293 lines
9.1 KiB
C++
293 lines
9.1 KiB
C++
/*=============================================================================
|
|
|
|
This file is part of FLINT.
|
|
|
|
FLINT is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation; either version 2 of the License, or
|
|
(at your option) any later version.
|
|
|
|
FLINT is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with FLINT; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
=============================================================================*/
|
|
/******************************************************************************
|
|
|
|
Copyright (C) 2013 Tom Bachmann
|
|
|
|
******************************************************************************/
|
|
|
|
#include <iostream>
|
|
#include <sstream>
|
|
#include <string>
|
|
|
|
#include "fmpz_poly_matxx.h"
|
|
#include "flintxx/test/helpers.h"
|
|
|
|
using namespace flint;
|
|
|
|
void
|
|
test_init()
|
|
{
|
|
fmpz_poly_matxx A(3, 4);
|
|
tassert(A.rows() == 3 && A.cols() == 4);
|
|
tassert(A.at(0, 0) == fmpz_polyxx::from_ground(0));
|
|
A.at(0, 0) = fmpz_polyxx::from_ground(1);
|
|
|
|
fmpz_poly_matxx B(A);
|
|
tassert(B.rows() == 3 && B.cols() == 4);
|
|
tassert(B.at(0, 0) == fmpz_polyxx::from_ground(1));
|
|
B.at(0, 0) = fmpz_polyxx::from_ground(0);
|
|
tassert(A.at(0, 0) == fmpz_polyxx::from_ground(1));
|
|
|
|
tassert(fmpz_poly_matxx::zero(3, 3).is_zero());
|
|
tassert(fmpz_poly_matxx::one(3, 3).is_one());
|
|
}
|
|
|
|
template<class Expr>
|
|
bool has_explicit_temporaries(const Expr&)
|
|
{
|
|
return Expr::ev_traits_t::rule_t::temporaries_t::len != 0;
|
|
}
|
|
void
|
|
test_arithmetic()
|
|
{
|
|
fmpz_poly_matxx A(10, 10);
|
|
fmpz_poly_matxx v(10, 1);
|
|
for(unsigned i = 0;i < 10;++i)
|
|
v.at(i, 0) = fmpz_polyxx::from_ground(i);
|
|
|
|
tassert(transpose(v).rows() == 1);
|
|
tassert(v.transpose().cols() == 10);
|
|
tassert((fmpzxx(2)*v).rows() == 10);
|
|
tassert((v*fmpzxx(2)).rows() == 10);
|
|
tassert((v*transpose(v)).rows() == 10
|
|
&& (v*transpose(v)).cols() == 10);
|
|
tassert(mul_classical(v, transpose(v)).rows() == 10);
|
|
tassert(mul_KS(v, transpose(v)).cols() == 10);
|
|
|
|
tassert(!has_explicit_temporaries(trace(transpose(v))));
|
|
tassert(!has_explicit_temporaries(trace(A + v*transpose(v))));
|
|
tassert(!has_explicit_temporaries(A + v*transpose(v)));
|
|
tassert(!has_explicit_temporaries(trace((v*transpose(v) + A))));
|
|
tassert(!has_explicit_temporaries(trace(v*transpose(v) + v*transpose(v))));
|
|
tassert(!has_explicit_temporaries(v*transpose(v) + v*transpose(v)));
|
|
|
|
tassert((transpose(v)).trace() == fmpz_polyxx::from_ground(0));
|
|
tassert(trace(A + v*transpose(v)) == fmpz_polyxx::from_ground(285));
|
|
tassert(trace(v*transpose(v) + A) == fmpz_polyxx::from_ground(285));
|
|
tassert(trace(v*transpose(v) + v*transpose(v))
|
|
== fmpz_polyxx::from_ground(2*285));
|
|
tassert(trace((A+A)*(fmpz_polyxx(1) + fmpz_polyxx(1))).is_zero());
|
|
|
|
for(unsigned i = 0;i < 10; ++i)
|
|
for(unsigned j = 0; j < 10; ++j)
|
|
