布尔矩阵乘法在Matlab [英] Boolean Matrix Multiplication in Matlab

问题描述

Matlab的是否有一个布尔值（有时也称为逻辑或二进制）矩阵乘法功能？我专门谈论通常是由一个圆圈表示，在一个句点来表示布尔矩阵乘法：

  CIJ =（AI1＆安培; B1J）|| （AI2＆安培; B2J）|| （AI3＆安培; B3J）|| ... || （AIK＆安培; BKJ）
 

我有一个很难定位之一，我现在假设不存在。如果是这样的话，是有一个快速的方法写一个.m文件，将完成这项任务？

一个例子是：

  [1 1 1; [1 0 1; [1 1 1
 1 0 1; * circledot * 1 0 0; = 1 1 1
 1 0 0] 0​​ 1 0] 1 0 1]
 

解决方案

您可以只允许MATLAB来执行标准的矩阵乘法，并将结果转换为逻辑：

  B1 = [1,1,1; 1,0,1; 1,0,0]
B2 = [1,0,1; 1,0,0; ​​0,1,0]
布特=（B1 * B2）大于0％或逻辑（B1 * B2）按纳坦的回答！布特=     1 1 1
     1 1 1
     1 0 1
 

然而，如果你要忠实履行布尔矩阵乘法运算符的逻辑与或操作，您可以使用 bsxfun 做和任何如下：

 回合=任何（bsxfun（@和，置换（B2，[3 2 1]），置换（B1，[1 3 2]）），3）;
 

这pretty以及混淆了过程，但它遵循的公式。

快速的测试数据： B1 =兰迪（2，M，N）-1; B2 =兰迪（2，N，M）-1;

Does Matlab have a Boolean (sometimes called logical or binary) matrix multiplication function? I'm specifically talking about what's usually denoted by a circle with a dot in it to denote Boolean matrix multiplication:

cij = (ai1 & b1j) || (ai2 & b2j) || (ai3 & b3j)|| ... || (aik & bkj)

I have had a hard time locating one and am now assuming one does not exist. If that is the case, is there a quick way to write a .m file that will accomplish this task?

An example would be:

[1 1 1;                [1 0 1;      [1 1 1
 1 0 1;   *circledot*   1 0 0;   =   1 1 1
 1 0 0]                 0 1 0]       1 0 1]

解决方案

You can just allow MATLAB to perform standard matrix multiplication and convert the result to logical:

b1 = [1,1,1;1,0,1;1,0,0]
b2 = [1,0,1;1,0,0;0,1,0]
bout = (b1*b2)>0 % or logical(b1*b2) as per natan's answer!

bout =

     1     1     1
     1     1     1
     1     0     1

However, if you want to faithfully perform the logical AND-OR operations of the Boolean matrix multiplication operator, you can do it with bsxfun and any as follows:

bout = any(bsxfun(@and,permute(b2,[3 2 1]),permute(b1,[1 3 2])),3);

That pretty well obfuscates the process, but it follows the formula.

Quick test data: b1 = randi(2,M,N)-1; b2 = randi(2,N,M)-1;.

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