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

类
struct	DefiniteInterval
struct	RationalIntegrand

函数
Result< SymbolicExpr >	accumulate_segments (Integrator &integrator, const SymbolicExpr &expr, const SymbolicExpr &value_expression, const std::string &var_name, const std::vector< SymbolicExpr > &partition, const std::optional< SymbolicExpr > &primitive, bool reversed, ComputationContext &context)
Result< Tribool >	certify_partition (const SymbolicExpr &expr, const std::string &var_name, const std::vector< SymbolicExpr > &partition, ComputationContext &context)
Result< SymbolicExpr >	equal_endpoint_integral (const SymbolicExpr &expr, const std::string &var_name, const SymbolicExpr &lower, const SymbolicExpr &upper, const DefiniteInterval &interval, ComputationContext &context)
Result< SymbolicExpr >	integrate_interval_checked (Integrator &integrator, const SymbolicExpr &expr, const std::string &var_name, const SymbolicExpr &lower, const SymbolicExpr &upper, ComputationContext &context)
Result< SymbolicExpr >	integrate_ordered_interval (Integrator &integrator, const SymbolicExpr &expr, const std::string &var_name, const SymbolicExpr &lower, const SymbolicExpr &upper, const DefiniteInterval &interval, ComputationContext &context)
Result< SymbolicExpr >	integrate_segment_primitive (Integrator &integrator, const SymbolicExpr &value_expression, const std::string &var_name, const SymbolicExpr &lower, const SymbolicExpr &upper, ComputationContext &context)
Result< RationalIntegrand >	reduced_integrand_checked (const SymbolicExpr &expr, const std::string &var_name, const DefiniteInterval &interval, ComputationContext &context)
Result< SymbolicExpr >	unresolved_integral (const SymbolicExpr &expr, const std::string &var_name, const SymbolicExpr &lower, const SymbolicExpr &upper)

---

类说明

LMCAS::anonymous_namespace{integration_definite.cpp}::RationalIntegrand

struct LMCAS::anonymous_namespace{integration_definite.cpp}::RationalIntegrand

在文件 integration_definite.cpp 第 62 行定义.

LMCAS::anonymous_namespace{integration_definite.cpp}::RationalIntegrand 的协作图:

类成员
int	divergence = 0
SymbolicExpr	expression

函数说明

accumulate_segments()

Result< SymbolicExpr > LMCAS::anonymous_namespace{integration_definite.cpp}::accumulate_segments	(	Integrator &	integrator,
		const SymbolicExpr &	expr,
		const SymbolicExpr &	value_expression,
		const std::string &	var_name,
		const std::vector< SymbolicExpr > &	partition,
		const std::optional< SymbolicExpr > &	primitive,
		bool	reversed,
		ComputationContext &	context )

在文件 integration_definite.cpp 第 95 行定义.

                                                    {
    detail::RewriteBudget transform_budget(context, (context).limits().max_recursion_depth,
                                            (context).limits().max_ast_nodes, "transform");
    SymbolicExpr sum = *SymbolicExpr::number(0);
    int infinity = 0;
    for (std::size_t i = 1; i < partition.size(); ++i) {
        std::optional<SymbolicExpr> local_primitive;
        if (!primitive) {
            auto integrated = integrate_segment_primitive(integrator, value_expression, var_name,
                partition[i - 1], partition[i], context);
            if (!integrated) { return integrated; }
            local_primitive = std::move(integrated.value());
        }
        auto segment = definite_segment_checked(expr, primitive ? *primitive : *local_primitive, var_name,
            partition[i - 1], partition[i], context);
        if (!segment) { return segment; }
        int contribution = infinity_sign(detail::node(segment.value()));
        if (contribution) {
            if (infinity && infinity != contribution) { return divergent<SymbolicExpr>(); }
            infinity = contribution;
        } else { sum = *SymbolicExpr::add(detail::make_expression_ptr(sum), detail::make_expression_ptr(segment.value())); }
    }
    if (infinity) { return *SymbolicExpr::infinity(infinity * (reversed ? -1 : 1)); }
    if (reversed) { sum = *SymbolicExpr::multiply(SymbolicExpr::number(-1), detail::make_expression_ptr(sum)); }
    return *detail::make_expression_ptr(detail::normalize_node(detail::node(sum), transform_budget));
} catch (const CasError& error) {
    return Result<SymbolicExpr>::failure(error);
} catch (const std::bad_alloc&) {
    return Result<SymbolicExpr>::failure(CasErrc::ResourceLimit, "allocation failed", "accumulate_segments");
} catch (const std::length_error& error) {
    return Result<SymbolicExpr>::failure(CasErrc::ResourceLimit, error.what(), "accumulate_segments");
} catch (const std::exception& error) {
    return Result<SymbolicExpr>::failure(CasErrc::InternalInvariant, error.what(), "accumulate_segments");
}

