c++ - 使用 Boost.Proto 构建 Eigen 表达式模板

Question

我想使用 Boost.Proto 将嵌入式领域特定语言转换为一系列使用 Eigen 库实现的矩阵运算。由于效率很重要，我希望 proto 生成 Eigen 表达式模板并避免过早评估。

我已经实现了一个可以生成矩阵乘法表达式的简单语法。下面的代码在没有警告的情况下编译（在 g++ 4.8.0 和 Intel C++ 2013.3 上，使用 Boost 1.54.0 和 Eigen 3.1.3）并且只要我的表达式只有一个乘法运算就可以工作。一旦我向链中添加更多乘法，它就会崩溃。Valgrind 告诉我这是因为 Eigen::GeneralProduct 表达式模板临时变量之一在评估完成之前被破坏。

我不明白为什么会发生这种情况，或者我能做些什么来防止它。感谢所有帮助！

#include <iostream>

#include <boost/fusion/container.hpp>
#include <boost/mpl/int.hpp>
#include <boost/mpl/void.hpp>
#include <boost/proto/proto.hpp>
#include <boost/ref.hpp>
#include <boost/type_traits/remove_const.hpp>
#include <boost/type_traits/remove_reference.hpp>
#include <boost/utility.hpp>

#include <Eigen/Dense>

namespace fusion = boost::fusion;
namespace mpl = boost::mpl;
namespace proto = boost::proto;

typedef Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic> matrix;

// Placeholders

const proto::terminal<mpl::int_<0> >::type I1 = {{}};
const proto::terminal<mpl::int_<1> >::type I2 = {{}};
const proto::terminal<mpl::int_<2> >::type I3 = {{}};

// Grammar

template<class Rule, class Callable = proto::callable>
struct External :
    proto::when<Rule, proto::external_transform> {};

struct matmul_transform : proto::callable {
    template<class Sig> struct result;

    template<class This, class MatrixExpr1, class MatrixExpr2>
    struct result<This(MatrixExpr1, MatrixExpr2)> {
            typedef typename Eigen::ProductReturnType<
                    typename boost::remove_const<typename boost::remove_reference<MatrixExpr1>::type>::type,
                    typename boost::remove_const<typename boost::remove_reference<MatrixExpr2>::type>::type>::Type
                    type;
    };

    template<class MatrixExpr1, class MatrixExpr2>
    typename result<matmul_transform(MatrixExpr1, MatrixExpr2)>::type
    operator()(const MatrixExpr1 &a, const MatrixExpr2 &b) const {
            return a * b;
    }
};


struct MatmulGrammar;

struct InputPlaceholder : proto::terminal<proto::_> {};

struct MatrixMultiplication :
    proto::multiplies<MatmulGrammar, MatmulGrammar> {};

struct MatmulGrammar : proto::or_<
    External<InputPlaceholder>,
    External<MatrixMultiplication> > {};

struct matmul_transforms : proto::external_transforms<
    proto::when<MatrixMultiplication, matmul_transform(MatmulGrammar(proto::_left), MatmulGrammar(proto::_right))>,
    proto::when<InputPlaceholder, proto::functional::at(proto::_data, proto::_value)> > {};

int main() {
    matrix mat1(2,2), mat2(2,2), mat3(2,2), result(2,2);

    mat1 << 1, 2, 3, 4;
    mat2 << 5, 6, 7, 8;
    mat3 << 1, 3, 6, 9;

    MatmulGrammar mmg;

    // THIS WORKS:
    result = mmg(I1 * I2,
            mpl::void_(),
            (proto::data = fusion::make_vector(boost::cref(mat1), boost::cref(mat2), boost::cref(mat3)),
             proto::transforms = matmul_transforms()));

    std::cout << result << std::endl;

    // THIS CRASHES:
    result = mmg(I1 * I2 * I3,
            mpl::void_(),
            (proto::data = fusion::make_vector(boost::cref(mat1), boost::cref(mat2), boost::cref(mat3)),
             proto::transforms = matmul_transforms()));

    std::cout << result << std::endl;

    return 0;
}

score 3 · Accepted Answer

这是我尝试将您的方法与评论中链接的解决方案合并。我已经复制了，stored_result_expression从这里开始。我对您的代码或演讲中的代码所做的更改都标有。do_wrap_expressionwrap_expression//CHANGED

