R Under development (unstable) (2023-06-22 r84597 ucrt) -- "Unsuffered Consequences"
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> #### Tests for psi(), rho() etc
> 
> library(robust)
Loading required package: fit.models
> 
> ### Test internal consistency
> ## (1) rho'(x) = psi(x)
> ## (2) psi'(x) = psp(x)
> 
> ## (3) chi(x) = pmin(R, rho(x))  ( *not* the definition for S-estimates !! )
> ##             but really chi() = 1/2 psi()^2  Huber; for the others chi() == rho()
> 
> ##
> x  <- seq(-4,4, length =  801)# large n
> x. <- seq(-4,4, length = 2001)# larger n
> 
> verbose <- TRUE
> for(ipsi in 1:3) { # later  1:4 --  ipsi = 4 nowhere documented
+     cat("ipsi = ", ipsi, "\n")
+     f.x <- cbind(psi = psi.weight(x, ips=ipsi), psp = psp.weight(x, ips=ipsi),
+                  chi = chi.weight(x, ips=ipsi), rho = rho.weight(x, ips=ipsi))
+     rhoF <- splinefun(x,f.x[,"rho"])
+     psiF <- splinefun(x,f.x[,"psi"])
+     pspF <- splinefun(x,f.x[,"psp"])
+ ##     chiF <- splinefun(x,f.x[,"chi"])
+     p1 <- psiF(x., deriv=1); p. <- pspF(x.)
+     r1 <- rhoF(x., deriv=1); ps <- psiF(x.)
+     if(verbose) {
+         cat("psi'(.) = psp(.):", all.equal(p1, p., tol = 1e-6),"\n")
+         cat("rho'(.) = psi(.):", all.equal(r1, ps, tol = 1e-6),"\n")
+         ## TODO: chi ?
+     }
+     stopifnot(all.equal(p1, p., tol = if(ipsi == 3) .05 else 1e-3),
+               all.equal(r1, ps, tol = 1e-4))
+     if(verbose) cat("\n---------------------\n\n")
+ }
ipsi =  1 
psi'(.) = psp(.): Mean relative difference: 0.0002375808 
rho'(.) = psi(.): TRUE 

---------------------

ipsi =  2 
psi'(.) = psp(.): Mean relative difference: 0.0002333463 
rho'(.) = psi(.): Mean relative difference: 1.896192e-06 

---------------------

ipsi =  3 
psi'(.) = psp(.): Mean relative difference: 0.03071846 
rho'(.) = psi(.): Mean relative difference: 5.115593e-06 

---------------------

> 
> 
> ### Plots --> ../man/weight.funs.Rd
> 
> proc.time()
   user  system elapsed 
   0.35    0.10    0.45