From 3cd82d1fa363401757f2517c24e5a420cca98969 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?R=C3=A9mi=20Louf?= <remilouf@gmail.com>
Date: Tue, 1 Jun 2021 12:18:12 +0200
Subject: [PATCH] add hmc test

---
 aehmc/hmc.py      |  7 +++--
 tests/test_hmc.py | 76 +++++++++++++++++++++++++----------------------
 2 files changed, 45 insertions(+), 38 deletions(-)

diff --git a/aehmc/hmc.py b/aehmc/hmc.py
index b514fb2..1b33125 100644
--- a/aehmc/hmc.py
+++ b/aehmc/hmc.py
@@ -38,6 +38,7 @@ def step(
         potential_energy: TensorVariable,
         potential_energy_grad: TensorVariable,
     ):
+        """Perform a single step of the HMC algorithm."""
         p = momentum_generator(srng)
         (
             q_new,
@@ -75,11 +76,11 @@ def propose(
         )
 
         # flip the momentum to keep detailed balance
-        new_p = -1.0 * new_p
+        flipped_p = -1.0 * new_p
 
         # compute transition-related quantities
         energy = potential_energy + kinetic_energy(p)
-        new_energy = new_potential_energy + kinetic_energy(new_p)
+        new_energy = new_potential_energy + kinetic_energy(flipped_p)
         delta_energy = energy - new_energy
         delta_energy = aet.where(aet.isnan(delta_energy), -np.inf, delta_energy)
         # is_transition_divergence = aet.abs(delta_energy) > divergence_threshold
@@ -93,7 +94,7 @@ def propose(
             final_potential_energy_grad,
         ) = ifelse(
             do_accept,
-            (new_q, new_p, new_potential_energy, new_potential_energy_grad),
+            (new_q, flipped_p, new_potential_energy, new_potential_energy_grad),
             (q, p, potential_energy, potential_energy_grad),
         )
 
diff --git a/tests/test_hmc.py b/tests/test_hmc.py
index 22f1206..8f5c58c 100644
--- a/tests/test_hmc.py
+++ b/tests/test_hmc.py
@@ -1,61 +1,67 @@
+from typing import Callable
+
 import aesara
 import aesara.tensor as aet
 import aesara_hmc.hmc as hmc
 import numpy as np
+import pytest
 from aesara.tensor.random.utils import RandomStream
 from aesara.tensor.var import TensorVariable
 
 
-def test_hmc():
-    def potential_fn(q: TensorVariable) -> TensorVariable:
-        return -1.0 / aet.power(aet.square(q[0]) + aet.square(q[1]), 0.5)
+def normal_logp(q: TensorVariable):
+    return aet.sum(aet.square(q - 3.0))
 
-    srng = RandomStream(seed=59)
-
-    step_size = aet.scalar("step_size")
-    inverse_mass_matrix = aet.vector("inverse_mass_matrix")
-    num_integration_steps = aet.scalar("num_integration_steps", dtype="int32")
 
+def build_trajectory_generator(
+    srng: RandomStream,
+    kernel_generator: Callable,
+    potential_fn: Callable,
+    num_states: int,
+) -> Callable:
     q = aet.vector("q")
     potential_energy = potential_fn(q)
     potential_energy_grad = aesara.grad(potential_energy, wrt=q)
 
-    kernel = hmc.kernel(
-        srng, potential_fn, step_size, inverse_mass_matrix, num_integration_steps
-    )
-    next_step = kernel(q, potential_energy, potential_energy_grad)
+    step_size = aet.scalar("step_size")
+    inverse_mass_matrix = aet.vector("inverse_mass_matrix")
+    num_integration_steps = aet.scalar("num_integration_steps", dtype="int32")
 
-    # Compile a function that returns the next state
-    step_fn = aesara.function(
-        (q, step_size, inverse_mass_matrix, num_integration_steps), next_step
+    kernel = kernel_generator(
+        srng, potential_fn, step_size, inverse_mass_matrix, num_integration_steps
     )
 
-    # Compile a function that integrates the trajectory integrating several times
-    trajectory, _ = aesara.scan(
+    trajectory, updates = aesara.scan(
         fn=kernel,
         outputs_info=[
             {"initial": q},
             {"initial": potential_energy},
             {"initial": potential_energy_grad},
         ],
-        n_steps=1000,
+        n_steps=num_states,
+    )
+    trajectory_generator = aesara.function(
+        (q, step_size, inverse_mass_matrix, num_integration_steps),
+        trajectory,
+        updates=updates,
+    )
+
+    return trajectory_generator
+
+
+def test_hmc():
+    """Test the HMC kernel on a simple potential."""
+    srng = RandomStream(seed=59)
+    step_size = 0.003
+    num_integration_steps = 10
+    initial_position = np.array([1.0])
+    inverse_mass_matrix = np.array([1.0])
+
+    trajectory_generator = build_trajectory_generator(
+        srng, hmc.kernel, normal_logp, 10_000
     )
-    traj = aesara.function(
-        (q, step_size, inverse_mass_matrix, num_integration_steps), trajectory
+    positions, *_ = trajectory_generator(
+        initial_position, step_size, inverse_mass_matrix, num_integration_steps
     )
 
-    # Run
-    step_size = 0.01
-    num_integration_steps = 3
-    q = np.array([1.0, 1.0])
-    inverse_mass_matrix = np.array([1.0, 1.0])
-
-    # This works
-    samples = []
-    for _ in range(1_000):
-        q, *_ = step_fn(q, step_size, inverse_mass_matrix, num_integration_steps)
-        samples.append(q)
-    print(np.mean(np.array(samples)))
-
-    # This doesn't
-    print(traj(q, step_size, inverse_mass_matrix, num_integration_steps))
+    assert np.mean(positions[9000:], axis=0) == pytest.approx(3, 1e-1)