R version 4.4.0 beta (2024-04-09 r86391 ucrt) -- "Puppy Cup"
Copyright (C) 2024 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64

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> library("matrixStats")
> 
> set.seed(1)
> x <- rnorm(1e4)
> 
> 
> # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
> # Variance estimators
> # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
> sigma2_a <- var(x)
> cat(sprintf("var(x) = %g\n", sigma2_a))
var(x) = 1.02487
> 
> sigma2_b <- varDiff(x)
> cat(sprintf("varDiff(x) = %g\n", sigma2_b))
varDiff(x) = 1.01224
> 
> d <- abs(sigma2_b - sigma2_a)
> cat(sprintf("Absolute difference = %g\n", d))
Absolute difference = 0.0126268
> stopifnot(d < 0.02)
> 
> 
> # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
> # Standard deviation estimators
> # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
> sigma_a <- sd(x)
> cat(sprintf("sd(x) = %g\n", sigma_a))
sd(x) = 1.01236
> 
> sigma_b <- sdDiff(x)
> cat(sprintf("sdDiff(x) = %g\n", sigma_b))
sdDiff(x) = 1.0061
> 
> d <- abs(sigma_b - sigma_a)
> cat(sprintf("Absolute difference = %g\n", d))
Absolute difference = 0.00625567
> stopifnot(d < 0.01)
> 
> # Sanity checks
> stopifnot(abs(sigma2_a - sigma_a ^ 2) < 1e-9)
> stopifnot(abs(sigma2_b - sigma_b ^ 2) < 1e-9)
> 
> 
> sigma_a2 <- mad(x)
> cat(sprintf("mad(x) = %g\n", sigma_a2))
mad(x) = 0.998376
> 
> sigma_b2 <- madDiff(x)
> cat(sprintf("madDiff(x) = %g\n", sigma_b2))
madDiff(x) = 1.02513
> 
> d <- abs(sigma_b2 - sigma_a2)
> cat(sprintf("Absolute difference = %g\n", d))
Absolute difference = 0.0267497
> stopifnot(d < 0.05)
> 
> 
> sigma_a3 <- IQR(x)
> cat(sprintf("IQR(x) = %g\n", sigma_a3))
IQR(x) = 1.35105
> 
> sigma_b3 <- iqrDiff(x)
> cat(sprintf("iqrDiff(x) = %g\n", sigma_b3))
iqrDiff(x) = 1.37797
> 
> d <- abs(sigma_b3 - sigma_a3)
> cat(sprintf("Absolute difference = %g\n", d))
Absolute difference = 0.0269152
> stopifnot(d < 0.05)
> 
> 
> 
> # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
> # Trimmed estimators
> # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
> y <- x
> outliers <- sample(length(x), size = 0.1 * length(x))
> y[outliers] <- 100 * y[outliers]
> 
> sigma_ao <- sd(y[-outliers])
> cat(sprintf("sd(y) = %g\n", sigma_ao))
sd(y) = 1.01166
> 
> sigma_bo <- sdDiff(y[-outliers])
> cat(sprintf("sdDiff(y) = %g\n", sigma_bo))
sdDiff(y) = 1.00743
> 
> d <- abs(sigma_b - sigma_a)
> cat(sprintf("Absolute difference = %g\n", d))
Absolute difference = 0.00625567
> stopifnot(d < 0.01)
> 
> sigma_bot <- sdDiff(y, trim = 0.05)
> cat(sprintf("sdDiff(y, trim = 0.05) = %g\n", sigma_bot))
sdDiff(y, trim = 0.05) = 7.74327
> 
> d <- abs(sigma_bot - sigma_a)
> cat(sprintf("Absolute difference = %g\n", d))
Absolute difference = 6.73091
> #stopifnot(d < 1e-3)
> 
> sigma_cot <- madDiff(y, trim = 0.05)
> cat(sprintf("madDiff(y, trim = 0.05) = %g\n", sigma_cot))
madDiff(y, trim = 0.05) = 1.15278
> 
> sigma_dot <- iqrDiff(y, trim = 0.05)
> cat(sprintf("iqrDiff(y, trim = 0.05) = %g\n", sigma_dot))
iqrDiff(y, trim = 0.05) = 1.55762
> 
> 
> fcns <- list(
+   varDiff = varDiff,
+   sdDiff  = sdDiff,
+   madDiff = madDiff,
+   iqrDiff = iqrDiff
+ )
> 
> for (name in names(fcns)) {
+   cat(sprintf("%s()...\n", name))
+   fcn <- fcns[[name]]
+ 
+   for (mode in c("integer", "double")) {
+     cat("mode: ", mode, "", sep = "")
+     for (n in 0:3) {
+       x <- runif(n, min = -5, max = 5)
+       storage.mode(x) <- mode
+       str(x)
+ 
+       y <- fcn(x)
+       yt <- fcn(x, trim = 0.1)
+       str(list("non-trimmed" = y, trimmed = yt))
+     } # for (mode ...)
+   }
+ 
+   cat(sprintf("%s()...DONE\n", name))
+ } # for (name ...)
varDiff()...
mode: integer int(0) 
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 int -4
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 int [1:2] 3 2
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 int [1:3] 1 4 -1
List of 2
 $ non-trimmed: num 16
 $ trimmed    : num 16
mode: double num(0) 
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 num -0.794
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 num [1:2] 0.897 -3.728
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 num [1:3] 2.07 -1.13 1.94
List of 2
 $ non-trimmed: num 9.83
 $ trimmed    : num 9.83
varDiff()...DONE
sdDiff()...
mode: integer int(0) 
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 int 2
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 int [1:2] -4 1
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 int [1:3] -2 1 -1
List of 2
 $ non-trimmed: num 2.5
 $ trimmed    : num 2.5
mode: double num(0) 
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 num -3.78
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 num [1:2] -2.04 2.38
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 num [1:3] 1.42 -2.14 1.14
List of 2
 $ non-trimmed: num 3.42
 $ trimmed    : num 3.42
sdDiff()...DONE
madDiff()...
mode: integer int(0) 
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 int -1
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 int [1:2] -1 4
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 int [1:3] -1 0 -3
List of 2
 $ non-trimmed: num 2.1
 $ trimmed    : num 2.1
mode: double num(0) 
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 num -1.13
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 num [1:2] -1.7 -1.21
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 num [1:3] -2.39 -0.464 3.086
List of 2
 $ non-trimmed: num 0.851
 $ trimmed    : num 0.851
madDiff()...DONE
iqrDiff()...
mode: integer int(0) 
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 int 3
List of 2
 $ non-trimmed: num 0
 $ trimmed    : num 0
 int [1:2] -3 4
List of 2
 $ non-trimmed: num 0
 $ trimmed    : num 0
 int [1:3] 0 -2 -2
List of 2
 $ non-trimmed: num 0.707
 $ trimmed    : num 0.707
mode: double num(0) 
List of 2
 $ non-trimmed: num NA
 $ trimmed    : num NA
 num -4.46
List of 2
 $ non-trimmed: num 0
 $ trimmed    : num 0
 num [1:2] 3.67 1.02
List of 2
 $ non-trimmed: num 0
 $ trimmed    : num 0
 num [1:3] -0.537 -2.733 2.857
List of 2
 $ non-trimmed: num 2.75
 $ trimmed    : num 2.75
iqrDiff()...DONE
> 
> proc.time()
   user  system elapsed 
   0.15    0.12    0.21