Nuts speed up ~1.5x (#1522)

* PERF Make NUTS 1.5x faster by moving E0 calculation outside of buildtree inner loop.

* STY Refactor creation of functions.

* DOC Adapt doc-string.

* STY Pep8.

* STY Only return scalar

* DOC Typo

* MAINT Move theano.tensor to tt. Remove obsolete p0 and q0 args from build_tree.

Author: twiecki

pymc3/step_methods/nuts.py

@@ -92,18 +92,40 @@ def __init__(self, vars=None, scaling=None, step_scale=0.25, is_cov=False, state
         self.m = 1
 
         shared = make_shared_replacements(vars, model)
-        self.leapfrog1_dE = leapfrog1_dE(
-            model.logpt, vars, shared, self.potential, profile=profile)
+
+        def create_hamiltonian(vars, shared, model):
+            dlogp = gradient(model.logpt, vars)
+            (logp, dlogp), q = join_nonshared_inputs(
+                [model.logpt, dlogp], vars, shared)
+            logp = CallableTensor(logp)
+            dlogp = CallableTensor(dlogp)
+
+            return Hamiltonian(logp, dlogp, self.potential), q
+
+        def create_energy_func(q):
+            p = tt.dvector('p')
+            p.tag.test_value = q.tag.test_value
+            E0 = energy(self.H, q, p)
+            E0_func = theano.function([q, p], E0)
+            E0_func.trust_input = True
+
+            return E0_func
+
+        self.H, q = create_hamiltonian(vars, shared, model)
+        self.compute_energy = create_energy_func(q)
+
+        self.leapfrog1_dE = leapfrog1_dE(self.H, q, profile=profile)
 
         super(NUTS, self).__init__(vars, shared, **kwargs)
 
     def astep(self, q0):
-        # Hamiltonian(self.logp, self.dlogp, self.potential)
-        H = self.leapfrog1_dE
+        leapfrog = self.leapfrog1_dE
         Emax = self.Emax
         e = self.step_size
 
         p0 = self.potential.random()
+        E0 = self.compute_energy(q0, p0)
+
         u = uniform()
         q = qn = qp = q0
         p = pn = pp = p0
@@ -115,10 +137,10 @@ def astep(self, q0):
 
             if v == -1:
                 qn, pn, _, _, q1, n1, s1, a, na = buildtree(
-                    H, qn, pn, u, v, j, e, Emax, q0, p0)
+                    leapfrog, qn, pn, u, v, j, e, Emax, E0)
             else:
                 _, _, qp, pp, q1, n1, s1, a, na = buildtree(
-                    H, qp, pp, u, v, j, e, Emax, q0, p0)
+                    leapfrog, qp, pp, u, v, j, e, Emax, E0)
 
             if s1 == 1 and bern(min(1, n1 * 1. / n)):
                 q = q1
@@ -147,24 +169,23 @@ def competence(var):
         return Competence.INCOMPATIBLE
 
 
-def buildtree(H, q, p, u, v, j, e, Emax, q0, p0):
+def buildtree(leapfrog1_dE, q, p, u, v, j, e, Emax, E0):
     if j == 0:
-        leapfrog1_dE = H
-        q1, p1, dE = leapfrog1_dE(q, p, array(v * e), q0, p0)
+        q1, p1, dE = leapfrog1_dE(q, p, array(v * e), E0)
 
         n1 = int(log(u) + dE <= 0)
         s1 = int(log(u) + dE < Emax)
         return q1, p1, q1, p1, q1, n1, s1, min(1, exp(-dE)), 1
     else:
         qn, pn, qp, pp, q1, n1, s1, a1, na1 = buildtree(
-            H, q, p, u, v, j - 1, e, Emax, q0, p0)
+            leapfrog1_dE, q, p, u, v, j - 1, e, Emax, E0)
         if s1 == 1:
             if v == -1:
                 qn, pn, _, _, q11, n11, s11, a11, na11 = buildtree(
-                    H, qn, pn, u, v, j - 1, e, Emax, q0, p0)
+                    leapfrog1_dE, qn, pn, u, v, j - 1, e, Emax, E0)
             else:
                 _, _, qp, pp, q11, n11, s11, a11, na11 = buildtree(
-                    H, qp, pp, u, v, j - 1, e, Emax, q0, p0)
+                    leapfrog1_dE, qp, pp, u, v, j - 1, e, Emax, E0)
 
             if bern(n11 * 1. / (max(n1 + n11, 1))):
                 q1 = q11
@@ -179,44 +200,33 @@ def buildtree(H, q, p, u, v, j, e, Emax, q0, p0):
     return
 
 
-def leapfrog1_dE(logp, vars, shared, pot, profile):
+def leapfrog1_dE(H, q, profile):
     """Computes a theano function that computes one leapfrog step and the energy difference between the beginning and end of the trajectory.
     Parameters
     ----------
-    logp : TensorVariable
-    vars : list of tensor variables
-    shared : list of shared variables not to compute leapfrog over
-    pot : quadpotential
-    porifle : Boolean
+    H : Hamiltonian
+    q : theano.tensor
+    profile : Boolean
 
     Returns
     -------
     theano function which returns
-    q_new, p_new, delta_E
+    q_new, p_new, dE
     """
-    dlogp = gradient(logp, vars)
-    (logp, dlogp), q = join_nonshared_inputs([logp, dlogp], vars, shared)
-    logp = CallableTensor(logp)
-    dlogp = CallableTensor(dlogp)
-
-    H = Hamiltonian(logp, dlogp, pot)
-
     p = tt.dvector('p')
     p.tag.test_value = q.tag.test_value
 
-    q0 = tt.dvector('q0')
-    q0.tag.test_value = q.tag.test_value
-    p0 = tt.dvector('p0')
-    p0.tag.test_value = p.tag.test_value
-
     e = tt.dscalar('e')
     e.tag.test_value = 1
 
     q1, p1 = leapfrog(H, q, p, 1, e)
     E = energy(H, q1, p1)
-    E0 = energy(H, q0, p0)
+
+    E0 = tt.dscalar('E0')
+    E0.tag.test_value = 1
+
     dE = E - E0
 
-    f = theano.function([q, p, e, q0, p0], [q1, p1, dE], profile=profile)
+    f = theano.function([q, p, e, E0], [q1, p1, dE], profile=profile)
     f.trust_input = True
     return f