使用“异或"，“非"或“布尔"乘法(使用本征矩阵库) [英] bool multiplication with exclusive-or, not or (with Eigen Matrix Library)
问题描述
我正在尝试实现汉明纠错码，为此，我需要获取布尔矢量(数据)并将其与布尔矩阵(汉明生成器矩阵)相乘，执行XOR操作(而不是看起来像什么)像OR一样是Eigen的默认bool行为).在这个简单的教程中找到了我正在做的一个例子: http://michael.dipperstein.com/hamming/
I'm trying to implement hamming error correcting codes, and to do this I need to take a bool Vector (the data) and multiply it with a bool Matrix(hamming generator matrix), performing XOR operations (instead of what looks like OR as Eigen's default bool behavior). An example of what I am doing is found in this simple tutorial: http://michael.dipperstein.com/hamming/
我不一定必须使用Eigen，因此，如果您有解决方案，请随时提出除Eigen之外的其他建议.
I don't necessarily have to use Eigen, so please feel free to suggest something other than Eigen if you have the solution.
例如，一些C ++代码可以编译，但不能以正确的方式正常工作:
So for example a bit of C++ code that compiles, but does not quite work the right way:
#include <Eigen/Dense>
#include <iostream>
using namespace std;
using namespace Eigen;
typedef Eigen::Matrix<bool, 4, 7> Matrix4by7Bool;
typedef Eigen::Matrix<bool, 1, 4> Vector4Bool;
int main()
{
Matrix4by7Bool gm;
gm << 0,1,1,1,0,0,0,
1,0,1,0,1,0,0,
1,1,0,0,0,1,0,
1,1,1,0,0,0,1;
Vector4Bool dm;
dm << 1,0,1,0;
cout << dm * gm;
}
当前导致:1 1 1 1 0 1 0
但我需要:1 0 1 1 0 1 0
currently results in: 1 1 1 1 0 1 0
but I need: 1 0 1 1 0 1 0
区别在于，默认行为是先相乘，然后再相乘.因为我需要XOR而不是OR，所以想知道用Eigen做到这一点的最佳方法是什么?
The difference is that the default behavior is to multiply and then OR each multiplication. Since I need XOR instead of OR, wondering what the best way to do this with Eigen is?
如果这没有道理，很乐意尝试详细阐述.
Happy to try and elaborate if this does not make sense.
顺便说一句，不确定是否重要，但是我正在使用G ++在MacBook Air上工作.今天刚刚下载了Eigen，所以它的问题可能是最新的(eigen3)
BTW, not sure if it matters but I'm working on a MacBook Air, using G++. Just downloaded Eigen today so its prob the newest available (eigen3)
谢谢你，
基思
Thank you,
Keith
更新:鉴于以下可接受的解决方案，我想重新发布正确的代码以供人们参考:
#include <Eigen/Dense>
#include <iostream>
using namespace std;
using namespace Eigen;
typedef Eigen::Array<bool, 4, 7> Array4by7Bool;
typedef Eigen::Array<bool, 4, 1> Array1by4Bool;
struct logical_xor {
bool operator() (bool a, bool b) const
{
return a != b;
}
};
int main()
{
Array4by7Bool gm;
gm << 0,1,1,1,0,0,0,
1,0,1,0,1,0,0,
1,1,0,0,0,1,0,
1,1,1,0,0,0,1;
Array1by4Bool dm;
dm << 1,0,1,0;
cout << "result: " << (gm.colwise() * dm).colwise().redux(logical_xor()) << endl;
}
推荐答案
您可以使用广播和部分归约来模拟matrix_vector乘积:
You can mimic a matrix_vector product using broadcasting and a partial reduction:
struct logical_xor { bool operator(bool a, bool b) { return a != b; }
result = (gm.array().colwise() * dm.transpose().array()).colwise().redux(logical_xor());
如果您将变量声明为Array，并且dm已经是列数组，那么它将简化为:
If you declare your variables as Array and dm is already a column array, then this simplifies to:
result = (gm.colwise() * dm).colwise().redux(logical_xor());
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