ENH: cache Blatt–Weisskopf polynomials (#428)

* DX: add test for Blatt–Weisskopf polynomials
* MAINT: move form factor tests to separate file

src/ampform/dynamics/form_factor.py

@@ -3,7 +3,7 @@
 from __future__ import annotations
 
 from functools import lru_cache
-from typing import Any
+from typing import Any, Callable
 
 import sympy as sp
 
@@ -63,16 +63,31 @@ class BlattWeisskopfSquared(sp.Expr):
     _latex_repr_ = R"B_{{{angular_momentum}}}^2\left({z}\right)"
 
     def evaluate(self) -> sp.Expr:
-        ell = self.angular_momentum
-        z = sp.Dummy("z", nonnegative=True, real=True)
-        expr = (
-            sp.Abs(SphericalHankel1(ell, 1)) ** 2
-            / sp.Abs(SphericalHankel1(ell, sp.sqrt(z))) ** 2
-            / z
-        )
-        if not ell.free_symbols:
-            expr = expr.doit().simplify()
-        return expr.xreplace({z: self.z})
+        z, ell = self.args
+        if ell.free_symbols:
+            return _formulate_blatt_weisskopf(ell, z)
+        expr = _get_polynomial_blatt_weisskopf(ell)(z)
+        return sp.sympify(expr)
+
+
+@lru_cache(maxsize=20)
+def _get_polynomial_blatt_weisskopf(ell: int | sp.Integer) -> Callable[[Any], Any]:
+    """Get the Blatt-Weisskopf factor as a fraction of polynomials.
+
+    See https://github.com/ComPWA/ampform/issues/426.
+    """
+    z = sp.Symbol("z", nonnegative=True, real=True)
+    expr = _formulate_blatt_weisskopf(ell, z)
+    expr = expr.doit().simplify()
+    return sp.lambdify(z, expr, "math")
+
+
+def _formulate_blatt_weisskopf(ell, z) -> sp.Expr:
+    return (
+        sp.Abs(SphericalHankel1(ell, 1)) ** 2
+        / sp.Abs(SphericalHankel1(ell, sp.sqrt(z))) ** 2
+        / z
+    )
 
 
 @unevaluated

tests/dynamics/test_dynamics.py

@@ -12,25 +12,13 @@
     PhaseSpaceFactorSWave,
     relativistic_breit_wigner_with_ff,
 )
-from ampform.dynamics.form_factor import BlattWeisskopfSquared
 
 if TYPE_CHECKING:
     from qrules import ParticleCollection
 
     from ampform.helicity import HelicityModel
 
 
-class TestBlattWeisskopfSquared:
-    def test_factorials(self):
-        z = sp.Symbol("z")
-        angular_momentum = sp.Symbol("L", integer=True)
-        form_factor = BlattWeisskopfSquared(z, angular_momentum)
-        form_factor_9 = form_factor.subs(angular_momentum, 8).evaluate()
-        factor, z_power, _ = form_factor_9.args
-        assert factor == 4392846440677
-        assert z_power == z**8
-
-
 class TestEnergyDependentWidth:
     @staticmethod
     def test_init():

tests/dynamics/test_form_factor.py

@@ -0,0 +1,39 @@
+import pytest
+import sympy as sp
+
+from ampform.dynamics.form_factor import _get_polynomial_blatt_weisskopf
+
+z = sp.Symbol("z", nonnegative=True, real=True)
+
+
+@pytest.mark.parametrize(
+    ("ell", "expected"),
+    [
+        (0, 1),
+        (1, 2 * z / (z + 1)),
+        (2, 13 * z**2 / (z**2 + 3 * z + 9)),
+        (3, 277 * z**3 / (z**3 + 6 * z**2 + 45 * z + 225)),
+        (4, 12746 * z**4 / (z**4 + 10 * z**3 + 135 * z**2 + 1575 * z + 11025)),
+        (
+            10,
+            451873017324894386
+            * z**10
+            / (
+                z**10
+                + 55 * z**9
+                + 4455 * z**8
+                + 386100 * z**7
+                + 33108075 * z**6
+                + 2681754075 * z**5
+                + 196661965500 * z**4
+                + 12417798393000 * z**3
+                + 628651043645625 * z**2
+                + 22561587455281875 * z
+                + 428670161650355625
+            ),
+        ),
+    ],
+)
+def test_get_polynomial_blatt_weisskopf(ell: int, expected: sp.Expr):
+    expr = _get_polynomial_blatt_weisskopf(ell)(z)
+    assert expr == expected