[R] approxfun asymmetry

[Jeff Newmiller]

Approxfun uses the two-point formula [1] for a line:

y = y_1 + (y_2 - y_1) * (x - x_1) / (x_2 - x_1)

so in the first simplified case you get

y = 1 + (1 - 1) * (0 - (-1000)) / (Inf - (-1000))
  = 1 + 0 * 1000 / Inf
  = 1 + 0 / Inf
  = 1 + 0
  = 1

while in the second case you get

y = 1 + (1 - 1) * (0 - (-Inf)) / (1000 - (-Inf))
  = 1 + 0 * Inf / Inf
  = 1 + NA / Inf
  = 1 + NA
  = NA

Zero times infinity is undefined.

[1] <https://en.m.wikipedia.org/wiki/Linear_equation>

On July 4, 2025 3:50:26 AM PDT, "Timothy Earl (Cefas) via R-help" <r-help using r-project.org> wrote:
>Hi,
>
>I'm seeing an asymmetry in how approxfun treats -Inf and Inf, which I don't understand from reading the help file.
>
>e.g. a simple step function
>tmp <- approxfun(x=c(-Inf, -0.2, 0.2,  Inf), y=c(-1, -1, 1, 1))
>tmp(c(-1, 0, 1))
># [1] NaN   0   1
>I expected: # [1] -1   0   1
>
>Clearly I can work round this by using type=2, and not specifying the end points (or by replacing -Inf by a large negative number), but I was wondering what I was missing about the different behaviour between positive and negative infinity.
>
>To simplify further:
>approxfun(x=c(-1000,  Inf), y=c(1, 1))(0)
># [1] 1
>
>approxfun(x=c(-Inf,  1000), y=c(1, 1))(0)
># [1] NaN
>
>Sessioninfo:
>R version 4.3.0 (2023-04-21 ucrt) -- "Already Tomorrow"
>Copyright (C) 2023 The R Foundation for Statistical Computing
>Platform: x86_64-w64-mingw32/x64 (64-bit)
>
>Thanks,
>
>Tim
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