Package 'pwlapprox2d'

Adaptive Piecewise Linear Approximation of a Continuous Function

Description

Approximates a continuous function $f$ on a domain $[a, b]$ by adaptively discretizing the domain and building a piecewise linear (PWL) envelope until the maximum error between the PWL and $f$ is within a given tolerance.

Usage

adaptive_pwl_fit(
  f,
  domain,
  tol = 0.001,
  max_iter = 50,
  initial_points = 5,
  smallconst = 1e-04
)

Arguments

f	A continuous function \( f(x) \) to approximate.
domain	Numeric vector of length 2 specifying the interval $[a, b]$.
tol	Numeric tolerance for maximum allowed approximation error (default 1e-3).
max_iter	Maximum number of refinement iterations (default 20).
initial_points	Initial number of discretization points (default 5).
smallconst	Numeric small constant used in building PWL envelope (default 1e-4).

Value

A list with components:

PWL

A matrix of piecewise linear segments: slope, intercept, lower bound, upper bound.

data

The final discretization points (x, y) used in fitting.

max_error

Maximum absolute error between \( f \) and the PWL approximation.

Examples

f <- function(x) log(x)
domain <- c(1, 10)
res <- adaptive_pwl_fit(f, domain, tol = 1e-4, initial_points = 10, smallconst = 0.01)

cat("x,y\n")
for(i in 1:nrow(res$data)) {
  cat(paste(res$data[i, 1], res$data[i, 2], sep = ","), "\n")
}

---

Core Optimization Function

Description

Core Optimization Function

Usage

optimize_main(
  choice = 1,
  accuracy = 0.01,
  init_points = 50,
  max_iter = 100,
  verbose = TRUE
)

Arguments

choice	Integer (1-6) selecting which built-in function to optimize
accuracy	Desired precision
init_points	Initial number of sampling points (minimum 2)
max_iter	Maximum number of iterations
verbose	Logical. Print progress.

Value

A list containing the optimization result

---