Relative Error When Appropriate, Absolute Otherwise — relErr • sfsmisc

relErrV():

Compute the signed relative error componentwise (“vectorized”) between the target and current vectors, using the absolute error, i.e., the difference in case the relative error is not well defined, i.e., when target is zero or infinite.

relErr():

simply the mean absolute value of the relative errors between target and current vectors; typically the “same” as all.equal.numeric(target, vector, tolerance=0, countEQ=TRUE).

Currently useful only when both vectors are finite.

Usage

relErrV(target, current, eps0 = .Machine$double.xmin)
relErr (target, current)

Arguments

target: numeric, possibly scalar.
current: numeric vector of length() a multiple of length(target); if an array (incl matrix), dimensions are preserved; for vectors, names(target) are preserved.
eps0: non-negative number; values abs(target) < eps0 should be treated as zero (and hence absolute instead of relative error be computed). This may be crucial when target is an "mpfr"-number vector.

Value

relErrV():: a numeric vector of the same length (or array of the same dimension) as current.
relErr():: a single number.

Author

Martin Maechler, originally as part of Matrix package's test-tools.R.

See also

all.equal.numeric() is similar in spirit but returns TRUE or string containing the mean relative or absolute error.

Examples

## relErrV() test example: showing how it works fine with {NA, Inf, 0} :
eps <- 1e-4*c(-9, -8, -6, -4, 0.5, 1, 5)
target  <- c(-1:1, 0,   0, NA, NaN, Inf, -Inf, Inf, 0 , Inf, 1 , -3:3)
current <- c(-1:1,1e-7,NaN,NA,  0 , Inf,  Inf,  0, Inf,  1, Inf, -3:3+ eps)
cbind(target, current, absE = current-target,
                       relE = relErrV(target,current)) -> M ; M
#>       target current   absE      relE
#>  [1,]     -1  -1e+00  0e+00  0.00e+00
#>  [2,]      0   0e+00  0e+00  0.00e+00
#>  [3,]      1   1e+00  0e+00  0.00e+00
#>  [4,]      0   1e-07  1e-07  1.00e-07
#>  [5,]      0     NaN    NaN       NaN
#>  [6,]     NA      NA     NA        NA
#>  [7,]    NaN   0e+00    NaN       NaN
#>  [8,]    Inf     Inf    NaN  0.00e+00
#>  [9,]   -Inf     Inf    Inf       Inf
#> [10,]    Inf   0e+00   -Inf      -Inf
#> [11,]      0     Inf    Inf       Inf
#> [12,]    Inf   1e+00   -Inf      -Inf
#> [13,]      1     Inf    Inf       Inf
#> [14,]     -3  -3e+00 -9e-04  3.00e-04
#> [15,]     -2  -2e+00 -8e-04  4.00e-04
#> [16,]     -1  -1e+00 -6e-04  6.00e-04
#> [17,]      0  -4e-04 -4e-04 -4.00e-04
#> [18,]      1   1e+00  5e-05  5.00e-05
#> [19,]      2   2e+00  1e-04  5.00e-05
#> [20,]      3   3e+00  5e-04  1.67e-04
stopifnot(exprs = {
         is.logical(isFr <- is.finite(rF <- M[,"relE"]))
  target==current | isFr == is.finite(aF <- M[,"absE"])
  identical(aF[!isFr] , rF[!isFr])
  identical(numeric(), relErrV(numeric(), integer())) # length 0 {used to fail}
})
tools::assertError(relErrV(1, numeric()), verbose=TRUE) # no longer allowed
#> Asserted error: length(current) == 0 differing from length(target)
## relErr() is pretty simple --- (possibly too simple, currently)
relErr
#> function (target, current) 
#> {
#>     n <- length(current)
#>     if (length(target) < n) 
#>         target <- rep(target, length.out = n)
#>     sum(abs(target - current))/sum(abs(target))
#> }
#> <bytecode: 0x5ec1bd55dfd8>
#> <environment: namespace:sfsmisc>
relErr(target, current) # NA (of course)
#> [1] NA
all.equal.numeric(target, current) ## "'is.NA' value mismatch ..."
#> [1] "'is.NA' value mismatch: 2 in current 2 in target"

## comparison after dropping NA's :
hasN <- is.na(target) | is.na(current)
all.equal(target[!hasN], current[!hasN], tolerance=0) # "Mean abs. diff.: Inf"
#> [1] "Mean absolute difference: Inf"
   relErr(target[!hasN], current[!hasN]) # NaN  (to improve?)
#> [1] NaN

## comparison after only keeping cases where both are finite:
finN <- is.finite(target) & is.finite(current)
all.equal(target[finN], current[finN], tol=0)          # "Mean abs.d.: 0.000279.."
#> [1] "Mean relative difference: 0.000279"
all.equal(target[finN], current[finN], tol=0, countEQ=TRUE) #   "  " : 0.000239..
#> [1] "Mean relative difference: 0.000193"
   relErr(target[finN], current[finN]) # 0.0002392929
#> [1] 0.000239