引用了 accumulate_segments(), LMCAS::context, LMCAS::detail::definite::definite_segment_checked(), LMCAS::detail::definite::divergent(), LMCAS::detail::definite::infinity_sign(), integrate_segment_primitive(), LMCAS::integrator, LMCAS::detail::make_expression_ptr(), LMCAS::detail::node() , 以及 LMCAS::detail::normalize_node().

被这些函数引用 accumulate_segments() , 以及 integrate_ordered_interval().

函数调用图:

这是这个函数的调用关系图:

certify_partition()

Result< Tribool > LMCAS::anonymous_namespace{integration_definite.cpp}::certify_partition	(	const SymbolicExpr &	expr,
		const std::string &	var_name,
		const std::vector< SymbolicExpr > &	partition,
		ComputationContext &	context )

在文件 integration_definite.cpp 第 52 行定义.

                                                                           {
    for (std::size_t i = 1; i < partition.size(); ++i) {
        auto continuous = certify_continuity_checked(expr, var_name,
            partition[i - 1], partition[i], context);
        if (!continuous || continuous.value() != Tribool::True) { return continuous; }
    }
    return Tribool::True;
}

引用了 LMCAS::detail::definite::certify_continuity_checked(), certify_partition(), LMCAS::context , 以及 LMCAS::True.

被这些函数引用 certify_partition() , 以及 integrate_ordered_interval().

函数调用图:

这是这个函数的调用关系图:

equal_endpoint_integral()

Result< SymbolicExpr > LMCAS::anonymous_namespace{integration_definite.cpp}::equal_endpoint_integral	(	const SymbolicExpr &	expr,
		const std::string &	var_name,
		const SymbolicExpr &	lower,
		const SymbolicExpr &	upper,
		const DefiniteInterval &	interval,
		ComputationContext &	context )

在文件 integration_definite.cpp 第 28 行定义.

                                                                       {
    detail::RewriteBudget transform_budget(context, (context).limits().max_recursion_depth,
                                            (context).limits().max_ast_nodes, "transform");
    if (interval.a.value().infinity) { return unresolved_integral(expr, var_name, lower, upper); }
    auto assumptions = real_assumptions(var_name, context);
    if (!assumptions) { return Result<SymbolicExpr>::failure(assumptions.error()); }
    detail::AssumptionFacts facts(assumptions.value());
    auto value = detail::make_expression_ptr(detail::substitute_node(detail::node(expr), var_name, detail::node(interval.lo), transform_budget));
    auto defined = detail::query_definedness(detail::node(value), facts, Domain::Real, context);
    if (!defined) { return Result<SymbolicExpr>::failure(defined.error()); }
    if (defined.value() == Tribool::False) { return divergent<SymbolicExpr>(); }
    return defined.value() == Tribool::True ? Result<SymbolicExpr>(*SymbolicExpr::number(0)) : unresolved_integral(expr, var_name, lower, upper);
} catch (const CasError& error) {
    return Result<SymbolicExpr>::failure(error);
} catch (const std::bad_alloc&) {
    return Result<SymbolicExpr>::failure(CasErrc::ResourceLimit, "allocation failed", "equal_endpoint_integral");
} catch (const std::length_error& error) {
    return Result<SymbolicExpr>::failure(CasErrc::ResourceLimit, error.what(), "equal_endpoint_integral");
} catch (const std::exception& error) {
    return Result<SymbolicExpr>::failure(CasErrc::InternalInvariant, error.what(), "equal_endpoint_integral");
}

引用了 LMCAS::Result< T >::Result(), LMCAS::context, LMCAS::detail::definite::divergent(), equal_endpoint_integral(), LMCAS::Result< T >::failure(), LMCAS::False, LMCAS::interval(), LMCAS::lower, LMCAS::detail::make_expression_ptr(), LMCAS::detail::node(), LMCAS::detail::query_definedness(), LMCAS::Real, LMCAS::detail::definite::real_assumptions(), LMCAS::detail::substitute_node(), LMCAS::True, unresolved_integral(), LMCAS::upper, LMCAS::Result< T >::value() , 以及 LMCAS::value.

