relErr: Relative Error When Appropriate, Absolute Otherwise

Description

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)

Value

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

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.

Author

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

Examples

Run this code

## 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
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
## relErr() is pretty simple --- (possibly too simple, currently)
relErr
relErr(target, current) # NA (of course)
all.equal.numeric(target, current) ## "'is.NA' value mismatch ..."

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

## 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.."
all.equal(target[finN], current[finN], tol=0, countEQ=TRUE) #   "  " : 0.000239..
   relErr(target[finN], current[finN]) # 0.0002392929