LMCAS::anonymous_namespace{integration_rational_coefficients.cpp} 命名空间参考

类型定义
using	RationalFactors = std::vector<std::pair<Polynomial<Rational>, int>>

函数
bool	rd_factor_complements (const Polynomial< Rational > &Q, const Polynomial< Rational > &fpoly, int mult, std::vector< Polynomial< Rational > > &q_over_fpow_l)
bool	rd_fill_coefficient_matrix (const Polynomial< Rational > &Q, const RationalFactors &factors, const std::vector< size_t > &unknown_offset_per_term, std::vector< std::vector< Rational > > &M)
void	rd_fill_factor_columns (const Polynomial< Rational > &fpoly, int mult, const std::vector< Polynomial< Rational > > &q_over_fpow_l, size_t col_off, std::vector< std::vector< Rational > > &M)
bool	rd_unknown_offsets (const RationalFactors &factors, std::vector< size_t > &unknown_offset_per_term, size_t &num_unknowns)
void	rd_unpack_numerators (const RationalFactors &factors, const std::vector< size_t > &unknown_offset_per_term, const std::vector< Rational > &sol, const std::string &var, std::vector< Polynomial< Rational > > &numerators_out)

类型定义说明

RationalFactors

using LMCAS::anonymous_namespace{integration_rational_coefficients.cpp}::RationalFactors = std::vector<std::pair<Polynomial<Rational>, int>>

在文件 integration_rational_coefficients.cpp 第 7 行定义.

函数说明

rd_factor_complements()

bool LMCAS::anonymous_namespace{integration_rational_coefficients.cpp}::rd_factor_complements	(	const Polynomial< Rational > &	Q,
		const Polynomial< Rational > &	fpoly,
		int	mult,
		std::vector< Polynomial< Rational > > &	q_over_fpow_l )

在文件 integration_rational_coefficients.cpp 第 25 行定义.

                                                    {
    const auto& var = Q.variable_name;
        Polynomial<Rational> remaining = Q;
        for (int t = 0; t < mult; ++t) {
            auto qr = remaining.div_mod(fpoly);
            if (!qr.second.is_zero()) {
                return false;
            }
            remaining = qr.first;
        }
        Polynomial<Rational> cur({Rational(1)}, var);
        for (int l = mult; l >= 1; --l) {
            Polynomial<Rational> factor_poly = remaining * cur;
            q_over_fpow_l[l] = factor_poly;
            cur = cur * fpoly;
        }
    return true;
}

引用了 LMCAS::Polynomial< CoeffType >::div_mod(), rd_factor_complements(), LMCAS::t , 以及 LMCAS::Polynomial< CoeffType >::variable_name.

被这些函数引用 rd_factor_complements() , 以及 rd_fill_coefficient_matrix().

函数调用图:

这是这个函数的调用关系图:

rd_fill_coefficient_matrix()

bool LMCAS::anonymous_namespace{integration_rational_coefficients.cpp}::rd_fill_coefficient_matrix	(	const Polynomial< Rational > &	Q,
		const RationalFactors &	factors,
		const std::vector< size_t > &	unknown_offset_per_term,
		std::vector< std::vector< Rational > > &	M )

在文件 integration_rational_coefficients.cpp 第 82 行定义.

                                       {
    for (size_t i = 0; i < factors.size(); ++i) {
        const auto& [fpoly, mult] = factors[i];
        std::vector<Polynomial<Rational>> complements(mult + 1, Polynomial<Rational>(Q.variable_name));
        if (!rd_factor_complements(Q, fpoly, mult, complements)) { return false; }
        rd_fill_factor_columns(fpoly, mult, complements, unknown_offset_per_term[i], M);
    }
    return true;
}

引用了 rd_factor_complements(), rd_fill_coefficient_matrix(), rd_fill_factor_columns() , 以及 LMCAS::Polynomial< CoeffType >::variable_name.

被这些函数引用 rd_fill_coefficient_matrix().

函数调用图:

这是这个函数的调用关系图:

rd_fill_factor_columns()

void LMCAS::anonymous_namespace{integration_rational_coefficients.cpp}::rd_fill_factor_columns	(	const Polynomial< Rational > &	fpoly,
		int	mult,
		const std::vector< Polynomial< Rational > > &	q_over_fpow_l,
		size_t	col_off,
		std::vector< std::vector< Rational > > &	M )

在文件 integration_rational_coefficients.cpp 第 46 行定义.

