Evaluate an inclusion function over an interval

evalfi: given an expression and an interval domain for each of its arguments, returns an interval guaranteed to contain the expression's true range over that domain – interval arithmetic, not a numeric evaluation at a point. The bound is conservative rather than tight where a variable appears more than once (the standard "dependency problem" of interval arithmetic: each occurrence is widened independently, as if they were unrelated variables that happened to share a domain) – evalfi(x = c(0, 3), "x*x-2*x+1") returns [-5, 10], not the true range [0, 4] that (x-1)^2 takes over [0, 3]. evalfi1 is the same but for the first derivative.

Usage

tda_evalfi(
  expr,
  ...,
  derivative = FALSE,
  options = list(),
  dir = tempfile("tda")
)

Arguments

expr

the expression, as a string, in TDA's language.

...

one interval per argument the expression uses, named for the argument, each as c(lower, upper) – evalfi(x = c(0, 3), expr = "...").

derivative

if TRUE, use evalfi1 (the first derivative's inclusion function) instead of evalfi.

options

a named list of further TDA options, passed through.

dir

working directory.

Value

A named numeric vector, c(lower, upper).

Details

^ is not a valid operator in an interval expression – write a power as repeated multiplication (x*x, not x^2).

See also

Other sequence analysis: tda_fml(), tda_frml(), tda_seq_info(), tda_seqgc(), tda_seqm(), tda_seqmd(), tda_seqpe(), tda_seqpm()

Examples

# true range of (x-1)^2 over [0,3] is [0,4] -- this is wider, since x
# appears twice and interval arithmetic cannot see they are the same x
tda_evalfi("x*x-2*x+1", x = c(0, 3))
#> lower upper 
#>    -5    10 
tda_evalfi("x*x-2*x+1", x = c(0, 3), derivative = TRUE)  # 2x-2, exact
#> lower upper 
#>    -2     4 
                                                         # here: [-2,4]