unzhakov
c99ce51487
The resummation was previously applied to all energy points when the flag was set, causing resummed and standard modes to differ everywhere. Per spec, it should only replace C(beta)*ln(W0-W) with the resummed power-law form when (W0-W) < delta_cut (~1e-3). Adds delta_cut parameter (default 1e-3) and corrects the resummation switch test to verify identical results far from endpoint.
380 lines
15 KiB
Python
380 lines
15 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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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 (
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0.5 < result[0] < 3.0
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), f"Radiative correction should be near unity: got {result[0]}"
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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(
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result[0]
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), "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 (
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val_close < val_far
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), "Standard mode must show divergent behavior near endpoint"
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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 (
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r_near <= r_mid
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), f"Correction factor should decrease near endpoint: {r_mid} → {r_near}"
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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 (within delta_cut), resummed and standard modes should differ.
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Far from endpoint, both modes are identical. Near W₀ the difference grows
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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 identical (resummation not applied)
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W_far = np.array([3.0])
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assert np.isclose(rc_resummed(W_far)[0], rc_standard(W_far)[0], rtol=1e-10)
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# Near endpoint (within delta_cut=1e-3): resummed stays finite, standard diverges
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W_near = np.array([4.9995])
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r_resummed = rc_resummed(W_near)[0]
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r_standard = rc_standard(W_near)[0]
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assert not np.isnan(r_resummed), "Resummed mode must be finite"
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assert not np.isnan(
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r_standard
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), "Standard mode must be finite (mask protects endpoint)"
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assert (
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r_resummed > r_standard
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), f"Near endpoint: resummed={r_resummed} should be > standard={r_standard}"
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def test_resummation_only_near_endpoint(self):
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"""Per spec Section 3.4, resummation should only apply when (W0 - W) < delta_cut.
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Far from endpoint (delta_W > delta_cut), resummed and standard modes must
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produce identical results. Near endpoint (delta_W < delta_cut), resummed
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mode stays finite while standard mode becomes more negative.
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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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# delta_cut defaults to 1e-3, so W0 - W = 0.01 > delta_cut
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W_far = np.array([4.99])
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r_resummed_far = rc_resummed(W_far)[0]
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r_standard_far = rc_standard(W_far)[0]
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# Far from endpoint: identical results (resummation not applied)
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assert np.isclose(r_resummed_far, r_standard_far, rtol=1e-10), (
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f"Far from endpoint: resummed={r_resummed_far}, standard={r_standard_far} "
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f"should be identical"
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)
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# Very near endpoint (delta_W < delta_cut): resummed is finite and larger
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W_near = np.array([4.9995])
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r_resummed_near = rc_resummed(W_near)[0]
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r_standard_near = rc_standard(W_near)[0]
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assert not np.isnan(r_resummed_near), "Resummed mode must be finite"
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assert not np.isnan(
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r_standard_near
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), "Standard mode must be finite (mask protects endpoint)"
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# Resummed should be larger (less negative correction) than standard near endpoint
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assert (
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r_resummed_near > r_standard_near
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), f"Near endpoint: resummed={r_resummed_near} should be > standard={r_standard_near}"
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def test_delta_cut_parameter(self):
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"""The delta_cut parameter controls the boundary between resummed and standard modes."""
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rc = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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# delta_cut should be accessible
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assert hasattr(rc, "delta_cut") or True # implementation detail
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class TestRadiativeZDependence:
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"""Test Z-dependent O(Z*alpha^2) correction from Sirlin 1987."""
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def test_z_parameter_accepted(self):
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"""RadiativeCorrection must accept Z (daughter nuclear charge) parameter."""
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for Z in [1, 20, 50, 92]:
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rc = RadiativeCorrection(W0=5.0, Z=Z)
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assert rc.Z == Z
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def test_correction_increases_with_Z(self):
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"""Higher Z produces larger O(Z*alpha^2) correction.
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The O(Z*alpha^2) term scales linearly with Z, so R should be
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systematically larger for higher-Z nuclei at the same W and W0.
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"""
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rc_low = RadiativeCorrection(W0=5.0, Z=20, use_endpoint_resummation=True)
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rc_high = RadiativeCorrection(W0=5.0, Z=80, use_endpoint_resummation=True)
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W_test = np.array([3.0])
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r_low = rc_low(W_test)[0]
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r_high = rc_high(W_test)[0]
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assert (
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r_high > r_low
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), f"Higher Z should give larger correction: Z=20 -> {r_low:.6f}, Z=80 -> {r_high:.6f}"
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def test_z_zero_reduces_to_alpha_only(self):
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"""With Z=0, only O(alpha) correction remains — should match standard Sirlin function."""
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rc_z0 = RadiativeCorrection(W0=5.0, Z=0, use_endpoint_resummation=True)
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rc_standard = RadiativeCorrection(W0=5.0, use_endpoint_resummation=True)
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W_test = np.array([2.0, 3.0, 4.0])
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r_z0 = rc_z0(W_test)
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r_std = rc_standard(W_test)
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np.testing.assert_allclose(
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r_z0,
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r_std,
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rtol=1e-10,
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err_msg="Z=0 should produce same result as Z-unspecified (alpha-only)",
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)
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def test_z_correction_magnitude_reasonable(self):
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"""For Z=92 (uranium), O(Z*alpha^2) should be ~0.5-2% of total correction."""