#include <iostream>

#include <boost/fusion/container.hpp>
#include <boost/mpl/int.hpp>
#include <boost/mpl/void.hpp>
#include <boost/proto/proto.hpp>
#include <boost/ref.hpp>
#include <boost/type_traits/remove_const.hpp>
#include <boost/type_traits/remove_reference.hpp>
#include <boost/utility.hpp>

#include <Eigen/Dense>

namespace fusion = boost::fusion;
namespace mpl = boost::mpl;
namespace proto = boost::proto;

typedef Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic> matrix;

// Placeholders

const proto::terminal<mpl::int_<0> >::type I1 = {{}};
const proto::terminal<mpl::int_<1> >::type I2 = {{}};
const proto::terminal<mpl::int_<2> >::type I3 = {{}};

// Grammar

template<class Rule, class Callable = proto::callable>
struct External :
    proto::when<Rule, proto::external_transform> {};

struct matmul_transform : proto::callable {
    template<class Sig> struct result;

    template<class This, class Expr, class MatrixExpr1, class MatrixExpr2>
    struct result<This(Expr, MatrixExpr1, MatrixExpr2)> {
            typedef typename Eigen::MatrixBase<
                        typename Eigen::ProductReturnType<
                            typename boost::remove_const<typename boost::remove_reference<MatrixExpr1>::type>::type,
                            typename boost::remove_const<typename boost::remove_reference<MatrixExpr2>::type>::type
                        >::Type 
                    >::PlainObject&
                    type; //CHANGED - THIS IS THE TYPE THAT IS USED IN THE CODE OF THE TALK
    };

    template<class Expr, class MatrixExpr1, class MatrixExpr2>
    typename result<matmul_transform(Expr, MatrixExpr1, MatrixExpr2)>::type
    operator()(Expr& expr, const MatrixExpr1 &a, const MatrixExpr2 &b) const { //CHANGED - ADDED THE expr PARAMETER
            expr.value = a*b; 
            return expr.value; 
    }
};


struct MatmulGrammar;

struct InputPlaceholder : proto::terminal<proto::_> {};

struct MatrixMultiplication :
    proto::multiplies<MatmulGrammar, MatmulGrammar> {};

struct MatmulGrammar : proto::or_<
    External<InputPlaceholder>,
    External<MatrixMultiplication> > {};

struct matmul_transforms : proto::external_transforms<
    proto::when<MatrixMultiplication, matmul_transform(proto::_, MatmulGrammar(proto::_left), MatmulGrammar(proto::_right))>, //CHANGED - ADAPTED TO THE NEW SIGNATURE OF matmul_transform
    proto::when<InputPlaceholder, proto::functional::at(proto::_data, proto::_value)> > {};

// THE FOLLOWING CODE BLOCK IS COPIED FROM https://github.com/barche/eigen-proto/blob/master/eigen_calculator_solution.cpp
//----------------------------------------------------------------------------------------------
/// Wraps a given expression, so the value that it represents can be stored inside the expression itself
template<typename ExprT, typename ValueT>
struct stored_result_expression :
  proto::extends< ExprT, stored_result_expression<ExprT, ValueT> >
{
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW

  typedef proto::extends< ExprT, stored_result_expression<ExprT, ValueT> > base_type;

  explicit stored_result_expression(ExprT const &expr = ExprT())
    : base_type(expr)
  {
  }

  /// Temporary storage for the result of the expression
  mutable ValueT value;
};

struct do_wrap_expression : proto::transform< do_wrap_expression >
{
  template<typename ExprT, typename StateT, typename DataT>
  struct impl : proto::transform_impl<ExprT, StateT, DataT>
  {
    typedef typename boost::result_of<MatmulGrammar(ExprT, StateT, DataT)>::type result_ref_type; //CHANGED - TO USE YOUR GRAMMAR
    typedef typename boost::remove_reference<result_ref_type>::type value_type;
    typedef typename boost::remove_const<typename boost::remove_reference<ExprT>::type>::type expr_val_type;
    typedef stored_result_expression<expr_val_type, value_type> result_type;

    result_type operator()(typename impl::expr_param expr, typename impl::state_param state, typename impl::data_param data)
    {
      return result_type(expr);
    }
  };
};

