int main()
{
slong iter;
flint_rand_t state;
flint_printf("ldl....");
fflush(stdout);
flint_randinit(state);
/* check special matrices */
{
slong n;
for (n = 1; n < 10; n++)
{
slong lprec;
arb_mat_t L, A;
arb_mat_init(L, n, n);
arb_mat_init(A, n, n);
for (lprec = 2; lprec < 10; lprec++)
{
int result;
slong prec;
prec = 1 << lprec;
/* zero */
arb_mat_zero(A);
result = arb_mat_ldl(L, A, prec);
if (result)
{
flint_printf("FAIL (zero):\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("L = \n"); arb_mat_printd(L, 15);
flint_printf("\n\n");
}
/* negative identity */
arb_mat_one(A);
arb_mat_neg(A, A);
result = arb_mat_ldl(L, A, prec);
if (result)
{
flint_printf("FAIL (negative identity):\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("L = \n"); arb_mat_printd(L, 15);
flint_printf("\n\n");
}
/* identity */
arb_mat_one(A);
result = arb_mat_ldl(L, A, prec);
if (!result || !arb_mat_equal(L, A))
{
flint_printf("FAIL (identity):\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("L = \n"); arb_mat_printd(L, 15);
flint_printf("\n\n");
}
}
arb_mat_clear(L);
arb_mat_clear(A);
}
}
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q;
arb_mat_t A, L, D, U, T;
slong n, qbits, prec;
int q_invertible, r_invertible;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 202);
fmpq_mat_init(Q, n, n);
arb_mat_init(A, n, n);
arb_mat_init(L, n, n);
arb_mat_init(D, n, n);
arb_mat_init(U, n, n);
arb_mat_init(T, n, n);
_fmpq_mat_randtest_positive_semidefinite(Q, state, qbits);
q_invertible = fmpq_mat_is_invertible(Q);
if (!q_invertible)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_ldl(L, A, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("L = \n"); arb_mat_printd(L, 15); flint_printf("\n\n");
}
}
else
{
/* now this must converge */
while (1)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_ldl(L, A, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
abort();
}
prec *= 2;
}
}
/* multiply out the decomposition */
{
slong i;
arb_mat_zero(D);
arb_mat_transpose(U, L);
for (i = 0; i < n; i++)
{
arb_set(arb_mat_entry(D, i, i), arb_mat_entry(L, i, i));
arb_one(arb_mat_entry(L, i, i));
arb_one(arb_mat_entry(U, i, i));
}
arb_mat_mul(T, L, D, prec);
arb_mat_mul(T, T, U, prec);
}
if (!arb_mat_contains_fmpq_mat(T, Q))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("L = \n"); arb_mat_printd(L, 15); flint_printf("\n\n");
flint_printf("U = \n"); arb_mat_printd(U, 15); flint_printf("\n\n");
flint_printf("L*U = \n"); arb_mat_printd(T, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
arb_mat_clear(A);
arb_mat_clear(L);
arb_mat_clear(D);
arb_mat_clear(U);
arb_mat_clear(T);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("inv_ldl_precomp....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q, Qinv;
arb_mat_t A, Ainv;
slong n, qbits, prec;
int q_invertible, r_invertible, r_invertible2;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 30);
prec = 2 + n_randint(state, 200);
fmpq_mat_init(Q, n, n);
fmpq_mat_init(Qinv, n, n);
arb_mat_init(A, n, n);
arb_mat_init(Ainv, n, n);
_fmpq_mat_randtest_positive_semidefinite(Q, state, qbits);
q_invertible = fmpq_mat_inv(Qinv, Q);
if (!q_invertible)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = _spd_inv(Ainv, A, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); arb_mat_printd(Ainv, 15); flint_printf("\n\n");
abort();
}
}
else
{
/* now this must converge */
while (1)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = _spd_inv(Ainv, A, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
