int main(void) { fmpz_mat_t A, B, C, D; slong i; FLINT_TEST_INIT(state); flint_printf("mul...."); fflush(stdout); for (i = 0; i < 100 * flint_test_multiplier(); i++) { slong m, n, k; m = n_randint(state, 50); n = n_randint(state, 50); k = n_randint(state, 50); fmpz_mat_init(A, m, n); fmpz_mat_init(B, n, k); fmpz_mat_init(C, m, k); fmpz_mat_init(D, m, k); fmpz_mat_randtest(A, state, n_randint(state, 200) + 1); fmpz_mat_randtest(B, state, n_randint(state, 200) + 1); /* Make sure noise in the output is ok */ fmpz_mat_randtest(C, state, n_randint(state, 200) + 1); fmpz_mat_mul(C, A, B); fmpz_mat_mul_classical_inline(D, A, B); if (!fmpz_mat_equal(C, D)) { flint_printf("FAIL: results not equal\n"); abort(); } fmpz_mat_mul(A, A, B); if (!fmpz_mat_equal(A, C)) { flint_printf("FAIL: aliasing failed\n"); abort(); } fmpz_mat_clear(A); fmpz_mat_clear(B); fmpz_mat_clear(C); fmpz_mat_clear(D); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return 0; }
void fmpq_mat_mul_fmpz_mat(fmpq_mat_t C, const fmpq_mat_t A, const fmpz_mat_t B) { slong i, j; fmpz_mat_t Aclear; fmpz_mat_t Cclear; fmpz * Aden; fmpz_mat_init(Aclear, A->r, A->c); fmpz_mat_init(Cclear, A->r, B->c); Aden = _fmpz_vec_init(A->r); fmpq_mat_get_fmpz_mat_rowwise(Aclear, Aden, A); fmpz_mat_mul(Cclear, Aclear, B); for (i = 0; i < C->r; i++) { for (j = 0; j < C->c; j++) { fmpz_set(fmpq_mat_entry_num(C, i, j), fmpz_mat_entry(Cclear, i, j)); fmpz_set(fmpq_mat_entry_den(C, i, j), Aden + i); fmpq_canonicalise(fmpq_mat_entry(C, i, j)); } } fmpz_mat_clear(Aclear); fmpz_mat_clear(Cclear); _fmpz_vec_clear(Aden, A->r); }
void _fmpz_holonomic_forward_bsplit_fmpz(fmpz_mat_t M, fmpz_t Q, const fmpz_holonomic_t op, long start, long a, long b) { long r = fmpz_holonomic_order(op); if (b - a == 1) { _fmpz_holonomic_eval_companion_matrix_fmpz(M, Q, op, start + a); } else { fmpz_mat_t L, R; fmpz_t Q2; long m = a + (b - a) / 2; fmpz_mat_init(L, r, r); fmpz_mat_init(R, r, r); fmpz_init(Q2); _fmpz_holonomic_forward_bsplit_fmpz(L, Q, op, start, a, m); _fmpz_holonomic_forward_bsplit_fmpz(R, Q2, op, start, m, b); fmpz_mat_mul(M, R, L); fmpz_mul(Q, Q, Q2); fmpz_mat_clear(L); fmpz_mat_clear(R); fmpz_clear(Q2); } }
int main(void) { slong i; FLINT_TEST_INIT(state); flint_printf("pow...."); fflush(stdout); for (i = 0; i < 100 * flint_test_multiplier(); i++) { fmpz_mat_t A, B, C; slong i, n; ulong e; n = n_randint(state, 10); e = n_randint(state, 20); fmpz_mat_init(A, n, n); fmpz_mat_init(B, n, n); fmpz_mat_init(C, n, n); fmpz_mat_randtest(A, state, n_randint(state, 200) + 1); fmpz_mat_randtest(B, state, n_randint(state, 200) + 1); /* Make sure noise in the output is ok */ fmpz_mat_randtest(B, state, n_randint(state, 200) + 1); fmpz_mat_pow(B, A, e); fmpz_mat_one(C); for (i = 0; i < e; i++) fmpz_mat_mul(C, C, A); if (!fmpz_mat_equal(C, B)) { flint_printf("FAIL: results not equal\n"); abort(); } fmpz_mat_pow(A, A, e); if (!fmpz_mat_equal(A, B)) { flint_printf("FAIL: aliasing failed\n"); abort(); } fmpz_mat_clear(A); fmpz_mat_clear(B); fmpz_mat_clear(C); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return 0; }
inline void subtractMultipleTo(DMatZZ& C, const DMatZZ& A, const DMatZZ& B) { DMatZZ D(C.ring(), A.numRows(), B.numColumns()); fmpz_mat_mul(D.fmpz_mat(), A.fmpz_mat(), B.fmpz_mat()); fmpz_mat_sub(C.fmpz_mat(), C.fmpz_mat(), D.fmpz_mat()); }
