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