R Under development (unstable) (2023-11-08 r85496 ucrt) -- "Unsuffered Consequences"
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> ##
> ##  ha d a m a r d . R  Test suite
> ##
> 
> 
> hadamard <- pracma::hadamard
> Toeplitz <- pracma::Toeplitz
> 
> all.equal(hadamard(2),
+           matrix(c(1, 1, 1, -1), 2, 2))
[1] TRUE
> all.equal(hadamard(4),
+           matrix(c(1,  1,  1,  1,
+                    1, -1,  1, -1,
+                    1,  1, -1, -1,
+                    1, -1, -1,  1), 4, 4))
[1] TRUE
> # H12 <- hadamard(12)
> # all.equal(t(H12) %*% H12,
> #           diag(12, 12, 12))
> # H20 <- hadamard(20)
> # all.equal(t(H20) %*% H20,
> #           diag(20, 20, 20))
> 
> all.equal(Toeplitz(c(1, 2, 4, 6, 8), c(1, 3, 5, 7, 9)),
+           matrix(c(1, 3, 5, 7, 9,
+                    2, 1, 3, 5, 7,
+                    4, 2, 1, 3, 5,
+                    6, 4, 2, 1, 3,
+                    8, 6, 4, 2, 1), 5, 5, byrow = TRUE))
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.12    0.04    0.15