inline void mult(const DMatZZ& A, const DMatZZ& B, DMatZZ& result_product) { // The A1 and B1 on the next line are switched because the memory layout expected // is the transpose of what we have for DMat. fmpz_mat_mul(result_product.fmpz_mat(), A.fmpz_mat(), B.fmpz_mat()); }
inline void mult(const DMatZZGMP& A, const DMatZZGMP& B, DMatZZGMP& result_product) { FlintZZMat A1(A); FlintZZMat B1(B); FlintZZMat result1(A.numRows(), B.numColumns()); fmpz_mat_mul(result1.value(), A1.value(), B1.value()); result1.toDMat(result_product); }
inline void subtractMultipleTo(DMatZZGMP& C, const DMatZZGMP& A, const DMatZZGMP& B) { FlintZZMat A1(A); FlintZZMat B1(B); FlintZZMat C1(C); FlintZZMat result1(A.numRows(), B.numColumns()); FlintZZMat D1(A.numRows(), B.numColumns()); fmpz_mat_mul(D1.value(), A1.value(), B1.value()); fmpz_mat_sub(C1.value(), C1.value(), D1.value()); C1.toDMat(C); }
void sample(void * arg, ulong count) { mat_mul_t * params = (mat_mul_t *) arg; long i, m = params->m, n = params->n, k = params->k; long bits = params->bits; int algorithm = params->algorithm; flint_rand_t rnd; fmpz_mat_t A, B, C; flint_rand_t state; flint_randinit(state); fmpz_mat_init(A, m, n); fmpz_mat_init(B, n, k); fmpz_mat_init(C, m, k); fmpz_mat_randbits(A, state, bits); fmpz_mat_randbits(B, state, bits); prof_start(); if (algorithm == 0) for (i = 0; i < count; i++) fmpz_mat_mul(C, A, B); else if (algorithm == 1) for (i = 0; i < count; i++) fmpz_mat_mul_classical(C, A, B); else if (algorithm == 2) for (i = 0; i < count; i++) fmpz_mat_mul_classical_inline(C, A, B); else if (algorithm == 3) for (i = 0; i < count; i++) fmpz_mat_mul_multi_mod(C, A, B); prof_stop(); fmpz_mat_clear(A); fmpz_mat_clear(B); fmpz_mat_clear(C); flint_randclear(state); }
void fmpz_mat_mul(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B) { long dim, m, n, k, ab, bb; m = A->r; n = A->c; k = B->c; if (C == A || C == B) { fmpz_mat_t t; fmpz_mat_init(t, m, k); fmpz_mat_mul(t, A, B); fmpz_mat_swap(C, t); fmpz_mat_clear(t); return; } dim = FLINT_MIN(FLINT_MIN(m, n), k); if (dim < 10) { fmpz_mat_mul_classical(C, A, B); return; } ab = fmpz_mat_max_bits(A); bb = fmpz_mat_max_bits(B); ab = FLINT_ABS(ab); bb = FLINT_ABS(bb); if (5*(ab + bb) > dim * dim) { fmpz_mat_mul_classical(C, A, B); } else { _fmpz_mat_mul_multi_mod(C, A, B, ab + bb + FLINT_BIT_COUNT(n) + 1); } }
int main(void) { fmpz_mat_t A, X, B, AX; fmpz_t den; slong i, m, n, r; int success; FLINT_TEST_INIT(state); flint_printf("solve_cramer...."); fflush(stdout); for (i = 0; i < 1000 * flint_test_multiplier(); i++) { m = n_randint(state, 4); n = n_randint(state, 10); fmpz_mat_init(A, m, m); fmpz_mat_init(B, m, n); fmpz_mat_init(X, m, n); fmpz_mat_init(AX, m, n); fmpz_init(den); fmpz_mat_randrank(A, state, m, 1+n_randint(state, 2)*n_randint(state, 100)); fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100)); /* Dense */ if (n_randint(state, 2)) fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m)); success = fmpz_mat_solve_cramer(X, den, A, B); fmpz_mat_mul(AX, A, X); fmpz_mat_scalar_divexact_fmpz(AX, AX, den); if (!fmpz_mat_equal(AX, B) || !success) { flint_printf("FAIL:\n"); flint_printf("AX != B!