本征函数指针 [英] function pointer with Eigen
问题描述
我对Python很熟练,但是对C ++和指针之类的东西还很陌生。我试图用Eigen软件包为线性代数编写一些用于求解ODE的代码(我以后将需要处理许多矩阵,因此我打算从中开始)。我对RK4使用以下代码,它们可以正常工作:
I am pretty competent with Python, but I'm pretty new to C++ and things like pointers. I try to write some codes for solving ODE with the Eigen package for linear algebra (I will need to deal with lots of matrices later, so I plan to start with it). I have the following code for RK4 and they work:
#include "../eigen-eigen-b3f3d4950030/Eigen/Dense"
using namespace Eigen;
VectorXd Func(const VectorXd& a)
{ // equations for solving simple harmonic oscillator
Vector2d ans;
ans(0) = a(1); // dy/dt
ans(1) = -a(0); // d2y/dt2
return ans;
}
MatrixXd RK4(VectorXd Func(const VectorXd& y), const Ref<const VectorXd>& y0, double h, int step_num)
{
MatrixXd y(step_num, y0.rows());
y.row(0) = y0;
for (int i=1; i<step_num; i++){
VectorXd y_old = y.row(i-1).transpose();
VectorXd k1 = h*Func(y_old);
VectorXd k2 = h*Func(y_old+k1/2);
VectorXd k3 = h*Func(y_old+k2/2);
VectorXd k4 = h*Func(y_old+k3);
VectorXd dy = (k1 + 2*k2 + 2*k3 + k4)/6;
y.row(i) = y.row(i-1) + dy.transpose();
}
return y;
}
int main()
{
Vector2d v1;
v1(0) = 1.4; v1(1) = -0.1;
double h = 0.1;
int step_num = 50;
MatrixXd sol = RK4(Func,v1,h,step_num);
return 0;
}
我有以下问题:
-
在函数参数中
&
是什么意思?通过参考?我只是从官方文档复制了代码,但是我不太确定是否我了解RK4的函数参数中的所有内容,例如VectorXd Func(const VectorXd& y)
。是否有其他方法可以接受Eigen :: MatrixXd和接受Eigen :: MatrixXd作为函数参数的函数?
What's the meaning of
&
in the function argument? Pass by reference? I just copied the code from the official documentation, but I'm not too sure if I understand every bit in the function arguments of RK4 such asVectorXd Func(const VectorXd& y)
. Are there alternative ways of accepting Eigen::MatrixXd and functions which accept Eigen::MatrixXd as function arguments?
据我所知,我们无法返回整数函数的2D数组,我们返回的只是数组的第一个元素(如果我写错了,请纠正我)。那么 Eigen :: MatrixX
呢?我们实际上通过/返回的是什么?矩阵的第一个元素还是由Eigen库定义的全新对象?
From what I understand, we cannot return a whole 2D array from a function, and what we are returning is just the first element of the array (correct me if I'm wrong). What about the Eigen::MatrixX
? What are we actually passing/returning? The first element of the matrix, or a completely new object defined by the Eigen library?
我不确定这些代码是否有效编写。我可以做些什么来优化这部分吗? (只是想知道我是否做过任何可能显着降低速度的操作。)
I'm not sure if these codes are written efficiently. Are there anything I can do to optimize this part? (Just wondering if I have done anything that may significantly slow down the speed).
谢谢
推荐答案
-
是的,
&
是通过-引用;后一种是用于传递函数的语法,该函数按引用获取向量并返回向量。Eigen :: Matrix
应该始终通过引用传递。有很多方法可以将一个函数传递给另一个函数,C ++中最惯用的方法可能是模板参数和std :: function
。
Yes,
&
is pass-by-reference; The latter one is syntax for passing a function, that takes a vector by reference and returns a vector. AnEigen::Matrix
should always be passed by reference. There are tons of ways to pass one function to another, the most idiomatic ones in C++ are probably template arguments andstd::function
.
您不能有多个返回参数,但是可以返回对
或元组
或 Matrix
对象。 RK4
返回整个矩阵。
You can't have multiple return arguments, but you can return a pair
or a tuple
or a Matrix
object. RK4
returns a whole matrix.
代码相当高效。如果它确实对性能至关重要,则可能需要优化一些内容,但我暂时不担心。
The code is fairly efficient. If it was really performance-critical there might be a few things that could be optimized, but I would not worry for now.
最大的一点是 RK4
非常通用,并且可以处理动态大小的类型,这些类型比其静态大小的计数器部分要昂贵得多( VectorXf
与 Vector2d
)。但这需要您为感兴趣的所有维度创建一个专门的版本,或者让编译器通过使用模板来为您完成。
The biggest point is that RK4
is very general and works with dynamically sized types, which are a lot more expensive than their statically sized counter parts (VectorXf
vs Vector2d
). But this would require you to create a specialized version for all dimensions you are interested in or to get the compiler to do it for you by using templates.
通常:读一本好书可以帮助您入门。
Generally: Read a good book to get you started.
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