空空间二进制矩阵：Java [英] Null Space Binary Matrix : Java

问题描述

这是我的问题：如何计算二进制矩阵的内核？

要在Java中计算内核（或者你喜欢的Null空间），它是在Real Space中非常简单，已经有很多类，所以不需要再发明轮子，我们只需要使用它们！

  double [] [] data = new double [3] [3]; 
 
 // ...填充矩阵
 
 SimpleMatrix m = new SimpleMatrix（data）; 
 
 SimpleSVD svd = m.svd（）; 
 
 SimpleMatrix nullSpace = svd.nullSpace（）; 
 
 nullSpace.print（）; 
  

（这些类来自： http：//efficient-java-matrix-library.googlecode。 com / svn-history / r244 / javadoc / ver0.14 / org / ejml / data / package-summary.html ）

问题是：全部这些课程只在Real领域工作，我需要在Z / 2Z（或者你喜欢的二进制空间）中进行，我不知道怎么做？

你知道Java中有什么好的API可以使用布尔矩阵吗？

或者你知道怎么做这个内核计算用布尔而不是真的...？

提前多多谢谢！

干杯！

解决方案

二进制m-by-n矩阵A的内核被定义为二进制向量x的集合，使得Ax = 0。 / p>

空格上的加法是布尔XOR：0 + 0 = 1 + 1 = 0; 0 + 1 = 1 + 0 = 1.

空间上的乘法是布尔值AND：0 * 0 = 0 * 1 = 1 * 0 = 0; 1 * 1 = 1.

要计算A的内核基础，构造[A; I]然后执行基本列操作以获得[B; C]其中B是列梯形式。 B列零列下面的C列是内核基础。

此过程在此处有更详细的描述： http://en.wikipedia.org/wiki/Kernel_(matrix)#Basis 请注意，所描述的算法适用于二进制的情况，即使它没有在维基百科页面上提及。

如果你找到一个已经做到这一点的库，我会感到惊讶，这对于实现，所以我建议你自己编写代码，而不是寻找现有的解决方案。

Here is my question: How to calcul the Kernel of a Binary Matrix ??

To calcul the Kernel (or Null Space if you prefer) in Java, it's pretty simple in the Real Space, there is already a lot of classes, so don't need to invent the wheel again, we just have to use them !

    double[][] data = new double[3][3];

    // ... fill the Matrix 

    SimpleMatrix m = new SimpleMatrix(data);

    SimpleSVD svd = m.svd();

    SimpleMatrix nullSpace = svd.nullSpace();

    nullSpace.print();   

(Theses classes came from : http://efficient-java-matrix-library.googlecode.com/svn-history/r244/javadoc/ver0.14/org/ejml/data/package-summary.html )

The problem is : all theses classes work only in the Real space, and I need to do it in Z/2Z (or in the Binary space if you prefer) and I don't have the idea of how to do it ?

Do you know any good API in Java to work with Boolean Matrix ?

Or do you have any idea of how to do this kernel calcul with booleans and not real... ?

Thanks a lot in advance !

Cheers !

解决方案

The kernel of binary m-by-n matrix A is defined to be the set of binary vectors x such that Ax = 0.

Addition on the space is Boolean XOR: 0 + 0 = 1 + 1 = 0; 0 + 1 = 1 + 0 = 1.
Multiplication on the space is Boolean AND: 0 * 0 = 0 * 1 = 1 * 0 = 0; 1 * 1 = 1.

To compute the kernel basis for A, construct [A; I] and then perform elementary column operations to obtain [B; C] where B is in column echelon form. The columns of C underneath zero-columns of B are the kernel basis.

The process is described in more detail here: http://en.wikipedia.org/wiki/Kernel_(matrix)#Basis Note that the described algorithm will work for the binary case as well, even though it is not mentioned on the Wikipedia page.

I'd be surprised if you find a library that already does this, and it's trivial to implement, so I advise just coding it up yourself rather than looking for an existing solution.

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