R Under development (unstable) (2023-11-08 r85496 ucrt) -- "Unsuffered Consequences"
Copyright (C) 2023 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> ##
> ##  s u b s p a c e . r  Test suite
> ##
> 
> 
> orth <- pracma::orth
> subspace <- pracma::subspace
> 
> is.null(orth(c()))
[1] TRUE
> M <- matrix(1:12, 3, 4)
> all.equal(orth(M),
+           matrix(c(-0.504533, -0.760776,
+                    -0.574516, -0.057141,
+                    -0.644497,  0.646495), 3, 2, byrow = TRUE),
+           tolerance = 1e-5)
[1] "Mean relative difference: 2"
> 
> H <- pracma::hadamard(8)
> A <- H[, 2:4]
> B <- H[, 5:8]
> all.equal(subspace(A, B), pi/2, tolerance = 1e-10)  
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.12    0.04    0.15