"""
Best strategy: Seed 80 at N=4000, upsample to N=8000,
then 50+ perturbation rounds with smart noise schedule.
"""
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 make_fns(N):
    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))
    return obj_smooth, obj_hard, grad_smooth, grad_hard


def optimize(N, init_params_np, adam_steps=40000, lr=0.003, temp=300.0):
    obj_smooth, obj_hard, grad_smooth, grad_hard = make_fns(N)
    params = jnp.array(init_params_np)

    lr_schedule = optax.warmup_cosine_decay_schedule(
        init_value=0.0, peak_value=lr, warmup_steps=min(1000, adam_steps//5),
        decay_steps=adam_steps - min(1000, adam_steps//5), end_value=lr * 1e-4,
    )
    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, temp)
        updates, opt_state = optimizer.update(grads, opt_state, params)
        params = optax.apply_updates(params, updates)
        if step >= adam_steps - 2000:
            hc = float(obj_hard(params))
            if hc < best_c1:
                best_c1 = hc
                best_params = params

    params_np = np.array(best_params, dtype=np.float64)
    for t in [1000.0, 10000.0]:
        def scipy_obj(p):
            p_jax = jnp.array(p)
            val = float(obj_smooth(p_jax, t))
            g = np.array(grad_smooth(p_jax, t), dtype=np.float64)
            return val, g
        result = scipy_minimize(
            scipy_obj, params_np, method='L-BFGS-B', jac=True,
            options={'maxiter': 5000, 'ftol': 1e-15, 'gtol': 1e-14, 'maxcor': 100},
        )
        params_np = result.x

    for _ in range(3):
        def scipy_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_hard, params_np, method='L-BFGS-B', jac=True,
            options={'maxiter': 20000, 'ftol': 1e-16, 'gtol': 1e-15, 'maxcor': 100},
        )
        params_np = result.x

    f = np.exp(np.clip(params_np, -8, 4))
    c1 = compute_c1_numpy(f, N)
    return params_np, f, c1


def run():
    # Phase 1: Seed 80 at N=4000
    N1 = 4000
    np.random.seed(80)
    init_f = np.ones(N1) * 0.5 + 0.02 * np.random.randn(N1)
    init_params = np.log(np.maximum(init_f, 1e-6))
    params, f, c1 = optimize(N1, init_params, adam_steps=80000, lr=0.005)
    sys.stdout.write(f"Seed 80 N=4000: C1={c1:.10f}\n")
    sys.stdout.flush()

    # Phase 2: Upsample to N=8000
    N2 = 8000
    old_f = np.exp(np.clip(params, -8, 4))
    new_f = np.interp(np.linspace(0, 1, N2), np.linspace(0, 1, N1), old_f)
    new_params = np.log(np.maximum(new_f, 1e-6))
    params, f, c1 = optimize(N2, new_params, adam_steps=40000, lr=0.002)
    sys.stdout.write(f"Upsample N=8000: C1={c1:.10f}\n")
    sys.stdout.flush()

    best_params = params
    best_f = f
    best_c1 = c1
    stale_count = 0

    # Phase 3: Many perturbation restarts
    for i in range(80):
        if stale_count >= 15:
            break  # Stop if no improvement for 15 rounds

        key = jax.random.PRNGKey(i * 31 + 11)
        # Vary noise scale - occasionally try larger perturbations
        if i % 10 == 9:
            noise_scale = 0.15  # occasional large perturbation
        elif i % 5 == 4:
            noise_scale = 0.08
        else:
            noise_scale = 0.02 + 0.01 * (i % 3)

        noise = noise_scale * jax.random.normal(key, shape=(N2,))
        perturbed = best_params + np.array(noise)

        steps = 15000 if noise_scale < 0.1 else 25000
        p, f_p, c1_p = optimize(N2, perturbed, adam_steps=steps, lr=0.001)

        improved = c1_p < best_c1
        if improved:
            best_c1 = c1_p
            best_params = p
            best_f = f_p
            stale_count = 0
        else:
            stale_count += 1

        if i % 5 == 0 or improved:
            sys.stdout.write(f"  P{i:2d} (s={noise_scale:.3f}): C1={c1_p:.10f}")
            if improved:
                sys.stdout.write(" ***")
            sys.stdout.write(f" [best={best_c1:.10f}]\n")
            sys.stdout.flush()

    sys.stdout.write(f"\nFinal C1: {best_c1:.10f}\n")
    sys.stdout.flush()
    return best_f, best_c1, best_c1, N2