"""
Key insight: use JAX's hard max directly (subgradient via jnp.max).
Phase 1: Adam with moderate temp smooth max for exploration.
Phase 2: L-BFGS with HARD max for exact convergence.
"""
import sys
import jax
import jax.numpy as jnp
import numpy as np
from scipy.optimize import minimize as scipy_minimize
import optax


def compute_c1_numpy(f_values, n_points):
    dx = 0.5 / n_points
    f_nn = np.maximum(f_values, 0.0)
    autoconv = np.convolve(f_nn, f_nn, mode='full') * dx
    integral_sq = (np.sum(f_nn) * dx) ** 2
    if integral_sq < 1e-12:
        return 1e10
    return np.max(autoconv) / integral_sq


def run():
    N = 4000
    dx = 0.5 / N

    @jax.jit
    def obj_smooth(params, temp):
        f = jnp.exp(jnp.clip(params, -8, 4))
        padded = jnp.zeros(2 * N)
        padded = padded.at[:N].set(f)
        fft_f = jnp.fft.rfft(padded)
        conv = jnp.fft.irfft(fft_f * fft_f, n=2 * N) * dx
        integral_sq = (jnp.sum(f) * dx) ** 2
        smooth_max = jax.nn.logsumexp(temp * conv) / temp
        return smooth_max / integral_sq

    @jax.jit
    def obj_hard(params):
        f = jnp.exp(jnp.clip(params, -8, 4))
        padded = jnp.zeros(2 * N)
        padded = padded.at[:N].set(f)
        fft_f = jnp.fft.rfft(padded)
        conv = jnp.fft.irfft(fft_f * fft_f, n=2 * N) * dx
        integral_sq = (jnp.sum(f) * dx) ** 2
        return jnp.max(conv) / integral_sq

    grad_smooth = jax.jit(jax.grad(obj_smooth))
    grad_hard = jax.jit(jax.grad(obj_hard))

    best_c1_overall = float('inf')
    best_f_overall = None

    for seed in range(5):
        np.random.seed(seed)
        # Flat initialization (near constant = best for gradient descent start)
        init_f = np.ones(N) * 0.5 + 0.02 * np.random.randn(N)
        params = jnp.array(np.log(np.maximum(init_f, 1e-6)))

        # Phase 1: Adam with smooth max for exploration
        adam_steps = 100000
        lr_schedule = optax.warmup_cosine_decay_schedule(
            init_value=0.0, peak_value=0.005, warmup_steps=2000,
            decay_steps=adam_steps - 2000, end_value=1e-6,
        )
        optimizer = optax.adam(learning_rate=lr_schedule)
        opt_state = optimizer.init(params)

        best_c1 = float('inf')
        best_params = params

        for step in range(adam_steps):
            loss, grads = jax.value_and_grad(obj_smooth)(params, 300.0)
            updates, opt_state = optimizer.update(grads, opt_state, params)
            params = optax.apply_updates(params, updates)

            if step % 25000 == 0 or step == adam_steps - 1:
                hc = float(obj_hard(params))
                sys.stdout.write(f"[{seed}] Adam {step:7d} | C1={hc:.10f}\n")
                sys.stdout.flush()
                if hc < best_c1:
                    best_c1 = hc
                    best_params = params

        # Phase 2: L-BFGS with HARD max (exact objective)
        sys.stdout.write(f"[{seed}] Phase 2: L-BFGS with hard max from C1={best_c1:.10f}\n")
        sys.stdout.flush()

        params_np = np.array(best_params, dtype=np.float64)

        # First do smooth L-BFGS to get close
        for temp in [1000.0, 10000.0]:
            def scipy_obj_smooth(p):
                p_jax = jnp.array(p)
                val = float(obj_smooth(p_jax, temp))
                g = np.array(grad_smooth(p_jax, temp), dtype=np.float64)
                return val, g

            result = scipy_minimize(
                scipy_obj_smooth, params_np, method='L-BFGS-B', jac=True,
                options={'maxiter': 5000, 'ftol': 1e-15, 'gtol': 1e-14, 'maxcor': 100},
            )
            params_np = result.x

        # Then hard max L-BFGS
        def scipy_obj_hard(p):
            p_jax = jnp.array(p)
            val = float(obj_hard(p_jax))
            g = np.array(grad_hard(p_jax), dtype=np.float64)
            return val, g

        result = scipy_minimize(
            scipy_obj_hard, params_np, method='L-BFGS-B', jac=True,
            options={'maxiter': 20000, 'ftol': 1e-15, 'gtol': 1e-14, 'maxcor': 100},
        )
        params_np = result.x

        f_final = np.exp(np.clip(params_np, -8, 4))
        c1_final = compute_c1_numpy(f_final, N)
        sys.stdout.write(f"[{seed}] Hard L-BFGS: C1={c1_final:.10f}\n")
        sys.stdout.flush()

        if c1_final < best_c1_overall:
            best_c1_overall = c1_final
            best_f_overall = f_final
            sys.stdout.write(f"*** GLOBAL BEST: C1={c1_final:.10f}\n")
            sys.stdout.flush()

    sys.stdout.write(f"\nFinal C1: {best_c1_overall:.10f}\n")
    sys.stdout.flush()
    return best_f_overall, best_c1_overall, best_c1_overall, N