Implement Kv Op

pytensor/link/jax/dispatch/scalar.py

@@ -31,6 +31,7 @@
     GammaIncInv,
     Iv,
     Ive,
+    Kv,
     Log1mexp,
     Psi,
     TriGamma,
@@ -293,6 +294,16 @@ def jax_funcify_Ive(op, **kwargs):
     return ive
 
 
+@jax_funcify.register(Kv)
+def jax_funcify_Kv(op, **kwargs):
+    kve = try_import_tfp_jax_op(op, jax_op_name="bessel_kve")
+
+    def kv(v, x):
+        return kve(v, x) / jnp.exp(jnp.abs(x))
+
+    return kv
+
+
 @jax_funcify.register(Log1mexp)
 def jax_funcify_Log1mexp(op, node, **kwargs):
     def log1mexp(x):

pytensor/scalar/math.py

@@ -1281,6 +1281,36 @@ def c_code(self, *args, **kwargs):
 ive = Ive(upgrade_to_float, name="ive")
 
 
+class Kv(BinaryScalarOp):
+    """Modified Bessel function of the second kind of real order v."""
+
+    nfunc_spec = ("scipy.special.kv", 2, 1)
+
+    @staticmethod
+    def st_impl(v, x):
+        return scipy.special.kv(v, x)
+
+    def impl(self, v, x):
+        return self.st_impl(v, x)
+
+    def L_op(self, inputs, outputs, output_grads):
+        v, x = inputs
+        [out] = outputs
+        [g_out] = output_grads
+        # -(v / x) * kv(v, x) - kv(v - 1, x)
+        dx = -(v / x) * out - self(v - 1, x)
+        return [
+            grad_not_implemented(self, 0, v),
+            g_out * dx,
+        ]
+
+    def c_code(self, *args, **kwargs):
+        raise NotImplementedError()
+
+
+kv = Kv(upgrade_to_float, name="kv")
+
+
 class Sigmoid(UnaryScalarOp):
     """
     Logistic sigmoid function (1 / (1 + exp(-x)), also known as expit or inverse logit

pytensor/tensor/math.py

@@ -1229,6 +1229,11 @@ def ive(v, x):
     """Exponentially scaled modified Bessel function of the first kind of order v (real)."""
 
 
+@scalar_elemwise
+def kv(v, x):
+    """Modified Bessel function of the second kind of real order v."""
+
+
 @scalar_elemwise
 def sigmoid(x):
     """Logistic sigmoid function (1 / (1 + exp(-x)), also known as expit or inverse logit"""
@@ -3040,6 +3045,7 @@ def nan_to_num(x, nan=0.0, posinf=None, neginf=None):
     "i1",
     "iv",
     "ive",
+    "kv",
     "sigmoid",
     "expit",
     "softplus",

tests/link/jax/test_scalar.py

@@ -21,6 +21,7 @@
     gammainccinv,
     gammaincinv,
     iv,
+    kv,
     log,
     log1mexp,
     polygamma,
@@ -153,11 +154,7 @@ def test_erfinv():
 
 @pytest.mark.parametrize(
     "op, test_values",
-    [
-        (erfcx, (0.7,)),
-        (erfcinv, (0.7,)),
-        (iv, (0.3, 0.7)),
-    ],
+    [(erfcx, (0.7,)), (erfcinv, (0.7,)), (iv, (0.3, 0.7)), (kv, (-2.5, 2.0))],
 )
 @pytest.mark.skipif(not TFP_INSTALLED, reason="Test requires tensorflow-probability")
 def test_tfp_ops(op, test_values):

tests/tensor/test_math_scipy.py

@@ -3,7 +3,7 @@
 import numpy as np
 import pytest
 
-from pytensor.gradient import verify_grad
+from pytensor.gradient import NullTypeGradError, verify_grad
 from pytensor.scalar import ScalarLoop
 from pytensor.tensor.elemwise import Elemwise
 
@@ -18,7 +18,7 @@
 from pytensor import tensor as pt
 from pytensor.compile.mode import get_default_mode
 from pytensor.configdefaults import config
-from pytensor.tensor import gammaincc, inplace, vector
+from pytensor.tensor import gammaincc, inplace, kv, vector
 from tests import unittest_tools as utt
 from tests.tensor.utils import (
     _good_broadcast_unary_chi2sf,
@@ -1196,3 +1196,23 @@ def test_unused_grad_loop_opt(self, wrt):
             [dd for i, dd in enumerate(expected_dds) if i in wrt],
             rtol=rtol,
         )
+
+
+def test_kv():
+    rng = np.random.default_rng(3772)
+    v = vector("v")
+    x = vector("x")
+
+    out = kv(v[:, None], x[None, :])
+    test_v = np.array([-3.7, 4, 4.5, 5], dtype=v.type.dtype)
+    test_x = np.linspace(0, 5, 10, dtype=x.type.dtype)
+
+    np.testing.assert_allclose(
+        out.eval({v: test_v, x: test_x}),
+        scipy.special.kv(test_v[:, None], test_x[None, :]),
+    )
+
+    with pytest.raises(NullTypeGradError):
+        grad(out.sum(), v)
+
+    verify_grad(lambda x: kv(4.5, x), [test_x + 0.5], rng=rng)