/// Wrap multiplies expressions so they can store a temporary result
struct wrap_expression :
  proto::or_
  <
    proto::terminal<proto::_>,
    proto::when
    <
      proto::multiplies<proto::_, proto::_>,
      do_wrap_expression(
        proto::functional::make_multiplies
        (
            wrap_expression(proto::_left), wrap_expression(proto::_right)
        ),
        proto::_state, //CHANGED - THESE EXTRA PARAMETERS ARE NEEDED TO CALCULATE result_ref_type IN do_wrap_expression
        proto::_env
      )
    >,
    proto::nary_expr< proto::_, proto::vararg<wrap_expression> >
  >
{
};
//--------------------------------------------------------------------------------------------------

int main() {
    matrix mat1(2,2), mat2(2,2), mat3(2,2), result(2,2);

    mat1 << 1, 1, 0, 1;
    mat2 << 1, 1, 0, 1;
    mat3 << 1, 1, 0, 1;

    MatmulGrammar mmg;
    wrap_expression wrap;

    //THIS WORKS:
     result = mmg( //THIS IS REALLY HORRIBLE, BUT IT WORKS. IT SHOULD PROBABLY BE HIDDEN BEHIND A FUNCTION
                wrap(
                    I1 * I2,
                    mpl::void_(),
                    ( proto::data = fusion::make_vector(boost::cref(mat1), boost::cref(mat2), boost::cref(mat3)),
                      proto::transforms = matmul_transforms() )
                ),
                mpl::void_(),
                ( proto::data = fusion::make_vector(boost::cref(mat1), boost::cref(mat2), boost::cref(mat3)),
                  proto::transforms = matmul_transforms() )
            );

    std::cout << result << std::endl;

    // THIS DOESN'T CRASH ANYMORE:
    result = mmg(
                wrap(
                    I1 * I2 * I3 * I1 * I2 * I3,
                    mpl::void_(),
                    ( proto::data = fusion::make_vector(boost::cref(mat1), boost::cref(mat2), boost::cref(mat3)),
                      proto::transforms = matmul_transforms() )
                ),
                mpl::void_(),
                ( proto::data = fusion::make_vector(boost::cref(mat1), boost::cref(mat2), boost::cref(mat3)),
                  proto::transforms = matmul_transforms() )
            );

    std::cout << result << std::endl;

    return 0;
}

score 3 · Accepted Answer

这是另一个似乎可行的解决方案。它不会干扰 proto 的表达式对象，而是将指向中间 Eigen 对象的共享指针保存为状态的一部分。与受 C++Now talk 启发的解决方案相比，它具有以下优点：

它不会强制对 Eigen 的表达式模板进行早期评估。
它需要对语法进行较少的更改，因此它对特定领域语言的语法的干扰较小。
保持中间对象存活的责任由状态承担，这可以说是它所属的地方。特别是，我相信这使得语法线程安全（如果 proto 是）。
它返回一个表达式模板，而不是一个矩阵。即使您将此模板存储在变量中并稍后在空闲时对其进行评估，您也应该是安全的，因为所有部分都包含在内。

缺点：

不是返回一个整洁的矩阵，而是一个笨拙的结构，您必须从中提取您真正感兴趣的部分。
临时对象分配在堆上而不是堆栈上。
无论您喜欢与否，都必须提供指向矩阵的共享指针。

#include <iostream>

#include <boost/fusion/include/container.hpp>
#include <boost/fusion/include/join.hpp>
#include <boost/make_shared.hpp>
#include <boost/mpl/int.hpp>
#include <boost/mpl/void.hpp>
#include <boost/proto/proto.hpp>
#include <boost/ref.hpp>
#include <boost/shared_ptr.hpp>
#include <boost/type_traits/remove_const.hpp>
#include <boost/type_traits/remove_reference.hpp>

#include <Eigen/Dense>

namespace fusion = boost::fusion;
namespace mpl = boost::mpl;
namespace proto = boost::proto;

typedef Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic> matrix;