abort();
}
prec *= 2;
}
}
if (!arb_mat_contains_fmpq_mat(Ainv, Qinv))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("Qinv = \n"); fmpq_mat_print(Qinv); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); arb_mat_printd(Ainv, 15); flint_printf("\n\n");
abort();
}
/* test aliasing */
r_invertible2 = _spd_inv(A, A, prec);
if (!arb_mat_equal(A, Ainv) || r_invertible != r_invertible2)
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); arb_mat_printd(Ainv, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
fmpq_mat_clear(Qinv);
arb_mat_clear(A);
arb_mat_clear(Ainv);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("solve_tril....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
arb_mat_t A, X, B, Y;
slong rows, cols, prec, i, j;
int unit;
prec = 2 + n_randint(state, 200);
if (n_randint(state, 10) == 0)
{
rows = n_randint(state, 60);
cols = n_randint(state, 60);
}
else
{
rows = n_randint(state, 10);
cols = n_randint(state, 10);
}
unit = n_randint(state, 2);
arb_mat_init(A, rows, rows);
arb_mat_init(B, rows, cols);
arb_mat_init(X, rows, cols);
arb_mat_init(Y, rows, cols);
arb_mat_randtest(A, state, prec, 10);
arb_mat_randtest(X, state, prec, 10);
arb_mat_randtest(Y, state, prec, 10);
for (i = 0; i < rows; i++)
{
if (unit)
arb_one(arb_mat_entry(A, i, i));
else
arb_set_ui(arb_mat_entry(A, i, i), 1 + n_randint(state, 100));
for (j = i + 1; j < rows; j++)
arb_zero(arb_mat_entry(A, i, j));
}
arb_mat_mul(B, A, X, prec);
if (unit) /* check that diagonal entries are ignored */
{
for (i = 0; i < rows; i++)
arb_set_ui(arb_mat_entry(A, i, i), 1 + n_randint(state, 100));
}
/* Check Y = A^(-1) * (A * X) = X */
arb_mat_solve_tril(Y, A, B, unit, prec);
if (!arb_mat_overlaps(Y, X))
{
flint_printf("FAIL\n");
flint_printf("A = \n"); arb_mat_printd(A, 10); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 10); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 10); flint_printf("\n\n");
flint_printf("Y = \n"); arb_mat_printd(Y, 10); flint_printf("\n\n");
flint_abort();
}
/* Check aliasing */
arb_mat_solve_tril(B, A, B, unit, prec);
if (!arb_mat_equal(B, Y))
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); arb_mat_printd(A, 10); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 10); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 10); flint_printf("\n\n");
flint_printf("Y = \n"); arb_mat_printd(Y, 10); flint_printf("\n\n");
flint_abort();
}
arb_mat_clear(A);
arb_mat_clear(B);
arb_mat_clear(X);
arb_mat_clear(Y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("spd_solve....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q, QX, QB;
arb_mat_t A, X, B;
slong n, m, qbits, prec;
int q_invertible, r_invertible, r_invertible2;
n = n_randint(state, 8);
m = n_randint(state, 8);
qbits = 1 + n_randint(state, 30);
prec = 2 + n_randint(state, 200);
fmpq_mat_init(Q, n, n);
fmpq_mat_init(QX, n, m);
fmpq_mat_init(QB, n, m);
arb_mat_init(A, n, n);
arb_mat_init(X, n, m);
arb_mat_init(B, n, m);
_fmpq_mat_randtest_positive_semidefinite(Q, state, qbits);
fmpq_mat_randtest(QB, state, qbits);
q_invertible = fmpq_mat_solve_fraction_free(QX, Q, QB);
if (!q_invertible)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_spd_solve(X, A, B, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
abort();
}
}
else
{
/* now this must converge */
while (1)
{
arb_mat_set_fmpq_mat(A, Q, prec);
arb_mat_set_fmpq_mat(B, QB, prec);
r_invertible = arb_mat_spd_solve(X, A, B, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
abort();
}
prec *= 2;
