from scipy import integrate
import pandas as pd
import numpy as np

def integrate_method(self, how='trapz', unit='s'):
    '''Numerically integrate the time series.

    @param how: the method to use (trapz by default)
    @return 

    Available methods:
     * trapz - trapezoidal
     * cumtrapz - cumulative trapezoidal
     * simps - Simpson's rule
     * romb - Romberger's rule

    See http://docs.scipy.org/doc/scipy/reference/integrate.html for the method details.
    or the source code
    https://github.com/scipy/scipy/blob/master/scipy/integrate/quadrature.py
    '''
    available_rules = set(['trapz', 'cumtrapz', 'simps', 'romb'])
    if how in available_rules:
        rule = integrate.__getattribute__(how)
    else:
        print('Unsupported integration rule: %s' % (how))
        print('Expecting one of these sample-based integration rules: %s' % (str(list(available_rules))))
        raise AttributeError
    
    result = rule(self.values, self.index.astype(np.int64) / 10**9)
    #result = rule(self.values)
    return result

pd.TimeSeries.integrate = integrate_method

x = np.abs(np.random.randn(10000))
ts = pd.Series(x, pd.date_range(start='2013-05-03', periods=len(x), freq='s'))

ts.integrate()

ts.integrate('cumtrapz')

ts.integrate('simps')

ts[:1+2**3].integrate('romb')

twos = pd.Series(2, pd.date_range(start='2012-01-23', periods=13, freq='1s'))
twos.plot()
print(twos.integrate('simps'))

twos_sparse = pd.Series(2, pd.date_range(start='2012-01-23 00:00', end='2012-01-23 00:12', freq='3s'))
twos_sparse.plot()
print(twos_sparse.integrate('simps'))

lin = pd.Series(np.arange(13), pd.date_range(start='2012-01-23', periods=13, freq='1s'))
lin.plot()
print(lin.integrate())

%timeit ts.integrate()

ts.integrate('homers')