// Placeholders

const proto::terminal<mpl::int_<0> >::type I1 = {{}};
const proto::terminal<mpl::int_<1> >::type I2 = {{}};
const proto::terminal<mpl::int_<2> >::type I3 = {{}};

// Grammar

template<class Rule, class Callable = proto::callable>
struct External :
    proto::when<Rule, proto::external_transform> {};

struct matmul_transform : proto::callable {
    template<class Sig> struct result;

    template<class This, class ExprList1, class ExprList2>
    struct result<This(ExprList1, ExprList2)> {
            typedef typename boost::remove_reference<
                    typename fusion::result_of::front<ExprList1>::type>::type::element_type M1;
            typedef typename boost::remove_reference<
                    typename fusion::result_of::front<ExprList2>::type>::type::element_type M2;
            typedef typename Eigen::ProductReturnType<
                    typename boost::remove_const<typename boost::remove_reference<M1>::type>::type,
                    typename boost::remove_const<typename boost::remove_reference<M2>::type>::type>::Type
                    product_return_type;
            typedef typename fusion::result_of::push_front<
                            const typename fusion::result_of::join<const ExprList1, const ExprList2>::type,
                            boost::shared_ptr<product_return_type> >::type
                    type;

    };

    template<class ExprList1, class ExprList2>
    typename result<matmul_transform(ExprList1, ExprList2)>::type
    operator()(const ExprList1 &a, const ExprList2 &b) const {
            typedef typename result<matmul_transform(ExprList1, ExprList2)>::product_return_type product_return_type;
            return push_front(join(a, b), boost::make_shared<product_return_type>(*front(a) * *front(b)));
    }
};

struct placeholder_transform : proto::callable {
    template<class Sig> struct result;

    template<class This, class Data, class Value>
    struct result<This(Data, Value)> {
            typedef typename boost::remove_const<typename boost::remove_reference<
                    typename fusion::result_of::at<Data, typename boost::remove_reference<Value>::type>::type>
                            ::type>::type ptr_type;
            typedef typename fusion::list<ptr_type> type;
    };

    template<class Data, class Value>
    typename result<placeholder_transform(Data, Value)>::type
    operator()(Data &data, Value value) const {
            return fusion::make_list(fusion::at<Value>(data));
    }
};

struct MatmulGrammar;

struct InputPlaceholder : proto::terminal<proto::_> {};

struct MatrixMultiplication :
    proto::multiplies<MatmulGrammar, MatmulGrammar> {};

struct MatmulGrammar : proto::or_<
    External<InputPlaceholder>,
    External<MatrixMultiplication> > {};

struct matmul_transforms : proto::external_transforms<
    proto::when<MatrixMultiplication, matmul_transform(MatmulGrammar(proto::_left), MatmulGrammar(proto::_right))>,
    proto::when<InputPlaceholder, placeholder_transform(proto::_data, proto::_value)> > {};

int main() {
    boost::shared_ptr<matrix> mat1 = boost::make_shared<matrix>(2,2);
    boost::shared_ptr<matrix> mat2 = boost::make_shared<matrix>(2,2);
    boost::shared_ptr<matrix> mat3 = boost::make_shared<matrix>(2,2);
    boost::shared_ptr<matrix> result = boost::make_shared<matrix>(2,2);

    *mat1 << 1, 1, 0, 1;
    *mat2 << 1, 1, 0, 1;
    *mat3 << 1, 1, 0, 1;

    MatmulGrammar mmg;

    // THIS WORKS:
    *result = *front(
            mmg(I1 * I2, mpl::void_(),
            (proto::data = fusion::make_vector(mat1, mat2, mat3),
             proto::transforms = matmul_transforms())));

    std::cout << *result << std::endl;

    // THIS WORKS, TOO:
    *result = *front(
            mmg(I1 * I2 * I3 * I3 * I2 * I1, mpl::void_(),
            (proto::data = fusion::make_vector(mat1, mat2, mat3),
             proto::transforms = matmul_transforms())));

    std::cout << *result << std::endl;

    return 0;
}

c++ - 使用 Boost.Proto 构建 Eigen 表达式模板

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