[R] Hadamard transformation

[Rui Barradas]

Às 18:45 de 18/09/2023, mohan radhakrishnan escreveu:
> Hello,
> 
> I am attempting to port the R code which is an answer to
> https://codegolf.stackexchange.com/questions/194229/implement-the-2d-hadamard-transform
> 
> 
> function(M){for(i in 1:log2(nrow(M)))T=T%x%matrix(1-2*!3:0,2)/2; print(T);
> T%*%M%*%T}
> 
> The code, 3 inputs and the corresponding outputs are shown in
> https://tio.run/##PYyxCsIwFEX3fkUcAu@VV7WvcSl2dOwi8QNqNSXQJhAqrYjfHoOIwz3D4XBDNOJYiGgerp@td9Diy/gAVlgnynr0A4MLfkkeUTdarnLq5mBXKAvON1W9J8YdZ1rmsk3T72jgV/TAVBHTAROYrs/00@jz5YSY/aOSFKmvGP1yD9sk4Wa7ARSSRowf
> 
> These are the inputs.
> 
> f(matrix(c(2,3,2,5),2,2,byrow=TRUE))
> f(matrix(1,4,4))
> f(lower.tri(diag(4),T))
> 
> My attempt to port this R code to another framework(Tensorflow) was only
> partially successful
> because I didn't fully understand the cryptic R code. The second input
> shown above works after
> hacking Tensorflow for a long time.
> 
> My question is this. Can anyone code this in a clear way so that I can
> understand ? I understand
> Kronecker Product and matrix multiplication and can port that code but I am
> missing something as the same ported code does not work for all inputs.
> 
> Thanks,
> Mohan
> 
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> 
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Hello,

Is this what you want?
(I have changed the notation a bit.)


H <- function(M){
   H0 <- 1
   Transf <- matrix(c(1, 1, 1, -1), 2L)
   for(i in 1:log2(nrow(M))) {
     H0 <- H0 %x% Transf/2
   }
   H0 %*% M %*% H0
}

x <- matrix(c(2, 3, 2, 5), 2, 2, byrow = TRUE)
y <- matrix(1, 4, 4)
z <- lower.tri(diag(4), TRUE)
z[] <- apply(z, 2, as.integer)
H(x)
H(y)
H(z)



Hope this helps,

Rui Barradas