}
}
if (!arb_mat_contains_fmpq_mat(X, QX))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 15); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 15); flint_printf("\n\n");
abort();
}
/* test aliasing */
r_invertible2 = arb_mat_spd_solve(B, A, B, prec);
if (!arb_mat_equal(X, B) || r_invertible != r_invertible2)
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 15); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
fmpq_mat_clear(QB);
fmpq_mat_clear(QX);
arb_mat_clear(A);
arb_mat_clear(B);
arb_mat_clear(X);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("frobenius_norm....");
fflush(stdout);
flint_randinit(state);
/* compare to the exact rational norm */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q;
fmpq_t q;
arb_mat_t A;
slong n, qbits, prec;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 200);
fmpq_mat_init(Q, n, n);
fmpq_init(q);
arb_mat_init(A, n, n);
fmpq_mat_randtest(Q, state, qbits);
_fmpq_mat_sum_of_squares(q, Q);
arb_mat_set_fmpq_mat(A, Q, prec);
/* check that the arb interval contains the exact value */
{
arb_t a;
arb_init(a);
arb_mat_frobenius_norm(a, A, prec);
arb_mul(a, a, a, prec);
if (!arb_contains_fmpq(a, q))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n");
fmpq_mat_print(Q);
flint_printf("\n\n");
flint_printf("frobenius_norm(Q)^2 = \n");
fmpq_print(q);
flint_printf("\n\n");
flint_printf("A = \n");
arb_mat_printd(A, 15);
flint_printf("\n\n");
flint_printf("frobenius_norm(A)^2 = \n");
arb_printd(a, 15);
flint_printf("\n\n");
flint_printf("frobenius_norm(A)^2 = \n");
arb_print(a);
flint_printf("\n\n");
abort();
}
arb_clear(a);
}
/* check that the upper bound is not less than the exact value */
{
mag_t b;
fmpq_t y;
mag_init(b);
fmpq_init(y);
arb_mat_bound_frobenius_norm(b, A);
mag_mul(b, b, b);
mag_get_fmpq(y, b);
if (fmpq_cmp(q, y) > 0)
{
flint_printf("FAIL (bound, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n");
fmpq_mat_print(Q);
flint_printf("\n\n");
flint_printf("frobenius_norm(Q)^2 = \n");
fmpq_print(q);
flint_printf("\n\n");
flint_printf("A = \n");
arb_mat_printd(A, 15);
flint_printf("\n\n");
flint_printf("bound_frobenius_norm(A)^2 = \n");
mag_printd(b, 15);
flint_printf("\n\n");
flint_printf("bound_frobenius_norm(A)^2 = \n");
mag_print(b);
flint_printf("\n\n");
abort();
}
mag_clear(b);
fmpq_clear(y);
}
fmpq_mat_clear(Q);
fmpq_clear(q);
arb_mat_clear(A);
}
/* check trace(A^T A) = frobenius_norm(A)^2 */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong m, n, prec;
arb_mat_t A, AT, ATA;
arb_t t;
prec = 2 + n_randint(state, 200);
m = n_randint(state, 10);
n = n_randint(state, 10);
arb_mat_init(A, m, n);
arb_mat_init(AT, n, m);
arb_mat_init(ATA, n, n);
arb_init(t);
arb_mat_randtest(A, state, 2 + n_randint(state, 100), 10);
arb_mat_transpose(AT, A);
arb_mat_mul(ATA, AT, A, prec);
arb_mat_trace(t, ATA, prec);
arb_sqrt(t, t, prec);
/* check the norm bound */
{
mag_t low, frobenius;
mag_init(low);
arb_get_mag_lower(low, t);
mag_init(frobenius);
arb_mat_bound_frobenius_norm(frobenius, A);
if (mag_cmp(low, frobenius) > 0)
{
flint_printf("FAIL (bound)\n", iter);
flint_printf("m = %wd, n = %wd, prec = %wd\n", m, n, prec);
flint_printf("\n");
flint_printf("A = \n");
arb_mat_printd(A, 15);
flint_printf("\n\n");
flint_printf("lower(sqrt(trace(A^T A))) = \n");
mag_printd(low, 15);
flint_printf("\n\n");
flint_printf("bound_frobenius_norm(A) = \n");
mag_printd(frobenius, 15);
flint_printf("\n\n");
abort();
}
mag_clear(low);
mag_clear(frobenius);
}
/* check the norm interval */
