relErr function

Relative Error When Appropriate, Absolute Otherwise

• 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.
  

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.

Returns

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

Author(s)

Martin Maechler, originally as part of list("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
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