A.at(i, j) = fmpz_polyxx::from_ground(i*j);
|
|
tassert(A == v*transpose(v));
|
|
tassert(A != transpose(v)*v);
|
|
A.at(0, 0) = fmpz_polyxx::from_ground(15);
|
|
tassert(A != v*transpose(v));
|
|
|
|
A.at(0, 0) = fmpz_polyxx::from_ground(0);
|
|
for(unsigned i = 0;i < 10; ++i)
|
|
for(unsigned j = 0; j < 10; ++j)
|
|
A.at(i, j) *= 2;
|
|
tassert(A == v*transpose(v) + v*transpose(v));
|
|
tassert(A - v*transpose(v) == v*transpose(v));
|
|
tassert(((-A) + A).is_zero());
|
|
tassert((A + A).at(0, 0) == A.at(0, 0) + A.at(0, 0));
|
|
|
|
tassert((A + A) == fmpzxx(2)*A && fmpz_polyxx::from_ground(2)*A == (A + A));
|
|
|
|
frandxx rand;
|
|
fmpzxx x(17);
|
|
A.set_randtest(rand, 3, 5);
|
|
fmpz_matxx B(A.rows(), A.cols());
|
|
B = A(x);
|
|
for(slong i = 0;i < A.rows();++i)
|
|
for(slong j = 0;j < A.cols();++j)
|
|
tassert(B.at(i, j) == A.at(i, j)(x));
|
|
tassert(A(x) == evaluate(A, x));
|
|
}
|
|
|
|
void
|
|
test_functions()
|
|
{
|
|
fmpz_poly_matxx A(2, 3), B(2, 2), empty(0, 15);
|
|
B.at(0, 0) = fmpz_polyxx::from_ground(1);
|
|
tassert(A.is_zero() && !A.is_empty() && !A.is_square() && !A.is_one());
|
|
tassert(!B.is_zero() == B.is_square());
|
|
tassert(empty.is_zero() && empty.is_empty());
|
|
|
|
// transpose tested in arithmetic
|
|
// mul tested in arithmetic
|
|
// trace tested in arithmetic
|
|
|
|
A.at(0, 0).set_coeff(35, 17);
|
|
tassert(A.max_length() == 36);
|
|
tassert(A.max_bits() == 5);
|
|
|
|
frandxx rand;
|
|
A.set_randtest(rand, 4, 10);
|
|
B.set_randtest(rand, 4, 10);
|
|
tassert(B*A == B.mul_classical(A));
|
|
tassert(B*A == B.mul_KS(A));
|
|
|
|
fmpz_poly_matxx tmp(B*A);
|
|
tmp.truncate(3);
|
|
tassert(tmp == B.mullow(A, 3));
|
|
|
|
tassert(sqr(B) == B*B);
|
|
tassert(B.sqr().sqr() == pow(B, 4u));
|
|
tassert(B.sqrlow(3) == B.mullow(B, 3));
|
|
tmp = pow(B, 5u);
|
|
tmp.truncate(7);
|
|
tassert(tmp == B.pow_trunc(5u, 7));
|
|
|
|
B.set_randtest(rand, 4, 10);
|
|
tassert(B.det() == B.det_fflu());
|
|
tassert(B.det()(fmpzxx(123)) == B(fmpzxx(123)).det());
|
|
tassert(B.det() == B.det_interpolate());
|
|
|
|
fmpz_matxx Bp(2, 2);
|
|
Bp.set_randdet(rand, fmpzxx(2*3*5));
|
|
tassert(fmpz_poly_matxx::from_ground(Bp).det()
|
|
== fmpz_polyxx::from_ground(2*3*5));
|
|
|
|
fmpz_poly_matxx C(3, 3);
|
|
C.at(0, 0).set_coeff(0, 1);
|
|
C.at(1, 1).set_coeff(0, 1);
|
|
tassert(rank(C) == 2);
|
|
|
|
Bp.set_randrank(rand, 1, 10);
|
|
B = fmpz_poly_matxx::from_ground(Bp);
|
|
tassert(!inv(B).get<0>());
|
|
Bp.set_randrank(rand, 2, 10);
|
|
B = fmpz_poly_matxx::from_ground(Bp);
|
|
fmpz_poly_matxx Binv(2, 2); bool worked; fmpz_polyxx d;
|
|
ltupleref(worked, Binv, d) = inv(B);
|
|
tassert(worked);
|
|
fmpz_poly_matxx eye(2, 2);
|
|
eye.at(0, 0).set_coeff(0, 1);eye.at(1, 1).set_coeff(0, 1);
|
|
tassert(eye.is_one());
|
|
tassert(Binv * B == d*eye);
|
|
|
|
fmpz_poly_matxx X(2, 3);
|
|
ltupleref(worked, X, d) = solve(B, A);
|
|
tassert(worked == true && (B*X) == A*d);
|
|
ltupleref(worked, X, d) = B.solve_fflu(A);
|
|
tassert(worked == true && (B*X) == A*d);
|
|
tassert(solve(B, A).get<1>() == X);
|
|
|
|