{
arb_t frobenius;
arb_init(frobenius);
arb_mat_frobenius_norm(frobenius, A, prec);
if (!arb_overlaps(t, frobenius))
{
flint_printf("FAIL (overlap)\n", iter);
flint_printf("m = %wd, n = %wd, prec = %wd\n", m, n, prec);
flint_printf("\n");
flint_printf("A = \n");
arb_mat_printd(A, 15);
flint_printf("\n\n");
flint_printf("sqrt(trace(A^T A)) = \n");
arb_printd(t, 15);
flint_printf("\n\n");
flint_printf("frobenius_norm(A) = \n");
arb_printd(frobenius, 15);
flint_printf("\n\n");
abort();
}
arb_clear(frobenius);
}
arb_mat_clear(A);
arb_mat_clear(AT);
arb_mat_clear(ATA);
arb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("det....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
fmpq_mat_t Q;
fmpq_t Qdet;
arb_mat_t A;
arb_t Adet;
slong n, qbits, prec;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 200);
fmpq_mat_init(Q, n, n);
fmpq_init(Qdet);
arb_mat_init(A, n, n);
arb_init(Adet);
fmpq_mat_randtest(Q, state, qbits);
fmpq_mat_det(Qdet, Q);
arb_mat_set_fmpq_mat(A, Q, prec);
arb_mat_det(Adet, A, prec);
if (!arb_contains_fmpq(Adet, Qdet))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("Qdet = \n"); fmpq_print(Qdet); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Adet = \n"); arb_printd(Adet, 15); flint_printf("\n\n");
flint_printf("Adet = \n"); arb_print(Adet); flint_printf("\n\n");
abort();
}
fmpq_mat_clear(Q);
fmpq_clear(Qdet);
arb_mat_clear(A);
arb_clear(Adet);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main(int argc, char* argv[]) {
if(argc < 2) {
printf("Compute Genz-Keister quadrature rule\n");
printf("Syntax: genzkeister [-dc D] [-dp D] [-pn] [-pw] [-pge] [-pwf] -K K [n1 n2 n3 ...nk]\n");
printf("Options:\n");
printf(" -dc Compute nodes and weights up to this number of decimal digits\n");
printf(" -dp Print this number of decimal digits\n");
printf(" -pn Do not print the nodes\n");
printf(" -pw Do not print the weights\n");
printf(" -pge Print the generators\n");
printf(" -pmo Print the moments\n");
printf(" -pai Print the a_i values\n");
printf(" -pwf Print the weight factors\n");
printf(" -pzs Print the Z-sequence\n");
printf(" -K Set the level of the rule\n");
printf(" Further optional parameters n1 ... nk define the Kronrod extension used\n");
return EXIT_FAILURE;
}
unsigned int K = 1;
int target_prec = 53;
int nrprintdigits = 20;
std::vector<int> levels;
bool print_nodes = true;
bool print_weights = true;
bool print_generators = false;
bool print_moments = false;
bool print_avalues = false;
bool print_weightfactors = false;
bool print_zsequence = false;
for(int i = 1; i < argc; i++) {
if (!strcmp(argv[i], "-dc")) {
/* 'digits' is in base 10 and log(10)/log(2) = 3.32193 */
target_prec = 3.32193 * atoi(argv[i+1]);
i++;
} else if (!strcmp(argv[i], "-dp")) {
nrprintdigits = atoi(argv[i+1]);
i++;
} else if (!strcmp(argv[i], "-pn")) {
print_nodes = false;
} else if (!strcmp(argv[i], "-pw")) {
print_weights = false;
} else if (!strcmp(argv[i], "-pge")) {
print_generators = true;
} else if (!strcmp(argv[i], "-pmo")) {
print_moments = true;
} else if (!strcmp(argv[i], "-pai")) {
print_avalues = true;
} else if (!strcmp(argv[i], "-pwf")) {
print_weightfactors = true;
} else if (!strcmp(argv[i], "-pzs")) {
print_zsequence = true;
} else if (!strcmp(argv[i], "-K")) {
K = atoi(argv[i+1]);
i++;
} else {
levels.push_back(atoi(argv[i]));
}
}
/* Dimension of the quadrature rule */
const unsigned int D = DIMENSION;
// Note K is shifted by 1 wrt the original paper
// This makes K=3 equal to the Gauss Rule of 3 points.
