:
+ for (unsigned 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 (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 "
+ << endl << A << endl
+ << "was not found to vanish!" << endl;
+ ++result;
+ }
+ }
+
+ return result;
}
/* 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 (unsigned size=3; size<7; ++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;
+ unsigned result = 0;
+ symbol a("a"), b("b"), c("c");
+
+ for (unsigned size=3; size<7; ++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(void)
{
- unsigned result = 0;
- symbol a("a");
-
- for (unsigned size=2; size<7; ++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;
+ unsigned result = 0;
+ symbol a("a");
+
+ for (unsigned size=2; size<7; ++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(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 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;
-
- 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;
+ 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;
}
git://www.ginac.de / ginac.git / blobdiff