被这些函数引用 equal_endpoint_integral() , 以及 integrate_interval_checked().

函数调用图:

这是这个函数的调用关系图:

integrate_interval_checked()

Result< SymbolicExpr > LMCAS::anonymous_namespace{integration_definite.cpp}::integrate_interval_checked	(	Integrator &	integrator,
		const SymbolicExpr &	expr,
		const std::string &	var_name,
		const SymbolicExpr &	lower,
		const SymbolicExpr &	upper,
		ComputationContext &	context )

在文件 integration_definite.cpp 第 163 行定义.

                                                                                       {
    DefiniteInterval interval(lower, upper, context);
    if (!interval.a && !is_undecided(interval.a.error())) { return Result<SymbolicExpr>::failure(interval.a.error()); }
    if (!interval.b && !is_undecided(interval.b.error())) { return Result<SymbolicExpr>::failure(interval.b.error()); }
    if (interval.a && interval.b) {
        auto order = compare_boundaries(interval.a.value(), interval.b.value(), context);
        if (!order) { return Result<SymbolicExpr>::failure(order.error()); }
        if (!order.value()) {
            return equal_endpoint_integral(expr, var_name, lower, upper, interval, context);
        }
        if (order.value() > 0) {
            std::swap(interval.lo, interval.hi);
            std::swap(interval.a.value(), interval.b.value());
            interval.reversed = true;
        }
    }
    return integrate_ordered_interval(integrator, expr, var_name, lower, upper, interval, context);
}

引用了 LMCAS::detail::definite::compare_boundaries(), LMCAS::context, equal_endpoint_integral(), LMCAS::Result< T >::error(), LMCAS::Result< T >::failure(), integrate_interval_checked(), integrate_ordered_interval(), LMCAS::integrator, LMCAS::interval(), LMCAS::detail::definite::is_undecided(), LMCAS::lower, LMCAS::order, LMCAS::upper , 以及 LMCAS::Result< T >::value().

被这些函数引用 integrate_interval_checked().

函数调用图:

这是这个函数的调用关系图:

integrate_ordered_interval()

Result< SymbolicExpr > LMCAS::anonymous_namespace{integration_definite.cpp}::integrate_ordered_interval	(	Integrator &	integrator,
		const SymbolicExpr &	expr,
		const std::string &	var_name,
		const SymbolicExpr &	lower,
		const SymbolicExpr &	upper,
		const DefiniteInterval &	interval,
		ComputationContext &	context )

在文件 integration_definite.cpp 第 133 行定义.

                                                                   {
    const auto unresolved = [&]() { return unresolved_integral(expr, var_name, lower, upper); };
    auto partition = definite_partition_checked(expr, var_name, interval.lo, interval.hi, context);
    if (!partition) { return is_undecided(partition.error()) ? unresolved() : Result<SymbolicExpr>::failure(partition.error()); }
    auto continuous = certify_partition(expr, var_name, partition.value(), context);
    if (!continuous) { return Result<SymbolicExpr>::failure(continuous.error()); }
    if (continuous.value() == Tribool::False) { return divergent<SymbolicExpr>(); }
    if (continuous.value() != Tribool::True) { return unresolved(); }
    auto reduced = reduced_integrand_checked(expr, var_name, interval, context);
    if (!reduced) { return Result<SymbolicExpr>::failure(reduced.error()); }
    if (reduced.value().divergence) {
        return *SymbolicExpr::infinity(reduced.value().divergence * (interval.reversed ? -1 : 1));
    }
    const auto& value_expression = reduced.value().expression;
    std::optional<SymbolicExpr> primitive;
    if (!needs_segment_expression(detail::node(value_expression))) {
        auto integrated = integrator.integrate_checked(value_expression, var_name, context);
        if (!integrated) { return is_undecided(integrated.error()) ? unresolved() : integrated; }
        if (contains_unevaluated_integral(detail::node(integrated.value()))) { return unresolved(); }
        primitive = std::move(integrated.value());
    }
    auto sum = accumulate_segments(integrator, expr, value_expression, var_name,
        partition.value(), primitive, interval.reversed, context);
    if (!sum && is_undecided(sum.error())) { return unresolved(); }
    return sum;
}

引用了 accumulate_segments(), certify_partition(), LMCAS::contains_unevaluated_integral(), LMCAS::context, LMCAS::detail::definite::definite_partition_checked(), LMCAS::detail::definite::divergent(), LMCAS::Result< T >::failure(), LMCAS::False, integrate_ordered_interval(), LMCAS::integrator, LMCAS::interval(), LMCAS::detail::definite::is_undecided(), LMCAS::lower, LMCAS::detail::definite::needs_segment_expression(), LMCAS::detail::node(), reduced_integrand_checked(), LMCAS::True, unresolved_integral() , 以及 LMCAS::upper.

