tests/test_padding.py

"""Padding must be a pure performance device: results must match exactly.

Observation arrays are padded to shapes that depend only on the deployment index
so XLA compiles each shape once per job rather than once per campaign. That is
only legitimate if the padded points provably change nothing downstream.
"""

import jax
import jax.numpy as jnp
import numpy as np

jax.config.update("jax_enable_x64", True)

from ballast.experiment import SYNTH_PARAMS as P
from ballast.experiment import _pad
from ballast.gp import (
    log_marginal_likelihood,
    posterior_ext_state,
    posterior_mean_field,
)
from ballast.policies import eig_utilities
from ballast.trajectory import Grid

SIGMA = 0.1


def _data(n=17, seed=0):
    k = jax.random.PRNGKey(seed)
    k1, k2, k3 = jax.random.split(k, 3)
    S = jax.random.uniform(k1, (n, 2), minval=-2, maxval=2)
    t = jax.random.uniform(k2, (n,), minval=0.0, maxval=4.0)
    y = jax.random.normal(k3, (n, 2))
    return S, t, y


def _grid():
    return Grid(jnp.linspace(-2, 2, 5), jnp.linspace(-2, 2, 5))


def test_pad_preserves_posterior_mean_field():
    S, t, y = _data()
    g = _grid()
    te = jnp.array([0.0, 1.0, 2.0])
    ref = posterior_mean_field(S, t, y, g.R, te, P, SIGMA)
    Sp, tp, yp, mp = _pad(np.asarray(S), np.asarray(t), np.asarray(y), 40)
    got = posterior_mean_field(Sp, tp, yp, g.R, te, P, SIGMA, mask=mp)
    np.testing.assert_allclose(got, ref, rtol=1e-10, atol=1e-12)


def test_pad_preserves_extended_state_posterior():
    S, t, y = _data(seed=1)
    g = _grid()
    m_ref, c_ref = posterior_ext_state(S, t, y, g.R, 4.0, P, SIGMA)
    Sp, tp, yp, mp = _pad(np.asarray(S), np.asarray(t), np.asarray(y), 33)
    m_got, c_got = posterior_ext_state(Sp, tp, yp, g.R, 4.0, P, SIGMA, mask=mp)
    np.testing.assert_allclose(m_got, m_ref, rtol=1e-9, atol=1e-11)
    np.testing.assert_allclose(c_got @ c_got.T, c_ref @ c_ref.T, rtol=1e-9, atol=1e-11)


def test_pad_preserves_eig_ranking():
    S, t, y = _data(seed=2)
    g = _grid()
    ref = eig_utilities(g, S, t, 4.0, P, SIGMA)
    Sp, tp, yp, mp = _pad(np.asarray(S), np.asarray(t), np.asarray(y), 64)
    got = eig_utilities(g, Sp, tp, 4.0, P, SIGMA, mask=mp)
    np.testing.assert_allclose(got, ref, rtol=1e-9, atol=1e-11)


def test_pad_shifts_marginal_likelihood_by_a_constant_only():
    """Each padded point adds an identity block: the log-likelihood picks up a
    fixed -log(2pi) per padded row and nothing else, so the optimiser's argmax
    over hyperparameters is unchanged."""
    S, t, y = _data(seed=3)
    ref = log_marginal_likelihood(P, S, t, y, SIGMA)
    n_pad = 11
    Sp, tp, yp, mp = _pad(np.asarray(S), np.asarray(t), np.asarray(y), 17 + n_pad)
    got = log_marginal_likelihood(P, Sp, tp, yp, SIGMA, mask=mp)
    shift = -0.5 * (2 * n_pad) * np.log(2 * np.pi)
    np.testing.assert_allclose(got, ref + shift, rtol=1e-9, atol=1e-10)