使用转置作为参数与Eigen 3库编写一个函数

Question

我想编写一个可以接受的函数：

1. 密集的阵列/矩阵，或
2. 密集阵列/矩阵的转置。

是否可以避免使用完美转发？

我曾尝试使用DenseBase类型参数。但那不能接受矩阵的转置。

我不喜欢使用完美的转发，因为用sfinae实现类型检查会很乏味。

当前解决方案

#include <Eigen/Eigen>
#include <iostream>

using namespace Eigen;

template <typename U>
auto f(U&& x) {
    auto x2 = std::forward<U>(x);
    auto max_x = x2.colwise().maxCoeff().eval();
    x2 = x2.rowwise() + max_x;
    return max_x;
}

int main() {
    Array<float, 3, 3> M1;
    M1 << 1, 2, 3, 
          4, 5, 6, 
          7, 8, 9;
    std::cout << M1 << "\n";
    // auto here might cause problem later ...
    // see eigen.tuxfamily.org/dox/TopicPitfalls.html
    auto max_x = f(M1.transpose());
    std::cout << M1 << "\n";
    std::cout << max_x << "\n";
}

结果：

// original
1 2 3
4 5 6
7 8 9
// Increase each row by max of the row.
 4  5  6
10 11 12
16 17 18
// Max of each row (not a column vector).
3 6 9

我用以下几行尝试了EigenBase：

template <typename U>
auto f(EigenBase<U>& x) {
...

编译错误：

test4.cpp:20:32: error: cannot bind non-const lvalue reference of type ‘Eigen::EigenBase<Eigen::Transpose<Eigen::Array<float, 3, 3> > >&’ to an rvalue of type ‘Eigen::EigenBase<Eigen::Transpose<Eigen::Array<float, 3, 3> > >’
     auto max_x = f(M1.transpose());
                    ~~~~~~~~~~~~^~

Answer 1

使用左值引用和右值引用参数重载函数似乎可以解决它。

我怀疑transpose是唯一产生临时c ++表达式的东西。如果我希望转置版本返回转置结果（列而不是行向量）而非转置版本返回非转置结果，则不会解决这个问题。

感谢kmdreko指点。

测试：

#include <Eigen/Eigen>
#include <iostream>

using namespace Eigen;

template <typename Derived>
auto f(DenseBase<Derived>& x) {
    auto max_x = x.colwise().maxCoeff().eval();
    x = x.rowwise() + max_x;
    return max_x;
}

template <typename Derived>
auto f(DenseBase<Derived>&& x) {
    return f(x).transpose().eval();
}

int main() {
    Array<float, 3, 3> M1, M2;
    M1 << 1, 2, 3, 
          4, 5, 6, 
          7, 8, 9;
    M2 = M1;
    std::cout << M1 << "\n";

    std::cout << "no transpose\n";
    Array<float, 3, 1> max_x = f(M1);
    std::cout << M1 << "\n";
    std::cout << max_x << "\n";

    std::cout << "transpose\n";
    Array<float, 1, 3> max_x2 = f(M2.transpose());
    std::cout << M2 << "\n";
    std::cout << max_x2 << "\n";
}

结果：

1 2 3
4 5 6
7 8 9
no transpose
 8 10 12
11 13 15
14 16 18
// returns column vector
7
8
9
transpose
 4  5  6
10 11 12
16 17 18
// returns row vector
3 6 9

Answer 2

在调用函数之前，使用auto type来保存转置表达式。

#include <Eigen/Eigen>
#include <iostream>

using namespace Eigen;

template <typename Derived>
auto f(DenseBase<Derived>& x) {
    auto max_x = x.colwise().maxCoeff().eval();
    x = x.rowwise() + max_x;
    return max_x;
}

int main() {
    Array<float, 3, 3> M1, M2;
    M1 << 1, 2, 3, 
          4, 5, 6, 
          7, 8, 9;
    M2 = M1;
    std::cout << M1 << "\n";

    std::cout << "no transpose\n";
    Array<float, 3, 1> max_x = f(M1);
    std::cout << M1 << "\n";
    std::cout << max_x << "\n";

    std::cout << "transpose\n";
    auto m2_t = M2.transpose();
    Array<float, 1, 3> max_x2 = f(m2_t);
    std::cout << M2 << "\n";
    std::cout << max_x2 << "\n";
}

结果：

1 2 3
4 5 6
7 8 9
no transpose
 8 10 12
11 13 15
14 16 18
7
8
9
transpose
 4  5  6
10 11 12
16 17 18
3 6 9