Matlab中的组合矩阵 [英] Combinations matrix in matlab

问题描述

此代码

 combinations = dec2base(0:power(2,N*M)-1,2) - '0'

生成大小为N * M的零和一的所有可能组合，并将所有这些组合存储在称为组合的矩阵中.我需要知道它是如何工作的，因为我不理解此代码.谢谢

generates all possible combinations of zeros and ones for a matrix of size N*M and stores all these combinations in a matrix called combinations. I need to know how it works , because i don't understand this code . Thank you

推荐答案

以M = 2，N = 3为例.那么power(2,N*M)-1是63，0:power(2,N*M)-1是向量[0 1 2 ... 63].

Consider M = 2, N = 3 as an example. Then power(2,N*M)-1 is 63, and 0:power(2,N*M)-1 is the vector [0 1 2 ... 63].

dec2base(..., 2)使用字符'0'和'1'作为数字"，将那些64数字转换为基数2.每个结果都排成一行，如果需要，用'0'左填充.这样就给出了64×6 char矩阵

dec2base(..., 2) converts those 64 numbers into base 2, using chars '0' and '1' as "digits". Each result is in a row, left-padded with '0''s if needed. So it gives the 64×6 char matrix

000000
000001
000010
....
111110
111111

要将这些字符转换为数字，请减去'0'.这利用了字符'0'和'1'的ASCII码是连续的事实，给出了'0'的0和'1'的1.所以最终结果是数值矩阵

To convert those chars into numbers, subtract '0'. That gives 0 for '0' and 1 for '1', exploiting the fact that the ASCII codes for chars '0' and '1' are consecutive. So the final result is the numeric matrix

0     0     0     0     0     0
0     0     0     0     0     1
0     0     0     0     1     0
....
1     1     1     1     1     0
1     1     1     1     1     1

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