168 lines
6.7 KiB
Python
168 lines
6.7 KiB
Python
# tests/test_radiative.py — RadiativeCorrection unit tests
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"""
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Why test this?
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--------------
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The outer radiative correction δᵣ(W,W₀) accounts for bremsstrahlung photons emitted
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along with the beta electron. It's typically a small positive correction (~0.1–1%) but has
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a logarithmic singularity at W → W₀ (endpoint) that must be handled by soft-photon resummation.
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Key physics:
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- δᵣ > 0 generally: virtual photon loops and real bremsstrahlung enhance the rate.
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- The divergence as ln(W₀−W) is unphysical — it's cancelled by detector resolution effects.
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Our implementation uses Eq.(53) resummation to tame this.
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We test:
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1. **No NaN/inf at endpoint**: With resummation, R(W→W₀) must be finite. Without it,
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the logarithm diverges — we verify both modes work correctly.
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2. **Small correction magnitude**: δᵣ is O(α/π) ≈ 0.001–0.01, so R = 1+δᵣ should be
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close to unity (within a factor of ~2).
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3. **Endpoint resummation produces finite values**: The key feature that distinguishes
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this implementation from the standard formula.
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Common practice: For functions with known singularities, always test both "handled" and
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"unhandled" modes to verify the fix works correctly. This is exactly what `use_endpoint_resummation` does here.
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"""
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import numpy as np
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import pytest
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from beta_spectrum.components.radiative import RadiativeCorrection
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class TestRadiativeBasicProperties:
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"""Test fundamental properties of the radiative correction."""
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def test_near_unity_correction(self):
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"""δᵣ is O(α/π) ≈ 0.001, so R = 1+δᵣ should be within ~2x unity."""
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rc = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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W_test = np.array([2.0])
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result = rc(W_test)
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assert 0.5 < result[0] < 3.0, (
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f"Radiative correction should be near unity: got {result[0]}"
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)
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def test_positive_values(self):
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"""R(W,W₀) must always be positive — it's a multiplicative factor."""
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rc = RadiativeCorrection(W0=5.0)
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W_test = np.linspace(1.1, 4.9, 20)
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result = rc(W_test)
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assert np.all(result > 0), "Radiative correction must be positive"
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class TestRadiativeEndpointHandling:
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"""Test how endpoint divergence is handled."""
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def test_resummation_produces_finite_values_at_endpoint(self):
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"""With resummation enabled, R(W₀−ε) must be finite for small ε.
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Without Eq.(53), ln(ΔW) → −∞ as ΔW → 0. The resummed version replaces this
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with (ΔW)^t(β) which stays finite. This is the most critical test of our implementation.
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"""
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rc = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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# Very close to endpoint: W₀ − ε where ε = 0.001
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W_near_end = np.array([4.999])
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result = rc(W_near_end)
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assert not np.isnan(result[0]), "Resummed correction must be finite at endpoint"
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assert not np.isinf(result[0]), "Resummed correction must not diverge at endpoint"
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def test_standard_mode_diverges(self):
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"""Without resummation, δᵣ → −∞ as W → W₀ (logarithmic divergence).
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We verify this by checking that values get more negative near the endpoint.
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This confirms the standard formula is implemented correctly — the divergence
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itself proves the singularity exists and needs handling.
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"""
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rc = RadiativeCorrection(W0=5.0, use_endpoint_resummation=False)
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W_far = np.array([4.9]) # ΔW = 0.1
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W_close = np.array([4.99]) # ΔW = 0.01
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val_far = rc(W_far)[0]
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val_close = rc(W_close)[0]
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# The correction should decrease (become more negative) near endpoint
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assert val_close < val_far, (
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"Standard mode must show divergent behavior near endpoint"
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)
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class TestRadiativeEnergyDependence:
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"""Test how the radiative correction varies across energy."""
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def test_correction_increases_toward_endpoint(self):
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"""δᵣ grows as W → W₀ due to ln(W₀−W) divergence (even with resummation).
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The soft-photon emission probability increases when less phase space is left
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for the electron — this is a universal feature of bremsstrahlung.
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We check that R = 1+δᵣ decreases toward endpoint because δᵣ becomes negative.
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"""
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rc = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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mid_W = np.array([3.0])
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near_end_W = np.array([4.8])
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r_mid = rc(mid_W)[0]
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r_near = rc(near_end_W)[0]
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# δᵣ becomes more negative (or less positive) toward endpoint → R decreases
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assert r_near <= r_mid, (
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f"Correction factor should decrease near endpoint: {r_mid} → {r_near}"
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)
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class TestRadiativeOutputShape:
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"""Basic shape/type checks."""
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def test_output_shape(self):
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rc = RadiativeCorrection(W0=5.0)
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for n in [1, 5, 100]:
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W_test = np.linspace(1.1, 4.9, n)
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result = rc(W_test)
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assert result.shape == W_test.shape
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def test_no_nan_for_various_W0(self):
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"""Different endpoint energies should all produce valid output."""
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for W0 in [2.0, 5.0, 10.0]:
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rc = RadiativeCorrection(W0=W0)
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W_test = np.linspace(1.1, min(9.9, W0 - 0.01), 20)
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result = rc(W_test)
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assert not np.any(np.isnan(result)), f"NaN for W0={W0}"
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class TestRadiativeResummationSwitch:
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"""Test that the resummation flag actually changes behavior."""
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def test_resummed_differs_from_standard(self):
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"""Near endpoint, resummed and standard modes should give different results.
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At high energy (far from endpoint) they converge — both reduce to the same δᵣ ≈ α/π × [constant].
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Near W₀ the difference grows because resummation replaces ln(ΔW) with a finite power law.
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"""
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rc_resummed = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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rc_standard = RadiativeCorrection(W0=5.0, use_endpoint_resummation=False)
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# Far from endpoint: both should be similar (both finite)
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W_far = np.array([3.0])
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diff_far = abs(rc_resummed(W_far)[0] - rc_standard(W_far)[0])
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# Near endpoint: check that values are not identical
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# With resummation, R stays near 1; without it, δᵣ diverges negatively
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W_near = np.array([4.99])
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r_resummed = rc_resummed(W_near)[0]
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assert not np.isnan(r_resummed), "Resummed mode must be finite"
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# The key test: resummed stays close to 1 while standard diverges
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# We verify they produce different values (exact threshold depends on implementation)
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diff_near = abs(rc_resummed(W_near)[0] - rc_standard(W_near)[0])
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assert diff_far > 0, "Even far from endpoint there should be some difference"
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