                                                       {
    const size_t rows = M.size();
        if (fpoly.degree() == 1) {
            for (int l = 1; l <= mult; ++l) {
                const auto& qpl = q_over_fpow_l[l];
                size_t this_col = col_off + static_cast<size_t>(l - 1);
                for (size_t k = 0; k < rows; ++k) {
                    Rational c = (k < qpl.coeffs.size()) ? qpl.coeffs[k] : Rational(0);
                    M[k][this_col] = c;
                }
            }
        } else if (fpoly.degree() == 2) {
            for (int l = 1; l <= mult; ++l) {
                const auto& qpl = q_over_fpow_l[l];
                size_t base_col = col_off + static_cast<size_t>(2 * (l - 1));
                size_t b_col = base_col;
                size_t c_col = base_col + 1;
                for (size_t k = 0; k < rows; ++k) {
                    Rational c = (k < qpl.coeffs.size()) ? qpl.coeffs[k] : Rational(0);
                    M[k][c_col] = c;
                }
                for (size_t k = 0; k < rows; ++k) {
                    if (k == 0) {
                        M[k][b_col] = Rational(0);
                    } else {
                        size_t src = k - 1;
                        Rational c = (src < qpl.coeffs.size()) ? qpl.coeffs[src] : Rational(0);
                        M[k][b_col] = c;
                    }
                }
            }
        }
}

引用了 LMCAS::c, LMCAS::Polynomial< CoeffType >::degree() , 以及 rd_fill_factor_columns().

被这些函数引用 rd_fill_coefficient_matrix() , 以及 rd_fill_factor_columns().

函数调用图:

这是这个函数的调用关系图:

rd_unknown_offsets()

bool LMCAS::anonymous_namespace{integration_rational_coefficients.cpp}::rd_unknown_offsets	(	const RationalFactors &	factors,
		std::vector< size_t > &	unknown_offset_per_term,
		size_t &	num_unknowns )

在文件 integration_rational_coefficients.cpp 第 9 行定义.

                                                                      {
    for (size_t i = 0; i < factors.size(); ++i) {
        unknown_offset_per_term.push_back(num_unknowns);
        const auto& [fpoly, mult] = factors[i];
        if (fpoly.degree() == 1) {
            num_unknowns += static_cast<size_t>(mult);
        } else if (fpoly.degree() == 2) {
            num_unknowns += static_cast<size_t>(2 * mult);
        } else {
            return false;
        }
    }
    return num_unknowns != 0;
}

引用了 rd_unknown_offsets().

被这些函数引用 rd_unknown_offsets().

函数调用图:

这是这个函数的调用关系图:

rd_unpack_numerators()

void LMCAS::anonymous_namespace{integration_rational_coefficients.cpp}::rd_unpack_numerators	(	const RationalFactors &	factors,
		const std::vector< size_t > &	unknown_offset_per_term,
		const std::vector< Rational > &	sol,
		const std::string &	var,
		std::vector< Polynomial< Rational > > &	numerators_out )

二次因子。

在文件 integration_rational_coefficients.cpp 第 94 行定义.

                                                                           {
    for (size_t i = 0; i < factors.size(); ++i) {
        const auto& [fpoly, mult] = factors[i];
        size_t col_off = unknown_offset_per_term[i];
        if (fpoly.degree() == 1) {
            for (int l = 1; l <= mult; ++l) {
                Rational A = sol[col_off + static_cast<size_t>(l - 1)];
                numerators_out.push_back(Polynomial<Rational>({A}, var));
            }
        } else { /** @brief 二次因子。 */
            for (int l = 1; l <= mult; ++l) {
                size_t base_col = col_off + static_cast<size_t>(2 * (l - 1));
                Rational B = sol[base_col];
                Rational C = sol[base_col + 1];
                numerators_out.push_back(
                    Polynomial<Rational>({C, B}, var));
            }
        }
    }
}

引用了 rd_unpack_numerators().

被这些函数引用 rd_unpack_numerators().

函数调用图:

这是这个函数的调用关系图: