add test for small antenna limit

tests/test_response.py

@@ -0,0 +1,86 @@
+import jax.numpy as jnp
+
+from jax_gw.detector.orbits import (
+    earthbound_ifo_pipeline,
+    EARTH_Z_LAT,
+    EARTH_Z_LON,
+    get_receiver_positions,
+    flatten_pairs,
+    get_separations,
+    get_arm_lengths,
+)
+from jax_gw.detector.pixel import (
+    flat_to_matrix_sky_indices,
+    get_directional_basis,
+    unflatten_sky_axis,
+)
+from jax_gw.detector.response import (
+    C_IN_AU_PER_S,
+    antenna_pattern,
+    sky_vmapped_antenna_pattern,
+    transfer_function,
+    response_function,
+    response_pipe,
+    get_path_response,
+    get_differential_strain_response,
+    get_pairwise_differential_strain_response,
+    create_cyclic_permutation_paths,
+)
+import pytest
+
+from jax import config
+
+config.update("jax_enable_x64", True)
+
+
+def test_small_antenna_limit_vs_analytic():
+    N_theta = 100
+    N_phi = 120
+    delta_phi = 2 * jnp.pi / N_phi
+    ecl_thetas_reduced = jnp.linspace(1 / N_theta, jnp.pi - 1 / N_theta, N_theta)
+    ecl_phis_reduced = jnp.arange(0, 2 * jnp.pi, delta_phi)[:N_phi]
+
+    flat_to_m_sky = flat_to_matrix_sky_indices(N_theta, N_phi)
+    ecl_thetas = ecl_thetas_reduced[flat_to_m_sky[:, 0]]
+    ecl_phis = ecl_phis_reduced[flat_to_m_sky[:, 1]]
+    sky_basis = get_directional_basis(ecl_thetas, ecl_phis)
+    _, u_hat, v_hat = sky_basis
+    FREQ_ROTATION = 365.25  # in 1/year
+    N_times = 4
+    times = jnp.linspace(0, 1 / FREQ_ROTATION, N_times)
+    r = 1  # in AU
+    L_arm = 4  # in km
+    orbits = earthbound_ifo_pipeline(
+        EARTH_Z_LAT,
+        EARTH_Z_LON,
+        times,
+        r,
+        L_arm,
+    )
+
+    separations = get_separations(orbits)
+    arms = flatten_pairs(separations)
+    arm_lengths = get_arm_lengths(arms)
+    arm_directions = arms / arm_lengths[..., None]
+    antennae = sky_vmapped_antenna_pattern(u_hat, v_hat, arm_directions)
+    response_sa = 0.5 * (
+        antennae[:, 0] + antennae[:, 1] - antennae[:, 2] - antennae[:, 3]
+    )
+    response_sa = unflatten_sky_axis(response_sa, axis=0, N_theta=N_theta, N_phi=N_phi)
+    response_plus = response_sa[..., 0]
+
+    u = ecl_phis_reduced
+    v = ecl_thetas_reduced
+    analytic_response = (jnp.cos(u[None, :]) ** 2 - jnp.sin(u[None, :]) ** 2) * (
+        jnp.cos(v[:, None]) ** 2 + 1
+    )
+    f_star = C_IN_AU_PER_S / arm_lengths[0, 0]
+    N_freqs = 5
+    freqs = jnp.linspace(0, 0.5 * f_star, N_freqs)
+    _, antennae_from_pipe = response_pipe(
+        orbits,
+        freqs,
+        sky_basis=sky_basis,
+    )
+    assert jnp.allclose(antennae_from_pipe, antennae, atol=1e-6)
+    assert jnp.allclose(response_plus[..., 0], analytic_response, atol=1e-6)