permxx perm(B.rows());
|
|
tassert(solve_fflu_precomp(perm, B.fflu(&perm, false).get<1>().evaluate(), A)
|
|
== B.solve_fflu(A).get<1>());
|
|
|
|
slong nullity;
|
|
tassert(nullspace(A).get<1>().rows() == 3);
|
|
tassert(nullspace(A).get<1>().cols() == 3);
|
|
ltupleref(nullity, C) = nullspace(A);
|
|
tassert(nullity == 3 - rank(A));
|
|
tassert(C.rank() == nullity);
|
|
tassert((A*C).is_zero());
|
|
|
|
if(0)
|
|
print_pretty(A, "x"); // make sure this compiles
|
|
}
|
|
|
|
void
|
|
test_extras()
|
|
{
|
|
fmpz_poly_matxx A(2, 2);
|
|
A.at(0, 0).set_coeff(0, 1);
|
|
|
|
fmpz_poly_matxx_srcref Asr(A);
|
|
const fmpz_poly_matxx& Acr = A;
|
|
tassert(A.at(0, 0) == Acr.at(0, 0));
|
|
tassert(A.at(0, 0) == Asr.at(0, 0));
|
|
}
|
|
|
|
void
|
|
test_randomisation()
|
|
{
|
|
frandxx rand, rand2;
|
|
fmpz_poly_matxx A(2, 2);
|
|
A.set_randtest(rand, 4, 5);
|
|
tassert(abs(A.at(0, 0).get_coeff(0)) <= 31);
|
|
tassert(A == fmpz_poly_matxx::randtest(2, 2, rand2, 4, 5));
|
|
A.set_randtest_unsigned(rand, 4, 5);
|
|
tassert(A.at(0, 0).get_coeff(0) >= 0);
|
|
tassert(A == fmpz_poly_matxx::randtest_unsigned(2, 2, rand2, 4, 5));
|
|
A.set_randtest_sparse(rand, 4, 5, 0.5);
|
|
tassert(abs(fmpz_polyxx_get_coeff(A.at(0, 0), 0)) <= 31);
|
|
tassert(A == fmpz_poly_matxx::randtest_sparse(2, 2, rand2, 4, 5, 0.5));
|
|
}
|
|
|
|
void
|
|
test_row_reduction()
|
|
{
|
|
frandxx state;
|
|
fmpz_poly_matxx A = fmpz_poly_matxx::randtest(5, 5, state, 7, 15);
|
|
slong rank1, rank2;
|
|
fmpz_polyxx den1, den2;
|
|
fmpz_poly_matxx res1(A.rows(), A.cols()), res2(A.rows(), A.cols());
|
|
|
|
tassert(find_pivot_any(A, 2, 4, 1)
|
|
== fmpz_poly_mat_find_pivot_any(A._mat(), 2, 4, 1));
|
|
tassert(find_pivot_partial(A, 2, 4, 1)
|
|
== fmpz_poly_mat_find_pivot_partial(A._mat(), 2, 4, 1));
|
|
tassert(A.fflu(0, false).get<1>().rows() == A.rows());
|
|
permxx p1(5), p2(5);
|
|
ltupleref(rank1, res1, den1) = fflu(A, &p1);
|
|
rank2 = fmpz_poly_mat_fflu(res2._mat(), den2._poly(), p2._data(),
|
|
A._mat(), false);
|
|
tassert(rank1 == rank2 && res1 == res2 && p1 == p2 && den1 == den2);
|
|
tassert(rank1 == A.fflu(0, false).get<0>());
|
|
|
|
ltupleref(rank1, res1, den1) = rref(A);
|
|
rank2 = fmpz_poly_mat_rref(res2._mat(), den2._poly(), A._mat());
|
|
tassert(rank1 == rank2 && res1 == res2 && p1 == p2 && den1 == den2);
|
|
}
|
|
|
|
void
|
|
test_prod()
|
|
{
|
|
fmpz_poly_mat_vecxx v1(10, 3, 3), v2(10, 3, 3), v3(9, 3, 3), v4(v1);
|
|
tassert(v1 == v2);
|
|
tassert(v1 != v3);
|
|
v1[0].at(0, 0).set_coeff(0, 7u);
|
|
tassert(v1 != v4);
|
|
|
|
frandxx rand;
|
|
fmpz_poly_matxx prod = fmpz_poly_matxx::one(3, 3);
|
|
for(slong i = 0;i < v1.size();++i)
|
|
{
|
|
v1[i].set_randtest(rand, 4, 17);
|
|
prod *= v1[i];
|
|
}
|
|
tassert(flint::prod(v1) == prod);
|
|
}
|
|
|
|
int
|
|
main()
|
|
{
|
|
std::cout << "fmpz_poly_matxx....";
|
|
|
|
test_init();
|
|
test_arithmetic();
|
|
test_functions();
|
|
test_extras();
|
|
test_randomisation();
|
|
test_row_reduction();
|
|
test_prod();
|
|
|
|
std::cout << "PASS" << std::endl;
|
|
return 0;
|
|
}
|