被这些函数引用 integrate_interval_checked() , 以及 integrate_ordered_interval().

函数调用图:

这是这个函数的调用关系图:

integrate_segment_primitive()

Result< SymbolicExpr > LMCAS::anonymous_namespace{integration_definite.cpp}::integrate_segment_primitive	(	Integrator &	integrator,
		const SymbolicExpr &	value_expression,
		const std::string &	var_name,
		const SymbolicExpr &	lower,
		const SymbolicExpr &	upper,
		ComputationContext &	context )

在文件 integration_definite.cpp 第 84 行定义.

                                                                                       {
    auto selected = segment_expression_checked(value_expression, var_name, lower, upper, context);
    if (!selected) { return selected; }
    auto integrated = integrator.integrate_checked(selected.value(), var_name, context);
    if (!integrated) { return integrated; }
    if (contains_unevaluated_integral(detail::node(integrated.value()))) { return undecided<SymbolicExpr>(); }
    return integrated;
}

引用了 LMCAS::contains_unevaluated_integral(), LMCAS::context, integrate_segment_primitive(), LMCAS::integrator, LMCAS::lower, LMCAS::detail::node(), LMCAS::detail::definite::segment_expression_checked(), LMCAS::detail::definite::undecided() , 以及 LMCAS::upper.

被这些函数引用 accumulate_segments() , 以及 integrate_segment_primitive().

函数调用图:

这是这个函数的调用关系图:

reduced_integrand_checked()

Result< RationalIntegrand > LMCAS::anonymous_namespace{integration_definite.cpp}::reduced_integrand_checked	(	const SymbolicExpr &	expr,
		const std::string &	var_name,
		const DefiniteInterval &	interval,
		ComputationContext &	context )

在文件 integration_definite.cpp 第 67 行定义.

                                                                                              {
    auto rational = rational_checked(detail::node(expr), var_name, context);
    if (!rational) { return Result<RationalIntegrand>::failure(rational.error()); }
    RationalIntegrand result{expr};
    if (rational.value() && interval.a && interval.b) {
        auto divergence = rational_divergence_checked(
            *rational.value(), interval.a.value(), interval.b.value(), context);
        if (!divergence) { return Result<RationalIntegrand>::failure(divergence.error()); }
        result.divergence = divergence.value();
        if (result.divergence) { return result; }
        result.expression = *SymbolicExpr::divide(poly_to_symbolic(rational.value()->numerator),
            poly_to_symbolic(rational.value()->denominator));
    }
    return result;
}

引用了 LMCAS::context, LMCAS::anonymous_namespace{integration_definite.cpp}::RationalIntegrand::divergence, LMCAS::divergence(), LMCAS::Result< T >::error(), LMCAS::anonymous_namespace{integration_definite.cpp}::RationalIntegrand::expression, LMCAS::Result< T >::failure(), LMCAS::interval(), LMCAS::detail::node(), LMCAS::rational(), LMCAS::detail::definite::rational_checked(), LMCAS::detail::definite::rational_divergence_checked(), reduced_integrand_checked() , 以及 LMCAS::Result< T >::value().

被这些函数引用 integrate_ordered_interval() , 以及 reduced_integrand_checked().

函数调用图:

这是这个函数的调用关系图:

unresolved_integral()

Result< SymbolicExpr > LMCAS::anonymous_namespace{integration_definite.cpp}::unresolved_integral	(	const SymbolicExpr &	expr,
		const std::string &	var_name,
		const SymbolicExpr &	lower,
		const SymbolicExpr &	upper )

在文件 integration_definite.cpp 第 22 行定义.

                                                                                     {
    return detail::expression_from_node(detail::make_node<IntegralNode>(detail::node(expr),
        var_name, detail::node(lower), detail::node(upper)));
}

引用了 LMCAS::detail::expression_from_node(), LMCAS::lower, LMCAS::detail::make_node(), LMCAS::detail::node(), unresolved_integral() , 以及 LMCAS::upper.

被这些函数引用 equal_endpoint_integral(), integrate_ordered_interval() , 以及 unresolved_integral().

函数调用图:

这是这个函数的调用关系图: