名称空间与友元函数的相关问题？

Question

/放在命名空间中的一个类 vector.h
namespace vector_namespace {
    class Vector {
    public:
        enum class Mode { Rect, Pol };

        Vector();
        Vector(double x, double y, Mode mode = Mode::Rect);
        friend std::ostream& operator<<(std::ostream& os, const Vector& vector);
    private:
        double X;
        double Y;
        double Mag;
        double Ang;
        Mode Mode;
    };
}

/vector.cpp
namespace vector_namespace {
Vector::Vector(const double x, const double y, const enum Mode mode) {
        Mode = mode;
        if (mode == Mode::Pol) {
            Mag = x;
            Ang = y;
            SetX();
            SetY();
        }
        else if (mode == Mode::Rect) {
            X = x;
            Y = y;
            SetMag();
            SetAng();
        }
        else {
            X = Y = Mag = Ang = 0.0;
            Mode = Mode::Rect;
        }
    }
std::ostream& operator<<(std::ostream& os, const Vector& vector) {
        if (vector.Mode == Vector::Mode::Rect) {
            os << "(x,y) = (" << vector.X << ", " << vector.Y << ")";
        }
        else if (vector.Mode == Vector::Mode::Pol) {
            os << "(m,a) = (" << vector.Mag << "," << vector.Ang * (45.0 / atan(1.0)) << ")";
        }
        else {
            os << "Vector object mode is invalid";
        }
        return os;
    }
}

上面的代码operator<<函数可以成功编译

/vector.cpp
namespace vector_namespace {
Vector::Vector(const double x, const double y, const enum Mode mode) {
        Mode = mode;
        if (mode == Mode::Pol) {
            Mag = x;
            Ang = y;
            SetX();
            SetY();
        }
        else if (mode == Mode::Rect) {
            X = x;
            Y = y;
            SetMag();
            SetAng();
        }
        else {
            X = Y = Mag = Ang = 0.0;
            Mode = Mode::Rect;
        }
    }
}
std::ostream& vector_namespace::operator<<(std::ostream& os, const Vector& vector) {
        if (vector.Mode == Vector::Mode::Rect) {
            os << "(x,y) = (" << vector.X << ", " << vector.Y << ")";
        }
        else if (vector.Mode == Vector::Mode::Pol) {
            os << "(m,a) = (" << vector.Mag << "," << vector.Ang * (45.0 / atan(1.0)) << ")";
        }
        else {
            os << "Vector object mode is invalid";
        }
        return os;
    }

而此时无法通过编译，请问为什么下面那种不能通过编译，明明也是把函数定义在了名称空间中，和上面一种放在大括号内有什么区别呢？

Answer 1

.h:
namespace vector_namespace {
    class Vector {
    public:
        enum Mode { Rect, Pol };
        Vector();
        Vector(double x, double y, Mode mode = Mode::Rect);
        friend std::ostream& operator<<(std::ostream& os, const Vector& vector);
    private:
        double X;
        double Y;
        double Mag;
        double Ang;
        Mode Mode;
    };
}

cpp:
#include <iostream>
using namespace std;

#include "vector.h"

namespace vector_namespace {
Vector::Vector(const double x, const double y, const enum Mode mode) {
        Mode = mode;
        if (mode == Mode::Pol) {
            Mag = x;
            Ang = y;
         
        }
        else if (mode == Mode::Rect) {
            X = x;
            Y = y;
          
        }
        else {
            X = Y = Mag = Ang = 0.0;
            Mode = Mode::Rect;
        }
    }
}
std::ostream& vector_namespace::operator<<(std::ostream& os, const Vector& vector) {
        if (vector.Mode == Vector::Mode::Rect) {
            os << "(x,y) = (" << vector.X << ", " << vector.Y << ")";
        }
        else if (vector.Mode == Vector::Mode::Pol) {
            os << "(m,a) = (" << vector.Mag << "," << vector.Ang * (45.0 / atan(1.0)) << ")";
        }
        else {
            os << "Vector object mode is invalid";
        }
        return os;
    }


void main()
{
}