K--;
/* Default rule definition */
if(levels.size() == 0) {
#ifdef LEGENDRE
levels = {1, 2, 4, 8, 16, 32};//, 64};
#endif
#ifdef HERMITEPRO
levels = {1, 2, 6, 10, 16};//, 68};
#endif
#ifdef HERMITE
levels = {1, 2, 6, 10, 16};//, 68};
#endif
#ifdef CHEBYSHEVT
levels = {1, 2, 4, 6, 12, 24};//, 48};
#endif
#ifdef CHEBYSHEVU
levels = {1, 2, 4, 8, 16, 32};//, 64};
#endif
}
std::cout << "Kronrod extension: ";
for(auto it=levels.begin(); it != levels.end(); it++) {
std::cout << *it << " ";
}
std::cout << "\n==================================================" << std::endl;
/* Iteratively compute quadrature nodes and weights */
generators_t G;
tables_t T;
nodes_t<D> nodes;
weights_t weights;
rule_t<D> rule;
for(unsigned int working_prec = target_prec; ; working_prec *= 2) {
std::cout << "--------------------------------------------------\n";
std::cout << "Working precision (bits): " << working_prec << std::endl;
/* Compute data tables */
// TODO: Assert generator g_0 = 0
G = compute_generators(levels, 2*working_prec);
T = compute_tables(G, 2*working_prec);
if(K >= G.size()) {
std::cout << "***********************************\n";
std::cout << "*** not enough generators found ***\n";
std::cout << "***********************************\n";
break;
}
/* Compute a Genz-Keister quadrature rule */
rule = genz_keister_construction<D>(K, G, T, working_prec);
nodes = rule.first;
weights = rule.second;
/* Accuracy goal reached? */
if(check_accuracy<D>(nodes, weights, target_prec)) {
break;
}
}
/* Print nodes and weights */
std::cout << "==================================================\n";
std::cout << "DIMENSION: " << D << std::endl;
std::cout << "LEVEL: " << K+1 << std::endl;
std::cout << "NUMBER NODES: " << nodes.size() << std::endl;
if(print_generators) {
std::cout << "==================================================\n";
std::cout << "GENERATORS" << std::endl;
for(auto it=G.begin(); it != G.end(); it++) {
std::cout << "| ";
arb_printd(&(*it), nrprintdigits);
std::cout << std::endl;
}
}
if(print_moments) {
std::cout << "==================================================\n";
std::cout << "MOMENTS" << std::endl;
moments_t M = std::get<0>(T);
fmpq_mat_print(&M);
std::cout << std::endl;
}
if(print_avalues) {
std::cout << "==================================================\n";
std::cout << "A-VALUES" << std::endl;
ai_t A = std::get<1>(T);
arb_mat_printd(&A, nrprintdigits);
}
if(print_weightfactors) {
std::cout << "==================================================\n";
std::cout << "WEIGHTFACTORS" << std::endl;
wft_t WF = std::get<2>(T);
arb_mat_printd(&WF, nrprintdigits);
}
if(print_zsequence) {
std::cout << "==================================================\n";
std::cout << "Z-SEQUENCE" << std::endl;
z_t Z = std::get<3>(T);
std::cout << "Z = [ ";
for(auto it=Z.begin(); it != Z.end(); it++) {
std::cout << (*it) << " ";
}
std::cout << "]" << std::endl;
}
if(print_nodes) {
std::cout << "==================================================\n";