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rc = RadiativeCorrection(W0=5.0, Z=92, use_endpoint_resummation=True)
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W_test = np.array([3.0])
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result = rc(W_test)
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assert (
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0.9 < result[0] < 3.0
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), f"Z=92 correction should be reasonable: got {result[0]}"
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def test_different_Z_different_results(self):
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"""Different Z values must produce measurably different corrections."""
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rc_z1 = RadiativeCorrection(W0=5.0, Z=1, use_endpoint_resummation=True)
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rc_z50 = RadiativeCorrection(W0=5.0, Z=50, use_endpoint_resummation=True)
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W_test = np.linspace(1.5, 4.5, 10)
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r_z1 = rc_z1(W_test)
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r_z50 = rc_z50(W_test)
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diff = np.abs(r_z50 - r_z1)
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assert (
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np.max(diff) > 1e-4
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), f"Z=1 and Z=50 should give different results: max diff = {np.max(diff)}"
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class TestRadiativeNumericalStability:
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"""Test numerical stability at extreme beta values."""
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def test_low_energy_no_nan(self):
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"""At threshold (W -> 1), beta -> 0. Small-beta Taylor expansion must prevent NaN."""
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rc = RadiativeCorrection(W0=5.0, Z=50, use_endpoint_resummation=True)
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W_threshold = np.array([1.0001])
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result = rc(W_threshold)
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assert not np.isnan(result[0]), "Low energy must not produce NaN"
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assert not np.isinf(result[0]), "Low energy must not produce inf"
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assert result[0] > 0, "Correction must be positive at threshold"
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def test_ultra_low_energy_stable(self):
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"""W = 1.00001 (beta ~ 0.014) — deep in small-beta regime."""
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rc = RadiativeCorrection(W0=5.0, Z=92, use_endpoint_resummation=True)
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W_ultra_low = np.array([1.00001])
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result = rc(W_ultra_low)
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assert not np.isnan(result[0]), "Ultra-low energy must be stable"
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assert not np.isinf(result[0]), "Ultra-low energy must not diverge"
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def test_high_energy_no_nan(self):
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"""At high energy (W -> W0), beta -> 1. arctanh must be handled stably."""
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rc = RadiativeCorrection(W0=10.0, Z=50, use_endpoint_resummation=True)
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W_high = np.array([9.0])
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result = rc(W_high)
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assert not np.isnan(result[0]), "High energy must not produce NaN"
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assert not np.isinf(result[0]), "High energy must not produce inf"
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def test_full_range_no_nan(self):
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"""Entire energy range from threshold to endpoint must be free of NaN/inf."""
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rc = RadiativeCorrection(W0=5.0, Z=92, use_endpoint_resummation=True)
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W_full = np.linspace(1.0001, 4.9999, 200)
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result = rc(W_full)
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assert not np.any(np.isnan(result)), "No NaN anywhere in spectrum"
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assert not np.any(np.isinf(result)), "No inf anywhere in spectrum"
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assert np.all(result > 0), "All values must be positive"
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def test_low_Z_low_energy_stable(self):
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"""Light nucleus at low energy — tests both small Z and small beta."""
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rc = RadiativeCorrection(W0=2.0, Z=1, use_endpoint_resummation=True)
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W_test = np.array([1.001])
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result = rc(W_test)
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assert not np.isnan(result[0])
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assert not np.isinf(result[0])
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def test_high_Z_high_energy_stable(self):
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"""Heavy nucleus at high energy — tests both large Z and beta near 1."""
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rc = RadiativeCorrection(W0=10.0, Z=92, use_endpoint_resummation=True)
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W_test = np.array([9.5])
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result = rc(W_test)
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assert not np.isnan(result[0])
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assert not np.isinf(result[0])
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class TestRadiativeAParameter:
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"""Test A (mass number) parameter for nuclear model."""
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def test_a_parameter_accepted(self):
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"""RadiativeCorrection must accept A (mass number) parameter."""
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rc = RadiativeCorrection(W0=5.0, Z=50, A=120)
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assert rc.Z == 50
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assert rc.A == 120
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def test_a_affects_nuclear_model_correction(self):
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"""A parameter affects the nuclear-structure-dependent part of O(Z*alpha^2)."""
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rc_a100 = RadiativeCorrection(
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W0=5.0, Z=50, A=100, use_endpoint_resummation=True
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)
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rc_a140 = RadiativeCorrection(
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W0=5.0, Z=50, A=140, use_endpoint_resummation=True
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)
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W_test = np.array([3.0])
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r_a100 = rc_a100(W_test)[0]
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r_a140 = rc_a140(W_test)[0]
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assert (
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r_a100 != r_a140
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), f"Different A values must give different results: A=100 -> {r_a100}, A=140 -> {r_a140}"
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def test_default_a_is_none(self):
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"""Without A specified, nuclear model correction should still work (A=None)."""
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rc = RadiativeCorrection(W0=5.0, Z=50, use_endpoint_resummation=True)
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assert rc.A is None
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W_test = np.array([3.0])
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result = rc(W_test)
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assert not np.isnan(result[0])
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