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 optimize_single(N, seed, adam_steps=80000, verbose=True):
    dx = 0.5 / N

    @jax.jit
    def objective_smooth(params, temp):
        f = jnp.exp(jnp.clip(params, -10, 5))
        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 objective_hard(params):
        f = jnp.exp(jnp.clip(params, -10, 5))
        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(objective_smooth))

    # Initialize
    np.random.seed(seed)
    x = np.linspace(0, 1, N)
    # Use best-known type of initialization: broad bump
    init = np.ones(N) * 0.5 + 0.05 * np.random.randn(N)
    params = jnp.array(np.log(np.maximum(init, 1e-6)))

    # Phase 1: Adam with increasing temperature
    lr_schedule = optax.warmup_cosine_decay_schedule(
        init_value=0.0, peak_value=0.008, 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):
        # Temperature annealing: start moderate, end high
        progress = min(step / (adam_steps * 0.7), 1.0)
        temp = 20.0 + progress * 280.0  # 20 -> 300

        loss, grads = jax.value_and_grad(objective_smooth)(params, temp)
        updates, opt_state = optimizer.update(grads, opt_state, params)
        params = optax.apply_updates(params, updates)

        if step % 10000 == 0 or step == adam_steps - 1:
            hard_c1 = float(objective_hard(params))
            if verbose:
                print(f"  Step {step:6d} | C1={hard_c1:.8f} | temp={temp:.0f}")
            if hard_c1 < best_c1:
                best_c1 = hard_c1
                best_params = params

    # Phase 2: L-BFGS-B polishing with very high temperature
    if verbose:
        print(f"  Phase 2: L-BFGS polishing from C1={best_c1:.8f}")

    params_np = np.array(best_params)
    for temp in [500.0, 1000.0, 5000.0]:
        def scipy_obj(p):
            p_jax = jnp.array(p)
            val = float(objective_smooth(p_jax, temp))
            g = np.array(grad_smooth(p_jax, temp), dtype=np.float64)
            return val, g

        result = scipy_minimize(
            scipy_obj, params_np, method='L-BFGS-B', jac=True,
            options={'maxiter': 3000, 'ftol': 1e-15, 'gtol': 1e-12},
        )
        params_np = result.x
        f_opt = np.exp(np.clip(params_np, -10, 5))
        c1 = compute_c1_numpy(f_opt, N)
        if verbose:
            print(f"    temp={temp:.0f}: C1={c1:.10f}")
        if c1 < best_c1:
            best_c1 = c1
            best_params = jnp.array(params_np)

    f_final = np.exp(np.clip(np.array(best_params), -10, 5))
    c1_final = compute_c1_numpy(f_final, N)
    return f_final, c1_final


def run():
    best_c1 = float('inf')
    best_f = None
    best_n = None

    configs = [
        (2000, 0, 100000),
        (2000, 1, 100000),
        (3000, 0, 80000),
    ]

    for N, seed, steps in configs:
        print(f"\n=== N={N}, seed={seed}, steps={steps} ===")
        f, c1 = optimize_single(N, seed, adam_steps=steps)
        print(f"  Result: C1={c1:.10f}")
        if c1 < best_c1:
            best_c1 = c1
            best_f = f
            best_n = N
            print(f"  *** NEW GLOBAL BEST: C1={c1:.10f}")

    print(f"\nFinal best C1: {best_c1:.10f}")
    return best_f, best_c1, best_c1, best_n