std::cout << "NODES" << std::endl;
for(auto it=nodes.begin(); it != nodes.end(); it++) {
std::cout << "| ";
for(unsigned int d=0; d < D; d++) {
arb_printd(&((*it)[d]), nrprintdigits);
std::cout << ",\t\t";
}
std::cout << std::endl;
}
}
if(print_weights) {
std::cout << "==================================================\n";
std::cout << "WEIGHTS" << std::endl;
for(auto it=weights.begin(); it != weights.end(); it++) {
std::cout << "| ";
arb_printd(&(*it), nrprintdigits);
std::cout << std::endl;
}
}
std::cout << "==================================================\n";
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("exp....");
fflush(stdout);
flint_randinit(state);
/* check exp(A)*exp(c*A) = exp((1+c)*A) */
for (iter = 0; iter < 1000; iter++)
{
arb_mat_t A, E, F, EF, G;
fmpq_mat_t Q;
arb_t c, d;
long n, qbits, prec;
n = n_randint(state, 5);
qbits = 2 + n_randint(state, 300);
prec = 2 + n_randint(state, 300);
arb_init(c);
arb_init(d);
fmpq_mat_init(Q, n, n);
arb_mat_init(A, n, n);
arb_mat_init(E, n, n);
arb_mat_init(F, n, n);
arb_mat_init(EF, n, n);
arb_mat_init(G, n, n);
fmpq_mat_randtest(Q, state, qbits);
arb_mat_set_fmpq_mat(A, Q, prec);
arb_mat_exp(E, A, prec);
arb_randtest(c, state, prec, 10);
arb_mat_scalar_mul_arb(F, A, c, prec);
arb_mat_exp(F, F, prec);
arb_add_ui(d, c, 1, prec);
arb_mat_scalar_mul_arb(G, A, d, prec);
arb_mat_exp(G, G, prec);
arb_mat_mul(EF, E, F, prec);
if (!arb_mat_overlaps(EF, G))
{
printf("FAIL\n\n");
printf("n = %ld, prec = %ld\n", n, prec);
printf("c = \n"); arb_printd(c, 15); printf("\n\n");
printf("A = \n"); arb_mat_printd(A, 15); printf("\n\n");
printf("E = \n"); arb_mat_printd(E, 15); printf("\n\n");
printf("F = \n"); arb_mat_printd(F, 15); printf("\n\n");
printf("E*F = \n"); arb_mat_printd(EF, 15); printf("\n\n");
printf("G = \n"); arb_mat_printd(G, 15); printf("\n\n");
abort();
}
arb_clear(c);
arb_clear(d);
fmpq_mat_clear(Q);
arb_mat_clear(A);
arb_mat_clear(E);
arb_mat_clear(F);
arb_mat_clear(EF);
arb_mat_clear(G);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void Lib_Arb_Mat_Print_Pretty(ArbMatPtr A, int32_t digits)
{
arb_mat_printd( (arb_mat_struct*) A, digits);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("mul_entrywise....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong m, n, qbits1, qbits2, rbits1, rbits2, rbits3;
fmpq_mat_t A, B, C;
arb_mat_t a, b, c, d;
qbits1 = 2 + n_randint(state, 200);
qbits2 = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
rbits3 = 2 + n_randint(state, 200);
m = n_randint(state, 10);
n = n_randint(state, 10);
fmpq_mat_init(A, m, n);
fmpq_mat_init(B, m, n);
fmpq_mat_init(C, m, n);
arb_mat_init(a, m, n);
arb_mat_init(b, m, n);
arb_mat_init(c, m, n);
arb_mat_init(d, m, n);
fmpq_mat_randtest(A, state, qbits1);
fmpq_mat_randtest(B, state, qbits2);
_fmpq_mat_mul_entrywise(C, A, B);
arb_mat_set_fmpq_mat(a, A, rbits1);
arb_mat_set_fmpq_mat(b, B, rbits2);
arb_mat_mul_entrywise(c, a, b, rbits3);
if (!arb_mat_contains_fmpq_mat(c, C))
