[问答] 求助：用R怎么产生Hadamard矩阵，有c语言程序，改编 [推广有奖]

11楼

mengqinqing 发表于 2012-4-16 22:02:48

epoh 发表于 2012-4-16 15:09
%H=hadamard(n), H'*H = N*EYE(N).

%%%%in Matlab

谢谢！
不过有一个问题，这两个软件输出的矩阵要求n是2的幂，可是我用c语言程序却可以得到比如n=15时的hadamard矩阵。
R
>  n=15
>  2*hadamard(n-4)-1
   [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,] 1 1 1 1 1 1 1 1 1    1    1    1
[2,] 1 -1 -1 1 -1 -1 -1 1 1    1 -1    1
[3,] 1 -1 1 -1 -1 -1 1 1 1 -1    1 -1
[4,] 1 1 -1 -1 -1 1 1 1 -1    1 -1 -1
[5,] 1 -1 -1 -1 1 1 1 -1 1 -1 -1    1
[6,] 1 -1 -1 1 1 1 -1 1 -1 -1    1 -1
[7,] 1 -1 1 1 1 -1 1 -1 -1    1 -1 -1
[8,] 1 1 1 1 -1 1 -1 -1 1 -1 -1 -1
[9,] 1 1 1 -1 1 -1 -1 1 -1 -1 -1    1
[10,] 1 1 -1 1 -1 -1 1 -1 -1 -1    1    1
[11,] 1 -1 1 -1 -1 1 -1 -1 -1    1    1    1
[12,] 1 1 -1 -1 1 -1 -1 -1 1    1    1 -1

C
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
1  -1  1  -1  1  -1  1  -1  1  -1  1  -1  1  -1  1
1  1  -1  -1  1  1  -1  -1  1  1  -1  -1  1  1  -1
1  -1  -1  1  1  -1  -1  1  1  -1  -1  1  1  -1  -1
1  1  1  1  -1  -1  -1  -1  1  1  1  1  -1  -1  -1
1  -1  1  -1  -1  1  -1  1  1  -1  1  -1  -1  1  -1
1  1  -1  -1  -1  -1  1  1  1  1  -1  -1  -1  -1  1
1  -1  -1  1  -1  1  1  -1  1  -1  -1  1  -1  1  1
1  1  1  1  1  1  1  1  -1  -1  -1  -1  -1  -1  -1
1  -1  1  -1  1  -1  1  -1  -1  1  -1  1  -1  1  -1
1  1  -1  -1  1  1  -1  -1  -1  -1  1  1  -1  -1  1
1  -1  -1  1  1  -1  -1  1  -1  1  1  -1  -1  1  1
1  1  1  1  -1  -1  -1  -1  -1  -1  -1  -1  1  1  1
1  -1  1  -1  -1  1  -1  1  -1  1  -1  1  1  -1  1
1  1  -1  -1  -1  -1  1  1  -1  -1  1  1  1  1  -1
不知道是怎么回事？

用自己的力量站在自己的位置

12楼

epoh 发表于 2013-1-23 18:37:30

mengqinqing 发表于 2012-4-16 22:02
谢谢！
不过有一个问题，这两个软件输出的矩阵要求n是2的幂，可是我用c语言程序却可以得到比如n=15时的h ...

请你确认,你的程序用C++使用hadamard(8)的结果
是(同MATLAB)

[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1 1 1 1 1 1 1 1
[2,] 1 -1 1 -1 1 -1 1 -1
[3,] 1 1 -1 -1 1 1 -1 -1
[4,] 1 -1 -1 1 1 -1 -1 1
[5,] 1 1 1 1 -1 -1 -1 -1
[6,] 1 -1 1 -1 -1 1 -1 1
[7,] 1 1 -1 -1 -1 -1 1 1
[8,] 1 -1 -1 1 -1 1 1 -1

还是
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1 1 1 1 1 1 1 1
[2,] 1 -1 -1 1 -1 -1 -1 1
[3,] 1 -1 1 -1 -1 -1 1 1
[4,] 1 1 -1 -1 -1 1 1 1
[5,] 1 -1 -1 -1 1 1 1 -1
[6,] 1 -1 -1 1 1 1 -1 1
[7,] 1 -1 1 1 1 -1 1 -1
[8,] 1 1 1 1 -1 1 -1 -1

13楼

ntsean 发表于 2013-1-23 22:56:53

这个用回归就可以了

hadamard <- function(n) {
if (n==2) return(matrix(c(1, -1, 1, 1), nrow = 2))
h <- matrix(NA, nrow=n, ncol=n)
n1 <- n/2
h[1:n1, 1:n1] <- h[(n1+1):n, (n1+1):n] <- h[1:n1, (n1+1):n] <- hadamard(n1)
h[(n1+1):n, 1:n1] <- -hadamard(n1)
return(h)
}

> hadamard(4)
[,1] [,2] [,3] [,4]
[1,] 1 1 1 1
[2,] -1 1 -1 1
[3,] -1 -1 1 1
[4,] 1 -1 -1 1
> hadamard(8)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1 1 1 1 1 1 1 1
[2,] -1 1 -1 1 -1 1 -1 1
[3,] -1 -1 1 1 -1 -1 1 1
[4,] 1 -1 -1 1 1 -1 -1 1
[5,] -1 -1 -1 -1 1 1 1 1
[6,] 1 -1 1 -1 -1 1 -1 1
[7,] 1 1 -1 -1 -1 -1 1 1
[8,] -1 1 1 -1 1 -1 -1 1

14楼

ntsean 发表于 2013-1-23 23:16:06

或者，如果和上面用一样定义的hadamard的话

hadamard <- function(n) {
  if (n==2) return(matrix(c(1, 1, 1, -1), nrow = 2))
  h <- matrix(NA, nrow=n, ncol=n)
  n1 <- n/2
  h[1:n1, 1:n1] <- h[(n1+1):n, 1:n1]  <- h[1:n1, (n1+1):n] <- hadamard(n1)
  h[(n1+1):n, (n1+1):n] <- -hadamard(n1)
  return(h)
}

> hadamard(8)
   [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1 1 1 1 1 1 1 1
[2,] 1 -1 1 -1 1 -1 1 -1
[3,] 1 1 -1 -1 1 1 -1 -1
[4,] 1 -1 -1 1 1 -1 -1 1
[5,] 1 1 1 1 -1 -1 -1 -1
[6,] 1 -1 1 -1 -1 1 -1 1
[7,] 1 1 -1 -1 -1 -1 1 1
[8,] 1 -1 -1 1 -1 1 1 -1