library(testthat)

context("Newton's Method Optimization")

# Test 1: Simple 2D quadratic function
test_that("Newton's method finds minimum of 2D quadratic function", {
  f <- function(x) x[1]^2 + x[2]^2
  res <- sm.newton(f, x0 = c(1, 1), tol = 1e-6, max_iter = 50, verbose = FALSE)

  # Check convergence
  expect_true(res$converged)

  # Check estimated minimum close to true minimum
  expect_equal(res$x_min, c(0, 0), tolerance = 1e-5)

  # Check function value at minimum
  expect_equal(res$f_min, 0, tolerance = 1e-5)

  # Iteration data frame should not be empty
  expect_true(nrow(res$iter_df) > 0)
})

# Test 2: Shifted quadratic function
test_that("Newton's method handles shifted quadratic function", {
  f <- function(x) (x[1]-3)^2 + (x[2]+2)^2
  res <- sm.newton(f, x0 = c(0, 0), tol = 1e-6, max_iter = 50, verbose = FALSE)

  expect_true(res$converged)
  expect_equal(res$x_min, c(3, -2), tolerance = 1e-5)
  expect_equal(res$f_min, 0, tolerance = 1e-5)
})

# Test 3: 1D quadratic function
test_that("Newton's method works on 1D functions", {
  f <- function(x) (x[1]-5)^2
  res <- sm.newton(f, x0 = c(0), tol = 1e-6, max_iter = 50, verbose = FALSE)

  expect_true(res$converged)
  expect_equal(res$x_min, 5, tolerance = 1e-5)
  expect_equal(res$f_min, 0, tolerance = 1e-5)
})

# Test 4: Check verbose mode runs without error
test_that("Newton's method verbose mode runs without error", {
  f <- function(x) x[1]^2 + x[2]^2
  expect_error(res <- sm.newton(f, x0 = c(1, 1), verbose = TRUE), NA)
})

# Test 5: Singular Hessian
test_that("Newton's method stops on singular Hessian", {
  f <- function(x) x[1]^2
  expect_error(sm.newton(f, x0 = c(0)), NA) # Should not error, Hessian is invertible
})