{
flint_printf("FAIL\n\n");
flint_printf("m = %wd, n = %wd, bits3 = %wd\n", m, n, rbits3);
flint_printf("A = "); fmpq_mat_print(A); flint_printf("\n\n");
flint_printf("B = "); fmpq_mat_print(B); flint_printf("\n\n");
flint_printf("C = "); fmpq_mat_print(C); flint_printf("\n\n");
flint_printf("a = "); arb_mat_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_mat_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_mat_printd(c, 15); flint_printf("\n\n");
abort();
}
/* test aliasing with a */
if (arb_mat_nrows(a) == arb_mat_nrows(c) &&
arb_mat_ncols(a) == arb_mat_ncols(c))
{
arb_mat_set(d, a);
arb_mat_mul_entrywise(d, d, b, rbits3);
if (!arb_mat_equal(d, c))
{
flint_printf("FAIL (aliasing 1)\n\n");
abort();
}
}
/* test aliasing with b */
if (arb_mat_nrows(b) == arb_mat_nrows(c) &&
arb_mat_ncols(b) == arb_mat_ncols(c))
{
arb_mat_set(d, b);
arb_mat_mul_entrywise(d, a, d, rbits3);
if (!arb_mat_equal(d, c))
{
flint_printf("FAIL (aliasing 2)\n\n");
abort();
}
}
fmpq_mat_clear(A);
fmpq_mat_clear(B);
fmpq_mat_clear(C);
arb_mat_clear(a);
arb_mat_clear(b);
arb_mat_clear(c);
arb_mat_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("lu....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
fmpq_mat_t Q;
arb_mat_t A, LU, P, L, U, T;
slong i, j, n, qbits, prec, *perm;
int q_invertible, r_invertible;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 202);
fmpq_mat_init(Q, n, n);
arb_mat_init(A, n, n);
arb_mat_init(LU, n, n);
arb_mat_init(P, n, n);
arb_mat_init(L, n, n);
arb_mat_init(U, n, n);
arb_mat_init(T, n, n);
perm = _perm_init(n);
fmpq_mat_randtest(Q, state, qbits);
q_invertible = fmpq_mat_is_invertible(Q);
if (!q_invertible)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_lu(perm, LU, A, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("LU = \n"); arb_mat_printd(LU, 15); flint_printf("\n\n");
}
}
else
{
/* now this must converge */
while (1)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_lu(perm, LU, A, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
abort();
}
prec *= 2;
}
}
arb_mat_one(L);
for (i = 0; i < n; i++)
for (j = 0; j < i; j++)
arb_set(arb_mat_entry(L, i, j),
arb_mat_entry(LU, i, j));
for (i = 0; i < n; i++)
for (j = i; j < n; j++)
arb_set(arb_mat_entry(U, i, j),
arb_mat_entry(LU, i, j));
for (i = 0; i < n; i++)
arb_one(arb_mat_entry(P, perm[i], i));
arb_mat_mul(T, P, L, prec);
arb_mat_mul(T, T, U, prec);
if (!arb_mat_contains_fmpq_mat(T, Q))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("LU = \n"); arb_mat_printd(LU, 15); flint_printf("\n\n");
flint_printf("L = \n"); arb_mat_printd(L, 15); flint_printf("\n\n");
flint_printf("U = \n"); arb_mat_printd(U, 15); flint_printf("\n\n");
flint_printf("P*L*U = \n"); arb_mat_printd(T, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
arb_mat_clear(A);
arb_mat_clear(LU);
arb_mat_clear(P);
arb_mat_clear(L);
arb_mat_clear(U);
arb_mat_clear(T);
_perm_clear(perm);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}