# Copyright (c) Rob Carnell 2026

trig <- function(x) {
  n <- length(x)
  y <- cos(x)
  s <- sum(y)
  y <- n - s + seq_len(n) * (1 - y) - sin(x)
  y
}

trigjac <- function(x) {
  n <- length(x)
  J <- matrix(0, n, n)
  for (p in 1:n) {
    J[, p] <- sin(x[p])
    J[p, p] <- (p + 1) * sin(x[p]) - cos(x[p])
  }
  J
}

n <- 10
xstart <- rep(1, n) / n

test_that("Trigonometric system solves correctly with global='dbldog'", {
  znlm <- nleqslv(
    xstart,
    trig,
    global = "dbldog",
    control = list(trace = 0)
  )

  # Convergence checks
  expect_equal(znlm$termcd, 1)
  expect_equal(znlm$message, "Function criterion near zero")

  # Residual check
  expect_true(all(abs(znlm$fvec) <= 1e-8))

  znlm <- nleqslv(
    xstart,
    trig,
    trigjac,
    global = "dbldog",
    control = list(trace = 0)
  )

  # Convergence checks
  expect_equal(znlm$termcd, 1)
  expect_equal(znlm$message, "Function criterion near zero")

  # Residual check
  expect_true(all(abs(znlm$fvec) <= 1e-8))
})

test_that("trig with testnslv", {
  temp <- testnslv(xstart, trig, global = c("cline", "qline", "gline"))
  expect_true(inherits(temp, "test.nleqslv"))
  expect_true(is.data.frame(temp$out))
  expect_true(all(temp$out$termcd %in% c(1,2)))
  expect_true(all(temp$out$Iter < 20))

  temp <- testnslv(xstart, trig, trigjac, global = c("cline", "qline", "gline"))
  expect_true(inherits(temp, "test.nleqslv"))
  expect_true(is.data.frame(temp$out))
  expect_true(all(temp$out$termcd %in% c(1,2)))
  expect_true(all(temp$out$Iter < 20))
})