change integration scheme

The old scheme using nquad only worked fast because the value of the integral was below the absolute tolerance, and it wasn't very accurate
after fixing the numerical issue nquad takes impractically long
since the integration is over a fit to data points we don't even know the function well enough for an nquad calculation to make sense
for this reason I've used simpsons rule for integration which is much faster and should be just as accurate
we still fit and use function evaluations for convenience

rmgpy/statmech/ndTorsions.py

@@ -31,6 +31,7 @@
 import os
 import os.path
 import subprocess
+import itertools
 
 import numdifftools as nd
 import numpy as np
@@ -597,12 +598,22 @@ def calc_partition_function(self, T):
         """
         calculate the classical/semiclassical partition function at a given temperature
         """
-        rngs = [(0.0, 2.0 * np.pi) for x in range(len(self.pivots))]
 
         def f(*phis):
-            return self.rootD(*phis) * np.exp(-self.V(*phis) / (constants.R * T))
-
-        intg = inte.nquad(f, ranges=rngs)[0]
+            return (self.rootD(*phis)) * np.exp(-self.V(*phis) / (constants.R * T))
+
+        rphis = np.linspace(0, 2.0*np.pi, 30)
+        Imat = np.zeros([len(rphis) for i in range(len(self.pivots))])
+        it = itertools.product(*[list(range(len(rphis))) for i in range(len(self.pivots))])
+
+        for coords in it:
+            Imat[coords] = f(*rphis[np.array(coords)])
+
+        for i in range(len(self.pivots)):
+            Imat = inte.simps(Imat, rphis)
+
+        intg = Imat
+
         Q = intg * (2.0 * np.pi * constants.kB * T / constants.h**2) ** (len(self.pivots) / 2.0) / np.prod(self.sigmas)
 
         if self.semiclassical:
@@ -612,7 +623,6 @@ def f(*phis):
             x = constants.h * freqs / (constants.kB * T)
             out = x / (1.0 - np.exp(-x))
             Q *= np.prod(out)
-
         return Q
 
     def get_partition_function(self, T):