# ================================
# Steepest Descent Test Suite
# ================================

tol_test <- 1e-4  # general tolerance for comparison

# ---- Test 1: Simple 2D Quadratic ----
quad <- function(x) x[1]^2 + 2*x[2]^2 + x[1]*x[2] - 3*x[1]
x0 <- c(0,0)
res_quad <- sm.steepest_descent(quad, x0 = x0, verbose = TRUE)
expected_quad <- c(12/7, -3/7)  # Analytical solution

if(res_quad$converged && all(abs(res_quad$x_min - expected_quad) < tol_test)){
  cat("✅ Quadratic Test Passed! x_min =", paste(round(res_quad$x_min,6), collapse=", "),
      "| f_min =", round(res_quad$f_min,6), "\n\n")
} else {
  cat("❌ Quadratic Test Failed! x_min =", paste(round(res_quad$x_min,6), collapse=", "),
      "| f_min =", round(res_quad$f_min,6), "\n\n")
}

# ---- Test 2: 1D Quadratic ----
f1d <- function(x) (x[1] - 5)^2
res_1d <- sm.steepest_descent(f1d, x0 = c(0), verbose = TRUE)

if(res_1d$converged && abs(res_1d$x_min - 5) < tol_test){
  cat("✅ 1D Quadratic Test Passed! x_min =", round(res_1d$x_min,6),
      "| f_min =", round(res_1d$f_min,6), "\n\n")
} else {
  cat("❌ 1D Quadratic Test Failed! x_min =", round(res_1d$x_min,6),
      "| f_min =", round(res_1d$f_min,6), "\n\n")
}

# ---- Test 3: Rosenbrock Function ----
rosenbrock <- function(x) 100*(x[2]-x[1]^2)^2 + (1-x[1])^2
res_ros <- sm.steepest_descent(rosenbrock, x0 = c(-1.2, 1), verbose = TRUE)

if(res_ros$converged && all(abs(res_ros$x_min - c(1,1)) < 1e-4)){
  cat("✅ Rosenbrock Test Passed! x_min =", paste(round(res_ros$x_min,6), collapse=", "),
      "| f_min =", round(res_ros$f_min,6), "\n\n")
} else {
  cat("❌ Rosenbrock Test Failed! x_min =", paste(round(res_ros$x_min,6), collapse=", "),
      "| f_min =", round(res_ros$f_min,6), "\n\n")
}

# ---- Test 4: High-Dimensional Quadratic ----
n <- 10
quad_n <- function(x) sum((1:n) * x^2)
x0_n <- rep(1, n)
res_nd <- sm.steepest_descent(quad_n, x0 = x0_n, verbose = FALSE)

# Use a looser tolerance for high-dimensional optimization
if(res_nd$converged && sqrt(sum(res_nd$x_min^2)) < 1e-4){
  cat("✅ High-Dimensional Quadratic Test Passed! x_min ~ 0 | f_min =", round(res_nd$f_min,6), "\n\n")
} else {
  cat("❌ High-Dimensional Quadratic Test Failed! x_min =", paste(round(res_nd$x_min,6), collapse=", "),
      "| f_min =", round(res_nd$f_min,6), "\n\n")
}

# ---- Test 5: Custom Step Size ----
res_fixed_alpha <- sm.steepest_descent(quad, x0 = x0, alpha = 0.1, verbose = TRUE)
if(res_fixed_alpha$converged){
  cat("✅ Fixed Step Size Test Passed! x_min =", paste(round(res_fixed_alpha$x_min,6), collapse=", "),
      "| f_min =", round(res_fixed_alpha$f_min,6), "\n\n")
} else {
  cat("❌ Fixed Step Size Test Failed! x_min =", paste(round(res_fixed_alpha$x_min,6), collapse=", "),
      "| f_min =", round(res_fixed_alpha$f_min,6), "\n\n")
}