ode_frobenius.cpp 文件参考

奇点分类与 Frobenius 系数递推。 更多...

#include <stdexcept>
#include "internal/expression_transform.hpp"
#include "limit_result.hpp"
#include "symbolic_ode_engine.hpp"
#include "internal/symbolic_ast.hpp"
#include "symbolic.hpp"
#include "poly_utils.hpp"
#include "internal/expression_analysis.hpp"
#include "lmmc/config.h"
#include "lmmc/numeric.h"
#include "internal/ode_support.hpp"
#include <cmath>
#include <limits>
#include <memory>
#include <string>
#include <utility>
#include <vector>

ode_frobenius.cpp 的引用(Include)关系图:

浏览该文件的源代码.

类
struct	LMCAS::OdeTaylorCoefficients

命名空间
namespace	LMCAS

函数
static std::shared_ptr< SymbolicExpr >	LMCAS::assemble_frobenius_polynomial (const std::vector< double > &a, const std::shared_ptr< SymbolicExpr > &x_minus_x0)
ODESingularityResult	LMCAS::classify_singular_point_checked (const std::shared_ptr< SymbolicExpr > &p, const std::shared_ptr< SymbolicExpr > &q, const std::shared_ptr< SymbolicExpr > &x0, const std::string &x)
ODESingularityResult	LMCAS::classify_singular_point_checked (const std::shared_ptr< SymbolicExpr > &p, const std::shared_ptr< SymbolicExpr > &q, const std::shared_ptr< SymbolicExpr > &x0, const std::string &x, ComputationContext &context)
static CasError	LMCAS::frobenius_arithmetic_failure ()
static Result< double >	LMCAS::frobenius_coefficient_limit (const std::shared_ptr< SymbolicExpr > &coefficient, const std::string &x, const std::shared_ptr< SymbolicExpr > &x0, double value, ComputationContext &context)
static Result< std::pair< double, double > >	LMCAS::frobenius_indicial_roots (double P0, double Q0)
static CasError	LMCAS::frobenius_unsupported_numeric ()
static FrobeniusSolutionResult	LMCAS::ordinary_frobenius_solution (const std::shared_ptr< SymbolicExpr > &p, const std::shared_ptr< SymbolicExpr > &q, const std::shared_ptr< SymbolicExpr > &x0, const std::string &x, const std::shared_ptr< SymbolicExpr > &x_minus_x0, FrobeniusSolution result, ComputationContext &context)
static Result< std::vector< double > >	LMCAS::ordinary_series_recurrence (const OdeTaylorCoefficients &coefficients, int order)
static Result< OdeTaylorCoefficients >	LMCAS::ordinary_taylor_coefficients (const std::shared_ptr< SymbolicExpr > &p, const std::shared_ptr< SymbolicExpr > &q, const std::shared_ptr< SymbolicExpr > &x0, const std::string &x, int order, ComputationContext &context)
static FrobeniusSolutionResult	LMCAS::singular_frobenius_solution (const std::shared_ptr< SymbolicExpr > &p, const std::shared_ptr< SymbolicExpr > &q, const std::shared_ptr< SymbolicExpr > &x0, const std::string &x, const std::shared_ptr< SymbolicExpr > &x_minus_x0, FrobeniusSolution result, ComputationContext &context)
static Result< std::vector< double > >	LMCAS::singular_series_recurrence (const OdeTaylorCoefficients &coefficients, double P0, double Q0, double r1, int order)
static Result< OdeTaylorCoefficients >	LMCAS::singular_taylor_coefficients (const std::shared_ptr< SymbolicExpr > &xp_expr, const std::shared_ptr< SymbolicExpr > &x2q_expr, const std::shared_ptr< SymbolicExpr > &x0, const std::string &x, int order, double P0, double Q0, ComputationContext &context)
FrobeniusSolutionResult	LMCAS::solve_frobenius_checked (const std::shared_ptr< SymbolicExpr > &p, const std::shared_ptr< SymbolicExpr > &q, const std::shared_ptr< SymbolicExpr > &x0, const std::string &x, int order)
FrobeniusSolutionResult	LMCAS::solve_frobenius_checked (const std::shared_ptr< SymbolicExpr > &p, const std::shared_ptr< SymbolicExpr > &q, const std::shared_ptr< SymbolicExpr > &x0, const std::string &x, int order, ComputationContext &context)
static FrobeniusSolutionResult	LMCAS::solve_frobenius_impl (const std::shared_ptr< SymbolicExpr > &, const std::shared_ptr< SymbolicExpr > &, const std::shared_ptr< SymbolicExpr > &, const std::string &, int, ODESingularityType, ComputationContext &)
static Result< void >	LMCAS::validate_frobenius_regular_singular_domain (const std::shared_ptr< SymbolicExpr > &p, const std::shared_ptr< SymbolicExpr > &q, const std::shared_ptr< SymbolicExpr > &x0, const std::string &x, ComputationContext &context, const std::string &operation)

详细描述

奇点分类与 Frobenius 系数递推。

在文件 ode_frobenius.cpp 中定义.

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类说明

LMCAS::OdeTaylorCoefficients

struct LMCAS::OdeTaylorCoefficients

在文件 ode_frobenius.cpp 第 43 行定义.

LMCAS::OdeTaylorCoefficients 的协作图:

类成员
vector< double >	p
vector< double >	q