\n"); flint_printf("A:\n"), fmpz_mat_print_pretty(A), flint_printf("\n"); flint_printf("B:\n"), fmpz_mat_print_pretty(B), flint_printf("\n"); flint_printf("X:\n"), fmpz_mat_print_pretty(X), flint_printf("\n"); flint_printf("den(X) = "), fmpz_print(den), flint_printf("\n"); flint_printf("AX:\n"), fmpz_mat_print_pretty(AX), flint_printf("\n"); abort(); } fmpz_mat_clear(A); fmpz_mat_clear(B); fmpz_mat_clear(X); fmpz_mat_clear(AX); fmpz_clear(den); } /* Test singular systems */ for (i = 0; i < 1000 * flint_test_multiplier(); i++) { m = 1 + n_randint(state, 3); n = 1 + n_randint(state, 10); r = n_randint(state, m); fmpz_mat_init(A, m, m); fmpz_mat_init(B, m, n); fmpz_mat_init(X, m, n); fmpz_mat_init(AX, m, n); fmpz_init(den); fmpz_mat_randrank(A, state, r, 1+n_randint(state, 2)*n_randint(state, 100)); fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100)); /* Dense */ if (n_randint(state, 2)) fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m)); success = fmpz_mat_solve_cramer(X, den, A, B); if (!fmpz_is_zero(den) || success) { flint_printf("FAIL:\n"); flint_printf("singular system gave nonzero determinant\n"); abort(); } fmpz_mat_clear(A); fmpz_mat_clear(B); fmpz_mat_clear(X); fmpz_mat_clear(AX); fmpz_clear(den); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return 0; }
int main(void) { fmpz_mat_t A, X, B, AX, AXm, Bm; fmpz_t mod; slong i, m, n, r; int success; FLINT_TEST_INIT(state); flint_printf("solve_dixon...."); fflush(stdout); for (i = 0; i < 100 * flint_test_multiplier(); i++) { m = n_randint(state, 20); n = n_randint(state, 20); fmpz_mat_init(A, m, m); fmpz_mat_init(B, m, n); fmpz_mat_init(Bm, m, n); fmpz_mat_init(X, m, n); fmpz_mat_init(AX, m, n); fmpz_mat_init(AXm, m, n); fmpz_init(mod); fmpz_mat_randrank(A, state, m, 1+n_randint(state, 2)*n_randint(state, 100)); fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100)); /* Dense */ if (n_randint(state, 2)) fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m)); success = fmpz_mat_solve_dixon(X, mod, A, B); fmpz_mat_set(AXm, X); fmpz_mat_mul(AX, A, AXm); fmpz_mat_scalar_mod_fmpz(AXm, AX, mod); fmpz_mat_scalar_mod_fmpz(Bm, B, mod); if (!fmpz_mat_equal(AXm, Bm) || !success) { flint_printf("FAIL:\n"); flint_printf("AX != B!\n"); flint_printf("A:\n"), fmpz_mat_print_pretty(A), flint_printf("\n"); flint_printf("B:\n"), fmpz_mat_print_pretty(B), flint_printf("\n"); flint_printf("X:\n"), fmpz_mat_print_pretty(X), flint_printf("\n"); flint_printf("mod = "), fmpz_print(mod), flint_printf("\n"); flint_printf("AX:\n"), fmpz_mat_print_pretty(AX), flint_printf("\n"); abort(); } fmpz_mat_clear(A); fmpz_mat_clear(B); fmpz_mat_clear(Bm); fmpz_mat_clear(X); fmpz_mat_clear(AX); fmpz_mat_clear(AXm); fmpz_clear(mod); } /* Test singular systems */ for (i = 0; i < 100 * flint_test_multiplier(); i++) { m = 1 + n_randint(state, 10); n = 1 + n_randint(state, 10); r = n_randint(state, m); fmpz_mat_init(A, m, m); fmpz_mat_init(B, m, n); fmpz_mat_init(X, m, n); fmpz_init(mod); fmpz_mat_randrank(A, state, r, 1+n_randint(state, 2)*n_randint(state, 100)); fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100)); /* Dense */ if (n_randint(state, 2)) fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m)); if (fmpz_mat_solve_dixon(X, mod, A, B) != 0) { flint_printf("FAIL:\n"); flint_printf("singular system, returned nonzero\n"); abort(); } fmpz_mat_clear(A); fmpz_mat_clear(B); fmpz_mat_clear(X); fmpz_clear(mod); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return 0; }
static inline void fmpz_mat_mul_mod(fmpz_mat_t a, fmpz_mat_t b, fmpz_mat_t c, fmpz_t p) { fmpz_mat_mul(a, b, c); fmpz_mat_scalar_mod_fmpz(a, a, p); }