feat: Add grad_log_prob method to Model

Added grad_log_prob method to Model instances, allowing users
to calculate the gradient of the log posterior evaluated at
the unconstrained parameters.

This feature is accompanied by a test: the grad_log_prob method is
validated by comparing the output against an analytical calculation
of the gradient.

stan/model.py

@@ -320,7 +320,8 @@ def log_prob(self, unconstrained_parameters: List[float], adjust_transform: bool
             unconstrained_parameters: A sequence of unconstrained parameters.
             adjust_transform: Apply jacobian adjust transform.
 
-        Returns: The log probability of the unconstrained parameters.
+        Returns:
+            The log probability of the unconstrained parameters.
 
         Notes:
             The unconstrained parameters are passed to the log_prob
@@ -346,6 +347,40 @@ async def go():
 
         return asyncio.run(go())
 
+    def grad_log_prob(self, unconstrained_parameters: List[float]) -> float:
+        """Calculate the gradient of the log posterior evaluated at
+           the unconstrained parameters.
+
+        Arguments:
+            unconstrained_parameters: A sequence of unconstrained parameters.
+            adjust_transform: Apply jacobian adjust transform.
+
+        Returns:
+            The gradient of the log posterior evalauted at the
+            unconstrained parameters.
+
+        Notes:
+            The unconstrained parameters are passed to the log_prob_grad
+            function in stan::model.
+        """
+        assert isinstance(self.data, dict)
+
+        payload = {
+            "data": self.data,
+            "unconstrained_parameters": unconstrained_parameters,
+        }
+
+        async def go():
+            async with stan.common.httpstan_server() as (host, port):
+                log_prob_grad_url = f"http://{host}:{port}/v1/{self.model_name}/log_prob_grad"
+                async with aiohttp.request("POST", log_prob_grad_url, json=payload) as resp:
+                    response_payload = await resp.json()
+                    if resp.status != 200:
+                        raise RuntimeError(response_payload)
+                    return (await resp.json())["log_prob_grad"]
+
+        return asyncio.run(go())
+
 
 def build(program_code, data=None, random_seed=None) -> Model:
     """Build (compile) a Stan program.

tests/test_grad_log_prob.py

@@ -0,0 +1,39 @@
+"""Test model with array parameter."""
+import random
+
+import numpy as np
+import pytest
+
+import stan
+
+program = """
+    parameters {
+        real y;
+    }
+    model {
+        y ~ normal(0, 1);
+    }
+"""
+
+num_samples = 1000
+num_chains = 4
+
+
+def gaussian_gradient(x: float, mean: float, var: float) -> float:
+    """Analytically evaluate Gaussian gradient."""
+    gradient = (mean - x) / (var ** 2)
+    return gradient
+
+
+@pytest.fixture
+def posterior(request):
+    return stan.build(request.param, random_seed=1)
+
+
+@pytest.mark.parametrize("posterior", [program], indirect=True)
+def test_grad_log_prob(posterior):
+    """Test log probability against sampled model with no restriction."""
+    y = random.uniform(0, 10)
+    lp__ = gaussian_gradient(y, 0, 1)
+    lp = posterior.grad_log_prob(unconstrained_parameters=[y])
+    assert np.allclose(lp__, lp)