added numerical integrator and libray call to __innit

gusto/__init__.py

@@ -21,3 +21,4 @@
 from gusto.timeloop import *                         # noqa
 from gusto.transport_methods import *                # noqa
 from gusto.wrappers import *                         # noqa
+from gusto.numerical_integrator import *             # noqa 

gusto/numerical_integrator.py

@@ -0,0 +1,56 @@
+import numpy as np
+
+
+class NumericalIntegral(object):
+    """
+    A class for numerically evaluating and tabulating some 1D integral.
+    :arg lower_bound: lower bound of integral
+    :arg upper_bound: upper_bound of integral
+    :arg num_points:  number of points to tabulate integral at
+    """
+    def __init__(self, lower_bound, upper_bound, num_points=500):
+
+        # if upper_bound <= lower_bound:
+        #     raise ValueError('lower_bound must be lower than upper_bound')
+        self.x = np.linspace(lower_bound, upper_bound, num_points)
+        self.x_double = np.linspace(lower_bound, upper_bound, 2*num_points-1)
+        self.lower_bound = lower_bound
+        self.upper_bound = upper_bound
+        self.num_points = num_points
+        self.tabulated = False
+
+    def tabulate(self, expression):
+        """
+        Tabulate some integral expression using Simpson's rule.
+        :arg expression: a function representing the integrand to be evaluated.
+                         Should take a numpy array as an argument.
+        """
+
+        self.cumulative = np.zeros_like(self.x)
+        self.interval_areas = np.zeros(len(self.x)-1)
+        # Evaluate expression in advance to make use of numpy optimisation
+        # We evaluate at the tabulation points and the midpoints of the intervals
+        f = expression(self.x_double)
+
+        # Just do Simpson's rule for evaluating area of each interval
+        self.interval_areas = ((self.x[1:] - self.x[:-1]) / 6.0
+                               * (f[2::2] + 4.0 * f[1::2] + f[:-1:2]))
+
+        # Add the interval areas together to create cumulative integral
+        for i in range(self.num_points - 1):
+            self.cumulative[i+1] = self.cumulative[i] + self.interval_areas[i]
+
+        self.tabulated = True
+
+    def evaluate_at(self, points):
+        """
+        Evaluates the integral at some point using linear interpolation.
+        :arg points: the point value, or array of point values to evaluate
+                     the integral at.
+        """
+        # Do linear interpolation from tabulated values
+        if not self.tabulated:
+            raise RuntimeError(
+                'Integral must be tabulated before we can evaluate it at a point')
+
+        return np.interp(points, self.x, self.cumulative)