inst/tinytest/test_rational.R

In minimaxApprox: Implementation of Remez Algorithm for Polynomial and Rational Function Approximation

# Copyright Avraham Adler (c) 2023
# SPDX-License-Identifier: MPL-2.0+

tol <- sqrt(.Machine$double.eps)

opts <- list(maxiter = 100L, miniter = 10L, conviter = 10L,
             showProgress = FALSE, convRatio = 1.000000001, tol = 1e-14,
             ztol = .Machine$double.eps)

# Test ratMat
x <- c(-0.4, 0.1, 0.3, 0.4)
E <- 0.5
y <- x ^ 2
altSign <- (-1) ^ (seq_along(x) - 1)
errVctr <- E * altSign
yVctr <- y + errVctr
control <- matrix(c(rep(1, 4L), x, x ^ 2, -(yVctr) * x, -(yVctr) * x ^ 2,
                    -altSign), nrow = length(x))
expect_identical(minimaxApprox:::ratMat(x, E, y, 2L, 2L, FALSE, "m"), control)

# Test ratCoeffs
# If the function is a pure polynomial then coeffs should recover it exactly IF
# we pass a one-term zero-degree polynomial in the denominator!
# Therefore for, for 4 data points and the function x² + 2x + 3, the
# coefficients should return c(3, 2, 1) and the error should be 0.
fn <- function(x) x ^ 2 + 2 * x + 3
x <- seq(0, 2, length.out = 4)
control <- c(3, 2, 1)
RR <- minimaxApprox:::ratCoeffs(x, 0, fn, 2L, 0L, TRUE, "m", 0, 2, opts$ztol)
expect_equal(RR$a, control, tolerance = tol)
expect_identical(RR$b, 1)
expect_equal(RR$E, 0, tolerance = tol)